Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 921x^{12} + 8986x^{10} + 46812x^{8} + 125072x^{6} + 152129x^{4} + 65614x^{2} + 5041 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.2 | ||
Root | \(-3.25431i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.j.485.15 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.25431i | − 1.62715i | −0.581457 | − | 0.813577i | \(-0.697517\pi\) | ||||
0.581457 | − | 0.813577i | \(-0.302483\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.59053 | −1.64763 | ||||||||
\(5\) | − 1.59288i | − 0.318576i | −0.987232 | − | 0.159288i | \(-0.949080\pi\) | ||||
0.987232 | − | 0.159288i | \(-0.0509198\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.8798 | 1.55425 | 0.777127 | − | 0.629344i | \(-0.216676\pi\) | ||||
0.777127 | + | 0.629344i | \(0.216676\pi\) | |||||||
\(8\) | 8.43039i | 1.05380i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.18373 | −0.518373 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.23818 | 0.710629 | 0.355315 | − | 0.934747i | \(-0.384374\pi\) | ||||
0.355315 | + | 0.934747i | \(0.384374\pi\) | |||||||
\(14\) | − 35.4062i | − 2.52901i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.07299 | 0.0670616 | ||||||||
\(17\) | 4.81648i | 0.283322i | 0.989915 | + | 0.141661i | \(0.0452444\pi\) | ||||
−0.989915 | + | 0.141661i | \(0.954756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.0886 | 1.32045 | 0.660227 | − | 0.751066i | \(-0.270460\pi\) | ||||
0.660227 | + | 0.751066i | \(0.270460\pi\) | |||||||
\(20\) | 10.4979i | 0.524896i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 36.6892i | 1.59518i | 0.603199 | + | 0.797590i | \(0.293892\pi\) | ||||
−0.603199 | + | 0.797590i | \(0.706108\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.4627 | 0.898509 | ||||||||
\(26\) | − 30.0639i | − 1.15630i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −71.7035 | −2.56084 | ||||||||
\(29\) | 24.4515i | 0.843156i | 0.906792 | + | 0.421578i | \(0.138524\pi\) | ||||
−0.906792 | + | 0.421578i | \(0.861476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 58.1821 | 1.87684 | 0.938421 | − | 0.345493i | \(-0.112288\pi\) | ||||
0.938421 | + | 0.345493i | \(0.112288\pi\) | |||||||
\(32\) | 30.2297i | 0.944680i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.6743 | 0.461009 | ||||||||
\(35\) | − 17.3302i | − 0.495148i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.7978 | 0.345887 | 0.172943 | − | 0.984932i | \(-0.444672\pi\) | ||||
0.172943 | + | 0.984932i | \(0.444672\pi\) | |||||||
\(38\) | − 81.6462i | − 2.14858i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.4286 | 0.335715 | ||||||||
\(41\) | − 12.4167i | − 0.302845i | −0.988469 | − | 0.151423i | \(-0.951615\pi\) | ||||
0.988469 | − | 0.151423i | \(-0.0483854\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19.6984 | −0.458102 | −0.229051 | − | 0.973414i | \(-0.573562\pi\) | ||||
−0.229051 | + | 0.973414i | \(0.573562\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 119.398 | 2.59561 | ||||||||
\(47\) | − 64.9463i | − 1.38184i | −0.722933 | − | 0.690918i | \(-0.757207\pi\) | ||||
0.722933 | − | 0.690918i | \(-0.242793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 69.3696 | 1.41571 | ||||||||
\(50\) | − 73.1007i | − 1.46201i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −60.8845 | −1.17086 | ||||||||
\(53\) | − 49.5059i | − 0.934073i | −0.884238 | − | 0.467037i | \(-0.845322\pi\) | ||||
0.884238 | − | 0.467037i | \(-0.154678\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 91.7208i | 1.63787i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 79.5728 | 1.37195 | ||||||||
\(59\) | 24.0917i | 0.408333i | 0.978936 | + | 0.204167i | \(0.0654484\pi\) | ||||
−0.978936 | + | 0.204167i | \(0.934552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −44.2401 | −0.725248 | −0.362624 | − | 0.931936i | \(-0.618119\pi\) | ||||
−0.362624 | + | 0.931936i | \(0.618119\pi\) | |||||||
\(62\) | − 189.343i | − 3.05391i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 102.669 | 1.60420 | ||||||||
\(65\) | − 14.7153i | − 0.226389i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 33.0898 | 0.493878 | 0.246939 | − | 0.969031i | \(-0.420575\pi\) | ||||
0.246939 | + | 0.969031i | \(0.420575\pi\) | |||||||
\(68\) | − 31.7432i | − 0.466811i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −56.3978 | −0.805683 | ||||||||
\(71\) | 74.9390i | 1.05548i | 0.849406 | + | 0.527739i | \(0.176960\pi\) | ||||
−0.849406 | + | 0.527739i | \(0.823040\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41.3762 | −0.566797 | −0.283399 | − | 0.959002i | \(-0.591462\pi\) | ||||
−0.283399 | + | 0.959002i | \(0.591462\pi\) | |||||||
\(74\) | − 41.6480i | − 0.562811i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −165.347 | −2.17562 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −63.9703 | −0.809751 | −0.404875 | − | 0.914372i | \(-0.632685\pi\) | ||||
−0.404875 | + | 0.914372i | \(0.632685\pi\) | |||||||
\(80\) | − 1.70914i | − 0.0213642i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −40.4076 | −0.492776 | ||||||||
\(83\) | 42.1858i | 0.508262i | 0.967170 | + | 0.254131i | \(0.0817895\pi\) | ||||
−0.967170 | + | 0.254131i | \(0.918211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.67208 | 0.0902597 | ||||||||
\(86\) | 64.1046i | 0.745402i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 111.111i | − 1.24844i | −0.781249 | − | 0.624220i | \(-0.785417\pi\) | ||||
0.781249 | − | 0.624220i | \(-0.214583\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 100.509 | 1.10450 | ||||||||
\(92\) | − 241.801i | − 2.62827i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −211.355 | −2.24846 | ||||||||
\(95\) | − 39.9632i | − 0.420665i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −108.103 | −1.11447 | −0.557233 | − | 0.830356i | \(-0.688137\pi\) | ||||
−0.557233 | + | 0.830356i | \(0.688137\pi\) | |||||||
\(98\) | − 225.750i | − 2.30357i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −148.041 | −1.48041 | ||||||||
\(101\) | 116.418i | 1.15265i | 0.817221 | + | 0.576324i | \(0.195514\pi\) | ||||
−0.817221 | + | 0.576324i | \(0.804486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −109.280 | −1.06097 | −0.530484 | − | 0.847695i | \(-0.677990\pi\) | ||||
−0.530484 | + | 0.847695i | \(0.677990\pi\) | |||||||
\(104\) | 77.8815i | 0.748861i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −161.107 | −1.51988 | ||||||||
\(107\) | − 43.1743i | − 0.403498i | −0.979437 | − | 0.201749i | \(-0.935337\pi\) | ||||
