Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,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, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
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: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.7 | ||
Root | \(-2.21837 - 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.7.b.d.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 | ||||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.0000i | 0.160000i | 0.996795 | + | 0.0800000i | \(0.0254920\pi\) | ||||
−0.996795 | + | 0.0800000i | \(0.974508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 529.850i | − 1.54475i | −0.635165 | − | 0.772376i | \(-0.719068\pi\) | ||||
0.635165 | − | 0.772376i | \(-0.280932\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 435.847 | 0.327458 | 0.163729 | − | 0.986505i | \(-0.447648\pi\) | ||||
0.163729 | + | 0.986505i | \(0.447648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 341.182i | − 0.155294i | −0.996981 | − | 0.0776472i | \(-0.975259\pi\) | ||||
0.996981 | − | 0.0776472i | \(-0.0247408\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 311.769i | 0.0923760i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7682.73 | 1.56375 | 0.781877 | − | 0.623432i | \(-0.214262\pi\) | ||||
0.781877 | + | 0.623432i | \(0.214262\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4300.52 | −0.626990 | −0.313495 | − | 0.949590i | \(-0.601500\pi\) | ||||
−0.313495 | + | 0.949590i | \(0.601500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 8259.54i | − 0.891863i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3175.32i | 0.260978i | 0.991450 | + | 0.130489i | \(0.0416547\pi\) | ||||
−0.991450 | + | 0.130489i | \(0.958345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15225.0 | 0.974400 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 19409.3i | 0.795821i | 0.917424 | + | 0.397910i | \(0.130264\pi\) | ||||
−0.917424 | + | 0.397910i | \(0.869736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 15297.3i | − 0.513488i | −0.966479 | − | 0.256744i | \(-0.917350\pi\) | ||||
0.966479 | − | 0.256744i | \(-0.0826497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6794.18 | 0.189058 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10597.0 | 0.247160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 61969.9i | − 1.22342i | −0.791082 | − | 0.611710i | \(-0.790482\pi\) | ||||
0.791082 | − | 0.611710i | \(-0.209518\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 5318.50i | − 0.0896592i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −33740.2 | −0.489549 | −0.244774 | − | 0.969580i | \(-0.578714\pi\) | ||||
−0.244774 | + | 0.969580i | \(0.578714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −99312.6 | −1.24911 | −0.624553 | − | 0.780983i | \(-0.714719\pi\) | ||||
−0.624553 | + | 0.780983i | \(0.714719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4860.00i | 0.0533333i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17726.4i | 0.170737i | 0.996349 | + | 0.0853685i | \(0.0272068\pi\) | ||||
−0.996349 | + | 0.0853685i | \(0.972793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −163092. | −1.38626 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 119762. | 0.902834 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 224406.i | − 1.50733i | −0.657260 | − | 0.753664i | \(-0.728285\pi\) | ||||
0.657260 | − | 0.753664i | \(-0.271715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8716.94i | 0.0523933i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −67038.5 | −0.361993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 199557. | 0.971651 | 0.485826 | − | 0.874056i | \(-0.338519\pi\) | ||||
0.485826 | + | 0.874056i | \(0.338519\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45671.7i | 0.201214i | 0.994926 | + | 0.100607i | \(0.0320784\pi\) | ||||
−0.994926 | + | 0.100607i | \(0.967922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 128754.i | − 0.514917i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6823.63 | 0.0248471 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −496811. | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 49498.3i | 0.150676i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 452032.i | − 1.26297i | −0.775387 | − | 0.631487i | \(-0.782445\pi\) | ||||
0.775387 | − | 0.631487i | \(-0.217555\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 394349. | 1.01371 | 0.506853 | − | 0.862032i | \(-0.330809\pi\) | ||||
0.506853 | + | 0.862032i | \(0.330809\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 237334. | 0.562570 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 230933.i | − 0.505842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 571742.i | − 1.15963i | −0.814749 | − | 0.579814i | \(-0.803125\pi\) | ||||
0.814749 | − | 0.579814i | \(-0.196875\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 324465. | 0.567458 | 0.283729 | − | 0.958904i | \(-0.408428\pi\) | ||||
0.283729 | + | 0.958904i | \(0.408428\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 153655.i | 0.250201i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 302561.i | 0.459467i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 758607. | 1.07609 | 0.538043 | − | 0.842918i | \(-0.319164\pi\) | ||||
0.538043 | + | 0.842918i | \(0.319164\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −180775. | −0.239891 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 238462.i | − 0.296462i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 86010.5i | − 0.100318i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 25015.4 | 0.0274089 | 0.0137045 | − | 0.999906i | \(-0.495638\pi\) | ||||
0.0137045 | + | 0.999906i | \(0.495638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 105911. | 0.109153 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.60937e6i | 1.56204i | 0.624508 | + | 0.781018i | \(0.285300\pi\) | ||||
−0.624508 | + | 0.781018i | \(0.714700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 647116.i | − 0.592203i | −0.955156 | − | 0.296101i | \(-0.904313\pi\) | ||||
0.955156 | − | 0.296101i | \(-0.0956867\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 165191. | 0.142698 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −233041. | −0.190231 | −0.0951156 | − | 0.995466i | \(-0.530322\pi\) | ||||
−0.0951156 | + | 0.995466i | \(0.530322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 525849.i | − 0.406052i | −0.979173 | − | 0.203026i | \(-0.934922\pi\) | ||||
0.979173 | − | 0.203026i | \(-0.0650776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 966015.i | − 0.706342i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.21523e6 | −0.842216 | −0.421108 | − | 0.907011i | \(-0.638359\pi\) | ||||
