Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,8,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(70.2866307339\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.00000 | 0.530330 | 0.265165 | − | 0.964203i | \(-0.414574\pi\) | ||||
0.265165 | + | 0.964203i | \(0.414574\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −92.0000 | −0.718750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 64.0000 | 0.0705240 | 0.0352620 | − | 0.999378i | \(-0.488773\pi\) | ||||
0.0352620 | + | 0.999378i | \(0.488773\pi\) | |||||||
\(8\) | −1320.00 | −0.911505 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 948.000 | 0.214750 | 0.107375 | − | 0.994219i | \(-0.465755\pi\) | ||||
0.107375 | + | 0.994219i | \(0.465755\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5098.00 | 0.643573 | 0.321787 | − | 0.946812i | \(-0.395717\pi\) | ||||
0.321787 | + | 0.946812i | \(0.395717\pi\) | |||||||
\(14\) | 384.000 | 0.0374010 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3856.00 | 0.235352 | ||||||||
\(17\) | 28386.0 | 1.40131 | 0.700653 | − | 0.713502i | \(-0.252892\pi\) | ||||
0.700653 | + | 0.713502i | \(0.252892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8620.00 | −0.288317 | −0.144158 | − | 0.989555i | \(-0.546047\pi\) | ||||
−0.144158 | + | 0.989555i | \(0.546047\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5688.00 | 0.113889 | ||||||||
\(23\) | −15288.0 | −0.262001 | −0.131001 | − | 0.991382i | \(-0.541819\pi\) | ||||
−0.131001 | + | 0.991382i | \(0.541819\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 30588.0 | 0.341306 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5888.00 | −0.0506891 | ||||||||
\(29\) | −36510.0 | −0.277983 | −0.138992 | − | 0.990294i | \(-0.544386\pi\) | ||||
−0.138992 | + | 0.990294i | \(0.544386\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −276808. | −1.66883 | −0.834416 | − | 0.551135i | \(-0.814195\pi\) | ||||
−0.834416 | + | 0.551135i | \(0.814195\pi\) | |||||||
\(32\) | 192096. | 1.03632 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 170316. | 0.743155 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −268526. | −0.871526 | −0.435763 | − | 0.900061i | \(-0.643521\pi\) | ||||
−0.435763 | + | 0.900061i | \(0.643521\pi\) | |||||||
\(38\) | −51720.0 | −0.152903 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 629718. | 1.42693 | 0.713465 | − | 0.700691i | \(-0.247125\pi\) | ||||
0.713465 | + | 0.700691i | \(0.247125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −685772. | −1.31535 | −0.657673 | − | 0.753303i | \(-0.728459\pi\) | ||||
−0.657673 | + | 0.753303i | \(0.728459\pi\) | |||||||
\(44\) | −87216.0 | −0.154352 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −91728.0 | −0.138947 | ||||||||
\(47\) | 583296. | 0.819495 | 0.409748 | − | 0.912199i | \(-0.365617\pi\) | ||||
0.409748 | + | 0.912199i | \(0.365617\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −819447. | −0.995026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −469016. | −0.462568 | ||||||||
\(53\) | −428058. | −0.394945 | −0.197473 | − | 0.980308i | \(-0.563273\pi\) | ||||
−0.197473 | + | 0.980308i | \(0.563273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −84480.0 | −0.0642830 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −219060. | −0.147423 | ||||||||
\(59\) | −1.30638e6 | −0.828109 | −0.414054 | − | 0.910252i | \(-0.635888\pi\) | ||||
−0.414054 | + | 0.910252i | \(0.635888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 300662. | 0.169599 | 0.0847997 | − | 0.996398i | \(-0.472975\pi\) | ||||
0.0847997 | + | 0.996398i | \(0.472975\pi\) | |||||||
\(62\) | −1.66085e6 | −0.885032 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 659008. | 0.314240 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 507244. | 0.206042 | 0.103021 | − | 0.994679i | \(-0.467149\pi\) | ||||
0.103021 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(68\) | −2.61151e6 | −1.00719 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.56063e6 | −1.84383 | −0.921913 | − | 0.387397i | \(-0.873374\pi\) | ||||
−0.921913 | + | 0.387397i | \(0.873374\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.36908e6 | −0.411907 | −0.205954 | − | 0.978562i | \(-0.566030\pi\) | ||||
−0.205954 | + | 0.978562i | \(0.566030\pi\) | |||||||
\(74\) | −1.61116e6 | −0.462196 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 793040. | 0.207228 | ||||||||
\(77\) | 60672.0 | 0.0151451 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.91372e6 | −1.57767 | −0.788836 | − | 0.614603i | \(-0.789316\pi\) | ||||
−0.788836 | + | 0.614603i | \(0.789316\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.77831e6 | 0.756744 | ||||||||
\(83\) | −4.37675e6 | −0.840191 | −0.420096 | − | 0.907480i | \(-0.638003\pi\) | ||||
−0.420096 | + | 0.907480i | \(0.638003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.11463e6 | −0.697568 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.25136e6 | −0.195746 | ||||||||
\(89\) | 8.52831e6 | 1.28232 | 0.641162 | − | 0.767405i | \(-0.278453\pi\) | ||||
0.641162 | + | 0.767405i | \(0.278453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 326272. | 0.0453874 | ||||||||
\(92\) | 1.40650e6 | 0.188313 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.49978e6 | 0.434603 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.82681e6 | 0.981981 | 0.490990 | − | 0.871165i | \(-0.336635\pi\) | ||||
0.490990 | + | 0.871165i | \(0.336635\pi\) | |||||||
\(98\) | −4.91668e6 | −0.527692 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.19864e7 | −1.15762 | −0.578808 | − | 0.815464i | \(-0.696482\pi\) | ||||
−0.578808 | + | 0.815464i | \(0.696482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.20939e6 | −0.650082 | −0.325041 | − | 0.945700i | \(-0.605378\pi\) | ||||
−0.325041 | + | 0.945700i | \(0.605378\pi\) | |||||||
\(104\) | −6.72936e6 | −0.586620 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.56835e6 | −0.209451 | ||||||||
\(107\) | 1.14261e7 | 0.901683 | 0.450842 | − | 0.892604i | \(-0.351124\pi\) | ||||
0.450842 | + | 0.892604i | \(0.351124\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.02095e6 | 0.297397 | 0.148698 | − | 0.988883i | \(-0.452492\pi\) | ||||
0.148698 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 246784. | 0.0165979 | ||||||||
\(113\) | −1.77063e7 | −1.15439 | −0.577197 | − | 0.816605i | \(-0.695853\pi\) | ||||
