Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,3,Mod(97,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(21.3624527258\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.97 |
Dual form | 784.3.c.e.97.3 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 0.717439i | − 0.239146i | −0.992825 | − | 0.119573i | \(-0.961847\pi\) | ||||
0.992825 | − | 0.119573i | \(-0.0381526\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.63103i | 1.32621i | 0.748528 | + | 0.663103i | \(0.230761\pi\) | ||||
−0.748528 | + | 0.663103i | \(0.769239\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.48528 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.75736 | 0.432487 | 0.216244 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216244 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 15.2913i | − 1.17625i | −0.808769 | − | 0.588126i | \(-0.799866\pi\) | ||||
0.808769 | − | 0.588126i | \(-0.200134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.75736 | 0.317157 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.76127i | − 0.221251i | −0.993862 | − | 0.110626i | \(-0.964715\pi\) | ||||
0.993862 | − | 0.110626i | \(-0.0352855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.18154i | 0.220081i | 0.993927 | + | 0.110041i | \(0.0350981\pi\) | ||||
−0.993927 | + | 0.110041i | \(0.964902\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 27.7279 | 1.20556 | 0.602781 | − | 0.797907i | \(-0.294059\pi\) | ||||
0.602781 | + | 0.797907i | \(0.294059\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.9706 | −0.758823 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 12.5446i | − 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.51472 | 0.121197 | 0.0605986 | − | 0.998162i | \(-0.480699\pi\) | ||||
0.0605986 | + | 0.998162i | \(0.480699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 48.8667i | 1.57635i | 0.615454 | + | 0.788173i | \(0.288973\pi\) | ||||
−0.615454 | + | 0.788173i | \(0.711027\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 3.41311i | − 0.103428i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.94113 | −0.0794899 | −0.0397449 | − | 0.999210i | \(-0.512655\pi\) | ||||
−0.0397449 | + | 0.999210i | \(0.512655\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.9706 | −0.281296 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 27.9590i | 0.681927i | 0.940077 | + | 0.340963i | \(0.110753\pi\) | ||||
−0.940077 | + | 0.340963i | \(0.889247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4853 | 0.243844 | 0.121922 | − | 0.992540i | \(-0.461094\pi\) | ||||
0.121922 | + | 0.992540i | \(0.461094\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 56.2662i | 1.25036i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 52.6790i | 1.12083i | 0.828212 | + | 0.560415i | \(0.189358\pi\) | ||||
−0.828212 | + | 0.560415i | \(0.810642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.69848 | −0.0529115 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 55.9706 | 1.05605 | 0.528024 | − | 0.849229i | \(-0.322933\pi\) | ||||
0.528024 | + | 0.849229i | \(0.322933\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 31.5462i | 0.573567i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.0526316 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 38.7206i | − 0.656281i | −0.944629 | − | 0.328141i | \(-0.893578\pi\) | ||||
0.944629 | − | 0.328141i | \(-0.106422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 90.5080i | 1.48374i | 0.670545 | + | 0.741869i | \(0.266060\pi\) | ||||
−0.670545 | + | 0.741869i | \(0.733940\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 101.397 | 1.55995 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.6396 | 0.517009 | 0.258505 | − | 0.966010i | \(-0.416770\pi\) | ||||
0.258505 | + | 0.966010i | \(0.416770\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 19.8931i | − 0.288306i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36.4264 | −0.513048 | −0.256524 | − | 0.966538i | \(-0.582577\pi\) | ||||
−0.256524 | + | 0.966538i | \(0.582577\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 52.6069i | 0.720642i | 0.932828 | + | 0.360321i | \(0.117333\pi\) | ||||
−0.932828 | + | 0.360321i | \(0.882667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.6102i | 0.181470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 33.7868 | 0.427681 | 0.213840 | − | 0.976869i | \(-0.431403\pi\) | ||||
0.213840 | + | 0.976869i | \(0.431403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 67.3675 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 127.577i | − 1.53708i | −0.639803 | − | 0.768539i | \(-0.720984\pi\) | ||||
0.639803 | − | 0.768539i | \(-0.279016\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.9411 | 0.293425 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 2.52160i | − 0.0289839i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 50.3314i | 0.565522i | 0.959190 | + | 0.282761i | \(0.0912503\pi\) | ||||
−0.959190 | + | 0.282761i | \(0.908750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 35.0589 | 0.376977 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.7279 | −0.291873 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 101.792i | − 1.04940i | −0.851287 | − | 0.524700i | \(-0.824177\pi\) | ||||
0.851287 | − | 0.524700i | \(-0.175823\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 40.3675 | 0.407753 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 59.6793i | − 0.590884i | −0.955361 | − | 0.295442i | \(-0.904533\pi\) | ||||
0.955361 | − | 0.295442i | \(-0.0954669\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 120.178i | 1.16678i | 0.812193 | + | 0.583388i | \(0.198273\pi\) | ||||
−0.812193 | + | 0.583388i | \(0.801727\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 113.610 | 1.06178 | 0.530889 | − | 0.847442i | \(-0.321858\pi\) | ||||
0.530889 | + | 0.847442i | \(0.321858\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −145.309 | −1.33311 | −0.666553 | − | 0.745457i | \(-0.732231\pi\) | ||||
−0.666553 | + | 0.745457i | \(0.732231\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.11008i | 0.0190097i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 34.5442 | 0.305700 | 0.152850 | − | 0.988249i | \(-0.451155\pi\) | ||||