−0.421108 | + | 0.907011i | \(0.638359\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −63506.4 | −0.0417565 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 82907.1i | − 0.0517648i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 4.07069e6i | − 2.41561i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.58160e6 | −0.892771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −525957. | −0.282641 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 617000.i | 0.315904i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.23094e6i | − 1.57731i | −0.614836 | − | 0.788655i | \(-0.710778\pi\) | ||||
0.614836 | − | 0.788655i | \(-0.289222\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.54813e6 | −0.721171 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.80119e6 | −0.801209 | −0.400604 | − | 0.916251i | \(-0.631200\pi\) | ||||
−0.400604 | + | 0.916251i | \(0.631200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.27863e6i | 0.968544i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 75759.9i | 0.0307920i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 50362.3 | 0.0195859 | 0.00979295 | − | 0.999952i | \(-0.496883\pi\) | ||||
0.00979295 | + | 0.999952i | \(0.496883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.23758e6 | 1.57788 | 0.788940 | − | 0.614471i | \(-0.210630\pi\) | ||||
0.788940 | + | 0.614471i | \(0.210630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 276328.i | 0.0985751i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 148703.i | − 0.0508524i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −388185. | −0.127331 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.54235e6 | −0.800357 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 4.40006e6i | − 1.33015i | −0.746778 | − | 0.665073i | \(-0.768400\pi\) | ||||
0.746778 | − | 0.665073i | \(-0.231600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 2.17763e6i | − 0.632488i | −0.948678 | − | 0.316244i | \(-0.897578\pi\) | ||||
0.948678 | − | 0.316244i | \(-0.102422\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.86690e6 | 0.521252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 305946. | 0.0821580 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.73506e6i | 1.48197i | 0.671522 | + | 0.740985i | \(0.265641\pi\) | ||||
−0.671522 | + | 0.740985i | \(0.734359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 3.49815e6i | − 0.870256i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.68244e6 | 0.403147 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.99695e6 | 0.692016 | 0.346008 | − | 0.938232i | \(-0.387537\pi\) | ||||
0.346008 | + | 0.938232i | \(0.387537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 135884.i | 0.0302493i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 8.03225e6i | − 1.72460i | −0.506400 | − | 0.862298i | \(-0.669024\pi\) | ||||
0.506400 | − | 0.862298i | \(-0.330976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.71040e6 | 0.975884 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.04503e6 | −0.208997 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2.42976e6i | − 0.469272i | −0.972083 | − | 0.234636i | \(-0.924610\pi\) | ||||
0.972083 | − | 0.234636i | \(-0.0753898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 8.06697e6i | − 1.50521i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.11078e6 | 0.560983 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.34862e6 | −0.932573 | −0.466286 | − | 0.884634i | \(-0.654408\pi\) | ||||
−0.466286 | + | 0.884634i | \(0.654408\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.11072e6i | − 1.53645i | −0.640183 | − | 0.768223i | \(-0.721141\pi\) | ||||
0.640183 | − | 0.768223i | \(-0.278859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 711952.i | 0.116171i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.23940e6 | 0.195747 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.34849e6 | 0.512064 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.00707e6i | − 0.297288i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 1.19063e6i | − 0.170875i | −0.996344 | − | 0.0854373i | \(-0.972771\pi\) | ||||
0.996344 | − | 0.0854373i | \(-0.0272287\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.07789e6 | 0.289034 | 0.144517 | − | 0.989502i | \(-0.453837\pi\) | ||||
0.144517 | + | 0.989502i | \(0.453837\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 106370. | 0.0143455 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.19700e6i | 0.287364i | 0.989624 | + | 0.143682i | \(0.0458942\pi\) | ||||
−0.989624 | + | 0.143682i | \(0.954106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 6.24588e6i | − 0.792564i | −0.918129 | − | 0.396282i | \(-0.870300\pi\) | ||||
0.918129 | − | 0.396282i | \(-0.129700\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.74451e6 | −0.953687 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.02840e7 | 1.22935 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 674804.i | − 0.0783278i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 771603.i | 0.0869927i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.87437e6 | −0.205313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.11658e7 | −1.18862 | −0.594311 | − | 0.804235i | \(-0.702575\pi\) | ||||
−0.594311 | + | 0.804235i | \(0.702575\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 7.04648e6i | − 0.729178i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 1.98625e6i | − 0.199857i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.10528e6 | −0.793211 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.14730e6 | 0.585264 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.62121e6i | − 0.242842i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 658854.i | − 0.0594120i | −0.999559 | − | 0.0297060i | \(-0.990543\pi\) | ||||
0.999559 | − | 0.0297060i | \(-0.00945711\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.69967e6 | 0.324800 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.04595e7 | −0.894198 | −0.447099 | − | 0.894484i | \(-0.647543\pi\) | ||||
−0.447099 | + | 0.894484i | \(0.647543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.94802e7i | 1.62214i | 0.584951 | + | 0.811069i | \(0.301114\pi\) | ||||
−0.584951 | + | 0.811069i | \(0.698886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 3.59990e6i | − 0.292048i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.62947e7 | −1.28819 | −0.644095 | − | 0.764946i | \(-0.722766\pi\) | ||||
