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: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 106x^{6} - 304x^{5} + 4359x^{4} - 8216x^{3} + 73366x^{2} - 69308x + 604693 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.1 | ||
Root | \(-1.23205 + 6.41320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.7.b.c.319.4 |
$q$-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 | ||||||||
\(5\) | − 195.235i | − 1.56188i | −0.624606 | − | 0.780940i | \(-0.714740\pi\) | ||||
0.624606 | − | 0.780940i | \(-0.285260\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 277.510i | 0.809067i | 0.914523 | + | 0.404533i | \(0.132566\pi\) | ||||
−0.914523 | + | 0.404533i | \(0.867434\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1753.29 | 1.31727 | 0.658636 | − | 0.752462i | \(-0.271134\pi\) | ||||
0.658636 | + | 0.752462i | \(0.271134\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1246.75i | − 0.567478i | −0.958902 | − | 0.283739i | \(-0.908425\pi\) | ||||
0.958902 | − | 0.283739i | \(-0.0915749\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3043.41i | 0.901752i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6888.35 | 1.40207 | 0.701033 | − | 0.713128i | \(-0.252722\pi\) | ||||
0.701033 | + | 0.713128i | \(0.252722\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4401.67 | −0.641737 | −0.320869 | − | 0.947124i | \(-0.603975\pi\) | ||||
−0.320869 | + | 0.947124i | \(0.603975\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 4325.95i | − 0.467115i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12728.7i | 1.04616i | 0.852283 | + | 0.523082i | \(0.175218\pi\) | ||||
−0.852283 | + | 0.523082i | \(0.824782\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −22491.7 | −1.43947 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8278.44i | − 0.339433i | −0.985493 | − | 0.169717i | \(-0.945715\pi\) | ||||
0.985493 | − | 0.169717i | \(-0.0542852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 43940.1i | 1.47495i | 0.675376 | + | 0.737474i | \(0.263981\pi\) | ||||
−0.675376 | + | 0.737474i | \(0.736019\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −27331.1 | −0.760527 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 54179.6 | 1.26367 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12186.4i | 0.240585i | 0.992738 | + | 0.120293i | \(0.0383833\pi\) | ||||
−0.992738 | + | 0.120293i | \(0.961617\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19434.9i | 0.327633i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −54739.6 | −0.794238 | −0.397119 | − | 0.917767i | \(-0.629990\pi\) | ||||
−0.397119 | + | 0.917767i | \(0.629990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −45453.4 | −0.571691 | −0.285845 | − | 0.958276i | \(-0.592274\pi\) | ||||
−0.285845 | + | 0.958276i | \(0.592274\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 47442.1i | − 0.520627i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 152336.i | 1.46727i | 0.679545 | + | 0.733634i | \(0.262177\pi\) | ||||
−0.679545 | + | 0.733634i | \(0.737823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40637.3 | 0.345411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −107379. | −0.809484 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 272550.i | 1.83071i | 0.402649 | + | 0.915354i | \(0.368089\pi\) | ||||
−0.402649 | + | 0.915354i | \(0.631911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 342303.i | − 2.05742i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 68615.3 | 0.370507 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 213175. | 1.03796 | 0.518978 | − | 0.854787i | \(-0.326313\pi\) | ||||
0.518978 | + | 0.854787i | \(0.326313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 83964.8i | − 0.369920i | −0.982746 | − | 0.184960i | \(-0.940784\pi\) | ||||
0.982746 | − | 0.184960i | \(-0.0592156\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 67434.9i | 0.269689i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −243409. | −0.886332 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 373099. | 1.24051 | 0.620254 | − | 0.784401i | \(-0.287030\pi\) | ||||
0.620254 | + | 0.784401i | \(0.287030\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 198420.i | − 0.604003i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 667812.i | − 1.86586i | −0.360057 | − | 0.932930i | \(-0.617243\pi\) | ||||
0.360057 | − | 0.932930i | \(-0.382757\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −399457. | −1.02684 | −0.513419 | − | 0.858138i | \(-0.671621\pi\) | ||||
−0.513419 | + | 0.858138i | \(0.671621\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 350611. | 0.831078 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 486555.i | 1.06576i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 435376.i | − 0.883046i | −0.897250 | − | 0.441523i | \(-0.854438\pi\) | ||||
0.897250 | − | 0.441523i | \(-0.145562\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −246583. | −0.431250 | −0.215625 | − | 0.976476i | \(-0.569179\pi\) | ||||
−0.215625 | + | 0.976476i | \(0.569179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1.34485e6i | − 2.18986i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 129048.i | 0.195972i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 80967.5 | 0.114853 | 0.0574263 | − | 0.998350i | \(-0.481711\pi\) | ||||
0.0574263 | + | 0.998350i | \(0.481711\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 345985. | 0.459127 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 684959.i | − 0.851561i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 859361.i | 1.00232i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 877030. | 0.960947 | 0.480474 | − | 0.877009i | \(-0.340465\pi\) | ||||
0.480474 | + | 0.877009i | \(0.340465\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 426049. | 0.439091 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.80491e6i | 1.75183i | 0.482470 | + | 0.875913i | \(0.339740\pi\) | ||||
−0.482470 | + | 0.875913i | \(0.660260\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 826267.i | 0.756151i | 0.925775 | + | 0.378076i | \(0.123414\pi\) | ||||
−0.925775 | + | 0.378076i | \(0.876586\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −844577. | −0.729577 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.34587e6 | 1.09863 | 0.549314 | − | 0.835616i | \(-0.314889\pi\) | ||||
0.549314 | + | 0.835616i | \(0.314889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 704622.i | 0.544098i | 0.962283 | + | 0.272049i | \(0.0877012\pi\) | ||||
−0.962283 | + | 0.272049i | \(0.912299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 189967.i | − 0.138902i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.55273e6 | 1.76917 | 0.884583 | − | 0.466382i | \(-0.154443\pi\) | ||||
