Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(783,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.783");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.f (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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 783.1 | ||
Character | \(\chi\) | \(=\) | 784.783 |
Dual form | 784.4.f.j.783.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8.86009 | −1.70513 | −0.852563 | − | 0.522625i | \(-0.824953\pi\) | ||||
−0.852563 | + | 0.522625i | \(0.824953\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.47612i | 0.668685i | 0.942452 | + | 0.334342i | \(0.108514\pi\) | ||||
−0.942452 | + | 0.334342i | \(0.891486\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 51.5012 | 1.90745 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 61.2337i | 1.67842i | 0.543805 | + | 0.839212i | \(0.316983\pi\) | ||||
−0.543805 | + | 0.839212i | \(0.683017\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.0928i | 0.257995i | 0.991645 | + | 0.128998i | \(0.0411759\pi\) | ||||
−0.991645 | + | 0.128998i | \(0.958824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 66.2391i | − 1.14019i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 100.394i | 1.43231i | 0.697943 | + | 0.716154i | \(0.254099\pi\) | ||||
−0.697943 | + | 0.716154i | \(0.745901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −73.6555 | −0.889355 | −0.444677 | − | 0.895691i | \(-0.646682\pi\) | ||||
−0.444677 | + | 0.895691i | \(0.646682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 96.8114i | − 0.877677i | −0.898566 | − | 0.438839i | \(-0.855390\pi\) | ||||
0.898566 | − | 0.438839i | \(-0.144610\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 69.1076 | 0.552861 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −217.083 | −1.54732 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 284.357 | 1.82082 | 0.910411 | − | 0.413706i | \(-0.135766\pi\) | ||||
0.910411 | + | 0.413706i | \(0.135766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 256.587 | 1.48660 | 0.743298 | − | 0.668961i | \(-0.233260\pi\) | ||||
0.743298 | + | 0.668961i | \(0.233260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 542.536i | − 2.86192i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 408.040 | 1.81301 | 0.906505 | − | 0.422194i | \(-0.138740\pi\) | ||||
0.906505 | + | 0.422194i | \(0.138740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 107.143i | − 0.439914i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 120.608i | − 0.459409i | −0.973260 | − | 0.229705i | \(-0.926224\pi\) | ||||
0.973260 | − | 0.229705i | \(-0.0737760\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 308.367i | 1.09362i | 0.837257 | + | 0.546809i | \(0.184158\pi\) | ||||
−0.837257 | + | 0.546809i | \(0.815842\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 385.029i | 1.27548i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 26.0454 | 0.0808322 | 0.0404161 | − | 0.999183i | \(-0.487132\pi\) | ||||
0.0404161 | + | 0.999183i | \(0.487132\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 889.504i | − 2.44226i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −311.059 | −0.806175 | −0.403087 | − | 0.915161i | \(-0.632063\pi\) | ||||
−0.403087 | + | 0.915161i | \(0.632063\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −457.791 | −1.12234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 652.595 | 1.51646 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −444.945 | −0.981812 | −0.490906 | − | 0.871213i | \(-0.663334\pi\) | ||||
−0.490906 | + | 0.871213i | \(0.663334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 488.804i | 1.02598i | 0.858394 | + | 0.512991i | \(0.171463\pi\) | ||||
−0.858394 | + | 0.512991i | \(0.828537\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −90.4072 | −0.172517 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 585.937i | 1.06841i | 0.845354 | + | 0.534206i | \(0.179389\pi\) | ||||
−0.845354 | + | 0.534206i | \(0.820611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 857.758i | 1.49655i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 416.209i | − 0.695704i | −0.937550 | − | 0.347852i | \(-0.886911\pi\) | ||||
0.937550 | − | 0.347852i | \(-0.113089\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 819.457i | 1.31384i | 0.753961 | + | 0.656919i | \(0.228141\pi\) | ||||
−0.753961 | + | 0.656919i | \(0.771859\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −612.300 | −0.942697 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 318.412i | − 0.453471i | −0.973956 | − | 0.226735i | \(-0.927195\pi\) | ||||
