Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(181,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.181");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 2160x^{4} + 976392x^{2} + 85162752 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5}\cdot 7^{3} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.4 | ||
Root | \(-10.7169i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.181 |
Dual form | 252.9.d.b.181.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 333.657i | 0.533851i | 0.963717 | + | 0.266926i | \(0.0860078\pi\) | ||||
−0.963717 | + | 0.266926i | \(0.913992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 560.525 | + | 2334.65i | 0.233455 | + | 0.972368i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24127.6 | 1.64795 | 0.823973 | − | 0.566629i | \(-0.191753\pi\) | ||||
0.823973 | + | 0.566629i | \(0.191753\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 43091.3i | 1.50875i | 0.656445 | + | 0.754374i | \(0.272059\pi\) | ||||
−0.656445 | + | 0.754374i | \(0.727941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 55998.7i | − | 0.670475i | −0.942134 | − | 0.335237i | \(-0.891183\pi\) | ||
0.942134 | − | 0.335237i | \(-0.108817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 208077.i | 1.59665i | 0.602225 | + | 0.798326i | \(0.294281\pi\) | ||||
−0.602225 | + | 0.798326i | \(0.705719\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 159742. | 0.570831 | 0.285416 | − | 0.958404i | \(-0.407868\pi\) | ||||
0.285416 | + | 0.958404i | \(0.407868\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 279298. | 0.715003 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 326089. | 0.461045 | 0.230523 | − | 0.973067i | \(-0.425956\pi\) | ||||
0.230523 | + | 0.973067i | \(0.425956\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.30508e6i | − | 1.41315i | −0.707636 | − | 0.706577i | \(-0.750238\pi\) | ||
0.707636 | − | 0.706577i | \(-0.249762\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −778974. | + | 187023.i | −0.519100 | + | 0.124630i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.59489e6 | 0.850989 | 0.425495 | − | 0.904961i | \(-0.360100\pi\) | ||||
0.425495 | + | 0.904961i | \(0.360100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.17224e6i | 1.47650i | 0.674526 | + | 0.738251i | \(0.264348\pi\) | ||||
−0.674526 | + | 0.738251i | \(0.735652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.46924e6 | 0.429754 | 0.214877 | − | 0.976641i | \(-0.431065\pi\) | ||||
0.214877 | + | 0.976641i | \(0.431065\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.11221e6i | − | 0.842720i | −0.906893 | − | 0.421360i | \(-0.861553\pi\) | ||
0.906893 | − | 0.421360i | \(-0.138447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.13642e6 | + | 2.61726e6i | −0.890998 | + | 0.454008i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.56996e6 | −0.832644 | −0.416322 | − | 0.909217i | \(-0.636681\pi\) | ||||
−0.416322 | + | 0.909217i | \(0.636681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.05034e6i | 0.879758i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.27843e7i | − | 1.05504i | −0.849544 | − | 0.527518i | \(-0.823123\pi\) | ||
0.849544 | − | 0.527518i | \(-0.176877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.65901e6i | − | 0.119820i | −0.998204 | − | 0.0599100i | \(-0.980919\pi\) | ||
0.998204 | − | 0.0599100i | \(-0.0190814\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.43777e7 | −0.805446 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.08767e7 | −0.539755 | −0.269877 | − | 0.962895i | \(-0.586983\pi\) | ||||
−0.269877 | + | 0.962895i | \(0.586983\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.55338e7 | 1.00480 | 0.502402 | − | 0.864634i | \(-0.332450\pi\) | ||||
0.502402 | + | 0.864634i | \(0.332450\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.79430e7i | − | 0.631834i | −0.948787 | − | 0.315917i | \(-0.897688\pi\) | ||
0.948787 | − | 0.315917i | \(-0.102312\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.35241e7 | + | 5.63296e7i | 0.384721 | + | 1.60241i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.32302e7 | 1.36663 | 0.683313 | − | 0.730125i | \(-0.260538\pi\) | ||||
0.683313 | + | 0.730125i | \(0.260538\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.08752e6i | 0.0439864i | 0.999758 | + | 0.0219932i | \(0.00700122\pi\) | ||||
−0.999758 | + | 0.0219932i | \(0.992999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.86844e7 | 0.357934 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.88773e7i | 1.57593i | 0.615721 | + | 0.787964i | \(0.288865\pi\) | ||||
−0.615721 | + | 0.787964i | \(0.711135\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00603e8 | + | 2.41538e7i | −1.46706 | + | 0.352224i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.94265e7 | −0.852375 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.44104e7i | 0.275733i | 0.990451 | + | 0.137867i | \(0.0440245\pi\) | ||||
−0.990451 | + | 0.137867i | \(0.955976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.28121e7i | − | 0.795808i | −0.917427 | − | 0.397904i | \(-0.869738\pi\) | ||
0.917427 | − | 0.397904i | \(-0.130262\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.72625e7i | 0.775316i | 0.921803 | + | 0.387658i | \(0.126716\pi\) | ||||
−0.921803 | + | 0.387658i | \(0.873284\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.14648e8 | −1.63754 | −0.818769 | − | 0.574123i | \(-0.805343\pi\) | ||||
