Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(165,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.i (of order \(3\), degree \(2\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.10 | ||
Character | \(\chi\) | \(=\) | 1148.165 |
Dual form | 1148.2.i.e.821.10 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.702089 | − | 1.21605i | 0.405351 | − | 0.702089i | −0.589011 | − | 0.808125i | \(-0.700482\pi\) |
0.994362 | + | 0.106036i | \(0.0338158\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.80784 | − | 3.13127i | −0.808489 | − | 1.40034i | −0.913910 | − | 0.405917i | \(-0.866952\pi\) |
0.105421 | − | 0.994428i | \(-0.466381\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.606375 | − | 2.57533i | 0.229188 | − | 0.973382i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.514141 | + | 0.890519i | 0.171380 | + | 0.296840i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82465 | − | 4.89243i | 0.851663 | − | 1.47512i | −0.0280437 | − | 0.999607i | \(-0.508928\pi\) |
0.879707 | − | 0.475517i | \(-0.157739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.54345 | 1.81483 | 0.907414 | − | 0.420238i | \(-0.138053\pi\) | ||||
0.907414 | + | 0.420238i | \(0.138053\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.07705 | −1.31089 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.69533 | + | 2.93640i | −0.411178 | + | 0.712181i | −0.995019 | − | 0.0996871i | \(-0.968216\pi\) |
0.583841 | + | 0.811868i | \(0.301549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.59869 | − | 4.50106i | −0.596181 | − | 1.03262i | −0.993379 | − | 0.114882i | \(-0.963351\pi\) |
0.397199 | − | 0.917733i | \(-0.369982\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.70601 | − | 2.54549i | −0.590499 | − | 0.555472i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.40505 | + | 2.43362i | 0.292974 | + | 0.507446i | 0.974512 | − | 0.224337i | \(-0.0720218\pi\) |
−0.681538 | + | 0.731783i | \(0.738688\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.03655 | + | 6.99151i | −0.807310 | + | 1.39830i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65643 | 1.08858 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.17600 | 0.404072 | 0.202036 | − | 0.979378i | \(-0.435244\pi\) | ||||
0.202036 | + | 0.979378i | \(0.435244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.13027 | + | 5.42179i | −0.562214 | + | 0.973783i | 0.435089 | + | 0.900387i | \(0.356717\pi\) |
−0.997303 | + | 0.0733954i | \(0.976616\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.96631 | − | 6.86985i | −0.690446 | − | 1.19589i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.16026 | + | 2.75705i | −1.54837 | + | 0.466027i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.320730 | − | 0.555521i | −0.0527277 | − | 0.0913271i | 0.838457 | − | 0.544968i | \(-0.183458\pi\) |
−0.891185 | + | 0.453641i | \(0.850125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.59409 | − | 7.95720i | 0.735643 | − | 1.27417i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.44365 | −0.677650 | −0.338825 | − | 0.940849i | \(-0.610029\pi\) | ||||
−0.338825 | + | 0.940849i | \(0.610029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.85897 | − | 3.21983i | 0.277118 | − | 0.479983i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.34820 | − | 5.79926i | −0.488386 | − | 0.845909i | 0.511525 | − | 0.859268i | \(-0.329081\pi\) |
−0.999911 | + | 0.0133593i | \(0.995747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.26462 | − | 3.12323i | −0.894946 | − | 0.446175i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.38055 | + | 4.12323i | 0.333343 | + | 0.577367i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.47639 | + | 4.28923i | −0.340158 | + | 0.589171i | −0.984462 | − | 0.175599i | \(-0.943814\pi\) |
0.644304 | + | 0.764770i | \(0.277147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.4260 | −2.75424 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.29805 | −0.966651 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.51446 | − | 9.55133i | 0.717922 | − | 1.24348i | −0.243900 | − | 0.969800i | \(-0.578427\pi\) |
0.961822 | − | 0.273676i | \(-0.0882397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.01946 | + | 10.4260i | 0.770713 | + | 1.33491i | 0.937173 | + | 0.348866i | \(0.113433\pi\) |
−0.166460 | + | 0.986048i | \(0.553234\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.60514 | − | 0.784093i | 0.328217 | − | 0.0987865i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11.8295 | − | 20.4893i | −1.46727 | − | 2.54138i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.29208 | + | 9.16615i | −0.646531 | + | 1.11982i | 0.337415 | + | 0.941356i | \(0.390447\pi\) |
−0.983946 | + | 0.178468i | \(0.942886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.94589 | 0.475030 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.70411 | −1.03299 | −0.516494 | − | 0.856291i | \(-0.672763\pi\) | ||||
−0.516494 | + | 0.856291i | \(0.672763\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.211460 | + | 0.366259i | −0.0247495 | + | 0.0428674i | −0.878135 | − | 0.478413i | \(-0.841212\pi\) |
0.853385 | + | 0.521281i | \(0.174545\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.66804 | + | 9.81733i | 0.654489 | + | 1.13361i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.8868 | − | 10.2410i | −1.24067 | − | 1.16707i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.11326 | + | 12.3205i | 0.800305 | + | 1.38617i | 0.919416 | + | 0.393287i | \(0.128662\pi\) |
−0.119111 | + | 0.992881i | \(0.538004\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.42889 | − | 4.20697i | 0.269877 | − | 0.467441i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.06521 | 0.555979 | 0.277989 | − | 0.960584i | \(-0.410332\pi\) | ||||
0.277989 | + | 0.960584i | \(0.410332\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.2595 | 1.32973 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.52774 | − | 2.64613i | 0.163791 | − | 0.283695i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.782283 | + | 1.35495i | 0.0829218 | + | 0.143625i | 0.904504 | − | 0.426466i | \(-0.140241\pi\) |
−0.821582 | + | 0.570090i | \(0.806908\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.96779 | − | 16.8515i | 0.415937 | − | 1.76652i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.39546 | + | 7.61317i | 0.455788 | + | 0.789448i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.39602 | + | 16.2744i | −0.964011 | + | 1.66972i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4451 | 1.66975 | 0.834873 | − | 0.550442i | \(-0.185541\pi\) | ||||
0.834873 | + | 0.550442i | \(0.185541\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.80907 | 0.583833 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.57025 | − | 9.64795i | 0.554260 | − | 0.960007i | −0.443700 | − | 0.896175i | \(-0.646335\pi\) |
0.997961 | − | 0.0638319i | \(-0.0203321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50083 | + | 4.33156i | 0.246414 | + | 0.426801i | 0.962528 | − | 0.271182i | \(-0.0874145\pi\) |
−0.716114 | + | 0.697983i | \(0.754081\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.07860 | + | 13.0751i | −0.300440 | + | 1.27600i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.14643 | + | 7.18184i | 0.400851 | + | 0.694294i | 0.993829 | − | 0.110925i | \(-0.0353812\pi\) |
−0.592978 | + | 0.805219i | \(0.702048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.51397 | + | 9.55048i | −0.528143 | + | 0.914770i | 0.471319 | + | 0.881963i | \(0.343778\pi\) |
−0.999462 | + | 0.0328071i | \(0.989555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.900725 | −0.0854930 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.26658 | −0.777654 | −0.388827 | − | 0.921311i | \(-0.627120\pi\) | ||||