0.979437 | − | 0.201749i | \(-0.0646626\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −75.3063 | −0.690884 | −0.345442 | − | 0.938440i | \(-0.612271\pi\) | ||||
−0.345442 | + | 0.938440i | \(0.612271\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.6738 | 0.104231 | ||||||||
\(113\) | 3.52202i | 0.0311683i | 0.999879 | + | 0.0155842i | \(0.00496080\pi\) | ||||
−0.999879 | + | 0.0155842i | \(0.995039\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 58.4414 | 0.508186 | ||||||||
\(116\) | − 161.149i | − 1.38921i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 78.4017 | 0.664421 | ||||||||
\(119\) | 52.4023i | 0.440355i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 143.971i | 1.18009i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −383.451 | −3.09235 | ||||||||
\(125\) | − 75.6024i | − 0.604820i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 237.588 | 1.87077 | 0.935385 | − | 0.353630i | \(-0.115053\pi\) | ||||
0.935385 | + | 0.353630i | \(0.115053\pi\) | |||||||
\(128\) | − 213.197i | − 1.66561i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −47.8882 | −0.368371 | ||||||||
\(131\) | − 64.9832i | − 0.496055i | −0.968753 | − | 0.248027i | \(-0.920218\pi\) | ||||
0.968753 | − | 0.248027i | \(-0.0797823\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 272.959 | 2.05232 | ||||||||
\(134\) | − 107.685i | − 0.803616i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −40.6048 | −0.298565 | ||||||||
\(137\) | − 125.513i | − 0.916152i | −0.888913 | − | 0.458076i | \(-0.848539\pi\) | ||||
0.888913 | − | 0.458076i | \(-0.151461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −83.9520 | −0.603971 | −0.301986 | − | 0.953312i | \(-0.597649\pi\) | ||||
−0.301986 | + | 0.953312i | \(0.597649\pi\) | |||||||
\(140\) | 114.215i | 0.815822i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 243.875 | 1.71743 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 38.9483 | 0.268609 | ||||||||
\(146\) | 134.651i | 0.922267i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −84.3444 | −0.569894 | ||||||||
\(149\) | − 208.842i | − 1.40162i | −0.713346 | − | 0.700812i | \(-0.752821\pi\) | ||||
0.713346 | − | 0.700812i | \(-0.247179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −62.1096 | −0.411322 | −0.205661 | − | 0.978623i | \(-0.565934\pi\) | ||||
−0.205661 | + | 0.978623i | \(0.565934\pi\) | |||||||
\(152\) | 211.507i | 1.39149i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 92.6771i | − 0.597917i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −107.364 | −0.683847 | −0.341923 | − | 0.939728i | \(-0.611078\pi\) | ||||
−0.341923 | + | 0.939728i | \(0.611078\pi\) | |||||||
\(158\) | 208.179i | 1.31759i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 48.1524 | 0.300952 | ||||||||
\(161\) | 399.170i | 2.47932i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 203.397 | 1.24783 | 0.623916 | − | 0.781491i | \(-0.285541\pi\) | ||||
0.623916 | + | 0.781491i | \(0.285541\pi\) | |||||||
\(164\) | 81.8324i | 0.498978i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 137.286 | 0.827021 | ||||||||
\(167\) | 316.071i | 1.89264i | 0.323230 | + | 0.946320i | \(0.395231\pi\) | ||||
−0.323230 | + | 0.946320i | \(0.604769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −83.6560 | −0.495006 | ||||||||
\(170\) | − 24.9673i | − 0.146867i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 129.823 | 0.754783 | ||||||||
\(173\) | − 114.001i | − 0.658963i | −0.944162 | − | 0.329482i | \(-0.893126\pi\) | ||||
0.944162 | − | 0.329482i | \(-0.106874\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 244.390 | 1.39651 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −361.590 | −2.03140 | ||||||||
\(179\) | − 145.784i | − 0.814436i | −0.913331 | − | 0.407218i | \(-0.866499\pi\) | ||||
0.913331 | − | 0.407218i | \(-0.133501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −347.607 | −1.92048 | −0.960241 | − | 0.279171i | \(-0.909940\pi\) | ||||
−0.960241 | + | 0.279171i | \(0.909940\pi\) | |||||||
\(182\) | − 327.089i | − 1.79719i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −309.304 | −1.68100 | ||||||||
\(185\) | − 20.3854i | − 0.110191i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 428.030i | 2.27676i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −130.053 | −0.684487 | ||||||||
\(191\) | − 74.8885i | − 0.392086i | −0.980595 | − | 0.196043i | \(-0.937191\pi\) | ||||
0.980595 | − | 0.196043i | \(-0.0628093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 31.8200 | 0.164871 | 0.0824353 | − | 0.996596i | \(-0.473730\pi\) | ||||
0.0824353 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(194\) | 351.801i | 1.81341i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −457.183 | −2.33256 | ||||||||
\(197\) | 165.104i | 0.838089i | 0.907966 | + | 0.419045i | \(0.137635\pi\) | ||||
−0.907966 | + | 0.419045i | \(0.862365\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 195.093 | 0.980365 | 0.490182 | − | 0.871620i | \(-0.336930\pi\) | ||||
0.490182 | + | 0.871620i | \(0.336930\pi\) | |||||||
\(200\) | 189.370i | 0.946848i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 378.859 | 1.87554 | ||||||||
\(203\) | 266.027i | 1.31048i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.7782 | −0.0964792 | ||||||||
\(206\) | 355.630i | 1.72636i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.91243 | 0.0476559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −182.295 | −0.863959 | −0.431980 | − | 0.901883i | \(-0.642185\pi\) | ||||
−0.431980 | + | 0.901883i | \(0.642185\pi\) | |||||||
\(212\) | 326.270i | 1.53901i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −140.503 | −0.656554 | ||||||||
\(215\) | 31.3771i | 0.145940i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 633.009 | 2.91709 | ||||||||
\(218\) | 245.070i | 1.12417i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 44.4955i | 0.201337i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −114.587 | −0.513843 | −0.256921 | − | 0.966432i | \(-0.582708\pi\) | ||||
−0.256921 | + | 0.966432i | \(0.582708\pi\) | |||||||
\(224\) | 328.893i | 1.46827i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.4618 | 0.0507157 | ||||||||
\(227\) | − 233.643i | − 1.02926i | −0.857411 | − | 0.514632i | \(-0.827929\pi\) | ||||
0.857411 | − | 0.514632i | \(-0.172071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 139.279 | 0.608206 | 0.304103 | − | 0.952639i | \(-0.401643\pi\) | ||||
0.304103 | + | 0.952639i | \(0.401643\pi\) | |||||||
\(230\) | − 190.187i | − 0.826898i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −206.136 | −0.888517 | ||||||||
\(233\) | 118.544i | 0.508772i | 0.967103 | + | 0.254386i | \(0.0818734\pi\) | ||||
