Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(119.955849786\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 620x^{2} - 700x + 83625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-16.8500\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 333.320 | 1.19252 | 0.596262 | − | 0.802790i | \(-0.296652\pi\) | ||||
0.596262 | + | 0.802790i | \(0.296652\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −988.659 | −1.08944 | −0.544720 | − | 0.838618i | \(-0.683364\pi\) | ||||
−0.544720 | + | 0.838618i | \(0.683364\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4473.12 | 1.01330 | 0.506648 | − | 0.862153i | \(-0.330885\pi\) | ||||
0.506648 | + | 0.862153i | \(0.330885\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5599.17 | −0.706841 | −0.353420 | − | 0.935465i | \(-0.614981\pi\) | ||||
−0.353420 | + | 0.935465i | \(0.614981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8999.65 | −0.688504 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 190.351 | 0.00939688 | 0.00469844 | − | 0.999989i | \(-0.498504\pi\) | ||||
0.00469844 | + | 0.999989i | \(0.498504\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12312.0 | 0.411804 | 0.205902 | − | 0.978573i | \(-0.433987\pi\) | ||||
0.205902 | + | 0.978573i | \(0.433987\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26693.8 | 0.628989 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −40349.6 | −0.691499 | −0.345749 | − | 0.938327i | \(-0.612375\pi\) | ||||
−0.345749 | + | 0.938327i | \(0.612375\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 32977.5 | 0.422111 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 65627.5 | 0.499681 | 0.249840 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249840 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −226405. | −1.36496 | −0.682480 | − | 0.730904i | \(-0.739098\pi\) | ||||
−0.682480 | + | 0.730904i | \(0.739098\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −120774. | −0.585026 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −329540. | −1.29918 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 608760. | 1.97579 | 0.987893 | − | 0.155134i | \(-0.0495808\pi\) | ||||
0.987893 | + | 0.155134i | \(0.0495808\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 151177. | 0.408095 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 78795.5 | 0.178549 | 0.0892746 | − | 0.996007i | \(-0.471545\pi\) | ||||
0.0892746 | + | 0.996007i | \(0.471545\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −105702. | −0.202743 | −0.101371 | − | 0.994849i | \(-0.532323\pi\) | ||||
−0.101371 | + | 0.994849i | \(0.532323\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 242991. | 0.397508 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −388155. | −0.545335 | −0.272667 | − | 0.962108i | \(-0.587906\pi\) | ||||
−0.272667 | + | 0.962108i | \(0.587906\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 153903. | 0.186880 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5139.48 | −0.00542529 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −53946.5 | −0.0497734 | −0.0248867 | − | 0.999690i | \(-0.507923\pi\) | ||||
−0.0248867 | + | 0.999690i | \(0.507923\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.49098e6 | 1.20838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −332424. | −0.237755 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.74850e6 | −1.74227 | −0.871133 | − | 0.491048i | \(-0.836614\pi\) | ||||
−0.871133 | + | 0.491048i | \(0.836614\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.42106e6 | −0.801603 | −0.400802 | − | 0.916165i | \(-0.631268\pi\) | ||||
−0.400802 | + | 0.916165i | \(0.631268\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −720732. | −0.363147 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.86632e6 | −0.842924 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87548e6 | 0.761819 | 0.380909 | − | 0.924612i | \(-0.375611\pi\) | ||||
0.380909 | + | 0.924612i | \(0.375611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.08944e6 | 0.399237 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.52967e6 | 0.507218 | 0.253609 | − | 0.967307i | \(-0.418382\pi\) | ||||
0.253609 | + | 0.967307i | \(0.418382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.26626e6 | 1.28356 | 0.641782 | − | 0.766887i | \(-0.278195\pi\) | ||||
0.641782 | + | 0.766887i | \(0.278195\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −890391. | −0.243706 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.42239e6 | −1.10392 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.27486e6 | 0.519111 | 0.259556 | − | 0.965728i | \(-0.416424\pi\) | ||||
0.259556 | + | 0.965728i | \(0.416424\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.13213e6 | −0.985199 | −0.492599 | − | 0.870256i | \(-0.663953\pi\) | ||||
−0.492599 | + | 0.870256i | \(0.663953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 63447.8 | 0.0112060 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.77194e6 | −0.288491 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.00547e7 | 1.51183 | 0.755915 | − | 0.654669i | \(-0.227192\pi\) | ||||
0.755915 | + | 0.654669i | \(0.227192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.53567e6 | 0.770061 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.11293e6 | 0.788060 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.10384e6 | 0.491086 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.40320e7 | 1.56106 | 0.780528 | − | 0.625121i | \(-0.214951\pi\) | ||||
0.780528 | + | 0.625121i | \(0.214951\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.26090e6 | 0.337765 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.58976e6 | 0.250112 | 0.125056 | − | 0.992150i | \(-0.460089\pi\) | ||||
0.125056 | + | 0.992150i | \(0.460089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.55403e6 | −0.230301 | −0.115150 | − | 0.993348i | \(-0.536735\pi\) | ||||
−0.115150 | + | 0.993348i | \(0.536735\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.89758e6 | 0.750083 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.86003e6 | 0.699185 | 0.349592 | − | 0.936902i | \(-0.386320\pi\) | ||||
0.349592 | + | 0.936902i | \(0.386320\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.59339e7 | −1.17850 | −0.589250 | − | 0.807951i | \(-0.700577\pi\) | ||||
−0.589250 | + | 0.807951i | \(0.700577\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.64365e7 | −1.14072 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.87858e7 | −1.87674 | −0.938370 | − | 0.345633i | \(-0.887664\pi\) | ||||
