Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(191,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.d (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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.13 | ||
Character | \(\chi\) | \(=\) | 912.191 |
Dual form | 912.2.d.b.191.14 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.372770 | − | 1.69146i | 0.215219 | − | 0.976566i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.46369i | 1.99622i | 0.0614408 | + | 0.998111i | \(0.480430\pi\) | ||||
−0.0614408 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.16484i | 0.818234i | 0.912482 | + | 0.409117i | \(0.134163\pi\) | ||||
−0.912482 | + | 0.409117i | \(0.865837\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.72208 | − | 1.26105i | −0.907362 | − | 0.420351i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.80522 | 0.845807 | 0.422904 | − | 0.906175i | \(-0.361011\pi\) | ||||
0.422904 | + | 0.906175i | \(0.361011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.91931 | −1.36437 | −0.682186 | − | 0.731179i | \(-0.738970\pi\) | ||||
−0.682186 | + | 0.731179i | \(0.738970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.55016 | + | 1.66393i | 1.94944 | + | 0.429625i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.05968i | − | 0.499547i | −0.968304 | − | 0.249773i | \(-0.919644\pi\) | ||
0.968304 | − | 0.249773i | \(-0.0803561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.66175 | + | 0.806989i | 0.799059 | + | 0.176099i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.97760 | −1.24642 | −0.623208 | − | 0.782056i | \(-0.714171\pi\) | ||||
−0.623208 | + | 0.782056i | \(0.714171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.9245 | −2.98490 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.14773 | + | 4.13422i | −0.605782 | + | 0.795631i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.58678i | 1.40883i | 0.709788 | + | 0.704415i | \(0.248791\pi\) | ||||
−0.709788 | + | 0.704415i | \(0.751209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.51027i | 1.16928i | 0.811293 | + | 0.584639i | \(0.198764\pi\) | ||||
−0.811293 | + | 0.584639i | \(0.801236\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.04570 | − | 4.74493i | 0.182034 | − | 0.825986i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.66318 | −1.63338 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.923673 | 0.151851 | 0.0759254 | − | 0.997113i | \(-0.475809\pi\) | ||||
0.0759254 | + | 0.997113i | \(0.475809\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.83377 | + | 8.32083i | −0.293639 | + | 1.33240i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.75873i | 0.743188i | 0.928395 | + | 0.371594i | \(0.121189\pi\) | ||||
−0.928395 | + | 0.371594i | \(0.878811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.87563i | − | 1.20102i | −0.799616 | − | 0.600511i | \(-0.794964\pi\) | ||
0.799616 | − | 0.600511i | \(-0.205036\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.62894 | − | 12.1505i | 0.839113 | − | 1.81129i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.70925 | 0.249320 | 0.124660 | − | 0.992200i | \(-0.460216\pi\) | ||||
0.124660 | + | 0.992200i | \(0.460216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.31346 | 0.330494 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.48388 | − | 0.767789i | −0.487840 | − | 0.107512i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.41385i | − | 0.194207i | −0.995274 | − | 0.0971033i | \(-0.969042\pi\) | ||
0.995274 | − | 0.0971033i | \(-0.0309577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.5216i | 1.68842i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.69146 | + | 0.372770i | 0.224040 | + | 0.0493746i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.1861 | 1.32612 | 0.663060 | − | 0.748566i | \(-0.269257\pi\) | ||||
0.663060 | + | 0.748566i | \(0.269257\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72471 | −0.220827 | −0.110413 | − | 0.993886i | \(-0.535218\pi\) | ||||
−0.110413 | + | 0.993886i | \(0.535218\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.72998 | − | 5.89289i | 0.343945 | − | 0.742434i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 21.9583i | − | 2.72359i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.78356i | 0.706574i | 0.935515 | + | 0.353287i | \(0.114936\pi\) | ||||
−0.935515 | + | 0.353287i | \(0.885064\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.22827 | + | 10.1109i | −0.268252 | + | 1.21721i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48172 | 0.531883 | 0.265941 | − | 0.963989i | \(-0.414317\pi\) | ||||
0.265941 | + | 0.963989i | \(0.414317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.82461 | −0.447637 | −0.223819 | − | 0.974631i | \(-0.571852\pi\) | ||||
−0.223819 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.56341 | + | 25.2442i | −0.642407 | + | 2.91495i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.07287i | 0.692068i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.14728i | 0.129079i | 0.997915 | + | 0.0645393i | \(0.0205578\pi\) | ||||
−0.997915 | + | 0.0645393i | \(0.979442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.81949 | + | 6.86538i | 0.646610 | + | 0.762821i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.6407 | 1.82655 | 0.913275 | − | 0.407343i | \(-0.133545\pi\) | ||||
0.913275 | + | 0.407343i | \(0.133545\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.19379 | 0.997206 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.8328 | + | 2.82813i | 1.37582 | + | 0.303207i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6918i | 1.13333i | 0.823947 | + | 0.566666i | \(0.191767\pi\) | ||||
−0.823947 | + | 0.566666i | \(0.808233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.6495i | − | 1.11637i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.0119 | + | 2.42683i | 1.14188 | + | 0.251651i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.46369 | −0.457965 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.86696 | −0.494165 | −0.247082 | − | 0.968995i | \(-0.579472\pi\) | ||||
−0.247082 | + | 0.968995i | \(0.579472\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.63606 | − | 3.53754i | −0.767453 | − | 0.355536i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.9361i | − | 1.08818i | −0.839026 | − | 0.544091i | \(-0.816875\pi\) | ||
0.839026 | − | 0.544091i | \(-0.183125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.6040i | − | 1.63604i | −0.575191 | − | 0.818019i | \(-0.695072\pi\) | ||
0.575191 | − | 0.818019i | \(-0.304928\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.60214 | + | 16.3449i | −0.351533 | + | 1.59510i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.45093 | 0.623635 | 0.311817 | − | 0.950142i | \(-0.399062\pi\) | ||||
0.311817 | + | 0.950142i | \(0.399062\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.24717 | −0.789936 | −0.394968 | − | 0.918695i | \(-0.629244\pi\) | ||||
−0.394968 | + | 0.918695i | \(0.629244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.344318 | − | 1.56236i | 0.0326812 | − | 0.148292i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.7853i | 1.48496i | 0.669869 | + | 0.742479i | \(0.266350\pi\) | ||||