0.152850 | + | 0.988249i | \(0.451155\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 183.865i | 1.59882i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 129.751i | − 1.10898i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −98.3675 | −0.812955 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.0589 | 0.163080 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 39.9814i | 0.319851i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 247.338 | 1.94754 | 0.973772 | − | 0.227526i | \(-0.0730636\pi\) | ||||
0.973772 | + | 0.227526i | \(0.0730636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 7.52255i | − 0.0583143i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 147.645i | − 1.12706i | −0.826096 | − | 0.563529i | \(-0.809443\pi\) | ||||
0.826096 | − | 0.563529i | \(-0.190557\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 83.1838 | 0.616176 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −32.5736 | −0.237763 | −0.118882 | − | 0.992908i | \(-0.537931\pi\) | ||||
−0.118882 | + | 0.992908i | \(0.537931\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 68.5857i | 0.493422i | 0.969089 | + | 0.246711i | \(0.0793499\pi\) | ||||
−0.969089 | + | 0.246711i | \(0.920650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.7939 | 0.268042 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 72.7461i | − 0.508714i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 23.3062i | 0.160732i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 92.3970 | 0.620114 | 0.310057 | − | 0.950718i | \(-0.399652\pi\) | ||||
0.310057 | + | 0.950718i | \(0.399652\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 91.7868 | 0.607860 | 0.303930 | − | 0.952694i | \(-0.401701\pi\) | ||||
0.303930 | + | 0.952694i | \(0.401701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 31.9155i | − 0.208598i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −324.037 | −2.09056 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.45631i | 0.0538618i | 0.999637 | + | 0.0269309i | \(0.00857341\pi\) | ||||
−0.999637 | + | 0.0269309i | \(0.991427\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 40.1555i | − 0.252550i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −221.978 | −1.36183 | −0.680913 | − | 0.732364i | \(-0.738417\pi\) | ||||
−0.680913 | + | 0.732364i | \(0.738417\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 22.6325 | 0.137166 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 168.841i | 1.01102i | 0.862820 | + | 0.505511i | \(0.168696\pi\) | ||||
−0.862820 | + | 0.505511i | \(0.831304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64.8234 | −0.383570 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 35.4815i | 0.207494i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 164.341i | 0.949947i | 0.880000 | + | 0.474974i | \(0.157542\pi\) | ||||
−0.880000 | + | 0.474974i | \(0.842458\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.7797 | −0.156947 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −185.184 | −1.03455 | −0.517273 | − | 0.855820i | \(-0.673053\pi\) | ||||
−0.517273 | + | 0.855820i | \(0.673053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 155.086i | 0.856830i | 0.903582 | + | 0.428415i | \(0.140928\pi\) | ||||
−0.903582 | + | 0.428415i | \(0.859072\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 64.9340 | 0.354831 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 19.5027i | − 0.105420i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 17.8937i | − 0.0956884i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −248.095 | −1.29893 | −0.649465 | − | 0.760392i | \(-0.725007\pi\) | ||||
−0.649465 | + | 0.760392i | \(0.725007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 154.338 | 0.799679 | 0.399840 | − | 0.916585i | \(-0.369066\pi\) | ||||
0.399840 | + | 0.916585i | \(0.369066\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 72.7461i | − 0.373057i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −181.103 | −0.919303 | −0.459651 | − | 0.888099i | \(-0.652026\pi\) | ||||
−0.459651 | + | 0.888099i | \(0.652026\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 348.707i | − 1.75229i | −0.482043 | − | 0.876147i | \(-0.660105\pi\) | ||||
0.482043 | − | 0.876147i | \(-0.339895\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 24.8518i | − 0.123641i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −185.397 | −0.904375 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 235.279 | 1.13661 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.8931i | 0.0951823i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −364.073 | −1.72547 | −0.862733 | − | 0.505660i | \(-0.831249\pi\) | ||||
−0.862733 | + | 0.505660i | \(0.831249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.1337i | 0.122694i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 69.5282i | 0.323387i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.7422 | 0.172339 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −57.5147 | −0.260248 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 123.231i | 0.552603i | 0.961071 | + | 0.276302i | \(0.0891089\pi\) | ||||
−0.961071 | + | 0.276302i | \(0.910891\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −160.971 | −0.715425 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 76.3756i | 0.336456i | 0.985748 | + | 0.168228i | \(0.0538045\pi\) | ||||
−0.985748 | + | 0.168228i | \(0.946195\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 357.286i | − 1.56020i | −0.625654 | − | 0.780101i | \(-0.715168\pi\) | ||||
0.625654 | − | 0.780101i | \(-0.284832\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −273.073 | −1.17199 | −0.585994 | − | 0.810315i | \(-0.699296\pi\) | ||||
−0.585994 | + | 0.810315i | \(0.699296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −349.316 | −1.48645 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 24.2400i | − 0.102278i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 265.103 | 1.10922 | 0.554608 | − | 0.832112i | \(-0.312868\pi\) | ||||
0.554608 | + | 0.832112i | \(0.312868\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 87.6383i | − 0.363644i | −0.983331 | − | 0.181822i | \(-0.941800\pi\) | ||||
