Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,10,Mod(1,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.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: | \(37.0825802038\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 24) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 72.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −830.000 | −0.593900 | −0.296950 | − | 0.954893i | \(-0.595969\pi\) | ||||
−0.296950 | + | 0.954893i | \(0.595969\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 672.000 | 0.105786 | 0.0528930 | − | 0.998600i | \(-0.483156\pi\) | ||||
0.0528930 | + | 0.998600i | \(0.483156\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 73468.0 | 1.51297 | 0.756486 | − | 0.654009i | \(-0.226914\pi\) | ||||
0.756486 | + | 0.654009i | \(0.226914\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −78242.0 | −0.759792 | −0.379896 | − | 0.925029i | \(-0.624040\pi\) | ||||
−0.379896 | + | 0.925029i | \(0.624040\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 161726. | 0.469634 | 0.234817 | − | 0.972040i | \(-0.424551\pi\) | ||||
0.234817 | + | 0.972040i | \(0.424551\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −653572. | −1.15054 | −0.575271 | − | 0.817963i | \(-0.695103\pi\) | ||||
−0.575271 | + | 0.817963i | \(0.695103\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.06670e6 | 0.794814 | 0.397407 | − | 0.917642i | \(-0.369910\pi\) | ||||
0.397407 | + | 0.917642i | \(0.369910\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.26422e6 | −0.647283 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82484e6 | −1.00420 | −0.502102 | − | 0.864808i | \(-0.667440\pi\) | ||||
−0.502102 | + | 0.864808i | \(0.667440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.57948e6 | −0.307175 | −0.153588 | − | 0.988135i | \(-0.549083\pi\) | ||||
−0.153588 | + | 0.988135i | \(0.549083\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −557760. | −0.0628263 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.60156e7 | 1.40487 | 0.702433 | − | 0.711749i | \(-0.252097\pi\) | ||||
0.702433 | + | 0.711749i | \(0.252097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.62683e7 | −1.45179 | −0.725896 | − | 0.687805i | \(-0.758575\pi\) | ||||
−0.725896 | + | 0.687805i | \(0.758575\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.44952e7 | −1.98475 | −0.992374 | − | 0.123263i | \(-0.960664\pi\) | ||||
−0.992374 | + | 0.123263i | \(0.960664\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.43242e7 | −0.428182 | −0.214091 | − | 0.976814i | \(-0.568679\pi\) | ||||
−0.214091 | + | 0.976814i | \(0.568679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.99020e7 | −0.988809 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.43860e7 | 0.424522 | 0.212261 | − | 0.977213i | \(-0.431917\pi\) | ||||
0.212261 | + | 0.977213i | \(0.431917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.09784e7 | −0.898554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.19421e7 | −0.128306 | −0.0641529 | − | 0.997940i | \(-0.520435\pi\) | ||||
−0.0641529 | + | 0.997940i | \(0.520435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.89740e8 | −1.75459 | −0.877294 | − | 0.479953i | \(-0.840654\pi\) | ||||
−0.877294 | + | 0.479953i | \(0.840654\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.49409e7 | 0.451240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.06710e8 | −0.646944 | −0.323472 | − | 0.946238i | \(-0.604850\pi\) | ||||
−0.323472 | + | 0.946238i | \(0.604850\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.02754e8 | −1.41393 | −0.706965 | − | 0.707249i | \(-0.749936\pi\) | ||||
−0.706965 | + | 0.707249i | \(0.749936\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.17695e7 | 0.337007 | 0.168503 | − | 0.985701i | \(-0.446107\pi\) | ||||
0.168503 | + | 0.985701i | \(0.446107\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.93705e7 | 0.160051 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.15315e8 | 0.910800 | 0.455400 | − | 0.890287i | \(-0.349496\pi\) | ||||
0.455400 | + | 0.890287i | \(0.349496\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.52833e8 | −1.74119 | −0.870597 | − | 0.491996i | \(-0.836267\pi\) | ||||
−0.870597 | + | 0.491996i | \(0.836267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.34233e8 | −0.278916 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.33284e8 | 0.732012 | 0.366006 | − | 0.930613i | \(-0.380725\pi\) | ||||
0.366006 | + | 0.930613i | \(0.380725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.25786e7 | −0.0803754 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.42465e8 | 0.683306 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.28250e9 | 1.47090 | 0.735450 | − | 0.677578i | \(-0.236971\pi\) | ||||
0.735450 | + | 0.677578i | \(0.236971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.96115e9 | 1.87528 | 0.937639 | − | 0.347611i | \(-0.113007\pi\) | ||||
0.937639 | + | 0.347611i | \(0.113007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.48061e8 | −0.829982 | −0.414991 | − | 0.909825i | \(-0.636215\pi\) | ||||
