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: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 53x^{6} - 2x^{5} + 2532x^{4} - 772x^{3} - 31349x^{2} - 33880x + 366025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 511.5 | ||
Root | \(-5.30399 + 3.63961i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.511 |
Dual form | 768.7.g.g.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 | ||||||||
\(5\) | −195.235 | −1.56188 | −0.780940 | − | 0.624606i | \(-0.785260\pi\) | ||||
−0.780940 | + | 0.624606i | \(0.785260\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 1753.29i | 1.31727i | 0.752462 | + | 0.658636i | \(0.228866\pi\) | ||||
−0.752462 | + | 0.658636i | \(0.771134\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1246.75 | 0.567478 | 0.283739 | − | 0.958902i | \(-0.408425\pi\) | ||||
0.283739 | + | 0.958902i | \(0.408425\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 4401.67i | 0.641737i | 0.947124 | + | 0.320869i | \(0.103975\pi\) | ||||
−0.947124 | + | 0.320869i | \(0.896025\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4325.95 | −0.467115 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 3788.00i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8278.44 | 0.339433 | 0.169717 | − | 0.985493i | \(-0.445715\pi\) | ||||
0.169717 | + | 0.985493i | \(0.445715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 43940.1i | − 1.47495i | −0.675376 | − | 0.737474i | \(-0.736019\pi\) | ||||
0.675376 | − | 0.737474i | \(-0.263981\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −27331.1 | −0.760527 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 54179.6i | − 1.26367i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12186.4 | 0.240585 | 0.120293 | − | 0.992738i | \(-0.461617\pi\) | ||||
0.120293 | + | 0.992738i | \(0.461617\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19434.9i | 0.327633i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 54739.6 | 0.794238 | 0.397119 | − | 0.917767i | \(-0.370010\pi\) | ||||
0.397119 | + | 0.917767i | \(0.370010\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 45453.4i | − 0.571691i | −0.958276 | − | 0.285845i | \(-0.907726\pi\) | ||||
0.958276 | − | 0.285845i | \(-0.0922744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 47442.1 | 0.520627 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 152336.i | − 1.46727i | −0.679545 | − | 0.733634i | \(-0.737823\pi\) | ||||
0.679545 | − | 0.733634i | \(-0.262177\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40637.3 | 0.345411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 107379.i | 0.809484i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 272550. | 1.83071 | 0.915354 | − | 0.402649i | \(-0.131911\pi\) | ||||
0.915354 | + | 0.402649i | \(0.131911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 342303.i | − 2.05742i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −68615.3 | −0.370507 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 213175.i | 1.03796i | 0.854787 | + | 0.518978i | \(0.173687\pi\) | ||||
−0.854787 | + | 0.518978i | \(0.826313\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 83964.8 | 0.369920 | 0.184960 | − | 0.982746i | \(-0.440784\pi\) | ||||
0.184960 | + | 0.982746i | \(0.440784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 67434.9i | − 0.269689i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −243409. | −0.886332 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 373099.i | − 1.24051i | −0.784401 | − | 0.620254i | \(-0.787030\pi\) | ||||
0.784401 | − | 0.620254i | \(-0.212970\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −198420. | −0.604003 | ||||||||
\(70\) | 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 | \(-0.328379\pi\) | ||||
0.513419 | + | 0.858138i | \(0.328379\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 350611.i | 0.831078i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −486555. | −1.06576 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 435376.i | 0.883046i | 0.897250 | + | 0.441523i | \(0.145562\pi\) | ||||
−0.897250 | + | 0.441523i | \(0.854438\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 246583.i | 0.431250i | 0.976476 | + | 0.215625i | \(0.0691789\pi\) | ||||
−0.976476 | + | 0.215625i | \(0.930821\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.34485e6 | −2.18986 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 129048.i | 0.195972i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −80967.5 | −0.114853 | −0.0574263 | − | 0.998350i | \(-0.518289\pi\) | ||||
−0.0574263 | + | 0.998350i | \(0.518289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 345985.i | 0.459127i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 684959. | 0.851561 | ||||||||
\(94\) | 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.i | − 0.439091i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.80491e6 | 1.75183 | 0.875913 | − | 0.482470i | \(-0.160260\pi\) | ||||
0.875913 | + | 0.482470i | \(0.160260\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | 1.34587e6i | 1.09863i | 0.835616 | + | 0.549314i | \(0.185111\pi\) | ||||
−0.835616 | + | 0.549314i | \(0.814889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −704622. | −0.544098 | −0.272049 | − | 0.962283i | \(-0.587701\pi\) | ||||