0.884583 | + | 0.466382i | \(0.154443\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.48508e6 | 1.63398 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 302960.i | − 0.189159i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.91159e6i | 1.13437i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.30246e6 | 0.735205 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 853307. | 0.458553 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.34062e6i | 0.686399i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 670190.i | 0.327180i | 0.986528 | + | 0.163590i | \(0.0523074\pi\) | ||||
−0.986528 | + | 0.163590i | \(0.947693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 708549. | 0.330066 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.73132e6 | 0.770128 | 0.385064 | − | 0.922890i | \(-0.374179\pi\) | ||||
0.385064 | + | 0.922890i | \(0.374179\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.22151e6i | − 0.519208i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 739549.i | 0.300584i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.77355e6 | −1.07863 | −0.539317 | − | 0.842103i | \(-0.681317\pi\) | ||||
−0.539317 | + | 0.842103i | \(0.681317\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.31042e6 | 1.60500 | 0.802500 | − | 0.596652i | \(-0.203503\pi\) | ||||
0.802500 | + | 0.596652i | \(0.203503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.37469e6i | − 0.847128i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 2.18591e6i | − 0.747522i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.61624e6 | −0.530154 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −633472. | −0.199423 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 213236.i | 0.0644616i | 0.999480 | + | 0.0322308i | \(0.0102612\pi\) | ||||
−0.999480 | + | 0.0322308i | \(0.989739\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.33710e6i | 1.55015i | 0.631868 | + | 0.775076i | \(0.282289\pi\) | ||||
−0.631868 | + | 0.775076i | \(0.717711\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.67387e6 | 0.467356 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.57866e6 | 2.30369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.08979e6i | 1.05682i | 0.848988 | + | 0.528412i | \(0.177212\pi\) | ||||
−0.848988 | + | 0.528412i | \(0.822788\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 4.24864e6i | − 1.05696i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.53233e6 | −0.846416 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.54126e6 | −0.355888 | −0.177944 | − | 0.984041i | \(-0.556945\pi\) | ||||
−0.177944 | + | 0.984041i | \(0.556945\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.33598e6i | 1.18785i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 7.66555e6i | − 1.64586i | −0.568140 | − | 0.822932i | \(-0.692337\pi\) | ||||
0.568140 | − | 0.822932i | \(-0.307663\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.27243e6 | 0.677969 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.06961e6 | −0.213912 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1.00380e7i | − 1.93870i | −0.245693 | − | 0.969348i | \(-0.579016\pi\) | ||||
0.245693 | − | 0.969348i | \(-0.420984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 6.24167e6i | − 1.16463i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.32306e6 | −0.599265 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.83296e6 | 1.54009 | 0.770047 | − | 0.637987i | \(-0.220233\pi\) | ||||
0.770047 | + | 0.637987i | \(0.220233\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.00091e6i | − 1.01200i | −0.862533 | − | 0.506001i | \(-0.831123\pi\) | ||||
0.862533 | − | 0.506001i | \(-0.168877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.30888e6i | 0.213573i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.37920e6 | 0.375765 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.20773e7 | 1.84690 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.05121e6i | − 0.155705i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 603085.i | 0.0865522i | 0.999063 | + | 0.0432761i | \(0.0137795\pi\) | ||||
−0.999063 | + | 0.0432761i | \(0.986220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.75593e6 | 1.07885 | 0.539426 | − | 0.842033i | \(-0.318641\pi\) | ||||
0.539426 | + | 0.842033i | \(0.318641\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.79437e6 | 0.511724 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.91770e6i | − 0.250832i | −0.992104 | − | 0.125416i | \(-0.959974\pi\) | ||||
0.992104 | − | 0.125416i | \(-0.0400265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.01444e7i | − 1.28726i | −0.765337 | − | 0.643629i | \(-0.777428\pi\) | ||||
0.765337 | − | 0.643629i | \(-0.222572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.81603e6 | −0.716207 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.29735e6 | 0.274624 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.06871e7i | 1.24050i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.09307e6i | 0.348721i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.71741e6 | −0.845342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.54322e6 | −1.01589 | −0.507946 | − | 0.861389i | \(-0.669595\pi\) | ||||
−0.507946 | + | 0.861389i | \(0.669595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.04102e7i | 1.07726i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.87410e6i | 0.892912i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.21938e7 | −1.19333 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.22692e6 | 0.592845 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 8.58805e6i | − 0.795642i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.58078e7i | 1.42547i | 0.701434 | + | 0.712735i | \(0.252544\pi\) | ||||
−0.701434 | + | 0.712735i | \(0.747456\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.46549e6 | −0.479823 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.48574e7 | −1.27018 | −0.635092 | − | 0.772437i | \(-0.719038\pi\) | ||||
−0.635092 | + | 0.772437i | \(0.719038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.28465e6i | 0.106974i | 0.998569 | + | 0.0534872i | \(0.0170336\pi\) | ||||
−0.998569 | + | 0.0534872i | \(0.982966\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 7.58464e6i | − 0.615317i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 262969. | 0.0207892 | 0.0103946 | − | 0.999946i | \(-0.496691\pi\) | ||||