−0.669869 | + | 0.742479i | \(0.733650\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 26.6821i | − | 2.48812i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.3908 | + | 6.20351i | 1.23798 | + | 0.573515i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.45889 | 0.408746 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.13071 | −0.284610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.04920 | + | 1.77391i | 0.725772 | + | 0.159948i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 44.2999i | − | 3.96230i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0378i | 0.979450i | 0.871877 | + | 0.489725i | \(0.162903\pi\) | ||||
−0.871877 | + | 0.489725i | \(0.837097\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.3213 | − | 2.93580i | −1.17288 | − | 0.258483i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.71368 | 0.149725 | 0.0748624 | − | 0.997194i | \(-0.476148\pi\) | ||||
0.0748624 | + | 0.997194i | \(0.476148\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.16484 | −0.187716 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.4539 | − | 14.0505i | −1.58826 | − | 1.20927i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.1694i | 1.21057i | 0.796009 | + | 0.605285i | \(0.206941\pi\) | ||||
−0.796009 | + | 0.605285i | \(0.793059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7288i | 0.910008i | 0.890489 | + | 0.455004i | \(0.150362\pi\) | ||||
−0.890489 | + | 0.455004i | \(0.849638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.637157 | − | 2.89113i | 0.0536583 | − | 0.243477i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.7998 | −1.15400 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.8650 | −2.81234 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.862387 | − | 3.91312i | 0.0711285 | − | 0.322749i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.92527i | 0.567340i | 0.958922 | + | 0.283670i | \(0.0915521\pi\) | ||||
−0.958922 | + | 0.283670i | \(0.908448\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.72975i | − | 0.140765i | −0.997520 | − | 0.0703824i | \(-0.977578\pi\) | ||
0.997520 | − | 0.0703824i | \(-0.0224220\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.59737 | + | 5.60664i | −0.209985 | + | 0.453270i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −29.0598 | −2.33414 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3245 | 1.22303 | 0.611514 | − | 0.791233i | \(-0.290561\pi\) | ||||
0.611514 | + | 0.791233i | \(0.290561\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.39147 | − | 0.527039i | −0.189656 | − | 0.0417969i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 12.9406i | − | 1.01986i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.20985i | − | 0.643045i | −0.946902 | − | 0.321523i | \(-0.895805\pi\) | ||
0.946902 | − | 0.321523i | \(-0.104195\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 21.1799 | + | 4.66770i | 1.64885 | + | 0.363380i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6368 | −1.05525 | −0.527624 | − | 0.849478i | \(-0.676917\pi\) | ||||
−0.527624 | + | 0.849478i | \(0.676917\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1996 | 0.861509 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.26105 | − | 2.72208i | 0.0964351 | − | 0.208163i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 0.190545i | − | 0.0144868i | −0.999974 | − | 0.00724342i | \(-0.997694\pi\) | ||
0.999974 | − | 0.00724342i | \(-0.00230567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 32.3092i | − | 2.44235i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.79708 | − | 17.2294i | 0.285406 | − | 1.29504i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.3680 | 1.37289 | 0.686443 | − | 0.727184i | \(-0.259171\pi\) | ||||
0.686443 | + | 0.727184i | \(0.259171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.1869 | 0.757188 | 0.378594 | − | 0.925563i | \(-0.376408\pi\) | ||||
0.378594 | + | 0.925563i | \(0.376408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.642922 | + | 2.91729i | −0.0475261 | + | 0.215652i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.12299i | 0.303128i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 5.77788i | − | 0.422520i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.94993 | − | 6.81435i | −0.651012 | − | 0.495671i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.8965 | −1.15023 | −0.575113 | − | 0.818074i | \(-0.695042\pi\) | ||||
−0.575113 | + | 0.818074i | \(0.695042\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.43616 | 0.319322 | 0.159661 | − | 0.987172i | \(-0.448960\pi\) | ||||
0.159661 | + | 0.987172i | \(0.448960\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −37.1416 | − | 8.18538i | −2.65976 | − | 0.586168i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.7467i | − | 1.19315i | −0.802557 | − | 0.596576i | \(-0.796528\pi\) | ||
0.802557 | − | 0.596576i | \(-0.203472\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.3295i | − | 0.732239i | −0.930568 | − | 0.366119i | \(-0.880686\pi\) | ||
0.930568 | − | 0.366119i | \(-0.119314\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.78267 | + | 2.15594i | 0.690016 | + | 0.152068i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.4242 | −1.15275 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.2415 | −1.48357 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.2715 | + | 7.53807i | 1.13095 | + | 0.523932i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.80522i | 0.194041i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1692i | 0.975450i | 0.872997 | + | 0.487725i | \(0.162173\pi\) | ||||
−0.872997 | + | 0.487725i | \(0.837827\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.67065 | − | 7.58066i | 0.114471 | − | 0.519419i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35.1544 | 2.39751 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.0937 | −0.956743 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.42570 | + | 6.46919i | −0.0963400 | + | 0.437147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.1322i | 0.681568i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.6776i | − | 0.715025i | −0.933908 | − | 0.357512i | \(-0.883625\pi\) | ||
0.933908 | − | 0.357512i | \(-0.116375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40.6258 | + | 18.8206i | 2.70838 | + | 1.25471i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.5808 | 1.69786 | 0.848928 | − | 0.528509i | \(-0.177249\pi\) | ||||
0.848928 | + | 0.528509i | \(0.177249\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.470101 | 0.0310652 | 0.0155326 | − | 0.999879i | \(-0.495056\pi\) | ||||
0.0155326 | + | 0.999879i | \(0.495056\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.2720 | + | 2.26378i | 0.675850 | + | 0.148946i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3842i | 0.811315i | 0.914025 | + | 0.405658i | \(0.132957\pi\) | ||||