−0.272049 | + | 0.962283i | \(0.587701\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | − 2.48508e6i | − 1.63398i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −302960. | −0.189159 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.91159e6i | 1.13437i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.30246e6 | −0.735205 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 853307.i | 0.458553i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.34062e6 | −0.686399 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 670190.i | − 0.327180i | −0.986528 | − | 0.163590i | \(-0.947693\pi\) | ||||
0.986528 | − | 0.163590i | \(-0.0523074\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 708549. | 0.330066 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.73132e6i | − 0.770128i | −0.922890 | − | 0.385064i | \(-0.874179\pi\) | ||||
0.922890 | − | 0.385064i | \(-0.125821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.22151e6 | −0.519208 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 739549.i | 0.300584i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.77355e6 | 1.07863 | 0.539317 | − | 0.842103i | \(-0.318683\pi\) | ||||
0.539317 | + | 0.842103i | \(0.318683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.31042e6i | 1.60500i | 0.596652 | + | 0.802500i | \(0.296497\pi\) | ||||
−0.596652 | + | 0.802500i | \(0.703503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.37469e6 | 0.847128 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.18591e6i | 0.747522i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.61624e6 | −0.530154 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 633472.i | 0.199423i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 213236. | 0.0644616 | 0.0322308 | − | 0.999480i | \(-0.489739\pi\) | ||||
0.0322308 | + | 0.999480i | \(0.489739\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 8.57866e6i | 2.30369i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.08979e6 | −1.05682 | −0.528412 | − | 0.848988i | \(-0.677212\pi\) | ||||
−0.528412 | + | 0.848988i | \(0.677212\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.24864e6i | 1.05696i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.53233e6 | −0.846416 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.54126e6i | 0.355888i | 0.984041 | + | 0.177944i | \(0.0569446\pi\) | ||||
−0.984041 | + | 0.177944i | \(0.943055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.33598e6 | 1.18785 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | − 1.06961e6i | − 0.213912i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.00380e7 | 1.93870 | 0.969348 | − | 0.245693i | \(-0.0790156\pi\) | ||||
0.969348 | + | 0.245693i | \(0.0790156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.24167e6i | 1.16463i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.32306e6 | −0.599265 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 8.83296e6i | − 1.54009i | −0.637987 | − | 0.770047i | \(-0.720233\pi\) | ||||
0.637987 | − | 0.770047i | \(-0.279767\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00091e6 | −1.01200 | −0.506001 | − | 0.862533i | \(-0.668877\pi\) | ||||
−0.506001 | + | 0.862533i | \(0.668877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.30888e6i | 0.213573i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.37920e6 | −0.375765 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.20773e7i | 1.84690i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.05121e6 | 0.155705 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 603085.i | − 0.0865522i | −0.999063 | − | 0.0432761i | \(-0.986220\pi\) | ||||
0.999063 | − | 0.0432761i | \(-0.0137795\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.75593e6 | 1.07885 | 0.539426 | − | 0.842033i | \(-0.318641\pi\) | ||||
0.539426 | + | 0.842033i | \(0.318641\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 3.79437e6i | − 0.511724i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.91770e6 | −0.250832 | −0.125416 | − | 0.992104i | \(-0.540026\pi\) | ||||
−0.125416 | + | 0.992104i | \(0.540026\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | 2.29735e6i | 0.274624i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.06871e7 | −1.24050 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3.09307e6i | − 0.348721i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.71741e6 | −0.845342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.54322e6i | 1.01589i | 0.861389 | + | 0.507946i | \(0.169595\pi\) | ||||
−0.861389 | + | 0.507946i | \(0.830405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.04102e7 | 1.07726 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.87410e6i | 0.892912i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.21938e7 | 1.19333 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.22692e6i | 0.592845i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.58805e6 | 0.795642 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.58078e7i | − 1.42547i | −0.701434 | − | 0.712735i | \(-0.747456\pi\) | ||||
0.701434 | − | 0.712735i | \(-0.252544\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.46549e6 | −0.479823 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.48574e7i | 1.27018i | 0.772437 | + | 0.635092i | \(0.219038\pi\) | ||||
−0.772437 | + | 0.635092i | \(0.780962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.28465e6 | 0.106974 | 0.0534872 | − | 0.998569i | \(-0.482966\pi\) | ||||
0.0534872 | + | 0.998569i | \(0.482966\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 7.58464e6i | − 0.615317i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −262969. | −0.0207892 | −0.0103946 | − | 0.999946i | \(-0.503309\pi\) | ||||
