Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(417,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.417");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 417.47 | ||
Character | \(\chi\) | \(=\) | 1216.417 |
Dual form | 1216.3.g.e.417.46 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 5.07504 | 1.69168 | 0.845840 | − | 0.533437i | \(-0.179100\pi\) | ||||
0.845840 | + | 0.533437i | \(0.179100\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.51741i | 1.10348i | 0.834016 | + | 0.551741i | \(0.186036\pi\) | ||||
−0.834016 | + | 0.551741i | \(0.813964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.74188 | −1.24884 | −0.624420 | − | 0.781089i | \(-0.714665\pi\) | ||||
−0.624420 | + | 0.781089i | \(0.714665\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 16.7560 | 1.86178 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.103239i | 0.00938532i | 0.999989 | + | 0.00469266i | \(0.00149373\pi\) | ||||
−0.999989 | + | 0.00469266i | \(0.998506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.16700 | 0.551308 | 0.275654 | − | 0.961257i | \(-0.411106\pi\) | ||||
0.275654 | + | 0.961257i | \(0.411106\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 28.0010i | 1.86674i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 24.4109 | 1.43594 | 0.717969 | − | 0.696075i | \(-0.245072\pi\) | ||||
0.717969 | + | 0.696075i | \(0.245072\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.40930 | + | 17.4958i | −0.389963 | + | 0.920830i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −44.3654 | −2.11264 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 10.9002 | 0.473923 | 0.236961 | − | 0.971519i | \(-0.423848\pi\) | ||||
0.236961 | + | 0.971519i | \(0.423848\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.44176 | −0.217670 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 39.3621 | 1.45785 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −12.9795 | −0.447570 | −0.223785 | − | 0.974639i | \(-0.571841\pi\) | ||||
−0.223785 | + | 0.974639i | \(0.571841\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 40.6764i | 1.31214i | 0.754699 | + | 0.656072i | \(0.227783\pi\) | ||||
−0.754699 | + | 0.656072i | \(0.772217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.523940i | 0.0158770i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 48.2325i | − | 1.37807i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −42.1034 | −1.13793 | −0.568965 | − | 0.822362i | \(-0.692656\pi\) | ||||
−0.568965 | + | 0.822362i | \(0.692656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36.3728 | 0.932636 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.13034i | − | 0.0275693i | −0.999905 | − | 0.0137847i | \(-0.995612\pi\) | ||
0.999905 | − | 0.0137847i | \(-0.00438793\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 63.9047i | 1.48616i | 0.669205 | + | 0.743078i | \(0.266635\pi\) | ||||
−0.669205 | + | 0.743078i | \(0.733365\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 92.4497i | 2.05444i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 17.7063 | 0.376729 | 0.188365 | − | 0.982099i | \(-0.439681\pi\) | ||||
0.188365 | + | 0.982099i | \(0.439681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 27.4204 | 0.559600 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 123.886 | 2.42915 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 52.4515 | 0.989651 | 0.494825 | − | 0.868992i | \(-0.335232\pi\) | ||||
0.494825 | + | 0.868992i | \(0.335232\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.569609 | −0.0103565 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −37.6025 | + | 88.7917i | −0.659693 | + | 1.55775i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −117.338 | −1.98878 | −0.994392 | − | 0.105753i | \(-0.966275\pi\) | ||||
−0.994392 | + | 0.105753i | \(0.966275\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 26.0056i | 0.426320i | 0.977017 | + | 0.213160i | \(0.0683756\pi\) | ||||
−0.977017 | + | 0.213160i | \(0.931624\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −146.479 | −2.32506 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 39.5432i | 0.608357i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 67.7026 | 1.01049 | 0.505243 | − | 0.862977i | \(-0.331403\pi\) | ||||
0.505243 | + | 0.862977i | \(0.331403\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 55.3191 | 0.801726 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 92.2133i | 1.29878i | 0.760456 | + | 0.649389i | \(0.224975\pi\) | ||||
−0.760456 | + | 0.649389i | \(0.775025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −20.5023 | −0.280853 | −0.140427 | − | 0.990091i | \(-0.544847\pi\) | ||||
−0.140427 | + | 0.990091i | \(0.544847\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −27.6171 | −0.368229 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.902499i | − | 0.0117208i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 72.3781i | 0.916178i | 0.888906 | + | 0.458089i | \(0.151466\pi\) | ||||
−0.888906 | + | 0.458089i | \(0.848534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 48.9599 | 0.604443 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 69.7748i | 0.840660i | 0.907371 | + | 0.420330i | \(0.138086\pi\) | ||||
−0.907371 | + | 0.420330i | \(0.861914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 134.685i | 1.58453i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −65.8716 | −0.757145 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.48968i | − | 0.0953896i | −0.998862 | − | 0.0476948i | \(-0.984813\pi\) | ||
0.998862 | − | 0.0476948i | \(-0.0151875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −62.6530 | −0.688495 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 206.434i | 2.21973i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −96.5313 | − | 40.8801i | −1.01612 | − | 0.430317i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 130.846i | − | 1.34893i | −0.738309 | − | 0.674463i | \(-0.764375\pi\) | ||
0.738309 | − | 0.674463i | \(-0.235625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72987i | 0.0174734i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 94.7330i | − | 0.937950i | −0.883211 | − | 0.468975i | \(-0.844623\pi\) | ||
0.883211 | − | 0.468975i | \(-0.155377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 100.957i | − | 0.980167i | −0.871676 | − | 0.490083i | \(-0.836966\pi\) | ||
0.871676 | − | 0.490083i | \(-0.163034\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 244.782i | − | 2.33125i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −48.4316 | −0.452632 | −0.226316 | − | 0.974054i | \(-0.572668\pi\) | ||||
−0.226316 | + | 0.974054i | \(0.572668\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 194.697 | 1.78621 | 0.893107 | − | 0.449845i | \(-0.148521\pi\) | ||||
