Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,7,Mod(511,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.511");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.g (of order \(2\), degree \(1\), not 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: | \(176.681536220\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 511.4 | ||
Root | \(1.28078 + 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.511 |
Dual form | 768.7.g.e.511.1 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 15.5885i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.0000 | 0.160000 | 0.0800000 | − | 0.996795i | \(-0.474508\pi\) | ||||
0.0800000 | + | 0.996795i | \(0.474508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 529.850i | 1.54475i | 0.635165 | + | 0.772376i | \(0.280932\pi\) | ||||
−0.635165 | + | 0.772376i | \(0.719068\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −243.000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 435.847i | − 0.327458i | −0.986505 | − | 0.163729i | \(-0.947648\pi\) | ||||
0.986505 | − | 0.163729i | \(-0.0523523\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 341.182 | 0.155294 | 0.0776472 | − | 0.996981i | \(-0.475259\pi\) | ||||
0.0776472 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 4300.52i | − 0.626990i | −0.949590 | − | 0.313495i | \(-0.898500\pi\) | ||||
0.949590 | − | 0.313495i | \(-0.101500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8259.54 | −0.891863 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3175.32i | − 0.260978i | −0.991450 | − | 0.130489i | \(-0.958345\pi\) | ||||
0.991450 | − | 0.130489i | \(-0.0416547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15225.0 | −0.974400 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3788.00i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −19409.3 | −0.795821 | −0.397910 | − | 0.917424i | \(-0.630264\pi\) | ||||
−0.397910 | + | 0.917424i | \(0.630264\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | 10597.0i | 0.247160i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −61969.9 | −1.22342 | −0.611710 | − | 0.791082i | \(-0.709518\pi\) | ||||
−0.611710 | + | 0.791082i | \(0.709518\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5318.50i | 0.0896592i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33740.2 | 0.489549 | 0.244774 | − | 0.969580i | \(-0.421286\pi\) | ||||
0.244774 | + | 0.969580i | \(0.421286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 99312.6i | 1.24911i | 0.780983 | + | 0.624553i | \(0.214719\pi\) | ||||
−0.780983 | + | 0.624553i | \(0.785281\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4860.00 | −0.0533333 | ||||||||
\(46\) | 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.i | 0.902834i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −224406. | −1.50733 | −0.753664 | − | 0.657260i | \(-0.771715\pi\) | ||||
−0.753664 | + | 0.657260i | \(0.771715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 8716.94i | − 0.0523933i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 67038.5 | 0.361993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 199557.i | − 0.971651i | −0.874056 | − | 0.485826i | \(-0.838519\pi\) | ||||
0.874056 | − | 0.485826i | \(-0.161481\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −45671.7 | −0.201214 | −0.100607 | − | 0.994926i | \(-0.532078\pi\) | ||||
−0.100607 | + | 0.994926i | \(0.532078\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 128754.i | − 0.514917i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6823.63 | 0.0248471 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 496811.i | − 1.65183i | −0.563791 | − | 0.825917i | \(-0.690658\pi\) | ||||
0.563791 | − | 0.825917i | \(-0.309342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 49498.3 | 0.150676 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 452032.i | 1.26297i | 0.775387 | + | 0.631487i | \(0.217555\pi\) | ||||
−0.775387 | + | 0.631487i | \(0.782445\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −394349. | −1.01371 | −0.506853 | − | 0.862032i | \(-0.669191\pi\) | ||||
−0.506853 | + | 0.862032i | \(0.669191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 237334.i | − 0.562570i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 230933. | 0.505842 | ||||||||
\(78\) | 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.i | 0.567458i | 0.958904 | + | 0.283729i | \(0.0915717\pi\) | ||||
−0.958904 | + | 0.283729i | \(0.908428\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 153655. | 0.250201 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 302561.i | − 0.459467i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −758607. | −1.07609 | −0.538043 | − | 0.842918i | \(-0.680836\pi\) | ||||
−0.538043 | + | 0.842918i | \(0.680836\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 180775.i | 0.239891i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 238462. | 0.296462 | ||||||||
\(94\) | 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.i | 0.109153i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.60937e6 | 1.56204 | 0.781018 | − | 0.624508i | \(-0.214700\pi\) | ||||
0.781018 | + | 0.624508i | \(0.214700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 647116.i | 0.592203i | 0.955156 | + | 0.296101i | \(0.0956867\pi\) | ||||
−0.955156 | + | 0.296101i | \(0.904313\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −165191. | −0.142698 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 233041.i | 0.190231i | 0.995466 | + | 0.0951156i | \(0.0303221\pi\) | ||||
−0.995466 | + | 0.0951156i | \(0.969678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 525849. | 0.406052 | 0.203026 | − | 0.979173i | \(-0.434922\pi\) | ||||
