Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (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: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 4826x^{6} + 8748877x^{4} + 7060845096x^{2} + 2140819627716 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.7 | ||
Root | \(-1.73205 - 35.9608i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.9.b.b.319.6 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 46.7654 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 197.353i | 0.315764i | 0.987458 | + | 0.157882i | \(0.0504666\pi\) | ||||
−0.987458 | + | 0.157882i | \(0.949533\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3794.06i | 1.58020i | 0.612978 | + | 0.790100i | \(0.289972\pi\) | ||||
−0.612978 | + | 0.790100i | \(0.710028\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2187.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16480.4 | −1.12563 | −0.562817 | − | 0.826581i | \(-0.690282\pi\) | ||||
−0.562817 | + | 0.826581i | \(0.690282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11110.6i | 0.389014i | 0.980901 | + | 0.194507i | \(0.0623106\pi\) | ||||
−0.980901 | + | 0.194507i | \(0.937689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9229.26i | 0.182306i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 66738.9 | 0.799067 | 0.399534 | − | 0.916719i | \(-0.369172\pi\) | ||||
0.399534 | + | 0.916719i | \(0.369172\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20481.8 | −0.157164 | −0.0785820 | − | 0.996908i | \(-0.525039\pi\) | ||||
−0.0785820 | + | 0.996908i | \(0.525039\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 177431.i | 0.912329i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 44505.2i | 0.159037i | 0.996833 | + | 0.0795187i | \(0.0253383\pi\) | ||||
−0.996833 | + | 0.0795187i | \(0.974662\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 351677. | 0.900293 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276. | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 725037.i | 1.02510i | 0.858656 | + | 0.512552i | \(0.171300\pi\) | ||||
−0.858656 | + | 0.512552i | \(0.828700\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44205.0i | 0.0478657i | 0.999714 | + | 0.0239329i | \(0.00761880\pi\) | ||||
−0.999714 | + | 0.0239329i | \(0.992381\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −770713. | −0.649885 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −748768. | −0.498971 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.85851e6i | 1.52522i | 0.646857 | + | 0.762611i | \(0.276083\pi\) | ||||
−0.646857 | + | 0.762611i | \(0.723917\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 519592.i | 0.224597i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10702.9 | −0.00378761 | −0.00189381 | − | 0.999998i | \(-0.500603\pi\) | ||||
−0.00189381 | + | 0.999998i | \(0.500603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 374259. | 0.109471 | 0.0547354 | − | 0.998501i | \(-0.482568\pi\) | ||||
0.0547354 | + | 0.998501i | \(0.482568\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 431610.i | 0.105255i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.11469e6i | 0.433365i | 0.976242 | + | 0.216683i | \(0.0695237\pi\) | ||||
−0.976242 | + | 0.216683i | \(0.930476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.63010e6 | −1.49703 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.12107e6 | 0.461342 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.99442e6i | 0.759703i | 0.925047 | + | 0.379852i | \(0.124025\pi\) | ||||
−0.925047 | + | 0.379852i | \(0.875975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.25245e6i | − 0.355435i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −957837. | −0.0907387 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.11289e7 | −0.918424 | −0.459212 | − | 0.888327i | \(-0.651868\pi\) | ||||
−0.459212 | + | 0.888327i | \(0.651868\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.30232e7i | − 1.66282i | −0.555657 | − | 0.831411i | \(-0.687533\pi\) | ||||
0.555657 | − | 0.831411i | \(-0.312467\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.29761e6i | 0.526734i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.19271e6 | −0.122837 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.77776e7 | 0.882212 | 0.441106 | − | 0.897455i | \(-0.354586\pi\) | ||||
0.441106 | + | 0.897455i | \(0.354586\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.08130e6i | 0.0918203i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.44380e7i | 0.961682i | 0.876808 | + | 0.480841i | \(0.159669\pi\) | ||||
−0.876808 | + | 0.480841i | \(0.840331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.70522e6 | 0.130474 | 0.0652368 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652368 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.64463e7 | 0.519784 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 6.25277e7i | − 1.77873i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 5.98403e7i | − 1.53633i | −0.640251 | − | 0.768166i | \(-0.721169\pi\) | ||||
0.640251 | − | 0.768166i | \(-0.278831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.83719e7 | −1.22996 | −0.614981 | − | 0.788542i | \(-0.710836\pi\) | ||||
−0.614981 | + | 0.788542i | \(0.710836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.31711e7i | 0.252317i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.39066e7i | 0.591844i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.20248e7 | −1.30733 | −0.653665 | − | 0.756784i | \(-0.726769\pi\) | ||||
−0.653665 | + | 0.756784i | \(0.726769\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.21544e7 | −0.614719 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.06726e6i | 0.0276353i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 4.04213e6i | − 0.0496267i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.81980e7 | −0.657387 | −0.328694 | − | 0.944437i | \(-0.606608\pi\) | ||||
−0.328694 | + | 0.944437i | \(0.606608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.60427e7 | −0.375211 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.64434e7i | 0.734606i | 0.930101 | + | 0.367303i | \(0.119719\pi\) | ||||
−0.930101 | + | 0.367303i | \(0.880281\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1.91556e8i | − 1.70195i | −0.525207 | − | 0.850974i | \(-0.676012\pi\) | ||||
0.525207 | − | 0.850974i | \(-0.323988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.50164e7 | −0.288081 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.44812e7 | 0.415635 | 0.207817 | − | 0.978168i | \(-0.433364\pi\) | ||||
0.207817 | + | 0.978168i | \(0.433364\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.72940e8i | 1.22515i | 0.790413 | + | 0.612574i | \(0.209866\pi\) | ||||