−0.388827 | + | 0.921311i | \(0.627120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.08022 | − | 8.79919i | 0.473733 | − | 0.820529i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.36426 | + | 5.82707i | 0.311026 | + | 0.538713i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.53418 | + | 6.14659i | 0.598987 | + | 0.563457i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4573 | − | 18.1125i | −0.950660 | − | 1.64659i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.702089 | + | 1.21605i | −0.0633053 | + | 0.109648i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1113 | 0.993828 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.12925 | 0.100205 | 0.0501024 | − | 0.998744i | \(-0.484045\pi\) | ||||
0.0501024 | + | 0.998744i | \(0.484045\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.11984 | + | 5.40371i | −0.274686 | + | 0.475771i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.46246 | − | 16.3895i | −0.826739 | − | 1.43195i | −0.900583 | − | 0.434684i | \(-0.856860\pi\) |
0.0738447 | − | 0.997270i | \(-0.476473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.1675 | + | 3.96315i | −1.14177 | + | 0.343648i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.2259 | − | 17.7118i | −0.880105 | − | 1.52439i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.18113 | + | 7.24193i | −0.357218 | + | 0.618720i | −0.987495 | − | 0.157650i | \(-0.949608\pi\) |
0.630277 | + | 0.776370i | \(0.282941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.1952 | 1.54330 | 0.771648 | − | 0.636050i | \(-0.219433\pi\) | ||||
0.771648 | + | 0.636050i | \(0.219433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.40296 | −0.791872 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.4829 | − | 32.0134i | 1.54562 | − | 2.67710i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.93385 | − | 6.81362i | −0.326688 | − | 0.565840i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.19634 | + | 5.42533i | −0.676022 | + | 0.447474i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.02318 | + | 10.4325i | 0.493438 | + | 0.854660i | 0.999971 | − | 0.00756013i | \(-0.00240649\pi\) |
−0.506533 | + | 0.862221i | \(0.669073\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.72091 | + | 4.71275i | −0.221424 | + | 0.383518i | −0.955241 | − | 0.295830i | \(-0.904404\pi\) |
0.733816 | + | 0.679348i | \(0.237737\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.48656 | −0.281871 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.6361 | 1.81818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4620 | + | 18.1207i | −0.834960 | + | 1.44619i | 0.0591032 | + | 0.998252i | \(0.481176\pi\) |
−0.894063 | + | 0.447941i | \(0.852157\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.47729 | + | 6.02284i | 0.275767 | + | 0.477642i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.11937 | − | 2.14278i | 0.561085 | − | 0.168875i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.54290 | − | 14.7967i | −0.669132 | − | 1.15897i | −0.978147 | − | 0.207913i | \(-0.933333\pi\) |
0.309015 | − | 0.951057i | \(-0.400001\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.3409 | + | 24.8391i | −1.11644 | + | 1.93372i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0854 | 1.01258 | 0.506289 | − | 0.862364i | \(-0.331017\pi\) | ||||
0.506289 | + | 0.862364i | \(0.331017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.8168 | 2.29360 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.67219 | − | 4.62837i | 0.204347 | − | 0.353940i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.61352 | − | 16.6511i | −0.730902 | − | 1.26596i | −0.956498 | − | 0.291739i | \(-0.905766\pi\) |
0.225596 | − | 0.974221i | \(-0.427567\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.5578 | + | 14.6349i | 1.17606 | + | 1.10630i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.74329 | − | 13.4118i | −0.582021 | − | 1.00809i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.36507 | − | 7.56052i | 0.326261 | − | 0.565100i | −0.655506 | − | 0.755190i | \(-0.727545\pi\) |
0.981767 | + | 0.190090i | \(0.0608780\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2949 | −0.839544 | −0.419772 | − | 0.907630i | \(-0.637890\pi\) | ||||
−0.419772 | + | 0.907630i | \(0.637890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.9048 | 1.24964 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.15966 | + | 2.00858i | −0.0852596 | + | 0.147674i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.57741 | + | 16.5886i | 0.700370 | + | 1.21308i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.42992 | − | 14.5672i | 0.249490 | − | 1.05960i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.45419 | + | 14.6431i | 0.611724 | + | 1.05954i | 0.990950 | + | 0.134233i | \(0.0428570\pi\) |
−0.379226 | + | 0.925304i | \(0.623810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.99344 | + | 3.45274i | −0.143491 | + | 0.248533i | −0.928809 | − | 0.370559i | \(-0.879166\pi\) |
0.785318 | + | 0.619093i | \(0.212499\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −33.2215 | −2.37904 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0163 | −0.856124 | −0.428062 | − | 0.903749i | \(-0.640803\pi\) | ||||
−0.428062 | + | 0.903749i | \(0.640803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.46266 | − | 9.46160i | 0.387238 | − | 0.670715i | −0.604839 | − | 0.796348i | \(-0.706763\pi\) |
0.992077 | + | 0.125632i | \(0.0400960\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.43103 | + | 12.8709i | 0.524144 | + | 0.907844i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.31947 | − | 5.60390i | 0.0926086 | − | 0.393317i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.80784 | + | 3.13127i | 0.126265 | + | 0.218697i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.44479 | + | 2.50245i | −0.100420 | + | 0.173932i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −29.3615 | −2.03098 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.98904 | −0.549988 | −0.274994 | − | 0.961446i | \(-0.588676\pi\) | ||||
−0.274994 | + | 0.961446i | \(0.588676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.11106 | + | 10.5847i | −0.418723 | + | 0.725249i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.03339 | + | 13.9142i | 0.547873 | + | 0.948943i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0648 | + | 11.3491i | 0.819010 | + | 0.770428i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.296927 | + | 0.514293i | 0.0200645 | + | 0.0347527i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.0933 | + | 19.2142i | −0.746217 | + | 1.29249i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.5999 | 1.84823 | 0.924115 | − | 0.382116i | \(-0.124804\pi\) | ||||
0.924115 | + | 0.382116i | \(0.124804\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.30143 | −0.553429 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.1657 | − | 21.0717i | 0.807468 | − | 1.39858i | −0.107144 | − | 0.994244i | \(-0.534171\pi\) |
0.914612 | − | 0.404332i | \(-0.132496\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.0548675 | − | 0.0950332i | −0.00362574 | − | 0.00627997i | 0.864207 | − | 0.503137i | \(-0.167821\pi\) |
−0.867833 | + | 0.496857i | \(0.834487\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −20.0972 | + | 6.04884i | −1.32230 | + | 0.397984i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.11476 | + | 7.12698i | 0.269567 | + | 0.466904i | 0.968750 | − | 0.248039i | \(-0.0797861\pi\) |