−0.644095 | + | 0.764946i | \(0.722766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −354529. | −0.0273179 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.91257e6i | − 0.669511i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 2.00798e7i | − 1.47084i | −0.677609 | − | 0.735422i | \(-0.736984\pi\) | ||||
0.677609 | − | 0.735422i | \(-0.263016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.97568e6 | −0.426910 | −0.213455 | − | 0.976953i | \(-0.568472\pi\) | ||||
−0.213455 | + | 0.976953i | \(0.568472\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.26184e6i | − 0.221802i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.46726e6i | 0.0973680i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.05791e6 | 0.327622 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.92078e7 | 1.21466 | 0.607331 | − | 0.794449i | \(-0.292240\pi\) | ||||
0.607331 | + | 0.794449i | \(0.292240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.38395e6i | 0.0854594i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.39524e6i | 0.144453i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.96168e6 | 0.351212 | 0.175606 | − | 0.984461i | \(-0.443811\pi\) | ||||
0.175606 | + | 0.984461i | \(0.443811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.28348e7 | −1.88988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.71645e6i | 0.265274i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.92686e7i | 1.05921i | 0.848243 | + | 0.529607i | \(0.177661\pi\) | ||||
−0.848243 | + | 0.529607i | \(0.822339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.48813e6 | 0.241172 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.18255e7 | 0.621278 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.74390e7i | − 0.895909i | −0.894056 | − | 0.447955i | \(-0.852153\pi\) | ||||
0.894056 | − | 0.447955i | \(-0.147847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.41844e7i | 1.21514i | 0.794265 | + | 0.607571i | \(0.207856\pi\) | ||||
−0.794265 | + | 0.607571i | \(0.792144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.81800e6 | −0.138501 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.63577e6 | 0.319075 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.19698e7i | 1.50418i | 0.659059 | + | 0.752091i | \(0.270955\pi\) | ||||
−0.659059 | + | 0.752091i | \(0.729045\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 3.71725e6i | − 0.171163i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.34865e7 | 1.05852 | 0.529259 | − | 0.848460i | \(-0.322470\pi\) | ||||
0.529259 | + | 0.848460i | \(0.322470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.74978e6 | 0.341924 | 0.170962 | − | 0.985278i | \(-0.445312\pi\) | ||||
0.170962 | + | 0.985278i | \(0.445312\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.34077e6i | − 0.0579189i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.78772e7i | 0.756231i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.48867e7 | 1.44533 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 389951. | 0.0158246 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.14848e7i | − 0.456584i | −0.973593 | − | 0.228292i | \(-0.926686\pi\) | ||||
0.973593 | − | 0.228292i | \(-0.0733140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.99114e6i | 0.155464i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.65099e6 | 0.0630194 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.08336e6 | 0.0405284 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.26208e7i | 1.92956i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.50876e7i | 0.901842i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −913434. | −0.0321942 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.30562e7 | −0.796841 | −0.398421 | − | 0.917203i | \(-0.630442\pi\) | ||||
−0.398421 | + | 0.917203i | \(0.630442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.00875e7i | − 0.341909i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.24296e7i | 1.41055i | 0.708935 | + | 0.705274i | \(0.249176\pi\) | ||||
−0.708935 | + | 0.705274i | \(0.750824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.01928e7 | −0.658513 | −0.329257 | − | 0.944240i | \(-0.606798\pi\) | ||||
−0.329257 | + | 0.944240i | \(0.606798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.57507e6 | 0.0823868 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.83594e6i | 0.183203i | 0.995796 | + | 0.0916016i | \(0.0291986\pi\) | ||||
−0.995796 | + | 0.0916016i | \(0.970801\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.45947e6i | 0.260598i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.63276e6 | −0.109830 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.30398e7 | −0.980458 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 5.19449e6i | − 0.151319i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 8.19718e6i | − 0.234434i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.39235e6 | 0.263746 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.94601e7 | 1.91536 | 0.957682 | − | 0.287828i | \(-0.0929332\pi\) | ||||
0.957682 | + | 0.287828i | \(0.0929332\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 1.50587e7i | − 0.407807i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 9.93621e6i | − 0.264294i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.65194e7 | −0.692906 | −0.346453 | − | 0.938067i | \(-0.612614\pi\) | ||||
−0.346453 | + | 0.938067i | \(0.612614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.89436e7 | −0.486254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 6.66729e6i | − 0.168146i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.40780e7i | 0.596676i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −989967. | −0.0241081 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.53620e7 | 1.32502 | 0.662511 | − | 0.749052i | \(-0.269491\pi\) | ||||
0.662511 | + | 0.749052i | \(0.269491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.23047e7i | 0.995206i | 0.867405 | + | 0.497603i | \(0.165786\pi\) | ||||
−0.867405 | + | 0.497603i | \(0.834214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 1.29239e6i | − 0.0298864i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.67810e7 | −1.06352 | −0.531760 | − | 0.846895i | \(-0.678469\pi\) | ||||
−0.531760 | + | 0.846895i | \(0.678469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.04064e6 | 0.202076 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 6.34558e7i | − 1.39466i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.79965e7i | 1.46961i | 0.678276 | + | 0.734807i | \(0.262727\pi\) | ||||
−0.678276 | + | 0.734807i | \(0.737273\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.85514e7 | −0.606884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.46547e7 | −0.515442 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.88698e6i | 0.162193i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.52346e7i | 1.72432i | 0.506637 | + | 0.862160i | \(0.330889\pi\) | ||||