−0.967103 | + | 0.254386i | \(0.918127\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −103.452 | −0.440220 | ||||||||
\(236\) | − 158.777i | − 0.672783i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 170.533 | 0.716526 | ||||||||
\(239\) | − 288.314i | − 1.20634i | −0.797614 | − | 0.603168i | \(-0.793905\pi\) | ||||
0.797614 | − | 0.603168i | \(-0.206095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 115.517 | 0.479324 | 0.239662 | − | 0.970856i | \(-0.422963\pi\) | ||||
0.239662 | + | 0.970856i | \(0.422963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 291.566 | 1.19494 | ||||||||
\(245\) | − 110.497i | − 0.451010i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 231.773 | 0.938354 | ||||||||
\(248\) | 490.498i | 1.97782i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −246.034 | −0.984135 | ||||||||
\(251\) | − 34.4392i | − 0.137208i | −0.997644 | − | 0.0686040i | \(-0.978145\pi\) | ||||
0.997644 | − | 0.0686040i | \(-0.0218545\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 773.185i | − 3.04403i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −283.135 | −1.10600 | ||||||||
\(257\) | − 208.411i | − 0.810937i | −0.914109 | − | 0.405469i | \(-0.867108\pi\) | ||||
0.914109 | − | 0.405469i | \(-0.132892\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 139.237 | 0.537596 | ||||||||
\(260\) | 96.9817i | 0.373007i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −211.475 | −0.807158 | ||||||||
\(263\) | 230.901i | 0.877952i | 0.898499 | + | 0.438976i | \(0.144659\pi\) | ||||
−0.898499 | + | 0.438976i | \(0.855341\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −78.8569 | −0.297573 | ||||||||
\(266\) | − 888.293i | − 3.33945i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −218.080 | −0.813730 | ||||||||
\(269\) | − 11.0843i | − 0.0412055i | −0.999788 | − | 0.0206027i | \(-0.993441\pi\) | ||||
0.999788 | − | 0.0206027i | \(-0.00655852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −100.794 | −0.371935 | −0.185968 | − | 0.982556i | \(-0.559542\pi\) | ||||
−0.185968 | + | 0.982556i | \(0.559542\pi\) | |||||||
\(272\) | 5.16801i | 0.0190000i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −408.458 | −1.49072 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 53.4162 | 0.192838 | 0.0964191 | − | 0.995341i | \(-0.469261\pi\) | ||||
0.0964191 | + | 0.995341i | \(0.469261\pi\) | |||||||
\(278\) | 273.206i | 0.982755i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 146.100 | 0.521787 | ||||||||
\(281\) | 369.254i | 1.31407i | 0.753859 | + | 0.657036i | \(0.228190\pi\) | ||||
−0.753859 | + | 0.657036i | \(0.771810\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −241.063 | −0.851814 | −0.425907 | − | 0.904767i | \(-0.640045\pi\) | ||||
−0.425907 | + | 0.904767i | \(0.640045\pi\) | |||||||
\(284\) | − 493.888i | − 1.73904i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 135.090i | − 0.470699i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 265.802 | 0.919728 | ||||||||
\(290\) | − 126.750i | − 0.437069i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 272.691 | 0.933874 | ||||||||
\(293\) | − 55.1299i | − 0.188157i | −0.995565 | − | 0.0940783i | \(-0.970010\pi\) | ||||
0.995565 | − | 0.0940783i | \(-0.0299904\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.3751 | 0.130085 | ||||||||
\(296\) | 107.891i | 0.364495i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −679.637 | −2.28066 | ||||||||
\(299\) | 338.941i | 1.13358i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −214.314 | −0.712006 | ||||||||
\(302\) | 202.124i | 0.669285i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.9197 | 0.0885518 | ||||||||
\(305\) | 70.4692i | 0.231047i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.5104 | 0.0407504 | 0.0203752 | − | 0.999792i | \(-0.493514\pi\) | ||||
0.0203752 | + | 0.999792i | \(0.493514\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −301.600 | −0.972904 | ||||||||
\(311\) | − 215.665i | − 0.693458i | −0.937965 | − | 0.346729i | \(-0.887292\pi\) | ||||
0.937965 | − | 0.346729i | \(-0.112708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 435.646 | 1.39184 | 0.695920 | − | 0.718120i | \(-0.254997\pi\) | ||||
0.695920 | + | 0.718120i | \(0.254997\pi\) | |||||||
\(314\) | 349.396i | 1.11272i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 421.598 | 1.33417 | ||||||||
\(317\) | − 313.816i | − 0.989956i | −0.868905 | − | 0.494978i | \(-0.835176\pi\) | ||||
0.868905 | − | 0.494978i | \(-0.164824\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 163.539i | − 0.511060i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1299.02 | 4.03423 | ||||||||
\(323\) | 120.839i | 0.374114i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 207.515 | 0.638507 | ||||||||
\(326\) | − 661.916i | − 2.03042i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 104.677 | 0.319138 | ||||||||
\(329\) | − 706.601i | − 2.14772i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 69.5045 | 0.209983 | 0.104992 | − | 0.994473i | \(-0.466518\pi\) | ||||
0.104992 | + | 0.994473i | \(0.466518\pi\) | |||||||
\(332\) | − 278.027i | − 0.837430i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1028.59 | 3.07962 | ||||||||
\(335\) | − 52.7081i | − 0.157338i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 108.794 | 0.322832 | 0.161416 | − | 0.986886i | \(-0.448394\pi\) | ||||
0.161416 | + | 0.986886i | \(0.448394\pi\) | |||||||
\(338\) | 272.243i | 0.805452i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −50.5631 | −0.148715 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 221.617 | 0.646113 | ||||||||
\(344\) | − 166.065i | − 0.482747i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −370.993 | −1.07224 | ||||||||
\(347\) | 382.854i | 1.10332i | 0.834068 | + | 0.551662i | \(0.186006\pi\) | ||||
−0.834068 | + | 0.551662i | \(0.813994\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −441.623 | −1.26540 | −0.632698 | − | 0.774399i | \(-0.718052\pi\) | ||||
−0.632698 | + | 0.774399i | \(0.718052\pi\) | |||||||
\(350\) | − 795.319i | − 2.27234i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 237.587i | − 0.673051i | −0.941674 | − | 0.336525i | \(-0.890748\pi\) | ||||
0.941674 | − | 0.336525i | \(-0.109252\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 119.369 | 0.336250 | ||||||||
\(356\) | 732.281i | 2.05697i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −474.427 | −1.32521 | ||||||||
\(359\) | 385.744i | 1.07450i | 0.843424 | + | 0.537248i | \(0.180536\pi\) | ||||