−0.699183 | + | 0.714943i | \(0.746453\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1060 | + | 20.9682i | −0.789710 | + | 1.36782i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.9766 | 1.29762 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.13997 | 0.461846 | 0.230923 | − | 0.972972i | \(-0.425825\pi\) | ||||
0.230923 | + | 0.972972i | \(0.425825\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.15955 | + | 10.6687i | −0.396771 | + | 0.687228i | −0.993326 | − | 0.115345i | \(-0.963203\pi\) |
0.596554 | + | 0.802573i | \(0.296536\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.07404 | + | 8.78850i | 0.325500 | + | 0.563782i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.54575 | + | 25.2625i | 0.0987546 | + | 1.61396i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.0044 | − | 29.4525i | −1.08197 | − | 1.87402i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.55623 | − | 6.15957i | 0.225367 | − | 0.390347i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.03854 | −0.381149 | −0.190575 | − | 0.981673i | \(-0.561035\pi\) | ||||
−0.190575 | + | 0.981673i | \(0.561035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.8751 | 0.998060 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.60728 | − | 14.9082i | 0.539009 | − | 0.933590i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.2858 | − | 24.7437i | −0.891123 | − | 1.54347i | −0.838531 | − | 0.544854i | \(-0.816585\pi\) |
−0.0525914 | − | 0.998616i | \(-0.516748\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.62513 | + | 0.489131i | −0.100981 | + | 0.0303931i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.11877 | + | 1.93776i | 0.0692501 | + | 0.119945i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3527 | − | 26.5917i | 0.946690 | − | 1.63971i | 0.194357 | − | 0.980931i | \(-0.437738\pi\) |
0.752333 | − | 0.658783i | \(-0.228929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.9076 | 1.10006 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.19693 | 0.134450 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.08035 | + | 10.5315i | −0.370726 | + | 0.642116i | −0.989677 | − | 0.143313i | \(-0.954224\pi\) |
0.618952 | + | 0.785429i | \(0.287558\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.92080 | − | 5.05897i | −0.177426 | − | 0.307311i | 0.763572 | − | 0.645722i | \(-0.223444\pi\) |
−0.940998 | + | 0.338412i | \(0.890110\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.7066 | − | 16.6563i | −1.07165 | − | 1.00809i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.8037 | + | 39.4971i | 1.37511 | + | 2.38176i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3917 | − | 19.7311i | 0.684463 | − | 1.18553i | −0.289142 | − | 0.957286i | \(-0.593370\pi\) |
0.973605 | − | 0.228239i | \(-0.0732968\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.43761 | −0.385410 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.36022 | −0.140799 | −0.0703995 | − | 0.997519i | \(-0.522427\pi\) | ||||
−0.0703995 | + | 0.997519i | \(0.522427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.0483699 | + | 0.0837790i | −0.00287529 | + | 0.00498015i | −0.867459 | − | 0.497508i | \(-0.834249\pi\) |
0.864584 | + | 0.502488i | \(0.167582\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.1937 | + | 22.8521i | 0.781527 | + | 1.35364i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.606375 | + | 2.57533i | −0.0357932 | + | 0.152017i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.75171 | + | 4.76611i | 0.161866 | + | 0.280359i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.5459 | − | 19.9981i | 0.676834 | − | 1.17231i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.8023 | 1.44897 | 0.724484 | − | 0.689292i | \(-0.242078\pi\) | ||||
0.724484 | + | 0.689292i | \(0.242078\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −39.8770 | −2.32173 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.9774 | − | 27.6737i | 0.927103 | − | 1.60579i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.19390 | + | 15.9243i | 0.531697 | + | 0.920927i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.69452 | + | 11.4438i | −0.155309 | + | 0.659612i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.82162 | − | 13.5474i | −0.449340 | − | 0.778281i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.7644 | − | 37.6971i | 1.24623 | − | 2.15853i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.46391 | −0.197696 | −0.0988480 | − | 0.995103i | \(-0.531516\pi\) | ||||
−0.0988480 | + | 0.995103i | \(0.531516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.02321 | 0.399537 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0094 | + | 22.5330i | −0.737697 | + | 1.27773i | 0.215833 | + | 0.976430i | \(0.430753\pi\) |
−0.953530 | + | 0.301298i | \(0.902580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47911 | − | 4.29394i | −0.140127 | − | 0.242708i | 0.787417 | − | 0.616421i | \(-0.211418\pi\) |
−0.927544 | + | 0.373713i | \(0.878085\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.16487 | − | 6.73987i | −0.403695 | − | 0.379749i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.50175 | − | 14.7255i | −0.477506 | − | 0.827065i | 0.522162 | − | 0.852847i | \(-0.325126\pi\) |
−0.999668 | + | 0.0257819i | \(0.991792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.14642 | − | 10.6459i | 0.344133 | − | 0.596056i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.6447 | 0.649942 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.6226 | 0.980545 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −26.4130 | + | 45.7486i | −1.46513 | + | 2.53768i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.74260 | + | 13.4106i | 0.428167 | + | 0.741607i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9653 | + | 5.10620i | −0.935325 | + | 0.281514i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.63472 | − | 9.75961i | −0.309712 | − | 0.536437i | 0.668587 | − | 0.743634i | \(-0.266899\pi\) |
−0.978299 | + | 0.207197i | \(0.933566\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.329801 | − | 0.571232i | 0.0180730 | − | 0.0313033i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.2689 | 2.09085 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.7342 | 1.61972 | 0.809862 | − | 0.586620i | \(-0.199542\pi\) | ||||
0.809862 | + | 0.586620i | \(0.199542\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.80387 | + | 10.0526i | −0.315223 | + | 0.545983i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.6838 | + | 30.6293i | 0.957633 | + | 1.65867i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.8420 | + | 14.2396i | −0.639410 | + | 0.768866i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.13353 | − | 12.3556i | −0.384056 | − | 0.665205i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.83350 | + | 11.8360i | −0.366841 | + | 0.635388i | −0.989070 | − | 0.147448i | \(-0.952894\pi\) |
0.622228 | + | 0.782836i | \(0.286228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4570 | −1.14857 | −0.574284 | − | 0.818656i | \(-0.694720\pi\) | ||||
−0.574284 | + | 0.818656i | \(0.694720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 37.0126 | 1.97559 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0513 | + | 17.4093i | −0.534974 | + | 0.926603i | 0.464190 | + | 0.885736i | \(0.346345\pi\) |
−0.999165 | + | 0.0408673i | \(0.986988\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.7356 | + | 27.2549i | 0.835159 | + | 1.44654i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.0622 | − | 3.63046i | 0.638397 | − | 0.192144i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.85540 | + | 11.8739i | 0.361814 | + | 0.626681i | 0.988260 | − | 0.152785i | \(-0.0488241\pi\) |
