Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (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: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.6140289600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 32x^{4} + 116x^{3} + 256x^{2} + 2778x + 7605 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(-2.90341 + 0.978064i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.6.c.k.449.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 29.2272i | − 1.87493i | −0.348081 | − | 0.937464i | \(-0.613167\pi\) | ||||
0.348081 | − | 0.937464i | \(-0.386833\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 44.5253i | 0.343449i | 0.985145 | + | 0.171724i | \(0.0549338\pi\) | ||||
−0.985145 | + | 0.171724i | \(0.945066\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −611.232 | −2.51536 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 349.258 | 0.870290 | 0.435145 | − | 0.900360i | \(-0.356697\pi\) | ||||
0.435145 | + | 0.900360i | \(0.356697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 255.040i | 0.418552i | 0.977857 | + | 0.209276i | \(0.0671108\pi\) | ||||
−0.977857 | + | 0.209276i | \(0.932889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1505.12i | − 1.26313i | −0.775322 | − | 0.631566i | \(-0.782412\pi\) | ||||
0.775322 | − | 0.631566i | \(-0.217588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2431.11 | 1.54498 | 0.772488 | − | 0.635030i | \(-0.219012\pi\) | ||||
0.772488 | + | 0.635030i | \(0.219012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1301.35 | 0.643942 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1435.50i | − 0.565825i | −0.959146 | − | 0.282913i | \(-0.908699\pi\) | ||||
0.959146 | − | 0.282913i | \(-0.0913007\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10762.4i | 2.84119i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2872.04 | −0.634156 | −0.317078 | − | 0.948400i | \(-0.602702\pi\) | ||||
−0.317078 | + | 0.948400i | \(0.602702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8940.96 | 1.67101 | 0.835507 | − | 0.549480i | \(-0.185174\pi\) | ||||
0.835507 | + | 0.549480i | \(0.185174\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 10207.8i | − 1.63173i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14536.6i | 1.74566i | 0.488024 | + | 0.872830i | \(0.337718\pi\) | ||||
−0.488024 | + | 0.872830i | \(0.662282\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7454.11 | 0.784756 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7504.01 | 0.697162 | 0.348581 | − | 0.937279i | \(-0.386664\pi\) | ||||
0.348581 | + | 0.937279i | \(0.386664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 13490.7i | − 1.11266i | −0.830961 | − | 0.556331i | \(-0.812209\pi\) | ||||
0.830961 | − | 0.556331i | \(-0.187791\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8449.69i | 0.557951i | 0.960298 | + | 0.278975i | \(0.0899948\pi\) | ||||
−0.960298 | + | 0.278975i | \(0.910005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14824.5 | 0.882043 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −43990.5 | −2.36828 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 28317.3i | − 1.38472i | −0.721553 | − | 0.692360i | \(-0.756571\pi\) | ||||
0.721553 | − | 0.692360i | \(-0.243429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 71054.8i | − 2.89672i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3530.13 | −0.132026 | −0.0660131 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660131 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45644.9 | 1.57061 | 0.785304 | − | 0.619110i | \(-0.212506\pi\) | ||||
0.785304 | + | 0.619110i | \(0.212506\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 27215.3i | − 0.863896i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 69849.6i | − 1.90098i | −0.310759 | − | 0.950489i | \(-0.600583\pi\) | ||||
0.310759 | − | 0.950489i | \(-0.399417\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −41955.6 | −1.06088 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −60090.2 | −1.41468 | −0.707339 | − | 0.706874i | \(-0.750105\pi\) | ||||
−0.707339 | + | 0.706874i | \(0.750105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 49204.6i | − 1.08068i | −0.841445 | − | 0.540342i | \(-0.818295\pi\) | ||||
0.841445 | − | 0.540342i | \(-0.181705\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15550.8i | 0.298900i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −981.509 | −0.0176940 | −0.00884702 | − | 0.999961i | \(-0.502816\pi\) | ||||
−0.00884702 | + | 0.999961i | \(0.502816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 166026. | 2.81167 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 38372.3i | 0.611396i | 0.952129 | + | 0.305698i | \(0.0988898\pi\) | ||||
−0.952129 | + | 0.305698i | \(0.901110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 83941.9i | 1.18900i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −39418.6 | −0.527504 | −0.263752 | − | 0.964591i | \(-0.584960\pi\) | ||||
−0.263752 | + | 0.964591i | \(0.584960\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11355.7 | −0.143751 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 261320.i | − 3.13303i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 51340.9i | − 0.554031i | −0.960865 | − | 0.277016i | \(-0.910655\pi\) | ||||
0.960865 | − | 0.277016i | \(-0.0893454\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −213477. | −2.18909 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −51557.0 | −0.502903 | −0.251451 | − | 0.967870i | \(-0.580908\pi\) | ||||
−0.251451 | + | 0.967870i | \(0.580908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6370.92i | − 0.0591710i | −0.999562 | − | 0.0295855i | \(-0.990581\pi\) | ||||
0.999562 | − | 0.0295855i | \(-0.00941873\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 5654.13i | − 0.0477426i | −0.999715 | − | 0.0238713i | \(-0.992401\pi\) | ||||