−0.914025 | + | 0.405658i | \(0.867043\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.62955i | 0.497697i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.94057 | + | 0.427670i | 0.126054 | + | 0.0277802i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.2387 | −0.921023 | −0.460511 | − | 0.887654i | \(-0.652334\pi\) | ||||
−0.460511 | + | 0.887654i | \(0.652334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0635 | 0.648250 | 0.324125 | − | 0.946014i | \(-0.394930\pi\) | ||||
0.324125 | + | 0.946014i | \(0.394930\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.7819 | − | 7.28424i | 0.884107 | − | 0.467284i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.3265i | 0.659739i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.91931i | − | 0.313008i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.20314 | − | 28.1471i | 0.393108 | − | 1.78375i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.45735 | 0.344465 | 0.172233 | − | 0.985056i | \(-0.444902\pi\) | ||||
0.172233 | + | 0.985056i | \(0.444902\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.7685 | −1.05423 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.42717 | − | 15.5509i | 0.214618 | − | 0.973838i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.8964i | 0.929214i | 0.885517 | + | 0.464607i | \(0.153804\pi\) | ||||
−0.885517 | + | 0.464607i | \(0.846196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.99961i | 0.124249i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.56733 | − | 20.6519i | 0.592203 | − | 1.27832i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.7471 | 0.662692 | 0.331346 | − | 0.943509i | \(-0.392497\pi\) | ||||
0.331346 | + | 0.943509i | \(0.392497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.31096 | 0.387679 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0848 | + | 3.98560i | 1.10677 | + | 0.243915i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8905i | 0.968862i | 0.874829 | + | 0.484431i | \(0.160973\pi\) | ||||
−0.874829 | + | 0.484431i | \(0.839027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.0632i | − | 0.975771i | −0.872908 | − | 0.487885i | \(-0.837768\pi\) | ||
0.872908 | − | 0.487885i | \(-0.162232\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.0133 | − | 3.96983i | −1.09021 | − | 0.240265i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −41.8666 | −2.52465 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.2121 | 1.51485 | 0.757424 | − | 0.652923i | \(-0.226458\pi\) | ||||
0.757424 | + | 0.652923i | \(0.226458\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.20979 | − | 17.7215i | 0.491507 | − | 1.06096i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 16.4958i | − | 0.984056i | −0.870579 | − | 0.492028i | \(-0.836256\pi\) | ||
0.870579 | − | 0.492028i | \(-0.163744\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.2030i | − | 0.725393i | −0.931907 | − | 0.362697i | \(-0.881856\pi\) | ||
0.931907 | − | 0.362697i | \(-0.118144\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.66393 | + | 7.55016i | −0.0985627 | + | 0.447233i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.3019 | −0.608102 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7577 | 0.750453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.81426 | + | 8.23227i | −0.106354 | + | 0.482584i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.2421i | 1.47466i | 0.675532 | + | 0.737330i | \(0.263914\pi\) | ||||
−0.675532 | + | 0.737330i | \(0.736086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.4677i | 2.64723i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.83010 | + | 11.5974i | −0.512374 | + | 0.672950i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.4057 | 1.70057 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.0495 | 0.982717 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.4980 | − | 4.07665i | −1.06268 | − | 0.234197i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 7.69858i | − | 0.440820i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.2212i | − | 1.61067i | −0.592820 | − | 0.805335i | \(-0.701985\pi\) | ||
0.592820 | − | 0.805335i | \(-0.298015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.0850 | − | 6.18946i | −1.59770 | − | 0.352106i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.2665 | 0.979093 | 0.489546 | − | 0.871977i | \(-0.337162\pi\) | ||||
0.489546 | + | 0.871977i | \(0.337162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.8219 | −1.28997 | −0.644984 | − | 0.764196i | \(-0.723136\pi\) | ||||
−0.644984 | + | 0.764196i | \(0.723136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.3040 | + | 12.1858i | 1.48206 | + | 0.686591i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.81008i | 0.326327i | 0.986599 | + | 0.163163i | \(0.0521698\pi\) | ||||
−0.986599 | + | 0.163163i | \(0.947830\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.2826i | 1.19160i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.40471 | − | 10.9115i | 0.134218 | − | 0.609021i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.05968 | 0.114604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 73.4183 | 4.07251 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.07430 | + | 13.9498i | −0.170009 | + | 0.771424i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.70026i | 0.204002i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 15.6647i | − | 0.861011i | −0.902588 | − | 0.430505i | \(-0.858335\pi\) | ||
0.902588 | − | 0.430505i | \(-0.141665\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.51432 | − | 1.16480i | −0.137784 | − | 0.0638306i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.8160 | −1.41048 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.67542 | 0.254686 | 0.127343 | − | 0.991859i | \(-0.459355\pi\) | ||||
0.127343 | + | 0.991859i | \(0.459355\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.7003 | + | 5.88430i | 1.45016 | + | 0.319591i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.2628i | 0.988984i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1622i | 1.08865i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −45.1318 | − | 9.94630i | −2.42981 | − | 0.535491i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.0331 | −0.699655 | −0.349828 | − | 0.936814i | \(-0.613760\pi\) | ||||
−0.349828 | + | 0.936814i | \(0.613760\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.58023 | −0.245174 | −0.122587 | − | 0.992458i | \(-0.539119\pi\) | ||||
−0.122587 | + | 0.992458i | \(0.539119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.4847 | − | 20.3375i | 0.826511 | − | 1.08554i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.5705i | − | 0.615837i | −0.951413 | − | 0.307918i | \(-0.900368\pi\) | ||
0.951413 | − | 0.307918i | \(-0.0996324\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.0050i | 1.06176i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.66214 | − | 7.54205i | 0.0879699 | − | 0.399167i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.5779 | −0.874946 | −0.437473 | − | 0.899232i | \(-0.644126\pi\) | ||||