−0.790413 | + | 0.612574i | \(0.790134\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.33679e8i | 0.880588i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.07735e8 | −0.660761 | −0.330380 | − | 0.943848i | \(-0.607177\pi\) | ||||
−0.330380 | + | 0.943848i | \(0.607177\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.78321e6 | −0.0502183 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.42989e7i | 0.129671i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.53212e8i | 1.26269i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.72450e7 | 0.267052 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −500524. | −0.00218678 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.46495e8i | 0.600044i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.05573e8i | − 0.790225i | −0.918633 | − | 0.395113i | \(-0.870706\pi\) | ||||
0.918633 | − | 0.395113i | \(-0.129294\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.75024e7 | 0.0632030 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.21055e7 | −0.109017 | −0.0545084 | − | 0.998513i | \(-0.517359\pi\) | ||||
−0.0545084 | + | 0.998513i | \(0.517359\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 7.77091e7i | − 0.248351i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.01844e7i | 0.0607688i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.85467e8 | 1.94583 | 0.972913 | − | 0.231171i | \(-0.0742558\pi\) | ||||
0.972913 | + | 0.231171i | \(0.0742558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.81121e8 | −1.55671 | −0.778354 | − | 0.627826i | \(-0.783945\pi\) | ||||
−0.778354 | + | 0.627826i | \(0.783945\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.88940e7i | 0.250204i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.83108e8i | − 0.437887i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.43088e8 | −0.323691 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.03590e8 | −0.864313 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.86338e8i | − 1.79827i | −0.437673 | − | 0.899134i | \(-0.644197\pi\) | ||||
0.437673 | − | 0.899134i | \(-0.355803\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2.60061e8i | − 0.500227i | −0.968217 | − | 0.250114i | \(-0.919532\pi\) | ||||
0.968217 | − | 0.250114i | \(-0.0804680\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.45958e8 | 0.266356 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.72397e6 | −0.0151143 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.08233e7i | 0.133026i | 0.997786 | + | 0.0665132i | \(0.0211875\pi\) | ||||
−0.997786 | + | 0.0665132i | \(0.978813\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.80331e8i | 0.438615i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.68855e8 | −0.251311 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.11086e8 | −0.582348 | −0.291174 | − | 0.956670i | \(-0.594046\pi\) | ||||
−0.291174 | + | 0.956670i | \(0.594046\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.52102e8i | − 0.205210i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.36188e8i | 0.946504i | 0.880927 | + | 0.473252i | \(0.156920\pi\) | ||||
−0.880927 | + | 0.473252i | \(0.843080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.92285e8 | 0.848668 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.47936e7 | −0.0523880 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 6.33738e8i | − 0.707498i | −0.935340 | − | 0.353749i | \(-0.884907\pi\) | ||||
0.935340 | − | 0.353749i | \(-0.115093\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.33428e9i | 1.42264i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.20446e8 | −0.530252 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.50585e9 | −1.46679 | −0.733396 | − | 0.679802i | \(-0.762066\pi\) | ||||
−0.733396 | + | 0.679802i | \(0.762066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.25523e8i | − 0.769157i | −0.923092 | − | 0.384579i | \(-0.874347\pi\) | ||||
0.923092 | − | 0.384579i | \(-0.125653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1.07669e9i | − 0.960031i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.64135e8 | −0.481611 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.09988e9 | −0.899458 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.88041e8i | 0.304110i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.94421e9i | − 1.46086i | −0.682986 | − | 0.730431i | \(-0.739319\pi\) | ||||
0.682986 | − | 0.730431i | \(-0.260681\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.05725e8 | 0.652781 | 0.326390 | − | 0.945235i | \(-0.394168\pi\) | ||||
0.326390 | + | 0.945235i | \(0.394168\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.02543e8 | −0.0709197 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.17129e9i | 1.44163i | 0.693130 | + | 0.720813i | \(0.256231\pi\) | ||||
−0.693130 | + | 0.720813i | \(0.743769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.33204e8i | 0.340002i | 0.985444 | + | 0.170001i | \(0.0543771\pi\) | ||||
−0.985444 | + | 0.170001i | \(0.945623\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.31374e8 | 0.509345 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.75083e9 | −1.61987 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.11224e6i | − 0.00119599i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.73328e7i | 0.0530125i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.37548e8 | 0.176909 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.80735e9 | −0.911828 | −0.455914 | − | 0.890024i | \(-0.650688\pi\) | ||||
−0.455914 | + | 0.890024i | \(0.650688\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.14285e9i | 0.555227i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.38610e7i | 0.0345670i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.67717e8 | −0.0756375 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.73276e8 | 0.0753289 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.41510e8i | 0.310848i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.30606e9i | 1.33688i | 0.743767 | + | 0.668439i | \(0.233037\pi\) | ||||
−0.743767 | + | 0.668439i | \(0.766963\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.69118e8 | 0.300098 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.39061e9 | −1.65357 | −0.826783 | − | 0.562521i | \(-0.809831\pi\) | ||||
−0.826783 | + | 0.562521i | \(0.809831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.51374e9i | 1.64133i | 0.571413 | + | 0.820663i | \(0.306395\pi\) | ||||
−0.571413 | + | 0.820663i | \(0.693605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 2.92413e9i | − 1.02695i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.03865e9 | 0.352408 | 0.176204 | − | 0.984354i | \(-0.443618\pi\) | ||||