0.973956 | − | 0.226735i | \(-0.0728053\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 532.843 | 0.730923 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −218.850 | −0.289421 | −0.144710 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144710 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −750.561 | −0.957762 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2519.43 | −3.10473 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 19.4544i | 0.0231703i | 0.999933 | + | 0.0115852i | \(0.00368775\pi\) | ||||
−0.999933 | + | 0.0115852i | \(0.996312\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2273.39 | −2.53483 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 550.658i | − 0.594698i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 306.810i | 0.321153i | 0.987023 | + | 0.160577i | \(0.0513354\pi\) | ||||
−0.987023 | + | 0.160577i | \(0.948665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3153.61i | 3.20151i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 852.974i | − 0.840337i | −0.907446 | − | 0.420169i | \(-0.861971\pi\) | ||||
0.907446 | − | 0.420169i | \(-0.138029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1780.77 | 1.70354 | 0.851770 | − | 0.523917i | \(-0.175530\pi\) | ||||
0.851770 | + | 0.523917i | \(0.175530\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 551.111i | 0.497924i | 0.968513 | + | 0.248962i | \(0.0800895\pi\) | ||||
−0.968513 | + | 0.248962i | \(0.919911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1050.78 | 0.923364 | 0.461682 | − | 0.887045i | \(-0.347246\pi\) | ||||
0.461682 | + | 0.887045i | \(0.347246\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3615.27 | −3.09141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 83.2124 | 0.0692741 | 0.0346370 | − | 0.999400i | \(-0.488972\pi\) | ||||
0.0346370 | + | 0.999400i | \(0.488972\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 723.774 | 0.586889 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 622.793i | 0.492113i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2418.57 | −1.81711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1068.60i | 0.783350i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1451.17i | 1.03837i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1318.65i | 0.921346i | 0.887570 | + | 0.460673i | \(0.152392\pi\) | ||||
−0.887570 | + | 0.460673i | \(0.847608\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 2732.16i | − 1.86476i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 524.951 | 0.350116 | 0.175058 | − | 0.984558i | \(-0.443989\pi\) | ||||
0.175058 | + | 0.984558i | \(0.443989\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 1622.94i | − 1.03467i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2010.48 | −1.25377 | −0.626886 | − | 0.779111i | \(-0.715671\pi\) | ||||
−0.626886 | + | 0.779111i | \(0.715671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1105.17 | 0.674386 | 0.337193 | − | 0.941436i | \(-0.390523\pi\) | ||||
0.337193 | + | 0.941436i | \(0.390523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −230.765 | −0.137829 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −740.486 | −0.433025 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2125.89i | 1.21756i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1446.19 | −0.795144 | −0.397572 | − | 0.917571i | \(-0.630147\pi\) | ||||
−0.397572 | + | 0.917571i | \(0.630147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 410.819i | 0.221404i | 0.993854 | + | 0.110702i | \(0.0353099\pi\) | ||||
−0.993854 | + | 0.110702i | \(0.964690\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5170.44i | 2.73206i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1918.28i | 0.994064i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2542.49i | 1.29244i | 0.763151 | + | 0.646220i | \(0.223651\pi\) | ||||
−0.763151 | + | 0.646220i | \(0.776349\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2756.01 | 1.37463 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 59.6937i | − 0.0286845i | −0.999897 | − | 0.0143423i | \(-0.995435\pi\) | ||||
0.999897 | − | 0.0143423i | \(-0.00456544\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4056.07 | 1.91372 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3811.33 | −1.76605 | −0.883023 | − | 0.469329i | \(-0.844496\pi\) | ||||
−0.883023 | + | 0.469329i | \(0.844496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2050.76 | 0.933439 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3793.35 | −1.69640 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 328.670i | − 0.144441i | −0.997389 | − | 0.0722205i | \(-0.976991\pi\) | ||||
0.997389 | − | 0.0722205i | \(-0.0230085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3942.25 | 1.67411 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3648.07i | 1.52329i | 0.647992 | + | 0.761647i | \(0.275609\pi\) | ||||
−0.647992 | + | 0.761647i | \(0.724391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 4446.07i | − 1.82582i | −0.408160 | − | 0.912911i | \(-0.633829\pi\) | ||||