−0.437473 | + | 0.899232i | \(0.644126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.16704 | + | 5.29548i | −0.0612535 | + | 0.277941i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 17.0719i | − | 0.893583i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 28.7461i | − | 1.50053i | −0.661136 | − | 0.750266i | \(-0.729925\pi\) | ||
0.661136 | − | 0.750266i | \(-0.270075\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00100 | − | 12.9537i | 0.312400 | − | 0.674340i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.06075 | 0.158906 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.2320 | −0.529795 | −0.264898 | − | 0.964277i | \(-0.585338\pi\) | ||||
−0.264898 | + | 0.964277i | \(0.585338\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −74.9315 | − | 16.5137i | −3.86945 | − | 0.852762i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 37.3217i | − | 1.92217i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.1932i | 1.34545i | 0.739891 | + | 0.672727i | \(0.234877\pi\) | ||||
−0.739891 | + | 0.672727i | \(0.765123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.6701 | + | 4.11458i | 0.956497 | + | 0.210796i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.8112 | 0.756817 | 0.378409 | − | 0.925639i | \(-0.376471\pi\) | ||||
0.378409 | + | 0.925639i | \(0.376471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.1074 | −1.38152 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.93159 | + | 21.4381i | −0.504851 | + | 1.08976i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 19.2711i | − | 0.977086i | −0.872540 | − | 0.488543i | \(-0.837529\pi\) | ||
0.872540 | − | 0.488543i | \(-0.162471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3120i | 0.622643i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.638808 | − | 2.89862i | 0.0322236 | − | 0.146216i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.12108 | −0.257670 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.91933 | −0.146517 | −0.0732585 | − | 0.997313i | \(-0.523340\pi\) | ||||
−0.0732585 | + | 0.997313i | \(0.523340\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.806989 | + | 3.66175i | −0.0404000 | + | 0.183317i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.97620i | 0.248499i | 0.992251 | + | 0.124250i | \(0.0396524\pi\) | ||||
−0.992251 | + | 0.124250i | \(0.960348\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 32.0260i | − | 1.59533i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.6449 | + | 25.9764i | −1.52276 | + | 1.29078i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.59111 | 0.128437 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7836 | −0.533213 | −0.266607 | − | 0.963805i | \(-0.585902\pi\) | ||||
−0.266607 | + | 0.963805i | \(0.585902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.9669 | + | 5.28191i | 1.18220 | + | 0.260537i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.0514i | 1.08508i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 74.2787i | 3.64620i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.1474 | + | 3.99939i | 0.888683 | + | 0.195851i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.1097 | −0.835864 | −0.417932 | − | 0.908478i | \(-0.637245\pi\) | ||||
−0.417932 | + | 0.908478i | \(0.637245\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6052 | −0.663076 | −0.331538 | − | 0.943442i | \(-0.607568\pi\) | ||||
−0.331538 | + | 0.943442i | \(0.607568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.65272 | − | 2.15545i | −0.226223 | − | 0.104802i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.7398i | 1.49110i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.73373i | − | 0.180688i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.14414 | + | 23.3418i | −0.248362 | + | 1.12695i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.4189 | 0.694534 | 0.347267 | − | 0.937766i | \(-0.387110\pi\) | ||||
0.347267 | + | 0.937766i | \(0.387110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.942348 | 0.0452863 | 0.0226432 | − | 0.999744i | \(-0.492792\pi\) | ||||
0.0226432 | + | 0.999744i | \(0.492792\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6239 | + | 57.2814i | −0.605268 | + | 2.74643i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.97760i | − | 0.285947i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.8985i | 0.901977i | 0.892530 | + | 0.450989i | \(0.148929\pi\) | ||||
−0.892530 | + | 0.450989i | \(0.851071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.29742 | − | 2.91739i | −0.299877 | − | 0.138923i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.1308 | −1.62160 | −0.810802 | − | 0.585320i | \(-0.800969\pi\) | ||||
−0.810802 | + | 0.585320i | \(0.800969\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.7250 | −2.26238 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.7138 | + | 2.58153i | 0.554045 | + | 0.122102i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 6.78994i | − | 0.320437i | −0.987082 | − | 0.160219i | \(-0.948780\pi\) | ||
0.987082 | − | 0.160219i | \(-0.0512199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.3493i | 0.628594i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.92580 | − | 0.644798i | −0.137466 | − | 0.0302952i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 47.5362 | 2.22853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6632 | −0.826251 | −0.413125 | − | 0.910674i | \(-0.635563\pi\) | ||||
−0.413125 | + | 0.910674i | \(0.635563\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.51519 | + | 6.48334i | 0.397455 | + | 0.302616i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.65256i | − | 0.402990i | −0.979490 | − | 0.201495i | \(-0.935420\pi\) | ||
0.979490 | − | 0.201495i | \(-0.0645799\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.34526i | 0.108993i | 0.998514 | + | 0.0544966i | \(0.0173554\pi\) | ||||
−0.998514 | + | 0.0544966i | \(0.982645\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.8326 | + | 49.1535i | −0.502351 | + | 2.27944i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.6672 | −1.32656 | −0.663281 | − | 0.748371i | \(-0.730836\pi\) | ||||
−0.663281 | + | 0.748371i | \(0.730836\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.5205 | −0.578143 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.71252 | − | 25.9208i | 0.263219 | − | 1.19437i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 22.0929i | − | 1.01583i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 14.9245i | − | 0.684783i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.78293 | + | 3.84861i | −0.0816349 | + | 0.176216i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0372 | −0.549995 | −0.274997 | − | 0.961445i | \(-0.588677\pi\) | ||||
−0.274997 | + | 0.961445i | \(0.588677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.54383 | −0.207181 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.8885 | − | 4.82385i | −0.995959 | − | 0.219493i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 21.7246i | − | 0.986462i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.7506i | − | 1.03093i | −0.856911 | − | 0.515464i | \(-0.827619\pi\) | ||