0.893107 | + | 0.449845i | \(0.148521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −213.676 | −1.92501 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 193.464i | − | 1.71207i | −0.516919 | − | 0.856034i | \(-0.672921\pi\) | ||
0.516919 | − | 0.856034i | \(-0.327079\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 60.1410i | 0.522965i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 120.090 | 1.02641 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −213.397 | −1.79326 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.989 | 0.999912 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 5.73653i | − | 0.0466385i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 107.911i | 0.863286i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 233.080i | − | 1.83528i | −0.397416 | − | 0.917638i | \(-0.630093\pi\) | ||
0.397416 | − | 0.917638i | \(-0.369907\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 324.319i | 2.51410i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 144.179i | − | 1.10060i | −0.834967 | − | 0.550300i | \(-0.814513\pi\) | ||
0.834967 | − | 0.550300i | \(-0.185487\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64.7712 | − | 152.946i | 0.487002 | − | 1.14997i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 217.176i | 1.60871i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 141.122 | 1.03009 | 0.515043 | − | 0.857164i | \(-0.327776\pi\) | ||||
0.515043 | + | 0.857164i | \(0.327776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 250.346i | 1.80105i | 0.434804 | + | 0.900525i | \(0.356818\pi\) | ||||
−0.434804 | + | 0.900525i | \(0.643182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 89.8601 | 0.637305 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.739910i | 0.00517420i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 71.6134i | − | 0.493885i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 139.160 | 0.946664 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 25.8510i | 0.173497i | 0.996230 | + | 0.0867484i | \(0.0276476\pi\) | ||||
−0.996230 | + | 0.0867484i | \(0.972352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 182.920i | − | 1.21139i | −0.795697 | − | 0.605695i | \(-0.792895\pi\) | ||
0.795697 | − | 0.605695i | \(-0.207105\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 409.030 | 2.67340 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −224.428 | −1.44793 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 303.651i | − | 1.93408i | −0.254618 | − | 0.967042i | \(-0.581950\pi\) | ||
0.254618 | − | 0.967042i | \(-0.418050\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 266.193 | 1.67417 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −95.2885 | −0.591854 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 114.570i | − | 0.702883i | −0.936210 | − | 0.351442i | \(-0.885692\pi\) | ||
0.936210 | − | 0.351442i | \(-0.114308\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.89079 | −0.0175199 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 193.042i | − | 1.15594i | −0.816058 | − | 0.577970i | \(-0.803845\pi\) | ||
0.816058 | − | 0.577970i | \(-0.196155\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −117.634 | −0.696060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −124.150 | + | 293.159i | −0.726026 | + | 1.71438i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 248.002 | 1.43354 | 0.716769 | − | 0.697311i | \(-0.245620\pi\) | ||||
0.716769 | + | 0.697311i | \(0.245620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 47.5712 | 0.271836 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −595.496 | −3.36439 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 213.534 | 1.19293 | 0.596464 | − | 0.802640i | \(-0.296572\pi\) | ||||
0.596464 | + | 0.802640i | \(0.296572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −140.186 | −0.774507 | −0.387253 | − | 0.921973i | \(-0.626576\pi\) | ||||
−0.387253 | + | 0.921973i | \(0.626576\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 131.979i | 0.721198i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 232.302i | − | 1.25568i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.52015i | 0.0134767i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −344.098 | −1.82063 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −171.684 | −0.898867 | −0.449434 | − | 0.893314i | \(-0.648374\pi\) | ||||
−0.449434 | + | 0.893314i | \(0.648374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 157.845i | 0.817848i | 0.912568 | + | 0.408924i | \(0.134096\pi\) | ||||
−0.912568 | + | 0.408924i | \(0.865904\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 200.683i | 1.02915i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.76133i | − | 0.0292453i | −0.999893 | − | 0.0146227i | \(-0.995345\pi\) | ||
0.999893 | − | 0.0146227i | \(-0.00465471\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 212.623 | 1.06846 | 0.534229 | − | 0.845340i | \(-0.320602\pi\) | ||||
0.534229 | + | 0.845340i | \(0.320602\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 343.593 | 1.70942 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 113.466 | 0.558943 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.23656 | 0.0304222 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 182.644 | 0.882340 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.80624 | − | 0.764926i | −0.00864229 | − | 0.00365993i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.05652 | 0.0192252 | 0.00961260 | − | 0.999954i | \(-0.496940\pi\) | ||||
0.00961260 | + | 0.999954i | \(0.496940\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 467.986i | 2.19712i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −352.588 | −1.63994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 355.588i | − | 1.63866i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −104.050 | −0.475114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 174.953 | 0.791643 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 80.1901i | 0.359597i | 0.983703 | + | 0.179798i | \(0.0575446\pi\) | ||||
−0.983703 | + | 0.179798i | \(0.942455\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −91.1822 | −0.405254 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 205.254 | 0.904201 | 0.452101 | − | 0.891967i | \(-0.350675\pi\) | ||||
0.452101 | + | 0.891967i | \(0.350675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.6000i | − | 0.0593886i | −0.999559 | − | 0.0296943i | \(-0.990547\pi\) | ||
0.999559 | − | 0.0296943i | \(-0.00945338\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 4.58021i | − | 0.0198278i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 215.348 | 0.924240 | 0.462120 | − | 0.886817i | \(-0.347089\pi\) | ||||