−0.506637 | + | 0.862160i | \(0.669111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.19886e6 | −0.163183 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.18902e8 | −2.32845 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.70643e7i | 1.09961i | 0.835293 | + | 0.549804i | \(0.185298\pi\) | ||||
−0.835293 | + | 0.549804i | \(0.814702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.61808e6i | 0.182387i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.62209e6 | 0.123586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.18779e7 | 0.952939 | 0.476469 | − | 0.879191i | \(-0.341916\pi\) | ||||
0.476469 | + | 0.879191i | \(0.341916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 5.03653e7i | − 0.910661i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.83098e7i | 1.39386i | 0.717138 | + | 0.696931i | \(0.245452\pi\) | ||||
−0.717138 | + | 0.696931i | \(0.754548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.61867e6 | 0.0809347 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.41330e7 | −0.416369 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 9.23410e7i | − 1.56872i | −0.620305 | − | 0.784361i | \(-0.712991\pi\) | ||||
0.620305 | − | 0.784361i | \(-0.287009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43951e7i | 0.408106i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.80778e7 | −0.462578 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.14348e7 | 0.185540 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.75593e7i | 0.600270i | 0.953897 | + | 0.300135i | \(0.0970317\pi\) | ||||
−0.953897 | + | 0.300135i | \(0.902968\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.55204e7i | 0.559189i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.85071e7 | −0.597183 | −0.298592 | − | 0.954381i | \(-0.596517\pi\) | ||||
−0.298592 | + | 0.954381i | \(0.596517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.21916e6 | −0.0797417 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.18098e6i | 0.0177778i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.70094e7i | − 0.400619i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.07783e8 | 1.57536 | 0.787681 | − | 0.616083i | \(-0.211281\pi\) | ||||
0.787681 | + | 0.616083i | \(0.211281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 785070. | 0.0113079 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.05735e8i | − 1.50096i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.48931e6i | 0.0907933i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.60574e7 | 0.910989 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.92976e7 | 1.07800 | 0.538999 | − | 0.842306i | \(-0.318803\pi\) | ||||
0.538999 | + | 0.842306i | \(0.318803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.67669e7i | 0.894777i | 0.894340 | + | 0.447389i | \(0.147646\pi\) | ||||
−0.894340 | + | 0.447389i | \(0.852354\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.30752e6i | 0.0569123i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.16970e8 | 1.52372 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.41992e7 | 0.310826 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.31805e6i | − 0.0293596i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 5.07275e7i | − 0.633595i | −0.948493 | − | 0.316798i | \(-0.897392\pi\) | ||||
0.948493 | − | 0.316798i | \(-0.102608\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.19683e7 | −0.393782 | −0.196891 | − | 0.980425i | \(-0.563084\pi\) | ||||
−0.196891 | + | 0.980425i | \(0.563084\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.05121e6 | −0.0735148 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.36555e7i | − 0.163631i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.14885e7i | 0.844972i | 0.906369 | + | 0.422486i | \(0.138842\pi\) | ||||
−0.906369 | + | 0.422486i | \(0.861158\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.96314e7 | −0.462087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.60820e7 | −0.875127 | −0.437563 | − | 0.899188i | \(-0.644158\pi\) | ||||
−0.437563 | + | 0.899188i | \(0.644158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.51721e7i | 0.172174i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 6.85901e7i | − 0.767960i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.00650e7 | 0.994986 | 0.497493 | − | 0.867468i | \(-0.334254\pi\) | ||||
0.497493 | + | 0.867468i | \(0.334254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.47056e7 | −0.160307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.39458e7i | − 0.365167i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 3.61550e6i | − 0.0383826i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.59392e7 | −0.376548 | −0.188274 | − | 0.982117i | \(-0.560289\pi\) | ||||
−0.188274 | + | 0.982117i | \(0.560289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.91021e7 | 0.300945 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.09802e8i | − 1.12075i | −0.828240 | − | 0.560373i | \(-0.810658\pi\) | ||||
0.828240 | − | 0.560373i | \(-0.189342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 5.53763e7i | − 0.557932i | −0.960301 | − | 0.278966i | \(-0.910008\pi\) | ||||
0.960301 | − | 0.278966i | \(-0.0899917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.76923e6 | 0.0474340 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.38248e7 | −0.528484 | −0.264242 | − | 0.964456i | \(-0.585122\pi\) | ||||
−0.264242 | + | 0.964456i | \(0.585122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.63235e8i | 2.55168i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.94008e7i | 0.855615i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.32851e7 | −0.409030 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.54755e7 | −0.610939 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 5.45307e7i | − 0.502442i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.71807e8i | 1.56328i | 0.623733 | + | 0.781638i | \(0.285615\pi\) | ||||
−0.623733 | + | 0.781638i | \(0.714385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.11430e7 | −0.189990 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.62267e7 | 0.232757 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 500308.i | 0.00438543i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.72463e7i | − 0.495634i | −0.968807 | − | 0.247817i | \(-0.920287\pi\) | ||||
0.968807 | − | 0.247817i | \(-0.0797131\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.67178e7 | 0.399536 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.13055e8 | 1.79989 | 0.899946 | − | 0.436001i | \(-0.143605\pi\) | ||||