−0.626445 | + | 0.779466i | \(0.715491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.00639 | + | 6.93927i | −0.210863 | + | 0.365225i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.3677 | −1.54140 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.52914 | 0.0800388 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5653 | + | 23.4959i | −0.708105 | + | 1.22647i | 0.257454 | + | 0.966291i | \(0.417116\pi\) |
−0.965559 | + | 0.260184i | \(0.916217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.514141 | − | 0.890519i | −0.0267651 | − | 0.0463586i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.54455 | + | 8.97839i | 0.495528 | + | 0.466135i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.27865 | + | 9.14288i | 0.273318 | + | 0.473401i | 0.969709 | − | 0.244262i | \(-0.0785455\pi\) |
−0.696391 | + | 0.717662i | \(0.745212\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.80115 | − | 13.5120i | 0.402850 | − | 0.697756i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.2385 | 0.733322 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9019 | 1.27913 | 0.639563 | − | 0.768739i | \(-0.279115\pi\) | ||||
0.639563 | + | 0.768739i | \(0.279115\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.792836 | − | 1.37323i | 0.0406182 | − | 0.0703528i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.37423 | − | 7.57640i | −0.223513 | − | 0.387136i | 0.732359 | − | 0.680918i | \(-0.238419\pi\) |
−0.955872 | + | 0.293783i | \(0.905086\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.3858 | + | 52.6036i | −0.631240 | + | 2.68093i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.28466 | − | 3.95715i | −0.116136 | − | 0.201153i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.64099 | − | 4.57433i | 0.133903 | − | 0.231927i | −0.791275 | − | 0.611461i | \(-0.790582\pi\) |
0.925178 | + | 0.379533i | \(0.123915\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.52812 | −0.481858 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.5740 | −1.34048 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.7192 | − | 44.5470i | 1.29408 | − | 2.24140i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.09690 | + | 7.09603i | 0.205617 | + | 0.356140i | 0.950329 | − | 0.311246i | \(-0.100746\pi\) |
−0.744712 | + | 0.667386i | \(0.767413\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.42536 | + | 18.7949i | −0.221545 | + | 0.940920i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.87990 | − | 10.1843i | −0.293628 | − | 0.508579i | 0.681037 | − | 0.732249i | \(-0.261529\pi\) |
−0.974665 | + | 0.223670i | \(0.928196\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.4828 | + | 35.4773i | −1.02032 | + | 1.76725i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.5642 | −0.872771 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.62380 | −0.179625 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.07097 | − | 12.2473i | 0.349637 | − | 0.605589i | −0.636548 | − | 0.771237i | \(-0.719638\pi\) |
0.986185 | + | 0.165648i | \(0.0529716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.87106 | + | 10.1690i | 0.289598 | + | 0.501598i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.2540 | − | 19.9932i | −1.04584 | − | 0.983802i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.15707 | − | 15.8605i | −0.449503 | − | 0.778562i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.7746 | − | 22.1263i | 0.625577 | − | 1.08353i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.94153 | −0.192556 | −0.0962781 | − | 0.995354i | \(-0.530694\pi\) | ||||
−0.0962781 | + | 0.995354i | \(0.530694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.9273 | −1.40983 | −0.704914 | − | 0.709292i | \(-0.749015\pi\) | ||||
−0.704914 | + | 0.709292i | \(0.749015\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.44290 | − | 5.96328i | 0.167400 | − | 0.289944i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.6866 | − | 23.7058i | −0.663896 | − | 1.14990i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.5004 | − | 9.18001i | 1.47602 | − | 0.444252i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.9534 | − | 44.9525i | −1.25304 | − | 2.17033i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.14579 | + | 3.71662i | −0.103359 | + | 0.179023i | −0.913067 | − | 0.407810i | \(-0.866292\pi\) |
0.809708 | + | 0.586834i | \(0.199626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.69228 | 0.0813259 | 0.0406629 | − | 0.999173i | \(-0.487053\pi\) | ||||
0.0406629 | + | 0.999173i | \(0.487053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.0476 | −0.529694 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.30260 | − | 12.6485i | 0.349331 | − | 0.605059i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.27633 | + | 3.94272i | 0.108643 | + | 0.188176i | 0.915221 | − | 0.402952i | \(-0.132016\pi\) |
−0.806578 | + | 0.591128i | \(0.798683\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.439606 | − | 7.18454i | −0.0209336 | − | 0.342121i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.29976 | − | 3.98329i | −0.109265 | − | 0.189252i | 0.806208 | − | 0.591632i | \(-0.201516\pi\) |
−0.915473 | + | 0.402380i | \(0.868183\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.82848 | − | 4.89907i | 0.134083 | − | 0.232238i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.9153 | 0.800064 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.72931 | 0.223190 | 0.111595 | − | 0.993754i | \(-0.464404\pi\) | ||||
0.111595 | + | 0.993754i | \(0.464404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.82465 | + | 4.89243i | −0.133007 | + | 0.230376i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.82064 | + | 6.61755i | 0.179509 | + | 0.310919i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −59.9398 | + | 18.0406i | −2.81002 | + | 0.845758i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.75437 | − | 16.8951i | −0.456290 | − | 0.790318i | 0.542471 | − | 0.840074i | \(-0.317489\pi\) |
−0.998761 | + | 0.0497565i | \(0.984155\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.58951 | + | 16.6095i | −0.447600 | + | 0.775266i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.57849 | 0.0735178 | 0.0367589 | − | 0.999324i | \(-0.488297\pi\) | ||||
0.0367589 | + | 0.999324i | \(0.488297\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.94122 | 0.229638 | 0.114819 | − | 0.993386i | \(-0.463371\pi\) | ||||
0.114819 | + | 0.993386i | \(0.463371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.8926 | − | 27.5267i | 0.737000 | − | 1.27652i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.6289 | − | 20.1418i | −0.538120 | − | 0.932051i | −0.999005 | − | 0.0445914i | \(-0.985801\pi\) |
0.460885 | − | 0.887460i | \(-0.347532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.3969 | + | 19.1870i | 0.941839 | + | 0.885972i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.6905 | + | 25.4448i | 0.676904 | + | 1.17243i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.5517 | + | 21.7402i | −0.577129 | + | 0.999617i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.9590 | 1.92521 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.09285 | −0.233186 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.76352 | + | 13.4468i | −0.354724 | + | 0.614401i | −0.987071 | − | 0.160285i | \(-0.948759\pi\) |
0.632346 | + | 0.774686i | \(0.282092\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.09868 | − | 3.63503i | −0.0956917 | − | 0.165743i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.39269 | − | 10.1620i | 0.108871 | − | 0.462385i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.7301 | − | 51.4940i | −1.34997 | − | 2.33822i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.98069 | + | 13.8230i | −0.361640 | + | 0.626378i | −0.988231 | − | 0.152970i | \(-0.951116\pi\) |