0.856911 | − | 0.515464i | \(-0.172381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.8867 | − | 3.06039i | −0.627976 | − | 0.138396i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1415 | −0.457677 | −0.228839 | − | 0.973464i | \(-0.573493\pi\) | ||||
−0.228839 | + | 0.973464i | \(0.573493\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.6264 | 0.703777 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.7905 | − | 34.0850i | 0.709728 | − | 1.53201i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.70223i | 0.435204i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.58305i | 0.249932i | 0.992161 | + | 0.124966i | \(0.0398821\pi\) | ||||
−0.992161 | + | 0.124966i | \(0.960118\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.08340 | + | 23.0662i | −0.227110 | + | 1.03052i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6877 | 0.788657 | 0.394328 | − | 0.918970i | \(-0.370977\pi\) | ||||
0.394328 | + | 0.918970i | \(0.370977\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.8153 | 2.17225 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.17488 | − | 18.9437i | 0.185413 | − | 0.841321i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.2328i | 0.719506i | 0.933048 | + | 0.359753i | \(0.117139\pi\) | ||||
−0.933048 | + | 0.359753i | \(0.882861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.27969i | − | 0.366272i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.13422 | − | 3.14773i | −0.182530 | − | 0.138976i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 74.1149 | 3.26589 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.79483 | 0.210876 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.322299 | − | 0.0710293i | −0.0141473 | − | 0.00311784i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.5735i | 1.47088i | 0.677590 | + | 0.735440i | \(0.263024\pi\) | ||||
−0.677590 | + | 0.735440i | \(0.736976\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 25.2490i | − | 1.10406i | −0.833824 | − | 0.552030i | \(-0.813853\pi\) | ||
0.833824 | − | 0.552030i | \(-0.186147\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −54.6498 | − | 12.0439i | −2.38511 | − | 0.525639i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.4091 | 0.584109 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.7317 | 0.553551 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.7275 | − | 12.8452i | −1.20327 | − | 0.557436i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 23.4097i | − | 1.01398i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.7949i | 1.24491i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.84702 | − | 31.0687i | 0.295471 | − | 1.34071i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.48977 | 0.279534 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.3432 | 1.90646 | 0.953232 | − | 0.302241i | \(-0.0977347\pi\) | ||||
0.953232 | + | 0.302241i | \(0.0977347\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.79738 | − | 17.2308i | 0.162961 | − | 0.739444i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 36.8128i | − | 1.57689i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1643i | 0.776648i | 0.921523 | + | 0.388324i | \(0.126946\pi\) | ||||
−0.921523 | + | 0.388324i | \(0.873054\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.69482 | + | 2.17495i | 0.200370 | + | 0.0928248i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.58678 | −0.323208 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.48367 | −0.105616 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.97387 | + | 1.53693i | 0.296024 | + | 0.0652389i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.5657i | 0.447681i | 0.974626 | + | 0.223841i | \(0.0718595\pi\) | ||||
−0.974626 | + | 0.223841i | \(0.928140\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.7427i | 1.63864i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.77306 | − | 2.15382i | −0.412619 | − | 0.0909344i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.0038 | 0.927349 | 0.463675 | − | 0.886006i | \(-0.346531\pi\) | ||||
0.463675 | + | 0.886006i | \(0.346531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −70.4608 | −2.96431 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.8625 | + | 12.5983i | −0.624165 | + | 0.529078i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 39.0018i | − | 1.63504i | −0.575898 | − | 0.817521i | \(-0.695348\pi\) | ||
0.575898 | − | 0.817521i | \(-0.304652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.8494i | 0.830671i | 0.909668 | + | 0.415335i | \(0.136336\pi\) | ||||
−0.909668 | + | 0.415335i | \(0.863664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.92572 | + | 26.8882i | −0.247551 | + | 1.12327i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 89.2127 | 3.72043 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5745 | 0.981420 | 0.490710 | − | 0.871323i | \(-0.336737\pi\) | ||||
0.490710 | + | 0.871323i | \(0.336737\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.65367 | − | 7.50360i | 0.0687241 | − | 0.311839i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0244i | 1.49455i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.96615i | − | 0.164261i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.6905 | + | 59.7723i | −1.14486 | + | 2.47128i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.02667 | 0.166199 | 0.0830993 | − | 0.996541i | \(-0.473518\pi\) | ||||
0.0830993 | + | 0.996541i | \(0.473518\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.51027 | −0.268251 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −28.3264 | − | 6.24266i | −1.16519 | − | 0.256789i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.6372i | 0.560012i | 0.959998 | + | 0.280006i | \(0.0903364\pi\) | ||||
−0.959998 | + | 0.280006i | \(0.909664\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.9031i | 0.815948i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.4719 | − | 3.85053i | −0.715079 | − | 0.157592i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.7181 | 1.62284 | 0.811418 | − | 0.584466i | \(-0.198696\pi\) | ||||
0.811418 | + | 0.584466i | \(0.198696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.7654 | −1.01020 | −0.505102 | − | 0.863060i | \(-0.668545\pi\) | ||||
−0.505102 | + | 0.863060i | \(0.668545\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.29337 | − | 15.7433i | 0.297009 | − | 0.641118i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 13.9745i | − | 0.568145i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.8822i | 0.847582i | 0.905760 | + | 0.423791i | \(0.139301\pi\) | ||||
−0.905760 | + | 0.423791i | \(0.860699\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.12245 | + | 27.7809i | −0.248094 | + | 1.12574i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.40833 | −0.340165 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.1009 | 1.53888 | 0.769441 | − | 0.638718i | \(-0.220535\pi\) | ||||
0.769441 | + | 0.638718i | \(0.220535\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.91818 | + | 35.9291i | −0.319292 | + | 1.44880i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.53753i | − | 0.263191i | −0.991303 | − | 0.131596i | \(-0.957990\pi\) | ||