0.203026 | + | 0.979173i | \(0.434922\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − 63506.4i | − 0.0417565i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −82907.1 | −0.0517648 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.07069e6i | 2.41561i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.58160e6 | 0.892771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 525957.i | 0.282641i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −617000. | −0.315904 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | − 1.80119e6i | − 0.801209i | −0.916251 | − | 0.400604i | \(-0.868800\pi\) | ||||
0.916251 | − | 0.400604i | \(-0.131200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.27863e6 | 0.968544 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 75759.9i | − 0.0307920i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −50362.3 | −0.0195859 | −0.00979295 | − | 0.999952i | \(-0.503117\pi\) | ||||
−0.00979295 | + | 0.999952i | \(0.503117\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.23758e6i | − 1.57788i | −0.614471 | − | 0.788940i | \(-0.710630\pi\) | ||||
0.614471 | − | 0.788940i | \(-0.289370\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −276328. | −0.0985751 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 148703.i | − 0.0508524i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −388185. | −0.127331 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.54235e6i | − 0.800357i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.40006e6 | −1.33015 | −0.665073 | − | 0.746778i | \(-0.731600\pi\) | ||||
−0.665073 | + | 0.746778i | \(0.731600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.17763e6i | 0.632488i | 0.948678 | + | 0.316244i | \(0.102422\pi\) | ||||
−0.948678 | + | 0.316244i | \(0.897578\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.86690e6 | −0.521252 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 305946.i | − 0.0821580i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.73506e6 | −1.48197 | −0.740985 | − | 0.671522i | \(-0.765641\pi\) | ||||
−0.740985 | + | 0.671522i | \(0.765641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 3.49815e6i | − 0.870256i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.68244e6 | 0.403147 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.99695e6i | 0.692016i | 0.938232 | + | 0.346008i | \(0.112463\pi\) | ||||
−0.938232 | + | 0.346008i | \(0.887537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 135884. | 0.0302493 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.03225e6i | 1.72460i | 0.506400 | + | 0.862298i | \(0.330976\pi\) | ||||
−0.506400 | + | 0.862298i | \(0.669024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.71040e6 | −0.975884 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.04503e6i | 0.208997i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.42976e6 | 0.469272 | 0.234636 | − | 0.972083i | \(-0.424610\pi\) | ||||
0.234636 | + | 0.972083i | \(0.424610\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 8.06697e6i | − 1.50521i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.11078e6 | 0.560983 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 5.34862e6i | − 0.932573i | −0.884634 | − | 0.466286i | \(-0.845592\pi\) | ||||
0.884634 | − | 0.466286i | \(-0.154408\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.11072e6 | −1.53645 | −0.768223 | − | 0.640183i | \(-0.778859\pi\) | ||||
−0.768223 | + | 0.640183i | \(0.778859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 711952.i | − 0.116171i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.23940e6 | −0.195747 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.34849e6i | − 0.512064i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.00707e6 | 0.297288 | ||||||||
\(190\) | 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.i | 0.0143455i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.19700e6 | 0.287364 | 0.143682 | − | 0.989624i | \(-0.454106\pi\) | ||||
0.143682 | + | 0.989624i | \(0.454106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.24588e6i | 0.792564i | 0.918129 | + | 0.396282i | \(0.129700\pi\) | ||||
−0.918129 | + | 0.396282i | \(0.870300\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.74451e6 | 0.953687 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.02840e7i | − 1.22935i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 674804. | 0.0783278 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 771603.i | 0.0869927i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.87437e6 | −0.205313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1.11658e7i | − 1.18862i | −0.804235 | − | 0.594311i | \(-0.797425\pi\) | ||||
0.804235 | − | 0.594311i | \(-0.202575\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.04648e6 | −0.729178 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.98625e6i | 0.199857i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.10528e6 | 0.793211 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 6.14730e6i | − 0.585264i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.62121e6 | 0.242842 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | − 1.04595e7i | − 0.894198i | −0.894484 | − | 0.447099i | \(-0.852457\pi\) | ||||
0.894484 | − | 0.447099i | \(-0.147543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.94802e7 | 1.62214 | 0.811069 | − | 0.584951i | \(-0.198886\pi\) | ||||
0.811069 | + | 0.584951i | \(0.198886\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.59990e6i | 0.292048i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.62947e7 | 1.28819 | 0.644095 | − | 0.764946i | \(-0.277234\pi\) | ||||