0.462120 | + | 0.886817i | \(0.347089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 97.6927i | 0.415714i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 367.321i | 1.54988i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 255.829 | 1.07041 | 0.535207 | − | 0.844721i | \(-0.320234\pi\) | ||||
0.535207 | + | 0.844721i | \(0.320234\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 101.170i | 0.419793i | 0.977724 | + | 0.209896i | \(0.0673126\pi\) | ||||
−0.977724 | + | 0.209896i | \(0.932687\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −105.785 | −0.435331 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 151.290i | 0.617508i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −53.1025 | + | 125.392i | −0.214990 | + | 0.507661i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 354.110i | 1.42213i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 321.296i | − | 1.28006i | −0.768348 | − | 0.640032i | \(-0.778921\pi\) | ||
0.768348 | − | 0.640032i | \(-0.221079\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.12532i | 0.00444792i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 683.532i | 2.68052i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 400.913i | 1.55997i | 0.625795 | + | 0.779987i | \(0.284774\pi\) | ||||
−0.625795 | + | 0.779987i | \(0.715226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 368.063 | 1.42109 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −217.485 | −0.833277 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −472.797 | −1.79771 | −0.898854 | − | 0.438248i | \(-0.855599\pi\) | ||||
−0.898854 | + | 0.438248i | \(0.855599\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 289.396i | 1.09206i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 43.0854i | − | 0.161369i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −417.786 | −1.55311 | −0.776555 | − | 0.630050i | \(-0.783034\pi\) | ||||
−0.776555 | + | 0.630050i | \(0.783034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 193.575 | 0.714298 | 0.357149 | − | 0.934047i | \(-0.383749\pi\) | ||||
0.357149 | + | 0.934047i | \(0.383749\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −317.966 | −1.16471 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 0.561800i | − | 0.00204291i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.5682i | 0.0562027i | 0.999605 | + | 0.0281014i | \(0.00894612\pi\) | ||||
−0.999605 | + | 0.0281014i | \(0.991054\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 681.575i | 2.44292i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.98179i | 0.0212875i | 0.999943 | + | 0.0106438i | \(0.00338808\pi\) | ||||
−0.999943 | + | 0.0106438i | \(0.996612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 52.8002i | − | 0.186573i | −0.995639 | − | 0.0932866i | \(-0.970263\pi\) | ||
0.995639 | − | 0.0932866i | \(-0.0297373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −489.900 | − | 207.468i | −1.71895 | − | 0.727959i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.88132i | 0.0344297i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 306.894 | 1.06192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 664.048i | − | 2.28195i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 284.326 | 0.970395 | 0.485197 | − | 0.874405i | \(-0.338748\pi\) | ||||
0.485197 | + | 0.874405i | \(0.338748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 647.403i | − | 2.19459i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.06368i | 0.0136824i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 78.1219 | 0.261277 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 558.647i | − | 1.85597i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 480.773i | − | 1.58671i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −143.483 | −0.470437 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −108.449 | −0.353253 | −0.176627 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176627 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 512.361i | − | 1.65813i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 404.664 | 1.30117 | 0.650585 | − | 0.759433i | \(-0.274524\pi\) | ||||
0.650585 | + | 0.759433i | \(0.274524\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −112.046 | −0.357974 | −0.178987 | − | 0.983851i | \(-0.557282\pi\) | ||||
−0.178987 | + | 0.983851i | \(0.557282\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 808.184i | − | 2.56566i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 191.095 | 0.602824 | 0.301412 | − | 0.953494i | \(-0.402542\pi\) | ||||
0.301412 | + | 0.953494i | \(0.402542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.33999i | − | 0.00420059i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −245.792 | −0.765708 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −180.868 | + | 427.088i | −0.559963 | + | 1.32225i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −39.0011 | −0.120003 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 988.096 | 3.02170 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −154.786 | −0.470475 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −143.451 | −0.433388 | −0.216694 | − | 0.976240i | \(-0.569527\pi\) | ||||
−0.216694 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −705.485 | −2.11857 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 373.543i | 1.11505i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 67.8835i | − | 0.201435i | −0.994915 | − | 0.100717i | \(-0.967886\pi\) | ||
0.994915 | − | 0.100717i | \(-0.0321138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 981.836i | − | 2.89627i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.19938 | −0.0123149 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 188.646 | 0.549989 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 305.218i | 0.884689i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 70.8633i | 0.204217i | 0.994773 | + | 0.102108i | \(0.0325589\pi\) | ||||
−0.994773 | + | 0.102108i | \(0.967441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 231.425i | 0.663110i | 0.943436 | + | 0.331555i | \(0.107573\pi\) | ||||
−0.943436 | + | 0.331555i | \(0.892427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 282.108 | 0.803726 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 77.6586 | 0.219996 | 0.109998 | − | 0.993932i | \(-0.464916\pi\) | ||||
0.109998 | + | 0.993932i | \(0.464916\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −508.778 | −1.43318 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1083.00 | −3.03361 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −265.945 | −0.740794 | −0.370397 | − | 0.928873i | \(-0.620778\pi\) | ||||