0.408160 | − | 0.912911i | \(-0.366171\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 4330.85i | − 1.74943i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3050.56i | 1.21233i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6147.52 | −2.40402 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 388.447i | 0.147157i | 0.997289 | + | 0.0735786i | \(0.0234420\pi\) | ||||
−0.997289 | + | 0.0735786i | \(0.976558\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2363.57 | −0.881522 | −0.440761 | − | 0.897624i | \(-0.645291\pi\) | ||||
−0.440761 | + | 0.897624i | \(0.645291\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 801.016 | 0.294164 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1273.45 | −0.460556 | −0.230278 | − | 0.973125i | \(-0.573963\pi\) | ||||
−0.230278 | + | 0.973125i | \(0.573963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −902.022 | −0.321320 | −0.160660 | − | 0.987010i | \(-0.551362\pi\) | ||||
−0.160660 | + | 0.987010i | \(0.551362\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 5191.46i | − 1.82178i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 901.679 | 0.307200 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 4985.91i | − 1.67413i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 4510.20i | − 1.49271i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2082.42i | 0.679429i | 0.940529 | + | 0.339714i | \(0.110330\pi\) | ||||
−0.940529 | + | 0.339714i | \(0.889670\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3687.65i | 1.18626i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2305.39 | −0.731285 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 7260.46i | − 2.24026i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1214.05 | −0.369528 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 587.200 | 0.176331 | 0.0881655 | − | 0.996106i | \(-0.471900\pi\) | ||||
0.0881655 | + | 0.996106i | \(0.471900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3559.13 | 1.05456 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6394.91 | 1.86980 | 0.934901 | − | 0.354908i | \(-0.115488\pi\) | ||||
0.934901 | + | 0.354908i | \(0.115488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3083.69i | − 0.889851i | −0.895568 | − | 0.444925i | \(-0.853230\pi\) | ||||
0.895568 | − | 0.444925i | \(-0.146770\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −412.960 | −0.116111 | −0.0580556 | − | 0.998313i | \(-0.518490\pi\) | ||||
−0.0580556 | + | 0.998313i | \(0.518490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 194.719i | 0.0540513i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2821.16i | 0.773225i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 3721.31i | − 1.00716i | −0.863948 | − | 0.503581i | \(-0.832016\pi\) | ||||
0.863948 | − | 0.503581i | \(-0.167984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 3230.26i | − 0.863399i | −0.902018 | − | 0.431699i | \(-0.857914\pi\) | ||||
0.902018 | − | 0.431699i | \(-0.142086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1140.21 | 0.301005 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 890.701i | − 0.229449i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1939.03 | 0.493499 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 181.422 | 0.0456226 | 0.0228113 | − | 0.999740i | \(-0.492738\pi\) | ||||
0.0228113 | + | 0.999740i | \(0.492738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5928.12 | 1.47311 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6650.04 | 1.63310 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 783.196i | − 0.190095i | −0.995473 | − | 0.0950475i | \(-0.969700\pi\) | ||||
0.995473 | − | 0.0950475i | \(-0.0303003\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14644.7 | 3.47313 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 4309.93i | − 1.01050i | −0.862973 | − | 0.505250i | \(-0.831400\pi\) | ||||
0.862973 | − | 0.505250i | \(-0.168600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 2325.52i | − 0.539077i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 172.367i | − 0.0395083i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7148.05i | 1.62016i | 0.586316 | + | 0.810082i | \(0.300578\pi\) | ||||
−0.586316 | + | 0.810082i | \(0.699422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4098.06 | 0.918597 | 0.459298 | − | 0.888282i | \(-0.348101\pi\) | ||||
0.459298 | + | 0.888282i | \(0.348101\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4231.72i | 0.927935i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8479.05 | −1.83919 | −0.919597 | − | 0.392862i | \(-0.871485\pi\) | ||||