−0.414991 | + | 0.909825i | \(0.636215\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.46613e8 | 0.181881 | 0.0909407 | − | 0.995856i | \(-0.471013\pi\) | ||||
0.0909407 | + | 0.995856i | \(0.471013\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.47308e9 | 0.999556 | 0.499778 | − | 0.866154i | \(-0.333415\pi\) | ||||
0.499778 | + | 0.866154i | \(0.333415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.66579e8 | −0.442287 | −0.221143 | − | 0.975241i | \(-0.570979\pi\) | ||||
−0.221143 | + | 0.975241i | \(0.570979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.85358e8 | −0.472040 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.08680e8 | 0.0496807 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.03960e9 | 1.28909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.67040e9 | 0.978321 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.08546e9 | 1.05246 | 0.526228 | − | 0.850344i | \(-0.323606\pi\) | ||||
0.526228 | + | 0.850344i | \(0.323606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.76317e9 | −0.819759 | −0.409880 | − | 0.912140i | \(-0.634429\pi\) | ||||
−0.409880 | + | 0.912140i | \(0.634429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.39200e8 | −0.121711 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.75041e9 | −0.667044 | −0.333522 | − | 0.942742i | \(-0.608237\pi\) | ||||
−0.333522 | + | 0.942742i | \(0.608237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.58704e9 | 0.360597 | 0.180299 | − | 0.983612i | \(-0.442294\pi\) | ||||
0.180299 | + | 0.983612i | \(0.442294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.74828e9 | −1.14955 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.17462e9 | 0.596397 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.16328e9 | 1.52305 | 0.761523 | − | 0.648138i | \(-0.224452\pi\) | ||||
0.761523 | + | 0.648138i | \(0.224452\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.46073e9 | −1.01131 | −0.505656 | − | 0.862735i | \(-0.668750\pi\) | ||||
−0.505656 | + | 0.862735i | \(0.668750\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.31097e9 | 0.182431 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.34930e10 | −1.77239 | −0.886194 | − | 0.463315i | \(-0.846660\pi\) | ||||
−0.886194 | + | 0.463315i | \(0.846660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.16820e8 | 0.0840802 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.11445e9 | −1.01131 | −0.505657 | − | 0.862734i | \(-0.668750\pi\) | ||||
−0.505657 | + | 0.862734i | \(0.668750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.28739e9 | −0.725016 | −0.362508 | − | 0.931981i | \(-0.618079\pi\) | ||||
−0.362508 | + | 0.931981i | \(0.618079\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.48269e9 | −0.422716 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.79271e9 | −0.152161 | −0.0760804 | − | 0.997102i | \(-0.524241\pi\) | ||||
−0.0760804 | + | 0.997102i | \(0.524241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.49559e8 | −0.0684735 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.58921e9 | −0.261313 | −0.130656 | − | 0.991428i | \(-0.541708\pi\) | ||||
−0.130656 | + | 0.991428i | \(0.541708\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.34516e10 | −1.62412 | −0.812060 | − | 0.583574i | \(-0.801654\pi\) | ||||
−0.812060 | + | 0.583574i | \(0.801654\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.32929e10 | −0.834350 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.18817e10 | 0.710544 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.13072e10 | 1.15845 | 0.579224 | − | 0.815169i | \(-0.303356\pi\) | ||||
0.579224 | + | 0.815169i | \(0.303356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.02497e10 | 1.05054 | 0.525269 | − | 0.850936i | \(-0.323965\pi\) | ||||
0.525269 | + | 0.850936i | \(0.323965\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.27339e10 | −0.602372 | −0.301186 | − | 0.953565i | \(-0.597382\pi\) | ||||
−0.301186 | + | 0.953565i | \(0.597382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.66200e9 | −0.255936 | −0.127968 | − | 0.991778i | \(-0.540845\pi\) | ||||
−0.127968 | + | 0.991778i | \(0.540845\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.57029e9 | −0.106231 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.18027e10 | 0.862219 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.80166e10 | −1.74074 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.34254e9 | 0.185557 | 0.0927783 | − | 0.995687i | \(-0.470425\pi\) | ||||
0.0927783 | + | 0.995687i | \(0.470425\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.69310e10 | 1.17874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.06141e9 | −0.0324949 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.26538e10 | −0.356824 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.53127e10 | 0.414649 | 0.207325 | − | 0.978272i | \(-0.433524\pi\) | ||||
0.207325 | + | 0.978272i | \(0.433524\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.24911e10 | 1.31211 | 0.656053 | − | 0.754714i | \(-0.272225\pi\) | ||||
0.656053 | + | 0.754714i | \(0.272225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.27719e9 | 0.102778 | 0.0513888 | − | 0.998679i | \(-0.483635\pi\) | ||||