0.0103946 | + | 0.999946i | \(0.496691\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.97414e7 | 2.29170 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.78684e6i | 0.509827i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.89260e7i | 1.38633i | 0.720781 | + | 0.693163i | \(0.243783\pi\) | ||||
−0.720781 | + | 0.693163i | \(0.756217\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.91538e6 | −0.136837 | −0.0684185 | − | 0.997657i | \(-0.521795\pi\) | ||||
−0.0684185 | + | 0.997657i | \(0.521795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 7.93382e6i | − 0.539491i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.48778e6i | 0.364172i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.84385e6 | 0.248982 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.10676e7 | 0.699895 | 0.349948 | − | 0.936769i | \(-0.386199\pi\) | ||||
0.349948 | + | 0.936769i | \(0.386199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.23170e7i | 1.37808i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.09641e7i | 1.26432i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 678718. | 0.0399843 | 0.0199922 | − | 0.999800i | \(-0.493636\pi\) | ||||
0.0199922 | + | 0.999800i | \(0.493636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.38184e6 | −0.194650 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 2.01166e6i | − 0.113144i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.11128e7i | − 0.610882i | −0.952211 | − | 0.305441i | \(-0.901196\pi\) | ||||
0.952211 | − | 0.305441i | \(-0.0988039\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.32114e7 | 2.85935 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.26216e6 | −0.0663101 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1.00441e7i | − 0.516007i | −0.966144 | − | 0.258004i | \(-0.916935\pi\) | ||||
0.966144 | − | 0.258004i | \(-0.0830647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 6.62102e6i | − 0.332673i | −0.986069 | − | 0.166336i | \(-0.946806\pi\) | ||||
0.986069 | − | 0.166336i | \(-0.0531938\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.39337e6 | −0.265077 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.94345e7 | −1.89617 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.44357e7i | − 1.14970i | −0.818257 | − | 0.574852i | \(-0.805060\pi\) | ||||
0.818257 | − | 0.574852i | \(-0.194940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.06775e7i | 0.491649i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.39627e7 | −0.629288 | −0.314644 | − | 0.949210i | \(-0.601885\pi\) | ||||
−0.314644 | + | 0.949210i | \(0.601885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.28834e7 | −1.89204 | −0.946018 | − | 0.324113i | \(-0.894934\pi\) | ||||
−0.946018 | + | 0.324113i | \(0.894934\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 1.33961e7i | − 0.578688i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1.51908e7i | − 0.642591i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.33119e7 | 0.965792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.36716e7 | −0.554803 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.00254e6i | 0.198878i | 0.995044 | + | 0.0994392i | \(0.0317049\pi\) | ||||
−0.995044 | + | 0.0994392i | \(0.968295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 4.16191e7i | − 1.62116i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.64145e6 | −0.253509 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.58695e7 | 0.593675 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.26138e7i | − 0.462536i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.81357e7i | − 1.01142i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.63929e7 | −0.577771 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.73510e7 | −0.945274 | −0.472637 | − | 0.881257i | \(-0.656698\pi\) | ||||
−0.472637 | + | 0.881257i | \(0.656698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.28802e7i | − 0.436564i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.37365e7i | 1.12155i | 0.827968 | + | 0.560775i | \(0.189497\pi\) | ||||
−0.827968 | + | 0.560775i | \(0.810503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.91891e7 | 1.60412 | 0.802058 | − | 0.597246i | \(-0.203738\pi\) | ||||
0.802058 | + | 0.597246i | \(0.203738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.31657e7 | 0.421222 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.97091e7i | 0.618712i | 0.950946 | + | 0.309356i | \(0.100113\pi\) | ||||
−0.950946 | + | 0.309356i | \(0.899887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 1.45145e7i | − 0.447126i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.09800e7 | −0.634293 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.03203e7 | −0.899758 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.80415e7i | 0.816867i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.09840e7i | − 0.314135i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.22748e7 | −1.18712 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.59711e7 | 0.440403 | 0.220202 | − | 0.975454i | \(-0.429328\pi\) | ||||
0.220202 | + | 0.975454i | \(0.429328\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.96129e6i | 0.0801951i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 7.28419e7i | − 1.93752i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.18400e6 | 0.239962 | 0.119981 | − | 0.992776i | \(-0.461717\pi\) | ||||
0.119981 | + | 0.992776i | \(0.461717\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.97930e7 | −1.02143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.70398e7i | 1.94291i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.39260e7i | 1.08853i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.87386e7 | −0.943380 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.95976e7 | 0.947721 | 0.473861 | − | 0.880600i | \(-0.342860\pi\) | ||||
0.473861 | + | 0.880600i | \(0.342860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 7.85281e7i | − 1.84735i | −0.383180 | − | 0.923674i | \(-0.625171\pi\) | ||||
0.383180 | − | 0.923674i | \(-0.374829\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.72268e6i | 0.109211i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.58915e7 | 1.49798 | 0.748989 | − | 0.662582i | \(-0.230540\pi\) | ||||
0.748989 | + | 0.662582i | \(0.230540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.30380e8 | −2.91425 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 2.97987e7i | − 0.654926i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.24524e6i | 0.199818i | 0.994997 | + | 0.0999090i | \(0.0318552\pi\) | ||||
−0.994997 | + | 0.0999090i | \(0.968145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.76711e7 | −0.588173 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.03033e7 | −0.424471 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.79880e7i | 1.60380i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.05595e7i | 0.213622i | 0.994279 | + | 0.106811i | \(0.0340640\pi\) | ||||