−0.818769 | + | 0.574123i | \(0.805343\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.44130e7 | −0.598003 | −0.299002 | − | 0.954253i | \(-0.596654\pi\) | ||||
−0.299002 | + | 0.954253i | \(0.596654\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.83510e8 | 1.73882 | 0.869411 | − | 0.494090i | \(-0.164499\pi\) | ||||
0.869411 | + | 0.494090i | \(0.164499\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.32990e7i | 0.304739i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.30738e8 | − | 3.13887e7i | 0.651948 | − | 0.156526i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.67782e8 | 1.71573 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.23525e8i | 0.915556i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.18914e7 | −0.237911 | −0.118956 | − | 0.992900i | \(-0.537955\pi\) | ||||
−0.118956 | + | 0.992900i | \(0.537955\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.29768e8i | 1.45932i | 0.683813 | + | 0.729658i | \(0.260321\pi\) | ||||
−0.683813 | + | 0.729658i | \(0.739679\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.85789e8 | + | 1.16633e8i | −1.55253 | + | 0.372746i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.92189e8 | −0.829432 | −0.414716 | − | 0.909951i | \(-0.636119\pi\) | ||||
−0.414716 | + | 0.909951i | \(0.636119\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9.34937e6i | − | 0.0250451i | −0.999922 | − | 0.0125226i | \(-0.996014\pi\) | ||
0.999922 | − | 0.0125226i | \(-0.00398616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.03969e9i | 2.48633i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.08802e8i | 0.246130i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.12014e8 | −1.64747 | −0.823736 | − | 0.566973i | \(-0.808114\pi\) | ||||
−0.823736 | + | 0.566973i | \(0.808114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.07626e7 | 0.0207019 | 0.0103510 | − | 0.999946i | \(-0.496705\pi\) | ||||
0.0103510 | + | 0.999946i | \(0.496705\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.35448e8 | 0.754414 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.58487e8i | 0.754620i | 0.926087 | + | 0.377310i | \(0.123151\pi\) | ||||
−0.926087 | + | 0.377310i | \(0.876849\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.95394e7 | + | 3.72942e8i | 0.133263 | + | 0.555058i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.57211e8 | 0.931010 | 0.465505 | − | 0.885045i | \(-0.345873\pi\) | ||||
0.465505 | + | 0.885045i | \(0.345873\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.94686e8i | 0.636010i | 0.948089 | + | 0.318005i | \(0.103013\pi\) | ||||
−0.948089 | + | 0.318005i | \(0.896987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.04113e9 | −1.27632 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 7.94129e8i | − | 0.886557i | −0.896384 | − | 0.443279i | \(-0.853815\pi\) | ||
0.896384 | − | 0.443279i | \(-0.146185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.56553e8 | + | 6.52064e8i | 0.166921 | + | 0.695246i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.85404e8 | −0.180595 | −0.0902976 | − | 0.995915i | \(-0.528782\pi\) | ||||
−0.0902976 | + | 0.995915i | \(0.528782\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.44977e9i | 1.35078i | 0.737462 | + | 0.675389i | \(0.236024\pi\) | ||||
−0.737462 | + | 0.675389i | \(0.763976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.32146e8i | 0.454302i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.35111e9i | − | 1.10491i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.13964e8 | 0.0856319 | 0.0428159 | − | 0.999083i | \(-0.486367\pi\) | ||||
0.0428159 | + | 0.999083i | \(0.486367\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.27036e8 | 0.668140 | 0.334070 | − | 0.942548i | \(-0.391578\pi\) | ||||
0.334070 | + | 0.942548i | \(0.391578\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.50846e9 | −1.66549 | −0.832747 | − | 0.553654i | \(-0.813233\pi\) | ||||
−0.832747 | + | 0.553654i | \(0.813233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.31010e9i | 0.835394i | 0.908586 | + | 0.417697i | \(0.137163\pi\) | ||||
−0.908586 | + | 0.417697i | \(0.862837\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.82781e8 | + | 7.61304e8i | 0.107633 | + | 0.448305i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.39210e9 | −0.788232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.02040e9i | 2.63120i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.73665e8 | −0.491224 | −0.245612 | − | 0.969368i | \(-0.578989\pi\) | ||||
−0.245612 | + | 0.969368i | \(0.578989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.90223e8i | 0.229425i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.04691e9 | − | 7.31529e8i | 1.37411 | − | 0.329908i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.41306e9 | 1.01158 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.64534e9i | 0.665329i | 0.943045 | + | 0.332665i | \(0.107948\pi\) | ||||
−0.943045 | + | 0.332665i | \(0.892052\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.98469e8i | 0.225392i | 0.993630 | + | 0.112696i | \(0.0359486\pi\) | ||||
−0.993630 | + | 0.112696i | \(0.964051\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.33903e8i | − | 0.194142i | −0.995277 | − | 0.0970712i | \(-0.969053\pi\) | ||