0.0513888 | + | 0.998679i | \(0.483635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.40992e10 | 0.980232 | 0.490116 | − | 0.871657i | \(-0.336954\pi\) | ||||
0.490116 | + | 0.871657i | \(0.336954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.18891e10 | 0.254297 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.95413e10 | 0.783899 | 0.391949 | − | 0.919987i | \(-0.371801\pi\) | ||||
0.391949 | + | 0.919987i | \(0.371801\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.42570e10 | −0.845094 | −0.422547 | − | 0.906341i | \(-0.638864\pi\) | ||||
−0.422547 | + | 0.906341i | \(0.638864\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.31187e10 | 0.587254 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.11368e10 | 0.874172 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.93264e10 | −0.466366 | −0.233183 | − | 0.972433i | \(-0.574914\pi\) | ||||
−0.233183 | + | 0.972433i | \(0.574914\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.83680e10 | 1.20253 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.75455e9 | 0.0679846 | 0.0339923 | − | 0.999422i | \(-0.489178\pi\) | ||||
0.0339923 | + | 0.999422i | \(0.489178\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.07625e10 | 0.148615 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.32650e7 | 0.000557617 0 | 0.000278809 | − | 1.00000i | \(-0.499911\pi\) | ||||
0.000278809 | 1.00000i | \(0.499911\pi\) | ||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.02404e10 | −0.252123 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.74801e10 | −0.785761 | −0.392881 | − | 0.919590i | \(-0.628521\pi\) | ||||
−0.392881 | + | 0.919590i | \(0.628521\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.17456e11 | 1.32286 | 0.661431 | − | 0.750006i | \(-0.269950\pi\) | ||||
0.661431 | + | 0.750006i | \(0.269950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.28801e10 | −0.979322 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.12220e10 | −0.420698 | −0.210349 | − | 0.977626i | \(-0.567460\pi\) | ||||
−0.210349 | + | 0.977626i | \(0.567460\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.48899e10 | 0.812227 | 0.406114 | − | 0.913823i | \(-0.366884\pi\) | ||||
0.406114 | + | 0.913823i | \(0.366884\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.45640e10 | −0.320321 | −0.160160 | − | 0.987091i | \(-0.551201\pi\) | ||||
−0.160160 | + | 0.987091i | \(0.551201\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.76523e10 | −0.153579 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.24326e10 | −0.779444 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.21053e11 | −1.75223 | −0.876116 | − | 0.482100i | \(-0.839874\pi\) | ||||
−0.876116 | + | 0.482100i | \(0.839874\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.91193e9 | 0.0762007 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.34604e10 | −0.603893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.99008e10 | −0.209959 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.57484e11 | 1.04205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.52457e11 | −1.62205 | −0.811024 | − | 0.585012i | \(-0.801090\pi\) | ||||
−0.811024 | + | 0.585012i | \(0.801090\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.13082e10 | 0.553462 | 0.276731 | − | 0.960947i | \(-0.410749\pi\) | ||||
0.276731 | + | 0.960947i | \(0.410749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.06665e10 | 0.239490 | 0.119745 | − | 0.992805i | \(-0.461792\pi\) | ||||
0.119745 | + | 0.992805i | \(0.461792\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.10345e11 | 1.16995 | 0.584974 | − | 0.811052i | \(-0.301105\pi\) | ||||
0.584974 | + | 0.811052i | \(0.301105\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.81003e11 | −1.51933 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.05700e11 | −0.540334 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.89155e10 | 0.491801 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.62584e9 | −0.0452957 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.07269e11 | −1.40700 | −0.703499 | − | 0.710697i | \(-0.748380\pi\) | ||||
−0.703499 | + | 0.710697i | \(0.748380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.85689e10 | 0.384220 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.81037e11 | −0.764596 | −0.382298 | − | 0.924039i | \(-0.624867\pi\) | ||||
−0.382298 | + | 0.924039i | \(0.624867\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.16041e11 | −0.464748 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.39318e10 | −0.210388 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.22927e11 | −1.93624 | −0.968119 | − | 0.250491i | \(-0.919408\pi\) | ||||
−0.968119 | + | 0.250491i | \(0.919408\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.04567e11 | 1.09893 | 0.549463 | − | 0.835518i | \(-0.314832\pi\) | ||||
0.549463 | + | 0.835518i | \(0.314832\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.04187e10 | −0.241380 | −0.120690 | − | 0.992690i | \(-0.538511\pi\) | ||||