−0.370397 | + | 0.928873i | \(0.620778\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −251.204 | − | 259.263i | −0.695857 | − | 0.718180i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 614.026 | 1.69153 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 113.119i | − | 0.309916i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.2136 | 0.0578028 | 0.0289014 | − | 0.999582i | \(-0.490799\pi\) | ||||
0.0289014 | + | 0.999582i | \(0.490799\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 18.9400i | − | 0.0513280i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −458.525 | −1.23592 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 724.367 | 1.94200 | 0.971001 | − | 0.239075i | \(-0.0768443\pi\) | ||||
0.971001 | + | 0.239075i | \(0.0768443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 547.651i | 1.46040i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −93.0243 | −0.246749 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −257.591 | −0.679659 | −0.339830 | − | 0.940487i | \(-0.610369\pi\) | ||||
−0.339830 | + | 0.940487i | \(0.610369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 1182.89i | − | 3.10470i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 649.965i | − | 1.69704i | −0.529166 | − | 0.848518i | \(-0.677495\pi\) | ||
0.529166 | − | 0.848518i | \(-0.322505\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.97945 | 0.0129336 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1070.79i | 2.76689i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 129.573i | 0.333093i | 0.986034 | + | 0.166547i | \(0.0532616\pi\) | ||||
−0.986034 | + | 0.166547i | \(0.946738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 266.085 | 0.680524 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 731.713i | − | 1.86186i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −399.339 | −1.01098 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 367.454i | − | 0.925576i | −0.886469 | − | 0.462788i | \(-0.846849\pi\) | ||
0.886469 | − | 0.462788i | \(-0.153151\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 328.716 | − | 776.206i | 0.823851 | − | 1.94538i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 401.016i | − | 1.00004i | −0.866014 | − | 0.500020i | \(-0.833326\pi\) | ||
0.866014 | − | 0.500020i | \(-0.166674\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 291.528i | 0.723394i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 270.131i | 0.666991i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.34669i | − | 0.0106798i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 563.440i | 1.37760i | 0.724950 | + | 0.688801i | \(0.241863\pi\) | ||||
−0.724950 | + | 0.688801i | \(0.758137\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 716.199 | 1.74258 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1025.76 | 2.48367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −384.976 | −0.927653 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1270.52i | 3.04680i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 260.123i | 0.620819i | 0.950603 | + | 0.310410i | \(0.100466\pi\) | ||||
−0.950603 | + | 0.310410i | \(0.899534\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 261.196 | 0.620417 | 0.310209 | − | 0.950669i | \(-0.399601\pi\) | ||||
0.310209 | + | 0.950669i | \(0.399601\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 296.687 | 0.701387 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −132.839 | −0.312561 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 227.337i | − | 0.532406i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.75507i | 0.00875308i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 460.860i | − | 1.06928i | −0.845080 | − | 0.534640i | \(-0.820447\pi\) | ||
0.845080 | − | 0.534640i | \(-0.179553\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 572.695i | − | 1.32262i | −0.750112 | − | 0.661311i | \(-0.770000\pi\) | ||
0.750112 | − | 0.661311i | \(-0.230000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 363.441i | − | 0.835496i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −80.7631 | + | 190.708i | −0.184813 | + | 0.436403i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 110.661i | − | 0.252075i | −0.992025 | − | 0.126038i | \(-0.959774\pi\) | ||
0.992025 | − | 0.126038i | \(-0.0402260\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 459.457 | 1.04185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 709.613i | 1.60184i | 0.598774 | + | 0.800918i | \(0.295655\pi\) | ||||
−0.598774 | + | 0.800918i | \(0.704345\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 46.8410 | 0.105261 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 131.195i | 0.293501i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 309.663i | − | 0.689672i | −0.938663 | − | 0.344836i | \(-0.887934\pi\) | ||
0.938663 | − | 0.344836i | \(-0.112066\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.116695 | 0.000258747 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 928.326i | − | 2.04928i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 345.682i | − | 0.759741i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 230.432 | 0.504228 | 0.252114 | − | 0.967698i | \(-0.418874\pi\) | ||||
0.252114 | + | 0.967698i | \(0.418874\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 960.865 | 2.09339 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 560.586i | 1.21602i | 0.793928 | + | 0.608011i | \(0.208032\pi\) | ||||
−0.793928 | + | 0.608011i | \(0.791968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −702.709 | −1.51773 | −0.758865 | − | 0.651248i | \(-0.774246\pi\) | ||||
−0.758865 | + | 0.651248i | \(0.774246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1138.98 | −2.44943 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 38.1953i | − | 0.0817887i | −0.999163 | − | 0.0408943i | \(-0.986979\pi\) | ||
0.999163 | − | 0.0408943i | \(-0.0130207\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −591.848 | −1.26194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1541.04i | − | 3.27185i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.59743 | −0.0139481 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40.3197 | − | 95.2079i | 0.0848835 | − | 0.200438i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 878.878 | 1.84251 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 438.004 | 0.914413 | 0.457206 | − | 0.889361i | \(-0.348850\pi\) | ||||
0.457206 | + | 0.889361i | \(0.348850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −301.755 | −0.627349 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −483.593 | −1.00123 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 721.930 | 1.48851 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 57.0979i | 0.117244i | 0.998280 | + | 0.0586220i | \(0.0186707\pi\) | ||||
−0.998280 | + | 0.0586220i | \(0.981329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 581.447i | − | 1.18905i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 208.671i | 0.424993i | 0.977162 | + | 0.212496i | \(0.0681593\pi\) | ||||