−0.577197 | + | 0.816605i | \(0.695853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.35892e6 | 0.199801 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.83828e6 | −0.439171 | ||||||||
\(119\) | 1.81670e6 | 0.0988257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.85885e7 | −0.953882 | ||||||||
\(122\) | 1.80397e6 | 0.0899436 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.54663e7 | 1.19947 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.67883e7 | −0.727267 | −0.363633 | − | 0.931542i | \(-0.618464\pi\) | ||||
−0.363633 | + | 0.931542i | \(0.618464\pi\) | |||||||
\(128\) | −2.06342e7 | −0.869668 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.68268e7 | −0.653960 | −0.326980 | − | 0.945031i | \(-0.606031\pi\) | ||||
−0.326980 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −551680. | −0.0203332 | ||||||||
\(134\) | 3.04346e6 | 0.109270 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.74695e7 | −1.27730 | ||||||||
\(137\) | 2.80449e7 | 0.931820 | 0.465910 | − | 0.884832i | \(-0.345727\pi\) | ||||
0.465910 | + | 0.884832i | \(0.345727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.18273e7 | −0.373537 | −0.186769 | − | 0.982404i | \(-0.559801\pi\) | ||||
−0.186769 | + | 0.982404i | \(0.559801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.33638e7 | −0.977836 | ||||||||
\(143\) | 4.83290e6 | 0.138208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.21449e6 | −0.218447 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.47044e7 | 0.626409 | ||||||||
\(149\) | −2.07846e7 | −0.514743 | −0.257371 | − | 0.966313i | \(-0.582856\pi\) | ||||
−0.257371 | + | 0.966313i | \(0.582856\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76112.0 | 0.00179901 | 0.000899505 | − | 1.00000i | \(-0.499714\pi\) | ||||
0.000899505 | 1.00000i | \(0.499714\pi\) | ||||||||
\(152\) | 1.13784e7 | 0.262802 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 364032. | 0.00803188 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.21825e7 | 0.663698 | 0.331849 | − | 0.943332i | \(-0.392328\pi\) | ||||
0.331849 | + | 0.943332i | \(0.392328\pi\) | |||||||
\(158\) | −4.14823e7 | −0.836687 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −978432. | −0.0184774 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.83435e7 | −1.05520 | −0.527601 | − | 0.849492i | \(-0.676908\pi\) | ||||
−0.527601 | + | 0.849492i | \(0.676908\pi\) | |||||||
\(164\) | −5.79341e7 | −1.02561 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.62605e7 | −0.445579 | ||||||||
\(167\) | −2.58365e7 | −0.429266 | −0.214633 | − | 0.976695i | \(-0.568855\pi\) | ||||
−0.214633 | + | 0.976695i | \(0.568855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.67589e7 | −0.585813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.30910e7 | 0.945405 | ||||||||
\(173\) | 6.35201e7 | 0.932716 | 0.466358 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466358 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.65549e6 | 0.0505418 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.11699e7 | 0.680055 | ||||||||
\(179\) | 8.09559e7 | 1.05503 | 0.527513 | − | 0.849547i | \(-0.323125\pi\) | ||||
0.527513 | + | 0.849547i | \(0.323125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.45032e7 | 0.808549 | 0.404274 | − | 0.914638i | \(-0.367524\pi\) | ||||
0.404274 | + | 0.914638i | \(0.367524\pi\) | |||||||
\(182\) | 1.95763e6 | 0.0240703 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.01802e7 | 0.238815 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.69099e7 | 0.300931 | ||||||||
\(188\) | −5.36632e7 | −0.589012 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.68274e7 | −0.590121 | −0.295060 | − | 0.955479i | \(-0.595340\pi\) | ||||
−0.295060 | + | 0.955479i | \(0.595340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.16377e8 | −1.16524 | −0.582621 | − | 0.812744i | \(-0.697973\pi\) | ||||
−0.582621 | + | 0.812744i | \(0.697973\pi\) | |||||||
\(194\) | 5.29609e7 | 0.520774 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.53891e7 | 0.715175 | ||||||||
\(197\) | −1.18816e8 | −1.10724 | −0.553622 | − | 0.832768i | \(-0.686755\pi\) | ||||
−0.553622 | + | 0.832768i | \(0.686755\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.50106e7 | −0.854646 | −0.427323 | − | 0.904099i | \(-0.640543\pi\) | ||||
−0.427323 | + | 0.904099i | \(0.640543\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.19185e7 | −0.613919 | ||||||||
\(203\) | −2.33664e6 | −0.0196045 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.32564e7 | −0.344758 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.96579e7 | 0.151466 | ||||||||
\(209\) | −8.17176e6 | −0.0619161 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.79246e8 | 1.31360 | 0.656798 | − | 0.754067i | \(-0.271910\pi\) | ||||
0.656798 | + | 0.754067i | \(0.271910\pi\) | |||||||
\(212\) | 3.93813e7 | 0.283867 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.85565e7 | 0.478190 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.77157e7 | −0.117693 | ||||||||
\(218\) | 2.41257e7 | 0.157718 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.44712e8 | 0.901843 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.06537e8 | 1.24718 | 0.623592 | − | 0.781750i | \(-0.285673\pi\) | ||||
0.623592 | + | 0.781750i | \(0.285673\pi\) | |||||||
\(224\) | 1.22941e7 | 0.0730853 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.06238e8 | −0.612209 | ||||||||
\(227\) | 4.33954e7 | 0.246237 | 0.123118 | − | 0.992392i | \(-0.460710\pi\) | ||||
0.123118 | + | 0.992392i | \(0.460710\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.61931e7 | −0.199160 | −0.0995799 | − | 0.995030i | \(-0.531750\pi\) | ||||
−0.0995799 | + | 0.995030i | \(0.531750\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.81932e7 | 0.253383 | ||||||||
\(233\) | 9.22347e7 | 0.477693 | 0.238846 | − | 0.971057i | \(-0.423231\pi\) | ||||
0.238846 | + | 0.971057i | \(0.423231\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.20187e8 | 0.595203 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.09002e7 | 0.0524102 | ||||||||
\(239\) | −4.98468e7 | −0.236181 | −0.118090 | − | 0.993003i | \(-0.537677\pi\) | ||||
−0.118090 | + | 0.993003i | \(0.537677\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.99374e8 | 0.917506 | 0.458753 | − | 0.888564i | \(-0.348296\pi\) | ||||