0.983331 | − | 0.181822i | \(-0.0581995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 161.234i | − 0.663513i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 63.9411 | 0.258871 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −91.5290 | −0.367586 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 495.655i | − 1.97472i | −0.158491 | − | 0.987360i | \(-0.550663\pi\) | ||||
0.158491 | − | 0.987360i | \(-0.449337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 131.912 | 0.521390 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 17.8937i | − 0.0701715i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 400.536i | − 1.55851i | −0.626709 | − | 0.779254i | \(-0.715598\pi\) | ||||
0.626709 | − | 0.779254i | \(-0.284402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29.8234 | 0.114266 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 32.3452 | 0.122986 | 0.0614928 | − | 0.998108i | \(-0.480414\pi\) | ||||
0.0614928 | + | 0.998108i | \(0.480414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 371.142i | 1.40054i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.1097 | 0.135242 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 306.963i | − 1.14113i | −0.821253 | − | 0.570564i | \(-0.806725\pi\) | ||||
0.821253 | − | 0.570564i | \(-0.193275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 75.9852i | − 0.280388i | −0.990124 | − | 0.140194i | \(-0.955227\pi\) | ||||
0.990124 | − | 0.140194i | \(-0.0447726\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −90.2498 | −0.328181 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 278.411 | 1.00509 | 0.502547 | − | 0.864550i | \(-0.332396\pi\) | ||||
0.502547 | + | 0.864550i | \(0.332396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 414.648i | 1.48619i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 394.690 | 1.40459 | 0.702296 | − | 0.711885i | \(-0.252158\pi\) | ||||
0.702296 | + | 0.711885i | \(0.252158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 146.396i | − 0.517301i | −0.965971 | − | 0.258650i | \(-0.916722\pi\) | ||||
0.965971 | − | 0.258650i | \(-0.0832778\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 19.8931i | 0.0698003i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 274.853 | 0.951048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −73.0294 | −0.250960 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 299.678i | − 1.02279i | −0.859345 | − | 0.511396i | \(-0.829128\pi\) | ||||
0.859345 | − | 0.511396i | \(-0.170872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 256.757 | 0.870364 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 59.6793i | − 0.200940i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 423.996i | − 1.41805i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −42.8162 | −0.141308 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −600.161 | −1.96774 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 20.9886i | − 0.0683666i | −0.999416 | − | 0.0341833i | \(-0.989117\pi\) | ||||
0.999416 | − | 0.0341833i | \(-0.0108830\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 86.2203 | 0.279030 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 182.039i | − 0.585336i | −0.956214 | − | 0.292668i | \(-0.905457\pi\) | ||||
0.956214 | − | 0.292668i | \(-0.0945430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 97.9286i | 0.312871i | 0.987688 | + | 0.156435i | \(0.0500003\pi\) | ||||
−0.987688 | + | 0.156435i | \(0.950000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −481.971 | −1.52041 | −0.760206 | − | 0.649682i | \(-0.774902\pi\) | ||||
−0.760206 | + | 0.649682i | \(0.774902\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.7208 | 0.0524162 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 81.5084i | − 0.253920i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.7279 | 0.0486933 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 290.084i | 0.892567i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 104.250i | 0.318808i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −225.007 | −0.679780 | −0.339890 | − | 0.940465i | \(-0.610390\pi\) | ||||
−0.339890 | + | 0.940465i | \(0.610390\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.9563 | −0.0749438 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 229.696i | 0.685661i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −264.368 | −0.784473 | −0.392237 | − | 0.919864i | \(-0.628299\pi\) | ||||
−0.392237 | + | 0.919864i | \(0.628299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 24.7833i | − 0.0731071i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 232.476i | 0.681749i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 131.912 | 0.382353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 191.257 | 0.551173 | 0.275586 | − | 0.961276i | \(-0.411128\pi\) | ||||
0.275586 | + | 0.961276i | \(0.411128\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 135.448i | − 0.388104i | −0.980991 | − | 0.194052i | \(-0.937837\pi\) | ||||
0.980991 | − | 0.194052i | \(-0.0621630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −191.823 | −0.546505 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 348.490i | − 0.987225i | −0.869682 | − | 0.493612i | \(-0.835676\pi\) | ||||
0.869682 | − | 0.493612i | \(-0.164324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 241.545i | − 0.680407i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −304.831 | −0.849110 | −0.424555 | − | 0.905402i | \(-0.639569\pi\) | ||||
−0.424555 | + | 0.905402i | \(0.639569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 343.515 | 0.951564 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 70.5727i | 0.194415i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −348.838 | −0.955720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 95.0042i | 0.258867i | 0.991588 | + | 0.129434i | \(0.0413159\pi\) | ||||
−0.991588 | + | 0.129434i | \(0.958684\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 237.240i | 0.642927i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 253.558 | 0.679781 | 0.339891 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339891 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 28.6842 | 0.0764912 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 53.7446i | − 0.142559i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −508.250 | −1.34103 | −0.670514 | − | 0.741897i | \(-0.733926\pi\) | ||||