0.999715 | − | 0.0238713i | \(-0.00759919\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 217953. | 1.75710 | 0.878550 | − | 0.477650i | \(-0.158511\pi\) | ||||
0.878550 | + | 0.477650i | \(0.158511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 424866. | 3.27299 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 129389.i | − 0.953240i | −0.879109 | − | 0.476620i | \(-0.841862\pi\) | ||||
0.879109 | − | 0.476620i | \(-0.158138\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 155889.i | − 1.05281i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 67015.9 | 0.433821 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −39070.1 | −0.242595 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 219322.i | − 1.30713i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106258.i | 0.584594i | 0.956328 | + | 0.292297i | \(0.0944195\pi\) | ||||
−0.956328 | + | 0.292297i | \(0.905580\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −394296. | −2.08616 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −132808. | −0.676155 | −0.338077 | − | 0.941118i | \(-0.609777\pi\) | ||||
−0.338077 | + | 0.941118i | \(0.609777\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 108246.i | 0.530619i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 301171.i | 1.37092i | 0.728110 | + | 0.685460i | \(0.240399\pi\) | ||||
−0.728110 | + | 0.685460i | \(0.759601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −139021. | −0.610298 | −0.305149 | − | 0.952305i | \(-0.598706\pi\) | ||||
−0.305149 | + | 0.952305i | \(0.598706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 246961. | 1.04612 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 89074.6i | 0.364262i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 433279.i | − 1.65377i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 195083. | 0.719869 | 0.359934 | − | 0.932978i | \(-0.382799\pi\) | ||||
0.359934 | + | 0.932978i | \(0.382799\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 161597. | 0.576755 | 0.288378 | − | 0.957517i | \(-0.406884\pi\) | ||||
0.288378 | + | 0.957517i | \(0.406884\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 919977.i | 3.17723i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 108055.i | − 0.349860i | −0.984581 | − | 0.174930i | \(-0.944030\pi\) | ||||
0.984581 | − | 0.174930i | \(-0.0559700\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −827636. | −2.59625 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 63915.9 | 0.194332 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 35513.9i | 0.104696i | 0.998629 | + | 0.0523479i | \(0.0166705\pi\) | ||||
−0.998629 | + | 0.0523479i | \(0.983330\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 377413.i | 1.04719i | 0.851967 | + | 0.523595i | \(0.175409\pi\) | ||||
−0.851967 | + | 0.523595i | \(0.824591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 306248. | 0.824814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.48598e6 | −3.88617 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 142405.i | − 0.361752i | −0.983506 | − | 0.180876i | \(-0.942107\pi\) | ||||
0.983506 | − | 0.180876i | \(-0.0578932\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 103176.i | 0.247540i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −457275. | −1.06671 | −0.533353 | − | 0.845893i | \(-0.679068\pi\) | ||||
−0.533353 | + | 0.845893i | \(0.679068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −871860. | −1.97811 | −0.989055 | − | 0.147549i | \(-0.952862\pi\) | ||||
−0.989055 | + | 0.147549i | \(0.952862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1.33408e6i | − 2.94478i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 525675.i | − 1.09929i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −479199. | −0.975802 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −330154. | −0.654837 | −0.327418 | − | 0.944879i | \(-0.606179\pi\) | ||||
−0.327418 | + | 0.944879i | \(0.606179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 152914.i | − 0.295498i | −0.989025 | − | 0.147749i | \(-0.952797\pi\) | ||||
0.989025 | − | 0.147749i | \(-0.0472029\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 714867.i | 1.31238i | 0.754596 | + | 0.656190i | \(0.227833\pi\) | ||||
−0.754596 | + | 0.656190i | \(0.772167\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 292872. | 0.524258 | 0.262129 | − | 0.965033i | \(-0.415575\pi\) | ||||
0.262129 | + | 0.965033i | \(0.415575\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.04151e6 | −3.56420 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 127879.i | − 0.217800i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 877421.i | 1.42325i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 849085. | 1.34458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −365716. | −0.565507 | −0.282754 | − | 0.959193i | \(-0.591248\pi\) | ||||
−0.282754 | + | 0.959193i | \(0.591248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.75627e6i | 2.65242i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 398099.i | 0.573907i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.43812e6 | −2.02621 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 383866. | 0.528687 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 748539.i | − 1.00798i | −0.863709 | − | 0.503990i | \(-0.831865\pi\) | ||||
0.863709 | − | 0.503990i | \(-0.168135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 424142.i | 0.546319i | 0.961969 | + | 0.273159i | \(0.0880687\pi\) | ||||
−0.961969 | + | 0.273159i | \(0.911931\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.02868e6 | −1.29625 | −0.648126 | − | 0.761533i | \(-0.724447\pi\) | ||||