−0.0103946 | + | 0.999946i | \(0.503309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.97414e7i | 2.29170i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.78684e6 | −0.509827 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 1.89260e7i | − 1.38633i | −0.720781 | − | 0.693163i | \(-0.756217\pi\) | ||||
0.720781 | − | 0.693163i | \(-0.243783\pi\) | |||||||
\(240\) | 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.i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.93382e6 | −0.539491 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.48778e6i | 0.364172i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.84385e6 | −0.248982 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.10676e7i | 0.699895i | 0.936769 | + | 0.349948i | \(0.113801\pi\) | ||||
−0.936769 | + | 0.349948i | \(0.886199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23170e7 | −1.37808 | ||||||||
\(254\) | 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 | ||||||||
\(259\) | 3.38184e6i | 0.194650i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.01166e6 | −0.113144 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | − 1.26216e6i | − 0.0663101i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00441e7 | 0.516007 | 0.258004 | − | 0.966144i | \(-0.416935\pi\) | ||||
0.258004 | + | 0.966144i | \(0.416935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.62102e6i | 0.332673i | 0.986069 | + | 0.166336i | \(0.0531938\pi\) | ||||
−0.986069 | + | 0.166336i | \(0.946806\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.39337e6 | −0.265077 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.94345e7i | 1.89617i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.44357e7 | −1.14970 | −0.574852 | − | 0.818257i | \(-0.694940\pi\) | ||||
−0.574852 | + | 0.818257i | \(0.694940\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.06775e7i | 0.491649i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.39627e7 | 0.629288 | 0.314644 | − | 0.949210i | \(-0.398115\pi\) | ||||
0.314644 | + | 0.949210i | \(0.398115\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4.28834e7i | − 1.89204i | −0.324113 | − | 0.946018i | \(-0.605066\pi\) | ||||
0.324113 | − | 0.946018i | \(-0.394934\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.33961e7 | 0.578688 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.51908e7i | 0.642591i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.33119e7 | 0.965792 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.36716e7i | 0.554803i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.00254e6 | 0.198878 | 0.0994392 | − | 0.995044i | \(-0.468295\pi\) | ||||
0.0994392 | + | 0.995044i | \(0.468295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 4.16191e7i | − 1.62116i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.64145e6 | 0.253509 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.58695e7i | 0.593675i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.26138e7 | 0.462536 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.81357e7i | 1.01142i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.63929e7 | −0.577771 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.73510e7i | 0.945274i | 0.881257 | + | 0.472637i | \(0.156698\pi\) | ||||
−0.881257 | + | 0.472637i | \(0.843302\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.28802e7 | −0.436564 | ||||||||
\(310\) | 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 | \(-0.796262\pi\) | ||||
−0.802058 | + | 0.597246i | \(0.796262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.31657e7i | 0.421222i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.97091e7 | −0.618712 | −0.309356 | − | 0.950946i | \(-0.600113\pi\) | ||||
−0.309356 | + | 0.950946i | \(0.600113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.45145e7i | 0.447126i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.09800e7 | −0.634293 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.03203e7i | 0.899758i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.80415e7 | 0.816867 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.09840e7i | − 0.314135i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.22748e7 | 1.18712 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.59711e7i | 0.440403i | 0.975454 | + | 0.220202i | \(0.0706715\pi\) | ||||
−0.975454 | + | 0.220202i | \(0.929328\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.96129e6 | −0.0801951 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 3.97930e7i | 1.02143i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.70398e7 | 1.94291 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.39260e7i | 1.08853i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.87386e7 | 0.943380 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.95976e7i | 0.947721i | 0.880600 | + | 0.473861i | \(0.157140\pi\) | ||||
−0.880600 | + | 0.473861i | \(0.842860\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.85281e7 | 1.84735 | 0.923674 | − | 0.383180i | \(-0.125171\pi\) | ||||
0.923674 | + | 0.383180i | \(0.125171\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 1.30380e8i | 2.91425i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.97987e7 | −0.654926 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | − 2.03033e7i | − 0.424471i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.79880e7 | −1.60380 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.05595e7i | − 0.213622i | −0.994279 | − | 0.106811i | \(-0.965936\pi\) | ||||