−0.670514 | + | 0.741897i | \(0.733926\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 177.450i | − 0.465748i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 477.761i | 1.24742i | 0.781656 | + | 0.623709i | \(0.214375\pi\) | ||||
−0.781656 | + | 0.623709i | \(0.785625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 88.9706 | 0.229898 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 170.220 | 0.437584 | 0.218792 | − | 0.975771i | \(-0.429788\pi\) | ||||
0.218792 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 104.292i | − 0.266732i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −105.926 | −0.269532 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 224.041i | 0.567193i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 244.550i | − 0.615995i | −0.951387 | − | 0.307997i | \(-0.900341\pi\) | ||||
0.951387 | − | 0.307997i | \(-0.0996588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −417.573 | −1.04133 | −0.520664 | − | 0.853762i | \(-0.674316\pi\) | ||||
−0.520664 | + | 0.853762i | \(0.674316\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 747.235 | 1.85418 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 446.716i | 1.10300i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.9920 | −0.0343784 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 308.212i | 0.753574i | 0.926300 | + | 0.376787i | \(0.122971\pi\) | ||||
−0.926300 | + | 0.376787i | \(0.877029\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.3696i | 0.0568603i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 845.970 | 2.03848 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 49.2061 | 0.118000 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 103.142i | − 0.246163i | −0.992397 | − | 0.123081i | \(-0.960722\pi\) | ||||
0.992397 | − | 0.123081i | \(-0.0392776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −165.220 | −0.392447 | −0.196224 | − | 0.980559i | \(-0.562868\pi\) | ||||
−0.196224 | + | 0.980559i | \(0.562868\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 446.996i | 1.05673i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 71.3535i | 0.167891i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −52.1909 | −0.121657 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −594.536 | −1.37943 | −0.689717 | − | 0.724079i | \(-0.742265\pi\) | ||||
−0.689717 | + | 0.724079i | \(0.742265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.6267i | 0.0938261i | 0.998899 | + | 0.0469131i | \(0.0149384\pi\) | ||||
−0.998899 | + | 0.0469131i | \(0.985062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.7208 | 0.0384386 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 115.945i | 0.265321i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 146.600i | 0.333941i | 0.985962 | + | 0.166971i | \(0.0533985\pi\) | ||||
−0.985962 | + | 0.166971i | \(0.946602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −107.360 | −0.242349 | −0.121174 | − | 0.992631i | \(-0.538666\pi\) | ||||
−0.121174 | + | 0.992631i | \(0.538666\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −333.749 | −0.749999 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 66.2892i | − 0.148298i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 135.161 | 0.301028 | 0.150514 | − | 0.988608i | \(-0.451907\pi\) | ||||
0.150514 | + | 0.988608i | \(0.451907\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 133.011i | 0.294925i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 65.8514i | − 0.145367i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 159.735 | 0.349530 | 0.174765 | − | 0.984610i | \(-0.444083\pi\) | ||||
0.174765 | + | 0.984610i | \(0.444083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −47.1838 | −0.102797 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 310.250i | − 0.672993i | −0.941685 | − | 0.336497i | \(-0.890758\pi\) | ||||
0.941685 | − | 0.336497i | \(-0.109242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 326.014 | 0.704135 | 0.352067 | − | 0.935975i | \(-0.385479\pi\) | ||||
0.352067 | + | 0.935975i | \(0.385479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 232.476i | 0.499949i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 595.558i | 1.27529i | 0.770332 | + | 0.637643i | \(0.220090\pi\) | ||||
−0.770332 | + | 0.637643i | \(0.779910\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.06688 | 0.0128809 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 49.8823 | 0.105459 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 79.3262i | − 0.167002i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 474.926 | 0.995652 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 506.680i | − 1.05779i | −0.848688 | − | 0.528894i | \(-0.822607\pi\) | ||||
0.848688 | − | 0.528894i | \(-0.177393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.9736i | 0.0935002i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 674.985 | 1.39172 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −211.302 | −0.433884 | −0.216942 | − | 0.976184i | \(-0.569608\pi\) | ||||
−0.216942 | + | 0.976184i | \(0.569608\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 159.255i | 0.325676i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 784.161 | 1.59707 | 0.798534 | − | 0.601949i | \(-0.205609\pi\) | ||||
0.798534 | + | 0.601949i | \(0.205609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 13.2198i | − 0.0268151i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 267.678i | 0.540764i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 171.492 | 0.343672 | 0.171836 | − | 0.985126i | \(-0.445030\pi\) | ||||
0.171836 | + | 0.985126i | \(0.445030\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 121.133 | 0.241782 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 20.0883i | − 0.0399370i | −0.999801 | − | 0.0199685i | \(-0.993643\pi\) | ||||
0.999801 | − | 0.0199685i | \(-0.00635659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 395.735 | 0.783634 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 46.5068i | 0.0917294i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 476.764i | 0.936668i | 0.883551 | + | 0.468334i | \(0.155146\pi\) | ||||