0.991303 | − | 0.131596i | \(-0.0420100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 48.8059i | 1.96168i | 0.194827 | + | 0.980838i | \(0.437585\pi\) | ||||
−0.194827 | + | 0.980838i | \(0.562415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.8159 | − | 24.7127i | 0.755056 | − | 0.991687i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.1462 | −0.927331 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 123.118 | 4.92473 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.74493 | + | 1.04570i | 0.189494 | + | 0.0417614i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.90247i | − | 0.0758566i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.5750i | 1.33660i | 0.743892 | + | 0.668300i | \(0.232978\pi\) | ||||
−0.743892 | + | 0.668300i | \(0.767022\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.9667 | + | 5.28187i | 0.952591 | + | 0.209935i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −49.2694 | −1.95520 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.3806 | −0.450916 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.1996 | − | 5.65169i | −0.482610 | − | 0.223577i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.6489i | 1.36855i | 0.729224 | + | 0.684275i | \(0.239881\pi\) | ||||
−0.729224 | + | 0.684275i | \(0.760119\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.619071i | − | 0.0244138i | −0.999925 | − | 0.0122069i | \(-0.996114\pi\) | ||
0.999925 | − | 0.0122069i | \(-0.00388567\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.1045 | − | 59.4622i | 0.515989 | − | 2.34132i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −50.0696 | −1.96844 | −0.984219 | − | 0.176954i | \(-0.943376\pi\) | ||||
−0.984219 | + | 0.176954i | \(0.943376\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.5744 | 1.12164 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.25371 | + | 23.8390i | −0.205909 | + | 0.934323i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.5827i | 1.54899i | 0.632579 | + | 0.774496i | \(0.281997\pi\) | ||||
−0.632579 | + | 0.774496i | \(0.718003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.64932i | 0.298884i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.4109 | + | 4.82304i | 0.406169 | + | 0.188165i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.6525 | −1.23301 | −0.616503 | − | 0.787352i | \(-0.711451\pi\) | ||||
−0.616503 | + | 0.787352i | \(0.711451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.73626 | 0.106428 | 0.0532141 | − | 0.998583i | \(-0.483053\pi\) | ||||
0.0532141 | + | 0.998583i | \(0.483053\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.1383 | + | 3.77699i | 0.665596 | + | 0.146686i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.66318i | − | 0.374722i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 45.3507i | − | 1.75599i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.0607 | − | 3.98029i | −0.698269 | − | 0.153887i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.83821 | −0.186777 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.1782 | 0.507982 | 0.253991 | − | 0.967207i | \(-0.418257\pi\) | ||||
0.253991 | + | 0.967207i | \(0.418257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 46.9784 | − | 61.7012i | 1.80820 | − | 2.37488i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.15582i | − | 0.121288i | −0.998159 | − | 0.0606441i | \(-0.980685\pi\) | ||
0.998159 | − | 0.0606441i | \(-0.0193155\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10.5362i | − | 0.404342i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.53575 | − | 43.2689i | 0.365411 | − | 1.65807i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.92376 | −0.341458 | −0.170729 | − | 0.985318i | \(-0.554612\pi\) | ||||
−0.170729 | + | 0.985318i | \(0.554612\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −63.2475 | −2.41656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.175240 | − | 0.795158i | 0.00668581 | − | 0.0303372i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.95515i | 0.264970i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.33135i | 0.202814i | 0.994845 | + | 0.101407i | \(0.0323344\pi\) | ||||
−0.994845 | + | 0.101407i | \(0.967666\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.65821 | − | 16.5309i | 0.290911 | − | 0.627956i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.8902 | −1.81658 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.80147 | 0.371257 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.9474 | + | 4.61646i | 0.792303 | + | 0.174610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.3162i | − | 0.918412i | −0.888330 | − | 0.459206i | \(-0.848134\pi\) | ||
0.888330 | − | 0.459206i | \(-0.151866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.923673i | 0.0348370i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.9051 | + | 2.84407i | 0.486034 | + | 0.107114i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.6749 | 0.890387 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.3457 | −0.613876 | −0.306938 | − | 0.951730i | \(-0.599304\pi\) | ||||
−0.306938 | + | 0.951730i | \(0.599304\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.44678 | − | 3.12298i | 0.0542583 | − | 0.117121i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 38.9158i | − | 1.45741i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 61.5979i | − | 2.30363i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.30775 | + | 24.0842i | −0.198222 | + | 0.899439i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.498558 | 0.0185931 | 0.00929654 | − | 0.999957i | \(-0.497041\pi\) | ||||
0.00929654 | + | 0.999957i | \(0.497041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.9450 | 1.33866 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.75139 | − | 17.0221i | 0.139516 | − | 0.633059i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 113.229i | − | 4.20522i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.74527i | 0.101817i | 0.998703 | + | 0.0509083i | \(0.0162116\pi\) | ||||
−0.998703 | + | 0.0509083i | \(0.983788\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.18354 | − | 26.0268i | −0.266057 | − | 0.963957i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.2213 | −0.599967 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.4648 | 1.23605 | 0.618025 | − | 0.786159i | \(-0.287933\pi\) | ||||
0.618025 | + | 0.786159i | \(0.287933\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.4670 | + | 3.84943i | 0.644278 | + | 0.141988i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.2242i | 0.597625i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.9919i | 0.992915i | 0.868061 | + | 0.496457i | \(0.165366\pi\) | ||||
−0.868061 | + | 0.496457i | \(0.834634\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.32083 | − | 1.83377i | −0.305673 | − | 0.0673653i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.1647 | −0.813143 | −0.406571 | − | 0.913619i | \(-0.633276\pi\) | ||||
−0.406571 | + | 0.913619i | \(0.633276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.9122 | −1.13254 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.2973 | − | 20.9848i | −1.65734 | − | 0.767792i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.9652i | 0.510279i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.8139i | 1.27038i | 0.772357 | + | 0.635189i | \(0.219078\pi\) | ||||