−0.843424 | + | 0.537248i | \(0.819464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 268.440 | 0.743600 | ||||||||
\(362\) | 1131.22i | 3.12492i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −662.410 | −1.81981 | ||||||||
\(365\) | 65.9073i | 0.180568i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 154.272 | 0.420361 | 0.210180 | − | 0.977663i | \(-0.432595\pi\) | ||||
0.210180 | + | 0.977663i | \(0.432595\pi\) | |||||||
\(368\) | 39.3669i | 0.106975i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −66.3403 | −0.179298 | ||||||||
\(371\) | − 538.613i | − 1.45179i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −440.608 | −1.18125 | −0.590627 | − | 0.806944i | \(-0.701120\pi\) | ||||
−0.590627 | + | 0.806944i | \(0.701120\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 547.523 | 1.45618 | ||||||||
\(377\) | 225.888i | 0.599171i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 556.553 | 1.46848 | 0.734239 | − | 0.678891i | \(-0.237539\pi\) | ||||
0.734239 | + | 0.678891i | \(0.237539\pi\) | |||||||
\(380\) | 263.379i | 0.693102i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −243.710 | −0.637985 | ||||||||
\(383\) | 125.668i | 0.328115i | 0.986451 | + | 0.164057i | \(0.0524582\pi\) | ||||
−0.986451 | + | 0.164057i | \(0.947542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 103.552i | − 0.268270i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 712.457 | 1.83623 | ||||||||
\(389\) | 67.1506i | 0.172624i | 0.996268 | + | 0.0863119i | \(0.0275081\pi\) | ||||
−0.996268 | + | 0.0863119i | \(0.972492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −176.713 | −0.451951 | ||||||||
\(392\) | 584.813i | 1.49187i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 537.298 | 1.36370 | ||||||||
\(395\) | 101.897i | 0.257967i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 342.588 | 0.862942 | 0.431471 | − | 0.902127i | \(-0.357995\pi\) | ||||
0.431471 | + | 0.902127i | \(0.357995\pi\) | |||||||
\(398\) | − 634.892i | − 1.59521i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 24.1022 | 0.0602555 | ||||||||
\(401\) | 370.533i | 0.924022i | 0.886874 | + | 0.462011i | \(0.152872\pi\) | ||||
−0.886874 | + | 0.462011i | \(0.847128\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 537.497 | 1.33374 | ||||||||
\(404\) | − 767.254i | − 1.89914i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 865.735 | 2.13235 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 320.164 | 0.782797 | 0.391398 | − | 0.920221i | \(-0.371991\pi\) | ||||
0.391398 | + | 0.920221i | \(0.371991\pi\) | |||||||
\(410\) | 64.3645i | 0.156987i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 720.211 | 1.74808 | ||||||||
\(413\) | 262.112i | 0.634653i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 67.1969 | 0.161920 | ||||||||
\(416\) | 279.268i | 0.671317i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 574.973i | 1.37225i | 0.727483 | + | 0.686126i | \(0.240690\pi\) | ||||
−0.727483 | + | 0.686126i | \(0.759310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 141.737 | 0.336668 | 0.168334 | − | 0.985730i | \(-0.446161\pi\) | ||||
0.168334 | + | 0.985730i | \(0.446161\pi\) | |||||||
\(422\) | 593.246i | 1.40580i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 417.354 | 0.984326 | ||||||||
\(425\) | 108.191i | 0.254568i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −481.323 | −1.12722 | ||||||||
\(428\) | 284.542i | 0.664817i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 102.111 | 0.237467 | ||||||||
\(431\) | − 391.659i | − 0.908722i | −0.890818 | − | 0.454361i | \(-0.849868\pi\) | ||||
0.890818 | − | 0.454361i | \(-0.150132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −343.995 | −0.794447 | −0.397223 | − | 0.917722i | \(-0.630026\pi\) | ||||
−0.397223 | + | 0.917722i | \(0.630026\pi\) | |||||||
\(434\) | − 2060.01i | − 4.74656i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 496.309 | 1.13832 | ||||||||
\(437\) | 920.481i | 2.10636i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.1143 | −0.0822650 | −0.0411325 | − | 0.999154i | \(-0.513097\pi\) | ||||
−0.0411325 | + | 0.999154i | \(0.513097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 144.802 | 0.327607 | ||||||||
\(443\) | − 382.066i | − 0.862452i | −0.902244 | − | 0.431226i | \(-0.858081\pi\) | ||||
0.902244 | − | 0.431226i | \(-0.141919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −176.987 | −0.397723 | ||||||||
\(446\) | 372.901i | 0.836101i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1117.02 | 2.49334 | ||||||||
\(449\) | 30.7104i | 0.0683974i | 0.999415 | + | 0.0341987i | \(0.0108879\pi\) | ||||
−0.999415 | + | 0.0341987i | \(0.989112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 23.2120i | − 0.0513540i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −760.346 | −1.67477 | ||||||||
\(455\) | − 160.099i | − 0.351867i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −412.699 | −0.903061 | −0.451531 | − | 0.892256i | \(-0.649122\pi\) | ||||
−0.451531 | + | 0.892256i | \(0.649122\pi\) | |||||||
\(458\) | − 453.258i | − 0.989645i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −385.160 | −0.837305 | ||||||||
\(461\) | 765.072i | 1.65959i | 0.558066 | + | 0.829797i | \(0.311544\pi\) | ||||
−0.558066 | + | 0.829797i | \(0.688456\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 113.587 | 0.245328 | 0.122664 | − | 0.992448i | \(-0.460856\pi\) | ||||
0.122664 | + | 0.992448i | \(0.460856\pi\) | |||||||
\(464\) | 26.2361i | 0.0565434i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 385.779 | 0.827852 | ||||||||
\(467\) | 756.817i | 1.62059i | 0.586019 | + | 0.810297i | \(0.300694\pi\) | ||||
−0.586019 | + | 0.810297i | \(0.699306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 360.010 | 0.767612 | ||||||||
\(470\) | 336.664i | 0.716305i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −203.102 | −0.430301 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 563.559 | 1.18644 | ||||||||
\(476\) | − 345.359i | − 0.725544i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −938.264 | −1.96290 | ||||||||
\(479\) | − 364.563i | − 0.761091i | −0.924762 | − | 0.380546i | \(-0.875736\pi\) | ||||
0.924762 | − | 0.380546i | \(-0.124264\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 118.228 | 0.245797 | ||||||||
\(482\) | − 375.929i | − 0.779935i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 172.195i | 0.355042i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −240.050 | −0.492915 | −0.246458 | − | 0.969154i | \(-0.579267\pi\) | ||||
−0.246458 | + | 0.969154i | \(0.579267\pi\) | |||||||