0.176204 | + | 0.984354i | \(0.443618\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.17338e8 | −0.136841 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2.79845e9i | − 0.887002i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 4.05969e9i | − 1.24423i | −0.782925 | − | 0.622116i | \(-0.786273\pi\) | ||||
0.782925 | − | 0.622116i | \(-0.213727\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.83737e9 | −0.544663 | −0.272331 | − | 0.962204i | \(-0.587795\pi\) | ||||
−0.272331 | + | 0.962204i | \(0.587795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.23677e8 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.70317e9i | − 0.472710i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.27565e8i | − 0.0611389i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.72979e9 | −0.710119 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.99843e9 | −0.755437 | −0.377719 | − | 0.925920i | \(-0.623291\pi\) | ||||
−0.377719 | + | 0.925920i | \(0.623291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 7.33464e8i | − 0.179018i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.15951e8i | 0.145675i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.06684e9 | −0.932233 | −0.466117 | − | 0.884723i | \(-0.654347\pi\) | ||||
−0.466117 | + | 0.884723i | \(0.654347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.08454e10 | −2.41016 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.58566e9i | 0.341701i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.67554e9i | 0.768243i | 0.923283 | + | 0.384122i | \(0.125496\pi\) | ||||
−0.923283 | + | 0.384122i | \(0.874504\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.18301e9 | −0.239887 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.83592e9 | −0.754787 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4.57397e9i | − 0.873542i | −0.899573 | − | 0.436771i | \(-0.856122\pi\) | ||||
0.899573 | − | 0.436771i | \(-0.143878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.80061e9i | 0.333843i | 0.985970 | + | 0.166922i | \(0.0533827\pi\) | ||||
−0.985970 | + | 0.166922i | \(0.946617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.97136e9 | −0.354908 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.79578e9 | −1.01340 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.08581e10i | − 1.84431i | −0.386823 | − | 0.922154i | \(-0.626428\pi\) | ||||
0.386823 | − | 0.922154i | \(-0.373572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.66764e7i | 0.0159552i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.87260e9 | −0.460734 | −0.230367 | − | 0.973104i | \(-0.573993\pi\) | ||||
−0.230367 | + | 0.973104i | \(0.573993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.08258e8 | −0.0792389 | −0.0396195 | − | 0.999215i | \(-0.512615\pi\) | ||||
−0.0396195 | + | 0.999215i | \(0.512615\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.89032e8i | − 0.0286520i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 4.06074e7i | − 0.00598519i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.52168e9 | −0.361491 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.72165e9 | −0.379543 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.13811e9i | 0.290108i | 0.989424 | + | 0.145054i | \(0.0463356\pi\) | ||||
−0.989424 | + | 0.145054i | \(0.953664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 2.19631e9i | − 0.290005i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.68555e9 | −0.216628 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.94480e8 | −0.0618677 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.41996e9i | 0.172986i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.57490e9i | 0.424125i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.54368e9 | 0.525060 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.39905e10 | −1.57499 | −0.787497 | − | 0.616318i | \(-0.788623\pi\) | ||||
−0.787497 | + | 0.616318i | \(0.788623\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 8.95818e9i | − 0.982621i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.84680e9i | 0.624995i | 0.949919 | + | 0.312497i | \(0.101166\pi\) | ||||
−0.949919 | + | 0.312497i | \(0.898834\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.27511e9 | 0.862177 | 0.431088 | − | 0.902310i | \(-0.358130\pi\) | ||||
0.431088 | + | 0.902310i | \(0.358130\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.63756e9 | −0.166324 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.37723e10i | 1.36386i | 0.731419 | + | 0.681928i | \(0.238858\pi\) | ||||
−0.731419 | + | 0.681928i | \(0.761142\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.19489e10i | − 1.15389i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.54784e9 | 0.239967 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.36693e9 | −0.125585 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.90735e9i | 0.350226i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.08759e9i | 0.707340i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.02325e9 | −0.684804 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.73215e9 | 0.227611 | 0.113806 | − | 0.993503i | \(-0.463696\pi\) | ||||
0.113806 | + | 0.993503i | \(0.463696\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.25157e9i | 0.508408i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.50845e9i | 0.278571i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.19153e10 | 1.69913 | 0.849567 | − | 0.527481i | \(-0.176863\pi\) | ||||
0.849567 | + | 0.527481i | \(0.176863\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.03828e9 | −0.381490 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7.28517e8i | − 0.0538793i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.08711e10i | − 0.785414i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.10750e8 | −0.0289935 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.17879e9 | 0.633093 | 0.316547 | − | 0.948577i | \(-0.397477\pi\) | ||||
0.316547 | + | 0.948577i | \(0.397477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.80632e10i | 1.21757i | 0.793335 | + | 0.608785i | \(0.208343\pi\) | ||||
−0.793335 | + | 0.608785i | \(0.791657\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.13635e9i | 0.0748657i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.40105e9 | 0.283438 | 0.141719 | − | 0.989907i | \(-0.454737\pi\) | ||||
0.141719 | + | 0.989907i | \(0.454737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.82289e9 | −0.303665 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.18415e10i | 0.729013i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.13107e8i | 0.0369113i | 0.999830 | + | 0.0184556i | \(0.00587494\pi\) | ||||