0.994279 | − | 0.106811i | \(-0.0340640\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.33017e7 | −0.264746 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.56354e7i | 1.48117i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.92271e7 | 0.370499 | 0.185250 | − | 0.982691i | \(-0.440691\pi\) | ||||
0.185250 | + | 0.982691i | \(0.440691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 2.08982e7i | − 0.396292i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.03211e7 | 0.192621 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.53936e7i | − 0.282764i | −0.989955 | − | 0.141382i | \(-0.954845\pi\) | ||||
0.989955 | − | 0.141382i | \(-0.0451545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.04472e7 | 0.188897 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.18517e7i | − 0.210953i | −0.994422 | − | 0.105476i | \(-0.966363\pi\) | ||||
0.994422 | − | 0.105476i | \(-0.0336367\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.49926e7 | 1.66459 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.10452e7i | 0.190564i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.48941e7 | −0.932561 | −0.466281 | − | 0.884637i | \(-0.654406\pi\) | ||||
−0.466281 | + | 0.884637i | \(0.654406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.76796e7i | 1.46679i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.69886e7 | 0.444634 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 8.50007e7i | − 1.37921i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.07085e7 | 0.810419 | 0.405209 | − | 0.914224i | \(-0.367199\pi\) | ||||
0.405209 | + | 0.914224i | \(0.367199\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 5.47823e7i | − 0.837000i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.15284e7 | −0.173542 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.13662e7i | 0.316916i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.03112e7 | −1.17383 | −0.586917 | − | 0.809647i | \(-0.699658\pi\) | ||||
−0.586917 | + | 0.809647i | \(0.699658\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.32353e7i | 0.622749i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.91580e7 | −0.839776 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 4.81417e7i | − 0.673561i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.71928e7 | −0.926648 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.64533e7i | 1.17527i | 0.809125 | + | 0.587637i | \(0.199942\pi\) | ||||
−0.809125 | + | 0.587637i | \(0.800058\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.94432e7 | 0.260569 | 0.130284 | − | 0.991477i | \(-0.458411\pi\) | ||||
0.130284 | + | 0.991477i | \(0.458411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.70177e7i | 0.489089i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.54931e8 | 2.01823 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.33011e7i | 0.299290i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.40750e7 | −0.431582 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 1.05362e8i | − 1.31599i | −0.753021 | − | 0.657996i | \(-0.771404\pi\) | ||||
0.753021 | − | 0.657996i | \(-0.228596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.32564e8 | 1.63291 | 0.816457 | − | 0.577407i | \(-0.195935\pi\) | ||||
0.816457 | + | 0.577407i | \(0.195935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2.51947e7i | − 0.306085i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.60275e7 | −0.671362 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 2.10479e7i | − 0.242102i | −0.992646 | − | 0.121051i | \(-0.961374\pi\) | ||||
0.992646 | − | 0.121051i | \(-0.0386265\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.58077e7 | 0.179386 | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 9.59744e7i | 1.04623i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.31971e7 | −0.894981 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 6.75484e7i | − 0.717102i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.37459e7 | −0.563114 | −0.281557 | − | 0.959544i | \(-0.590851\pi\) | ||||
−0.281557 | + | 0.959544i | \(0.590851\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 2.60931e7i | − 0.269828i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.36640e7 | 0.241538 | 0.120769 | − | 0.992681i | \(-0.461464\pi\) | ||||
0.120769 | + | 0.992681i | \(0.461464\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.80452e7i | 0.282563i | 0.989969 | + | 0.141281i | \(0.0451222\pi\) | ||||
−0.989969 | + | 0.141281i | \(0.954878\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.33728e8 | −1.33004 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3.61101e7i | − 0.354550i | −0.984161 | − | 0.177275i | \(-0.943272\pi\) | ||||
0.984161 | − | 0.177275i | \(-0.0567283\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.03539e8 | 1.00365 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 6.37536e7i | − 0.610157i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.96930e7 | 0.753072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.90012e7i | 0.923761i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.62298e7 | −0.610236 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.70272e7i | 0.427900i | 0.976845 | + | 0.213950i | \(0.0686330\pi\) | ||||
−0.976845 | + | 0.213950i | \(0.931367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.51933e7 | 0.136527 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 5.50636e7i | − 0.488679i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.71227e8 | −1.50088 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 9.69668e7i | 0.819178i | 0.912270 | + | 0.409589i | \(0.134328\pi\) | ||||