−0.919597 | + | 0.392862i | \(0.871485\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13214.6 | 2.83561 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1108.37 | 0.235301 | 0.117651 | − | 0.993055i | \(-0.462464\pi\) | ||||
0.117651 | + | 0.993055i | \(0.462464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 925.763 | 0.194455 | 0.0972277 | − | 0.995262i | \(-0.469002\pi\) | ||||
0.0972277 | + | 0.995262i | \(0.469002\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4878.88i | 1.01403i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5166.04 | −1.05150 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 2718.37i | − 0.547607i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 700.439i | − 0.139659i | −0.997559 | − | 0.0698295i | \(-0.977754\pi\) | ||||
0.997559 | − | 0.0698295i | \(-0.0222455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 3326.46i | − 0.656523i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 13292.8i | − 2.59706i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1170.72 | 0.226436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7557.43i | 1.43288i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3654.36 | −0.686059 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2959.79 | −0.550242 | −0.275121 | − | 0.961410i | \(-0.588718\pi\) | ||||
−0.275121 | + | 0.961410i | \(0.588718\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15777.8 | −2.90475 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1808.61 | −0.329765 | −0.164882 | − | 0.986313i | \(-0.552724\pi\) | ||||
−0.164882 | + | 0.986313i | \(0.552724\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 4552.38i | − 0.822095i | −0.911614 | − | 0.411047i | \(-0.865163\pi\) | ||||
0.911614 | − | 0.411047i | \(-0.134837\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 730.924 | 0.129504 | 0.0647520 | − | 0.997901i | \(-0.479374\pi\) | ||||
0.0647520 | + | 0.997901i | \(0.479374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17412.3i | 3.05611i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 4882.89i | − 0.849023i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 7394.61i | − 1.27383i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 835.704i | 0.142635i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9310.03 | −1.57445 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8937.09i | 1.48407i | 0.670362 | + | 0.742035i | \(0.266139\pi\) | ||||
−0.670362 | + | 0.742035i | \(0.733861\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21014.6 | 3.45823 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4380.54 | −0.714431 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6813.13 | −1.10129 | −0.550645 | − | 0.834740i | \(-0.685618\pi\) | ||||
−0.550645 | + | 0.834740i | \(0.685618\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −737.270 | −0.118121 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15711.8i | 2.49514i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6412.70 | −1.00072 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8017.29i | − 1.24032i | −0.784476 | − | 0.620159i | \(-0.787068\pi\) | ||||
0.784476 | − | 0.620159i | \(-0.212932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 5566.53i | − 0.853781i | −0.904303 | − | 0.426890i | \(-0.859609\pi\) | ||||
0.904303 | − | 0.426890i | \(-0.140391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 2625.14i | − 0.399201i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 6508.41i | − 0.981326i | −0.871350 | − | 0.490663i | \(-0.836755\pi\) | ||||
0.871350 | − | 0.490663i | \(-0.163245\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3111.63 | 0.465206 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8739.25i | 1.28479i | 0.766373 | + | 0.642396i | \(0.222059\pi\) | ||||
−0.766373 | + | 0.642396i | \(0.777941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1433.86 | −0.209048 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21428.7 | 3.09839 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6126.36 | −0.878543 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4591.08 | 0.653004 | 0.326502 | − | 0.945196i | \(-0.394130\pi\) | ||||
0.326502 | + | 0.945196i | \(0.394130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 6211.45i | − 0.876301i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9198.07 | −1.27683 | −0.638415 | − | 0.769692i | \(-0.720410\pi\) | ||||
−0.638415 | + | 0.769692i | \(0.720410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 12857.5i | − 1.77056i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3438.67i | 0.469763i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 6586.09i | − 0.892625i | −0.894877 | − | 0.446312i | \(-0.852737\pi\) | ||||
0.894877 | − | 0.446312i | \(-0.147263\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 11683.3i | − 1.57101i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −921.517 | −0.122943 | −0.0614717 | − | 0.998109i | \(-0.519579\pi\) | ||||