−0.994279 | + | 0.106811i | \(0.965936\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.33017e7 | −0.264746 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.56354e7 | −1.48117 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.92271e7i | 0.370499i | 0.982691 | + | 0.185250i | \(0.0593094\pi\) | ||||
−0.982691 | + | 0.185250i | \(0.940691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 2.08982e7i | − 0.396292i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.03211e7 | −0.192621 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.53936e7 | −0.282764 | −0.141382 | − | 0.989955i | \(-0.545155\pi\) | ||||
−0.141382 | + | 0.989955i | \(0.545155\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 1.04472e7i | − 0.188897i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.18517e7i | 0.210953i | 0.994422 | + | 0.105476i | \(0.0336367\pi\) | ||||
−0.994422 | + | 0.105476i | \(0.966363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.49926e7 | 1.66459 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.10452e7 | −0.190564 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5.48941e7i | − 0.932561i | −0.884637 | − | 0.466281i | \(-0.845594\pi\) | ||||
0.884637 | − | 0.466281i | \(-0.154406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.76796e7i | 1.46679i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.69886e7 | −0.444634 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.50007e7 | −1.37921 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5.07085e7i | − 0.810419i | −0.914224 | − | 0.405209i | \(-0.867199\pi\) | ||||
0.914224 | − | 0.405209i | \(-0.132801\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.90414e7i | 0.299765i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.11684e8 | −1.73204 | −0.866021 | − | 0.500007i | \(-0.833331\pi\) | ||||
−0.866021 | + | 0.500007i | \(0.833331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.47823e7 | 0.837000 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.15284e7i | − 0.173542i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.13662e7i | 0.316916i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.03112e7 | 1.17383 | 0.586917 | − | 0.809647i | \(-0.300342\pi\) | ||||
0.586917 | + | 0.809647i | \(0.300342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.32353e7 | 0.622749 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.91580e7i | 0.839776i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.81417e7i | 0.673561i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.71928e7 | −0.926648 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.64533e7 | −1.17527 | −0.587637 | − | 0.809125i | \(-0.699942\pi\) | ||||
−0.587637 | + | 0.809125i | \(0.699942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.94432e7i | 0.260569i | 0.991477 | + | 0.130284i | \(0.0415890\pi\) | ||||
−0.991477 | + | 0.130284i | \(0.958411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.70177e7i | 0.489089i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.54931e8 | −2.01823 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.33011e7 | 0.299290 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.40750e7i | 0.431582i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.05362e8i | 1.31599i | 0.753021 | + | 0.657996i | \(0.228596\pi\) | ||||
−0.753021 | + | 0.657996i | \(0.771404\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.32564e8 | 1.63291 | 0.816457 | − | 0.577407i | \(-0.195935\pi\) | ||||
0.816457 | + | 0.577407i | \(0.195935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.51947e7 | 0.306085 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.60275e7i | − 0.671362i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 5.71422e7i | − 0.675403i | −0.941253 | − | 0.337702i | \(-0.890351\pi\) | ||||
0.941253 | − | 0.337702i | \(-0.109649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.87485e6 | 0.115137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.10479e7 | −0.242102 | −0.121051 | − | 0.992646i | \(-0.538626\pi\) | ||||
−0.121051 | + | 0.992646i | \(0.538626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.58077e7i | − 0.179386i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.32402e6i | − 0.0372169i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.46748e7 | −0.714490 | −0.357245 | − | 0.934011i | \(-0.616284\pi\) | ||||
−0.357245 | + | 0.934011i | \(0.616284\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.59744e7 | −1.04623 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 8.31971e7i | − 0.894981i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 6.75484e7i | − 0.717102i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.37459e7 | 0.563114 | 0.281557 | − | 0.959544i | \(-0.409149\pi\) | ||||
0.281557 | + | 0.959544i | \(0.409149\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.60931e7 | −0.269828 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 2.36640e7i | − 0.241538i | −0.992681 | − | 0.120769i | \(-0.961464\pi\) | ||||
0.992681 | − | 0.120769i | \(-0.0385360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.80452e7i | − 0.282563i | −0.989969 | − | 0.141281i | \(-0.954878\pi\) | ||||
0.989969 | − | 0.141281i | \(-0.0451222\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.33728e8 | −1.33004 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.61101e7 | 0.354550 | 0.177275 | − | 0.984161i | \(-0.443272\pi\) | ||||
0.177275 | + | 0.984161i | \(0.443272\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.03539e8i | 1.00365i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 6.37536e7i | − 0.610157i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.96930e7 | −0.753072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.90012e7 | 0.923761 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.62298e7i | 0.610236i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 4.70272e7i | − 0.427900i | −0.976845 | − | 0.213950i | \(-0.931367\pi\) | ||||
0.976845 | − | 0.213950i | \(-0.0686330\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.51933e7 | 0.136527 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.50636e7 | 0.488679 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.71227e8i | − 1.50088i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 9.56947e7i | − 0.828516i | −0.910160 | − | 0.414258i | \(-0.864041\pi\) | ||||
0.910160 | − | 0.414258i | \(-0.135959\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.40259e7 | 0.205472 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.69668e7 | 0.819178 | 0.409589 | − | 0.912270i | \(-0.365672\pi\) | ||||