−0.120690 | + | 0.992690i | \(0.538511\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.51286e11 | 0.839732 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.91400e11 | 0.925900 | 0.462950 | − | 0.886384i | \(-0.346791\pi\) | ||||
0.462950 | + | 0.886384i | \(0.346791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.04469e11 | 0.323745 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.78687e10 | −0.200148 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.65943e11 | 0.765230 | 0.382615 | − | 0.923908i | \(-0.375024\pi\) | ||||
0.382615 | + | 0.923908i | \(0.375024\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.63874e10 | 0.0449085 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.21656e11 | 0.860403 | 0.430201 | − | 0.902733i | \(-0.358443\pi\) | ||||
0.430201 | + | 0.902733i | \(0.358443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.99263e11 | 0.762987 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.83177e11 | 0.704988 | 0.352494 | − | 0.935814i | \(-0.385334\pi\) | ||||
0.352494 | + | 0.935814i | \(0.385334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.70279e11 | −1.59170 | −0.795850 | − | 0.605494i | \(-0.792975\pi\) | ||||
−0.795850 | + | 0.605494i | \(0.792975\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.09775e10 | −0.0950544 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.67505e11 | 1.92087 | 0.960437 | − | 0.278498i | \(-0.0898366\pi\) | ||||
0.960437 | + | 0.278498i | \(0.0898366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.72512e11 | 0.373272 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.61712e11 | −0.540924 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.14512e11 | −0.635449 | −0.317724 | − | 0.948183i | \(-0.602919\pi\) | ||||
−0.317724 | + | 0.948183i | \(0.602919\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.95667e11 | 0.377892 | 0.188946 | − | 0.981987i | \(-0.439493\pi\) | ||||
0.188946 | + | 0.981987i | \(0.439493\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.23582e11 | 0.233390 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.17663e12 | 2.12553 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.63692e11 | 0.642656 | 0.321328 | − | 0.946968i | \(-0.395871\pi\) | ||||
0.321328 | + | 0.946968i | \(0.395871\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.02508e9 | −0.0135729 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.24852e11 | 1.03410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.20311e11 | −0.349199 | −0.174600 | − | 0.984640i | \(-0.555863\pi\) | ||||
−0.174600 | + | 0.984640i | \(0.555863\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.96326e11 | −1.54572 | −0.772862 | − | 0.634574i | \(-0.781175\pi\) | ||||
−0.772862 | + | 0.634574i | \(0.781175\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.04458e11 | −0.303986 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.27505e11 | −0.185611 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.96850e11 | 1.39150 | 0.695748 | − | 0.718286i | \(-0.255073\pi\) | ||||
0.695748 | + | 0.718286i | \(0.255073\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.11011e11 | 1.10874 | 0.554372 | − | 0.832269i | \(-0.312959\pi\) | ||||
0.554372 | + | 0.832269i | \(0.312959\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.97163e11 | −0.914466 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.24677e11 | −0.160212 | −0.0801062 | − | 0.996786i | \(-0.525526\pi\) | ||||
−0.0801062 | + | 0.996786i | \(0.525526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.13417e11 | −0.633364 | −0.316682 | − | 0.948532i | \(-0.602569\pi\) | ||||
−0.316682 | + | 0.948532i | \(0.602569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.59626e11 | −0.434741 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.29234e11 | −0.846756 | −0.423378 | − | 0.905953i | \(-0.639156\pi\) | ||||
−0.423378 | + | 0.905953i | \(0.639156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.92988e12 | −2.19652 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.36403e10 | 0.0477349 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.10073e12 | 1.18048 | 0.590240 | − | 0.807227i | \(-0.299033\pi\) | ||||
0.590240 | + | 0.807227i | \(0.299033\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.26400e12 | 1.30345 | 0.651723 | − | 0.758457i | \(-0.274047\pi\) | ||||
0.651723 | + | 0.758457i | \(0.274047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.82843e12 | 1.84911 | 0.924557 | − | 0.381045i | \(-0.124436\pi\) | ||||
0.924557 | + | 0.381045i | \(0.124436\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.95640e10 | 0.0968671 | 0.0484336 | − | 0.998826i | \(-0.484577\pi\) | ||||
0.0484336 | + | 0.998826i | \(0.484577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.17088e10 | −0.0684376 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.26898e12 | −3.00287 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.26262e11 | 0.744726 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.32763e12 | 1.15230 | 0.576150 | − | 0.817344i | \(-0.304554\pi\) | ||||