−0.883551 | + | 0.468334i | \(0.844854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 52.4558 | 0.102253 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −796.904 | −1.54739 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 250.613i | 0.484744i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 117.905 | 0.227176 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 854.274i | 1.63968i | 0.572592 | + | 0.819841i | \(0.305938\pi\) | ||||
−0.572592 | + | 0.819841i | \(0.694062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 593.002i | − 1.13385i | −0.823771 | − | 0.566923i | \(-0.808134\pi\) | ||||
0.823771 | − | 0.566923i | \(-0.191866\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 183.801 | 0.348769 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 239.838 | 0.453379 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 328.555i | − 0.618748i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 427.529 | 0.802118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 753.352i | 1.40814i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 132.858i | 0.247408i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 855.191 | 1.58076 | 0.790380 | − | 0.612617i | \(-0.209883\pi\) | ||||
0.790380 | + | 0.612617i | \(0.209883\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 111.265 | 0.204908 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 963.546i | − 1.76797i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −415.897 | −0.760323 | −0.380161 | − | 0.924920i | \(-0.624132\pi\) | ||||
−0.380161 | + | 0.924920i | \(0.624132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 767.986i | 1.39888i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.6969i | 0.0266732i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.9920 | −0.0252108 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −584.220 | −1.04887 | −0.524435 | − | 0.851451i | \(-0.675723\pi\) | ||||
−0.524435 | + | 0.851451i | \(0.675723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 160.333i | − 0.286822i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.8377 | −0.0228835 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 911.147i | − 1.61838i | −0.587548 | − | 0.809189i | \(-0.699907\pi\) | ||||
0.587548 | − | 0.809189i | \(-0.300093\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 229.063i | 0.405422i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 699.999 | 1.23023 | 0.615113 | − | 0.788439i | \(-0.289110\pi\) | ||||
0.615113 | + | 0.788439i | \(0.289110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 562.463 | 0.985049 | 0.492525 | − | 0.870299i | \(-0.336074\pi\) | ||||
0.492525 | + | 0.870299i | \(0.336074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 177.993i | 0.310634i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −526.014 | −0.914807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 661.659i | − 1.14672i | −0.819302 | − | 0.573362i | \(-0.805639\pi\) | ||||
0.819302 | − | 0.573362i | \(-0.194361\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 110.728i | − 0.191240i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 266.272 | 0.456727 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 860.382 | 1.47074 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 823.029i | − 1.40209i | −0.713116 | − | 0.701046i | \(-0.752717\pi\) | ||||
0.713116 | − | 0.701046i | \(-0.247283\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204.338 | −0.346924 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 129.930i | 0.219848i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 622.256i | 1.04934i | 0.851307 | + | 0.524668i | \(0.175811\pi\) | ||||
−0.851307 | + | 0.524668i | \(0.824189\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −250.176 | −0.419055 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 512.845 | 0.856168 | 0.428084 | − | 0.903739i | \(-0.359189\pi\) | ||||
0.428084 | + | 0.903739i | \(0.359189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 680.160i | − 1.13171i | −0.824504 | − | 0.565857i | \(-0.808546\pi\) | ||||
0.824504 | − | 0.565857i | \(-0.191454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 293.927 | 0.487441 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 652.278i | − 1.07815i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.7381i | 0.0638189i | 0.999491 | + | 0.0319095i | \(0.0101588\pi\) | ||||
−0.999491 | + | 0.0319095i | \(0.989841\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 805.529 | 1.31838 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 401.103 | 0.654329 | 0.327164 | − | 0.944967i | \(-0.393907\pi\) | ||||
0.327164 | + | 0.944967i | \(0.393907\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 133.011i | 0.216278i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −959.044 | −1.55437 | −0.777183 | − | 0.629275i | \(-0.783352\pi\) | ||||
−0.777183 | + | 0.629275i | \(0.783352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1004.53i | 1.62283i | 0.584469 | + | 0.811416i | \(0.301303\pi\) | ||||
−0.584469 | + | 0.811416i | \(0.698697\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 347.836i | − 0.560123i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −739.382 | −1.18301 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.2721 | 0.0227625 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.0624i | 0.0175873i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 386.514 | 0.612542 | 0.306271 | − | 0.951944i | \(-0.400919\pi\) | ||||
0.306271 | + | 0.951944i | \(0.400919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 261.200i | 0.412639i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1640.11i | 2.58284i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −309.088 | −0.483706 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −992.147 | −1.54781 | −0.773906 | − | 0.633301i | \(-0.781700\pi\) | ||||
−0.773906 | + | 0.633301i | \(0.781700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 944.986i | 1.46965i | 0.678256 | + | 0.734826i | \(0.262736\pi\) | ||||
−0.678256 | + | 0.734826i | \(0.737264\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.8823 | 0.0773368 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.89088i | − 0.00446812i | −0.999998 | − | 0.00223406i | \(-0.999289\pi\) | ||||