0.626591 | + | 0.779348i | \(0.284450\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.9915 | −1.08493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.11148 | −0.185548 | −0.0927742 | − | 0.995687i | \(-0.529573\pi\) | ||||
−0.0927742 | + | 0.995687i | \(0.529573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.68903 | + | 6.38959i | −0.166146 | + | 0.287773i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.5018 | − | 18.1897i | −0.472023 | − | 0.817568i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.27795 | + | 22.4159i | −0.236749 | + | 1.00549i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.57719 | + | 6.19587i | 0.160137 | + | 0.277365i | 0.934918 | − | 0.354865i | \(-0.115473\pi\) |
−0.774781 | + | 0.632230i | \(0.782140\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.18712 | − | 15.9126i | 0.410450 | − | 0.710921i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.71388 | 0.210182 | 0.105091 | − | 0.994463i | \(-0.466487\pi\) | ||||
0.105091 | + | 0.994463i | \(0.466487\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.2804 | −1.79245 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.9341 | − | 36.2588i | 0.929714 | − | 1.61031i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.10920 | + | 15.7776i | 0.403758 | + | 0.699330i | 0.994176 | − | 0.107768i | \(-0.0343704\pi\) |
−0.590418 | + | 0.807098i | \(0.701037\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.815013 | + | 0.766668i | 0.0360540 | + | 0.0339154i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.6993 | − | 25.4599i | −0.648990 | − | 1.12408i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.04217 | − | 15.6615i | 0.398446 | − | 0.690128i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.8300 | −1.66376 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.9982 | −1.18509 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.47594 | + | 9.48461i | −0.239905 | + | 0.415528i | −0.960687 | − | 0.277634i | \(-0.910450\pi\) |
0.720782 | + | 0.693162i | \(0.243783\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.81057 | − | 16.9924i | −0.428986 | − | 0.743026i | 0.567797 | − | 0.823168i | \(-0.307796\pi\) |
−0.996783 | + | 0.0801426i | \(0.974462\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.7198 | − | 8.64407i | 1.25343 | − | 0.377258i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.6137 | − | 18.3835i | −0.462340 | − | 0.800796i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.55165 | − | 13.0798i | 0.328333 | − | 0.568689i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3408 | 0.492151 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.54345 | −0.283428 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.9922 | − | 25.9672i | 0.648167 | − | 1.12266i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.12934 | − | 10.6163i | −0.264500 | − | 0.458128i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.9755 | + | 21.8272i | −1.42036 | + | 0.940164i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2361 | − | 19.4616i | −0.483080 | − | 0.836719i | 0.516731 | − | 0.856148i | \(-0.327149\pi\) |
−0.999811 | + | 0.0194288i | \(0.993815\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.93004 | + | 13.7352i | −0.340310 | + | 0.589435i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.8734 | 1.70799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.78852 | −0.247499 | −0.123750 | − | 0.992313i | \(-0.539492\pi\) | ||||
−0.123750 | + | 0.992313i | \(0.539492\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.18971 | + | 10.7209i | −0.264170 | + | 0.457556i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.65474 | − | 9.79430i | −0.240900 | − | 0.417251i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.0427 | − | 10.8481i | 1.53269 | − | 0.461309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.62836 | + | 2.82041i | 0.0691202 | + | 0.119720i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.11253 | + | 7.12312i | −0.174254 | + | 0.301816i | −0.939903 | − | 0.341442i | \(-0.889085\pi\) |
0.765649 | + | 0.643258i | \(0.222418\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −29.0768 | −1.22982 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.8968 | 1.13558 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.2648 | − | 17.7792i | 0.432611 | − | 0.749305i | −0.564486 | − | 0.825443i | \(-0.690926\pi\) |
0.997097 | + | 0.0761377i | \(0.0242589\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.9446 | + | 25.8848i | 0.628725 | + | 1.08898i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.36150 | − | 8.80620i | −0.393146 | − | 0.369825i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.9832 | + | 20.7556i | 0.502364 | + | 0.870120i | 0.999996 | + | 0.00273173i | \(0.000869538\pi\) |
−0.497632 | + | 0.867388i | \(0.665797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.2432 | + | 29.8661i | −0.721605 | + | 1.24986i | 0.238752 | + | 0.971081i | \(0.423262\pi\) |
−0.960356 | + | 0.278775i | \(0.910072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.7424 | 0.991853 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.6863 | −0.946083 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.5178 | − | 35.5379i | 0.854168 | − | 1.47946i | −0.0232459 | − | 0.999730i | \(-0.507400\pi\) |
0.877414 | − | 0.479733i | \(-0.159267\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.79914 | + | 4.84826i | 0.116328 | + | 0.201487i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.07141 | − | 13.0446i | 0.127424 | − | 0.541180i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.9898 | + | 24.2311i | 0.579400 | + | 1.00355i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.1641 | − | 21.0688i | 0.502922 | − | 0.871087i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.21910 | 0.256690 | 0.128345 | − | 0.991730i | \(-0.459034\pi\) | ||||
0.128345 | + | 0.991730i | \(0.459034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.5385 | 1.34072 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.43650 | + | 14.6124i | −0.347031 | + | 0.601075i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.46159 | + | 2.53155i | 0.0600204 | + | 0.103958i | 0.894474 | − | 0.447119i | \(-0.147550\pi\) |
−0.834454 | + | 0.551078i | \(0.814217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.43387 | − | 31.5723i | 0.304759 | − | 1.29434i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.67055 | − | 13.2858i | −0.313935 | − | 0.543751i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.74150 | − | 11.6766i | 0.275450 | − | 0.477094i | −0.694798 | − | 0.719205i | \(-0.744506\pi\) |
0.970249 | + | 0.242111i | \(0.0778397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.1493 | −1.43377 | −0.716886 | − | 0.697191i | \(-0.754433\pi\) | ||||
−0.716886 | + | 0.697191i | \(0.754433\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.8835 | −0.443211 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.8100 | + | 65.4889i | −1.53720 | + | 2.66250i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.8523 | − | 27.4570i | −0.643425 | − | 1.11444i | −0.984663 | − | 0.174468i | \(-0.944180\pi\) |
0.341238 | − | 0.939977i | \(-0.389154\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.88826 | − | 5.53899i | −0.238604 | − | 0.224451i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.9088 | − | 37.9472i | −0.886336 | − | 1.53518i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.373837 | + | 0.647504i | −0.0150991 | + | 0.0261525i | −0.873476 | − | 0.486867i | \(-0.838140\pi\) |
0.858377 | + | 0.513019i | \(0.171473\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.07705 | 0.204727 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.6618 | 0.670780 | 0.335390 | − | 0.942079i | \(-0.391132\pi\) | ||||