0.644095 | + | 0.764946i | \(0.277234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 354529.i | 0.0273179i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.91257e6 | 0.669511 | ||||||||
\(238\) | 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.i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.26184e6 | −0.221802 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.46726e6i | − 0.0973680i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.05791e6 | −0.327622 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1.92078e7i | − 1.21466i | −0.794449 | − | 0.607331i | \(-0.792240\pi\) | ||||
0.794449 | − | 0.607331i | \(-0.207760\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.38395e6 | −0.0854594 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | − 3.28348e7i | − 1.88988i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.71645e6 | 0.265274 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.92686e7i | − 1.05921i | −0.848243 | − | 0.529607i | \(-0.822339\pi\) | ||||
0.848243 | − | 0.529607i | \(-0.177661\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.48813e6 | −0.241172 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.18255e7i | − 0.621278i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.74390e7 | 0.895909 | 0.447955 | − | 0.894056i | \(-0.352153\pi\) | ||||
0.447955 | + | 0.894056i | \(0.352153\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 6.63577e6i | 0.319075i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.19698e7 | 1.50418 | 0.752091 | − | 0.659059i | \(-0.229045\pi\) | ||||
0.752091 | + | 0.659059i | \(0.229045\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.71725e6i | 0.171163i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.34865e7 | −1.05852 | −0.529259 | − | 0.848460i | \(-0.677530\pi\) | ||||
−0.529259 | + | 0.848460i | \(0.677530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7.74978e6i | − 0.341924i | −0.985278 | − | 0.170962i | \(-0.945312\pi\) | ||||
0.985278 | − | 0.170962i | \(-0.0546876\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.34077e6 | 0.0579189 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.78772e7i | 0.756231i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.48867e7 | 1.44533 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 389951.i | 0.0158246i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.14848e7 | −0.456584 | −0.228292 | − | 0.973593i | \(-0.573314\pi\) | ||||
−0.228292 | + | 0.973593i | \(0.573314\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 3.99114e6i | − 0.155464i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.65099e6 | −0.0630194 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 1.08336e6i | − 0.0405284i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.26208e7 | −1.92956 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.50876e7i | 0.901842i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −913434. | −0.0321942 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.30562e7i | − 0.796841i | −0.917203 | − | 0.398421i | \(-0.869558\pi\) | ||||
0.917203 | − | 0.398421i | \(-0.130442\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00875e7 | −0.341909 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 4.24296e7i | − 1.41055i | −0.708935 | − | 0.705274i | \(-0.750824\pi\) | ||||
0.708935 | − | 0.705274i | \(-0.249176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.01928e7 | 0.658513 | 0.329257 | − | 0.944240i | \(-0.393202\pi\) | ||||
0.329257 | + | 0.944240i | \(0.393202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.57507e6i | − 0.0823868i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.83594e6 | −0.183203 | −0.0916016 | − | 0.995796i | \(-0.529199\pi\) | ||||
−0.0916016 | + | 0.995796i | \(0.529199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.45947e6i | 0.260598i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.63276e6 | −0.109830 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.30398e7i | − 0.980458i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.19449e6 | −0.151319 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.19718e6i | 0.234434i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.39235e6 | −0.263746 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 6.94601e7i | − 1.91536i | −0.287828 | − | 0.957682i | \(-0.592933\pi\) | ||||
0.287828 | − | 0.957682i | \(-0.407067\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.50587e7 | 0.407807 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 1.89436e7i | − 0.486254i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.66729e6 | −0.168146 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.40780e7i | − 0.596676i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 989967. | 0.0241081 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 5.53620e7i | − 1.32502i | −0.749052 | − | 0.662511i | \(-0.769491\pi\) | ||||
0.749052 | − | 0.662511i | \(-0.230509\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.23047e7 | −0.995206 | −0.497603 | − | 0.867405i | \(-0.665786\pi\) | ||||
−0.497603 | + | 0.867405i | \(0.665786\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 9.04064e6i | 0.202076i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.34558e7 | −1.39466 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 6.79965e7i | − 1.46961i | −0.678276 | − | 0.734807i | \(-0.737273\pi\) | ||||