0.899946 | + | 0.436001i | \(0.143605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.49116e8i | 1.24447i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.11822e6i | 0.0174644i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.39509e8 | −1.95098 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.04068e7 | −0.727611 | −0.363806 | − | 0.931475i | \(-0.618523\pi\) | ||||
−0.363806 | + | 0.931475i | \(0.618523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.25210e8i | − 0.995697i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.29271e8i | − 1.80155i | −0.434290 | − | 0.900773i | \(-0.643001\pi\) | ||||
0.434290 | − | 0.900773i | \(-0.356999\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.21874e7 | −0.249926 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.34279e7 | 0.563427 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.29225e7i | − 0.0979930i | −0.998799 | − | 0.0489965i | \(-0.984398\pi\) | ||||
0.998799 | − | 0.0489965i | \(-0.0156023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 2.08946e8i | − 1.56593i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.62904e7 | −0.120664 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.29423e7 | 0.0947525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.72601e6i | 0.0559092i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 3.78762e7i | − 0.270934i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.99955e7 | −0.565656 | −0.282828 | − | 0.959171i | \(-0.591273\pi\) | ||||
−0.282828 | + | 0.959171i | \(0.591273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.28458e8 | −0.897957 | −0.448979 | − | 0.893543i | \(-0.648212\pi\) | ||||
−0.448979 | + | 0.893543i | \(0.648212\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.25752e8i | − 0.869031i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.17525e8i | − 0.802969i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.37953e8 | 0.931890 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.84923e7 | 0.323884 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.15115e7i | 0.0760241i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.66083e6i | − 0.0304370i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.33768e7 | −0.538421 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.10832e7 | −0.453942 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.90048e8i | 1.83180i | 0.401410 | + | 0.915899i | \(0.368520\pi\) | ||||
−0.401410 | + | 0.915899i | \(0.631480\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.42022e8i | − 0.887067i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.05170e7 | 0.0649684 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.91198e7 | −0.177921 | −0.0889604 | − | 0.996035i | \(-0.528354\pi\) | ||||
−0.0889604 | + | 0.996035i | \(0.528354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.10982e7i | 0.0670713i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 8.34700e7i | − 0.498972i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.02937e8 | −1.79134 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.93203e7 | 0.113015 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.95014e8i | 1.12849i | 0.825606 | + | 0.564247i | \(0.190834\pi\) | ||||
−0.825606 | + | 0.564247i | \(0.809166\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.38836e7i | 0.193979i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.21978e7 | 0.295640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.06065e8 | 1.71510 | 0.857548 | − | 0.514404i | \(-0.171987\pi\) | ||||
0.857548 | + | 0.514404i | \(0.171987\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 2.43046e7i | − 0.134755i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 3.12871e7i | − 0.171639i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.27388e8 | 1.77716 | 0.888578 | − | 0.458725i | \(-0.151694\pi\) | ||||
0.888578 | + | 0.458725i | \(0.151694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.37293e8 | −0.737461 | −0.368731 | − | 0.929536i | \(-0.620208\pi\) | ||||
−0.368731 | + | 0.929536i | \(0.620208\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.85601e7i | − 0.0986544i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.83443e7i | 0.254297i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.84639e8 | 1.48172 | 0.740861 | − | 0.671658i | \(-0.234417\pi\) | ||||
0.740861 | + | 0.671658i | \(0.234417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.23910e7 | 0.166874 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.71918e8i | − 0.876583i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9.78068e7i | − 0.493587i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.65814e6 | 0.00828236 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.11468e8 | −1.53992 | −0.769962 | − | 0.638090i | \(-0.779725\pi\) | ||||
−0.769962 | + | 0.638090i | \(0.779725\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.57865e7i | 0.321952i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.42479e7i | 0.165909i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.54519e7 | −0.361831 | −0.180916 | − | 0.983499i | \(-0.557906\pi\) | ||||
−0.180916 | + | 0.983499i | \(0.557906\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.14139e7 | 0.386498 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 9.73636e7i | − 0.457587i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 2.08861e8i | − 0.971800i | −0.874014 | − | 0.485900i | \(-0.838492\pi\) | ||||
0.874014 | − | 0.485900i | \(-0.161508\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.88006e7 | −0.132672 | −0.0663359 | − | 0.997797i | \(-0.521131\pi\) | ||||
−0.0663359 | + | 0.997797i | \(0.521131\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.20725e8 | −0.550611 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.16320e7i | − 0.142843i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 2.89154e8i | − 1.29290i | −0.762958 | − | 0.646448i | \(-0.776254\pi\) | ||||
0.762958 | − | 0.646448i | \(-0.223746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.60312e8 | 0.709763 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.04793e6 | 0.0265145 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.53775e8i | 1.53584i | 0.640548 | + | 0.767919i | \(0.278707\pi\) | ||||
−0.640548 | + | 0.767919i | \(0.721293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 1.05191e7i | − 0.0452226i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.88929e8 | 0.804348 | 0.402174 | − | 0.915563i | \(-0.368255\pi\) | ||||
0.402174 | + | 0.915563i | \(0.368255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.45244e7 | 0.356377 | 0.178189 | − | 0.983996i | \(-0.442976\pi\) | ||||