−0.648126 | + | 0.761533i | \(0.724447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 454507. | 0.560416 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 614128.i | 0.741087i | 0.928815 | + | 0.370544i | \(0.120829\pi\) | ||||
−0.928815 | + | 0.370544i | \(0.879171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 28686.8i | 0.0331750i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.36204e6 | 1.54239 | 0.771197 | − | 0.636597i | \(-0.219658\pi\) | ||||
0.771197 | + | 0.636597i | \(0.219658\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 354377. | 0.393027 | 0.196514 | − | 0.980501i | \(-0.437038\pi\) | ||||
0.196514 | + | 0.980501i | \(0.437038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.23722e6i | − 2.43049i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 620031.i | 0.646653i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.12152e6 | 1.14632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 826955. | 0.828509 | 0.414255 | − | 0.910161i | \(-0.364042\pi\) | ||||
0.414255 | + | 0.910161i | \(0.364042\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 501358.i | − 0.492432i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1.47307e6i | − 1.39121i | −0.718426 | − | 0.695603i | \(-0.755137\pi\) | ||||
0.718426 | − | 0.695603i | \(-0.244863\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −647248. | −0.599545 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.75548e6 | 1.59513 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 669755.i | − 0.597072i | −0.954398 | − | 0.298536i | \(-0.903502\pi\) | ||||
0.954398 | − | 0.298536i | \(-0.0964982\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.15210e6i | 0.989032i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 161730. | 0.136273 | 0.0681367 | − | 0.997676i | \(-0.478295\pi\) | ||||
0.0681367 | + | 0.997676i | \(0.478295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 709813. | 0.587112 | 0.293556 | − | 0.955942i | \(-0.405161\pi\) | ||||
0.293556 | + | 0.955942i | \(0.405161\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 331897.i | 0.269523i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.25136e6i | − 0.979904i | −0.871749 | − | 0.489952i | \(-0.837014\pi\) | ||||
0.871749 | − | 0.489952i | \(-0.162986\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.46500e6 | −4.20320 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.14718e6 | −0.866692 | −0.433346 | − | 0.901228i | \(-0.642667\pi\) | ||||
−0.433346 | + | 0.901228i | \(0.642667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.01151e6i | 0.750766i | 0.926870 | + | 0.375383i | \(0.122489\pi\) | ||||
−0.926870 | + | 0.375383i | \(0.877511\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 334118.i | 0.239439i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −845528. | −0.595502 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50055e6 | −1.03877 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 161999.i | − 0.110241i | −0.998480 | − | 0.0551204i | \(-0.982446\pi\) | ||||
0.998480 | − | 0.0551204i | \(-0.0175542\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.75885e6i | 2.47266i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 366109. | 0.236828 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 600677. | 0.382142 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.50687e6i | 0.942907i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.20761e6i | − 0.731276i | −0.930757 | − | 0.365638i | \(-0.880851\pi\) | ||||
0.930757 | − | 0.365638i | \(-0.119149\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −186204. | −0.110941 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.90780e6 | −1.70476 | −0.852382 | − | 0.522920i | \(-0.824843\pi\) | ||||
−0.852382 | + | 0.522920i | \(0.824843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.27324e6i | − 0.734597i | −0.930103 | − | 0.367298i | \(-0.880283\pi\) | ||||
0.930103 | − | 0.367298i | \(-0.119717\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.34305e6i | − 0.750659i | −0.926891 | − | 0.375330i | \(-0.877530\pi\) | ||||
0.926891 | − | 0.375330i | \(-0.122470\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00308e6 | −0.551899 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −165255. | −0.0895140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 3.65912e6i | − 1.95151i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 6.37016e6i | − 3.29444i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −376225. | −0.191627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.59250e6 | 0.798929 | 0.399464 | − | 0.916749i | \(-0.369196\pi\) | ||||
0.399464 | + | 0.916749i | \(0.369196\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 8.88526e6i | − 4.39096i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1.34715e6i | − 0.646163i | −0.946371 | − | 0.323082i | \(-0.895281\pi\) | ||||
0.946371 | − | 0.323082i | \(-0.104719\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.78169e6 | −1.78726 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.12270e6 | 1.45427 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.40840e6i | 0.646385i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.61456e6i | − 0.719832i | −0.932985 | − | 0.359916i | \(-0.882805\pi\) | ||||
0.932985 | − | 0.359916i | \(-0.117195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.78417e6 | 0.784103 | 0.392052 | − | 0.919943i | \(-0.371765\pi\) | ||||
0.392052 | + | 0.919943i | \(0.371765\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.74484e6 | −1.18919 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.02848e6i | 0.439299i | 0.975579 | + | 0.219650i | \(0.0704914\pi\) | ||||
−0.975579 | + | 0.219650i | \(0.929509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1.95869e6i | − 0.813383i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −719588. | −0.294678 | −0.147339 | − | 0.989086i | \(-0.547071\pi\) | ||||