0.995277 | − | 0.0970712i | \(-0.0309475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.41592e9 | 0.819708 | 0.409854 | − | 0.912151i | \(-0.365580\pi\) | ||||
0.409854 | + | 0.912151i | \(0.365580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.37207e9 | 0.449887 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.20541e9 | −0.369440 | −0.184720 | − | 0.982791i | \(-0.559138\pi\) | ||||
−0.184720 | + | 0.982791i | \(0.559138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.76959e9i | − | 0.821007i | −0.911859 | − | 0.410504i | \(-0.865353\pi\) | ||
0.911859 | − | 0.410504i | \(-0.134647\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.73268e8 | − | 1.71380e9i | −0.242373 | − | 0.475660i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.96633e9 | −2.40894 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.72275e9i | − | 1.44182i | −0.693031 | − | 0.720908i | \(-0.743725\pi\) | ||
0.693031 | − | 0.720908i | \(-0.256275\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.85419e9 | 0.940700 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.33650e8i | 0.0535591i | 0.999641 | + | 0.0267796i | \(0.00852522\pi\) | ||||
−0.999641 | + | 0.0267796i | \(0.991475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.93976e8 | + | 3.72352e9i | 0.198667 | + | 0.827474i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.04999e8 | −0.0637494 | −0.0318747 | − | 0.999492i | \(-0.510148\pi\) | ||||
−0.0318747 | + | 0.999492i | \(0.510148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.19211e9i | − | 0.444508i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 6.13017e9i | − | 1.17075i | −0.810763 | − | 0.585374i | \(-0.800948\pi\) | ||
0.810763 | − | 0.585374i | \(-0.199052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.43372e9i | 0.636632i | 0.947985 | + | 0.318316i | \(0.103117\pi\) | ||||
−0.947985 | + | 0.318316i | \(0.896883\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.73879e9 | 1.17829 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.30404e9 | −1.24064 | −0.620318 | − | 0.784351i | \(-0.712996\pi\) | ||||
−0.620318 | + | 0.784351i | \(0.712996\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.46382e9 | −0.715947 | −0.357974 | − | 0.933732i | \(-0.616532\pi\) | ||||
−0.357974 | + | 0.933732i | \(0.616532\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5.02284e9i | − | 0.783075i | −0.920162 | − | 0.391537i | \(-0.871943\pi\) | ||
0.920162 | − | 0.391537i | \(-0.128057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.74074e9 | + | 2.33864e9i | −1.43570 | + | 0.344696i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.83990e9 | 0.550463 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.99782e9i | − | 0.678125i | −0.940764 | − | 0.339063i | \(-0.889890\pi\) | ||
0.940764 | − | 0.339063i | \(-0.110110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.26556e9 | 0.563232 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.88350e9i | 0.861240i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.23547e8 | + | 3.43017e9i | 0.100328 | + | 0.417879i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.53540e8 | 0.0639660 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.40127e10i | − | 1.57750i | −0.614714 | − | 0.788750i | \(-0.710729\pi\) | ||
0.614714 | − | 0.788750i | \(-0.289271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.19762e9i | − | 0.983182i | −0.870826 | − | 0.491591i | \(-0.836415\pi\) | ||
0.870826 | − | 0.491591i | \(-0.163585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.63979e10i | − | 1.70848i | −0.519876 | − | 0.854242i | \(-0.674022\pi\) | ||
0.519876 | − | 0.854242i | \(-0.325978\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.51375e9 | 0.942138 | 0.471069 | − | 0.882096i | \(-0.343868\pi\) | ||||
0.471069 | + | 0.882096i | \(0.343868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.86773e9 | 0.759778 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.16521e10 | 1.07052 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.20353e10i | 1.07876i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.60058e9 | − | 2.30499e9i | 0.819434 | − | 0.196737i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.91615e9 | 0.409556 | 0.204778 | − | 0.978808i | \(-0.434353\pi\) | ||||
0.204778 | + | 0.978808i | \(0.434353\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 3.62907e9i | − | 0.288149i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.07250e10 | 1.60685 | 0.803425 | − | 0.595406i | \(-0.203009\pi\) | ||||
0.803425 | + | 0.595406i | \(0.203009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.14884e10i | − | 2.32880i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.98950e9 | − | 1.05247e10i | −0.649470 | − | 0.760387i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.68352e9 | 0.185092 | 0.0925459 | − | 0.995708i | \(-0.470500\pi\) | ||||
0.0925459 | + | 0.995708i | \(0.470500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.30154e10i | 0.877312i | 0.898655 | + | 0.438656i | \(0.144545\pi\) | ||||
−0.898655 | + | 0.438656i | \(0.855455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.69314e10i | − | 1.09042i | −0.838299 | − | 0.545211i | \(-0.816450\pi\) | ||
0.838299 | − | 0.545211i | \(-0.183550\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.51952e9i | 0.536416i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.74172e10 | −1.65061 | −0.825307 | − | 0.564685i | \(-0.808998\pi\) | ||||