−0.938370 | + | 0.345633i | \(0.887664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.34493e7 | −0.824628 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.08179e6 | −0.235614 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −188192. | −0.0102373 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 521609. | 0.0267668 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.12748e6 | −0.103085 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.50486e7 | −0.689145 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.83742e7 | −1.22917 | −0.614583 | − | 0.788852i | \(-0.710676\pi\) | ||||
−0.614583 | + | 0.788852i | \(0.710676\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.85396e6 | 0.117053 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.96447e7 | −1.92940 | −0.964702 | − | 0.263345i | \(-0.915174\pi\) | ||||
−0.964702 | + | 0.263345i | \(0.915174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.21724e7 | −0.448636 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.56074e6 | −0.229501 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.74212e7 | −0.911097 | −0.455549 | − | 0.890211i | \(-0.650557\pi\) | ||||
−0.455549 | + | 0.890211i | \(0.650557\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.65774e7 | 0.523557 | 0.261779 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261779 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.04802e7 | 0.314849 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.50457e7 | −0.716238 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.18750e7 | 0.595881 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.15539e6 | −0.107895 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.98906e7 | −1.48322 | −0.741612 | − | 0.670829i | \(-0.765938\pi\) | ||||
−0.741612 | + | 0.670829i | \(0.765938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.23738e7 | −1.71065 | −0.855327 | − | 0.518089i | \(-0.826644\pi\) | ||||
−0.855327 | + | 0.518089i | \(0.826644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 138766. | 0.00313229 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.54653e7 | −1.62775 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.92342e7 | 1.01536 | 0.507678 | − | 0.861547i | \(-0.330504\pi\) | ||||
0.507678 | + | 0.861547i | \(0.330504\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.45655e6 | 0.0287367 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.98920e7 | 0.753347 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.71331e7 | −1.39503 | −0.697516 | − | 0.716569i | \(-0.745712\pi\) | ||||
−0.697516 | + | 0.716569i | \(0.745712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.02565e7 | −0.697657 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.07665e7 | 0.511175 | 0.255588 | − | 0.966786i | \(-0.417731\pi\) | ||||
0.255588 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.13979e7 | −0.500376 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.97544e6 | 0.137268 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.21239e7 | −1.35273 | −0.676365 | − | 0.736567i | \(-0.736446\pi\) | ||||
−0.676365 | + | 0.736567i | \(0.736446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.26035e7 | −0.459865 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.42096e7 | 1.00590 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.85504e7 | 1.02368 | 0.511838 | − | 0.859082i | \(-0.328965\pi\) | ||||
0.511838 | + | 0.859082i | \(0.328965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03261e8 | −1.29437 | −0.647187 | − | 0.762332i | \(-0.724055\pi\) | ||||
−0.647187 | + | 0.762332i | \(0.724055\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.83687e7 | 0.462806 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.02912e8 | 2.35617 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 851462. | 0.00952181 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.94598e7 | 0.209663 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.21640e8 | −1.26316 | −0.631581 | − | 0.775310i | \(-0.717594\pi\) | ||||
−0.631581 | + | 0.775310i | \(0.717594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.18867e7 | 0.419397 | 0.209698 | − | 0.977766i | \(-0.432752\pi\) | ||||
0.209698 | + | 0.977766i | \(0.432752\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.03905e7 | 0.486662 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.58032e7 | −0.333649 | −0.166824 | − | 0.985987i | \(-0.553351\pi\) | ||||
−0.166824 | + | 0.985987i | \(0.553351\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.16124e8 | −1.04457 | −0.522284 | − | 0.852772i | \(-0.674920\pi\) | ||||
−0.522284 | + | 0.852772i | \(0.674920\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.06381e7 | −0.439836 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.48832e7 | −0.544372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.62641e7 | 0.212924 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.94148e7 | −0.230500 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.50730e7 | 0.417279 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.32929e7 | −0.463838 | −0.231919 | − | 0.972735i | \(-0.574500\pi\) | ||||
−0.231919 | + | 0.972735i | \(0.574500\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.13012e7 | −0.292842 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.52327e7 | −0.241775 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.23837e8 | 1.48704 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.15189e8 | −0.741066 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.06581e6 | −0.00664210 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.53064e7 | 0.515127 | 0.257564 | − | 0.966261i | \(-0.417080\pi\) | ||||
0.257564 | + | 0.966261i | \(0.417080\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.40406e7 | 0.140704 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.04507e7 | −0.513241 | −0.256621 | − | 0.966512i | \(-0.582609\pi\) | ||||
−0.256621 | + | 0.966512i | \(0.582609\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.41674e8 | −1.32986 | −0.664928 | − | 0.746907i | \(-0.731538\pi\) | ||||
−0.664928 | + | 0.746907i | \(0.731538\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.19404e8 | 0.637351 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.85048e8 | 1.47629 | 0.738146 | − | 0.674641i | \(-0.235702\pi\) | ||||
0.738146 | + | 0.674641i | \(0.235702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.29380e8 | −0.650324 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.14213e7 | −0.299709 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.64433e8 | −0.779108 | −0.389554 | − | 0.921004i | \(-0.627371\pi\) | ||||