0.678276 | − | 0.734807i | \(-0.262727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.85514e7 | 0.606884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.46547e7i | 0.515442i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.88698e6 | −0.162193 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | − 1.18902e8i | − 2.32845i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.70643e7 | 1.09961 | 0.549804 | − | 0.835293i | \(-0.314702\pi\) | ||||
0.549804 | + | 0.835293i | \(0.314702\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 9.61808e6i | − 0.182387i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.62209e6 | −0.123586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 5.18779e7i | − 0.952939i | −0.879191 | − | 0.476469i | \(-0.841916\pi\) | ||||
0.879191 | − | 0.476469i | \(-0.158084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.03653e7 | 0.910661 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | − 2.41330e7i | − 0.416369i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.23410e7 | −1.56872 | −0.784361 | − | 0.620305i | \(-0.787009\pi\) | ||||
−0.784361 | + | 0.620305i | \(0.787009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.43951e7i | − 0.408106i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.80778e7 | 0.462578 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.14348e7i | − 0.185540i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.75593e7 | −0.600270 | −0.300135 | − | 0.953897i | \(-0.597032\pi\) | ||||
−0.300135 | + | 0.953897i | \(0.597032\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 5.21916e6i | − 0.0797417i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.18098e6 | 0.0177778 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.70094e7i | 0.400619i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.07783e8 | −1.57536 | −0.787681 | − | 0.616083i | \(-0.788719\pi\) | ||||
−0.787681 | + | 0.616083i | \(0.788719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 785070.i | − 0.0113079i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.05735e8 | 1.50096 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.48931e6i | 0.0907933i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.60574e7 | 0.910989 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.92976e7i | 1.07800i | 0.842306 | + | 0.538999i | \(0.181197\pi\) | ||||
−0.842306 | + | 0.538999i | \(0.818803\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.67669e7 | 0.894777 | 0.447389 | − | 0.894340i | \(-0.352354\pi\) | ||||
0.447389 | + | 0.894340i | \(0.352354\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 4.30752e6i | − 0.0569123i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.16970e8 | −1.52372 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.41992e7i | − 0.310826i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.31805e6 | 0.0293596 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | − 6.05121e6i | − 0.0735148i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.36555e7 | −0.163631 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 7.14885e7i | − 0.844972i | −0.906369 | − | 0.422486i | \(-0.861158\pi\) | ||||
0.906369 | − | 0.422486i | \(-0.138842\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.96314e7 | 0.462087 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.60820e7i | 0.875127i | 0.899188 | + | 0.437563i | \(0.144158\pi\) | ||||
−0.899188 | + | 0.437563i | \(0.855842\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.51721e7 | −0.172174 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 1.47056e7i | − 0.160307i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.39458e7 | −0.365167 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.61550e6i | 0.0383826i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.59392e7 | 0.376548 | 0.188274 | − | 0.982117i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982117i | \(0.439711\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.91021e7i | − 0.300945i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.09802e8 | 1.12075 | 0.560373 | − | 0.828240i | \(-0.310658\pi\) | ||||
0.560373 | + | 0.828240i | \(0.310658\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | − 5.38248e7i | − 0.528484i | −0.964456 | − | 0.264242i | \(-0.914878\pi\) | ||||
0.964456 | − | 0.264242i | \(-0.0851217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.63235e8 | 2.55168 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 8.94008e7i | − 0.855615i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.32851e7 | 0.409030 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.54755e7i | 0.610939i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.45307e7 | 0.502442 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 2.62267e7i | 0.232757i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 500308. | 0.00438543 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.72463e7i | 0.495634i | 0.968807 | + | 0.247817i | \(0.0797131\pi\) | ||||
−0.968807 | + | 0.247817i | \(0.920287\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.67178e7 | −0.399536 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 2.13055e8i | − 1.79989i | −0.436001 | − | 0.899946i | \(-0.643605\pi\) | ||||
0.436001 | − | 0.899946i | \(-0.356395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.49116e8 | −1.24447 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.11822e6i | 0.0174644i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.39509e8 | −1.95098 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 9.04068e7i | − 0.727611i | −0.931475 | − | 0.363806i | \(-0.881477\pi\) | ||||
0.931475 | − | 0.363806i | \(-0.118523\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.25210e8 | −0.995697 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.29271e8i | 1.80155i | 0.434290 | + | 0.900773i | \(0.356999\pi\) | ||||