0.409589 | + | 0.912270i | \(0.365672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.70248e7i | − 0.475908i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 8.31797e7i | − 0.685807i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.85324e8 | 1.50961 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.16768e7 | −0.415905 | −0.207952 | − | 0.978139i | \(-0.566680\pi\) | ||||
−0.207952 | + | 0.978139i | \(0.566680\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.19494e8i | 0.950240i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.28417e8i | − 1.79483i | −0.441185 | − | 0.897416i | \(-0.645442\pi\) | ||||
0.441185 | − | 0.897416i | \(-0.354558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.52381e8 | 2.73614 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.10121e7 | −0.391426 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.31906e8i | − 1.00025i | −0.865952 | − | 0.500127i | \(-0.833287\pi\) | ||||
0.865952 | − | 0.500127i | \(-0.166713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 1.10853e8i | − 0.830780i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.66735e7 | 0.123502 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.61316e8 | 1.18102 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.67089e8i | 1.93279i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.56477e8i | 1.11931i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.21687e7 | 0.0860462 | 0.0430231 | − | 0.999074i | \(-0.486301\pi\) | ||||
0.0430231 | + | 0.999074i | \(0.486301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.96786e7 | 0.626879 | 0.313440 | − | 0.949608i | \(-0.398519\pi\) | ||||
0.313440 | + | 0.949608i | \(0.398519\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.72980e7i | 0.672398i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.02675e8i | 2.06797i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.39832e7 | −0.0944579 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.18014e7 | 0.345986 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.82466e7i | 0.450712i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 2.62760e8i | − 1.71592i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.37692e8 | −0.889174 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.12488e7 | 0.455000 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.72097e8i | 1.71843i | 0.511613 | + | 0.859216i | \(0.329048\pi\) | ||||
−0.511613 | + | 0.859216i | \(0.670952\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.35449e7i | 0.584279i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.37567e8 | 0.849815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.84749e8 | 1.12881 | 0.564404 | − | 0.825499i | \(-0.309106\pi\) | ||||
0.564404 | + | 0.825499i | \(0.309106\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 2.04035e7i | − 0.123307i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.64390e7i | 0.217827i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.20821e8 | 0.714443 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.70881e7 | −0.216948 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.60239e7i | − 0.555666i | −0.960629 | − | 0.277833i | \(-0.910384\pi\) | ||||
0.960629 | − | 0.277833i | \(-0.0896162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.66690e7i | 0.324422i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.88266e8 | −1.06631 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.37375e8 | 1.33018 | 0.665089 | − | 0.746764i | \(-0.268393\pi\) | ||||
0.665089 | + | 0.746764i | \(0.268393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.98381e8i | − 2.76323i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.63867e7i | 0.0898963i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.26674e8 | −1.77328 | −0.886641 | − | 0.462458i | \(-0.846968\pi\) | ||||
−0.886641 | + | 0.462458i | \(0.846968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 971103. | 0.00521623 | 0.00260812 | − | 0.999997i | \(-0.499170\pi\) | ||||
0.00260812 | + | 0.999997i | \(0.499170\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9.40116e6i | − 0.0499709i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 2.86290e8i | − 1.50592i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.87315e8 | 0.975092 | 0.487546 | − | 0.873097i | \(-0.337892\pi\) | ||||
0.487546 | + | 0.873097i | \(0.337892\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.20903e8 | −0.622876 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.84293e7i | − 0.348910i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.77860e8i | 2.41154i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.91484e7 | −0.295444 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.47232e7 | 0.418878 | 0.209439 | − | 0.977822i | \(-0.432836\pi\) | ||||
0.209439 | + | 0.977822i | \(0.432836\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.93410e8i | − 0.946528i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.98940e7i | 0.144818i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.30616e8 | −1.10592 | −0.552962 | − | 0.833206i | \(-0.686503\pi\) | ||||
−0.552962 | + | 0.833206i | \(0.686503\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.73209e8 | 1.77174 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.58135e8i | 0.743199i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.65098e8i | 1.69875i | 0.527791 | + | 0.849374i | \(0.323020\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.63307e8 | 1.21294 | 0.606469 | − | 0.795107i | \(-0.292585\pi\) | ||||
0.606469 | + | 0.795107i | \(0.292585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.06630e7 | 0.413502 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2.54286e8i | − 1.14830i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.38978e8i | 0.621413i | 0.950506 | + | 0.310707i | \(0.100566\pi\) | ||||
−0.950506 | + | 0.310707i | \(0.899434\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.58121e7 | −0.158554 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.89925e8 | 0.832642 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.20201e8i | 1.82421i | 0.409953 | + | 0.912106i | \(0.365545\pi\) | ||||
−0.409953 | + | 0.912106i | \(0.634455\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 1.66595e8i | − 0.716205i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.25856e7 | 0.0535818 | 0.0267909 | − | 0.999641i | \(-0.491471\pi\) | ||||
0.0267909 | + | 0.999641i | \(0.491471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.43243e8 | −1.02558 | −0.512789 | − | 0.858515i | \(-0.671388\pi\) | ||||