0.458753 | + | 0.888564i | \(0.348296\pi\) | |||||||
\(242\) | −1.11531e8 | −0.505872 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.76609e7 | −0.121900 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.39448e7 | −0.185553 | ||||||||
\(248\) | 3.65387e8 | 1.52115 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.94678e8 | 1.57538 | 0.787689 | − | 0.616073i | \(-0.211277\pi\) | ||||
0.787689 | + | 0.616073i | \(0.211277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.44930e7 | −0.0562649 | ||||||||
\(254\) | −1.00730e8 | −0.385691 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.08158e8 | −0.775451 | ||||||||
\(257\) | −1.42885e8 | −0.525076 | −0.262538 | − | 0.964922i | \(-0.584559\pi\) | ||||
−0.262538 | + | 0.964922i | \(0.584559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.71857e7 | −0.0614635 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.00961e8 | −0.346815 | ||||||||
\(263\) | 4.40241e8 | 1.49226 | 0.746131 | − | 0.665799i | \(-0.231909\pi\) | ||||
0.746131 | + | 0.665799i | \(0.231909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.31008e6 | −0.0107833 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.66664e7 | −0.148092 | ||||||||
\(269\) | −2.75405e8 | −0.862657 | −0.431329 | − | 0.902195i | \(-0.641955\pi\) | ||||
−0.431329 | + | 0.902195i | \(0.641955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.24670e8 | −1.29616 | −0.648080 | − | 0.761572i | \(-0.724428\pi\) | ||||
−0.648080 | + | 0.761572i | \(0.724428\pi\) | |||||||
\(272\) | 1.09456e8 | 0.329800 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.68269e8 | 0.494172 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.16158e8 | −1.45916 | −0.729581 | − | 0.683894i | \(-0.760285\pi\) | ||||
−0.729581 | + | 0.683894i | \(0.760285\pi\) | |||||||
\(278\) | −7.09638e7 | −0.198098 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.11043e8 | 0.836273 | 0.418137 | − | 0.908384i | \(-0.362683\pi\) | ||||
0.418137 | + | 0.908384i | \(0.362683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.94308e8 | 1.55869 | 0.779344 | − | 0.626596i | \(-0.215552\pi\) | ||||
0.779344 | + | 0.626596i | \(0.215552\pi\) | |||||||
\(284\) | 5.11578e8 | 1.32525 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.89974e7 | 0.0732957 | ||||||||
\(287\) | 4.03020e7 | 0.100633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.95426e8 | 0.963658 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.25956e8 | 0.296058 | ||||||||
\(293\) | 1.15515e8 | 0.268288 | 0.134144 | − | 0.990962i | \(-0.457172\pi\) | ||||
0.134144 | + | 0.990962i | \(0.457172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.54454e8 | 0.794400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.24708e8 | −0.272984 | ||||||||
\(299\) | −7.79382e7 | −0.168617 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.38894e7 | −0.0927635 | ||||||||
\(302\) | 456672. | 0.000954070 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.32387e7 | −0.0678558 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.60600e8 | 0.514032 | 0.257016 | − | 0.966407i | \(-0.417261\pi\) | ||||
0.257016 | + | 0.966407i | \(0.417261\pi\) | |||||||
\(308\) | −5.58182e6 | −0.0108855 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.76795e8 | −1.08733 | −0.543663 | − | 0.839303i | \(-0.682963\pi\) | ||||
−0.543663 | + | 0.839303i | \(0.682963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.60074e8 | 0.848053 | 0.424026 | − | 0.905650i | \(-0.360616\pi\) | ||||
0.424026 | + | 0.905650i | \(0.360616\pi\) | |||||||
\(314\) | 1.93095e8 | 0.351979 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.36062e8 | 1.13395 | ||||||||
\(317\) | 6.25561e7 | 0.110297 | 0.0551483 | − | 0.998478i | \(-0.482437\pi\) | ||||
0.0551483 | + | 0.998478i | \(0.482437\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.46115e7 | −0.0596970 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.87059e6 | −0.00979910 | ||||||||
\(323\) | −2.44687e8 | −0.404020 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.50061e8 | −0.559606 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.31228e8 | −1.30065 | ||||||||
\(329\) | 3.73309e7 | 0.0577941 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.84236e8 | 1.03707 | 0.518535 | − | 0.855057i | \(-0.326478\pi\) | ||||
0.518535 | + | 0.855057i | \(0.326478\pi\) | |||||||
\(332\) | 4.02661e8 | 0.603888 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.55019e8 | −0.227652 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.26313e8 | 0.891429 | 0.445714 | − | 0.895175i | \(-0.352950\pi\) | ||||
0.445714 | + | 0.895175i | \(0.352950\pi\) | |||||||
\(338\) | −2.20553e8 | −0.310674 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.62414e8 | −0.358382 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.05151e8 | −0.140697 | ||||||||
\(344\) | 9.05219e8 | 1.19894 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.81120e8 | 0.494647 | ||||||||
\(347\) | −1.25340e9 | −1.61041 | −0.805203 | − | 0.593000i | \(-0.797943\pi\) | ||||
−0.805203 | + | 0.593000i | \(0.797943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.65350e8 | 0.334142 | 0.167071 | − | 0.985945i | \(-0.446569\pi\) | ||||
0.167071 | + | 0.985945i | \(0.446569\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.82107e8 | 0.222550 | ||||||||
\(353\) | −5.69636e8 | −0.689264 | −0.344632 | − | 0.938738i | \(-0.611996\pi\) | ||||
−0.344632 | + | 0.938738i | \(0.611996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.84605e8 | −0.921671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.85735e8 | 0.559512 | ||||||||
\(359\) | −9.32541e8 | −1.06374 | −0.531872 | − | 0.846825i | \(-0.678511\pi\) | ||||
−0.531872 | + | 0.846825i | \(0.678511\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.19567e8 | −0.916874 | ||||||||
\(362\) | 3.87019e8 | 0.428798 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00170e7 | −0.0326222 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.52565e8 | 0.900318 | 0.450159 | − | 0.892948i | \(-0.351367\pi\) | ||||
0.450159 | + | 0.892948i | \(0.351367\pi\) | |||||||
\(368\) | −5.89505e7 | −0.0616624 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.73957e7 | −0.0278531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.81183e8 | −0.380323 | −0.190162 | − | 0.981753i | \(-0.560901\pi\) | ||||
−0.190162 | + | 0.981753i | \(0.560901\pi\) | |||||||