−0.977162 | + | 0.212496i | \(0.931841\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −316.843 | −0.642683 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.54437 | −0.0192816 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 806.117i | − | 1.62197i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 158.463i | 0.317561i | 0.987314 | + | 0.158781i | \(0.0507562\pi\) | ||||
−0.987314 | + | 0.158781i | \(0.949244\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 979.696i | − | 1.95548i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −374.731 | −0.744992 | −0.372496 | − | 0.928034i | \(-0.621498\pi\) | ||||
−0.372496 | + | 0.928034i | \(0.621498\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 522.680 | 1.03501 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −596.998 | −1.17751 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −426.947 | −0.838795 | −0.419398 | − | 0.907803i | \(-0.637759\pi\) | ||||
−0.419398 | + | 0.907803i | \(0.637759\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 179.229 | 0.350741 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −291.645 | + | 688.670i | −0.568510 | + | 1.34244i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 557.022 | 1.08160 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.82797i | 0.00353573i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1258.62 | 2.42509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 534.084i | − | 1.02511i | −0.858654 | − | 0.512556i | \(-0.828699\pi\) | ||
0.858654 | − | 0.512556i | \(-0.171301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −203.523 | −0.389146 | −0.194573 | − | 0.980888i | \(-0.562332\pi\) | ||||
−0.194573 | + | 0.980888i | \(0.562332\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 241.426 | 0.459859 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 992.950i | 1.88416i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −410.185 | −0.775397 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1966.12 | −3.70268 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8.10116i | − | 0.0151992i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 267.217i | − | 0.499471i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1083.69 | 2.01805 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.83084i | 0.00525203i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 607.359i | − | 1.12266i | −0.827592 | − | 0.561330i | \(-0.810290\pi\) | ||
0.827592 | − | 0.561330i | \(-0.189710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −711.448 | −1.31022 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1074.22i | 1.97105i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −389.263 | −0.711632 | −0.355816 | − | 0.934556i | \(-0.615797\pi\) | ||||
−0.355816 | + | 0.934556i | \(0.615797\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 435.749i | 0.793715i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 96.1693 | − | 227.087i | 0.174536 | − | 0.412136i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 632.720i | − | 1.14416i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 1178.94i | − | 2.12422i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 568.180i | 1.02007i | 0.860153 | + | 0.510036i | \(0.170368\pi\) | ||||
−0.860153 | + | 0.510036i | \(0.829632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 458.005i | 0.819329i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.7899i | 0.0227983i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −556.694 | −0.988799 | −0.494399 | − | 0.869235i | \(-0.664612\pi\) | ||||
−0.494399 | + | 0.869235i | \(0.664612\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1067.42 | 1.88924 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −428.001 | −0.754852 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 106.338i | 0.186886i | 0.995625 | + | 0.0934430i | \(0.0297873\pi\) | ||||
−0.995625 | + | 0.0934430i | \(0.970213\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 918.783i | − | 1.60908i | −0.593901 | − | 0.804538i | \(-0.702413\pi\) | ||
0.593901 | − | 0.804538i | \(-0.297587\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −871.301 | −1.52060 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −59.3165 | −0.103159 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −823.280 | −1.42683 | −0.713414 | − | 0.700743i | \(-0.752852\pi\) | ||||
−0.713414 | + | 0.700743i | \(0.752852\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 801.068i | 1.38354i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 609.963i | − | 1.04985i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.41502i | 0.00928819i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 662.587i | 1.13263i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 809.611i | 1.37923i | 0.724174 | + | 0.689617i | \(0.242221\pi\) | ||||
−0.724174 | + | 0.689617i | \(0.757779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −711.666 | − | 301.384i | −1.20826 | − | 0.511688i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 29.2390i | − | 0.0494737i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −581.819 | −0.981144 | −0.490572 | − | 0.871401i | \(-0.663212\pi\) | ||||
−0.490572 | + | 0.871401i | \(0.663212\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1177.40i | − | 1.97882i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1079.07 | 1.80749 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 9.59418i | − | 0.0160170i | −0.999968 | − | 0.00800849i | \(-0.997451\pi\) | ||
0.999968 | − | 0.00800849i | \(-0.00254921\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 629.588i | − | 1.04757i | −0.851851 | − | 0.523784i | \(-0.824520\pi\) | ||
0.851851 | − | 0.523784i | \(-0.175480\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1134.43 | 1.88130 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 667.547i | 1.10338i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 872.028i | − | 1.43662i | −0.695723 | − | 0.718310i | \(-0.744916\pi\) | ||
0.695723 | − | 0.718310i | \(-0.255084\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 575.842 | 0.945553 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 126.901 | 0.207694 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 180.485i | − | 0.294428i | −0.989105 | − | 0.147214i | \(-0.952969\pi\) | ||
0.989105 | − | 0.147214i | \(-0.0470307\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.6508 | 0.0514647 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 198.869 | 0.322316 | 0.161158 | − | 0.986929i | \(-0.448477\pi\) | ||||
0.161158 | + | 0.986929i | \(0.448477\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 156.095i | − | 0.252174i | −0.992019 | − | 0.126087i | \(-0.959758\pi\) | ||