−0.825307 | + | 0.564685i | \(0.808998\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.63126e10 | −1.54930 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.98680e9 | 0.337305 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9.59511e9i | − | 0.528915i | −0.964397 | − | 0.264457i | \(-0.914807\pi\) | ||
0.964397 | − | 0.264457i | \(-0.0851929\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.68263e9 | − | 1.53386e10i | −0.194385 | − | 0.809636i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.78953e10 | 0.924492 | 0.462246 | − | 0.886752i | \(-0.347044\pi\) | ||||
0.462246 | + | 0.886752i | \(0.347044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.40516e10i | 0.695601i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.75716e10 | −1.33630 | −0.668152 | − | 0.744025i | \(-0.732914\pi\) | ||||
−0.668152 | + | 0.744025i | \(0.732914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.23133e9i | − | 0.150171i | −0.997177 | − | 0.0750855i | \(-0.976077\pi\) | ||
0.997177 | − | 0.0750855i | \(-0.0239230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.87948e10 | + | 4.51241e9i | −0.855449 | + | 0.205384i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.43217e9 | −0.280905 | −0.140452 | − | 0.990087i | \(-0.544856\pi\) | ||||
−0.140452 | + | 0.990087i | \(0.544856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.94535e9i | − | 0.382728i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.77606e10i | 0.729575i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.57203e10i | − | 1.03541i | −0.855558 | − | 0.517707i | \(-0.826786\pi\) | ||
0.855558 | − | 0.517707i | \(-0.173214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.25006e10 | −1.25694 | −0.628469 | − | 0.777835i | \(-0.716318\pi\) | ||||
−0.628469 | + | 0.777835i | \(0.716318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.62375e10 | 2.13209 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.84809e10 | 1.40238 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.57138e10i | − | 0.918909i | −0.888201 | − | 0.459454i | \(-0.848045\pi\) | ||
0.888201 | − | 0.459454i | \(-0.151955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.98468e10 | − | 7.16589e9i | 1.02588 | − | 0.246303i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.96516e8 | −0.0234822 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.24082e10i | 0.402581i | 0.979532 | + | 0.201291i | \(0.0645136\pi\) | ||||
−0.979532 | + | 0.201291i | \(0.935486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.05827e10 | −0.655201 | −0.327600 | − | 0.944816i | \(-0.606240\pi\) | ||||
−0.327600 | + | 0.944816i | \(0.606240\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.56403e10i | − | 0.479392i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.87321e9 | − | 9.29915e8i | 0.116509 | − | 0.0279725i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.23479e9 | 0.122722 | 0.0613611 | − | 0.998116i | \(-0.480456\pi\) | ||||
0.0613611 | + | 0.998116i | \(0.480456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.21039e10i | − | 1.19776i | −0.800838 | − | 0.598882i | \(-0.795612\pi\) | ||
0.800838 | − | 0.598882i | \(-0.204388\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.32387e10i | 0.911419i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.07786e10i | 1.09793i | 0.835845 | + | 0.548965i | \(0.184978\pi\) | ||||
−0.835845 | + | 0.548965i | \(0.815022\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.88976e8 | 0.0100997 | 0.00504984 | − | 0.999987i | \(-0.498393\pi\) | ||||
0.00504984 | + | 0.999987i | \(0.498393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.29911e10 | −0.841312 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.69794e10 | −0.663814 | −0.331907 | − | 0.943312i | \(-0.607692\pi\) | ||||
−0.331907 | + | 0.943312i | \(0.607692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00666e11i | 2.43320i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.05907e9 | − | 3.35670e10i | −0.188035 | − | 0.783190i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.34464e10 | 1.45460 | 0.727298 | − | 0.686322i | \(-0.240776\pi\) | ||||
0.727298 | + | 0.686322i | \(0.240776\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5.53281e10i | − | 1.22502i | −0.790464 | − | 0.612508i | \(-0.790161\pi\) | ||
0.790464 | − | 0.612508i | \(-0.209839\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.29238e10 | −1.36928 | −0.684638 | − | 0.728883i | \(-0.740040\pi\) | ||||
−0.684638 | + | 0.728883i | \(0.740040\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.29439e10i | 1.95413i | 0.212943 | + | 0.977065i | \(0.431695\pi\) | ||||
−0.212943 | + | 0.977065i | \(0.568305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.09664e9 | − | 2.53932e10i | −0.126008 | − | 0.524840i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.54493e10 | 0.708211 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.81156e10i | 1.14161i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.92837e10i | 0.556268i | 0.960542 | + | 0.278134i | \(0.0897159\pi\) | ||||
−0.960542 | + | 0.278134i | \(0.910284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.87260e10i | 1.28393i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.14472e9 | −0.147200 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.87418e10 | 1.75544 | 0.877718 | − | 0.479178i | \(-0.159065\pi\) | ||||