\(374\) | 1.61460e8 | 0.159593 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.69951e8 | −0.746974 | ||||||||
\(377\) | −1.86128e8 | −0.178903 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.48353e9 | −1.39978 | −0.699889 | − | 0.714251i | \(-0.746767\pi\) | ||||
−0.699889 | + | 0.714251i | \(0.746767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.40964e8 | −0.312959 | ||||||||
\(383\) | −7.61930e8 | −0.692978 | −0.346489 | − | 0.938054i | \(-0.612626\pi\) | ||||
−0.346489 | + | 0.938054i | \(0.612626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.98262e8 | −0.617963 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.12067e8 | −0.705799 | ||||||||
\(389\) | −1.60902e9 | −1.38592 | −0.692959 | − | 0.720977i | \(-0.743693\pi\) | ||||
−0.692959 | + | 0.720977i | \(0.743693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.33965e8 | −0.367144 | ||||||||
\(392\) | 1.08167e9 | 0.906971 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.12896e8 | −0.587205 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.88016e9 | −1.50809 | −0.754046 | − | 0.656822i | \(-0.771900\pi\) | ||||
−0.754046 | + | 0.656822i | \(0.771900\pi\) | |||||||
\(398\) | −5.70064e8 | −0.453245 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.68592e8 | −0.208012 | −0.104006 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104006 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.41117e9 | −1.07402 | ||||||||
\(404\) | 1.10275e9 | 0.832037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.40198e7 | −0.0103969 | ||||||||
\(407\) | −2.54563e8 | −0.187161 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.99478e7 | 0.0650069 | 0.0325034 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325034 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.63264e8 | 0.467247 | ||||||||
\(413\) | −8.36083e7 | −0.0584015 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.79305e8 | 0.666947 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.90306e7 | −0.0328360 | ||||||||
\(419\) | −1.69054e9 | −1.12273 | −0.561367 | − | 0.827567i | \(-0.689724\pi\) | ||||
−0.561367 | + | 0.827567i | \(0.689724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.13333e9 | −0.740232 | −0.370116 | − | 0.928985i | \(-0.620682\pi\) | ||||
−0.370116 | + | 0.928985i | \(0.620682\pi\) | |||||||
\(422\) | 1.07548e9 | 0.696639 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.65037e8 | 0.359995 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.92424e7 | 0.0119608 | ||||||||
\(428\) | −1.05120e9 | −0.648085 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.19943e9 | −1.32324 | −0.661621 | − | 0.749839i | \(-0.730131\pi\) | ||||
−0.661621 | + | 0.749839i | \(0.730131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.51738e8 | 0.0898227 | 0.0449114 | − | 0.998991i | \(-0.485699\pi\) | ||||
0.0449114 | + | 0.998991i | \(0.485699\pi\) | |||||||
\(434\) | −1.06294e8 | −0.0624160 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.69927e8 | −0.213754 | ||||||||
\(437\) | 1.31783e8 | 0.0755393 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.90763e8 | 0.558912 | 0.279456 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279456 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.68271e8 | 0.478275 | ||||||||
\(443\) | −1.77376e9 | −0.969351 | −0.484675 | − | 0.874694i | \(-0.661062\pi\) | ||||
−0.484675 | + | 0.874694i | \(0.661062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.23922e9 | 0.661419 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.21765e7 | 0.0221614 | ||||||||
\(449\) | 2.77010e8 | 0.144422 | 0.0722110 | − | 0.997389i | \(-0.476994\pi\) | ||||
0.0722110 | + | 0.997389i | \(0.476994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.96973e8 | 0.306434 | ||||||||
\(452\) | 1.62898e9 | 0.829720 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.60372e8 | 0.130587 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.94758e9 | −1.44464 | −0.722320 | − | 0.691559i | \(-0.756924\pi\) | ||||
−0.722320 | + | 0.691559i | \(0.756924\pi\) | |||||||
\(458\) | −2.17159e8 | −0.105620 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.76687e9 | 1.31533 | 0.657667 | − | 0.753309i | \(-0.271543\pi\) | ||||
0.657667 | + | 0.753309i | \(0.271543\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.63553e8 | −0.217053 | −0.108527 | − | 0.994094i | \(-0.534613\pi\) | ||||
−0.108527 | + | 0.994094i | \(0.534613\pi\) | |||||||
\(464\) | −1.40783e8 | −0.0654238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.53408e8 | 0.253335 | ||||||||
\(467\) | −4.17922e8 | −0.189883 | −0.0949415 | − | 0.995483i | \(-0.530266\pi\) | ||||
−0.0949415 | + | 0.995483i | \(0.530266\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.24636e7 | 0.0145309 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.72442e9 | 0.754825 | ||||||||
\(473\) | −6.50112e8 | −0.282471 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.67137e8 | −0.0710310 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.99081e8 | −0.125254 | ||||||||
\(479\) | 1.50973e9 | 0.627660 | 0.313830 | − | 0.949479i | \(-0.398388\pi\) | ||||
0.313830 | + | 0.949479i | \(0.398388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.36895e9 | −0.560891 | ||||||||
\(482\) | 1.19624e9 | 0.486581 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.71014e9 | 0.685603 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.29460e8 | −0.364653 | −0.182326 | − | 0.983238i | \(-0.558363\pi\) | ||||
−0.182326 | + | 0.983238i | \(0.558363\pi\) | |||||||
\(488\) | −3.96874e8 | −0.154591 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.12803e9 | −1.95508 | −0.977541 | − | 0.210743i | \(-0.932412\pi\) | ||||
−0.977541 | + | 0.210743i | \(0.932412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.03637e9 | −0.389540 | ||||||||
\(494\) | −2.63669e8 | −0.0984043 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.06737e9 | −0.392762 | ||||||||
\(497\) | −3.55880e8 | −0.130034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.10649e8 | −0.147951 | −0.0739757 | − | 0.997260i | \(-0.523569\pi\) | ||||
−0.0739757 | + | 0.997260i | \(0.523569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.36807e9 | 0.835470 | ||||||||
\(503\) | 5.02041e9 | 1.75894 | 0.879470 | − | 0.475954i | \(-0.157897\pi\) | ||||
0.879470 | + | 0.475954i | \(0.157897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.69581e7 | −0.0298389 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.54452e9 | 0.522723 | ||||||||