0.992019 | − | 0.126087i | \(-0.0402418\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 429.055 | 0.690911 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 74.2157i | 0.119126i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −731.431 | −1.17029 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.16673 | − | 3.88203i | −0.0146200 | − | 0.00619143i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1027.78 | −1.63400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1023.23 | −1.62161 | −0.810804 | − | 0.585318i | \(-0.800970\pi\) | ||||
−0.810804 | + | 0.585318i | \(0.800970\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.5870 | 0.0325229 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1286.00 | 2.02519 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 196.522 | 0.308512 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1545.13i | 2.41804i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 139.425i | − | 0.217512i | −0.994068 | − | 0.108756i | \(-0.965313\pi\) | ||
0.994068 | − | 0.108756i | \(-0.0346867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.119878i | − | 0.000186436i | −1.00000 | 9.32179e-5i | \(-0.999970\pi\) | |||
1.00000 | 9.32179e-5i | \(-2.96722e-5\pi\) | ||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1789.40 | −2.77426 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −820.768 | −1.26857 | −0.634287 | − | 0.773097i | \(-0.718706\pi\) | ||||
−0.634287 | + | 0.773097i | \(0.718706\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.1138i | − | 0.0186654i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1804.63i | − | 2.77208i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 66.8769i | 0.102415i | 0.998688 | + | 0.0512074i | \(0.0163070\pi\) | ||||
−0.998688 | + | 0.0512074i | \(0.983693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 795.492 | 1.21449 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −343.537 | −0.522887 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 810.587 | 1.23003 | 0.615013 | − | 0.788517i | \(-0.289151\pi\) | ||||
0.615013 | + | 0.788517i | \(0.289151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1079.30 | −1.63282 | −0.816411 | − | 0.577471i | \(-0.804040\pi\) | ||||
−0.816411 | + | 0.577471i | \(0.804040\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 887.894 | 1.33921 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 843.865 | + | 357.369i | 1.26897 | + | 0.537397i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −141.480 | −0.212114 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 406.968i | 0.608323i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.68477 | −0.00400115 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 747.743i | 1.11106i | 0.831497 | + | 0.555529i | \(0.187484\pi\) | ||||
−0.831497 | + | 0.555529i | \(0.812516\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −214.199 | −0.317332 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 695.960 | 1.02801 | 0.514003 | − | 0.857788i | \(-0.328162\pi\) | ||||
0.514003 | + | 0.857788i | \(0.328162\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1143.84i | 1.68459i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1041.67 | 1.52962 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −532.703 | −0.779946 | −0.389973 | − | 0.920826i | \(-0.627516\pi\) | ||||
−0.389973 | + | 0.920826i | \(0.627516\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 778.626i | 1.13668i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 69.0205i | − | 0.100466i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 375.920 | 0.545602 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 281.522i | 0.407413i | 0.979032 | + | 0.203706i | \(0.0652988\pi\) | ||||
−0.979032 | + | 0.203706i | \(0.934701\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 15.1223i | − | 0.0218215i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1381.26 | −1.98743 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 27.5927i | − | 0.0395878i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1092.90 | 1.56352 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1219.64i | 1.73986i | 0.493176 | + | 0.869929i | \(0.335836\pi\) | ||||
−0.493176 | + | 0.869929i | \(0.664164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 311.957 | − | 736.632i | 0.443751 | − | 1.04784i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 495.794i | 0.703254i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 828.144i | 1.17135i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1212.52i | 1.71019i | 0.518471 | + | 0.855095i | \(0.326501\pi\) | ||||
−0.518471 | + | 0.855095i | \(0.673499\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1212.77i | 1.70572i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 443.383i | 0.621855i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.08239 | −0.00570963 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1298.34 | 1.81080 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −317.916 | −0.442164 | −0.221082 | − | 0.975255i | \(-0.570959\pi\) | ||||
−0.221082 | + | 0.975255i | \(0.570959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 882.555i | 1.22407i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 513.442i | 0.710154i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 70.6315 | 0.0974228 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 968.731 | 1.33250 | 0.666252 | − | 0.745726i | \(-0.267897\pi\) | ||||
0.666252 | + | 0.745726i | \(0.267897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −977.504 | −1.34088 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1559.97i | 2.13403i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 639.217i | − | 0.872056i | −0.899933 | − | 0.436028i | \(-0.856385\pi\) | ||
0.899933 | − | 0.436028i | \(-0.143615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 767.800i | 1.04463i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.98952i | 0.00948374i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1114.79i | − | 1.50851i | −0.656580 | − | 0.754256i | \(-0.727998\pi\) | ||
0.656580 | − | 0.754256i | \(-0.272002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −269.497 | + | 636.370i | −0.363694 | + | 0.858799i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 790.850i | 1.06440i | 0.846618 | + | 0.532201i | \(0.178635\pi\) | ||||
−0.846618 | + | 0.532201i | \(0.821365\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −142.631 | −0.191450 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1169.15i | 1.56512i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 423.383 | 0.565265 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.95691i | − | 0.00526885i | −0.999997 | − | 0.00263443i | \(-0.999161\pi\) | ||