−0.434290 | + | 0.900773i | \(0.643001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.21874e7 | 0.249926 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 7.34279e7i | − 0.563427i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.29225e7 | 0.0979930 | 0.0489965 | − | 0.998799i | \(-0.484398\pi\) | ||||
0.0489965 | + | 0.998799i | \(0.484398\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 2.08946e8i | − 1.56593i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.62904e7 | −0.120664 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.29423e7i | 0.0947525i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.72601e6 | 0.0559092 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.78762e7i | 0.270934i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.99955e7 | 0.565656 | 0.282828 | − | 0.959171i | \(-0.408727\pi\) | ||||
0.282828 | + | 0.959171i | \(0.408727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.28458e8i | 0.897957i | 0.893543 | + | 0.448979i | \(0.148212\pi\) | ||||
−0.893543 | + | 0.448979i | \(0.851788\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.25752e8 | 0.869031 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.17525e8i | − 0.802969i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.37953e8 | 0.931890 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.84923e7i | 0.323884i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.15115e7 | 0.0760241 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.66083e6i | 0.0304370i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.33768e7 | 0.538421 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.10832e7i | 0.453942i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.90048e8 | −1.83180 | −0.915899 | − | 0.401410i | \(-0.868520\pi\) | ||||
−0.915899 | + | 0.401410i | \(0.868520\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 1.42022e8i | − 0.887067i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.05170e7 | 0.0649684 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 2.91198e7i | − 0.177921i | −0.996035 | − | 0.0889604i | \(-0.971646\pi\) | ||||
0.996035 | − | 0.0889604i | \(-0.0283545\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.10982e7 | 0.0670713 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.34700e7i | 0.498972i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.02937e8 | 1.79134 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 1.93203e7i | − 0.113015i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.95014e8 | −1.12849 | −0.564247 | − | 0.825606i | \(-0.690834\pi\) | ||||
−0.564247 | + | 0.825606i | \(0.690834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.38836e7i | 0.193979i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.21978e7 | 0.295640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.06065e8i | 1.71510i | 0.514404 | + | 0.857548i | \(0.328013\pi\) | ||||
−0.514404 | + | 0.857548i | \(0.671987\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.43046e7 | −0.134755 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.12871e7i | 0.171639i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.27388e8 | −1.77716 | −0.888578 | − | 0.458725i | \(-0.848306\pi\) | ||||
−0.888578 | + | 0.458725i | \(0.848306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.37293e8i | 0.737461i | 0.929536 | + | 0.368731i | \(0.120208\pi\) | ||||
−0.929536 | + | 0.368731i | \(0.879792\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.85601e7 | 0.0986544 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 3.23910e7i | 0.166874i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.71918e8 | −0.876583 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.78068e7i | 0.493587i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.65814e6 | −0.00828236 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.11468e8i | 1.53992i | 0.638090 | + | 0.769962i | \(0.279725\pi\) | ||||
−0.638090 | + | 0.769962i | \(0.720275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.57865e7 | −0.321952 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 8.14139e7i | 0.386498i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.73636e7 | −0.457587 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.08861e8i | 0.971800i | 0.874014 | + | 0.485900i | \(0.161508\pi\) | ||||
−0.874014 | + | 0.485900i | \(0.838492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.88006e7 | 0.132672 | 0.0663359 | − | 0.997797i | \(-0.478869\pi\) | ||||
0.0663359 | + | 0.997797i | \(0.478869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.20725e8i | 0.550611i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.16320e7 | 0.142843 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | 6.04793e6i | 0.0265145i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.53775e8 | 1.53584 | 0.767919 | − | 0.640548i | \(-0.221293\pi\) | ||||
0.767919 | + | 0.640548i | \(0.221293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.05191e7i | 0.0452226i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.88929e8 | −0.804348 | −0.402174 | − | 0.915563i | \(-0.631745\pi\) | ||||
−0.402174 | + | 0.915563i | \(0.631745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 8.45244e7i | − 0.356377i | −0.983996 | − | 0.178189i | \(-0.942976\pi\) | ||||
0.983996 | − | 0.178189i | \(-0.0570237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.20281e7 | −0.0502253 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 4.01948e8i | − 1.66229i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.25551e8 | 0.923855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.92185e7i | − 0.118538i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.76098e8 | −1.91313 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.49408e8i | 1.39074i | 0.718653 | + | 0.695369i | \(0.244759\pi\) | ||||