−0.389554 | + | 0.921004i | \(0.627371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.91807e8 | −0.882684 | −0.441342 | − | 0.897339i | \(-0.645497\pi\) | ||||
−0.441342 | + | 0.897339i | \(0.645497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.12991e7 | 0.222858 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.89369e7 | −0.291080 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.38567e8 | 0.568805 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.95745e8 | −0.781328 | −0.390664 | − | 0.920533i | \(-0.627755\pi\) | ||||
−0.390664 | + | 0.920533i | \(0.627755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80488e8 | −0.700692 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.71309e6 | −0.00646979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.21264e7 | 0.0813103 | 0.0406552 | − | 0.999173i | \(-0.487055\pi\) | ||||
0.0406552 | + | 0.999173i | \(0.487055\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.01856e8 | −2.15250 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.78424e7 | 0.166560 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.31785e7 | −0.180257 | −0.0901283 | − | 0.995930i | \(-0.528728\pi\) | ||||
−0.0901283 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.79815e7 | −0.0593560 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.71476e8 | −0.872856 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.24549e8 | 1.32983 | 0.664913 | − | 0.746921i | \(-0.268469\pi\) | ||||
0.664913 | + | 0.746921i | \(0.268469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.90392e8 | 0.581108 | 0.290554 | − | 0.956859i | \(-0.406160\pi\) | ||||
0.290554 | + | 0.956859i | \(0.406160\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.49463e8 | −0.444595 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.47512e8 | 0.427723 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.99208e8 | −1.12855 | −0.564274 | − | 0.825587i | \(-0.690844\pi\) | ||||
−0.564274 | + | 0.825587i | \(0.690844\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.65049e8 | −0.454987 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.27895e7 | 0.195703 | 0.0978513 | − | 0.995201i | \(-0.468803\pi\) | ||||
0.0978513 | + | 0.995201i | \(0.468803\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.89021e8 | 0.758012 | 0.379006 | − | 0.925394i | \(-0.376266\pi\) | ||||
0.379006 | + | 0.925394i | \(0.376266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.10804e8 | −0.283528 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.79019e7 | −0.194519 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.10302e8 | −0.999912 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.78864e8 | −0.901276 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.83123e8 | 0.657565 | 0.328783 | − | 0.944406i | \(-0.393362\pi\) | ||||
0.328783 | + | 0.944406i | \(0.393362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.16132e8 | −2.07769 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.80444e7 | −0.195009 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.25924e8 | 0.488780 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.04504e8 | 0.220876 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.99235e7 | −0.144402 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.73670e8 | −0.955930 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.92928e8 | 1.95854 | 0.979272 | − | 0.202548i | \(-0.0649224\pi\) | ||||
0.979272 | + | 0.202548i | \(0.0649224\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.89588e7 | 0.132964 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.26280e8 | −1.18061 | −0.590306 | − | 0.807180i | \(-0.700993\pi\) | ||||
−0.590306 | + | 0.807180i | \(0.700993\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.79093e8 | 1.80476 | 0.902378 | − | 0.430945i | \(-0.141820\pi\) | ||||
0.902378 | + | 0.430945i | \(0.141820\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.40235e8 | −0.433061 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.09806e7 | 0.142782 | 0.0713910 | − | 0.997448i | \(-0.477256\pi\) | ||||
0.0713910 | + | 0.997448i | \(0.477256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.93559e8 | 0.506324 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.39221e8 | −0.403674 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.34360e6 | 0.00386967 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.84646e8 | −0.298366 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.30215e8 | 0.680407 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.83753e8 | 0.594109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.06576e8 | 1.22250 | 0.611248 | − | 0.791439i | \(-0.290668\pi\) | ||||
0.611248 | + | 0.791439i | \(0.290668\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.43786e8 | 0.658596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.25137e8 | 0.908487 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.60177e8 | −0.654969 | −0.327484 | − | 0.944857i | \(-0.606201\pi\) | ||||
−0.327484 | + | 0.944857i | \(0.606201\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.77217e8 | 1.08354 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.01274e9 | −1.38311 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.62045e8 | 0.885846 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.63132e8 | 0.476099 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.70884e8 | −0.605008 | −0.302504 | − | 0.953148i | \(-0.597823\pi\) | ||||
−0.302504 | + | 0.953148i | \(0.597823\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.67595e8 | −0.588818 | −0.294409 | − | 0.955680i | \(-0.595123\pi\) | ||||
−0.294409 | + | 0.955680i | \(0.595123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.10208e8 | 0.136032 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.70784e8 | 0.327651 | 0.163826 | − | 0.986489i | \(-0.447617\pi\) | ||||
0.163826 | + | 0.986489i | \(0.447617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.09871e8 | 0.604869 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.08119e6 | 0.00591053 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.52540e8 | 1.08656 | 0.543279 | − | 0.839552i | \(-0.317183\pi\) | ||||
0.543279 | + | 0.839552i | \(0.317183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.42287e8 | −0.830417 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.40835e7 | −0.0154538 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.42203e9 | 1.53068 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.33407e8 | −0.457683 | −0.228842 | − | 0.973464i | \(-0.573494\pi\) | ||||