−0.912270 | + | 0.409589i | \(0.865672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.70248e7 | 0.475908 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.31797e7i | 0.685807i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.85324e8 | 1.50961 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.16768e7i | 0.415905i | 0.978139 | + | 0.207952i | \(0.0666799\pi\) | ||||
−0.978139 | + | 0.207952i | \(0.933320\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.19494e8 | 0.950240 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | − 5.10121e7i | − 0.391426i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.31906e8 | 1.00025 | 0.500127 | − | 0.865952i | \(-0.333287\pi\) | ||||
0.500127 | + | 0.865952i | \(0.333287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.10853e8i | 0.830780i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.66735e7 | 0.123502 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1.61316e8i | − 1.18102i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.67089e8 | 1.93279 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.56477e8i | 1.11931i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.21687e7 | −0.0860462 | −0.0430231 | − | 0.999074i | \(-0.513699\pi\) | ||||
−0.0430231 | + | 0.999074i | \(0.513699\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.96786e7i | 0.626879i | 0.949608 | + | 0.313440i | \(0.101481\pi\) | ||||
−0.949608 | + | 0.313440i | \(0.898519\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.72980e7 | −0.672398 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 3.02675e8i | − 2.06797i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.39832e7 | −0.0944579 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 5.18014e7i | − 0.345986i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.82466e7 | 0.450712 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 2.62760e8i | − 1.71592i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.37692e8 | 0.889174 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.12488e7i | 0.455000i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.72097e8 | −1.71843 | −0.859216 | − | 0.511613i | \(-0.829048\pi\) | ||||
−0.859216 | + | 0.511613i | \(0.829048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 9.35449e7i | − 0.584279i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.37567e8 | 0.849815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.84749e8i | − 1.12881i | −0.825499 | − | 0.564404i | \(-0.809106\pi\) | ||||
0.825499 | − | 0.564404i | \(-0.190894\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.04035e7 | −0.123307 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.64390e7i | 0.217827i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.20821e8 | −0.714443 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 3.70881e7i | − 0.216948i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.60239e7 | 0.555666 | 0.277833 | − | 0.960629i | \(-0.410384\pi\) | ||||
0.277833 | + | 0.960629i | \(0.410384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 5.66690e7i | − 0.324422i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.88266e8 | −1.06631 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.37375e8i | − 1.33018i | −0.746764 | − | 0.665089i | \(-0.768393\pi\) | ||||
0.746764 | − | 0.665089i | \(-0.231607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.98381e8 | −2.76323 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.63867e7i | 0.0898963i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.26674e8 | 1.77328 | 0.886641 | − | 0.462458i | \(-0.153032\pi\) | ||||
0.886641 | + | 0.462458i | \(0.153032\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 971103.i | 0.00521623i | 0.999997 | + | 0.00260812i | \(0.000830190\pi\) | ||||
−0.999997 | + | 0.00260812i | \(0.999170\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.40116e6 | 0.0499709 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 1.20903e8i | 0.622876i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.84293e7 | −0.348910 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.77860e8i | 2.41154i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.91484e7 | 0.295444 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.47232e7i | 0.418878i | 0.977822 | + | 0.209439i | \(0.0671638\pi\) | ||||
−0.977822 | + | 0.209439i | \(0.932836\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.93410e8 | 0.946528 | ||||||||
\(590\) | 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 | ||||||||
\(595\) | − 3.73209e8i | − 1.77174i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.58135e8 | 0.743199 | ||||||||
\(598\) | 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 | \(-0.707415\pi\) | ||||
−0.606469 | + | 0.795107i | \(0.707415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.06630e7i | 0.413502i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.54286e8 | 1.14830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1.38978e8i | − 0.621413i | −0.950506 | − | 0.310707i | \(-0.899434\pi\) | ||||
0.950506 | − | 0.310707i | \(-0.100566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.58121e7 | −0.158554 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 1.89925e8i | − 0.832642i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.20201e8 | 1.82421 | 0.912106 | − | 0.409953i | \(-0.134455\pi\) | ||||
0.912106 | + | 0.409953i | \(0.134455\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 1.66595e8i | − 0.716205i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.25856e7 | −0.0535818 | −0.0267909 | − | 0.999641i | \(-0.508529\pi\) | ||||