−0.0614717 | + | 0.998109i | \(0.519579\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15881.3i | 2.08602i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8919.80 | −1.16260 | −0.581301 | − | 0.813689i | \(-0.697456\pi\) | ||||
−0.581301 | + | 0.813689i | \(0.697456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9719.33 | 1.25710 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4651.11 | −0.596991 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2380.49 | 0.303229 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7287.34i | 0.921262i | 0.887592 | + | 0.460631i | \(0.152377\pi\) | ||||
−0.887592 | + | 0.460631i | \(0.847623\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4320.07 | −0.537990 | −0.268995 | − | 0.963142i | \(-0.586692\pi\) | ||||
−0.268995 | + | 0.963142i | \(0.586692\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3102.86i | 0.383534i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3983.60i | 0.488757i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24985.8i | 3.04300i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 7792.27i | − 0.942061i | −0.882117 | − | 0.471030i | \(-0.843882\pi\) | ||||
0.882117 | − | 0.471030i | \(-0.156118\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17813.0 | 2.13784 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 1636.15i | − 0.193531i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9791.94 | −1.14991 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6318.16 | −0.736665 | −0.368332 | − | 0.929694i | \(-0.620071\pi\) | ||||
−0.368332 | + | 0.929694i | \(0.620071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 122.350 | 0.0141639 | 0.00708195 | − | 0.999975i | \(-0.497746\pi\) | ||||
0.00708195 | + | 0.999975i | \(0.497746\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1341.37 | 0.154184 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6938.02i | 0.791867i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6560.78 | 0.738362 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4982.96i | 0.556893i | 0.960452 | + | 0.278447i | \(0.0898195\pi\) | ||||
−0.960452 | + | 0.278447i | \(0.910180\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 680.814i | 0.0755608i | 0.999286 | + | 0.0377804i | \(0.0120287\pi\) | ||||
−0.999286 | + | 0.0377804i | \(0.987971\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 18835.6i | − 2.07608i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7130.70i | 0.780566i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9117.30 | 0.991219 | 0.495610 | − | 0.868545i | \(-0.334945\pi\) | ||||
0.495610 | + | 0.868545i | \(0.334945\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4410.08i | − 0.472978i | −0.971634 | − | 0.236489i | \(-0.924003\pi\) | ||||
0.971634 | − | 0.236489i | \(-0.0759968\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −145.443 | −0.0154936 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12813.4 | 1.35582 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14077.1 | 1.47959 | 0.739797 | − | 0.672830i | \(-0.234921\pi\) | ||||
0.739797 | + | 0.672830i | \(0.234921\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7385.27 | 0.771083 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3639.90i | − 0.377522i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7812.25 | 0.799654 | 0.399827 | − | 0.916591i | \(-0.369070\pi\) | ||||
0.399827 | + | 0.916591i | \(0.369070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 21793.9i | − 2.21624i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 17552.0i | − 1.77327i | −0.462470 | − | 0.886635i | \(-0.653037\pi\) | ||||
0.462470 | − | 0.886635i | \(-0.346963\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5236.81i | 0.525648i | 0.964844 | + | 0.262824i | \(0.0846539\pi\) | ||||
−0.964844 | + | 0.262824i | \(0.915346\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 16996.1i | − 1.69500i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11941.1 | −1.18323 | −0.591617 | − | 0.806219i | \(-0.701510\pi\) | ||||
−0.591617 | + | 0.806219i | \(0.701510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 22526.7i | − 2.20377i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18882.5 | −1.83555 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5090.16 | −0.491689 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16019.9 | −1.53774 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5774.82 | 0.550852 | 0.275426 | − | 0.961322i | \(-0.411181\pi\) | ||||
0.275426 | + | 0.961322i | \(0.411181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4934.34i | 0.467748i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2293.75 | −0.214750 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 2923.50i | − 0.272026i | −0.990707 | − | 0.136013i | \(-0.956571\pi\) | ||||