\(509\) | 3.24926e9 | 1.09212 | 0.546062 | − | 0.837745i | \(-0.316126\pi\) | ||||
0.546062 | + | 0.837745i | \(0.316126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.76212e7 | −0.0290493 | ||||||||
\(512\) | 1.39223e9 | 0.458423 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.57312e8 | −0.278463 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.52965e8 | 0.175987 | ||||||||
\(518\) | −1.03114e8 | −0.0325959 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.10950e9 | 0.653503 | 0.326752 | − | 0.945110i | \(-0.394046\pi\) | ||||
0.326752 | + | 0.945110i | \(0.394046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.28911e9 | 1.61669 | 0.808345 | − | 0.588709i | \(-0.200364\pi\) | ||||
0.808345 | + | 0.588709i | \(0.200364\pi\) | |||||||
\(524\) | 1.54806e9 | 0.470034 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.64144e9 | 0.791391 | ||||||||
\(527\) | −7.85747e9 | −2.33854 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.17110e9 | −0.931355 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.07546e7 | 0.0146145 | ||||||||
\(533\) | 3.21030e9 | 0.918334 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.69562e8 | −0.187808 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.65243e9 | −0.457493 | ||||||||
\(539\) | −7.76836e8 | −0.213682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.04614e9 | 0.827101 | 0.413551 | − | 0.910481i | \(-0.364288\pi\) | ||||
0.413551 | + | 0.910481i | \(0.364288\pi\) | |||||||
\(542\) | −2.54802e9 | −0.687393 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.45284e9 | 1.45220 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.85537e9 | 1.26843 | 0.634215 | − | 0.773157i | \(-0.281323\pi\) | ||||
0.634215 | + | 0.773157i | \(0.281323\pi\) | |||||||
\(548\) | −2.58013e9 | −0.669746 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.14716e8 | 0.0801472 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.42478e8 | −0.111264 | ||||||||
\(554\) | −3.09695e9 | −0.773838 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.08811e9 | 0.268480 | ||||||||
\(557\) | 1.27762e9 | 0.313263 | 0.156631 | − | 0.987657i | \(-0.449937\pi\) | ||||
0.156631 | + | 0.987657i | \(0.449937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.49607e9 | −0.846522 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.86626e9 | 0.443501 | ||||||||
\(563\) | 4.71265e9 | 1.11297 | 0.556487 | − | 0.830856i | \(-0.312149\pi\) | ||||
0.556487 | + | 0.830856i | \(0.312149\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.56585e9 | 0.826619 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.34003e9 | 1.68066 | ||||||||
\(569\) | −4.57800e9 | −1.04180 | −0.520898 | − | 0.853619i | \(-0.674403\pi\) | ||||
−0.520898 | + | 0.853619i | \(0.674403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.95119e9 | 1.11297 | 0.556485 | − | 0.830858i | \(-0.312150\pi\) | ||||
0.556485 | + | 0.830858i | \(0.312150\pi\) | |||||||
\(572\) | −4.44627e8 | −0.0993367 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.41812e8 | 0.0533686 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.51847e9 | −1.84606 | −0.923031 | − | 0.384725i | \(-0.874296\pi\) | ||||
−0.923031 | + | 0.384725i | \(0.874296\pi\) | |||||||
\(578\) | 2.37256e9 | 0.511057 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.80112e8 | −0.0592536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.05799e8 | −0.0848147 | ||||||||
\(584\) | 1.80719e9 | 0.375455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.93088e8 | 0.142281 | ||||||||
\(587\) | −5.62247e8 | −0.114735 | −0.0573673 | − | 0.998353i | \(-0.518271\pi\) | ||||
−0.0573673 | + | 0.998353i | \(0.518271\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.38608e9 | 0.481152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.03544e9 | −0.205115 | ||||||||
\(593\) | 3.62110e9 | 0.713099 | 0.356549 | − | 0.934277i | \(-0.383953\pi\) | ||||
0.356549 | + | 0.934277i | \(0.383953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.91219e9 | 0.369971 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.67629e8 | −0.0894227 | ||||||||
\(599\) | 7.48104e9 | 1.42222 | 0.711112 | − | 0.703079i | \(-0.248192\pi\) | ||||
0.711112 | + | 0.703079i | \(0.248192\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.81270e9 | −1.09224 | −0.546119 | − | 0.837707i | \(-0.683895\pi\) | ||||
−0.546119 | + | 0.837707i | \(0.683895\pi\) | |||||||
\(602\) | −2.63336e8 | −0.0491953 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7.00230e6 | −0.00129304 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.84051e9 | −0.696993 | −0.348497 | − | 0.937310i | \(-0.613308\pi\) | ||||
−0.348497 | + | 0.937310i | \(0.613308\pi\) | |||||||
\(608\) | −1.65587e9 | −0.298788 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.97364e9 | 0.527405 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.70484e9 | −0.298932 | −0.149466 | − | 0.988767i | \(-0.547755\pi\) | ||||
−0.149466 | + | 0.988767i | \(0.547755\pi\) | |||||||
\(614\) | 1.56360e9 | 0.272606 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.00870e7 | −0.0138048 | ||||||||
\(617\) | −2.80809e9 | −0.481297 | −0.240649 | − | 0.970612i | \(-0.577360\pi\) | ||||
−0.240649 | + | 0.970612i | \(0.577360\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.54365e9 | −0.431063 | −0.215532 | − | 0.976497i | \(-0.569148\pi\) | ||||
−0.215532 | + | 0.976497i | \(0.569148\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.46077e9 | −0.576642 | ||||||||
\(623\) | 5.45812e8 | 0.0904346 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.76045e9 | 0.449748 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.96079e9 | −0.477033 | ||||||||
\(629\) | −7.62238e9 | −1.22127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51146e8 | −0.0239494 | −0.0119747 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119747 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(632\) | 9.12611e9 | 1.43806 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.75337e8 | 0.0584936 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.17754e9 | −0.640373 | ||||||||
\(638\) | −2.07669e8 | −0.0316591 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.23625e10 | 1.85397 | 0.926987 | − | 0.375094i | \(-0.122390\pi\) | ||||