0.335390 | + | 0.942079i | \(0.391132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.5345 | − | 23.4425i | 0.543999 | − | 0.942235i | −0.454670 | − | 0.890660i | \(-0.650243\pi\) |
0.998669 | − | 0.0515745i | \(-0.0164240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.94758 | + | 13.7656i | 0.318926 | + | 0.552395i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.96380 | − | 1.19302i | 0.158806 | − | 0.0477975i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.0952736 | + | 0.165019i | 0.00381095 | + | 0.00660075i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.6144 | + | 35.7052i | −0.823261 | + | 1.42593i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.17497 | 0.0867219 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1258 | −0.920625 | −0.460312 | − | 0.887757i | \(-0.652263\pi\) | ||||
−0.460312 | + | 0.887757i | \(0.652263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.60902 | + | 9.71511i | −0.222939 | + | 0.386141i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.04150 | − | 3.53599i | −0.0810146 | − | 0.140321i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −40.9922 | − | 20.4367i | −1.62417 | − | 0.809732i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.47514 | − | 7.75117i | −0.177034 | − | 0.306632i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.92755 | + | 11.9989i | −0.273622 | + | 0.473927i | −0.969786 | − | 0.243955i | \(-0.921555\pi\) |
0.696165 | + | 0.717882i | \(0.254888\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.61525 | −0.260880 | −0.130440 | − | 0.991456i | \(-0.541639\pi\) | ||||
−0.130440 | + | 0.991456i | \(0.541639\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.5606 | 0.888324 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.52037 | + | 4.36540i | −0.0990858 | + | 0.171622i | −0.911306 | − | 0.411729i | \(-0.864925\pi\) |
0.812221 | + | 0.583350i | \(0.198258\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.1528 | − | 53.9582i | −1.22285 | − | 2.11805i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.2717 | − | 6.70332i | 0.872896 | − | 0.262724i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.98470 | − | 13.8299i | −0.312465 | − | 0.541206i | 0.666430 | − | 0.745567i | \(-0.267821\pi\) |
−0.978895 | + | 0.204362i | \(0.934488\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −34.2132 | + | 59.2589i | −1.33682 | + | 2.31544i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.434881 | −0.0169663 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.81563 | 0.187590 | 0.0937952 | − | 0.995592i | \(-0.470100\pi\) | ||||
0.0937952 | + | 0.995592i | \(0.470100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3200 | − | 19.6068i | 0.440296 | − | 0.762616i | −0.557415 | − | 0.830234i | \(-0.688207\pi\) |
0.997711 | + | 0.0676184i | \(0.0215400\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.5770 | + | 26.9801i | 0.604960 | + | 1.04782i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.2143 | + | 34.0662i | 1.40433 | + | 1.32103i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.05739 | + | 5.29556i | 0.118383 | + | 0.205045i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.3776 | − | 33.5630i | 0.749182 | − | 1.29762i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.0114 | 2.62555 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0840 | −0.581446 | −0.290723 | − | 0.956807i | \(-0.593896\pi\) | ||||
−0.290723 | + | 0.956807i | \(0.593896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.8325 | + | 39.5470i | −0.878822 | + | 1.52216i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.7237 | − | 25.5021i | −0.565876 | − | 0.980126i | −0.996968 | − | 0.0778181i | \(-0.975205\pi\) |
0.431091 | − | 0.902308i | \(-0.358129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.97190 | − | 42.3515i | 0.382686 | − | 1.62530i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.0829 | − | 29.5884i | −0.654617 | − | 1.13383i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.287704 | + | 0.498319i | −0.0110087 | + | 0.0190676i | −0.871477 | − | 0.490436i | \(-0.836838\pi\) |
0.860469 | + | 0.509504i | \(0.170171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.2352 | 1.15523 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.154087 | −0.00587880 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.2041 | + | 28.0664i | −0.617328 | + | 1.06924i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.7720 | + | 32.5140i | 0.714120 | + | 1.23689i | 0.963298 | + | 0.268434i | \(0.0865063\pi\) |
−0.249178 | + | 0.968458i | \(0.580160\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.52247 | − | 14.9603i | 0.133808 | − | 0.568293i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.8939 | − | 56.9740i | −1.24774 | − | 2.16115i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.69533 | − | 2.93640i | 0.0642152 | − | 0.111224i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5557 | 0.437078 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1046 | −1.17480 | −0.587402 | − | 0.809295i | \(-0.699849\pi\) | ||||
−0.587402 | + | 0.809295i | \(0.699849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.66696 | + | 2.88725i | −0.0628705 | + | 0.108895i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.9990 | + | 29.4432i | 0.640220 | + | 1.10889i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.4690 | − | 20.1955i | −0.807424 | − | 0.759529i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.92717 | + | 5.07001i | 0.109932 | + | 0.190408i | 0.915743 | − | 0.401765i | \(-0.131603\pi\) |
−0.805810 | + | 0.592174i | \(0.798270\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.31444 | + | 12.6690i | −0.274313 | + | 0.475124i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.5928 | −0.658856 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −133.657 | −4.99847 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.01289 | − | 8.68259i | 0.187210 | − | 0.324257i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.8968 | − | 24.0700i | −0.518264 | − | 0.897660i | −0.999775 | − | 0.0212200i | \(-0.993245\pi\) |
0.481510 | − | 0.876440i | \(-0.340088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6716 | − | 3.81390i | 0.471916 | − | 0.142037i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.64911 | + | 14.9807i | 0.321664 | + | 0.557138i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.78352 | + | 15.2135i | −0.326212 | + | 0.565015i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5974 | 0.578474 | 0.289237 | − | 0.957257i | \(-0.406598\pi\) | ||||
0.289237 | + | 0.957257i | \(0.406598\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.8231 | 1.06752 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.53344 | − | 13.0483i | 0.278635 | − | 0.482609i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.8286 | + | 34.3442i | 0.732386 | + | 1.26853i | 0.955861 | + | 0.293821i | \(0.0949269\pi\) |
−0.223474 | + | 0.974710i | \(0.571740\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.8058 | + | 15.8568i | 1.17317 | + | 0.584887i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.8965 | + | 51.7823i | 1.10125 | + | 1.90742i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.47389 | − | 11.2131i | 0.238146 | − | 0.412481i | −0.722036 | − | 0.691855i | \(-0.756794\pi\) |
0.960182 | + | 0.279374i | \(0.0901270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −47.7545 | −1.75430 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.12957 | −0.188186 | −0.0940929 | − | 0.995563i | \(-0.529995\pi\) | ||||