−0.228842 | + | 0.973464i | \(0.573494\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.74419e7 | 0.0595164 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.33347e7 | 0.0542252 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.62154e8 | −0.560885 | −0.280443 | − | 0.959871i | \(-0.590481\pi\) | ||||
−0.280443 | + | 0.959871i | \(0.590481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.06312e8 | 0.397878 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.67459e8 | −0.353195 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.15646e8 | −0.109117 | −0.0545585 | − | 0.998511i | \(-0.517375\pi\) | ||||
−0.0545585 | + | 0.998511i | \(0.517375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.66104e8 | 0.709660 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.05029e8 | 0.368375 | 0.184188 | − | 0.982891i | \(-0.441035\pi\) | ||||
0.184188 | + | 0.982891i | \(0.441035\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.47407e9 | −1.31646 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.70570e7 | −0.0675808 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.19744e9 | −1.89275 | −0.946377 | − | 0.323064i | \(-0.895287\pi\) | ||||
−0.946377 | + | 0.323064i | \(0.895287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.68058e6 | −0.00649793 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.34041e9 | 1.11394 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.58258e8 | 0.619052 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.11407e9 | 0.893602 | 0.446801 | − | 0.894633i | \(-0.352563\pi\) | ||||
0.446801 | + | 0.894633i | \(0.352563\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.28654e8 | 0.259020 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.42853e9 | −1.10633 | −0.553164 | − | 0.833072i | \(-0.686580\pi\) | ||||
−0.553164 | + | 0.833072i | \(0.686580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.26768e9 | 0.964809 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.77140e8 | 0.132503 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.72306e9 | 2.00206 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.37234e9 | −1.71453 | −0.857264 | − | 0.514877i | \(-0.827838\pi\) | ||||
−0.857264 | + | 0.514877i | \(0.827838\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.40373e8 | 0.526022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.71733e9 | 1.89809 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.71064e9 | −1.17487 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.47589e8 | −0.302276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.38513e9 | −0.919904 | −0.459952 | − | 0.887944i | \(-0.652133\pi\) | ||||
−0.459952 | + | 0.887944i | \(0.652133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.39264e8 | 0.482850 | 0.241425 | − | 0.970419i | \(-0.422385\pi\) | ||||
0.241425 | + | 0.970419i | \(0.422385\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82965e8 | −0.181778 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.27729e6 | 0.00396653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.40495e9 | 0.873299 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.76235e8 | 0.413520 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.16527e8 | −0.130269 | −0.0651345 | − | 0.997876i | \(-0.520748\pi\) | ||||
−0.0651345 | + | 0.997876i | \(0.520748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.82129e9 | −1.07813 | −0.539066 | − | 0.842263i | \(-0.681223\pi\) | ||||
−0.539066 | + | 0.842263i | \(0.681223\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.90624e8 | −0.344032 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.96783e8 | −0.284762 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.17781e8 | 0.0664428 | 0.0332214 | − | 0.999448i | \(-0.489423\pi\) | ||||
0.0332214 | + | 0.999448i | \(0.489423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.12196e8 | 0.0622932 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.01738e8 | −0.438146 | −0.219073 | − | 0.975708i | \(-0.570303\pi\) | ||||
−0.219073 | + | 0.975708i | \(0.570303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.35143e9 | 1.80289 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.61705e9 | 0.856339 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.22662e8 | −0.116087 | −0.0580436 | − | 0.998314i | \(-0.518486\pi\) | ||||
−0.0580436 | + | 0.998314i | \(0.518486\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.52462e8 | 0.180923 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.95409e9 | 0.987646 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.84515e9 | 0.918315 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.44172e9 | 0.706603 | 0.353301 | − | 0.935510i | \(-0.385059\pi\) | ||||
0.353301 | + | 0.935510i | \(0.385059\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.74668e6 | −0.00180843 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.98623e9 | 0.944228 | 0.472114 | − | 0.881537i | \(-0.343491\pi\) | ||||
0.472114 | + | 0.881537i | \(0.343491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.07392e7 | 0.0237580 | 0.0118790 | − | 0.999929i | \(-0.496219\pi\) | ||||
0.0118790 | + | 0.999929i | \(0.496219\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.03756e9 | 0.939779 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.73869e8 | −0.0789976 | −0.0394988 | − | 0.999220i | \(-0.512576\pi\) | ||||
−0.0394988 | + | 0.999220i | \(0.512576\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.85421e9 | −0.829956 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.32932e9 | −0.586216 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.72819e8 | −0.205438 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.06018e8 | 0.173827 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.93270e7 | −0.0165911 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.39851e9 | 1.82865 | 0.914326 | − | 0.404980i | \(-0.132721\pi\) | ||||
0.914326 | + | 0.404980i | \(0.132721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.40855e9 | −1.39657 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.07708e9 | −0.434945 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.67715e9 | 1.86159 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.47748e9 | −0.971985 | −0.485993 | − | 0.873963i | \(-0.661542\pi\) | ||||
−0.485993 | + | 0.873963i | \(0.661542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.08259e9 | 0.805423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.94868e9 | 1.12420 | 0.562099 | − | 0.827070i | \(-0.309994\pi\) | ||||