0.999997 | − | 0.00263443i | \(-0.000838565\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1630.59i | − | 2.16546i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1009.24 | 1.33675 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 270.891i | 0.357848i | 0.983863 | + | 0.178924i | \(0.0572616\pi\) | ||||
−0.983863 | + | 0.178924i | \(0.942738\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.71106i | 0.00752445i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 341.236 | 0.448404 | 0.224202 | − | 0.974543i | \(-0.428022\pi\) | ||||
0.224202 | + | 0.974543i | \(0.428022\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1702.02 | −2.23069 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2256.78i | 2.95005i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −840.963 | −1.09643 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 616.420 | 0.801587 | 0.400793 | − | 0.916168i | \(-0.368735\pi\) | ||||
0.400793 | + | 0.916168i | \(0.368735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2034.65i | 2.63898i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1106.79 | 1.43182 | 0.715908 | − | 0.698194i | \(-0.246013\pi\) | ||||
0.715908 | + | 0.698194i | \(0.246013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 221.352i | − | 0.285615i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1867.93 | 2.40403 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.7762 | + | 8.37505i | 0.0253867 | + | 0.0107510i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.51997 | −0.0121895 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −510.901 | −0.652492 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1675.37 | 2.13422 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1201.49 | 1.52667 | 0.763335 | − | 0.646002i | \(-0.223560\pi\) | ||||
0.763335 | + | 0.646002i | \(0.223560\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2399.46 | −3.04115 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1691.24i | 2.13810i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 186.382i | 0.235034i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1468.70i | 1.84742i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −889.940 | −1.11661 | −0.558306 | − | 0.829635i | \(-0.688549\pi\) | ||||
−0.558306 | + | 0.829635i | \(0.688549\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 432.227 | 0.540960 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 142.253i | − | 0.177594i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.11663i | − | 0.00263590i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 525.745i | − | 0.653099i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2120.28 | −2.62736 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −881.557 | −1.08969 | −0.544844 | − | 0.838537i | \(-0.683411\pi\) | ||||
−0.544844 | + | 0.838537i | \(0.683411\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1251.06 | 1.54261 | 0.771305 | − | 0.636466i | \(-0.219604\pi\) | ||||
0.771305 | + | 0.636466i | \(0.219604\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 982.400 | 1.20836 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 632.129 | 0.775618 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1118.06 | − | 473.489i | −1.36850 | − | 0.579546i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1049.81 | −1.28183 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1171.84i | 1.42734i | 0.700484 | + | 0.713668i | \(0.252968\pi\) | ||||
−0.700484 | + | 0.713668i | \(0.747032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1287.88 | 1.56485 | 0.782427 | − | 0.622742i | \(-0.213981\pi\) | ||||
0.782427 | + | 0.622742i | \(0.213981\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 2.85115i | − | 0.00345594i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.5777 | 0.0152088 | 0.00760440 | − | 0.999971i | \(-0.497579\pi\) | ||||
0.00760440 | + | 0.999971i | \(0.497579\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −399.573 | −0.481994 | −0.240997 | − | 0.970526i | \(-0.577474\pi\) | ||||
−0.240997 | + | 0.970526i | \(0.577474\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 79.0090i | 0.0950770i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 669.358 | 0.803551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1065.09 | 1.27556 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1601.11i | 1.91291i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1372.17i | 1.63548i | 0.575589 | + | 0.817739i | \(0.304773\pi\) | ||||
−0.575589 | + | 0.817739i | \(0.695227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −672.532 | −0.799681 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.3578i | 0.0360116i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 649.035i | − | 0.768089i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1057.67 | −1.24873 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 267.963i | − | 0.315622i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −458.937 | −0.539291 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 238.338i | − | 0.279412i | −0.990193 | − | 0.139706i | \(-0.955384\pi\) | ||
0.990193 | − | 0.139706i | \(-0.0446157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1617.48 | − | 684.988i | −1.89179 | − | 0.801156i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 794.657i | − | 0.927254i | −0.886030 | − | 0.463627i | \(-0.846548\pi\) | ||
0.886030 | − | 0.463627i | \(-0.153452\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 424.661i | 0.494367i | 0.968969 | + | 0.247184i | \(0.0795051\pi\) | ||||
−0.968969 | + | 0.247184i | \(0.920495\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 50.1481i | 0.0582440i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 715.215i | − | 0.828755i | −0.910105 | − | 0.414377i | \(-0.863999\pi\) | ||
0.910105 | − | 0.414377i | \(-0.136001\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1368.33i | 1.58188i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1557.50 | 1.79642 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.47220 | −0.00859862 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 485.224 | 0.557089 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2192.45i | − | 2.51140i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 943.342i | − | 1.07811i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −444.385 | −0.506710 | −0.253355 | − | 0.967373i | \(-0.581534\pi\) | ||||
−0.253355 | + | 0.967373i | \(0.581534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1442.96 | 1.64160 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 931.618 | 1.05746 | 0.528728 | − | 0.848792i | \(-0.322669\pi\) | ||||
0.528728 | + | 0.848792i | \(0.322669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1085.52i | − | 1.22935i | −0.788781 | − | 0.614675i | \(-0.789287\pi\) | ||