\(488\) | − 372.962i | − 0.764266i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −359.593 | −0.733863 | ||||||||
\(491\) | 837.796i | 1.70630i | 0.521662 | + | 0.853152i | \(0.325312\pi\) | ||||
−0.521662 | + | 0.853152i | \(0.674688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −117.770 | −0.238885 | ||||||||
\(494\) | − 754.262i | − 1.52685i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 62.4286 | 0.125864 | ||||||||
\(497\) | 815.320i | 1.64048i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 644.663 | 1.29191 | 0.645955 | − | 0.763376i | \(-0.276460\pi\) | ||||
0.645955 | + | 0.763376i | \(0.276460\pi\) | |||||||
\(500\) | 498.260i | 0.996521i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −112.076 | −0.223259 | ||||||||
\(503\) | − 10.5076i | − 0.0208898i | −0.999945 | − | 0.0104449i | \(-0.996675\pi\) | ||||
0.999945 | − | 0.0104449i | \(-0.00332478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 185.439 | 0.367206 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1565.83 | −3.08234 | ||||||||
\(509\) | − 915.705i | − 1.79903i | −0.436893 | − | 0.899514i | \(-0.643921\pi\) | ||||
0.436893 | − | 0.899514i | \(-0.356079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −450.164 | −0.880947 | ||||||||
\(512\) | 68.6188i | 0.134021i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −678.233 | −1.31952 | ||||||||
\(515\) | 174.069i | 0.337999i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − 453.121i | − 0.874752i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 124.056 | 0.238569 | ||||||||
\(521\) | − 235.989i | − 0.452953i | −0.974017 | − | 0.226477i | \(-0.927279\pi\) | ||||
0.974017 | − | 0.226477i | \(-0.0727207\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 151.331 | 0.289351 | 0.144676 | − | 0.989479i | \(-0.453786\pi\) | ||||
0.144676 | + | 0.989479i | \(0.453786\pi\) | |||||||
\(524\) | 428.274i | 0.817316i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 751.425 | 1.42856 | ||||||||
\(527\) | 280.233i | 0.531752i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −817.095 | −1.54460 | ||||||||
\(530\) | 256.625i | 0.484198i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1798.94 | −3.38147 | ||||||||
\(533\) | − 114.707i | − 0.215211i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −68.7715 | −0.128545 | ||||||||
\(536\) | 278.960i | 0.520448i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −36.0716 | −0.0670477 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −300.434 | −0.555331 | −0.277665 | − | 0.960678i | \(-0.589561\pi\) | ||||
−0.277665 | + | 0.960678i | \(0.589561\pi\) | |||||||
\(542\) | 328.016i | 0.605196i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −145.601 | −0.267649 | ||||||||
\(545\) | 119.954i | 0.220099i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 324.960 | 0.594077 | 0.297038 | − | 0.954866i | \(-0.404001\pi\) | ||||
0.297038 | + | 0.954866i | \(0.404001\pi\) | |||||||
\(548\) | 827.196i | 1.50948i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 613.455i | 1.11335i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −695.983 | −1.25856 | ||||||||
\(554\) | − 173.833i | − 0.313778i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 553.289 | 0.995123 | ||||||||
\(557\) | 45.2931i | 0.0813162i | 0.999173 | + | 0.0406581i | \(0.0129454\pi\) | ||||
−0.999173 | + | 0.0406581i | \(0.987055\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −181.977 | −0.325540 | ||||||||
\(560\) | − 18.5950i | − 0.0332054i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1201.67 | 2.13820 | ||||||||
\(563\) | − 728.842i | − 1.29457i | −0.762249 | − | 0.647284i | \(-0.775905\pi\) | ||||
0.762249 | − | 0.647284i | \(-0.224095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.61016 | 0.00992948 | ||||||||
\(566\) | 784.495i | 1.38603i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −631.765 | −1.11226 | ||||||||
\(569\) | 146.146i | 0.256847i | 0.991719 | + | 0.128423i | \(0.0409916\pi\) | ||||
−0.991719 | + | 0.128423i | \(0.959008\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −398.941 | −0.698672 | −0.349336 | − | 0.936998i | \(-0.613593\pi\) | ||||
−0.349336 | + | 0.936998i | \(0.613593\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −439.626 | −0.765899 | ||||||||
\(575\) | 824.139i | 1.43328i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 252.489 | 0.437589 | 0.218795 | − | 0.975771i | \(-0.429788\pi\) | ||||
0.218795 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(578\) | − 865.000i | − 1.49654i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −256.690 | −0.442569 | ||||||||
\(581\) | 458.972i | 0.789969i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − 348.818i | − 0.597290i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −179.410 | −0.306160 | ||||||||
\(587\) | − 985.570i | − 1.67900i | −0.543363 | − | 0.839498i | \(-0.682849\pi\) | ||||
0.543363 | − | 0.839498i | \(-0.317151\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1459.71 | 2.47829 | ||||||||
\(590\) | − 124.884i | − 0.211669i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.7319 | 0.0231957 | ||||||||
\(593\) | − 795.418i | − 1.34135i | −0.741753 | − | 0.670673i | \(-0.766005\pi\) | ||||
0.741753 | − | 0.670673i | \(-0.233995\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 83.4705 | 0.140287 | ||||||||
\(596\) | 1376.38i | 2.30936i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1103.02 | 1.84451 | ||||||||
\(599\) | 114.903i | 0.191825i | 0.995390 | + | 0.0959126i | \(0.0305769\pi\) | ||||
−0.995390 | + | 0.0959126i | \(0.969423\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 294.608 | 0.490196 | 0.245098 | − | 0.969498i | \(-0.421180\pi\) | ||||
0.245098 | + | 0.969498i | \(0.421180\pi\) | |||||||
\(602\) | 697.444i | 1.15854i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 409.336 | 0.677708 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 435.121 | 0.716838 | 0.358419 | − | 0.933561i | \(-0.383316\pi\) | ||||
0.358419 | + | 0.933561i | \(0.383316\pi\) | |||||||
\(608\) | 758.423i | 1.24741i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 229.329 | 0.375949 | ||||||||
\(611\) | − 599.985i | − 0.981973i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −628.161 | −1.02473 | −0.512366 | − | 0.858767i | \(-0.671231\pi\) | ||||
−0.512366 | + | 0.858767i | \(0.671231\pi\) | |||||||
\(614\) | − 40.7126i | − 0.0663072i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 215.080i | 0.348590i | 0.984694 | + | 0.174295i | \(0.0557646\pi\) | ||||
−0.984694 | + | 0.174295i | \(0.944235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −956.887 | −1.54586 | −0.772929 | − | 0.634492i | \(-0.781209\pi\) | ||||