0.576150 | + | 0.817344i | \(0.304554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.25309e12 | −1.06741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.06447e12 | −0.873568 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.37834e12 | −1.11039 | −0.555197 | − | 0.831719i | \(-0.687357\pi\) | ||||
−0.555197 | + | 0.831719i | \(0.687357\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.13645e12 | −0.882439 | −0.441219 | − | 0.897399i | \(-0.645454\pi\) | ||||
−0.441219 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.18576e11 | −0.471609 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.03451e11 | −0.149574 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.91132e12 | −1.38001 | −0.690004 | − | 0.723806i | \(-0.742391\pi\) | ||||
−0.690004 | + | 0.723806i | \(0.742391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.79892e12 | 1.25302 | 0.626509 | − | 0.779414i | \(-0.284483\pi\) | ||||
0.626509 | + | 0.779414i | \(0.284483\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.62776e12 | −1.11373 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.65330e12 | −1.09174 | −0.545872 | − | 0.837869i | \(-0.683801\pi\) | ||||
−0.545872 | + | 0.837869i | \(0.683801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.49491e10 | 0.0356506 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.86891e11 | 0.492926 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.05237e12 | −0.647828 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.43255e12 | 1.44641 | 0.723207 | − | 0.690632i | \(-0.242667\pi\) | ||||
0.723207 | + | 0.690632i | \(0.242667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.35462e12 | 0.791697 | 0.395849 | − | 0.918316i | \(-0.370451\pi\) | ||||
0.395849 | + | 0.918316i | \(0.370451\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.55443e11 | −0.144260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.63312e11 | −0.368271 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.05528e12 | 1.10306 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.04689e11 | −0.108019 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.93152e12 | −1.49604 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.25578e11 | 0.364163 | 0.182082 | − | 0.983283i | \(-0.441716\pi\) | ||||
0.182082 | + | 0.983283i | \(0.441716\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.22266e12 | −0.593636 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.32193e12 | −1.10893 | −0.554467 | − | 0.832206i | \(-0.687078\pi\) | ||||
−0.554467 | + | 0.832206i | \(0.687078\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.49981e12 | 1.15538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.11892e11 | 0.0963499 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.15050e12 | 0.506452 | 0.253226 | − | 0.967407i | \(-0.418508\pi\) | ||||
0.253226 | + | 0.967407i | \(0.418508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.48140e12 | 1.50800 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.26347e12 | −1.36897 | −0.684483 | − | 0.729029i | \(-0.739972\pi\) | ||||
−0.684483 | + | 0.729029i | \(0.739972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.36261e11 | 0.262674 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.14577e12 | 1.25812 | 0.629059 | − | 0.777357i | \(-0.283440\pi\) | ||||
0.629059 | + | 0.777357i | \(0.283440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.86591e12 | 1.12824 | 0.564119 | − | 0.825694i | \(-0.309216\pi\) | ||||
0.564119 | + | 0.825694i | \(0.309216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.34854e12 | −0.514470 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.40532e12 | 1.27899 | 0.639494 | − | 0.768796i | \(-0.279144\pi\) | ||||
0.639494 | + | 0.768796i | \(0.279144\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.05904e11 | −0.184194 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.79159e12 | 0.642290 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.19783e11 | 0.145933 | 0.0729665 | − | 0.997334i | \(-0.476753\pi\) | ||||
0.0729665 | + | 0.997334i | \(0.476753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.03230e12 | 0.353418 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.91495e9 | 0.00130011 | 0.000650055 | − | 1.00000i | \(-0.499793\pi\) | ||||
0.000650055 | 1.00000i | \(0.499793\pi\) | ||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.02043e10 | −0.0295054 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.79764e11 | −0.310957 | −0.155479 | − | 0.987839i | \(-0.549692\pi\) | ||||
−0.155479 | + | 0.987839i | \(0.549692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.20416e11 | −0.100179 | −0.0500897 | − | 0.998745i | \(-0.515951\pi\) | ||||
−0.0500897 | + | 0.998745i | \(0.515951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.52287e12 | −0.765588 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50671e11 | 0.134744 | 0.0673721 | − | 0.997728i | \(-0.478539\pi\) | ||||
0.0673721 | + | 0.997728i | \(0.478539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.12075e12 | 0.325330 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.91821e12 | 1.40681 | 0.703404 | − | 0.710790i | \(-0.251662\pi\) | ||||