0.926987 | + | 0.375094i | \(0.122390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.86744e9 | −0.425359 | −0.212680 | − | 0.977122i | \(-0.568219\pi\) | ||||
−0.212680 | + | 0.977122i | \(0.568219\pi\) | |||||||
\(644\) | 9.00157e7 | 0.0132806 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.46812e9 | −0.214264 | ||||||||
\(647\) | −4.10640e9 | −0.596068 | −0.298034 | − | 0.954555i | \(-0.596331\pi\) | ||||
−0.298034 | + | 0.954555i | \(0.596331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.23845e9 | −0.177837 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.36760e9 | 0.758427 | ||||||||
\(653\) | 6.91100e9 | 0.971280 | 0.485640 | − | 0.874159i | \(-0.338587\pi\) | ||||
0.485640 | + | 0.874159i | \(0.338587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.42819e9 | 0.335830 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.23986e8 | 0.0306499 | ||||||||
\(659\) | −3.42444e9 | −0.466112 | −0.233056 | − | 0.972463i | \(-0.574873\pi\) | ||||
−0.233056 | + | 0.972463i | \(0.574873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.76437e9 | −0.911008 | −0.455504 | − | 0.890234i | \(-0.650541\pi\) | ||||
−0.455504 | + | 0.890234i | \(0.650541\pi\) | |||||||
\(662\) | 4.10541e9 | 0.549989 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.77731e9 | 0.765839 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.58165e8 | 0.0728320 | ||||||||
\(668\) | 2.37696e9 | 0.308535 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.85028e8 | 0.0364215 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.74959e9 | 0.221250 | 0.110625 | − | 0.993862i | \(-0.464715\pi\) | ||||
0.110625 | + | 0.993862i | \(0.464715\pi\) | |||||||
\(674\) | 3.75788e9 | 0.472752 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.38182e9 | 0.421053 | ||||||||
\(677\) | 8.30011e9 | 1.02807 | 0.514036 | − | 0.857769i | \(-0.328150\pi\) | ||||
0.514036 | + | 0.857769i | \(0.328150\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.64916e8 | 0.0692532 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.57448e9 | −0.190061 | ||||||||
\(683\) | −1.21232e10 | −1.45594 | −0.727969 | − | 0.685610i | \(-0.759536\pi\) | ||||
−0.727969 | + | 0.685610i | \(0.759536\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.30908e8 | −0.0746160 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.64434e9 | −0.309569 | ||||||||
\(689\) | −2.18224e9 | −0.254176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.21846e9 | 0.947583 | 0.473791 | − | 0.880637i | \(-0.342885\pi\) | ||||
0.473791 | + | 0.880637i | \(0.342885\pi\) | |||||||
\(692\) | −5.84385e9 | −0.670390 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.52038e9 | −0.854046 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.78752e10 | 1.99957 | ||||||||
\(698\) | 1.59210e9 | 0.177205 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.72231e9 | −0.517775 | −0.258888 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258888 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.31469e9 | 0.251275 | ||||||||
\(704\) | 6.24740e8 | 0.0674831 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.41781e9 | −0.365537 | ||||||||
\(707\) | −7.67131e8 | −0.0816397 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.78975e9 | 0.293970 | 0.146985 | − | 0.989139i | \(-0.453043\pi\) | ||||
0.146985 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.12574e10 | −1.16885 | ||||||||
\(713\) | 4.23184e9 | 0.437236 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.44794e9 | −0.758299 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.59524e9 | −0.564136 | ||||||||
\(719\) | −1.51985e9 | −0.152493 | −0.0762463 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762463 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.61401e8 | −0.0458464 | ||||||||
\(722\) | −4.91740e9 | −0.486246 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.93429e9 | −0.581144 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.11761e9 | 0.783534 | 0.391767 | − | 0.920065i | \(-0.371864\pi\) | ||||
0.391767 | + | 0.920065i | \(0.371864\pi\) | |||||||
\(728\) | −4.30679e8 | −0.0413708 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.94663e10 | −1.84320 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.03241e10 | 0.968249 | 0.484124 | − | 0.874999i | \(-0.339138\pi\) | ||||
0.484124 | + | 0.874999i | \(0.339138\pi\) | |||||||
\(734\) | 5.11539e9 | 0.477466 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.93676e9 | −0.271517 | ||||||||
\(737\) | 4.80867e8 | 0.0442475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.35365e10 | −1.23382 | −0.616908 | − | 0.787035i | \(-0.711615\pi\) | ||||
−0.616908 | + | 0.787035i | \(0.711615\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.64374e8 | −0.0147713 | ||||||||
\(743\) | −1.71936e10 | −1.53782 | −0.768910 | − | 0.639356i | \(-0.779201\pi\) | ||||
−0.768910 | + | 0.639356i | \(0.779201\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.28710e9 | −0.201697 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.47571e9 | −0.216294 | ||||||||
\(749\) | 7.31269e8 | 0.0635903 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.12478e10 | 0.969013 | 0.484506 | − | 0.874788i | \(-0.338999\pi\) | ||||
0.484506 | + | 0.874788i | \(0.338999\pi\) | |||||||
\(752\) | 2.24919e9 | 0.192870 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.11677e9 | −0.0948775 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.63068e10 | −1.36626 | −0.683131 | − | 0.730296i | \(-0.739382\pi\) | ||||
−0.683131 | + | 0.730296i | \(0.739382\pi\) | |||||||
\(758\) | −8.90118e9 | −0.742345 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.14069e9 | −0.505093 | −0.252546 | − | 0.967585i | \(-0.581268\pi\) | ||||
−0.252546 | + | 0.967585i | \(0.581268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.57341e8 | 0.0209736 | ||||||||
\(764\) | 5.22812e9 | 0.424149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.57158e9 | −0.367507 | ||||||||
\(767\) | −6.65993e9 | −0.532949 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.45069e10 | 1.94333 | 0.971664 | − | 0.236368i | \(-0.0759569\pi\) | ||||
0.971664 | + | 0.236368i | \(0.0759569\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.07067e10 | 0.837518 | ||||||||
\(773\) | −1.01722e10 | −0.792110 | −0.396055 | − | 0.918227i | \(-0.629621\pi\) | ||||