−0.772929 | + | 0.634492i | \(0.781209\pi\) | |||||||
\(620\) | 610.792i | 0.985148i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −701.842 | −1.12836 | ||||||||
\(623\) | − 1208.86i | − 1.94039i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 441.143 | 0.705828 | ||||||||
\(626\) | − 1417.73i | − 2.26474i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 707.585 | 1.12673 | ||||||||
\(629\) | 61.6404i | 0.0979975i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −637.996 | −1.01109 | −0.505544 | − | 0.862801i | \(-0.668708\pi\) | ||||
−0.505544 | + | 0.862801i | \(0.668708\pi\) | |||||||
\(632\) | − 539.295i | − 0.853315i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1021.25 | −1.61081 | ||||||||
\(635\) | − 378.449i | − 0.595983i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 640.849 | 1.00604 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −339.598 | −0.530622 | ||||||||
\(641\) | 958.209i | 1.49487i | 0.664337 | + | 0.747433i | \(0.268714\pi\) | ||||
−0.664337 | + | 0.747433i | \(0.731286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −294.864 | −0.458575 | −0.229288 | − | 0.973359i | \(-0.573640\pi\) | ||||
−0.229288 | + | 0.973359i | \(0.573640\pi\) | |||||||
\(644\) | − 2630.74i | − 4.08500i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 393.247 | 0.608742 | ||||||||
\(647\) | − 1005.11i | − 1.55350i | −0.629809 | − | 0.776750i | \(-0.716867\pi\) | ||||
0.629809 | − | 0.776750i | \(-0.283133\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 675.317i | − 1.03895i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1340.49 | −2.05597 | ||||||||
\(653\) | 1035.63i | 1.58595i | 0.609253 | + | 0.792976i | \(0.291469\pi\) | ||||
−0.609253 | + | 0.792976i | \(0.708531\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −103.510 | −0.158031 | ||||||||
\(656\) | − 13.3229i | − 0.0203093i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2299.50 | −3.49468 | ||||||||
\(659\) | − 572.524i | − 0.868777i | −0.900726 | − | 0.434388i | \(-0.856965\pi\) | ||||
0.900726 | − | 0.434388i | \(-0.143035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −717.443 | −1.08539 | −0.542695 | − | 0.839930i | \(-0.682596\pi\) | ||||
−0.542695 | + | 0.839930i | \(0.682596\pi\) | |||||||
\(662\) | − 226.189i | − 0.341675i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −355.643 | −0.535606 | ||||||||
\(665\) | − 434.791i | − 0.653821i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −897.106 | −1.34499 | ||||||||
\(668\) | − 2083.08i | − 3.11838i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −171.529 | −0.256013 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 872.035 | 1.29574 | 0.647872 | − | 0.761749i | \(-0.275659\pi\) | ||||
0.647872 | + | 0.761749i | \(0.275659\pi\) | |||||||
\(674\) | − 354.050i | − 0.525297i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 551.338 | 0.815588 | ||||||||
\(677\) | 1276.05i | 1.88487i | 0.334394 | + | 0.942433i | \(0.391468\pi\) | ||||
−0.334394 | + | 0.942433i | \(0.608532\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1176.14 | −1.73216 | ||||||||
\(680\) | 64.6786i | 0.0951156i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 411.727i | 0.602822i | 0.953494 | + | 0.301411i | \(0.0974575\pi\) | ||||
−0.953494 | + | 0.301411i | \(0.902542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −199.927 | −0.291864 | ||||||||
\(686\) | − 721.210i | − 1.05133i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −21.1361 | −0.0307210 | ||||||||
\(689\) | − 457.344i | − 0.663780i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −832.518 | −1.20480 | −0.602401 | − | 0.798194i | \(-0.705789\pi\) | ||||
−0.602401 | + | 0.798194i | \(0.705789\pi\) | |||||||
\(692\) | 751.325i | 1.08573i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1245.92 | 1.79528 | ||||||||
\(695\) | 133.726i | 0.192411i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 59.8046 | 0.0858029 | ||||||||
\(698\) | 1437.18i | 2.05899i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1610.66 | −2.30094 | ||||||||
\(701\) | − 90.8137i | − 0.129549i | −0.997900 | − | 0.0647744i | \(-0.979367\pi\) | ||||
0.997900 | − | 0.0647744i | \(-0.0206328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 321.080 | 0.456728 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −773.182 | −1.09516 | ||||||||
\(707\) | 1266.60i | 1.79151i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −684.473 | −0.965406 | −0.482703 | − | 0.875784i | \(-0.660345\pi\) | ||||
−0.482703 | + | 0.875784i | \(0.660345\pi\) | |||||||
\(710\) | − 388.463i | − 0.547131i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 936.711 | 1.31560 | ||||||||
\(713\) | 2134.65i | 2.99390i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 960.795i | 1.34189i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1255.33 | 1.74837 | ||||||||
\(719\) | − 1246.85i | − 1.73415i | −0.498182 | − | 0.867073i | \(-0.665999\pi\) | ||||
0.498182 | − | 0.867073i | \(-0.334001\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1188.94 | −1.64901 | ||||||||
\(722\) | − 873.586i | − 1.20995i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2290.92 | 3.16425 | ||||||||
\(725\) | 549.248i | 0.757583i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −837.811 | −1.15242 | −0.576211 | − | 0.817301i | \(-0.695469\pi\) | ||||
−0.576211 | + | 0.817301i | \(0.695469\pi\) | |||||||
\(728\) | 847.334i | 1.16392i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 214.483 | 0.293812 | ||||||||
\(731\) | − 94.8768i | − 0.129790i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 62.9218 | 0.0858415 | 0.0429208 | − | 0.999078i | \(-0.486334\pi\) | ||||
0.0429208 | + | 0.999078i | \(0.486334\pi\) | |||||||
\(734\) | − 502.050i | − 0.683992i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1109.10 | −1.50694 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1180.19 | −1.59701 | −0.798504 | − | 0.601989i | \(-0.794375\pi\) | ||||
−0.798504 | + | 0.601989i | \(0.794375\pi\) | |||||||
\(740\) | 134.350i | 0.181555i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1752.81 | −2.36228 | ||||||||
\(743\) | 496.072i | 0.667661i | 0.942633 | + | 0.333830i | \(0.108341\pi\) | ||||
−0.942633 | + | 0.333830i | \(0.891659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −332.660 | −0.446524 | ||||||||
\(746\) | 1433.88i | 1.92208i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 469.727i | − 0.627139i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 408.480 | 0.543914 | 0.271957 | − | 0.962309i | \(-0.412329\pi\) | ||||