−0.147339 | + | 0.989086i | \(0.547071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.43422e6 | 1.38695 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.14191e6i | 0.454848i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 412535.i | − 0.159881i | −0.996800 | − | 0.0799403i | \(-0.974527\pi\) | ||||
0.996800 | − | 0.0799403i | \(-0.0254730\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.58669e6 | −1.75361 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.26083e6 | 0.475580 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 4.01227e6i | − 1.49320i | −0.665273 | − | 0.746600i | \(-0.731685\pi\) | ||||
0.665273 | − | 0.746600i | \(-0.268315\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 732485.i | − 0.265427i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 725543. | 0.259457 | 0.129728 | − | 0.991550i | \(-0.458589\pi\) | ||||
0.129728 | + | 0.991550i | \(0.458589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.10564e6 | 1.09607 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 4.16948e6i | − 1.45240i | −0.687485 | − | 0.726199i | \(-0.741285\pi\) | ||||
0.687485 | − | 0.726199i | \(-0.258715\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.24594e6i | 2.79874i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −710805. | −0.238164 | −0.119082 | − | 0.992884i | \(-0.537995\pi\) | ||||
−0.119082 | + | 0.992884i | \(0.537995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.16059e6 | −0.714712 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.88161e6i | 1.26774i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.60119e6i | − 0.828315i | −0.910205 | − | 0.414157i | \(-0.864076\pi\) | ||||
0.910205 | − | 0.414157i | \(-0.135924\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.16374e6 | 0.994874 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.82517e6 | 0.566817 | 0.283409 | − | 0.958999i | \(-0.408535\pi\) | ||||
0.283409 | + | 0.958999i | \(0.408535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.28030e6i | 0.699407i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.07703e6i | 1.51923i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 527537. | 0.155935 | 0.0779677 | − | 0.996956i | \(-0.475157\pi\) | ||||
0.0779677 | + | 0.996956i | \(0.475157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.80241e6 | 2.57038 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 157180.i | − 0.0453442i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.06319e6i | 1.14427i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.11729e6 | 0.589175 | 0.294587 | − | 0.955625i | \(-0.404818\pi\) | ||||
0.294587 | + | 0.955625i | \(0.404818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.67556e6 | 0.460738 | 0.230369 | − | 0.973103i | \(-0.426007\pi\) | ||||
0.230369 | + | 0.973103i | \(0.426007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 5.16472e6i | − 1.40345i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.03235e6i | 0.539423i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.60341e6 | 0.682965 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.44216e6 | −0.373957 | −0.186978 | − | 0.982364i | \(-0.559869\pi\) | ||||
−0.186978 | + | 0.982364i | \(0.559869\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.49118e6i | 1.40749i | 0.710452 | + | 0.703746i | \(0.248491\pi\) | ||||
−0.710452 | + | 0.703746i | \(0.751509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 3.48986e6i | − 0.874186i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.57088e6 | −0.884329 | −0.442165 | − | 0.896934i | \(-0.645789\pi\) | ||||
−0.442165 | + | 0.896934i | \(0.645789\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.06121e6 | −2.21865 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.15711e6i | 0.522231i | 0.965308 | + | 0.261116i | \(0.0840904\pi\) | ||||
−0.965308 | + | 0.261116i | \(0.915910\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 5.70174e6i | − 1.34970i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.15945e6 | 0.973689 | 0.486845 | − | 0.873489i | \(-0.338148\pi\) | ||||
0.486845 | + | 0.873489i | \(0.338148\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.62083e6 | 0.606733 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.72304e6i | − 1.08138i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 6.32204e6i | − 1.41601i | −0.706207 | − | 0.708006i | \(-0.749595\pi\) | ||||
0.706207 | − | 0.708006i | \(-0.250405\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.61987e7 | 3.58880 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.12007e6 | −1.77954 | −0.889769 | − | 0.456411i | \(-0.849135\pi\) | ||||
−0.889769 | + | 0.456411i | \(0.849135\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.51746e6i | 1.19615i | 0.801439 | + | 0.598076i | \(0.204068\pi\) | ||||
−0.801439 | + | 0.598076i | \(0.795932\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.98287e6i | 1.69382i | 0.531737 | + | 0.846909i | \(0.321539\pi\) | ||||
−0.531737 | + | 0.846909i | \(0.678461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.11007e6 | 0.652888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.15814e6 | −0.655963 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4.71172e6i | − 0.968338i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.73084e7i | 3.48307i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.21796e6 | 1.43739 | 0.718697 | − | 0.695323i | \(-0.244739\pi\) | ||||
0.718697 | + | 0.695323i | \(0.244739\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.70742e6 | −0.730650 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1.86809e6i | − 0.364358i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.74447e6i | 0.333305i | 0.986016 | + | 0.166652i | \(0.0532958\pi\) | ||||