−0.0940929 | + | 0.995563i | \(0.529995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.7779 | − | 37.7204i | 0.797879 | − | 1.38197i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.60423 | + | 4.51066i | 0.0952838 | + | 0.165036i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.0099 | − | 6.32354i | 0.767684 | − | 0.231057i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.51888 | − | 16.4872i | −0.347349 | − | 0.601626i | 0.638429 | − | 0.769681i | \(-0.279585\pi\) |
−0.985778 | + | 0.168055i | \(0.946251\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.23959 | + | 7.34319i | −0.154499 | + | 0.267601i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.6758 | 0.716077 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.8052 | 1.19233 | 0.596163 | − | 0.802864i | \(-0.296691\pi\) | ||||
0.596163 | + | 0.802864i | \(0.296691\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.1458 | − | 19.3050i | 0.404565 | − | 0.700727i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.6336 | − | 35.7384i | −0.747966 | − | 1.29552i | −0.948796 | − | 0.315889i | \(-0.897697\pi\) |
0.200830 | − | 0.979626i | \(-0.435636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.2521 | + | 19.9915i | 0.769377 | + | 0.723739i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.30312 | + | 10.9173i | 0.227890 | + | 0.394717i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0836 | − | 62.4987i | 1.30290 | − | 2.25670i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.2060 | 1.30562 | 0.652811 | − | 0.757520i | \(-0.273589\pi\) | ||||
0.652811 | + | 0.757520i | \(0.273589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.1196 | −1.44487 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.8148 | − | 20.4638i | 0.424949 | − | 0.736033i | −0.571467 | − | 0.820625i | \(-0.693625\pi\) |
0.996416 | + | 0.0845923i | \(0.0269588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.2710 | − | 43.7707i | −0.907762 | − | 1.57229i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.546177 | + | 2.31966i | −0.0195940 | + | 0.0832174i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.59869 | + | 4.50106i | 0.0931078 | + | 0.161267i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.5860 | + | 42.5842i | −0.879757 | + | 1.52378i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.3084 | 0.439865 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 75.6545 | 2.70022 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.61785 | + | 7.99835i | −0.164609 | + | 0.285110i | −0.936516 | − | 0.350624i | \(-0.885969\pi\) |
0.771908 | + | 0.635735i | \(0.219303\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.5580 | − | 37.3395i | −0.767484 | − | 1.32932i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.01264 | + | 21.2891i | −0.178229 | + | 0.756955i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.3881 | + | 68.2221i | 1.39871 | + | 2.42264i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.5727 | − | 21.7766i | 0.445909 | − | 0.772338i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.1963 | 1.45925 | 0.729624 | − | 0.683848i | \(-0.239695\pi\) | ||||
0.729624 | + | 0.683848i | \(0.239695\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.7052 | 0.803254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.804407 | + | 1.39327i | −0.0284223 | + | 0.0492289i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.19460 | + | 2.06910i | 0.0421564 | + | 0.0730171i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.5803 | − | 18.4188i | −0.690114 | − | 0.649178i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.53790 | + | 14.7881i | 0.300548 | + | 0.520565i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.00729 | + | 3.47673i | −0.0705725 | + | 0.122235i | −0.899152 | − | 0.437636i | \(-0.855816\pi\) |
0.828580 | + | 0.559871i | \(0.189149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.1749 | 0.919124 | 0.459562 | − | 0.888146i | \(-0.348006\pi\) | ||||
0.459562 | + | 0.888146i | \(0.348006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.20264 | −0.287679 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.8884 | + | 53.5002i | −1.08197 | + | 1.87403i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5477 | + | 20.0011i | 0.404002 | + | 0.699751i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.0466 | − | 5.13068i | 0.595657 | − | 0.179280i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0242 | + | 34.6829i | 0.698849 | + | 1.21044i | 0.968866 | + | 0.247586i | \(0.0796373\pi\) |
−0.270017 | + | 0.962856i | \(0.587029\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.84418 | + | 15.3186i | −0.308289 | + | 0.533972i | −0.977988 | − | 0.208661i | \(-0.933090\pi\) |
0.669699 | + | 0.742632i | \(0.266423\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 64.0408 | 2.22961 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.9098 | 0.970520 | 0.485260 | − | 0.874370i | \(-0.338725\pi\) | ||||
0.485260 | + | 0.874370i | \(0.338725\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.7037 | + | 47.9843i | −0.962191 | + | 1.66656i | −0.245210 | + | 0.969470i | \(0.578857\pi\) |
−0.716981 | + | 0.697093i | \(0.754476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.9960 | − | 27.7060i | −0.554897 | − | 0.961109i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.7916 | − | 13.1005i | 0.685739 | − | 0.453906i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.6563 | − | 40.9739i | −0.818659 | − | 1.41796i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.7062 | + | 30.6680i | −0.612015 | + | 1.06004i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.1671 | −1.59386 | −0.796932 | − | 0.604069i | \(-0.793545\pi\) | ||||
−0.796932 | + | 0.604069i | \(0.793545\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.2650 | −0.836726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.65709 | + | 2.87016i | −0.0570730 | + | 0.0988534i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −53.9039 | − | 93.3643i | −1.85435 | − | 3.21183i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −52.9866 | + | 15.9479i | −1.82064 | + | 0.547976i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0679199 | + | 0.117641i | 0.00233101 | + | 0.00403742i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.901286 | − | 1.56107i | 0.0308957 | − | 0.0535129i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.7110 | −1.59935 | −0.799677 | − | 0.600430i | \(-0.794996\pi\) | ||||
−0.799677 | + | 0.600430i | \(0.794996\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.3235 | −0.660851 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.0046 | + | 24.2566i | −0.478387 | + | 0.828590i | −0.999693 | − | 0.0247798i | \(-0.992112\pi\) |
0.521306 | + | 0.853370i | \(0.325445\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.86802 | − | 8.43166i | −0.166095 | − | 0.287685i | 0.770949 | − | 0.636897i | \(-0.219782\pi\) |
−0.937044 | + | 0.349213i | \(0.886449\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.70601 | + | 2.54549i | 0.0922205 | + | 0.0867502i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.40180 | − | 9.35620i | −0.183880 | − | 0.318489i | 0.759319 | − | 0.650719i | \(-0.225532\pi\) |
−0.943198 | + | 0.332230i | \(0.892199\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.7593 | + | 60.2050i | −1.18185 | + | 2.04703i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.72780 | 0.262450 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 80.3698 | 2.72636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.6285 | + | 59.9783i | −1.17334 | + | 2.03229i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.45510 | + | 14.6447i | 0.286162 | + | 0.495647i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.73763 | − | 28.6153i | 0.227774 | − | 0.967374i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.06337 | − | 12.2341i | −0.238513 | − | 0.413117i | 0.721775 | − | 0.692128i | \(-0.243327\pi\) |