−0.718653 | + | 0.695369i | \(0.755241\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.74058e8 | 0.686251 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 6.46187e7i | − 0.252370i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.56440e7 | −0.215278 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 4.94695e8i | 1.86082i | 0.366518 | + | 0.930411i | \(0.380550\pi\) | ||||
−0.366518 | + | 0.930411i | \(0.619450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.09626e7 | −0.115387 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.19819e7i | 0.0442396i | 0.999755 | + | 0.0221198i | \(0.00704153\pi\) | ||||
−0.999755 | + | 0.0221198i | \(0.992958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.69762e7 | −0.318175 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.26349e8i | 0.457961i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.21595e8 | 1.87324 | 0.936621 | − | 0.350345i | \(-0.113936\pi\) | ||||
0.936621 | + | 0.350345i | \(0.113936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 3.60238e7i | − 0.128193i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.58269e7 | 0.337902 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 4.10833e8i | − 1.43552i | −0.696292 | − | 0.717759i | \(-0.745168\pi\) | ||||
0.696292 | − | 0.717759i | \(-0.254832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.48526e7 | −0.293806 | −0.146903 | − | 0.989151i | \(-0.546931\pi\) | ||||
−0.146903 | + | 0.989151i | \(0.546931\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.08605e7i | 0.140205i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.55727e7 | 0.154967 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.16306e7i | 0.207692i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.02705e7 | 0.0343016 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 5.76722e7i | 0.187523i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.04369e8 | 1.30320 | 0.651602 | − | 0.758561i | \(-0.274097\pi\) | ||||
0.651602 | + | 0.758561i | \(0.274097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.32544e7i | 0.0423400i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.63048e8 | 0.516266 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.05590e8i | 0.645268i | 0.946524 | + | 0.322634i | \(0.104568\pi\) | ||||
−0.946524 | + | 0.322634i | \(0.895432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00725e6 | −0.00313374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.03667e8i | 0.936542i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.65633e7 | −0.234079 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.25719e8i | 0.381037i | 0.981684 | + | 0.190518i | \(0.0610169\pi\) | ||||
−0.981684 | + | 0.190518i | \(0.938983\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.61168e7 | −0.168614 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 8.47517e7i | − 0.252461i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.59217e8 | 0.765534 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.54010e8i | 0.743737i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.36521e8 | 0.396320 | 0.198160 | − | 0.980170i | \(-0.436503\pi\) | ||||
0.198160 | + | 0.980170i | \(0.436503\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.66503e8i | 0.767072i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.52655e6 | −0.0157720 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.52724e8i | 2.41296i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.19437e8 | 0.335119 | 0.167559 | − | 0.985862i | \(-0.446411\pi\) | ||||
0.167559 | + | 0.985862i | \(0.446411\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.38933e8i | 0.386543i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.85739e7 | −0.134009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.97406e6i | − 0.00813638i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.13014e8 | 0.849192 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | − 9.31516e7i | − 0.246477i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.95506e8 | 0.775448 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.94298e7i | − 0.232744i | −0.993206 | − | 0.116372i | \(-0.962873\pi\) | ||||
0.993206 | − | 0.116372i | \(-0.0371265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.43489e7 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.62992e8i | 1.95329i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.28445e8 | 0.326141 | 0.163071 | − | 0.986614i | \(-0.447860\pi\) | ||||
0.163071 | + | 0.986614i | \(0.447860\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 5.08471e7i | − 0.128057i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.16533e8 | −0.540907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.15451e8i | 1.77275i | 0.462972 | + | 0.886373i | \(0.346783\pi\) | ||||
−0.462972 | + | 0.886373i | \(0.653217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.28723e7 | 0.0562154 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 3.45246e8i | − 0.841708i | −0.907128 | − | 0.420854i | \(-0.861730\pi\) | ||||
0.907128 | − | 0.420854i | \(-0.138270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.80011e7 | −0.212823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 7.88451e7i | − 0.189153i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.23477e8 | −0.293860 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 4.35525e7i | 0.101198i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.03668e8 | −0.930544 | −0.465272 | − | 0.885168i | \(-0.654044\pi\) | ||||