−0.986016 | + | 0.166652i | \(0.946704\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.03797e6 | 0.196297 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.10988e6 | −1.70533 | −0.852666 | − | 0.522457i | \(-0.825015\pi\) | ||||
−0.852666 | + | 0.522457i | \(0.825015\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.32277e6i | 0.801022i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.67553e6i | − 0.485869i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.94465e6 | −1.06875 | −0.534374 | − | 0.845248i | \(-0.679452\pi\) | ||||
−0.534374 | + | 0.845248i | \(0.679452\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.10307e7 | 1.96341 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.53195e6i | 0.446207i | 0.974795 | + | 0.223103i | \(0.0716187\pi\) | ||||
−0.974795 | + | 0.223103i | \(0.928381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 8.95078e6i | − 1.54647i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.91009e6 | −0.840030 | −0.420015 | − | 0.907517i | \(-0.637975\pi\) | ||||
−0.420015 | + | 0.907517i | \(0.637975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.19085e6 | 0.371160 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.61647e7i | 4.38957i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.95112e6i | 0.485579i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.16211e6 | −0.678259 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.90160e6 | −0.952522 | −0.476261 | − | 0.879304i | \(-0.658008\pi\) | ||||
−0.476261 | + | 0.879304i | \(0.658008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6.73830e6i | − 1.07720i | −0.842562 | − | 0.538600i | \(-0.818953\pi\) | ||||
0.842562 | − | 0.538600i | \(-0.181047\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 1.34572e7i | − 2.11071i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.37569e6 | 0.679842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.15773e6 | 0.332093 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.91382e6i | 0.291799i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.33649e7i | 2.00000i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.17757e6 | 0.767634 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.56711e6 | −0.964675 | −0.482337 | − | 0.875986i | \(-0.660212\pi\) | ||||
−0.482337 | + | 0.875986i | \(0.660212\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.54821e7i | 3.70881i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.27471e7i | − 1.82156i | −0.412896 | − | 0.910778i | \(-0.635483\pi\) | ||||
0.412896 | − | 0.910778i | \(-0.364517\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.78997e7 | −3.95064 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.98226e6 | −0.979755 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 43702.0i | − 0.00607699i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 1.22479e7i | − 1.67273i | −0.548175 | − | 0.836364i | \(-0.684677\pi\) | ||||
0.548175 | − | 0.836364i | \(-0.315323\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.44066e6 | 0.465707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.53640e7 | −2.06109 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.23945e6i | 0.297763i | 0.988855 | + | 0.148882i | \(0.0475673\pi\) | ||||
−0.988855 | + | 0.148882i | \(0.952433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.39237e6i | 0.965664i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.95223e6 | 0.511755 | 0.255877 | − | 0.966709i | \(-0.417636\pi\) | ||||
0.255877 | + | 0.966709i | \(0.417636\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.99947e6 | 0.898411 | 0.449206 | − | 0.893428i | \(-0.351707\pi\) | ||||
0.449206 | + | 0.893428i | \(0.351707\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.64949e6i | 1.22777i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 3.20338e6i | − 0.400561i | −0.979739 | − | 0.200280i | \(-0.935815\pi\) | ||||
0.979739 | − | 0.200280i | \(-0.0641853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.46927e6 | −0.554039 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.70854e6 | −0.209983 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 9.89002e6i | − 1.20511i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.35926e7i | 1.62820i | 0.580722 | + | 0.814102i | \(0.302770\pi\) | ||||
−0.580722 | + | 0.814102i | \(0.697230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.17365e7 | 2.58168 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.08936e7 | 2.46062 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 713635.i | 0.0833373i | 0.999131 | + | 0.0416687i | \(0.0132674\pi\) | ||||
−0.999131 | + | 0.0416687i | \(0.986733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 8.55984e6i | − 0.982946i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.09641e6 | 0.580359 | 0.290180 | − | 0.956972i | \(-0.406285\pi\) | ||||
0.290180 | + | 0.956972i | \(0.406285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 136310. | 0.0153937 | 0.00769683 | − | 0.999970i | \(-0.497550\pi\) | ||||
0.00769683 | + | 0.999970i | \(0.497550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.26943e7i | 4.78164i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.23096e6i | 0.686409i | 0.939261 | + | 0.343204i | \(0.111512\pi\) | ||||
−0.939261 | + | 0.343204i | \(0.888488\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.73754e6 | −0.408359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.15501e6 | −0.233532 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.37774e7i | − 1.48087i | −0.672128 | − | 0.740435i | \(-0.734620\pi\) | ||||
0.672128 | − | 0.740435i | \(-0.265380\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.85147e6i | 0.936058i | 0.883713 | + | 0.468029i | \(0.155036\pi\) | ||||
−0.883713 | + | 0.468029i | \(0.844964\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.22847e7 | 1.28866 | 0.644329 | − | 0.764748i | \(-0.277137\pi\) | ||||