−0.999830 | + | 0.0184556i | \(0.994125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.65641e10 | −0.975299 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.67709e9 | 0.154183 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.31234e8i | 0.0411989i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.46445e10i | − 0.807253i | −0.914924 | − | 0.403626i | \(-0.867750\pi\) | ||||
0.914924 | − | 0.403626i | \(-0.132250\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.34072e7 | −0.00126254 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.27432e10 | −1.20048 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 1.37672e10i | − 0.711230i | −0.934633 | − | 0.355615i | \(-0.884272\pi\) | ||||
0.934633 | − | 0.355615i | \(-0.115728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.85090e9i | 0.346436i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.05561e9 | −0.398779 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.02771e8 | 0.0195210 | 0.00976048 | − | 0.999952i | \(-0.496893\pi\) | ||||
0.00976048 | + | 0.999952i | \(0.496893\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 9.61369e9i | − 0.456237i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.88378e10i | 1.34019i | 0.742274 | + | 0.670097i | \(0.233747\pi\) | ||||
−0.742274 | + | 0.670097i | \(0.766253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.23400e10 | 0.561658 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.18505e8 | 0.0364903 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.15555e10i | 0.504649i | 0.967643 | + | 0.252325i | \(0.0811951\pi\) | ||||
−0.967643 | + | 0.252325i | \(0.918805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.97023e9i | 0.127082i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.50142e9 | −0.0629409 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.18096e10 | 0.485118 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.13939e10i | − 0.861247i | −0.902532 | − | 0.430623i | \(-0.858294\pi\) | ||||
0.902532 | − | 0.430623i | \(-0.141706\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 3.63409e9i | − 0.143385i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.83492e9 | 0.109639 | 0.0548194 | − | 0.998496i | \(-0.482542\pi\) | ||||
0.0548194 | + | 0.998496i | \(0.482542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.91145e8 | −0.0186204 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.43931e8i | 0.0350849i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4.71095e10i | − 1.71684i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.93438e10 | 1.40599 | 0.702997 | − | 0.711193i | \(-0.251845\pi\) | ||||
0.702997 | + | 0.711193i | \(0.251845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.20561e10 | 1.12342 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.22236e10i | − 1.45129i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1.15199e10i | − 0.388378i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.71763e10 | −0.898766 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.17809e10 | −1.03112 | −0.515561 | − | 0.856853i | \(-0.672417\pi\) | ||||
−0.515561 | + | 0.856853i | \(0.672417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.53716e9i | 0.0807643i | 0.999184 | + | 0.0403821i | \(0.0128575\pi\) | ||||
−0.999184 | + | 0.0403821i | \(0.987142\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.62482e9i | 0.144455i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.34705e10 | 0.719395 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.73514e10 | 2.62759 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 8.56309e9i | − 0.252814i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.95521e9i | 0.172579i | 0.996270 | + | 0.0862894i | \(0.0275010\pi\) | ||||
−0.996270 | + | 0.0862894i | \(0.972499\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.61421e10 | 1.02816 | 0.514081 | − | 0.857741i | \(-0.328133\pi\) | ||||
0.514081 | + | 0.857741i | \(0.328133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.69156e9 | −0.186883 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 9.11545e8i | − 0.0249949i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.40899e10i | 0.917840i | 0.888478 | + | 0.458920i | \(0.151764\pi\) | ||||
−0.888478 | + | 0.458920i | \(0.848236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.88740e10 | −0.499011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.28042e10 | 1.89035 | 0.945174 | − | 0.326567i | \(-0.105892\pi\) | ||||
0.945174 | + | 0.326567i | \(0.105892\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.61878e10i | − 0.412808i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 4.14499e10i | − 1.03823i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.63688e10 | −0.894836 | −0.447418 | − | 0.894325i | \(-0.647656\pi\) | ||||
−0.447418 | + | 0.894325i | \(0.647656\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.76388e8 | 0.00426346 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.21618e10i | − 0.288806i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 8.31927e9i | − 0.194106i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.39306e10 | 0.548643 | 0.274321 | − | 0.961638i | \(-0.411547\pi\) | ||||
0.274321 | + | 0.961638i | \(0.411547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.82578e9 | 0.153781 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.37304e10i | − 0.304004i | −0.988380 | − | 0.152002i | \(-0.951428\pi\) | ||||
0.988380 | − | 0.152002i | \(-0.0485720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.34930e10i | 1.16405i | 0.813170 | + | 0.582026i | \(0.197740\pi\) | ||||
−0.813170 | + | 0.582026i | \(0.802260\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.07980e8 | −0.00872623 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.41485e8 | 0.00507718 | 0.00253859 | − | 0.999997i | \(-0.499192\pi\) | ||||
0.00253859 | + | 0.999997i | \(0.499192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.74492e10i | 1.39407i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.77973e9i | 0.0768029i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.16794e9 | −0.123224 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.20297e9 | −0.141494 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.31098e10i | 0.253234i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.58734e10i | 0.301528i | 0.988570 | + | 0.150764i | \(0.0481734\pi\) | ||||
−0.988570 | + | 0.150764i | \(0.951827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.17598e10 | −0.593332 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.89659e9 | −0.145094 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.14855e10i | − 0.207579i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.42808e10i | 1.14279i | 0.820676 | + | 0.571393i | \(0.193597\pi\) | ||||