0.562099 | + | 0.827070i | \(0.309994\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.24923e7 | 0.00469544 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.08693e9 | 0.402793 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.51232e9 | −0.552583 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.77793e9 | 1.00085 | 0.500425 | − | 0.865780i | \(-0.333177\pi\) | ||||
0.500425 | + | 0.865780i | \(0.333177\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.30694e8 | −0.295127 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.53359e7 | −0.0123802 | −0.00619011 | − | 0.999981i | \(-0.501970\pi\) | ||||
−0.00619011 | + | 0.999981i | \(0.501970\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.63220e8 | 0.298265 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.47742e8 | 0.288892 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.25851e8 | 0.0759118 | 0.0379559 | − | 0.999279i | \(-0.487915\pi\) | ||||
0.0379559 | + | 0.999279i | \(0.487915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.21788e9 | −1.39837 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.42337e8 | −0.0792517 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.51310e8 | −0.274639 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.73626e9 | −0.552585 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.48735e9 | 0.780999 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.35395e9 | 1.65860 | 0.829302 | − | 0.558801i | \(-0.188738\pi\) | ||||
0.829302 | + | 0.558801i | \(0.188738\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.52388e8 | −0.0465796 | −0.0232898 | − | 0.999729i | \(-0.507414\pi\) | ||||
−0.0232898 | + | 0.999729i | \(0.507414\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.80293e8 | 0.265503 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.30964e7 | −0.0128264 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.77674e9 | −0.521829 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00366e9 | −0.580755 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.41189e8 | −0.126206 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.95323e9 | 0.833794 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.12086e9 | −0.591020 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.88428e8 | 0.189364 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.17832e9 | −1.67757 | −0.838784 | − | 0.544465i | \(-0.816733\pi\) | ||||
−0.838784 | + | 0.544465i | \(0.816733\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.78804e9 | 0.747307 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.31109e9 | −1.40539 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.45053e9 | 1.94640 | 0.973198 | − | 0.229968i | \(-0.0738623\pi\) | ||||
0.973198 | + | 0.229968i | \(0.0738623\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.03596e9 | −0.267201 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.08005e8 | 0.205771 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.24906e9 | −0.565541 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.47863e9 | −1.36034 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.12387e9 | −1.01114 | −0.505570 | − | 0.862785i | \(-0.668718\pi\) | ||||
−0.505570 | + | 0.862785i | \(0.668718\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.91845e8 | 0.143307 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.29895e7 | −0.00549742 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.22608e9 | −1.47040 | −0.735199 | − | 0.677851i | \(-0.762912\pi\) | ||||
−0.735199 | + | 0.677851i | \(0.762912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.59490e9 | −2.23805 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.25414e8 | −0.121049 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.66211e9 | 0.833372 | 0.416686 | − | 0.909050i | \(-0.363191\pi\) | ||||
0.416686 | + | 0.909050i | \(0.363191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.17442e9 | 1.61273 | 0.806363 | − | 0.591421i | \(-0.201433\pi\) | ||||
0.806363 | + | 0.591421i | \(0.201433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.28428e9 | 0.729287 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.33063e9 | −0.291890 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.58603e9 | −0.777138 | −0.388569 | − | 0.921420i | \(-0.627031\pi\) | ||||
−0.388569 | + | 0.921420i | \(0.627031\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.13094e9 | −0.242139 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.07392e9 | 1.07332 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.41309e8 | −0.0504352 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.36054e9 | −0.280975 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.64466e9 | 0.743744 | 0.371872 | − | 0.928284i | \(-0.378716\pi\) | ||||
0.371872 | + | 0.928284i | \(0.378716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.78749e9 | −0.562096 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.66686e8 | 0.192632 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.35245e9 | 1.84176 | 0.920882 | − | 0.389841i | \(-0.127470\pi\) | ||||
0.920882 | + | 0.389841i | \(0.127470\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.27283e7 | −0.0122083 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.13535e9 | 0.603081 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.87909e9 | −0.927566 | −0.463783 | − | 0.885949i | \(-0.653508\pi\) | ||||
−0.463783 | + | 0.885949i | \(0.653508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.85323e9 | 0.536138 | 0.268069 | − | 0.963400i | \(-0.413614\pi\) | ||||
0.268069 | + | 0.963400i | \(0.413614\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.36723e9 | 0.253940 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.73863e8 | 0.0319200 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.08828e8 | 0.128641 | 0.0643206 | − | 0.997929i | \(-0.479512\pi\) | ||||
0.0643206 | + | 0.997929i | \(0.479512\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.75185e9 | 0.314294 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.17335e9 | 0.385465 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.15658e9 | −0.728827 | −0.364413 | − | 0.931237i | \(-0.618730\pi\) | ||||
−0.364413 | + | 0.931237i | \(0.618730\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.09132e8 | −0.122932 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.45359e9 | 1.10612 | 0.553061 | − | 0.833141i | \(-0.313460\pi\) | ||||