0.644329 | + | 0.764748i | \(0.277137\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.54494e7 | 1.60762 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.75512e6i | − 0.181170i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.48164e7i | − 2.52099i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.18794e7 | 2.20500 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.75131e7 | 1.75101 | 0.875506 | − | 0.483207i | \(-0.160528\pi\) | ||||
0.875506 | + | 0.483207i | \(0.160528\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.06889e7i | 1.06029i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.78084e6i | 0.369181i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.67291e7 | 3.55842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.24879e7 | −1.20045 | −0.600223 | − | 0.799832i | \(-0.704922\pi\) | ||||
−0.600223 | + | 0.799832i | \(0.704922\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.50652e6i | − 0.525231i | −0.964901 | − | 0.262615i | \(-0.915415\pi\) | ||||
0.964901 | − | 0.262615i | \(-0.0845850\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.74623e6i | 0.257915i | 0.991650 | + | 0.128957i | \(0.0411630\pi\) | ||||
−0.991650 | + | 0.128957i | \(0.958837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.23292e6 | −0.114901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.16353e7 | 1.07604 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.24705e7i | − 1.14446i | −0.820092 | − | 0.572232i | \(-0.806078\pi\) | ||||
0.820092 | − | 0.572232i | \(-0.193922\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.00755e7i | 2.71831i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.75360e7 | −1.57296 | −0.786478 | − | 0.617618i | \(-0.788098\pi\) | ||||
−0.786478 | + | 0.617618i | \(0.788098\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.04528e6 | 0.805227 | 0.402613 | − | 0.915370i | \(-0.368102\pi\) | ||||
0.402613 | + | 0.915370i | \(0.368102\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.12193e7i | − 0.991250i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.12281e6i | 0.358821i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.18777e7 | −1.88989 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.59418e7 | 1.36689 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 9.09208e6i | − 0.773794i | −0.922123 | − | 0.386897i | \(-0.873547\pi\) | ||||
0.922123 | − | 0.386897i | \(-0.126453\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.55584e7i | − 1.30465i | −0.757940 | − | 0.652325i | \(-0.773794\pi\) | ||||
0.757940 | − | 0.652325i | \(-0.226206\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.28597e6 | 0.190281 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.23965e7 | 1.02431 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5.22623e6i | − 0.428684i | −0.976759 | − | 0.214342i | \(-0.931239\pi\) | ||||
0.976759 | − | 0.214342i | \(-0.0687607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.00653e7i | 2.43038i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.22203e6 | 0.579577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.01073e7 | −1.60199 | −0.800994 | − | 0.598672i | \(-0.795695\pi\) | ||||
−0.800994 | + | 0.598672i | \(0.795695\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 9.50515e6i | − 0.751840i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.12944e7i | − 0.880608i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.79493e7 | 1.38949 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.57869e7 | 1.21339 | 0.606695 | − | 0.794934i | \(-0.292495\pi\) | ||||
0.606695 | + | 0.794934i | \(0.292495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.53402e7i | 2.69700i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2.29559e6i | − 0.172721i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.13552e6 | 0.383680 | 0.191840 | − | 0.981426i | \(-0.438555\pi\) | ||||
0.191840 | + | 0.981426i | \(0.438555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 599930. | 0.0445068 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.28347e7i | − 0.945502i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 3.98087e7i | − 2.89188i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.90785e6 | 0.209773 | 0.104886 | − | 0.994484i | \(-0.466552\pi\) | ||||
0.104886 | + | 0.994484i | \(0.466552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 283667. | 0.0203222 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1.03575e7i | − 0.736898i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.85123e6i | − 0.550937i | −0.961310 | − | 0.275468i | \(-0.911167\pi\) | ||||
0.961310 | − | 0.275468i | \(-0.0888329\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.50435e7 | −1.74533 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.03051e7 | −1.40544 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.41173e7i | − 0.970491i | −0.874378 | − | 0.485245i | \(-0.838730\pi\) | ||||
0.874378 | − | 0.485245i | \(-0.161270\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 2.43955e7i | − 1.65440i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.20049e6 | −0.282937 | −0.141468 | − | 0.989943i | \(-0.545182\pi\) | ||||
−0.141468 | + | 0.989943i | \(0.545182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.81218e7 | 1.21243 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1.18490e6i | − 0.0787425i | −0.999225 | − | 0.0393712i | \(-0.987465\pi\) | ||||
0.999225 | − | 0.0393712i | \(-0.0125355\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2.34544e7i | − 1.53788i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 251752. | 0.0163971 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.94605e6 | 0.255307 | 0.127653 | − | 0.991819i | \(-0.459255\pi\) | ||||