−0.820676 | + | 0.571393i | \(0.806403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.92246e10 | −0.336219 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.06597e11 | 1.83408 | 0.917040 | − | 0.398795i | \(-0.130571\pi\) | ||||
0.917040 | + | 0.398795i | \(0.130571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.83882e10i | 0.819127i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 7.11311e9i | − 0.118478i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.27191e10 | −1.51965 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.59553e10 | 1.22506 | 0.612528 | − | 0.790449i | \(-0.290153\pi\) | ||||
0.612528 | + | 0.790449i | \(0.290153\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.44281e10i | 0.546465i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 6.63220e10i | − 1.03606i | −0.855362 | − | 0.518031i | \(-0.826665\pi\) | ||||
0.855362 | − | 0.518031i | \(-0.173335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.50863e10 | −0.231962 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.23750e10 | 0.489979 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.87347e10i | 1.02401i | 0.858982 | + | 0.512006i | \(0.171097\pi\) | ||||
−0.858982 | + | 0.512006i | \(0.828903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.40578e10i | 0.206174i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.09479e9 | −0.0302462 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.78040e10 | 0.537414 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.48509e10i | − 0.487811i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 2.96370e10i | − 0.408474i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.24827e10 | −0.983747 | −0.491874 | − | 0.870667i | \(-0.663688\pi\) | ||||
−0.491874 | + | 0.870667i | \(0.663688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.21199e11 | 1.61991 | 0.809957 | − | 0.586489i | \(-0.199490\pi\) | ||||
0.809957 | + | 0.586489i | \(0.199490\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.23983e10i | 0.821364i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.95019e9i | 0.0382479i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.63303e10 | 0.974707 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.43388e10 | −0.306141 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.18916e8i | − 0.00147343i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.07520e10i | 0.131243i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.04215e10 | −0.846853 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.42228e11 | 1.68511 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 3.08763e10i | − 0.360442i | −0.983626 | − | 0.180221i | \(-0.942319\pi\) | ||||
0.983626 | − | 0.180221i | \(-0.0576813\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 3.86059e10i | − 0.444073i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.41301e10 | −0.386858 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.59776e11 | −1.78468 | −0.892341 | − | 0.451361i | \(-0.850939\pi\) | ||||
−0.892341 | + | 0.451361i | \(0.850939\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 5.03517e10i | − 0.554274i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.48500e10i | − 0.161109i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.27038e11 | 2.42771 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.63820e10 | −0.278058 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.27428e10i | 0.444061i | 0.975040 | + | 0.222030i | \(0.0712684\pi\) | ||||
−0.975040 | + | 0.222030i | \(0.928732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.15825e9i | 0.0425856i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.14365e10 | −0.519302 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.01627e10 | 0.200685 | 0.100343 | − | 0.994953i | \(-0.468006\pi\) | ||||
0.100343 | + | 0.994953i | \(0.468006\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 2.12618e10i | − 0.208644i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.81469e10i | 0.175578i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.07200e10 | −0.579272 | −0.289636 | − | 0.957137i | \(-0.593534\pi\) | ||||
−0.289636 | + | 0.957137i | \(0.593534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.73024e11 | 1.62765 | 0.813825 | − | 0.581110i | \(-0.197381\pi\) | ||||
0.813825 | + | 0.581110i | \(0.197381\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9.09216e10i | − 0.843429i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.56514e10i | 0.143180i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.41388e10 | 0.759089 | 0.379545 | − | 0.925173i | \(-0.376081\pi\) | ||||
0.379545 | + | 0.925173i | \(0.376081\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.23566e10 | 0.376883 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 2.21467e11i | − 1.94359i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9.87905e10i | − 0.855148i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.79545e9 | −0.0409455 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.93365e10 | 0.247091 | 0.123545 | − | 0.992339i | \(-0.460574\pi\) | ||||
0.123545 | + | 0.992339i | \(0.460574\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 9.05397e8i | − 0.00752277i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.01541e11i | 0.832323i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.15955e10 | 0.498116 | 0.249058 | − | 0.968489i | \(-0.419879\pi\) | ||||
0.249058 | + | 0.968489i | \(0.419879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.99719e10 | −0.398711 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.49355e10i | 0.196300i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.86673e11i | 1.45002i | 0.688740 | + | 0.725008i | \(0.258164\pi\) | ||||
−0.688740 | + | 0.725008i | \(0.741836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.79316e10 | 0.597332 | 0.298666 | − | 0.954358i | \(-0.403458\pi\) | ||||
0.298666 | + | 0.954358i | \(0.403458\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.88795e10 | 0.294071 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.12975e10i | 0.0843255i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.32801e11i | − 0.978242i | −0.872216 | − | 0.489121i | \(-0.837318\pi\) | ||||
0.872216 | − | 0.489121i | \(-0.162682\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.28644e11 | −0.935233 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.34955e10 | −0.168585 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.41461e11i | − 1.00183i | −0.865496 | − | 0.500916i | \(-0.832997\pi\) | ||||
0.865496 | − | 0.500916i | \(-0.167003\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 9.87797e7i | 0 0.000690506i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.08559e11 | 0.749076 | 0.374538 | − | 0.927212i | \(-0.377801\pi\) | ||||