0.877718 | + | 0.479178i | \(0.159065\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.84236e10 | 0.316992 | 0.158496 | − | 0.987360i | \(-0.449335\pi\) | ||||
0.158496 | + | 0.987360i | \(0.449335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.82605e10i | − | 0.309119i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.43123e10 | + | 5.96125e10i | 0.234576 | + | 0.977039i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.28072e10 | −1.49685 | −0.748427 | − | 0.663217i | \(-0.769191\pi\) | ||||
−0.748427 | + | 0.663217i | \(0.769191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.06679e11i | 1.66651i | 0.552886 | + | 0.833257i | \(0.313527\pi\) | ||||
−0.552886 | + | 0.833257i | \(0.686473\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.76308e10 | 0.424843 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.90061e10i | 1.32602i | 0.748612 | + | 0.663008i | \(0.230720\pi\) | ||||
−0.748612 | + | 0.663008i | \(0.769280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.18907e10 | − | 1.00575e10i | 0.614375 | − | 0.147505i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.91157e10 | −0.413903 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.92176e10i | − | 1.38876i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.08443e11i | − | 1.47181i | −0.677086 | − | 0.735904i | \(-0.736758\pi\) | ||
0.677086 | − | 0.735904i | \(-0.263242\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.49280e10i | − | 0.466839i | −0.972376 | − | 0.233420i | \(-0.925008\pi\) | ||
0.972376 | − | 0.233420i | \(-0.0749916\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.30827e10 | −0.947485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.27935e10 | −0.674152 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.79787e11 | −2.22767 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.16188e10i | − | 0.874202i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.23930e11 | + | 6.31483e10i | −1.46832 | + | 0.748180i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.47596e10 | −0.989464 | −0.494732 | − | 0.869046i | \(-0.664734\pi\) | ||||
−0.494732 | + | 0.869046i | \(0.664734\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.81650e10i | − | 0.319245i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.64069e10 | −0.183264 | −0.0916320 | − | 0.995793i | \(-0.529208\pi\) | ||||
−0.0916320 | + | 0.995793i | \(0.529208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.78516e10i | 0.736129i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.98369e10 | + | 1.24274e11i | 0.319045 | + | 1.32886i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.61798e11 | 1.68094 | 0.840471 | − | 0.541857i | \(-0.182279\pi\) | ||||
0.840471 | + | 0.541857i | \(0.182279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.33116e10i | 0.648390i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.20561e10i | 0.418597i | 0.977852 | + | 0.209298i | \(0.0671180\pi\) | ||||
−0.977852 | + | 0.209298i | \(0.932882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.45952e10i | 0.928272i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.48271e11 | 1.41451 | 0.707256 | − | 0.706957i | \(-0.249933\pi\) | ||||
0.707256 | + | 0.706957i | \(0.249933\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.03731e9 | −0.0756078 | −0.0378039 | − | 0.999285i | \(-0.512036\pi\) | ||||
−0.0378039 | + | 0.999285i | \(0.512036\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.46156e10 | 0.408146 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.50045e11i | 1.35369i | 0.736126 | + | 0.676845i | \(0.236653\pi\) | ||||
−0.736126 | + | 0.676845i | \(0.763347\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.87364e9 | + | 1.17011e9i | −0.0427710 | + | 0.0102688i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.58517e11 | −1.37215 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.31985e11i | 1.11166i | 0.831296 | + | 0.555830i | \(0.187599\pi\) | ||||
−0.831296 | + | 0.555830i | \(0.812401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.71557e11 | 2.25632 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.77348e11i | − | 1.43419i | −0.696976 | − | 0.717094i | \(-0.745472\pi\) | ||
0.696976 | − | 0.717094i | \(-0.254528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.04731e10 | + | 4.36216e10i | 0.0835613 | + | 0.348043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.94212e10 | −0.694597 | −0.347299 | − | 0.937755i | \(-0.612901\pi\) | ||||
−0.347299 | + | 0.937755i | \(0.612901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.85319e10i | 0.525285i | 0.964893 | + | 0.262642i | \(0.0845939\pi\) | ||||
−0.964893 | + | 0.262642i | \(0.915406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.22713e11i | 0.915944i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.66702e9i | − | 0.0270121i | −0.999909 | − | 0.0135061i | \(-0.995701\pi\) | ||
0.999909 | − | 0.0135061i | \(-0.00429924\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.77200e11 | 1.27145 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.49244e10 | −0.459797 | −0.229898 | − | 0.973215i | \(-0.573839\pi\) | ||||
−0.229898 | + | 0.973215i | \(0.573839\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.79839e10 | 0.676105 | 0.338052 | − | 0.941127i | \(-0.390232\pi\) | ||||
0.338052 | + | 0.941127i | \(0.390232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.16922e11i | − | 0.796403i | −0.917298 | − | 0.398202i | \(-0.869634\pi\) | ||