−0.396055 | + | 0.918227i | \(0.629621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.16514e10 | −0.895080 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.65411e9 | −0.734994 | ||||||||
\(779\) | −5.42817e9 | −0.411408 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.27148e9 | −0.395962 | ||||||||
\(782\) | −2.60379e9 | −0.194707 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.15979e9 | −0.234181 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.79135e9 | 0.716030 | 0.358015 | − | 0.933716i | \(-0.383454\pi\) | ||||
0.358015 | + | 0.933716i | \(0.383454\pi\) | |||||||
\(788\) | 1.09311e10 | 0.795832 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.13320e9 | −0.0814124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.53277e9 | 0.109150 | ||||||||
\(794\) | −1.12809e10 | −0.799786 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.74098e9 | 0.614277 | ||||||||
\(797\) | −9.75782e9 | −0.682729 | −0.341365 | − | 0.939931i | \(-0.610889\pi\) | ||||
−0.341365 | + | 0.939931i | \(0.610889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.65574e10 | 1.14836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.61155e9 | −0.110315 | ||||||||
\(803\) | −1.29789e9 | −0.0884572 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.46700e9 | −0.569583 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.58221e10 | 1.05517 | ||||||||
\(809\) | 2.78706e9 | 0.185066 | 0.0925330 | − | 0.995710i | \(-0.470504\pi\) | ||||
0.0925330 | + | 0.995710i | \(0.470504\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.99983e9 | −0.526633 | −0.263316 | − | 0.964710i | \(-0.584816\pi\) | ||||
−0.263316 | + | 0.964710i | \(0.584816\pi\) | |||||||
\(812\) | 2.14971e8 | 0.0140907 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.52738e9 | −0.0992569 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.91135e9 | 0.379236 | ||||||||
\(818\) | 5.39687e8 | 0.0344751 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.02402e10 | 0.645813 | 0.322906 | − | 0.946431i | \(-0.395340\pi\) | ||||
0.322906 | + | 0.946431i | \(0.395340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.78682e10 | −1.74265 | −0.871324 | − | 0.490707i | \(-0.836738\pi\) | ||||
−0.871324 | + | 0.490707i | \(0.836738\pi\) | |||||||
\(824\) | 9.51640e9 | 0.592553 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.01650e8 | −0.0309721 | ||||||||
\(827\) | 2.35125e10 | 1.44554 | 0.722769 | − | 0.691090i | \(-0.242869\pi\) | ||||
0.722769 | + | 0.691090i | \(0.242869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.28598e10 | −0.783960 | −0.391980 | − | 0.919974i | \(-0.628210\pi\) | ||||
−0.391980 | + | 0.919974i | \(0.628210\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.35962e9 | 0.202236 | ||||||||
\(833\) | −2.32608e10 | −1.39434 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.51802e8 | 0.0445022 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.01433e10 | −0.595420 | ||||||||
\(839\) | 7.99832e9 | 0.467554 | 0.233777 | − | 0.972290i | \(-0.424891\pi\) | ||||
0.233777 | + | 0.972290i | \(0.424891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.59169e10 | −0.922725 | ||||||||
\(842\) | −6.79996e9 | −0.392567 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.64907e10 | −0.944147 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.18966e9 | −0.0672716 | ||||||||
\(848\) | −1.65059e9 | −0.0929510 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.10523e9 | 0.228341 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.20827e9 | −0.232157 | −0.116079 | − | 0.993240i | \(-0.537032\pi\) | ||||
−0.116079 | + | 0.993240i | \(0.537032\pi\) | |||||||
\(854\) | 1.15454e8 | 0.00634318 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50824e10 | −0.821888 | ||||||||
\(857\) | 3.19307e10 | 1.73291 | 0.866453 | − | 0.499259i | \(-0.166394\pi\) | ||||
0.866453 | + | 0.499259i | \(0.166394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.18002e10 | 1.17350 | 0.586752 | − | 0.809767i | \(-0.300406\pi\) | ||||
0.586752 | + | 0.809767i | \(0.300406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.31966e10 | −0.701755 | ||||||||
\(863\) | 1.04728e10 | 0.554657 | 0.277329 | − | 0.960775i | \(-0.410551\pi\) | ||||
0.277329 | + | 0.960775i | \(0.410551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.10427e8 | 0.0476357 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.62985e9 | 0.0845916 | ||||||||
\(869\) | −6.55421e9 | −0.338806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.58593e9 | 0.132603 | ||||||||
\(872\) | −5.30765e9 | −0.271078 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.90695e8 | 0.0400608 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.77787e10 | 0.890024 | 0.445012 | − | 0.895525i | \(-0.353199\pi\) | ||||
0.445012 | + | 0.895525i | \(0.353199\pi\) | |||||||
\(878\) | 5.94458e9 | 0.296408 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.64253e9 | 0.376549 | 0.188274 | − | 0.982116i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982116i | \(0.439711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.76375e10 | 1.35094 | 0.675472 | − | 0.737386i | \(-0.263940\pi\) | ||||
0.675472 | + | 0.737386i | \(0.263940\pi\) | |||||||
\(884\) | −1.33135e10 | −0.648200 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.06425e10 | −0.514076 | ||||||||
\(887\) | 3.23087e10 | 1.55449 | 0.777243 | − | 0.629200i | \(-0.216617\pi\) | ||||
0.777243 | + | 0.629200i | \(0.216617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.07445e9 | −0.0512897 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.90014e10 | −0.896414 | ||||||||
\(893\) | −5.02801e9 | −0.236274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.32059e9 | −0.0613325 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.66206e9 | 0.0765914 | ||||||||
\(899\) | 1.01063e10 | 0.463908 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.21509e10 | −0.553439 | ||||||||
\(902\) | 3.58184e9 | 0.162511 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.33723e10 | 1.05223 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.27142e10 | −1.01082 | −0.505409 | − | 0.862880i | \(-0.668658\pi\) | ||||
−0.505409 | + | 0.862880i | \(0.668658\pi\) | |||||||
\(908\) | −3.99238e9 | −0.176983 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.50925e9 | −0.329065 | −0.164533 | − | 0.986372i | \(-0.552612\pi\) | ||||
−0.164533 | + | 0.986372i | \(0.552612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.14916e9 | −0.180431 | ||||||||