0.999998 | − | 0.00223406i | \(-0.000711124\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 184.208i | − 0.283833i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −323.059 | −0.494730 | −0.247365 | − | 0.968922i | \(-0.579565\pi\) | ||||
−0.247365 | + | 0.968922i | \(0.579565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 979.036 | 1.49471 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 446.384i | 0.679428i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −295.955 | −0.449098 | −0.224549 | − | 0.974463i | \(-0.572091\pi\) | ||||
−0.224549 | + | 0.974463i | \(0.572091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.7511i | 0.0313935i | 0.999877 | + | 0.0156968i | \(0.00499664\pi\) | ||||
−0.999877 | + | 0.0156968i | \(0.995003\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.2633i | 0.0622373i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 97.4558 | 0.146111 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 88.4104 | 0.132153 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 430.579i | 0.641698i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 627.044 | 0.931714 | 0.465857 | − | 0.884860i | \(-0.345746\pi\) | ||||
0.465857 | + | 0.884860i | \(0.345746\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 237.979i | 0.352561i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 109.246i | 0.161368i | 0.996740 | + | 0.0806838i | \(0.0257104\pi\) | ||||
−0.996740 | + | 0.0806838i | \(0.974290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54.7948 | 0.0804623 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −793.566 | −1.16188 | −0.580941 | − | 0.813946i | \(-0.697315\pi\) | ||||
−0.580941 | + | 0.813946i | \(0.697315\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 215.996i | − 0.315323i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −256.331 | −0.373116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 855.862i | − 1.24218i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 183.889i | 0.266121i | 0.991108 | + | 0.133060i | \(0.0424804\pi\) | ||||
−0.991108 | + | 0.133060i | \(0.957520\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −454.794 | −0.654380 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 105.161 | 0.150877 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 195.913i | 0.280277i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1043.82 | −1.48905 | −0.744525 | − | 0.667595i | \(-0.767324\pi\) | ||||
−0.744525 | + | 0.667595i | \(0.767324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 12.2984i | − 0.0174942i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 250.613i | 0.355479i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −980.558 | −1.38301 | −0.691507 | − | 0.722369i | \(-0.743053\pi\) | ||||
−0.691507 | + | 0.722369i | \(0.743053\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 286.690 | 0.403221 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1354.97i | 1.90038i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 482.382 | 0.674660 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 190.195i | − 0.265265i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 778.484i | − 1.08273i | −0.840787 | − | 0.541366i | \(-0.817907\pi\) | ||||
0.840787 | − | 0.541366i | \(-0.182093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −62.8751 | −0.0869642 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −66.6762 | −0.0919672 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 735.255i | − 1.01135i | −0.862723 | − | 0.505677i | \(-0.831243\pi\) | ||||
0.862723 | − | 0.505677i | \(-0.168757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 490.632 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 39.4380i | − 0.0539508i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 478.860i | 0.653288i | 0.945147 | + | 0.326644i | \(0.105918\pi\) | ||||
−0.945147 | + | 0.326644i | \(0.894082\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 164.793 | 0.223600 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9045 | 0.0269344 | 0.0134672 | − | 0.999909i | \(-0.495713\pi\) | ||||
0.0134672 | + | 0.999909i | \(0.495713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 45.8739i | − 0.0619080i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.3095 | −0.0582901 | −0.0291450 | − | 0.999575i | \(-0.509278\pi\) | ||||
−0.0291450 | + | 0.999575i | \(0.509278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 612.687i | 0.822399i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1082.53i | − 1.44917i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −225.330 | −0.300040 | −0.150020 | − | 0.988683i | \(-0.547934\pi\) | ||||
−0.150020 | + | 0.988683i | \(0.547934\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −355.602 | −0.472247 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 608.641i | 0.806147i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 935.779 | 1.23617 | 0.618084 | − | 0.786112i | \(-0.287909\pi\) | ||||
0.618084 | + | 0.786112i | \(0.287909\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 94.6386i | − 0.124689i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1402.71i | − 1.84325i | −0.388081 | − | 0.921625i | \(-0.626862\pi\) | ||||
0.388081 | − | 0.921625i | \(-0.373138\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 211.632 | 0.276644 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −592.087 | −0.771952 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 1.72330i | − 0.00224097i | −0.999999 | − | 0.00112048i | \(-0.999643\pi\) | ||||
0.999999 | − | 0.00112048i | \(-0.000356661\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −287.360 | −0.372711 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 224.258i | 0.290113i | 0.989423 | + | 0.145057i | \(0.0463364\pi\) | ||||
−0.989423 | + | 0.145057i | \(0.953664\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 927.029i | − 1.19617i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −116.912 | −0.150079 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −173.294 | −0.221887 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 44.0908i | − 0.0563101i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.0740 | −0.0714319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 70.2034i | − 0.0892038i | −0.999005 | − | 0.0446019i | \(-0.985798\pi\) | ||||