0.990707 | − | 0.136013i | \(-0.0434289\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 528.892i | 0.0489107i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 14580.3i | − 1.34012i | −0.742308 | − | 0.670059i | \(-0.766269\pi\) | ||||
0.742308 | − | 0.670059i | \(-0.233731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28547.9i | 2.60798i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −23576.8 | −2.14080 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 874.052i | − 0.0784127i | −0.999231 | − | 0.0392064i | \(-0.987517\pi\) | ||||
0.999231 | − | 0.0392064i | \(-0.0124830\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33768.8 | 3.01133 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5065.24 | 0.449002 | 0.224501 | − | 0.974474i | \(-0.427925\pi\) | ||||
0.224501 | + | 0.974474i | \(0.427925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6376.94 | 0.561921 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18170.0 | −1.59163 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 15623.5i | − 1.36051i | −0.732978 | − | 0.680253i | \(-0.761870\pi\) | ||||
0.732978 | − | 0.680253i | \(-0.238130\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15989.4 | 1.37612 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13313.3i | 1.13913i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1594.86i | 0.135671i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2912.04i | 0.246290i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8426.11i | 0.708550i | 0.935141 | + | 0.354275i | \(0.115272\pi\) | ||||
−0.935141 | + | 0.354275i | \(0.884728\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1830.09 | −0.153010 | −0.0765050 | − | 0.997069i | \(-0.524376\pi\) | ||||
−0.0765050 | + | 0.997069i | \(0.524376\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25760.0i | 2.12926i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2794.55 | 0.229683 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22915.2 | −1.87276 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1458.49 | 0.118525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4120.17 | −0.332954 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 32322.2i | − 2.59741i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3788.15 | −0.301045 | −0.150522 | − | 0.988607i | \(-0.548096\pi\) | ||||
−0.150522 | + | 0.988607i | \(0.548096\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 39392.6i | 3.11325i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7855.78i | 0.617440i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 6463.45i | − 0.505223i | −0.967568 | − | 0.252612i | \(-0.918710\pi\) | ||||
0.967568 | − | 0.252612i | \(-0.0812895\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25174.0i | 1.95701i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20944.5 | −1.61936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 27028.2i | − 2.06718i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1915.55 | −0.145717 | −0.0728587 | − | 0.997342i | \(-0.523212\pi\) | ||||
−0.0728587 | + | 0.997342i | \(0.523212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3729.02 | −0.282148 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 54467.6 | 4.09915 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 220.298 | 0.0164911 | 0.00824553 | − | 0.999966i | \(-0.497375\pi\) | ||||
0.00824553 | + | 0.999966i | \(0.497375\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 622.106i | 0.0463225i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18909.3 | 1.39318 | 0.696590 | − | 0.717470i | \(-0.254700\pi\) | ||||
0.696590 | + | 0.717470i | \(0.254700\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 25001.7i | − 1.83238i | −0.400748 | − | 0.916188i | \(-0.631250\pi\) | ||||
0.400748 | − | 0.916188i | \(-0.368750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3441.68i | − 0.250922i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 6690.41i | − 0.485233i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19401.0i | 1.39978i | 0.714251 | + | 0.699890i | \(0.246767\pi\) | ||||
−0.714251 | + | 0.699890i | \(0.753233\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20941.5 | 1.50311 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 19047.3i | − 1.35310i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4656.08 | −0.329069 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16828.3 | −1.18327 | −0.591633 | − | 0.806208i | \(-0.701516\pi\) | ||||
−0.591633 | + | 0.806208i | \(0.701516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18899.1 | −1.32211 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11282.9 | 0.785305 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5988.30i | 0.414688i | 0.978268 | + | 0.207344i | \(0.0664820\pi\) | ||||