−0.960288 | + | 0.279011i | \(0.909993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.4134 | − | 30.1610i | 0.587341 | − | 1.01730i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.6737 | −1.26926 | −0.634630 | − | 0.772816i | \(-0.718847\pi\) | ||||
−0.634630 | + | 0.772816i | \(0.718847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1033 | 0.676531 | 0.338266 | − | 0.941051i | \(-0.390160\pi\) | ||||
0.338266 | + | 0.941051i | \(0.390160\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.9972 | + | 48.4926i | −0.941116 | + | 1.63006i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.0666 | + | 38.2205i | 0.740924 | + | 1.28332i | 0.952075 | + | 0.305864i | \(0.0989453\pi\) |
−0.211152 | + | 0.977453i | \(0.567721\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.684750 | − | 2.90819i | 0.0229658 | − | 0.0975377i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.7215 | − | 23.7664i | −0.459689 | − | 0.796204i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.4019 | + | 30.1410i | −0.582332 | + | 1.00863i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.5653 | −1.05511 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.8198 | 0.862097 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.81146 | + | 11.7978i | −0.227175 | + | 0.393479i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.39658 | − | 14.5433i | −0.279731 | − | 0.484508i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0245 | + | 11.3113i | 0.400152 | + | 0.376416i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.4194 | + | 35.3674i | 0.678763 | + | 1.17565i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.928746 | + | 1.60863i | −0.0308385 | + | 0.0534138i | −0.881033 | − | 0.473055i | \(-0.843151\pi\) |
0.850194 | + | 0.526469i | \(0.176484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.4556 | 0.379957 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5018 | 0.480466 | 0.240233 | − | 0.970715i | \(-0.422776\pi\) | ||||
0.240233 | + | 0.970715i | \(0.422776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.3074 | − | 24.7812i | 0.473506 | − | 0.820137i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −30.5611 | − | 52.9334i | −1.01032 | − | 1.74992i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.9460 | + | 14.4308i | −1.58332 | + | 0.476546i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.5812 | − | 18.3272i | −0.349041 | − | 0.604557i | 0.637038 | − | 0.770832i | \(-0.280159\pi\) |
−0.986079 | + | 0.166275i | \(0.946826\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.43198 | + | 4.21231i | −0.0801364 | + | 0.138800i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −56.9549 | −1.87469 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.17857 | 0.170270 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.57156 | + | 4.45406i | −0.0844610 | + | 0.146291i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.8573 | + | 51.7143i | 0.979585 | + | 1.69669i | 0.663889 | + | 0.747831i | \(0.268905\pi\) |
0.315696 | + | 0.948860i | \(0.397762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.22196 | + | 36.3138i | 0.0728217 | + | 1.19014i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.2676 | + | 31.6403i | 0.598053 | + | 1.03586i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34.6288 | − | 59.9789i | 1.13248 | − | 1.96152i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.1335 | −0.396384 | −0.198192 | − | 0.980163i | \(-0.563507\pi\) | ||||
−0.198192 | + | 0.980163i | \(0.563507\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.96221 | −0.227203 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.40677 | + | 11.0969i | −0.208855 | + | 0.361747i | −0.951354 | − | 0.308100i | \(-0.900307\pi\) |
0.742499 | + | 0.669847i | \(0.233640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.40505 | − | 2.43362i | −0.0457548 | − | 0.0792497i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −51.8144 | + | 15.5951i | −1.68552 | + | 0.507307i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.61260 | + | 14.9175i | 0.279872 | + | 0.484752i | 0.971353 | − | 0.237642i | \(-0.0763747\pi\) |
−0.691481 | + | 0.722395i | \(0.743041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.38368 | + | 2.39660i | −0.0449161 | + | 0.0777969i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.8760 | −0.774231 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.2346 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.5676 | − | 52.9447i | 0.989145 | − | 1.71325i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.63067 | − | 14.9488i | −0.278990 | − | 0.483225i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.1150 | + | 15.1591i | 0.520381 | + | 0.489513i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.09722 | − | 7.09660i | −0.132169 | − | 0.228923i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.26371 | + | 7.38496i | −0.137396 | + | 0.237977i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.4152 | 0.464043 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.5678 | −0.886522 | −0.443261 | − | 0.896393i | \(-0.646179\pi\) | ||||
−0.443261 | + | 0.896393i | \(0.646179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.3726 | − | 21.4300i | 0.397465 | − | 0.688430i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.40478 | + | 9.36136i | 0.173448 | + | 0.300420i | 0.939623 | − | 0.342211i | \(-0.111176\pi\) |
−0.766175 | + | 0.642632i | \(0.777843\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0331 | − | 46.8586i | 0.353705 | − | 1.50222i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 37.0885 | + | 64.2393i | 1.18778 | + | 2.05730i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.2352 | − | 36.7804i | 0.679373 | − | 1.17671i | −0.295797 | − | 0.955251i | \(-0.595585\pi\) |
0.975170 | − | 0.221457i | \(-0.0710813\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.83869 | 0.282486 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.3398 | −0.362053 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.8082 | + | 53.3614i | −0.982630 | + | 1.70196i | −0.330602 | + | 0.943770i | \(0.607252\pi\) |
−0.652028 | + | 0.758195i | \(0.726082\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.7235 | + | 37.6261i | 0.692167 | + | 1.19887i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.70172 | + | 24.2157i | −0.181488 | + | 0.770794i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.24356 | − | 10.8142i | −0.198534 | − | 0.343870i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1466 | + | 36.6271i | −0.671745 | + | 1.16350i | 0.305664 | + | 0.952140i | \(0.401122\pi\) |
−0.977409 | + | 0.211357i | \(0.932212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.8243 | −0.502169 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.5024 | −1.25231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.6547 | + | 21.9186i | −0.400778 | + | 0.694168i | −0.993820 | − | 0.111003i | \(-0.964594\pi\) |
0.593042 | + | 0.805172i | \(0.297927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.81419 | − | 3.14226i | −0.0573983 | − | 0.0994168i |
(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 | 1148.2.i.e.165.10 | ✓ | 30 | |
7.2 | even | 3 | inner | 1148.2.i.e.821.10 | yes | 30 | |
7.3 | odd | 6 | 8036.2.a.r.1.10 | 15 | |||
7.4 | even | 3 | 8036.2.a.q.1.6 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.10 | ✓ | 30 | 1.1 | even | 1 | trivial | |
1148.2.i.e.821.10 | yes | 30 | 7.2 | even | 3 | inner | |
8036.2.a.q.1.6 | 15 | 7.4 | even | 3 | |||
8036.2.a.r.1.10 | 15 | 7.3 | odd | 6 |