−0.0267909 | + | 0.999641i | \(0.508529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 2.43243e8i | − 1.02558i | −0.858515 | − | 0.512789i | \(-0.828612\pi\) | ||||
0.858515 | − | 0.512789i | \(-0.171388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.82161e7 | 0.201334 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.24693e7i | − 0.0929234i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.96966e7 | −0.367397 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.20302e8i | − 0.488059i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.39440e7 | 0.337317 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | 1.30844e8i | 0.511016i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.06644e7 | 0.196013 | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − 4.20644e8i | − 1.58227i | −0.611639 | − | 0.791137i | \(-0.709490\pi\) | ||||
0.611639 | − | 0.791137i | \(-0.290510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.38333e8 | −0.515523 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 1.90083e8i | 0.688970i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.98645e8 | −1.07254 | −0.536272 | − | 0.844045i | \(-0.680168\pi\) | ||||
−0.536272 | + | 0.844045i | \(0.680168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.38014e8i | 1.20285i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.70681e7 | −0.342279 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 3.27357e8i | − 1.14384i | −0.820309 | − | 0.571920i | \(-0.806199\pi\) | ||||
0.820309 | − | 0.571920i | \(-0.193801\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.03255e8 | −1.39629 | −0.698145 | − | 0.715956i | \(-0.745991\pi\) | ||||
−0.698145 | + | 0.715956i | \(0.745991\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.33874e8i | 0.459364i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.38481e8 | 0.810941 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.05373e8i | 0.355103i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.46420e8 | 0.822995 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − 8.51985e7i | − 0.277026i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.50729e8 | 1.45261 | 0.726306 | − | 0.687371i | \(-0.241235\pi\) | ||||
0.726306 | + | 0.687371i | \(0.241235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.43385e8i | 0.777470i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.31605e8 | −0.733341 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.93405e8i | − 1.86247i | −0.364418 | − | 0.931235i | \(-0.618732\pi\) | ||||
0.364418 | − | 0.931235i | \(-0.381268\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.41493e8 | −1.68470 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00258e7i | 0.0617617i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.39802e8 | 1.03889 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 2.84794e8i | − 0.863170i | −0.902072 | − | 0.431585i | \(-0.857955\pi\) | ||||
0.902072 | − | 0.431585i | \(-0.142045\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.18233e8 | 0.355254 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 8.41545e8i | − 2.50682i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.77066e8 | 1.11357 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 4.09928e6i | − 0.0120026i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.51280e8 | −0.439165 | −0.219583 | − | 0.975594i | \(-0.570470\pi\) | ||||
−0.219583 | + | 0.975594i | \(0.570470\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.36404e7i | 0.154392i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.63622e8 | −1.32311 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.00880e8i | 1.41734i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.04474e8 | −1.69605 | −0.848025 | − | 0.529956i | \(-0.822208\pi\) | ||||
−0.848025 | + | 0.529956i | \(0.822208\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1.05796e8i | − 0.294349i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.59300e8 | 1.54304 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 4.26766e8i | − 1.16754i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.95027e8 | 0.800396 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.92148e8i | 0.516951i | 0.966018 | + | 0.258476i | \(0.0832201\pi\) | ||||
−0.966018 | + | 0.258476i | \(0.916780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.29297e8 | −0.611777 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 2.98578e7i | − 0.0790029i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.86196e8 | 0.488604 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | − 3.13099e8i | − 0.801549i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.99936e8 | −1.52333 | −0.761663 | − | 0.647973i | \(-0.775617\pi\) | ||||
−0.761663 | + | 0.647973i | \(0.775617\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 1.23676e8i | − 0.311475i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.54150e8 | 1.63409 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.83646e7i | 0.119838i | 0.998203 | + | 0.0599190i | \(0.0190842\pi\) | ||||
−0.998203 | + | 0.0599190i | \(0.980916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.55461e7 | −0.210255 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | − 5.99197e7i | − 0.143750i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.73491e8 | −0.888863 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 1.99551e8i | − 0.471123i | −0.971859 | − | 0.235562i | \(-0.924307\pi\) | ||||