0.127653 | + | 0.991819i | \(0.459255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 2.41696e7i | − 1.55340i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22109e6i | 0.0774479i | 0.999250 | + | 0.0387239i | \(0.0123293\pi\) | ||||
−0.999250 | + | 0.0387239i | \(0.987671\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.46533e7 | −0.923276 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.91652e7 | 1.19964 | 0.599822 | − | 0.800134i | \(-0.295238\pi\) | ||||
0.599822 | + | 0.800134i | \(0.295238\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.70442e6i | 0.603473i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 900323.i | − 0.0552599i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.50951e6 | −0.579886 | −0.289943 | − | 0.957044i | \(-0.593636\pi\) | ||||
−0.289943 | + | 0.957044i | \(0.593636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.30539e7 | −2.60841 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 526263.i | 0.0316777i | 0.999875 | + | 0.0158389i | \(0.00504187\pi\) | ||||
−0.999875 | + | 0.0158389i | \(0.994958\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.89173e7i | 1.12410i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.82431e7 | 1.07710 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.09870e7 | −1.23118 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 3.09101e7i | − 1.80176i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.05915e7i | 1.18509i | 0.805538 | + | 0.592544i | \(0.201877\pi\) | ||||
−0.805538 | + | 0.592544i | \(0.798123\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.95751e7 | −1.11947 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.76109e6 | 0.327389 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.16413e7i | 0.657382i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.08952e7i | 1.16520i | 0.812760 | + | 0.582599i | \(0.197964\pi\) | ||||
−0.812760 | + | 0.582599i | \(0.802036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.27178e7 | 0.704766 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.40939e7 | 1.32686 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.71851e7i | − 0.940509i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 4.72694e6i | − 0.255503i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.38823e7 | 1.82013 | 0.910063 | − | 0.414470i | \(-0.136033\pi\) | ||||
0.910063 | + | 0.414470i | \(0.136033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.25428e6 | −0.440684 | −0.220342 | − | 0.975423i | \(-0.570717\pi\) | ||||
−0.220342 | + | 0.975423i | \(0.570717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 2.07459e7i | − 1.10079i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3.27974e7i | − 1.71903i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.94098e6 | 0.361586 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.99898e6 | 0.103503 | 0.0517513 | − | 0.998660i | \(-0.483520\pi\) | ||||
0.0517513 | + | 0.998660i | \(0.483520\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.28086e7i | − 0.659176i | −0.944125 | − | 0.329588i | \(-0.893090\pi\) | ||||
0.944125 | − | 0.329588i | \(-0.106910\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.83308e7i | − 1.44044i | −0.693745 | − | 0.720221i | \(-0.744040\pi\) | ||||
0.693745 | − | 0.720221i | \(-0.255960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.91663e6 | −0.400087 | −0.200043 | − | 0.979787i | \(-0.564108\pi\) | ||||
−0.200043 | + | 0.979787i | \(0.564108\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.65739e7 | −1.83725 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2.23126e7i | − 1.11414i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.62263e7i | 4.74767i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.18676e7 | −1.07250 | −0.536249 | − | 0.844060i | \(-0.680159\pi\) | ||||
−0.536249 | + | 0.844060i | \(0.680159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.22625e7 | −0.597847 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.35289e7i | 1.62499i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.73961e6i | − 0.0833188i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.95637e7 | 1.40763 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.08673e7 | 0.987739 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 6.73771e6i | − 0.317059i | −0.987354 | − | 0.158529i | \(-0.949325\pi\) | ||||
0.987354 | − | 0.158529i | \(-0.0506753\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 2.01368e7i | − 0.936565i | −0.883579 | − | 0.468283i | \(-0.844873\pi\) | ||||
0.883579 | − | 0.468283i | \(-0.155127\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.31020e7 | −1.06823 | −0.534117 | − | 0.845410i | \(-0.679356\pi\) | ||||
−0.534117 | + | 0.845410i | \(0.679356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.76535e6 | 0.448932 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.79582e7i | 1.27785i | 0.769267 | + | 0.638927i | \(0.220622\pi\) | ||||
−0.769267 | + | 0.638927i | \(0.779378\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.47125e7i | 1.11652i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −342800. | −0.0153989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.78144e7 | 0.795658 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.13812e7i | 1.39359i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.75058e7i | − 1.64664i | −0.567574 | − | 0.823322i | \(-0.692118\pi\) | ||||
0.567574 | − | 0.823322i | \(-0.307882\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.73477e6 | −0.206693 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.94116e6 | −0.0842601 | −0.0421300 | − | 0.999112i | \(-0.513414\pi\) | ||||
−0.0421300 | + | 0.999112i | \(0.513414\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.90752e7i | − 1.68655i | −0.537481 | − | 0.843276i | \(-0.680624\pi\) | ||||