−0.465272 | + | 0.885168i | \(0.654044\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 2.15737e7i | − 0.0493400i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.80482e8 | −1.31715 | −0.658574 | − | 0.752516i | \(-0.728840\pi\) | ||||
−0.658574 | + | 0.752516i | \(0.728840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.78621e8i | 0.627250i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.73381e7 | −0.0834002 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 9.29335e7i | 0.202772i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.10093e8 | 0.671357 | 0.335679 | − | 0.941977i | \(-0.391034\pi\) | ||||
0.335679 | + | 0.941977i | \(0.391034\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.32902e8i | 0.500342i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.11843e8 | 1.09112 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.45100e8i | − 0.306942i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.97017e8 | 0.413571 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.35222e7i | 0.153156i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.14701e8 | −0.237115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.73439e8i | − 1.17642i | −0.808708 | − | 0.588210i | \(-0.799833\pi\) | ||||
0.808708 | − | 0.588210i | \(-0.200167\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00368e8 | 0.611538 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 6.43890e8i | − 1.30101i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.55824e7 | −0.0312474 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 6.99630e7i | − 0.139241i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.24736e8 | −1.23402 | −0.617009 | − | 0.786956i | \(-0.711656\pi\) | ||||
−0.617009 | + | 0.786956i | \(0.711656\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36187e8i | 0.266991i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.84341e8 | 0.358695 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.71876e8i | 0.331947i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.36489e7 | 0.0645034 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.71847e8i | 0.517253i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.88696e8 | −1.86731 | −0.933657 | − | 0.358169i | \(-0.883401\pi\) | ||||
−0.933657 | + | 0.358169i | \(0.883401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.02063e8i | 0.753757i | 0.926263 | + | 0.376879i | \(0.123003\pi\) | ||||
−0.926263 | + | 0.376879i | \(0.876997\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.76997e8 | −0.701563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.99389e7i | 0.110723i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.27096e8 | 0.783177 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 4.39284e7i | − 0.0799638i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.26365e8 | −1.13187 | −0.565937 | − | 0.824448i | \(-0.691486\pi\) | ||||
−0.565937 | + | 0.824448i | \(0.691486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.23953e8i | − 1.47810i | −0.673652 | − | 0.739049i | \(-0.735275\pi\) | ||||
0.673652 | − | 0.739049i | \(-0.264725\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.03441e8 | −0.184218 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.02093e7i | − 0.0534102i | −0.999643 | − | 0.0267051i | \(-0.991498\pi\) | ||||
0.999643 | − | 0.0267051i | \(-0.00850150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.17842e7 | −0.0382366 | −0.0191183 | − | 0.999817i | \(-0.506086\pi\) | ||||
−0.0191183 | + | 0.999817i | \(0.506086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.98360e8i | 0.868440i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.25299e9 | −2.16777 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.60645e8i | 0.275936i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.79461e7 | −0.0988208 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 5.51909e8i | − 0.934505i | −0.884124 | − | 0.467252i | \(-0.845244\pi\) | ||||
0.884124 | − | 0.467252i | \(-0.154756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.18104e8 | −0.366670 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 3.66118e8i | − 0.611136i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.42081e7 | −0.156141 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.38010e8i | 1.37911i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.20807e8 | 0.197410 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.96774e8i | 0.319286i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.15243e8 | 0.669045 | 0.334523 | − | 0.942388i | \(-0.391425\pi\) | ||||
0.334523 | + | 0.942388i | \(0.391425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.09005e7i | 0.0334395i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.44449e8 | −0.706121 | −0.353061 | − | 0.935600i | \(-0.614859\pi\) | ||||
−0.353061 | + | 0.935600i | \(0.614859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.67604e8i | 0.737733i | 0.929482 | + | 0.368866i | \(0.120254\pi\) | ||||
−0.929482 | + | 0.368866i | \(0.879746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.78679e8 | −0.436610 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 5.43830e8i | 0.834461i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.49192e8 | −0.379730 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.69503e8i | − 0.256521i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.07874e6 | −0.00913631 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.26917e8i | − 0.487993i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.21425e8 | −1.06953 | −0.534765 | − | 0.845001i | \(-0.679600\pi\) | ||||
−0.534765 | + | 0.845001i | \(0.679600\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 8.41700e8i | − 1.22257i | −0.791409 | − | 0.611287i | \(-0.790652\pi\) | ||||