0.553061 | + | 0.833141i | \(0.313460\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.63841e9 | −1.63338 | −0.816692 | − | 0.577074i | \(-0.804194\pi\) | ||||
−0.816692 | + | 0.577074i | \(0.804194\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.94201e8 | 0.133079 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.94065e9 | −1.64705 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.59237e9 | −1.24393 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.48697e9 | −0.240916 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.15878e8 | 0.0185662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.63824e9 | −0.734937 | −0.367468 | − | 0.930036i | \(-0.619775\pi\) | ||||
−0.367468 | + | 0.930036i | \(0.619775\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.70891e9 | 0.267797 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.45770e9 | −1.46581 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.61731e8 | −0.132094 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.11513e9 | 0.169073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.64527e9 | 0.846607 | 0.423304 | − | 0.905988i | \(-0.360870\pi\) | ||||
0.423304 | + | 0.905988i | \(0.360870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.82868e9 | 0.716292 | 0.358146 | − | 0.933666i | \(-0.383409\pi\) | ||||
0.358146 | + | 0.933666i | \(0.383409\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.51284e8 | 0.139589 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.29901e9 | −0.333715 | −0.166858 | − | 0.985981i | \(-0.553362\pi\) | ||||
−0.166858 | + | 0.985981i | \(0.553362\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.22944e10 | −1.76543 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.04360e9 | −0.858544 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.17082e10 | 1.64548 | 0.822742 | − | 0.568416i | \(-0.192443\pi\) | ||||
0.822742 | + | 0.568416i | \(0.192443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.65476e10 | −2.30086 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.11010e9 | 0.427855 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.96735e9 | −0.948350 | −0.474175 | − | 0.880431i | \(-0.657254\pi\) | ||||
−0.474175 | + | 0.880431i | \(0.657254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.92769e9 | −0.394294 | −0.197147 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197147 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.87768e7 | 0.00383482 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.05729e9 | −0.535008 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.64804e9 | −0.345529 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.30327e9 | −0.297409 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.35659e9 | −0.812260 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.40230e10 | 1.77332 | 0.886662 | − | 0.462417i | \(-0.153018\pi\) | ||||
0.886662 | + | 0.462417i | \(0.153018\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.49095e8 | −0.0812354 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.19699e8 | 0.0272124 | 0.0136062 | − | 0.999907i | \(-0.495669\pi\) | ||||
0.0136062 | + | 0.999907i | \(0.495669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.38729e10 | −1.70068 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.44217e9 | 0.296320 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.71753e8 | −0.0326364 | −0.0163182 | − | 0.999867i | \(-0.505194\pi\) | ||||
−0.0163182 | + | 0.999867i | \(0.505194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.14005e9 | −1.08650 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.52519e9 | 0.767793 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.02055e8 | 0.0351819 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.99526e9 | 0.691250 | 0.345625 | − | 0.938373i | \(-0.387667\pi\) | ||||
0.345625 | + | 0.938373i | \(0.387667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.22392e9 | −0.367975 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.52558e9 | 0.624354 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.49988e7 | 0.00167781 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.69629e9 | −0.852337 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.22308e10 | −1.34104 | −0.670520 | − | 0.741891i | \(-0.733929\pi\) | ||||
−0.670520 | + | 0.741891i | \(0.733929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.49505e9 | 0.813637 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.49326e9 | 0.375465 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.56039e9 | −0.272482 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.58261e9 | −0.377518 | −0.188759 | − | 0.982023i | \(-0.560447\pi\) | ||||
−0.188759 | + | 0.982023i | \(0.560447\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.65838e9 | 0.173037 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.13534e9 | 0.943868 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.34825e9 | −0.854131 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.43970e9 | 0.449818 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.18977e10 | 1.19375 | 0.596874 | − | 0.802335i | \(-0.296409\pi\) | ||||
0.596874 | + | 0.802335i | \(0.296409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.52506e9 | 0.250899 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.17880e9 | 0.509618 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.16423e9 | 0.210921 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.49319e10 | −1.44127 | −0.720634 | − | 0.693316i | \(-0.756149\pi\) | ||||
−0.720634 | + | 0.693316i | \(0.756149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.01205e7 | −0.00190515 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.37369e10 | −1.28832 | −0.644161 | − | 0.764890i | \(-0.722793\pi\) | ||||
−0.644161 | + | 0.764890i | \(0.722793\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.38508e9 | −0.128667 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.38926e9 | 0.771947 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.78972e9 | −0.618865 | −0.309433 | − | 0.950921i | \(-0.600139\pi\) | ||||
−0.309433 | + | 0.950921i | \(0.600139\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.86130e9 | 0.168055 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.45145e9 | 0.398144 | 0.199072 | − | 0.979985i | \(-0.436207\pi\) | ||||
0.199072 | + | 0.979985i | \(0.436207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.99627e10 | −1.76878 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.74132e9 | −0.328400 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.75955e9 | −0.761720 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.03314e9 | 0.0890058 | 0.0445029 | − | 0.999009i | \(-0.485830\pi\) | ||||