−0.512789 | + | 0.858515i | \(0.671388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 4.82161e7i | − 0.201334i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.24693e7i | 0.0929234i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.96966e7 | −0.367397 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.20302e8 | 0.488059 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.39440e7i | 0.337317i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.45064e7i | 0.216950i | 0.994099 | + | 0.108475i | \(0.0345967\pi\) | ||||
−0.994099 | + | 0.108475i | \(0.965403\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.48764e8 | 0.586526 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.30844e8 | 0.511016 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 5.06644e7i | − 0.196013i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 1.62278e8i | − 0.621954i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.69420e8 | −0.643268 | −0.321634 | − | 0.946864i | \(-0.604232\pi\) | ||||
−0.321634 | + | 0.946864i | \(0.604232\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.20644e8 | 1.58227 | 0.791137 | − | 0.611639i | \(-0.209490\pi\) | ||||
0.791137 | + | 0.611639i | \(0.209490\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.38333e8i | − 0.515523i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.19909e8i | 1.18117i | 0.806974 | + | 0.590587i | \(0.201104\pi\) | ||||
−0.806974 | + | 0.590587i | \(0.798896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.73756e8 | 1.36727 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.90083e8 | 0.688970 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.98645e8i | 1.07254i | 0.844045 | + | 0.536272i | \(0.180168\pi\) | ||||
−0.844045 | + | 0.536272i | \(0.819832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 3.38014e8i | − 1.20285i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.70681e7 | −0.342279 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.27357e8 | 1.14384 | 0.571920 | − | 0.820309i | \(-0.306199\pi\) | ||||
0.571920 | + | 0.820309i | \(0.306199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 4.03255e8i | − 1.39629i | −0.715956 | − | 0.698145i | \(-0.754009\pi\) | ||||
0.715956 | − | 0.698145i | \(-0.245991\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.33874e8i | 0.459364i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.38481e8 | −0.810941 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.05373e8 | 0.355103 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 2.46420e8i | − 0.822995i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1.47215e8i | − 0.487285i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.48356e8 | −0.486697 | −0.243349 | − | 0.969939i | \(-0.578246\pi\) | ||||
−0.243349 | + | 0.969939i | \(0.578246\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.51985e7 | 0.277026 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.50729e8i | 1.45261i | 0.687371 | + | 0.726306i | \(0.258765\pi\) | ||||
−0.687371 | + | 0.726306i | \(0.741235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.43385e8i | 0.777470i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.31605e8 | 0.733341 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.93405e8 | −1.86247 | −0.931235 | − | 0.364418i | \(-0.881268\pi\) | ||||
−0.931235 | + | 0.364418i | \(0.881268\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.41493e8i | 1.68470i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 2.00258e7i | − 0.0617617i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.39802e8 | 1.03889 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.84794e8 | 0.863170 | 0.431585 | − | 0.902072i | \(-0.357955\pi\) | ||||
0.431585 | + | 0.902072i | \(0.357955\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.18233e8i | 0.355254i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 8.41545e8i | − 2.50682i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.77066e8 | −1.11357 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.09928e6 | −0.0120026 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.51280e8i | 0.439165i | 0.975594 | + | 0.219583i | \(0.0704695\pi\) | ||||
−0.975594 | + | 0.219583i | \(0.929530\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.36404e7i | − 0.154392i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.63622e8 | −1.32311 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.00880e8 | −1.41734 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 6.04474e8i | − 1.69605i | −0.529956 | − | 0.848025i | \(-0.677792\pi\) | ||||
0.529956 | − | 0.848025i | \(-0.322208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1.05796e8i | − 0.294349i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.59300e8 | −1.54304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.26766e8 | −1.16754 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.95027e8i | − 0.800396i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1.92148e8i | − 0.516951i | −0.966018 | − | 0.258476i | \(-0.916780\pi\) | ||||
0.966018 | − | 0.258476i | \(-0.0832201\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.29297e8 | −0.611777 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.98578e7 | 0.0790029 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.86196e8i | 0.488604i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.33711e8i | − 0.347989i | −0.984747 | − | 0.173994i | \(-0.944333\pi\) | ||||
0.984747 | − | 0.173994i | \(-0.0556675\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.13099e8 | −0.801549 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.99936e8i | 1.52333i | 0.647973 | + | 0.761663i | \(0.275617\pi\) | ||||
−0.647973 | + | 0.761663i | \(0.724383\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.23676e8i | 0.311475i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.54150e8 | 1.63409 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.83646e7 | −0.119838 | −0.0599190 | − | 0.998203i | \(-0.519084\pi\) | ||||
−0.0599190 | + | 0.998203i | \(0.519084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 8.55461e7i | − 0.210255i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.69904e7i | 0.0901826i | 0.998983 | + | 0.0450913i | \(0.0143579\pi\) | ||||
−0.998983 | + | 0.0450913i | \(0.985642\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.16311e7 | 0.100681 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.99197e7 | −0.143750 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.73491e8i | 0.888863i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.99551e8i | 0.471123i | 0.971859 | + | 0.235562i | \(0.0756929\pi\) | ||||