0.703404 | + | 0.710790i | \(0.251662\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.02063e12 | 0.839102 | 0.419551 | − | 0.907732i | \(-0.362188\pi\) | ||||
0.419551 | + | 0.907732i | \(0.362188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.29184e12 | −0.353672 | −0.176836 | − | 0.984240i | \(-0.556586\pi\) | ||||
−0.176836 | + | 0.984240i | \(0.556586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.91167e11 | 0.0774366 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.52757e11 | 0.0662587 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.59014e12 | 0.659774 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.29259e12 | −1.83126 | −0.915629 | − | 0.402024i | \(-0.868307\pi\) | ||||
−0.915629 | + | 0.402024i | \(0.868307\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.56093e12 | −0.625053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.12201e12 | 0.751290 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.42622e12 | 1.50347 | 0.751734 | − | 0.659466i | \(-0.229218\pi\) | ||||
0.751734 | + | 0.659466i | \(0.229218\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.85597e12 | −0.428175 | −0.214087 | − | 0.976814i | \(-0.568678\pi\) | ||||
−0.214087 | + | 0.976814i | \(0.568678\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.59916e12 | 1.48054 | 0.740269 | − | 0.672311i | \(-0.234698\pi\) | ||||
0.740269 | + | 0.672311i | \(0.234698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.77361e11 | −0.194123 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.05288e12 | −0.657054 | −0.328527 | − | 0.944495i | \(-0.606552\pi\) | ||||
−0.328527 | + | 0.944495i | \(0.606552\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.29343e12 | 0.486855 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.04254e12 | 1.86770 | 0.933848 | − | 0.357669i | \(-0.116429\pi\) | ||||
0.933848 | + | 0.357669i | \(0.116429\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.42286e12 | −0.493652 | −0.246826 | − | 0.969060i | \(-0.579388\pi\) | ||||
−0.246826 | + | 0.969060i | \(0.579388\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.64536e11 | 0.0722842 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.07994e12 | −0.798155 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.39398e13 | −2.65464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.42076e12 | −1.01857 | −0.509287 | − | 0.860597i | \(-0.670091\pi\) | ||||
−0.509287 | + | 0.860597i | \(0.670091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.70581e12 | −1.04392 | −0.521961 | − | 0.852969i | \(-0.674799\pi\) | ||||
−0.521961 | + | 0.852969i | \(0.674799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.61838e11 | 0.155601 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.01096e12 | −1.58445 | −0.792224 | − | 0.610231i | \(-0.791077\pi\) | ||||
−0.792224 | + | 0.610231i | \(0.791077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.28284e12 | 0.396157 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.90801e12 | −0.322548 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.93638e12 | 0.656819 | 0.328410 | − | 0.944535i | \(-0.393487\pi\) | ||||
0.328410 | + | 0.944535i | \(0.393487\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.31725e12 | −0.214159 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.24826e12 | −0.681811 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.61506e12 | 0.409026 | 0.204513 | − | 0.978864i | \(-0.434439\pi\) | ||||
0.204513 | + | 0.978864i | \(0.434439\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.04673e13 | −1.61636 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.31790e12 | 0.198378 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.29669e12 | 0.935845 | 0.467923 | − | 0.883769i | \(-0.345003\pi\) | ||||
0.467923 | + | 0.883769i | \(0.345003\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.68482e12 | −0.244147 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.77108e12 | 0.682714 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.23756e12 | −0.451791 | −0.225895 | − | 0.974152i | \(-0.572531\pi\) | ||||
−0.225895 | + | 0.974152i | \(0.572531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.37097e11 | −0.0878005 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.83546e12 | 0.650005 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.73928e12 | −0.496459 | −0.248230 | − | 0.968701i | \(-0.579849\pi\) | ||||
−0.248230 | + | 0.968701i | \(0.579849\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.19604e12 | −0.932106 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.14796e12 | −1.04251 | −0.521256 | − | 0.853400i | \(-0.674536\pi\) | ||||
−0.521256 | + | 0.853400i | \(0.674536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.83974e12 | −0.978809 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.90382e12 | −0.234815 | −0.117408 | − | 0.993084i | \(-0.537458\pi\) | ||||
−0.117408 | + | 0.993084i | \(0.537458\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.95774e12 | 0.957945 | 0.478972 | − | 0.877830i | \(-0.341009\pi\) | ||||