0.0445029 | + | 0.999009i | \(0.485830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.28512e9 | 0.451100 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.41237e10 | −2.03999 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.56909e9 | 0.131466 | 0.0657328 | − | 0.997837i | \(-0.479061\pi\) | ||||
0.0657328 | + | 0.997837i | \(0.479061\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.87319e9 | 0.404545 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.35877e9 | −0.111764 | −0.0558818 | − | 0.998437i | \(-0.517797\pi\) | ||||
−0.0558818 | + | 0.998437i | \(0.517797\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.57532e10 | 1.28390 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.62535e7 | 0.00373533 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.53893e10 | 1.23150 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.01788e10 | 1.60012 | 0.800061 | − | 0.599918i | \(-0.204800\pi\) | ||||
0.800061 | + | 0.599918i | \(0.204800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.97414e8 | −0.0469445 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.53602e9 | −0.353221 | −0.176610 | − | 0.984281i | \(-0.556513\pi\) | ||||
−0.176610 | + | 0.984281i | \(0.556513\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.46626e9 | −0.576165 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.62501e10 | 1.24275 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.70129e8 | 0.0735273 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.84241e9 | 0.513961 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.29175e9 | −0.0961636 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.64108e10 | 1.21084 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.78287e10 | −1.30379 | −0.651896 | − | 0.758308i | \(-0.726026\pi\) | ||||
−0.651896 | + | 0.758308i | \(0.726026\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.43582e9 | 0.104071 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.84593e10 | 2.04459 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.95678e9 | 0.566606 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.85499e8 | 0.0342692 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.20827e9 | 0.294442 | 0.147221 | − | 0.989104i | \(-0.452967\pi\) | ||||
0.147221 | + | 0.989104i | \(0.452967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.38857e7 | −0.00512445 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.32986e9 | 0.503944 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.90835e10 | 1.30063 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.32968e10 | 0.898383 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.14628e10 | −0.767775 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.62494e10 | −1.74301 | −0.871505 | − | 0.490387i | \(-0.836855\pi\) | ||||
−0.871505 | + | 0.490387i | \(0.836855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.23174e10 | 0.810864 | 0.405432 | − | 0.914125i | \(-0.367121\pi\) | ||||
0.405432 | + | 0.914125i | \(0.367121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.14059e9 | −0.335503 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.57100e10 | −1.66361 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.30141e9 | −0.0834902 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.03550e9 | 0.256687 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.47049e10 | −0.927386 | −0.463693 | − | 0.885996i | \(-0.653476\pi\) | ||||
−0.463693 | + | 0.885996i | \(0.653476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.76241e10 | −1.72738 | −0.863691 | − | 0.504021i | \(-0.831853\pi\) | ||||
−0.863691 | + | 0.504021i | \(0.831853\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.98282e9 | −0.246946 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.85420e9 | −0.482873 | −0.241436 | − | 0.970417i | \(-0.577619\pi\) | ||||
−0.241436 | + | 0.970417i | \(0.577619\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34405e10 | −1.42898 | −0.714489 | − | 0.699647i | \(-0.753341\pi\) | ||||
−0.714489 | + | 0.699647i | \(0.753341\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.07786e10 | 0.651568 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.92957e7 | 0.00175609 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.02551e10 | 0.609588 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.45633e9 | 0.262687 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.79573e10 | 1.04972 | 0.524862 | − | 0.851187i | \(-0.324117\pi\) | ||||
0.524862 | + | 0.851187i | \(0.324117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.29429e10 | −0.750319 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.96532e9 | −0.112989 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.04655e10 | −0.596710 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.15694e8 | −0.0291608 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.80355e9 | −0.437639 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.45632e10 | −1.36625 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.22147e10 | 1.77719 | 0.888593 | − | 0.458696i | \(-0.151683\pi\) | ||||
0.888593 | + | 0.458696i | \(0.151683\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.99170e9 | 0.163695 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.32148e9 | 0.234531 | 0.117265 | − | 0.993101i | \(-0.462587\pi\) | ||||
0.117265 | + | 0.993101i | \(0.462587\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.65926e10 | 0.893179 | 0.446590 | − | 0.894739i | \(-0.352638\pi\) | ||||
0.446590 | + | 0.894739i | \(0.352638\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.10335e9 | 0.112305 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.34157e10 | −1.76975 | −0.884876 | − | 0.465827i | \(-0.845757\pi\) | ||||
−0.884876 | + | 0.465827i | \(0.845757\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.07068e10 | −1.61316 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.10782e10 | 0.577299 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.01757e10 | 0.526013 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.05012e10 | −0.538485 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.02293e10 | 0.520352 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.48779e10 | 0.750783 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.35786e10 | −1.18038 | −0.590188 | − | 0.807266i | \(-0.700946\pi\) | ||||