0.271957 | + | 0.962309i | \(0.412329\pi\) | |||||||
\(752\) | − 69.6864i | − 0.0926681i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 735.108 | 0.974944 | ||||||||
\(755\) | 98.9332i | 0.131037i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −757.992 | −1.00131 | −0.500655 | − | 0.865647i | \(-0.666907\pi\) | ||||
−0.500655 | + | 0.865647i | \(0.666907\pi\) | |||||||
\(758\) | − 1811.20i | − 2.38944i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 336.905 | 0.443297 | ||||||||
\(761\) | 1353.55i | 1.77865i | 0.457278 | + | 0.889324i | \(0.348825\pi\) | ||||
−0.457278 | + | 0.889324i | \(0.651175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −819.316 | −1.07381 | ||||||||
\(764\) | 493.555i | 0.646014i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 408.962 | 0.533893 | ||||||||
\(767\) | 222.563i | 0.290173i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −550.877 | −0.716355 | −0.358178 | − | 0.933654i | \(-0.616602\pi\) | ||||
−0.358178 | + | 0.933654i | \(0.616602\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −209.711 | −0.271646 | ||||||||
\(773\) | − 885.139i | − 1.14507i | −0.819880 | − | 0.572535i | \(-0.805960\pi\) | ||||
0.819880 | − | 0.572535i | \(-0.194040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1306.93 | 1.68636 | ||||||||
\(776\) | − 911.352i | − 1.17442i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 218.529 | 0.280886 | ||||||||
\(779\) | − 311.517i | − 0.399893i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 575.078i | 0.735394i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 74.4326 | 0.0949395 | ||||||||
\(785\) | 171.018i | 0.217857i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1481.78 | −1.88283 | −0.941413 | − | 0.337255i | \(-0.890502\pi\) | ||||
−0.941413 | + | 0.337255i | \(0.890502\pi\) | |||||||
\(788\) | − 1088.12i | − 1.38086i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 331.605 | 0.419753 | ||||||||
\(791\) | 38.3188i | 0.0484435i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −408.698 | −0.515382 | ||||||||
\(794\) | − 1114.89i | − 1.40414i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1285.76 | −1.61528 | ||||||||
\(797\) | 69.4562i | 0.0871471i | 0.999050 | + | 0.0435735i | \(0.0138743\pi\) | ||||
−0.999050 | + | 0.0435735i | \(0.986126\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 312.812 | 0.391505 | ||||||||
\(800\) | 679.043i | 0.848803i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1205.83 | 1.50353 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 635.830 | 0.789851 | ||||||||
\(806\) | − 1749.18i | − 2.17020i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −981.446 | −1.21466 | ||||||||
\(809\) | − 881.324i | − 1.08940i | −0.838631 | − | 0.544700i | \(-0.816644\pi\) | ||||
0.838631 | − | 0.544700i | \(-0.183356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1048.72 | −1.29312 | −0.646560 | − | 0.762863i | \(-0.723793\pi\) | ||||
−0.646560 | + | 0.762863i | \(0.723793\pi\) | |||||||
\(812\) | − 1753.26i | − 2.15919i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 323.986i | − 0.397529i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −494.205 | −0.604902 | ||||||||
\(818\) | − 1041.91i | − 1.27373i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 130.349 | 0.158962 | ||||||||
\(821\) | − 983.682i | − 1.19815i | −0.800692 | − | 0.599076i | \(-0.795535\pi\) | ||||
0.800692 | − | 0.599076i | \(-0.204465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −977.362 | −1.18756 | −0.593780 | − | 0.804627i | \(-0.702365\pi\) | ||||
−0.593780 | + | 0.804627i | \(0.702365\pi\) | |||||||
\(824\) | − 921.270i | − 1.11805i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 852.993 | 1.03268 | ||||||||
\(827\) | − 23.7343i | − 0.0286993i | −0.999897 | − | 0.0143496i | \(-0.995432\pi\) | ||||
0.999897 | − | 0.0143496i | \(-0.00456779\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 908.389 | 1.09576 | 0.547882 | − | 0.836555i | \(-0.315434\pi\) | ||||
0.547882 | + | 0.836555i | \(0.315434\pi\) | |||||||
\(830\) | − 218.679i | − 0.263469i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 948.474 | 1.13999 | ||||||||
\(833\) | 334.117i | 0.401101i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 503.463 | 0.602950 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1871.14 | 2.23287 | ||||||||
\(839\) | − 780.010i | − 0.929690i | −0.885392 | − | 0.464845i | \(-0.846110\pi\) | ||||
0.885392 | − | 0.464845i | \(-0.153890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 243.123 | 0.289088 | ||||||||
\(842\) | − 461.256i | − 0.547810i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1201.42 | 1.42349 | ||||||||
\(845\) | 133.254i | 0.157697i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 53.1191i | − 0.0626404i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 352.088 | 0.414221 | ||||||||
\(851\) | 469.541i | 0.551752i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 642.554 | 0.753287 | 0.376644 | − | 0.926358i | \(-0.377078\pi\) | ||||
0.376644 | + | 0.926358i | \(0.377078\pi\) | |||||||
\(854\) | 1566.37i | 1.83416i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 363.977 | 0.425206 | ||||||||
\(857\) | 442.968i | 0.516883i | 0.966027 | + | 0.258441i | \(0.0832088\pi\) | ||||
−0.966027 | + | 0.258441i | \(0.916791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −95.7522 | −0.111469 | −0.0557347 | − | 0.998446i | \(-0.517750\pi\) | ||||
−0.0557347 | + | 0.998446i | \(0.517750\pi\) | |||||||
\(860\) | − 206.792i | − 0.240456i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1274.58 | −1.47863 | ||||||||
\(863\) | − 576.575i | − 0.668105i | −0.942554 | − | 0.334053i | \(-0.891584\pi\) | ||||
0.942554 | − | 0.334053i | \(-0.108416\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −181.589 | −0.209930 | ||||||||
\(866\) | 1119.47i | 1.29269i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4171.86 | −4.80630 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 305.690 | 0.350964 | ||||||||
\(872\) | − 634.862i | − 0.728053i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2995.53 | 3.42738 | ||||||||
\(875\) | − 822.538i | − 0.940043i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 909.291 | 1.03682 | 0.518410 | − | 0.855132i | \(-0.326524\pi\) | ||||
0.518410 | + | 0.855132i | \(0.326524\pi\) | |||||||
\(878\) | 117.527i | 0.133858i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 864.536i | 0.981312i | 0.871353 | + | 0.490656i | \(0.163243\pi\) | ||||
−0.871353 | + | 0.490656i | \(0.836757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.93310 | −0.00218924 | −0.00109462 | − | 0.999999i | \(-0.500348\pi\) | ||||