0.478972 | + | 0.877830i | \(0.341009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.60552e12 | −0.904536 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.65724e11 | 0.0192405 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.55077e13 | 1.77897 | 0.889483 | − | 0.456969i | \(-0.151065\pi\) | ||||
0.889483 | + | 0.456969i | \(0.151065\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.36241e12 | 0.600618 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.49750e12 | −0.608463 | −0.304231 | − | 0.952598i | \(-0.598400\pi\) | ||||
−0.304231 | + | 0.952598i | \(0.598400\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.81389e12 | −0.412228 | −0.206114 | − | 0.978528i | \(-0.566082\pi\) | ||||
−0.206114 | + | 0.978528i | \(0.566082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.89910e11 | 0.105739 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.34373e11 | 0.0974857 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.01006e12 | 0.104155 | 0.0520775 | − | 0.998643i | \(-0.483416\pi\) | ||||
0.0520775 | + | 0.998643i | \(0.483416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.41222e12 | 0.645953 | 0.322976 | − | 0.946407i | \(-0.395317\pi\) | ||||
0.322976 | + | 0.946407i | \(0.395317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.99682e12 | 0.198830 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.71682e13 | 1.67035 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.22428e13 | −2.13924 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.11992e13 | 1.05262 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.11599e12 | −0.103699 | −0.0518494 | − | 0.998655i | \(-0.516512\pi\) | ||||
−0.0518494 | + | 0.998655i | \(0.516512\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.15141e11 | −0.0467877 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.48457e13 | 1.33312 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.36680e13 | −1.19989 | −0.599947 | − | 0.800040i | \(-0.704812\pi\) | ||||
−0.599947 | + | 0.800040i | \(0.704812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.31659e12 | −0.201089 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.00745e12 | 0.509882 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.94960e11 | −0.0499352 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.54771e13 | −1.27035 | −0.635174 | − | 0.772369i | \(-0.719071\pi\) | ||||
−0.635174 | + | 0.772369i | \(0.719071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.55212e12 | 0.694192 | 0.347096 | − | 0.937830i | \(-0.387168\pi\) | ||||
0.347096 | + | 0.937830i | \(0.387168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.56499e12 | 0.600619 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.90808e13 | 2.28353 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.29284e12 | −0.637029 | −0.318515 | − | 0.947918i | \(-0.603184\pi\) | ||||
−0.318515 | + | 0.947918i | \(0.603184\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.55958e12 | −0.498399 | −0.249199 | − | 0.968452i | \(-0.580167\pi\) | ||||
−0.249199 | + | 0.968452i | \(0.580167\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.63826e13 | 1.21789 | 0.608944 | − | 0.793214i | \(-0.291594\pi\) | ||||
0.608944 | + | 0.793214i | \(0.291594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.16258e13 | 1.59029 | 0.795144 | − | 0.606420i | \(-0.207395\pi\) | ||||
0.795144 | + | 0.606420i | \(0.207395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.45319e12 | −0.464379 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.04853e12 | 0.430587 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.73801e13 | −1.21094 | −0.605471 | − | 0.795868i | \(-0.707015\pi\) | ||||
−0.605471 | + | 0.795868i | \(0.707015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.22240e11 | 0.00842617 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.72063e12 | 0.251051 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.04261e12 | 0.136367 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.70838e13 | 1.11661 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.42386e12 | 0.286109 | 0.143054 | − | 0.989715i | \(-0.454308\pi\) | ||||
0.143054 | + | 0.989715i | \(0.454308\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.01532e13 | −0.642966 | −0.321483 | − | 0.946915i | \(-0.604181\pi\) | ||||
−0.321483 | + | 0.946915i | \(0.604181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.64047e13 | 1.65467 | 0.827337 | − | 0.561706i | \(-0.189855\pi\) | ||||
0.827337 | + | 0.561706i | \(0.189855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.60032e12 | 0.0982104 | 0.0491052 | − | 0.998794i | \(-0.484363\pi\) | ||||
0.0491052 | + | 0.998794i | \(0.484363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.48795e12 | 0.0903683 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.31656e13 | 1.37802 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.34917e12 | 0.491543 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.79451e12 | 0.103493 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.44970e13 | −0.827525 | −0.413763 | − | 0.910385i | \(-0.635786\pi\) | ||||
−0.413763 | + | 0.910385i | \(0.635786\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.26716e13 | −0.708661 | −0.354330 | − | 0.935120i | \(-0.615291\pi\) | ||||