0.374538 | + | 0.927212i | \(0.377801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.65925e11 | 1.13019 | 0.565093 | − | 0.825027i | \(-0.308840\pi\) | ||||
0.565093 | + | 0.825027i | \(0.308840\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.55181e9i | 0.0306068i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 3.11207e11i | − 2.06584i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.08463e11 | 0.710821 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.57856e10 | 0.102139 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.90774e11i | 1.21876i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 8.74514e10i | − 0.551632i | −0.961210 | − | 0.275816i | \(-0.911052\pi\) | ||||
0.961210 | − | 0.275816i | \(-0.0889480\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.45215e10 | −0.526444 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.05703e10 | 0.249525 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 9.58858e10i | − 0.582367i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.34458e10i | 0.320561i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.77089e11 | −1.64129 | −0.820647 | − | 0.571435i | \(-0.806387\pi\) | ||||
−0.820647 | + | 0.571435i | \(0.806387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.47094e10 | 0.0860498 | 0.0430249 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430249 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.45414e9i | 0.0199572i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.14667e11i | 1.22503i | 0.790458 | + | 0.612517i | \(0.209843\pi\) | ||||
−0.790458 | + | 0.612517i | \(0.790157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.83408e11 | 1.03381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.84333e9 | −0.0436693 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 8.93518e10i | − 0.491418i | −0.969344 | − | 0.245709i | \(-0.920979\pi\) | ||||
0.969344 | − | 0.245709i | \(-0.0790207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 6.33609e9i | − 0.0344236i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.10331e9 | 0.0434912 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.96460e11 | −1.04167 | −0.520837 | − | 0.853656i | \(-0.674380\pi\) | ||||
−0.520837 | + | 0.853656i | \(0.674380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.55340e11i | 1.33756i | 0.743460 | + | 0.668780i | \(0.233183\pi\) | ||||
−0.743460 | + | 0.668780i | \(0.766817\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.46770e10i | 0.179468i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.53361e10 | 0.0784202 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.22679e10 | −0.163030 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.54609e11i | 0.771847i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.79431e11i | 1.87173i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.16723e11 | 1.54390 | 0.771950 | − | 0.635683i | \(-0.219282\pi\) | ||||
0.771950 | + | 0.635683i | \(0.219282\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.59681e10 | 0.173261 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.24064e11i | 1.06664i | 0.845914 | + | 0.533319i | \(0.179055\pi\) | ||||
−0.845914 | + | 0.533319i | \(0.820945\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 2.20807e11i | − 1.03880i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.05328e11 | −0.954686 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.78839e11 | −1.28136 | −0.640679 | − | 0.767809i | \(-0.721347\pi\) | ||||
−0.640679 | + | 0.767809i | \(0.721347\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.35279e11i | 0.614422i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.11087e11i | 0.947620i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.66017e10 | −0.295535 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.74979e11 | −1.20611 | −0.603056 | − | 0.797699i | \(-0.706051\pi\) | ||||
−0.603056 | + | 0.797699i | \(0.706051\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.36748e11i | − 0.592909i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 1.14686e11i | − 0.491552i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.14299e8 | −0.00302656 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.85728e10 | 0.203463 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.21009e11i | − 0.501123i | −0.968101 | − | 0.250562i | \(-0.919385\pi\) | ||||
0.968101 | − | 0.250562i | \(-0.0806152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.85474e10i | − 0.239710i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.95170e10 | −0.0790053 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.90031e11 | −1.16082 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.24092e11i | 1.28258i | 0.767301 | + | 0.641288i | \(0.221599\pi\) | ||||
−0.767301 | + | 0.641288i | \(0.778401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1.30871e11i | − 0.512111i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.96735e9 | −0.00761244 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.61367e10 | 0.138269 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.89853e11i | − 0.718358i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 4.10633e11i | − 1.53652i | −0.640138 | − | 0.768260i | \(-0.721123\pi\) | ||||
0.640138 | − | 0.768260i | \(-0.278877\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.26775e11 | 2.68942 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.59252e10 | −0.314461 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.54979e11i | 0.922894i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.06772e10i | 0.0382225i | 0.999817 | + | 0.0191112i | \(0.00608367\pi\) | ||||
−0.999817 | + | 0.0191112i | \(0.993916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.04604e10 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.49776e10 | 0.0874746 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.08286e11i | − 0.721515i | −0.932660 | − | 0.360757i | \(-0.882518\pi\) | ||||
0.932660 | − | 0.360757i | \(-0.117482\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 7.96495e10i | − 0.272919i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.92981e11 | −0.993048 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.82789e11 | −0.612875 | −0.306437 | − | 0.951891i | \(-0.599137\pi\) | ||||
−0.306437 | + | 0.951891i | \(0.599137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1.06422e10i | − 0.0352986i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.51013e11i | 1.80803i | 0.427498 | + | 0.904016i | \(0.359395\pi\) | ||||