0.791409 | − | 0.611287i | \(-0.209348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.22157e7 | 0.0897573 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 2.23932e8i | − 0.320882i | −0.987045 | − | 0.160441i | \(-0.948708\pi\) | ||||
0.987045 | − | 0.160441i | \(-0.0512917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.71191e9 | 2.43655 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 2.57363e7i | − 0.0363842i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.62329e7 | 0.107050 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.06972e8i | − 0.149212i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.68879e7 | 0.0233991 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.96910e8i | 0.408644i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.72405e9 | −2.35709 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 8.20277e8i | − 1.11403i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.82214e8 | −0.245831 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.79727e8i | 0.910988i | 0.890239 | + | 0.455494i | \(0.150537\pi\) | ||||
−0.890239 | + | 0.455494i | \(0.849463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.91076e8 | −0.520679 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | − 1.42390e7i | − 0.0185873i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.54361e8 | 1.23767 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.27998e8i | 0.422595i | 0.977422 | + | 0.211297i | \(0.0677689\pi\) | ||||
−0.977422 | + | 0.211297i | \(0.932231\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.59410e8 | 0.460056 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.54225e8i | 0.196133i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.43492e8 | 1.19210 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 7.01381e8i | 0.869171i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.61412e8 | 0.814381 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 6.69698e7i | − 0.0819303i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.46253e8 | 0.177782 | 0.0888908 | − | 0.996041i | \(-0.471668\pi\) | ||||
0.0888908 | + | 0.996041i | \(0.471668\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.14775e8i | 0.380193i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.23237e8 | −1.10801 | −0.554006 | − | 0.832513i | \(-0.686901\pi\) | ||||
−0.554006 | + | 0.832513i | \(0.686901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.07136e8i | − 0.127761i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.01414e7 | 0.0475660 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4.29334e8i | − 0.505529i | −0.967528 | − | 0.252764i | \(-0.918660\pi\) | ||||
0.967528 | − | 0.252764i | \(-0.0813397\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.34545e8 | −0.157423 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 9.09733e7i | − 0.105772i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.16653e8 | −1.05907 | −0.529537 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529537 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 2.38126e7i | − 0.0273399i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.31870e8 | −0.150456 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 2.66845e7i | − 0.0302554i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.53496e8 | 0.736330 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 5.66291e7i | − 0.0634104i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.15577e7 | 0.0462455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.74117e9i | − 1.92558i | −0.270247 | − | 0.962791i | \(-0.587105\pi\) | ||||
0.270247 | − | 0.962791i | \(-0.412895\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.15039e8 | 0.566068 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 5.75119e8i | − 0.628203i | −0.949389 | − | 0.314102i | \(-0.898297\pi\) | ||||
0.949389 | − | 0.314102i | \(-0.101703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.24528e9 | 2.43743 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | 3.30636e8i | 0.352373i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.27781e8 | −0.135351 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.57661e8i | 0.692376i | 0.938165 | + | 0.346188i | \(0.112524\pi\) | ||||
−0.938165 | + | 0.346188i | \(0.887476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.39400e7 | 0.0459782 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.46412e8i | − 0.152274i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.15349e8 | 0.325989 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | 1.24918e8i | 0.126810i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.05005e9 | −1.05956 | −0.529780 | − | 0.848135i | \(-0.677726\pi\) | ||||
−0.529780 | + | 0.848135i | \(0.677726\pi\) | |||||||
\(998\) | 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 | 768.7.g.e.511.4 | 4 | ||
4.3 | odd | 2 | inner | 768.7.g.e.511.1 | 4 | ||
8.3 | odd | 2 | 768.7.g.c.511.3 | 4 | |||
8.5 | even | 2 | 768.7.g.c.511.2 | 4 | |||
16.3 | odd | 4 | 384.7.b.d.319.6 | yes | 8 | ||
16.5 | even | 4 | 384.7.b.d.319.7 | yes | 8 | ||
16.11 | odd | 4 | 384.7.b.d.319.4 | yes | 8 | ||
16.13 | even | 4 | 384.7.b.d.319.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.d.319.1 | ✓ | 8 | 16.13 | even | 4 | ||
384.7.b.d.319.4 | yes | 8 | 16.11 | odd | 4 | ||
384.7.b.d.319.6 | yes | 8 | 16.3 | odd | 4 | ||
384.7.b.d.319.7 | yes | 8 | 16.5 | even | 4 | ||
768.7.g.c.511.2 | 4 | 8.5 | even | 2 | |||
768.7.g.c.511.3 | 4 | 8.3 | odd | 2 | |||
768.7.g.e.511.1 | 4 | 4.3 | odd | 2 | inner | ||
768.7.g.e.511.4 | 4 | 1.1 | even | 1 | trivial |