0.537481 | − | 0.843276i | \(-0.319376\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.87662e7i | 0.800878i | 0.916323 | + | 0.400439i | \(0.131142\pi\) | ||||
−0.916323 | + | 0.400439i | \(0.868858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.73119e6 | −0.200778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.79859e7 | 2.44697 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.05422e7i | 0.862020i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 1.07004e7i | − 0.444035i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.56788e7 | −1.05968 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26209e7 | −1.74908 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.75561e7i | − 0.716489i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.79416e7i | 1.12780i | 0.825842 | + | 0.563901i | \(0.190700\pi\) | ||||
−0.825842 | + | 0.563901i | \(0.809300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.15133e7 | 1.26498 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.32374e7 | 0.528452 | 0.264226 | − | 0.964461i | \(-0.414884\pi\) | ||||
0.264226 | + | 0.964461i | \(0.414884\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.34018e7i | 0.532092i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 5.91332e6i | − 0.232224i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.80433e7 | 1.09532 | 0.547660 | − | 0.836701i | \(-0.315519\pi\) | ||||
0.547660 | + | 0.836701i | \(0.315519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.52951e7 | −1.37109 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1.53254e7i | − 0.592117i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.89411e6i | 0.148836i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.96341e7 | −0.746400 | −0.373200 | − | 0.927751i | \(-0.621739\pi\) | ||||
−0.373200 | + | 0.927751i | \(0.621739\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.60401e7 | 1.36273 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.49871e7i | 3.19631i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 2.71944e7i | − 1.01188i | −0.862567 | − | 0.505942i | \(-0.831145\pi\) | ||||
0.862567 | − | 0.505942i | \(-0.168855\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.72133e7 | −1.37732 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.74326e7 | 1.00993 | 0.504966 | − | 0.863139i | \(-0.331505\pi\) | ||||
0.504966 | + | 0.863139i | \(0.331505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.07720e7i | − 0.394472i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.42413e7i | − 0.516029i | −0.966141 | − | 0.258014i | \(-0.916932\pi\) | ||||
0.966141 | − | 0.258014i | \(-0.0830682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.25491e7 | 0.452323 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.92535e7 | −1.40743 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.25786e7i | 1.16198i | 0.813910 | + | 0.580992i | \(0.197335\pi\) | ||||
−0.813910 | + | 0.580992i | \(0.802665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.93173e7i | 1.03477i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.34097e7 | −0.470841 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.13117e7 | 1.79229 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.45598e6i | 0.120090i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.03932e6i | 0.138913i | 0.997585 | + | 0.0694564i | \(0.0221265\pi\) | ||||
−0.997585 | + | 0.0694564i | \(0.977874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.06946e8 | −3.65894 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.98023e7 | 1.01438 | 0.507191 | − | 0.861834i | \(-0.330684\pi\) | ||||
0.507191 | + | 0.861834i | \(0.330684\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 6.18993e6i | − 0.209606i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.70486e7i | 0.906586i | 0.891362 | + | 0.453293i | \(0.149751\pi\) | ||||
−0.891362 | + | 0.453293i | \(0.850249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.37672e7 | −0.459082 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.33220e8 | −4.41974 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.15761e7i | 1.04226i | 0.853479 | + | 0.521128i | \(0.174489\pi\) | ||||
−0.853479 | + | 0.521128i | \(0.825511\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.09960e7i | 0.359288i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.93658e7 | −0.629572 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.49963e6 | −0.210235 | −0.105117 | − | 0.994460i | \(-0.533522\pi\) | ||||
−0.105117 | + | 0.994460i | \(0.533522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 4.65443e7i | − 1.49794i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.34950e7i | 0.429966i | 0.976618 | + | 0.214983i | \(0.0689695\pi\) | ||||
−0.976618 | + | 0.214983i | \(0.931030\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.56449e8 | −4.95975 |
(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 | 800.6.c.k.449.1 | 6 | ||
4.3 | odd | 2 | 800.6.c.j.449.6 | 6 | |||
5.2 | odd | 4 | 160.6.a.f.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 800.6.a.o.1.3 | 3 | |||
5.4 | even | 2 | inner | 800.6.c.k.449.6 | 6 | ||
20.3 | even | 4 | 800.6.a.n.1.1 | 3 | |||
20.7 | even | 4 | 160.6.a.g.1.3 | yes | 3 | ||
20.19 | odd | 2 | 800.6.c.j.449.1 | 6 | |||
40.27 | even | 4 | 320.6.a.x.1.1 | 3 | |||
40.37 | odd | 4 | 320.6.a.y.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.f.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
160.6.a.g.1.3 | yes | 3 | 20.7 | even | 4 | ||
320.6.a.x.1.1 | 3 | 40.27 | even | 4 | |||
320.6.a.y.1.3 | 3 | 40.37 | odd | 4 | |||
800.6.a.n.1.1 | 3 | 20.3 | even | 4 | |||
800.6.a.o.1.3 | 3 | 5.3 | odd | 4 | |||
800.6.c.j.449.1 | 6 | 20.19 | odd | 2 | |||
800.6.c.j.449.6 | 6 | 4.3 | odd | 2 | |||
800.6.c.k.449.1 | 6 | 1.1 | even | 1 | trivial | ||
800.6.c.k.449.6 | 6 | 5.4 | even | 2 | inner |