0.971859 | − | 0.235562i | \(-0.0756929\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.72527e8 | −0.404085 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.04199e9i | − 2.42115i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.79819e8 | −1.10609 | −0.553045 | − | 0.833152i | \(-0.686534\pi\) | ||||
−0.553045 | + | 0.833152i | \(0.686534\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 3.47888e8i | − 0.795636i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.43069e8 | 0.551537 | 0.275769 | − | 0.961224i | \(-0.411068\pi\) | ||||
0.275769 | + | 0.961224i | \(0.411068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.95540e8i | − 0.440211i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.26798e8 | 0.729953 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 1.05802e7i | 0.0230850i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.17077e7 | −0.198549 | −0.0992744 | − | 0.995060i | \(-0.531652\pi\) | ||||
−0.0992744 | + | 0.995060i | \(0.531652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 9.88289e8i | − 2.12314i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.27176e7 | −0.112381 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.40946e8i | 0.509692i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.17087e9 | 2.45785 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 3.13587e7i | − 0.0653240i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.98471e8 | 1.65063 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.23454e8i | − 1.07388i | −0.843622 | − | 0.536938i | \(-0.819581\pi\) | ||||
0.843622 | − | 0.536938i | \(-0.180419\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.73232e8 | 0.352693 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.08406e8i | 1.43137i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.04683e8 | 0.209921 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 8.29483e8i | − 1.65085i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.58874e7 | −0.0313818 | −0.0156909 | − | 0.999877i | \(-0.504995\pi\) | ||||
−0.0156909 | + | 0.999877i | \(0.504995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.04935e9i | − 2.05721i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.96751e7 | 0.0382842 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.00364e8i | 1.35262i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.89635e8 | 1.32200 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.56573e8i | 0.297917i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.17580e8 | 0.977534 | 0.488767 | − | 0.872414i | \(-0.337447\pi\) | ||||
0.488767 | + | 0.872414i | \(0.337447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 9.43642e8i | − 1.76907i | −0.466476 | − | 0.884534i | \(-0.654476\pi\) | ||||
0.466476 | − | 0.884534i | \(-0.345524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.03212e8 | −0.192069 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 3.00908e8i | − 0.555855i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00071e8 | 0.366875 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 8.40744e7i | − 0.153042i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.51239e8 | 1.17682 | 0.588411 | − | 0.808562i | \(-0.299754\pi\) | ||||
0.588411 | + | 0.808562i | \(0.299754\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | − 6.24440e8i | − 1.10401i | −0.833840 | − | 0.552007i | \(-0.813862\pi\) | ||||
0.833840 | − | 0.552007i | \(-0.186138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.96016e8 | −1.04615 | −0.523076 | − | 0.852286i | \(-0.675216\pi\) | ||||
−0.523076 | + | 0.852286i | \(0.675216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 3.80915e8i | − 0.663782i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.79924e8 | 0.484289 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.49658e9i | 2.57064i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.66445e8 | −0.283854 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 2.17656e8i | 0.363320i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.38892e8 | 1.05891 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 3.61446e8i | − 0.594830i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.68485e8 | 1.09237 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.55116e8i | 0.251691i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.12761e9 | −1.81683 | −0.908414 | − | 0.418072i | \(-0.862706\pi\) | ||||
−0.908414 | + | 0.418072i | \(0.862706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.08825e8i | 0.334105i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.47949e8 | −0.870557 | −0.435279 | − | 0.900296i | \(-0.643350\pi\) | ||||
−0.435279 | + | 0.900296i | \(0.643350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.34544e8i | 1.00111i | 0.865704 | + | 0.500556i | \(0.166871\pi\) | ||||
−0.865704 | + | 0.500556i | \(0.833129\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.36801e8 | −0.371000 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1.20080e9i | − 1.86826i | −0.356928 | − | 0.934132i | \(-0.616176\pi\) | ||||
0.356928 | − | 0.934132i | \(-0.383824\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.95977e9 | −3.02801 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.63396e8i | 0.557600i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.63340e8 | −1.16321 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 4.65160e8i | − 0.703960i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.13118e8 | −0.320316 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.72036e8i | − 0.555342i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.11977e6 | 0.00907270 | 0.00453635 | − | 0.999990i | \(-0.498556\pi\) | ||||