−0.971859 | + | 0.235562i | \(0.924307\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.72527e8 | −0.404085 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.04199e9 | 2.42115 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.79819e8i | − 1.10609i | −0.833152 | − | 0.553045i | \(-0.813466\pi\) | ||||
0.833152 | − | 0.553045i | \(-0.186534\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 3.47888e8i | − 0.795636i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.43069e8 | −0.551537 | −0.275769 | − | 0.961224i | \(-0.588932\pi\) | ||||
−0.275769 | + | 0.961224i | \(0.588932\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.95540e8 | −0.440211 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3.26798e8i | − 0.729953i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2.65775e8i | − 0.589017i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.11830e8 | 0.905605 | 0.452802 | − | 0.891611i | \(-0.350424\pi\) | ||||
0.452802 | + | 0.891611i | \(0.350424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.05802e7 | −0.0230850 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 9.17077e7i | − 0.198549i | −0.995060 | − | 0.0992744i | \(-0.968348\pi\) | ||||
0.995060 | − | 0.0992744i | \(-0.0316522\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 9.88289e8i | − 2.12314i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.27176e7 | 0.112381 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.40946e8 | 0.509692 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.17087e9i | − 2.45785i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.13587e7i | 0.0653240i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.98471e8 | 1.65063 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.23454e8 | 1.07388 | 0.536938 | − | 0.843622i | \(-0.319581\pi\) | ||||
0.536938 | + | 0.843622i | \(0.319581\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.73232e8i | 0.352693i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.08406e8i | 1.43137i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.04683e8 | −0.209921 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.29483e8 | −1.65085 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.58874e7i | 0.0313818i | 0.999877 | + | 0.0156909i | \(0.00499477\pi\) | ||||
−0.999877 | + | 0.0156909i | \(0.995005\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.04935e9i | 2.05721i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.96751e7 | 0.0382842 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.00364e8 | −1.35262 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.89635e8i | 1.32200i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.56573e8i | 0.297917i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.17580e8 | −0.977534 | −0.488767 | − | 0.872414i | \(-0.662553\pi\) | ||||
−0.488767 | + | 0.872414i | \(0.662553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.43642e8 | −1.76907 | −0.884534 | − | 0.466476i | \(-0.845524\pi\) | ||||
−0.884534 | + | 0.466476i | \(0.845524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.03212e8i | 0.192069i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.00908e8i | 0.555855i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00071e8 | 0.366875 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.40744e7 | 0.153042 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.51239e8i | 1.17682i | 0.808562 | + | 0.588411i | \(0.200246\pi\) | ||||
−0.808562 | + | 0.588411i | \(0.799754\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.12175e8i | 0.201231i | 0.994925 | + | 0.100615i | \(0.0320812\pi\) | ||||
−0.994925 | + | 0.100615i | \(0.967919\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.14722e8 | 1.09476 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.24440e8 | −1.10401 | −0.552007 | − | 0.833840i | \(-0.686138\pi\) | ||||
−0.552007 | + | 0.833840i | \(0.686138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.96016e8i | 1.04615i | 0.852286 | + | 0.523076i | \(0.175216\pi\) | ||||
−0.852286 | + | 0.523076i | \(0.824784\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.80915e8i | 0.663782i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.79924e8 | 0.484289 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.49658e9 | −2.57064 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.66445e8i | − 0.283854i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.46780e7i | 0.0756497i | 0.999284 | + | 0.0378249i | \(0.0120429\pi\) | ||||
−0.999284 | + | 0.0378249i | \(0.987957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.26291e8 | 0.884785 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.17656e8 | 0.363320 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6.38892e8i | − 1.05891i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.61446e8i | 0.594830i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.68485e8 | 1.09237 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.55116e8 | −0.251691 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1.12761e9i | − 1.81683i | −0.418072 | − | 0.908414i | \(-0.637294\pi\) | ||||
0.418072 | − | 0.908414i | \(-0.362706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.08825e8i | 0.334105i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.47949e8 | 0.870557 | 0.435279 | − | 0.900296i | \(-0.356650\pi\) | ||||
0.435279 | + | 0.900296i | \(0.356650\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.34544e8 | 1.00111 | 0.500556 | − | 0.865704i | \(-0.333129\pi\) | ||||
0.500556 | + | 0.865704i | \(0.333129\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.36801e8i | 0.371000i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.20080e9i | 1.86826i | 0.356928 | + | 0.934132i | \(0.383824\pi\) | ||||
−0.356928 | + | 0.934132i | \(0.616176\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.95977e9 | −3.02801 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.63396e8 | −0.557600 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 7.63340e8i | − 1.16321i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 4.65160e8i | − 0.703960i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.13118e8 | 0.320316 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.72036e8 | −0.555342 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6.11977e6i | − 0.00907270i | −0.999990 | − | 0.00453635i | \(-0.998556\pi\) | ||||
0.999990 | − | 0.00453635i | \(-0.00144397\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 7.79819e7i | − 0.114823i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.39118e8 | 0.788417 | 0.394209 | − | 0.919021i | \(-0.371019\pi\) | ||||
0.394209 | + | 0.919021i | \(0.371019\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.91469e8 | −0.713861 | −0.356931 | − | 0.934131i | \(-0.616177\pi\) | ||||