−0.772357 | + | 0.635189i | \(0.780922\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.03434 | − | 9.23090i | 0.0741354 | − | 0.336393i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.72105 | 0.280998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.8163 | −0.538508 | −0.269254 | − | 0.963069i | \(-0.586777\pi\) | ||||
−0.269254 | + | 0.963069i | \(0.586777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.25080 | + | 28.3633i | −0.226890 | + | 1.02952i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 35.3771i | − | 1.28242i | −0.767366 | − | 0.641209i | \(-0.778433\pi\) | ||
0.767366 | − | 0.641209i | \(-0.221567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 17.8538i | − | 0.646352i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −25.0263 | − | 11.5939i | −0.904827 | − | 0.419177i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.1087 | −1.80932 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.8083 | 0.822490 | 0.411245 | − | 0.911525i | \(-0.365094\pi\) | ||||
0.411245 | + | 0.911525i | \(0.365094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.1967 | + | 5.55294i | 0.907438 | + | 0.199984i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.905503i | 0.0325687i | 0.999867 | + | 0.0162843i | \(0.00518370\pi\) | ||||
−0.999867 | + | 0.0162843i | \(0.994816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 97.1625i | − | 3.49018i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.38226 | + | 0.745393i | 0.121338 | + | 0.0267408i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.75873 | −0.170499 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.5722 | 0.449870 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.3654 | − | 23.8812i | −1.12091 | − | 0.853443i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 68.4038i | 2.44144i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.3507i | − | 0.903656i | −0.892105 | − | 0.451828i | \(-0.850772\pi\) | ||
0.892105 | − | 0.451828i | \(-0.149228\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.00618 | − | 18.1782i | 0.142624 | − | 0.647162i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.1728 | −1.21504 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.48440 | 0.301290 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.35254 | − | 10.6748i | 0.0834359 | − | 0.378594i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.6954i | 1.33524i | 0.744502 | + | 0.667620i | \(0.232687\pi\) | ||||
−0.744502 | + | 0.667620i | \(0.767313\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.52051i | − | 0.124547i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.4830 | − | 29.1041i | 0.476397 | − | 1.02834i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.7289 | −0.378615 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 57.7626 | 2.03586 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.8782 | + | 5.92351i | 0.946158 | + | 0.208517i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.4859i | 1.38825i | 0.719855 | + | 0.694124i | \(0.244208\pi\) | ||||
−0.719855 | + | 0.694124i | \(0.755792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.16418i | 0.146224i | 0.997324 | + | 0.0731121i | \(0.0232931\pi\) | ||||
−0.997324 | + | 0.0731121i | \(0.976707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.1703 | − | 5.98789i | −0.952904 | − | 0.210004i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.6462 | 1.28366 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.87563 | 0.275533 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.4296 | + | 28.9889i | −0.469269 | + | 1.01296i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.4613i | 0.469802i | 0.972019 | + | 0.234901i | \(0.0754766\pi\) | ||||
−0.972019 | + | 0.234901i | \(0.924523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.833750i | 0.0290627i | 0.999894 | + | 0.0145313i | \(0.00462563\pi\) | ||||
−0.999894 | + | 0.0145313i | \(0.995374\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.6066 | + | 70.8157i | −0.543352 | + | 2.46549i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.3703 | −0.847439 | −0.423719 | − | 0.905794i | \(-0.639276\pi\) | ||||
−0.423719 | + | 0.905794i | \(0.639276\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0706 | −0.453960 | −0.226980 | − | 0.973899i | \(-0.572885\pi\) | ||||
−0.226980 | + | 0.973899i | \(0.572885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.39832 | − | 42.6453i | 0.326024 | − | 1.47935i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.76499i | − | 0.165097i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 60.8705i | − | 2.10651i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.9149 | − | 20.4926i | −0.930314 | − | 0.708328i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.2217 | 1.66480 | 0.832399 | − | 0.554176i | \(-0.186967\pi\) | ||||
0.832399 | + | 0.554176i | \(0.186967\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5593 | −0.984802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.9020 | − | 6.14914i | −0.960996 | − | 0.211787i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.9916i | 1.71976i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.77750i | − | 0.232878i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.6409 | − | 4.54892i | −0.708394 | − | 0.156118i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.52134 | −0.189269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.0086 | 1.43835 | 0.719174 | − | 0.694830i | \(-0.244521\pi\) | ||||
0.719174 | + | 0.694830i | \(0.244521\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.1505 | + | 5.62894i | 0.415540 | + | 0.192506i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.5704i | 1.48834i | 0.667992 | + | 0.744168i | \(0.267154\pi\) | ||||
−0.667992 | + | 0.744168i | \(0.732846\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.94535i | − | 0.271092i | −0.990771 | − | 0.135546i | \(-0.956721\pi\) | ||
0.990771 | − | 0.135546i | \(-0.0432788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.84024 | + | 17.4253i | −0.130875 | + | 0.593851i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.8058 | −0.640158 | −0.320079 | − | 0.947391i | \(-0.603709\pi\) | ||||
−0.320079 | + | 0.947391i | \(0.603709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.850531 | 0.0289189 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.75569 | − | 21.5792i | 0.161512 | − | 0.732867i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.21837i | 0.109176i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 28.4511i | − | 0.964029i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.2483 | + | 6.13749i | 0.448386 | + | 0.207723i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 95.9022 | 3.24209 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −56.7762 | −1.91719 | −0.958597 | − | 0.284765i | \(-0.908085\pi\) | ||||