−0.354330 | + | 0.935120i | \(0.615291\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.35703e13 | −1.85837 | −0.929183 | − | 0.369619i | \(-0.879488\pi\) | ||||
−0.929183 | + | 0.369619i | \(0.879488\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.82723e13 | −0.991145 | −0.495573 | − | 0.868567i | \(-0.665042\pi\) | ||||
−0.495573 | + | 0.868567i | \(0.665042\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.07343e12 | 0.111335 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.36187e12 | 0.492642 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.97905e12 | 0.155194 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.04126e12 | 0.308467 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.94386e12 | 0.199370 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.94648e13 | 0.964564 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.92303e12 | 0.339675 | 0.169837 | − | 0.985472i | \(-0.445676\pi\) | ||||
0.169837 | + | 0.985472i | \(0.445676\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.10020e13 | −1.49127 | −0.745636 | − | 0.666353i | \(-0.767854\pi\) | ||||
−0.745636 | + | 0.666353i | \(0.767854\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.53092e13 | −2.63438 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.85685e12 | −0.0867191 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.81550e13 | −1.30208 | −0.651038 | − | 0.759045i | \(-0.725666\pi\) | ||||
−0.651038 | + | 0.759045i | \(0.725666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.36881e13 | 1.07429 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.02473e13 | −0.909347 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.28510e13 | −1.00655 | −0.503273 | − | 0.864127i | \(-0.667871\pi\) | ||||
−0.503273 | + | 0.864127i | \(0.667871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.60788e13 | 1.13767 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.86180e12 | −0.421992 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.16648e13 | 1.34199 | 0.670995 | − | 0.741462i | \(-0.265867\pi\) | ||||
0.670995 | + | 0.741462i | \(0.265867\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.10217e13 | 1.70553 | 0.852767 | − | 0.522292i | \(-0.174923\pi\) | ||||
0.852767 | + | 0.522292i | \(0.174923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.80203e13 | −1.15390 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.26511e13 | −0.915196 | −0.457598 | − | 0.889159i | \(-0.651290\pi\) | ||||
−0.457598 | + | 0.889159i | \(0.651290\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.39781e12 | −0.256055 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.06846e13 | 1.20504 | 0.602521 | − | 0.798103i | \(-0.294163\pi\) | ||||
0.602521 | + | 0.798103i | \(0.294163\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.76850e13 | −0.688002 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.84827e12 | −0.0705639 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.39449e13 | −0.905643 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.68073e13 | −0.623914 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.91408e13 | −0.703949 | −0.351975 | − | 0.936010i | \(-0.614490\pi\) | ||||
−0.351975 | + | 0.936010i | \(0.614490\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.98467e13 | −1.79949 | −0.899746 | − | 0.436414i | \(-0.856248\pi\) | ||||
−0.899746 | + | 0.436414i | \(0.856248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.06649e12 | 0.0381461 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.74066e13 | 0.611205 | 0.305603 | − | 0.952159i | \(-0.401142\pi\) | ||||
0.305603 | + | 0.952159i | \(0.401142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.18325e13 | 1.10751 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.09397e13 | −0.715286 | −0.357643 | − | 0.933858i | \(-0.616420\pi\) | ||||
−0.357643 | + | 0.933858i | \(0.616420\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.05692e13 | 0.357748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.74629e13 | −1.57751 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.68052e12 | −0.318836 | −0.159418 | − | 0.987211i | \(-0.550962\pi\) | ||||
−0.159418 | + | 0.987211i | \(0.550962\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.69946e12 | 0.152000 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.45555e12 | 0.142815 | 0.0714074 | − | 0.997447i | \(-0.477251\pi\) | ||||
0.0714074 | + | 0.997447i | \(0.477251\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 72.10.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 24.10.a.a.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 144.10.a.e.1.1 | 1 | |||
12.11 | even | 2 | 48.10.a.f.1.1 | 1 | |||
24.5 | odd | 2 | 192.10.a.j.1.1 | 1 | |||
24.11 | even | 2 | 192.10.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
24.10.a.a.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
48.10.a.f.1.1 | 1 | 12.11 | even | 2 | |||
72.10.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
144.10.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
192.10.a.c.1.1 | 1 | 24.11 | even | 2 | |||
192.10.a.j.1.1 | 1 | 24.5 | odd | 2 |