−0.356931 | + | 0.934131i | \(0.616177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.48778e8i | 0.935980i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.95698e8i | 0.996897i | 0.866919 | + | 0.498448i | \(0.166097\pi\) | ||||
−0.866919 | + | 0.498448i | \(0.833903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.85984e8 | −0.264710 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.03530e8 | 0.146364 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.70534e8i | − 0.941600i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1.72450e9i | − 2.40544i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.47380e8 | −0.342758 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.63756e8 | 0.500646 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.87742e9i | 2.56678i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.96629e8i | 0.267045i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.17159e9 | −1.58063 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.10192e9 | −1.47682 | −0.738411 | − | 0.674351i | \(-0.764423\pi\) | ||||
−0.738411 | + | 0.674351i | \(0.764423\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.38592e8i | 0.583942i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 3.89543e8i | − 0.515229i | −0.966248 | − | 0.257615i | \(-0.917063\pi\) | ||||
0.966248 | − | 0.257615i | \(-0.0829365\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.32331e8 | −0.568073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.55540e8 | 0.333576 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.80458e8i | 0.623085i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.13853e9i | 1.46690i | 0.679746 | + | 0.733448i | \(0.262090\pi\) | ||||
−0.679746 | + | 0.733448i | \(0.737910\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.26360e8 | 0.545754 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.32594e8 | −1.05883 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 2.74092e8i | − 0.346315i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00783e8i | 0.252050i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.92474e8 | 0.738962 | 0.369481 | − | 0.929238i | \(-0.379535\pi\) | ||||
0.369481 | + | 0.929238i | \(0.379535\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.78872e8 | −0.221663 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5.25900e8i | − 0.647528i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2.35791e9i | − 2.88464i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.16456e7 | −0.0749348 | −0.0374674 | − | 0.999298i | \(-0.511929\pi\) | ||||
−0.0374674 | + | 0.999298i | \(0.511929\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.66782e8 | −0.926137 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.10725e8i | 0.372913i | 0.982463 | + | 0.186457i | \(0.0597004\pi\) | ||||
−0.982463 | + | 0.186457i | \(0.940300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.96763e8i | − 0.830902i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.05232e8 | −0.243192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.13722e8 | −0.133904 | −0.0669522 | − | 0.997756i | \(-0.521328\pi\) | ||||
−0.0669522 | + | 0.997756i | \(0.521328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.98023e8i | 0.582707i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 3.07234e8i | − 0.357214i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.25518e8 | −0.607168 | −0.303584 | − | 0.952805i | \(-0.598183\pi\) | ||||
−0.303584 | + | 0.952805i | \(0.598183\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.17743e8 | 0.135184 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.26258e8i | 0.258148i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 7.69687e8i | − 0.872686i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.04323e9 | −1.17547 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.27045e8 | 0.366209 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 1.51423e9i | − 1.68504i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.50448e8i | 0.608747i | 0.952553 | + | 0.304373i | \(0.0984470\pi\) | ||||
−0.952553 | + | 0.304373i | \(0.901553\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.72647e8 | 0.519476 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.54851e9 | −1.69144 | −0.845722 | − | 0.533624i | \(-0.820830\pi\) | ||||
−0.845722 | + | 0.533624i | \(0.820830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.19618e9i | 1.29855i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 4.37124e8i | − 0.471618i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.73673e9 | 1.86229 | 0.931146 | − | 0.364645i | \(-0.118810\pi\) | ||||
0.931146 | + | 0.364645i | \(0.118810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.41959e8 | 0.151292 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.71223e8i | 0.181366i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.96734e8i | 0.838789i | 0.907804 | + | 0.419395i | \(0.137758\pi\) | ||||
−0.907804 | + | 0.419395i | \(0.862242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.74402e8 | −0.391769 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.58999e8 | 0.685383 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 5.78562e8i | − 0.598082i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.33810e8i | 0.342988i | 0.985185 | + | 0.171494i | \(0.0548594\pi\) | ||||
−0.985185 | + | 0.171494i | \(0.945141\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.48965e8 | −0.254267 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.98054e9 | −2.01054 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.81174e8i | − 0.485531i | −0.970085 | − | 0.242765i | \(-0.921945\pi\) | ||||
0.970085 | − | 0.242765i | \(-0.0780545\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 4.61619e7i | − 0.0463007i |
(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.c.319.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 384.7.b.c.319.5 | yes | 8 | |
8.3 | odd | 2 | inner | 384.7.b.c.319.4 | yes | 8 | |
8.5 | even | 2 | inner | 384.7.b.c.319.8 | yes | 8 | |
16.3 | odd | 4 | 768.7.g.g.511.5 | 8 | |||
16.5 | even | 4 | 768.7.g.g.511.8 | 8 | |||
16.11 | odd | 4 | 768.7.g.g.511.4 | 8 | |||
16.13 | even | 4 | 768.7.g.g.511.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.c.319.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
384.7.b.c.319.4 | yes | 8 | 8.3 | odd | 2 | inner | |
384.7.b.c.319.5 | yes | 8 | 4.3 | odd | 2 | inner | |
384.7.b.c.319.8 | yes | 8 | 8.5 | even | 2 | inner | |
768.7.g.g.511.1 | 8 | 16.13 | even | 4 | |||
768.7.g.g.511.4 | 8 | 16.11 | odd | 4 | |||
768.7.g.g.511.5 | 8 | 16.3 | odd | 4 | |||
768.7.g.g.511.8 | 8 | 16.5 | even | 4 |