0.917298 | − | 0.398202i | \(-0.130366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.30844e11 | + | 5.54232e10i | −1.53238 | + | 0.367908i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.45203e10 | 0.226232 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8.93119e10i | − | 0.570567i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.32605e11 | 0.836457 | 0.418229 | − | 0.908342i | \(-0.362651\pi\) | ||||
0.418229 | + | 0.908342i | \(0.362651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 2.06505e10i | − | 0.127009i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.12781e11 | − | 2.21335e11i | −0.684983 | − | 1.34429i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.82510e11 | 1.08107 | 0.540536 | − | 0.841321i | \(-0.318221\pi\) | ||||
0.540536 | + | 0.841321i | \(0.318221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.16413e10i | 0.243602i | 0.992555 | + | 0.121801i | \(0.0388669\pi\) | ||||
−0.992555 | + | 0.121801i | \(0.961133\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.19404e11i | 0.681402i | 0.940172 | + | 0.340701i | \(0.110664\pi\) | ||||
−0.940172 | + | 0.340701i | \(0.889336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.08453e11i | − | 1.73864i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.16240e11 | −1.73926 | −0.869629 | − | 0.493705i | \(-0.835642\pi\) | ||||
−0.869629 | + | 0.493705i | \(0.835642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.43395e11 | −0.779057 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.31924e10 | 0.175994 | 0.0879969 | − | 0.996121i | \(-0.471953\pi\) | ||||
0.0879969 | + | 0.996121i | \(0.471953\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.67799e11i | − | 0.878990i | −0.898245 | − | 0.439495i | \(-0.855157\pi\) | ||
0.898245 | − | 0.439495i | \(-0.144843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.89153e10 | − | 1.62087e11i | −0.198991 | − | 0.828822i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.20900e10 | 0.263179 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.00279e10i | − | 0.197457i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.56218e10 | 0.466119 | 0.233059 | − | 0.972462i | \(-0.425126\pi\) | ||||
0.233059 | + | 0.972462i | \(0.425126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 7.73296e10i | − | 0.368122i | −0.982915 | − | 0.184061i | \(-0.941076\pi\) | ||
0.982915 | − | 0.184061i | \(-0.0589243\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.69900e10 | + | 1.36827e10i | −0.268114 | + | 0.0643712i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.15222e10 | 0.190808 | 0.0954042 | − | 0.995439i | \(-0.469586\pi\) | ||||
0.0954042 | + | 0.995439i | \(0.469586\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.74908e10i | − | 0.442793i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.83108e11i | − | 1.25625i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.32923e11i | 1.02164i | 0.859687 | + | 0.510822i | \(0.170659\pi\) | ||||
−0.859687 | + | 0.510822i | \(0.829341\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.11948e9 | 0.0133704 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.33640e11 | 0.989957 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.07467e11 | 0.445044 | 0.222522 | − | 0.974928i | \(-0.428571\pi\) | ||||
0.222522 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.31861e11i | 1.35873i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.93338e11 | − | 4.64183e10i | 0.773818 | − | 0.185785i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.41741e10 | −0.293540 | −0.146770 | − | 0.989171i | \(-0.546888\pi\) | ||||
−0.146770 | + | 0.989171i | \(0.546888\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.08476e11i | − | 0.806673i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.46900e11 | −1.32733 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.87359e11i | − | 0.701065i | −0.936550 | − | 0.350533i | \(-0.886001\pi\) | ||
0.936550 | − | 0.350533i | \(-0.113999\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.03728e11 | + | 4.89128e10i | −0.753892 | + | 0.181001i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.10759e10 | 0.329649 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.65939e11i | 1.31000i | 0.755629 | + | 0.655000i | \(0.227331\pi\) | ||||
−0.755629 | + | 0.655000i | \(0.772669\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 8.22757e10i | − | 0.288139i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.01274e11i | − | 1.04363i | −0.853060 | − | 0.521813i | \(-0.825256\pi\) | ||
0.853060 | − | 0.521813i | \(-0.174744\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.62428e11 | −0.889487 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.65721e11 | 0.890940 | 0.445470 | − | 0.895297i | \(-0.353037\pi\) | ||||
0.445470 | + | 0.895297i | \(0.353037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.14572e11 | 1.36033 | 0.680166 | − | 0.733058i | \(-0.261908\pi\) | ||||
0.680166 | + | 0.733058i | \(0.261908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 2.70934e11i | − | 0.879505i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.20315e11 | − | 5.01129e11i | −0.382291 | − | 1.59229i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.44651e11 | 1.39785 | 0.698924 | − | 0.715196i | \(-0.253663\pi\) | ||||