\(914\) | −1.76855e10 | −0.766136 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.32976e9 | 0.143146 | ||||||||
\(917\) | −1.07691e9 | −0.0461199 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.49374e10 | −1.05986 | −0.529928 | − | 0.848043i | \(-0.677781\pi\) | ||||
−0.529928 | + | 0.848043i | \(0.677781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.66012e10 | 0.697561 | ||||||||
\(923\) | −2.83481e10 | −1.18664 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.78132e9 | −0.115110 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.01342e9 | −0.288079 | ||||||||
\(929\) | 8.66205e9 | 0.354459 | 0.177229 | − | 0.984170i | \(-0.443287\pi\) | ||||
0.177229 | + | 0.984170i | \(0.443287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.06363e9 | 0.286883 | ||||||||
\(932\) | −8.48559e9 | −0.343342 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.50753e9 | −0.100701 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.82655e10 | −1.12245 | −0.561226 | − | 0.827663i | \(-0.689670\pi\) | ||||
−0.561226 | + | 0.827663i | \(0.689670\pi\) | |||||||
\(938\) | 1.94782e8 | 0.00770616 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.67082e10 | 1.82738 | 0.913691 | − | 0.406410i | \(-0.133220\pi\) | ||||
0.913691 | + | 0.406410i | \(0.133220\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.62713e9 | −0.373857 | ||||||||
\(944\) | −5.03740e9 | −0.194897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.90067e9 | −0.149803 | ||||||||
\(947\) | −4.67392e10 | −1.78837 | −0.894184 | − | 0.447701i | \(-0.852243\pi\) | ||||
−0.894184 | + | 0.447701i | \(0.852243\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.97958e9 | −0.265093 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.39805e9 | −0.0900801 | ||||||||
\(953\) | 3.82420e10 | 1.43125 | 0.715625 | − | 0.698484i | \(-0.246142\pi\) | ||||
0.715625 | + | 0.698484i | \(0.246142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.58591e9 | 0.169755 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.05837e9 | 0.332867 | ||||||||
\(959\) | 1.79487e9 | 0.0657157 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.91101e10 | 1.78500 | ||||||||
\(962\) | −8.21367e9 | −0.297457 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.83424e10 | −0.659457 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.90012e10 | 1.74267 | 0.871333 | − | 0.490692i | \(-0.163256\pi\) | ||||
0.871333 | + | 0.490692i | \(0.163256\pi\) | |||||||
\(968\) | 2.45368e10 | 0.869468 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.72929e10 | −0.956713 | −0.478357 | − | 0.878166i | \(-0.658767\pi\) | ||||
−0.478357 | + | 0.878166i | \(0.658767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.56947e8 | −0.0263433 | ||||||||
\(974\) | −5.57676e9 | −0.193386 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.15935e9 | 0.0399155 | ||||||||
\(977\) | 3.94482e9 | 0.135331 | 0.0676653 | − | 0.997708i | \(-0.478445\pi\) | ||||
0.0676653 | + | 0.997708i | \(0.478445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.08484e9 | 0.275380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.07682e10 | −1.03684 | ||||||||
\(983\) | 4.74320e8 | 0.0159270 | 0.00796351 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796351 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.21824e9 | −0.206585 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.04292e9 | 0.133366 | ||||||||
\(989\) | 1.04841e10 | 0.344622 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.22197e10 | 0.398843 | 0.199421 | − | 0.979914i | \(-0.436094\pi\) | ||||
0.199421 | + | 0.979914i | \(0.436094\pi\) | |||||||
\(992\) | −5.31737e10 | −1.72944 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.13528e9 | −0.0689609 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.60690e10 | 1.15266 | 0.576330 | − | 0.817217i | \(-0.304484\pi\) | ||||
0.576330 | + | 0.817217i | \(0.304484\pi\) | |||||||
\(998\) | −2.46390e9 | −0.0784631 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.8.a.i.1.1 | 1 | ||
3.2 | odd | 2 | 75.8.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 225.8.b.f.199.2 | 2 | |||
5.3 | odd | 4 | 225.8.b.f.199.1 | 2 | |||
5.4 | even | 2 | 9.8.a.a.1.1 | 1 | |||
15.2 | even | 4 | 75.8.b.c.49.1 | 2 | |||
15.8 | even | 4 | 75.8.b.c.49.2 | 2 | |||
15.14 | odd | 2 | 3.8.a.a.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 144.8.a.b.1.1 | 1 | |||
35.34 | odd | 2 | 441.8.a.a.1.1 | 1 | |||
40.19 | odd | 2 | 576.8.a.x.1.1 | 1 | |||
40.29 | even | 2 | 576.8.a.w.1.1 | 1 | |||
45.4 | even | 6 | 81.8.c.c.55.1 | 2 | |||
45.14 | odd | 6 | 81.8.c.a.55.1 | 2 | |||
45.29 | odd | 6 | 81.8.c.a.28.1 | 2 | |||
45.34 | even | 6 | 81.8.c.c.28.1 | 2 | |||
60.59 | even | 2 | 48.8.a.g.1.1 | 1 | |||
105.44 | odd | 6 | 147.8.e.b.67.1 | 2 | |||
105.59 | even | 6 | 147.8.e.a.79.1 | 2 | |||
105.74 | odd | 6 | 147.8.e.b.79.1 | 2 | |||
105.89 | even | 6 | 147.8.e.a.67.1 | 2 | |||
105.104 | even | 2 | 147.8.a.b.1.1 | 1 | |||
120.29 | odd | 2 | 192.8.a.i.1.1 | 1 | |||
120.59 | even | 2 | 192.8.a.a.1.1 | 1 | |||
165.164 | even | 2 | 363.8.a.b.1.1 | 1 | |||
195.194 | odd | 2 | 507.8.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.8.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
9.8.a.a.1.1 | 1 | 5.4 | even | 2 | |||
48.8.a.g.1.1 | 1 | 60.59 | even | 2 | |||
75.8.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
75.8.b.c.49.1 | 2 | 15.2 | even | 4 | |||
75.8.b.c.49.2 | 2 | 15.8 | even | 4 | |||
81.8.c.a.28.1 | 2 | 45.29 | odd | 6 | |||
81.8.c.a.55.1 | 2 | 45.14 | odd | 6 | |||
81.8.c.c.28.1 | 2 | 45.34 | even | 6 | |||
81.8.c.c.55.1 | 2 | 45.4 | even | 6 | |||
144.8.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
147.8.a.b.1.1 | 1 | 105.104 | even | 2 | |||
147.8.e.a.67.1 | 2 | 105.89 | even | 6 | |||
147.8.e.a.79.1 | 2 | 105.59 | even | 6 | |||
147.8.e.b.67.1 | 2 | 105.44 | odd | 6 | |||
147.8.e.b.79.1 | 2 | 105.74 | odd | 6 | |||
192.8.a.a.1.1 | 1 | 120.59 | even | 2 | |||
192.8.a.i.1.1 | 1 | 120.29 | odd | 2 | |||
225.8.a.i.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.8.b.f.199.1 | 2 | 5.3 | odd | 4 | |||
225.8.b.f.199.2 | 2 | 5.2 | odd | 4 | |||
363.8.a.b.1.1 | 1 | 165.164 | even | 2 | |||
441.8.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
507.8.a.a.1.1 | 1 | 195.194 | odd | 2 | |||
576.8.a.w.1.1 | 1 | 40.29 | even | 2 | |||
576.8.a.x.1.1 | 1 | 40.19 | odd | 2 |