−0.958597 | + | 0.284765i | \(0.908085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.6961 | + | 9.40951i | 1.44010 | + | 0.317375i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.57381i | − | 0.0530229i | −0.999649 | − | 0.0265114i | \(-0.991560\pi\) | ||
0.999649 | − | 0.0265114i | \(-0.00843984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.4647i | − | 0.419472i | −0.977758 | − | 0.209736i | \(-0.932740\pi\) | ||
0.977758 | − | 0.209736i | \(-0.0672604\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 76.9068 | + | 16.9490i | 2.58519 | + | 0.569734i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.1556 | 1.75122 | 0.875608 | − | 0.483023i | \(-0.160461\pi\) | ||||
0.875608 | + | 0.483023i | \(0.160461\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.8952 | −0.801419 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.3250 | + | 19.2589i | 0.546908 | + | 0.645199i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.70925i | 0.0571979i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 81.9888i | 2.74058i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.9616 | − | 49.7386i | 0.365996 | − | 1.66072i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −49.3920 | −1.64731 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.91208 | −0.0970153 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.35555 | − | 28.8386i | 0.211499 | − | 0.959688i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.4713i | 1.51152i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.3056i | 0.375396i | 0.982227 | + | 0.187698i | \(0.0601027\pi\) | ||||
−0.982227 | + | 0.187698i | \(0.939897\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.7910 | + | 29.7690i | −0.457418 | + | 0.987374i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.71121 | −0.222352 | −0.111176 | − | 0.993801i | \(-0.535462\pi\) | ||||
−0.111176 | + | 0.993801i | \(0.535462\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.6808 | 1.54491 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.0219 | − | 2.86980i | −0.430489 | − | 0.0948727i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.70984i | 0.122510i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 42.0708i | − | 1.38779i | −0.720077 | − | 0.693894i | \(-0.755893\pi\) | ||
0.720077 | − | 0.693894i | \(-0.244107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −47.7351 | − | 10.5200i | −1.57293 | − | 0.346647i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.0470 | −0.725686 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.7854 | −0.453260 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.9385 | + | 45.1974i | −0.687710 | + | 1.48448i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 9.30385i | − | 0.305250i | −0.988284 | − | 0.152625i | \(-0.951227\pi\) | ||
0.988284 | − | 0.152625i | \(-0.0487726\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.31346i | 0.0758205i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.43643 | − | 29.2056i | 0.210719 | − | 0.956149i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.7906 | 0.843444 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.8896 | −1.92384 | −0.961920 | − | 0.273330i | \(-0.911875\pi\) | ||||
−0.961920 | + | 0.273330i | \(0.911875\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.50731 | + | 38.6023i | −0.277626 | + | 1.25974i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 52.4642i | − | 1.71028i | −0.518393 | − | 0.855142i | \(-0.673470\pi\) | ||
0.518393 | − | 0.855142i | \(-0.326530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 28.4458i | − | 0.926321i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 30.4171 | − | 39.9497i | 0.989469 | − | 1.29956i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.4365 | 0.469123 | 0.234561 | − | 0.972101i | \(-0.424635\pi\) | ||||
0.234561 | + | 0.972101i | \(0.424635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.8145 | 0.610744 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.82753 | + | 2.16582i | 0.318679 | + | 0.0702317i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.1564i | 0.555750i | 0.960617 | + | 0.277875i | \(0.0896301\pi\) | ||||
−0.960617 | + | 0.277875i | \(0.910370\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 70.9568i | − | 2.29611i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35.9987 | + | 7.93353i | 1.16367 | + | 0.256455i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.6744 | −0.990529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3836 | −0.367212 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.5600 | − | 8.13496i | −0.565862 | − | 0.262146i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.8016i | 0.637437i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.16814i | − | 0.134038i | −0.997752 | − | 0.0670192i | \(-0.978651\pi\) | ||
0.997752 | − | 0.0670192i | \(-0.0213489\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.767789 | − | 3.48388i | 0.0246649 | − | 0.111918i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.92051 | 0.189998 | 0.0949991 | − | 0.995477i | \(-0.469715\pi\) | ||||
0.0949991 | + | 0.995477i | \(0.469715\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.2262 | −0.744599 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27.3681 | − | 124.184i | 0.876482 | − | 3.97708i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 23.2708i | − | 0.744498i | −0.928133 | − | 0.372249i | \(-0.878587\pi\) | ||
0.928133 | − | 0.372249i | \(-0.121413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.9930i | 0.958581i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.4495 | + | 10.4001i | 0.716757 | + | 0.332050i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.59799 | 0.146653 | 0.0733266 | − | 0.997308i | \(-0.476638\pi\) | ||||
0.0733266 | + | 0.997308i | \(0.476638\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 74.7519 | 2.38179 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.25884 | + | 1.37934i | 0.199221 | + | 0.0439050i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.0774i | 1.49697i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 19.3619i | − | 0.615050i | −0.951540 | − | 0.307525i | \(-0.900499\pi\) | ||
0.951540 | − | 0.307525i | \(-0.0995007\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.4963 | − | 5.83934i | −0.840834 | − | 0.185306i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.1076 | 1.46171 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.8378 | −1.45170 | −0.725848 | − | 0.687855i | \(-0.758553\pi\) | ||||
−0.725848 | + | 0.687855i | \(0.758553\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.90748 | + | 3.81867i | −0.0919885 | + | 0.120817i |
(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 | 912.2.d.b.191.13 | yes | 24 | |
3.2 | odd | 2 | inner | 912.2.d.b.191.11 | ✓ | 24 | |
4.3 | odd | 2 | inner | 912.2.d.b.191.12 | yes | 24 | |
12.11 | even | 2 | inner | 912.2.d.b.191.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.2.d.b.191.11 | ✓ | 24 | 3.2 | odd | 2 | inner | |
912.2.d.b.191.12 | yes | 24 | 4.3 | odd | 2 | inner | |
912.2.d.b.191.13 | yes | 24 | 1.1 | even | 1 | trivial | |
912.2.d.b.191.14 | yes | 24 | 12.11 | even | 2 | inner |