0.698924 | + | 0.715196i | \(0.253663\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.59103e9i | 0.0110518i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.60251e11 | −0.792517 | −0.396258 | − | 0.918139i | \(-0.629692\pi\) | ||||
−0.396258 | + | 0.918139i | \(0.629692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.68056e10i | 0.139559i | 0.997562 | + | 0.0697797i | \(0.0222296\pi\) | ||||
−0.997562 | + | 0.0697797i | \(0.977770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.73156e10 | − | 1.97075e11i | −0.139607 | − | 0.581479i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.50890e11 | 1.59178 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.82049e11i | − | 1.09248i | −0.837628 | − | 0.546240i | \(-0.816058\pi\) | ||
0.837628 | − | 0.546240i | \(-0.183942\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.60161e10i | 0.100874i | 0.998727 | + | 0.0504369i | \(0.0160614\pi\) | ||||
−0.998727 | + | 0.0504369i | \(0.983939\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.64506e11i | − | 1.01041i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.68149e11 | −2.35746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.16068e11 | 1.65586 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.52977e11 | −0.402855 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.27297e11i | − | 0.853184i | −0.904444 | − | 0.426592i | \(-0.859714\pi\) | ||
0.904444 | − | 0.426592i | \(-0.140286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.58914e11 | + | 6.61898e11i | 0.405936 | + | 1.69077i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.14889e10 | 0.180778 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.29152e11i | − | 1.55927i | −0.626232 | − | 0.779636i | \(-0.715404\pi\) | ||
0.626232 | − | 0.779636i | \(-0.284596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.30278e11 | −0.565023 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 4.32921e11i | − | 1.04123i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.24435e11 | + | 2.98754e10i | −0.296318 | + | 0.0711428i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.75487e11 | 0.643142 | 0.321571 | − | 0.946885i | \(-0.395789\pi\) | ||||
0.321571 | + | 0.946885i | \(0.395789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.31344e11i | − | 0.765942i | −0.923760 | − | 0.382971i | \(-0.874901\pi\) | ||
0.923760 | − | 0.382971i | \(-0.125099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.19283e11i | 0.497021i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.05716e11i | 0.686167i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.05208e11 | −0.231566 | −0.115783 | − | 0.993275i | \(-0.536938\pi\) | ||||
−0.115783 | + | 0.993275i | \(0.536938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.65593e11 | 0.578918 | 0.289459 | − | 0.957190i | \(-0.406525\pi\) | ||||
0.289459 | + | 0.957190i | \(0.406525\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.81754e11 | −0.602349 | −0.301175 | − | 0.953569i | \(-0.597379\pi\) | ||||
−0.301175 | + | 0.953569i | \(0.597379\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.61031e11i | 0.340950i | 0.985362 | + | 0.170475i | \(0.0545303\pi\) | ||||
−0.985362 | + | 0.170475i | \(0.945470\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.46563e11 | + | 2.87633e11i | 0.304401 | + | 0.597392i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.65056e11 | −0.339535 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.23152e11i | 0.248539i | 0.992248 | + | 0.124270i | \(0.0396588\pi\) | ||||
−0.992248 | + | 0.124270i | \(0.960341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.93913e11 | −0.787437 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3.47381e11i | − | 0.681364i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.06151e11 | + | 8.58643e11i | 0.400545 | + | 1.66832i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.54771e11 | 0.485771 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.07583e11i | 1.71431i | 0.515056 | + | 0.857156i | \(0.327771\pi\) | ||||
−0.515056 | + | 0.857156i | \(0.672229\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.59324e11i | − | 1.40768i | −0.710359 | − | 0.703840i | \(-0.751467\pi\) | ||
0.710359 | − | 0.703840i | \(-0.248533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.59744e11i | − | 0.293394i | −0.989181 | − | 0.146697i | \(-0.953136\pi\) | ||
0.989181 | − | 0.146697i | \(-0.0468643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.96333e11 | −0.894807 | −0.447404 | − | 0.894332i | \(-0.647651\pi\) | ||||
−0.447404 | + | 0.894332i | \(0.647651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.64967e11 | 0.473290 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.28432e12 | 2.25213 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.68690e11i | − | 0.814353i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.21853e11 | + | 1.25291e11i | −0.890257 | + | 0.213741i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.74134e11 | −0.970543 | −0.485272 | − | 0.874363i | \(-0.661279\pi\) | ||||
−0.485272 | + | 0.874363i | \(0.661279\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.34834e11i | 0.223819i | 0.993718 | + | 0.111909i | \(0.0356967\pi\) | ||||
−0.993718 | + | 0.111909i | \(0.964303\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.79034e11 | 0.459002 | 0.229501 | − | 0.973308i | \(-0.426291\pi\) | ||||