0.178189 | + | 0.983996i | \(0.442976\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.20281e7i | 0.0502253i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 4.01948e8i | − 1.66229i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.25551e8 | 0.923855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.92185e7 | −0.118538 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 4.76098e8i | − 1.91313i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 3.49408e8i | − 1.39074i | −0.718653 | − | 0.695369i | \(-0.755241\pi\) | ||||
0.718653 | − | 0.695369i | \(-0.244759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.74058e8 | −0.686251 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.46187e7 | 0.252370 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.56440e7i | 0.215278i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 1.09844e8i | − 0.420991i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.70070e8 | −1.02542 | −0.512710 | − | 0.858562i | \(-0.671359\pi\) | ||||
−0.512710 | + | 0.858562i | \(0.671359\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.94695e8 | 1.86082 | 0.930411 | − | 0.366518i | \(-0.119450\pi\) | ||||
0.930411 | + | 0.366518i | \(0.119450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3.09626e7i | − 0.115387i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1.19819e7i | − 0.0442396i | −0.999755 | − | 0.0221198i | \(-0.992958\pi\) | ||||
0.999755 | − | 0.0221198i | \(-0.00704153\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.69762e7 | 0.318175 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.26349e8 | −0.457961 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5.21595e8i | − 1.87324i | −0.350345 | − | 0.936621i | \(-0.613936\pi\) | ||||
0.350345 | − | 0.936621i | \(-0.386064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 3.60238e7i | − 0.128193i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.58269e7 | 0.337902 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.10833e8 | −1.43552 | −0.717759 | − | 0.696292i | \(-0.754832\pi\) | ||||
−0.717759 | + | 0.696292i | \(0.754832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 8.48526e7i | − 0.293806i | −0.989151 | − | 0.146903i | \(-0.953069\pi\) | ||||
0.989151 | − | 0.146903i | \(-0.0469305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 4.08605e7i | − 0.140205i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.55727e7 | −0.154967 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.16306e7 | −0.207692 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.02705e7i | − 0.0343016i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.99059e7i | 0.0658891i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.39619e8 | −1.11416 | −0.557079 | − | 0.830460i | \(-0.688078\pi\) | ||||
−0.557079 | + | 0.830460i | \(0.688078\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.76722e7 | 0.187523 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.04369e8i | 1.30320i | 0.758561 | + | 0.651602i | \(0.225903\pi\) | ||||
−0.758561 | + | 0.651602i | \(0.774097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1.32544e7i | − 0.0423400i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.63048e8 | −0.516266 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.05590e8 | −0.645268 | −0.322634 | − | 0.946524i | \(-0.604568\pi\) | ||||
−0.322634 | + | 0.946524i | \(0.604568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.00725e6i | 0.00313374i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.03667e8i | 0.936542i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.65633e7 | −0.234079 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.25719e8 | 0.381037 | 0.190518 | − | 0.981684i | \(-0.438983\pi\) | ||||
0.190518 | + | 0.981684i | \(0.438983\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 5.61168e7i | − 0.168614i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.47517e7i | 0.252461i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.59217e8 | −0.765534 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.54010e8 | −0.743737 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1.36521e8i | − 0.396320i | −0.980170 | − | 0.198160i | \(-0.936503\pi\) | ||||
0.980170 | − | 0.198160i | \(-0.0634966\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.66503e8i | 0.767072i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.52655e6 | −0.0157720 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.52724e8 | 2.41296 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.19437e8i | 0.335119i | 0.985862 | + | 0.167559i | \(0.0535886\pi\) | ||||
−0.985862 | + | 0.167559i | \(0.946411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1.38933e8i | − 0.386543i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.85739e7 | 0.134009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.97406e6 | 0.00813638 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3.13014e8i | − 0.849192i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 2.90874e8i | − 0.782561i | −0.920272 | − | 0.391280i | \(-0.872032\pi\) | ||||
0.920272 | − | 0.391280i | \(-0.127968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.42875e8 | −0.914807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.31516e7 | −0.246477 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.95506e8i | 0.775448i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.94298e7i | 0.232744i | 0.993206 | + | 0.116372i | \(0.0371265\pi\) | ||||
−0.993206 | + | 0.116372i | \(0.962873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.62992e8 | −1.95329 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.28445e8i | − 0.326141i | −0.986614 | − | 0.163071i | \(-0.947860\pi\) | ||||
0.986614 | − | 0.163071i | \(-0.0521398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 5.08471e7i | − 0.128057i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.16533e8 | −0.540907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.15451e8 | 1.77275 | 0.886373 | − | 0.462972i | \(-0.153217\pi\) | ||||
0.886373 | + | 0.462972i | \(0.153217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.28723e7i | 0.0562154i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.45246e8i | 0.841708i | 0.907128 | + | 0.420854i | \(0.138270\pi\) | ||||
−0.907128 | + | 0.420854i | \(0.861730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.80011e7 | 0.212823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.88451e7 | 0.189153 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.23477e8i | 0.293860i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.75422e8i | 0.414157i | 0.978324 | + | 0.207079i | \(0.0663956\pi\) | ||||