0.999005 | − | 0.0446019i | \(-0.0142019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 23.2057i | − 0.0294116i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1383.98 | 1.74525 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 266.272 | 0.334933 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1305.38i | − 1.63787i | −0.573889 | − | 0.818933i | \(-0.694566\pi\) | ||||
0.573889 | − | 0.818933i | \(-0.305434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 198.140 | 0.247985 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 427.076i | 0.533179i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 250.270i | 0.311668i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −220.227 | −0.272897 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 762.765 | 0.942849 | 0.471424 | − | 0.881907i | \(-0.343740\pi\) | ||||
0.471424 | + | 0.881907i | \(0.343740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1214.98i | 1.49813i | 0.662498 | + | 0.749064i | \(0.269496\pi\) | ||||
−0.662498 | + | 0.749064i | \(0.730504\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.5147 | −0.0670538 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1471.94i | − 1.80606i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.8446i | 0.0536654i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −583.368 | −0.710557 | −0.355279 | − | 0.934760i | \(-0.615614\pi\) | ||||
−0.355279 | + | 0.934760i | \(0.615614\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1030.74 | −1.25242 | −0.626210 | − | 0.779655i | \(-0.715395\pi\) | ||||
−0.626210 | + | 0.779655i | \(0.715395\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 64.7487i | 0.0784833i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −152.102 | −0.183920 | −0.0919599 | − | 0.995763i | \(-0.529313\pi\) | ||||
−0.0919599 | + | 0.995763i | \(0.529313\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 614.410i | 0.741146i | 0.928803 | + | 0.370573i | \(0.120839\pi\) | ||||
−0.928803 | + | 0.370573i | \(0.879161\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 199.743i | − 0.240365i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1119.59 | −1.34082 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 613.014 | 0.732395 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1546.14i | − 1.84284i | −0.388568 | − | 0.921420i | \(-0.627030\pi\) | ||||
0.388568 | − | 0.921420i | \(-0.372970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −828.647 | −0.985311 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 283.166i | − 0.335903i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 429.846i | − 0.508693i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −105.030 | −0.123711 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −81.5513 | −0.0958300 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1235.15i | 1.44800i | 0.689798 | + | 0.724002i | \(0.257699\pi\) | ||||
−0.689798 | + | 0.724002i | \(0.742301\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −235.279 | −0.275180 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1100.68i | − 1.28434i | −0.766561 | − | 0.642172i | \(-0.778034\pi\) | ||||
0.766561 | − | 0.642172i | \(-0.221966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 591.771i | 0.688906i | 0.938803 | + | 0.344453i | \(0.111936\pi\) | ||||
−0.938803 | + | 0.344453i | \(0.888064\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 64.7271 | 0.0750024 | 0.0375012 | − | 0.999297i | \(-0.488060\pi\) | ||||
0.0375012 | + | 0.999297i | \(0.488060\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1089.75 | −1.25983 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 197.190i | − 0.227440i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 160.736 | 0.184967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 529.684i | − 0.608133i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 863.732i | − 0.989384i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −304.192 | −0.346855 | −0.173427 | − | 0.984847i | \(-0.555484\pi\) | ||||
−0.173427 | + | 0.984847i | \(0.555484\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −215.001 | −0.244597 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 863.732i | − 0.980400i | −0.871610 | − | 0.490200i | \(-0.836924\pi\) | ||||
0.871610 | − | 0.490200i | \(-0.163076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 567.456 | 0.642645 | 0.321323 | − | 0.946970i | \(-0.395873\pi\) | ||||
0.321323 | + | 0.946970i | \(0.395873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 184.208i | − 0.208144i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 889.761i | − 1.00311i | −0.865125 | − | 0.501556i | \(-0.832761\pi\) | ||||
0.865125 | − | 0.501556i | \(-0.167239\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 320.492 | 0.359699 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −220.279 | −0.246673 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1227.96i | − 1.37202i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −304.191 | −0.339120 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 171.753i | 0.191049i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 210.521i | − 0.233652i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1028.38 | −1.13633 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −373.978 | −0.412324 | −0.206162 | − | 0.978518i | \(-0.566097\pi\) | ||||
−0.206162 | + | 0.978518i | \(0.566097\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 506.395i | − 0.557091i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1133.75 | −1.24451 | −0.622256 | − | 0.782814i | \(-0.713784\pi\) | ||||
−0.622256 | + | 0.782814i | \(0.713784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 606.932i | − 0.664766i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 430.579i | 0.470578i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −456.302 | −0.496521 | −0.248260 | − | 0.968693i | \(-0.579859\pi\) | ||||