0.229501 | + | 0.973308i | \(0.426291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.83305e11i | 0.457677i | 0.973464 | + | 0.228838i | \(0.0734928\pi\) | ||||
−0.973464 | + | 0.228838i | \(0.926507\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.46916e10 | − | 1.44495e11i | −0.0555415 | − | 0.231337i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.55657e11 | 1.34553 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.18612e10i | − | 0.0964109i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 4.25571e11i | − | 0.651528i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.67910e11i | 0.558267i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.83725e11 | −0.721115 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.97993e11 | −0.735858 | −0.367929 | − | 0.929854i | \(-0.619933\pi\) | ||||
−0.367929 | + | 0.929854i | \(0.619933\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.98004e11 | −1.15859 | −0.579297 | − | 0.815117i | \(-0.696673\pi\) | ||||
−0.579297 | + | 0.815117i | \(0.696673\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.03669e10i | 0.0724873i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.00336e12 | + | 2.40896e11i | −1.41899 | + | 0.340684i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.12582e11 | −0.438230 | −0.219115 | − | 0.975699i | \(-0.570317\pi\) | ||||
−0.219115 | + | 0.975699i | \(0.570317\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.10028e12i | 1.51600i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.45450e11 | 0.608460 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.16004e12i | 1.55743i | 0.627377 | + | 0.778716i | \(0.284129\pi\) | ||||
−0.627377 | + | 0.778716i | \(0.715871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.44593e11 | − | 1.06877e12i | −0.724892 | − | 1.42261i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.50809e11 | 0.589856 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 9.95746e11i | − | 1.29179i | −0.763428 | − | 0.645893i | \(-0.776485\pi\) | ||
0.763428 | − | 0.645893i | \(-0.223515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.68630e11i | 0.725222i | 0.931941 | + | 0.362611i | \(0.118115\pi\) | ||||
−0.931941 | + | 0.362611i | \(0.881885\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.66482e11i | 0.842833i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.13162e12 | 1.40702 | 0.703512 | − | 0.710684i | \(-0.251614\pi\) | ||||
0.703512 | + | 0.710684i | \(0.251614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.73187e11 | 0.953278 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.59922e11 | −0.193882 | −0.0969411 | − | 0.995290i | \(-0.530906\pi\) | ||||
−0.0969411 | + | 0.995290i | \(0.530906\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.80250e10i | 0.0457147i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.63779e11 | − | 6.82159e11i | −0.193635 | − | 0.806513i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.50338e11 | −0.997006 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.09312e11i | 0.356687i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.40368e12 | 1.60532 | 0.802660 | − | 0.596436i | \(-0.203417\pi\) | ||||
0.802660 | + | 0.596436i | \(0.203417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.57502e12i | 1.77178i | 0.463896 | + | 0.885890i | \(0.346451\pi\) | ||||
−0.463896 | + | 0.885890i | \(0.653549\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.18276e10 | − | 5.24055e9i | 0.0243531 | − | 0.00584690i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.31282e11 | 0.692859 | 0.346429 | − | 0.938076i | \(-0.387394\pi\) | ||||
0.346429 | + | 0.938076i | \(0.387394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.38567e12i | 2.59705i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.48559e12i | 1.59106i | 0.605916 | + | 0.795528i | \(0.292807\pi\) | ||||
−0.605916 | + | 0.795528i | \(0.707193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.36966e11i | − | 0.889126i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.34700e11 | 0.245317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.22790e12 | −1.27312 | −0.636558 | − | 0.771228i | \(-0.719643\pi\) | ||||
−0.636558 | + | 0.771228i | \(0.719643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.37123e11 | −0.445976 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.74247e12i | 1.76354i | 0.471680 | + | 0.881770i | \(0.343648\pi\) | ||||
−0.471680 | + | 0.881770i | \(0.656352\pi\) | |||||||
\(998\) | 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 | 252.9.d.b.181.4 | 6 | ||
3.2 | odd | 2 | 28.9.b.a.13.4 | yes | 6 | ||
7.6 | odd | 2 | inner | 252.9.d.b.181.3 | 6 | ||
12.11 | even | 2 | 112.9.c.d.97.3 | 6 | |||
21.2 | odd | 6 | 196.9.h.b.129.3 | 12 | |||
21.5 | even | 6 | 196.9.h.b.129.4 | 12 | |||
21.11 | odd | 6 | 196.9.h.b.117.4 | 12 | |||
21.17 | even | 6 | 196.9.h.b.117.3 | 12 | |||
21.20 | even | 2 | 28.9.b.a.13.3 | ✓ | 6 | ||
84.83 | odd | 2 | 112.9.c.d.97.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.9.b.a.13.3 | ✓ | 6 | 21.20 | even | 2 | ||
28.9.b.a.13.4 | yes | 6 | 3.2 | odd | 2 | ||
112.9.c.d.97.3 | 6 | 12.11 | even | 2 | |||
112.9.c.d.97.4 | 6 | 84.83 | odd | 2 | |||
196.9.h.b.117.3 | 12 | 21.17 | even | 6 | |||
196.9.h.b.117.4 | 12 | 21.11 | odd | 6 | |||
196.9.h.b.129.3 | 12 | 21.2 | odd | 6 | |||
196.9.h.b.129.4 | 12 | 21.5 | even | 6 | |||
252.9.d.b.181.3 | 6 | 7.6 | odd | 2 | inner | ||
252.9.d.b.181.4 | 6 | 1.1 | even | 1 | trivial |