0.788781 | − | 0.614675i | \(-0.210713\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 3285.59i | − | 3.71254i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 175.875i | − | 0.198281i | −0.995073 | − | 0.0991403i | \(-0.968391\pi\) | ||
0.995073 | − | 0.0991403i | \(-0.0316092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2037.56i | 2.29197i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.05454i | 0.00567289i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −131.191 | + | 309.785i | −0.146911 | + | 0.346904i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1178.15i | 1.31637i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 396.472 | 0.441997 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 527.961i | − | 0.587276i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1280.39 | 1.42108 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2835.16i | − | 3.13971i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 773.461i | − | 0.854653i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 145.717 | 0.160658 | 0.0803289 | − | 0.996768i | \(-0.474403\pi\) | ||||
0.0803289 | + | 0.996768i | \(0.474403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 1587.35i | − | 1.74626i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1028.87i | − | 1.12939i | −0.825301 | − | 0.564693i | \(-0.808995\pi\) | ||
0.825301 | − | 0.564693i | \(-0.191005\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.20345 | −0.00788987 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −728.183 | −0.795828 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1260.39i | 1.37447i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −291.356 | −0.317036 | −0.158518 | − | 0.987356i | \(-0.550672\pi\) | ||||
−0.158518 | + | 0.987356i | \(0.550672\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −550.381 | −0.597591 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 660.893i | 0.716027i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 229.117 | 0.247694 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1691.64i | − | 1.82485i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1427.31 | 1.53640 | 0.768198 | − | 0.640212i | \(-0.221154\pi\) | ||||
0.768198 | + | 0.640212i | \(0.221154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −203.166 | + | 479.741i | −0.218224 | + | 0.515297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2053.68 | 2.20116 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.9047 | −0.0148713 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1215.98 | 1.29773 | 0.648867 | − | 0.760902i | \(-0.275243\pi\) | ||||
0.648867 | + | 0.760902i | \(0.275243\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −568.638 | −0.605578 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −68.4668 | −0.0727596 | −0.0363798 | − | 0.999338i | \(-0.511583\pi\) | ||||
−0.0363798 | + | 0.999338i | \(0.511583\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 12.3210i | − | 0.0130657i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 1898.53i | − | 2.00903i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1667.83i | − | 1.76117i | −0.473888 | − | 0.880585i | \(-0.657150\pi\) | ||
0.473888 | − | 0.880585i | \(-0.342850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −146.940 | −0.154837 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 969.815 | 1.01978 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1414.36i | 1.48411i | 0.670339 | + | 0.742055i | \(0.266149\pi\) | ||||
−0.670339 | + | 0.742055i | \(0.733851\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 947.248i | − | 0.991883i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 6.80049i | − | 0.00710605i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1233.67 | −1.28641 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −693.573 | −0.721720 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −811.521 | −0.842701 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −870.893 | −0.902480 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −395.648 | −0.409150 | −0.204575 | − | 0.978851i | \(-0.565581\pi\) | ||||
−0.204575 | + | 0.978851i | \(0.565581\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −917.912 | + | 2167.49i | −0.947278 | + | 2.23683i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −136.128 | −0.140194 | −0.0700970 | − | 0.997540i | \(-0.522331\pi\) | ||||
−0.0700970 | + | 0.997540i | \(0.522331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2188.49i | − | 2.24922i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −197.932 | −0.203007 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1270.95i | − | 1.30087i | −0.759564 | − | 0.650433i | \(-0.774588\pi\) | ||
0.759564 | − | 0.650433i | \(-0.225412\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.876462 | 0.000895262 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3262.35 | 3.32553 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.7076i | 0.0129274i | 0.999979 | + | 0.00646368i | \(0.00205747\pi\) | ||||
−0.999979 | + | 0.00646368i | \(0.997943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.7876 | 0.0322717 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −785.546 | −0.795892 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 696.576i | 0.704323i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 133.052i | 0.134260i | 0.997744 | + | 0.0671299i | \(0.0213842\pi\) | ||||
−0.997744 | + | 0.0671299i | \(0.978616\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −728.022 | −0.733154 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1173.13i | 1.17902i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 568.469i | 0.570180i | 0.958501 | + | 0.285090i | \(0.0920235\pi\) | ||||
−0.958501 | + | 0.285090i | \(0.907977\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1657.28 | −1.65894 |
(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 | 1216.3.g.e.417.47 | yes | 48 | |
4.3 | odd | 2 | inner | 1216.3.g.e.417.3 | yes | 48 | |
8.3 | odd | 2 | inner | 1216.3.g.e.417.48 | yes | 48 | |
8.5 | even | 2 | inner | 1216.3.g.e.417.4 | yes | 48 | |
19.18 | odd | 2 | inner | 1216.3.g.e.417.1 | ✓ | 48 | |
76.75 | even | 2 | inner | 1216.3.g.e.417.45 | yes | 48 | |
152.37 | odd | 2 | inner | 1216.3.g.e.417.46 | yes | 48 | |
152.75 | even | 2 | inner | 1216.3.g.e.417.2 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.3.g.e.417.1 | ✓ | 48 | 19.18 | odd | 2 | inner | |
1216.3.g.e.417.2 | yes | 48 | 152.75 | even | 2 | inner | |
1216.3.g.e.417.3 | yes | 48 | 4.3 | odd | 2 | inner | |
1216.3.g.e.417.4 | yes | 48 | 8.5 | even | 2 | inner | |
1216.3.g.e.417.45 | yes | 48 | 76.75 | even | 2 | inner | |
1216.3.g.e.417.46 | yes | 48 | 152.37 | odd | 2 | inner | |
1216.3.g.e.417.47 | yes | 48 | 1.1 | even | 1 | trivial | |
1216.3.g.e.417.48 | yes | 48 | 8.3 | odd | 2 | inner |