−0.248260 | + | 0.968693i | \(0.579859\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.0580 | −0.0163496 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 557.007i | 0.603474i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.7948 | 0.0603187 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1019.74i | 1.10005i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 951.540i | 1.02426i | 0.858907 | + | 0.512131i | \(0.171144\pi\) | ||||
−0.858907 | + | 0.512131i | \(0.828856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −130.602 | −0.139981 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 118.654 | 0.126903 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1295.71i | 1.38283i | 0.722460 | + | 0.691413i | \(0.243011\pi\) | ||||
−0.722460 | + | 0.691413i | \(0.756989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 70.2578 | 0.0748219 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1356.89i | − 1.44197i | −0.692952 | − | 0.720984i | \(-0.743690\pi\) | ||||
0.692952 | − | 0.720984i | \(-0.256310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 775.245i | 0.822105i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 709.462 | 0.749168 | 0.374584 | − | 0.927193i | \(-0.377786\pi\) | ||||
0.374584 | + | 0.927193i | \(0.377786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 804.426 | 0.847657 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 345.784i | 0.363601i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 936.603 | 0.982794 | 0.491397 | − | 0.870936i | \(-0.336486\pi\) | ||||
0.491397 | + | 0.870936i | \(0.336486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1645.13i | − 1.72265i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 11.9961i | − 0.0125351i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1426.95 | −1.48486 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 964.014 | 1.00105 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1023.42i | 1.06054i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1374.37 | −1.42127 | −0.710635 | − | 0.703561i | \(-0.751592\pi\) | ||||
−0.710635 | + | 0.703561i | \(0.751592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 11.2838i | − 0.0116448i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 31.4617i | − 0.0324014i | −0.999869 | − | 0.0162007i | \(-0.994843\pi\) | ||||
0.999869 | − | 0.0162007i | \(-0.00515706\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 208.118 | 0.213454 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −541.897 | −0.554654 | −0.277327 | − | 0.960776i | \(-0.589449\pi\) | ||||
−0.277327 | + | 0.960776i | \(0.589449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 239.445i | 0.244581i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1232.98 | −1.25687 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 22.4198i | − 0.0228075i | −0.999935 | − | 0.0114038i | \(-0.996370\pi\) | ||||
0.999935 | − | 0.0114038i | \(-0.00363001\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 1200.90i | − 1.21918i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 290.735 | 0.293969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −678.035 | −0.684193 | −0.342096 | − | 0.939665i | \(-0.611137\pi\) | ||||
−0.342096 | + | 0.939665i | \(0.611137\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 161.429i | 0.162567i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2312.28 | 2.32390 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 876.163i | 0.878799i | 0.898292 | + | 0.439400i | \(0.144809\pi\) | ||||
−0.898292 | + | 0.439400i | \(0.855191\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.8953i | 0.0369322i |
(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 | 784.3.c.e.97.2 | 4 | ||
4.3 | odd | 2 | 98.3.b.b.97.4 | 4 | |||
7.2 | even | 3 | 784.3.s.c.129.2 | 4 | |||
7.3 | odd | 6 | 784.3.s.c.705.2 | 4 | |||
7.4 | even | 3 | 112.3.s.b.33.1 | 4 | |||
7.5 | odd | 6 | 112.3.s.b.17.1 | 4 | |||
7.6 | odd | 2 | inner | 784.3.c.e.97.3 | 4 | ||
12.11 | even | 2 | 882.3.c.f.685.1 | 4 | |||
21.5 | even | 6 | 1008.3.cg.l.577.2 | 4 | |||
21.11 | odd | 6 | 1008.3.cg.l.145.2 | 4 | |||
28.3 | even | 6 | 98.3.d.a.19.1 | 4 | |||
28.11 | odd | 6 | 14.3.d.a.5.1 | yes | 4 | ||
28.19 | even | 6 | 14.3.d.a.3.1 | ✓ | 4 | ||
28.23 | odd | 6 | 98.3.d.a.31.1 | 4 | |||
28.27 | even | 2 | 98.3.b.b.97.3 | 4 | |||
56.5 | odd | 6 | 448.3.s.c.129.2 | 4 | |||
56.11 | odd | 6 | 448.3.s.d.257.1 | 4 | |||
56.19 | even | 6 | 448.3.s.d.129.1 | 4 | |||
56.53 | even | 6 | 448.3.s.c.257.2 | 4 | |||
84.11 | even | 6 | 126.3.n.c.19.2 | 4 | |||
84.23 | even | 6 | 882.3.n.b.325.2 | 4 | |||
84.47 | odd | 6 | 126.3.n.c.73.2 | 4 | |||
84.59 | odd | 6 | 882.3.n.b.19.2 | 4 | |||
84.83 | odd | 2 | 882.3.c.f.685.2 | 4 | |||
140.19 | even | 6 | 350.3.k.a.101.2 | 4 | |||
140.39 | odd | 6 | 350.3.k.a.201.2 | 4 | |||
140.47 | odd | 12 | 350.3.i.a.199.3 | 8 | |||
140.67 | even | 12 | 350.3.i.a.299.2 | 8 | |||
140.103 | odd | 12 | 350.3.i.a.199.2 | 8 | |||
140.123 | even | 12 | 350.3.i.a.299.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.3.d.a.3.1 | ✓ | 4 | 28.19 | even | 6 | ||
14.3.d.a.5.1 | yes | 4 | 28.11 | odd | 6 | ||
98.3.b.b.97.3 | 4 | 28.27 | even | 2 | |||
98.3.b.b.97.4 | 4 | 4.3 | odd | 2 | |||
98.3.d.a.19.1 | 4 | 28.3 | even | 6 | |||
98.3.d.a.31.1 | 4 | 28.23 | odd | 6 | |||
112.3.s.b.17.1 | 4 | 7.5 | odd | 6 | |||
112.3.s.b.33.1 | 4 | 7.4 | even | 3 | |||
126.3.n.c.19.2 | 4 | 84.11 | even | 6 | |||
126.3.n.c.73.2 | 4 | 84.47 | odd | 6 | |||
350.3.i.a.199.2 | 8 | 140.103 | odd | 12 | |||
350.3.i.a.199.3 | 8 | 140.47 | odd | 12 | |||
350.3.i.a.299.2 | 8 | 140.67 | even | 12 | |||
350.3.i.a.299.3 | 8 | 140.123 | even | 12 | |||
350.3.k.a.101.2 | 4 | 140.19 | even | 6 | |||
350.3.k.a.201.2 | 4 | 140.39 | odd | 6 | |||
448.3.s.c.129.2 | 4 | 56.5 | odd | 6 | |||
448.3.s.c.257.2 | 4 | 56.53 | even | 6 | |||
448.3.s.d.129.1 | 4 | 56.19 | even | 6 | |||
448.3.s.d.257.1 | 4 | 56.11 | odd | 6 | |||
784.3.c.e.97.2 | 4 | 1.1 | even | 1 | trivial | ||
784.3.c.e.97.3 | 4 | 7.6 | odd | 2 | inner | ||
784.3.s.c.129.2 | 4 | 7.2 | even | 3 | |||
784.3.s.c.705.2 | 4 | 7.3 | odd | 6 | |||
882.3.c.f.685.1 | 4 | 12.11 | even | 2 | |||
882.3.c.f.685.2 | 4 | 84.83 | odd | 2 | |||
882.3.n.b.19.2 | 4 | 84.59 | odd | 6 | |||
882.3.n.b.325.2 | 4 | 84.23 | even | 6 | |||
1008.3.cg.l.145.2 | 4 | 21.11 | odd | 6 | |||
1008.3.cg.l.577.2 | 4 | 21.5 | even | 6 |