−0.590188 | + | 0.807266i | \(0.700946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.64433e9 | −0.379646 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.32265e10 | 0.651673 | 0.325836 | − | 0.945426i | \(-0.394354\pi\) | ||||
0.325836 | + | 0.945426i | \(0.394354\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.61758e10 | 0.790685 | 0.395343 | − | 0.918534i | \(-0.370626\pi\) | ||||
0.395343 | + | 0.918534i | \(0.370626\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.47356e10 | 1.19956 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.57010e9 | 0.267997 | 0.133999 | − | 0.990982i | \(-0.457218\pi\) | ||||
0.133999 | + | 0.990982i | \(0.457218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.80524e10 | 1.33910 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.37720e9 | 0.112588 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.77896e9 | −0.224571 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.61824e10 | 1.22076 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.09995e9 | −0.282197 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.48584e10 | −0.682044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.02688e7 | −0.000467715 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.82159e9 | −0.127523 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.44188e10 | −1.54357 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.37708e9 | 0.417294 | 0.208647 | − | 0.977991i | \(-0.433094\pi\) | ||||
0.208647 | + | 0.977991i | \(0.433094\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.88794e9 | 0.0833707 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.79943e10 | −1.22675 | −0.613374 | − | 0.789793i | \(-0.710188\pi\) | ||||
−0.613374 | + | 0.789793i | \(0.710188\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.29566e10 | −0.998297 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.27891e10 | 0.551907 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.90816e10 | 2.10197 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.88071e10 | 1.64933 | 0.824665 | − | 0.565622i | \(-0.191364\pi\) | ||||
0.824665 | + | 0.565622i | \(0.191364\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.68091e10 | −1.13077 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.56489e9 | −0.358522 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00754e10 | 0.834002 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.86189e9 | −0.0767670 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.98348e9 | −0.326691 | −0.163346 | − | 0.986569i | \(-0.552229\pi\) | ||||
−0.163346 | + | 0.986569i | \(0.552229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.89486e9 | 0.0769578 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.69096e10 | 0.681627 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.83810e8 | 0.0113550 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.97710e10 | −1.18224 | −0.591119 | − | 0.806584i | \(-0.701314\pi\) | ||||
−0.591119 | + | 0.806584i | \(0.701314\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.64355e10 | −1.04198 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.39177e9 | −0.210944 | −0.105472 | − | 0.994422i | \(-0.533635\pi\) | ||||
−0.105472 | + | 0.994422i | \(0.533635\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.17936e9 | −0.123467 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.48634e9 | 0.250028 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.59034e10 | 0.608507 | 0.304254 | − | 0.952591i | \(-0.401593\pi\) | ||||
0.304254 | + | 0.952591i | \(0.401593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.38875e10 | −0.907275 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.18648e9 | −0.0824352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.42029e10 | −1.28008 | −0.640041 | − | 0.768341i | \(-0.721082\pi\) | ||||
−0.640041 | + | 0.768341i | \(0.721082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.05450e10 | −1.50635 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.92611e9 | −0.292326 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.71102e10 | 0.992586 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.37465e10 | 0.863115 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.45896e9 | 0.233062 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.39617e10 | 0.500141 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.86938e10 | 0.664821 | 0.332411 | − | 0.943135i | \(-0.392138\pi\) | ||||
0.332411 | + | 0.943135i | \(0.392138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.32772e7 | −0.00223416 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.04205e10 | 1.76742 | 0.883711 | − | 0.468033i | \(-0.155037\pi\) | ||||
0.883711 | + | 0.468033i | \(0.155037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.63894e10 | −0.570384 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.98545e9 | 0.172261 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.64060e10 | −0.562822 | −0.281411 | − | 0.959587i | \(-0.590802\pi\) | ||||
−0.281411 | + | 0.959587i | \(0.590802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.49758e10 | 1.53193 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.16158e10 | −0.392833 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.03584e10 | 1.69096 | 0.845482 | − | 0.534004i | \(-0.179313\pi\) | ||||
0.845482 | + | 0.534004i | \(0.179313\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.19339e10 | −0.397884 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.03613e10 | −0.343009 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.26504e9 | 0.140196 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.66269e10 | 1.19548 | 0.597739 | − | 0.801691i | \(-0.296066\pi\) | ||||
0.597739 | + | 0.801691i | \(0.296066\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.17775e10 | −0.705808 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.87065e10 | −1.24567 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.37142e10 | 1.07741 | 0.538704 | − | 0.842495i | \(-0.318914\pi\) | ||||
0.538704 | + | 0.842495i | \(0.318914\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.19822e10 | −0.380240 |
(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 | 384.8.a.m.1.4 | ✓ | 4 | |
4.3 | odd | 2 | 384.8.a.q.1.4 | yes | 4 | ||
8.3 | odd | 2 | 384.8.a.p.1.1 | yes | 4 | ||
8.5 | even | 2 | 384.8.a.t.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.m.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
384.8.a.p.1.1 | yes | 4 | 8.3 | odd | 2 | ||
384.8.a.q.1.4 | yes | 4 | 4.3 | odd | 2 | ||
384.8.a.t.1.1 | yes | 4 | 8.5 | even | 2 |