−0.978324 | + | 0.207079i | \(0.933604\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.99419e8 | 0.701286 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.35525e7 | 0.101198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.03668e8i | − 0.930544i | −0.885168 | − | 0.465272i | \(-0.845956\pi\) | ||||
0.885168 | − | 0.465272i | \(-0.154044\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.15737e7i | 0.0493400i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.80482e8 | 1.31715 | 0.658574 | − | 0.752516i | \(-0.271160\pi\) | ||||
0.658574 | + | 0.752516i | \(0.271160\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.78621e8 | −0.627250 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.73381e7i | 0.0834002i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 6.80851e7i | − 0.150892i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.90678e8 | 1.29889 | 0.649444 | − | 0.760409i | \(-0.275002\pi\) | ||||
0.649444 | + | 0.760409i | \(0.275002\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.29335e7 | 0.202772 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.10093e8i | 0.671357i | 0.941977 | + | 0.335679i | \(0.108966\pi\) | ||||
−0.941977 | + | 0.335679i | \(0.891034\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 2.32902e8i | − 0.500342i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.11843e8 | −1.09112 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.45100e8 | 0.306942 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.97017e8i | − 0.413571i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.35222e7i | 0.153156i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.14701e8 | −0.237115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.73439e8 | −1.17642 | −0.588210 | − | 0.808708i | \(-0.700167\pi\) | ||||
−0.588210 | + | 0.808708i | \(0.700167\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00368e8i | 0.611538i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.43890e8i | 1.30101i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.55824e7 | 0.0312474 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.99630e7 | 0.139241 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.24736e8i | 1.23402i | 0.786956 | + | 0.617009i | \(0.211656\pi\) | ||||
−0.786956 | + | 0.617009i | \(0.788344\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36187e8i | 0.266991i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.84341e8 | 0.358695 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.71876e8 | 0.331947 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.36489e7i | 0.0645034i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 2.71847e8i | − 0.517253i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.88696e8 | 1.86731 | 0.933657 | − | 0.358169i | \(-0.116599\pi\) | ||||
0.933657 | + | 0.358169i | \(0.116599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.02063e8 | −0.753757 | −0.376879 | − | 0.926263i | \(-0.623003\pi\) | ||||
−0.376879 | + | 0.926263i | \(0.623003\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.76997e8i | 0.701563i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.99389e7i | 0.110723i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.27096e8 | 0.783177 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.39284e7 | −0.0799638 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 6.26365e8i | − 1.13187i | −0.824448 | − | 0.565937i | \(-0.808514\pi\) | ||||
0.824448 | − | 0.565937i | \(-0.191486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.23953e8i | 1.47810i | 0.673652 | + | 0.739049i | \(0.264725\pi\) | ||||
−0.673652 | + | 0.739049i | \(0.735275\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.03441e8 | 0.184218 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.02093e7 | 0.0534102 | 0.0267051 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267051 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.17842e7i | 0.0382366i | 0.999817 | + | 0.0191183i | \(0.00608591\pi\) | ||||
−0.999817 | + | 0.0191183i | \(0.993914\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.98360e8i | 0.868440i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.25299e9 | −2.16777 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.60645e8 | 0.275936 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 5.79461e7i | − 0.0988208i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.51909e8i | 0.934505i | 0.884124 | + | 0.467252i | \(0.154756\pi\) | ||||
−0.884124 | + | 0.467252i | \(0.845244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.18104e8 | 0.366670 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.66118e8 | 0.611136 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.42081e7i | 0.156141i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.38010e8i | 1.37911i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.20807e8 | 0.197410 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.96774e8 | 0.319286 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.15243e8i | 0.669045i | 0.942388 | + | 0.334523i | \(0.108575\pi\) | ||||
−0.942388 | + | 0.334523i | \(0.891425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 2.09005e7i | − 0.0334395i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.44449e8 | 0.706121 | 0.353061 | − | 0.935600i | \(-0.385141\pi\) | ||||
0.353061 | + | 0.935600i | \(0.385141\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.67604e8 | −0.737733 | −0.368866 | − | 0.929482i | \(-0.620254\pi\) | ||||
−0.368866 | + | 0.929482i | \(0.620254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.78679e8i | 0.436610i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.95476e8i | 0.926472i | 0.886235 | + | 0.463236i | \(0.153312\pi\) | ||||
−0.886235 | + | 0.463236i | \(0.846688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.85952e7 | 0.0750835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.43830e8 | 0.834461 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 2.49192e8i | − 0.379730i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.69503e8i | 0.256521i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.07874e6 | 0.00913631 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.26917e8 | 0.487993 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.21425e8i | 1.06953i | 0.845001 | + | 0.534765i | \(0.179600\pi\) | ||||
−0.845001 | + | 0.534765i | \(0.820400\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1.79030e8i | − 0.263609i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.77300e8 | −0.990497 | −0.495248 | − | 0.868751i | \(-0.664923\pi\) | ||||
−0.495248 | + | 0.868751i | \(0.664923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.41700e8 | −1.22257 | −0.611287 | − | 0.791409i | \(-0.709348\pi\) | ||||