−0.427498 | + | 0.904016i | \(0.640605\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.74921e11 | 0.567829 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.27659e11 | −0.409987 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.06705e11i | 0.656786i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.25385e11i | 1.33728i | 0.743586 | + | 0.668640i | \(0.233123\pi\) | ||||
−0.743586 | + | 0.668640i | \(0.766877\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.40223e11 | −0.436152 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.13237e10 | 0.157954 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.55433e11i | − 1.38689i | −0.720512 | − | 0.693443i | \(-0.756093\pi\) | ||||
0.720512 | − | 0.693443i | \(-0.243907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 3.43007e10i | − 0.103356i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.60243e11 | −1.67047 | −0.835233 | − | 0.549897i | \(-0.814667\pi\) | ||||
−0.835233 | + | 0.549897i | \(0.814667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.56144e11 | −1.93598 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.88052e10i | 0.0841056i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1.23649e11i | − 0.357279i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.49195e11 | 0.712581 | 0.356290 | − | 0.934375i | \(-0.384041\pi\) | ||||
0.356290 | + | 0.934375i | \(0.384041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.90187e11 | −0.538225 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 5.13512e11i | − 1.43824i | −0.694884 | − | 0.719121i | \(-0.744544\pi\) | ||||
0.694884 | − | 0.719121i | \(-0.255456\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.55459e10i | 0.0430932i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.07188e11 | −1.39151 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.19214e8 | 0.000595276 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 4.02747e11i | − 1.08250i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.41538e10i | 0.197281i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.59507e10 | −0.0420050 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.88847e11 | 0.492279 | 0.246139 | − | 0.969234i | \(-0.420838\pi\) | ||||
0.246139 | + | 0.969234i | \(0.420838\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.71888e11i | 0.443545i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 4.08754e11i | − 1.04413i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.55802e11 | 0.646861 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.53241e10 | −0.138499 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.98231e8i | 0.00123480i | 1.00000 | 0.000617401i | \(0.000196525\pi\) | |||||
−1.00000 | 0.000617401i | \(0.999803\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.41132e11i | 0.346288i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.79388e11 | −0.435777 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.10635e10 | −0.146865 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 3.33240e10i | − 0.0793550i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.13903e11i | − 0.504340i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.76114e11 | −1.11152 | −0.555760 | − | 0.831343i | \(-0.687573\pi\) | ||||
−0.555760 | + | 0.831343i | \(0.687573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.86403e11 | −1.81787 | −0.908933 | − | 0.416942i | \(-0.863102\pi\) | ||||
−0.908933 | + | 0.416942i | \(0.863102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.42063e10i | 0.192745i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 8.11289e10i | − 0.183885i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.66549e9 | −0.0172049 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.21916e10 | −0.204906 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 7.14924e11i | − 1.57357i | −0.617224 | − | 0.786787i | \(-0.711743\pi\) | ||||
0.617224 | − | 0.786787i | \(-0.288257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.90745e11i | 0.851715i | 0.904790 | + | 0.425858i | \(0.140028\pi\) | ||||
−0.904790 | + | 0.425858i | \(0.859972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.71042e11 | −0.585087 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.83361e11 | −1.03336 | −0.516678 | − | 0.856180i | \(-0.672831\pi\) | ||||
−0.516678 | + | 0.856180i | \(0.672831\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.59993e11i | 1.39740i | 0.715414 | + | 0.698701i | \(0.246238\pi\) | ||||
−0.715414 | + | 0.698701i | \(0.753762\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 5.07782e11i | − 1.06481i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.75964e11 | −1.19623 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.45288e11 | −0.298872 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.52111e9i | 0.00921176i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 8.61080e11i | − 1.73778i | −0.495003 | − | 0.868891i | \(-0.664833\pi\) | ||||
0.495003 | − | 0.868891i | \(-0.335167\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.54319e10 | −0.0508387 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.34338e11 | −0.266005 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.36624e11i | 0.267979i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.17191e11i | 0.421996i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.37689e10 | −0.0457486 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.27219e11 | −0.242567 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 5.20403e11i | − 0.982977i | −0.870884 | − | 0.491489i | \(-0.836453\pi\) | ||||
0.870884 | − | 0.491489i | \(-0.163547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 8.84014e9i | − 0.0165422i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.53509e11 | 1.58229 | 0.791143 | − | 0.611632i | \(-0.209486\pi\) | ||||
0.791143 | + | 0.611632i | \(0.209486\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.12057e11 | −0.389476 | −0.194738 | − | 0.980855i | \(-0.562386\pi\) | ||||
−0.194738 | + | 0.980855i | \(0.562386\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 1.89902e9i | − 0.00345555i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.67543e11i | 0.842905i | 0.906851 | + | 0.421452i | \(0.138480\pi\) | ||||
−0.906851 | + | 0.421452i | \(0.861520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.25070e11 | 0.223403 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.17927e11 | −0.208707 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.86192e11i | 1.72935i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.97520e11i | 0.343192i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.27279e11 | −0.219129 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.55812e11 | −0.948190 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.09851e11i | 0.861876i | 0.902382 | + | 0.430938i | \(0.141817\pi\) | ||||