−0.00109462 | + | 0.999999i | \(0.500348\pi\) | |||||||
\(884\) | − 293.249i | − 0.331730i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1243.36 | −1.40334 | ||||||||
\(887\) | 743.312i | 0.838007i | 0.907985 | + | 0.419004i | \(0.137621\pi\) | ||||
−0.907985 | + | 0.419004i | \(0.862379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2584.90 | 2.90765 | ||||||||
\(890\) | 575.970i | 0.647157i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 755.189 | 0.846624 | ||||||||
\(893\) | − 1629.41i | − 1.82465i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −232.217 | −0.259460 | ||||||||
\(896\) | − 2319.54i | − 2.58877i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 99.9413 | 0.111293 | ||||||||
\(899\) | 1422.64i | 1.58247i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 238.444 | 0.264644 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −29.6920 | −0.0328452 | ||||||||
\(905\) | 553.697i | 0.611820i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −715.123 | −0.788449 | −0.394225 | − | 0.919014i | \(-0.628987\pi\) | ||||
−0.394225 | + | 0.919014i | \(0.628987\pi\) | |||||||
\(908\) | 1539.83i | 1.69585i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −521.013 | −0.572542 | ||||||||
\(911\) | − 382.652i | − 0.420035i | −0.977698 | − | 0.210018i | \(-0.932648\pi\) | ||||
0.977698 | − | 0.210018i | \(-0.0673521\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1343.05i | 1.46942i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −917.924 | −1.00210 | ||||||||
\(917\) | − 707.003i | − 0.770995i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −383.352 | −0.417140 | −0.208570 | − | 0.978007i | \(-0.566881\pi\) | ||||
−0.208570 | + | 0.978007i | \(0.566881\pi\) | |||||||
\(920\) | 492.684i | 0.535526i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2489.78 | 2.70042 | ||||||||
\(923\) | 692.300i | 0.750054i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 287.474 | 0.310782 | ||||||||
\(926\) | − 369.646i | − 0.399186i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −739.163 | −0.796512 | ||||||||
\(929\) | 216.559i | 0.233110i | 0.993184 | + | 0.116555i | \(0.0371851\pi\) | ||||
−0.993184 | + | 0.116555i | \(0.962815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1740.39 | 1.86938 | ||||||||
\(932\) | − 781.268i | − 0.838270i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2462.92 | 2.63696 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 931.108 | 0.993712 | 0.496856 | − | 0.867833i | \(-0.334488\pi\) | ||||
0.496856 | + | 0.867833i | \(0.334488\pi\) | |||||||
\(938\) | − 1171.58i | − 1.24902i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 681.801 | 0.725320 | ||||||||
\(941\) | 1364.86i | 1.45043i | 0.688522 | + | 0.725215i | \(0.258260\pi\) | ||||
−0.688522 | + | 0.725215i | \(0.741740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 455.557 | 0.483093 | ||||||||
\(944\) | 25.8500i | 0.0273835i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 564.949i | 0.596567i | 0.954477 | + | 0.298283i | \(0.0964141\pi\) | ||||
−0.954477 | + | 0.298283i | \(0.903586\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −382.241 | −0.402783 | ||||||||
\(950\) | − 1834.00i | − 1.93052i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −441.772 | −0.464046 | ||||||||
\(953\) | 199.814i | 0.209668i | 0.994490 | + | 0.104834i | \(0.0334311\pi\) | ||||
−0.994490 | + | 0.104834i | \(0.966569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −119.288 | −0.124909 | ||||||||
\(956\) | 1900.15i | 1.98760i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1186.40 | −1.23841 | ||||||||
\(959\) | − 1365.55i | − 1.42393i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2424.16 | 2.52254 | ||||||||
\(962\) | − 384.752i | − 0.399950i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −761.319 | −0.789751 | ||||||||
\(965\) | − 50.6855i | − 0.0525238i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −267.827 | −0.276967 | −0.138483 | − | 0.990365i | \(-0.544223\pi\) | ||||
−0.138483 | + | 0.990365i | \(0.544223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 560.377 | 0.577708 | ||||||||
\(971\) | − 1748.88i | − 1.80111i | −0.434745 | − | 0.900554i | \(-0.643161\pi\) | ||||
0.434745 | − | 0.900554i | \(-0.356839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −913.380 | −0.938725 | ||||||||
\(974\) | 781.196i | 0.802050i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −47.4690 | −0.0486363 | ||||||||
\(977\) | 917.940i | 0.939549i | 0.882786 | + | 0.469775i | \(0.155665\pi\) | ||||
−0.882786 | + | 0.469775i | \(0.844335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 728.237i | 0.743099i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2726.45 | 2.77642 | ||||||||
\(983\) | 652.287i | 0.663568i | 0.943355 | + | 0.331784i | \(0.107650\pi\) | ||||
−0.943355 | + | 0.331784i | \(0.892350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 262.990 | 0.266995 | ||||||||
\(986\) | 383.261i | 0.388703i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1527.51 | −1.54606 | ||||||||
\(989\) | − 722.717i | − 0.730755i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 573.705 | 0.578915 | 0.289458 | − | 0.957191i | \(-0.406525\pi\) | ||||
0.289458 | + | 0.957191i | \(0.406525\pi\) | |||||||
\(992\) | 1758.83i | 1.77302i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2653.30 | 2.66932 | ||||||||
\(995\) | − 310.759i | − 0.312321i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −333.026 | −0.334028 | −0.167014 | − | 0.985955i | \(-0.553413\pi\) | ||||
−0.167014 | + | 0.985955i | \(0.553413\pi\) | |||||||
\(998\) | − 2097.93i | − 2.10214i | ||||||||
\(999\) | 0 | 0 |
(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 | 1089.3.b.j.485.2 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.j.485.15 | 16 | ||
11.2 | odd | 10 | 99.3.l.a.26.8 | yes | 32 | ||
11.6 | odd | 10 | 99.3.l.a.80.1 | yes | 32 | ||
11.10 | odd | 2 | 1089.3.b.i.485.15 | 16 | |||
33.2 | even | 10 | 99.3.l.a.26.1 | ✓ | 32 | ||
33.17 | even | 10 | 99.3.l.a.80.8 | yes | 32 | ||
33.32 | even | 2 | 1089.3.b.i.485.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.26.1 | ✓ | 32 | 33.2 | even | 10 | ||
99.3.l.a.26.8 | yes | 32 | 11.2 | odd | 10 | ||
99.3.l.a.80.1 | yes | 32 | 11.6 | odd | 10 | ||
99.3.l.a.80.8 | yes | 32 | 33.17 | even | 10 | ||
1089.3.b.i.485.2 | 16 | 33.32 | even | 2 | |||
1089.3.b.i.485.15 | 16 | 11.10 | odd | 2 | |||
1089.3.b.j.485.2 | 16 | 1.1 | even | 1 | trivial | ||
1089.3.b.j.485.15 | 16 | 3.2 | odd | 2 | inner |