−0.611287 | + | 0.791409i | \(0.709348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.22157e7i | 0.0897573i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.23932e8i | 0.320882i | 0.987045 | + | 0.160441i | \(0.0512917\pi\) | ||||
−0.987045 | + | 0.160441i | \(0.948708\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.71191e9 | −2.43655 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.57363e7 | 0.0363842 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.62329e7i | − 0.107050i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.06972e8i | − 0.149212i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.68879e7 | 0.0233991 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.96910e8 | 0.408644 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1.72405e9i | − 2.35709i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.20277e8i | 1.11403i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.82214e8 | 0.245831 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.79727e8 | −0.910988 | −0.455494 | − | 0.890239i | \(-0.650537\pi\) | ||||
−0.455494 | + | 0.890239i | \(0.650537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.91076e8i | 0.520679i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.24099e8i | 1.22226i | 0.791530 | + | 0.611130i | \(0.209285\pi\) | ||||
−0.791530 | + | 0.611130i | \(0.790715\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.41417e8 | 0.185819 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.42390e7 | −0.0185873 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.54361e8i | 1.23767i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 3.27998e8i | − 0.422595i | −0.977422 | − | 0.211297i | \(-0.932231\pi\) | ||||
0.977422 | − | 0.211297i | \(-0.0677689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.59410e8 | −0.460056 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.54225e8 | −0.196133 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 9.43492e8i | − 1.19210i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1.57249e8i | − 0.197401i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.75671e8 | −1.09218 | −0.546090 | − | 0.837727i | \(-0.683884\pi\) | ||||
−0.546090 | + | 0.837727i | \(0.683884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.01381e8 | 0.869171 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.61412e8i | 0.814381i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.69698e7i | 0.0819303i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.46253e8 | −0.177782 | −0.0888908 | − | 0.996041i | \(-0.528332\pi\) | ||||
−0.0888908 | + | 0.996041i | \(0.528332\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.14775e8 | −0.380193 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.23237e8i | 1.10801i | 0.832513 | + | 0.554006i | \(0.186901\pi\) | ||||
−0.832513 | + | 0.554006i | \(0.813099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.07136e8i | − 0.127761i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.01414e7 | 0.0475660 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.29334e8 | −0.505529 | −0.252764 | − | 0.967528i | \(-0.581340\pi\) | ||||
−0.252764 | + | 0.967528i | \(0.581340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 1.34545e8i | − 0.157423i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.09733e7i | 0.105772i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.16653e8 | 1.05907 | 0.529537 | − | 0.848287i | \(-0.322366\pi\) | ||||
0.529537 | + | 0.848287i | \(0.322366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.38126e7 | 0.0273399 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.31870e8i | 0.150456i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.66845e7i | − 0.0302554i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.53496e8 | 0.736330 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.66291e7 | −0.0634104 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.15577e7i | 0.0462455i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.74117e9i | 1.92558i | 0.270247 | + | 0.962791i | \(0.412895\pi\) | ||||
−0.270247 | + | 0.962791i | \(0.587105\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.15039e8 | −0.566068 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.75119e8 | 0.628203 | 0.314102 | − | 0.949389i | \(-0.398297\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.24528e9i | − 2.43743i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 8.09741e7i | − 0.0873639i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.49329e8 | 0.160125 | 0.0800625 | − | 0.996790i | \(-0.474488\pi\) | ||||
0.0800625 | + | 0.996790i | \(0.474488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.30636e8 | 0.352373 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.27781e8i | − 0.135351i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 6.57661e8i | − 0.692376i | −0.938165 | − | 0.346188i | \(-0.887476\pi\) | ||||
0.938165 | − | 0.346188i | \(-0.112524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.39400e7 | −0.0459782 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.46412e8 | 0.152274 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 3.15349e8i | − 0.325989i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.37005e9i | 1.40771i | 0.710341 | + | 0.703857i | \(0.248541\pi\) | ||||
−0.710341 | + | 0.703857i | \(0.751459\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.08278e9 | 1.10584 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.24918e8 | 0.126810 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.05005e9i | − 1.05956i | −0.848135 | − | 0.529780i | \(-0.822274\pi\) | ||||
0.848135 | − | 0.529780i | \(-0.177726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 2.34742e8i | − 0.235447i |
(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 | 384.7.b.d.319.7 | yes | 8 | |
4.3 | odd | 2 | inner | 384.7.b.d.319.4 | yes | 8 | |
8.3 | odd | 2 | inner | 384.7.b.d.319.6 | yes | 8 | |
8.5 | even | 2 | inner | 384.7.b.d.319.1 | ✓ | 8 | |
16.3 | odd | 4 | 768.7.g.e.511.1 | 4 | |||
16.5 | even | 4 | 768.7.g.c.511.2 | 4 | |||
16.11 | odd | 4 | 768.7.g.c.511.3 | 4 | |||
16.13 | even | 4 | 768.7.g.e.511.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.d.319.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
384.7.b.d.319.4 | yes | 8 | 4.3 | odd | 2 | inner | |
384.7.b.d.319.6 | yes | 8 | 8.3 | odd | 2 | inner | |
384.7.b.d.319.7 | yes | 8 | 1.1 | even | 1 | trivial | |
768.7.g.c.511.2 | 4 | 16.5 | even | 4 | |||
768.7.g.c.511.3 | 4 | 16.11 | odd | 4 | |||
768.7.g.e.511.1 | 4 | 16.3 | odd | 4 | |||
768.7.g.e.511.4 | 4 | 16.13 | even | 4 |