−0.902382 | + | 0.430938i | \(0.858183\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.99895e10i | 0.167494i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.67923e10 | −0.127472 | −0.0637359 | − | 0.997967i | \(-0.520302\pi\) | ||||
−0.0637359 | + | 0.997967i | \(0.520302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.22619e11 | 0.366201 | 0.183101 | − | 0.983094i | \(-0.441387\pi\) | ||||
0.183101 | + | 0.983094i | \(0.441387\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.02711e11i | − 0.167435i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.12545e11i | 0.828014i | 0.910274 | + | 0.414007i | \(0.135871\pi\) | ||||
−0.910274 | + | 0.414007i | \(0.864129\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.79956e11 | 1.24871 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.88253e10 | −0.125070 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.33125e10i | − 0.0681094i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 2.97183e11i | − 0.463160i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.31245e10 | −0.0357193 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.20503e10 | −0.0490674 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00061e11i | 0.607054i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.64050e10i | 0.0998735i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.62919e11 | 0.242872 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.10957e11 | −0.902779 | −0.451390 | − | 0.892327i | \(-0.649072\pi\) | ||||
−0.451390 | + | 0.892327i | \(0.649072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.67182e11i | 0.244869i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 9.42463e11i | − 1.36833i | −0.729328 | − | 0.684165i | \(-0.760167\pi\) | ||||
0.729328 | − | 0.684165i | \(-0.239833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.61994e11 | 1.38449 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.12487e11 | 0.303143 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.21810e11i | − 0.172269i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.39974e11i | 1.17762i | 0.808273 | + | 0.588808i | \(0.200403\pi\) | ||||
−0.808273 | + | 0.588808i | \(0.799597\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.54270e11 | −0.909323 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.71521e11 | −0.374107 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00527e12i | 1.37315i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 4.18933e11i | − 0.567316i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.01174e12 | −1.35834 | −0.679169 | − | 0.733982i | \(-0.737660\pi\) | ||||
−0.679169 | + | 0.733982i | \(0.737660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.76760e11 | 0.235280 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.73428e11i | 0.360841i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2.17065e11i | − 0.284016i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.06278e12 | 1.37875 | 0.689374 | − | 0.724406i | \(-0.257886\pi\) | ||||
0.689374 | + | 0.724406i | \(0.257886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.86989e11 | 0.497778 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.62998e11i | − 0.335424i | −0.985836 | − | 0.167712i | \(-0.946362\pi\) | ||||
0.985836 | − | 0.167712i | \(-0.0536379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.76334e8i | 0 0.000602372i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.65809e10 | −0.0960269 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.60464e11 | 0.572526 | 0.286263 | − | 0.958151i | \(-0.407587\pi\) | ||||
0.286263 | + | 0.958151i | \(0.407587\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.11673e10i | 0.0507560i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.44066e11i | 0.787423i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.73103e11 | −0.209862 | −0.104931 | − | 0.994480i | \(-0.533462\pi\) | ||||
−0.104931 | + | 0.994480i | \(0.533462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.83694e11 | 0.461288 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5.58795e11i | − 0.666200i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.60070e12i | 3.07480i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.50937e11 | 0.997709 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.19150e11 | 0.138545 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.78747e11i | 0.206125i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 6.52116e11i | − 0.745794i | −0.927873 | − | 0.372897i | \(-0.878365\pi\) | ||||
0.927873 | − | 0.372897i | \(-0.121635\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.39250e10 | −0.0725063 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.61429e11 | −0.856549 | −0.428275 | − | 0.903649i | \(-0.640878\pi\) | ||||
−0.428275 | + | 0.903649i | \(0.640878\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.20481e12i | − 2.45991i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.82729e11i | 0.202203i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.01203e12 | −1.11075 | −0.555374 | − | 0.831600i | \(-0.687425\pi\) | ||||
−0.555374 | + | 0.831600i | \(0.687425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.35180e12 | 1.47158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.78219e11i | 0.408383i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.43816e12i | − 1.54026i | −0.637886 | − | 0.770131i | \(-0.720191\pi\) | ||||
0.637886 | − | 0.770131i | \(-0.279809\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.28509e11 | −0.455214 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.75210e11 | −0.395372 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.66565e10i | 0.0174100i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1.76628e12i | − 1.83132i | −0.401953 | − | 0.915660i | \(-0.631669\pi\) | ||||
0.401953 | − | 0.915660i | \(-0.368331\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.27770e11 | 0.131411 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.05229e11 | −0.107360 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.33822e11i | 0.945112i | 0.881301 | + | 0.472556i | \(0.156669\pi\) | ||||
−0.881301 | + | 0.472556i | \(0.843331\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.92357e11i | 0.293529i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.9.b.b.319.7 | yes | 8 | |
4.3 | odd | 2 | inner | 384.9.b.b.319.3 | yes | 8 | |
8.3 | odd | 2 | inner | 384.9.b.b.319.6 | yes | 8 | |
8.5 | even | 2 | inner | 384.9.b.b.319.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.b.b.319.2 | ✓ | 8 | 8.5 | even | 2 | inner | |
384.9.b.b.319.3 | yes | 8 | 4.3 | odd | 2 | inner | |
384.9.b.b.319.6 | yes | 8 | 8.3 | odd | 2 | inner | |
384.9.b.b.319.7 | yes | 8 | 1.1 | even | 1 | trivial |