0.00453635 | + | 0.999990i | \(0.498556\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 4.91469e8i | 0.713861i | 0.934131 | + | 0.356931i | \(0.116177\pi\) | ||||
−0.934131 | + | 0.356931i | \(0.883823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.48778e8 | 0.935980 | ||||||||
\(886\) | 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 | ||||||||
\(891\) | 1.03530e8i | 0.146364i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.70534e8 | 0.941600 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.72450e9i | 2.40544i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.47380e8 | −0.342758 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3.63756e8i | − 0.500646i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.87742e9 | 2.56678 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.96629e8i | 0.267045i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.17159e9 | 1.58063 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.10192e9i | − 1.47682i | −0.674351 | − | 0.738411i | \(-0.735577\pi\) | ||||
0.674351 | − | 0.738411i | \(-0.264423\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.38592e8 | −0.583942 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.89543e8i | 0.515229i | 0.966248 | + | 0.257615i | \(0.0829365\pi\) | ||||
−0.966248 | + | 0.257615i | \(0.917063\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.32331e8 | −0.568073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.55540e8i | − 0.333576i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.80458e8 | 0.623085 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | − 8.32594e8i | − 1.05883i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.74092e8 | 0.346315 | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 1.78872e8i | 0.221663i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.25900e8 | −0.647528 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 2.35791e9i | − 2.88464i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.16456e7 | 0.0749348 | 0.0374674 | − | 0.999298i | \(-0.488071\pi\) | ||||
0.0374674 | + | 0.999298i | \(0.488071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 7.66782e8i | − 0.926137i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.10725e8 | −0.372913 | −0.186457 | − | 0.982463i | \(-0.559700\pi\) | ||||
−0.186457 | + | 0.982463i | \(0.559700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.96763e8i | 0.830902i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.05232e8 | −0.243192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.13722e8i | 0.133904i | 0.997756 | + | 0.0669522i | \(0.0213275\pi\) | ||||
−0.997756 | + | 0.0669522i | \(0.978672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.98023e8 | 0.582707 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 3.07234e8i | − 0.357214i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.25518e8 | 0.607168 | 0.303584 | − | 0.952805i | \(-0.401817\pi\) | ||||
0.303584 | + | 0.952805i | \(0.401817\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.17743e8i | 0.135184i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.26258e8 | −0.258148 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.69687e8i | 0.872686i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.04323e9 | −1.17547 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 3.27045e8i | − 0.366209i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.51423e9 | −1.68504 | ||||||||
\(966\) | 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 | ||||||||
\(971\) | − 1.54851e9i | − 1.69144i | −0.533624 | − | 0.845722i | \(-0.679170\pi\) | ||||
0.533624 | − | 0.845722i | \(-0.320830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.19618e9 | −1.29855 | ||||||||
\(974\) | 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 | ||||||||
\(979\) | − 1.41959e8i | − 0.151292i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.71223e8 | 0.181366 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 6.58999e8i | 0.685383i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.78562e8 | 0.598082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 3.33810e8i | − 0.342988i | −0.985185 | − | 0.171494i | \(-0.945141\pi\) | ||||
0.985185 | − | 0.171494i | \(-0.0548594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.48965e8 | −0.254267 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.98054e9i | 2.01054i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.81174e8 | −0.485531 | −0.242765 | − | 0.970085i | \(-0.578055\pi\) | ||||
−0.242765 | + | 0.970085i | \(0.578055\pi\) | |||||||
\(998\) | 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 | 768.7.g.g.511.5 | 8 | ||
4.3 | odd | 2 | inner | 768.7.g.g.511.1 | 8 | ||
8.3 | odd | 2 | inner | 768.7.g.g.511.8 | 8 | ||
8.5 | even | 2 | inner | 768.7.g.g.511.4 | 8 | ||
16.3 | odd | 4 | 384.7.b.c.319.8 | yes | 8 | ||
16.5 | even | 4 | 384.7.b.c.319.5 | yes | 8 | ||
16.11 | odd | 4 | 384.7.b.c.319.1 | ✓ | 8 | ||
16.13 | even | 4 | 384.7.b.c.319.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.c.319.1 | ✓ | 8 | 16.11 | odd | 4 | ||
384.7.b.c.319.4 | yes | 8 | 16.13 | even | 4 | ||
384.7.b.c.319.5 | yes | 8 | 16.5 | even | 4 | ||
384.7.b.c.319.8 | yes | 8 | 16.3 | odd | 4 | ||
768.7.g.g.511.1 | 8 | 4.3 | odd | 2 | inner | ||
768.7.g.g.511.4 | 8 | 8.5 | even | 2 | inner | ||
768.7.g.g.511.5 | 8 | 1.1 | even | 1 | trivial | ||
768.7.g.g.511.8 | 8 | 8.3 | odd | 2 | inner |