−0.978268 | + | 0.207344i | \(0.933518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7992.00 | 0.547890 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 14163.0i | − 0.966087i | −0.875596 | − | 0.483043i | \(-0.839531\pi\) | ||||
0.875596 | − | 0.483043i | \(-0.160469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 16419.5i | − 1.11442i | −0.830371 | − | 0.557210i | \(-0.811872\pi\) | ||||
0.830371 | − | 0.557210i | \(-0.188128\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30176.5i | 2.03795i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 18081.5i | − 1.21507i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18589.4 | 1.24303 | 0.621517 | − | 0.783401i | \(-0.286517\pi\) | ||||
0.621517 | + | 0.783401i | \(0.286517\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 314.962i | 0.0208543i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5262.43 | −0.346734 | −0.173367 | − | 0.984857i | \(-0.555465\pi\) | ||||
−0.173367 | + | 0.984857i | \(0.555465\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7988.96 | −0.523814 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4798.33 | −0.313085 | −0.156543 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156543 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5492.16 | 0.356622 | 0.178311 | − | 0.983974i | \(-0.442937\pi\) | ||||
0.178311 | + | 0.983974i | \(0.442937\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21016.1i | 1.35805i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2210.69 | −0.141484 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 39960.8i | 2.54526i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40965.0i | 2.59679i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 4615.33i | − 0.291178i | −0.989345 | − | 0.145589i | \(-0.953492\pi\) | ||||
0.989345 | − | 0.145589i | \(-0.0465077\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 18450.4i | − 1.15851i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9858.36 | −0.616090 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 21435.3i | − 1.32702i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2406.03 | −0.148257 | −0.0741284 | − | 0.997249i | \(-0.523617\pi\) | ||||
−0.0741284 | + | 0.997249i | \(0.523617\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21395.2 | −1.31220 | −0.656098 | − | 0.754675i | \(-0.727794\pi\) | ||||
−0.656098 | + | 0.754675i | \(0.727794\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20426.0 | 1.24693 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4800.83 | 0.291716 | 0.145858 | − | 0.989306i | \(-0.453406\pi\) | ||||
0.145858 | + | 0.989306i | \(0.453406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 27245.6i | − 1.64790i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10334.4 | 0.619323 | 0.309661 | − | 0.950847i | \(-0.399784\pi\) | ||||
0.309661 | + | 0.950847i | \(0.399784\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3924.60i | 0.234117i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42203.0i | 2.50608i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29036.0i | 1.71636i | 0.513346 | + | 0.858182i | \(0.328406\pi\) | ||||
−0.513346 | + | 0.858182i | \(0.671594\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 4690.96i | − 0.276032i | −0.990430 | − | 0.138016i | \(-0.955927\pi\) | ||||
0.990430 | − | 0.138016i | \(-0.0440725\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10756.6 | 0.630092 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 27529.0i | − 1.59809i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5202.64 | −0.300666 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29931.3 | −1.72203 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13736.5 | −0.786779 | −0.393389 | − | 0.919372i | \(-0.628698\pi\) | ||||
−0.393389 | + | 0.919372i | \(0.628698\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15002.1 | −0.855453 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17305.2i | 0.982414i | 0.871043 | + | 0.491207i | \(0.163444\pi\) | ||||
−0.871043 | + | 0.491207i | \(0.836556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −56659.5 | −3.18825 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 26134.4i | − 1.46413i | −0.681233 | − | 0.732067i | \(-0.738556\pi\) | ||||
0.681233 | − | 0.732067i | \(-0.261444\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 15030.6i | − 0.838378i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27321.8i | 1.51731i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 3761.57i | − 0.207989i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28243.1 | 1.55487 | 0.777436 | − | 0.628962i | \(-0.216520\pi\) | ||||
0.777436 | + | 0.628962i | \(0.216520\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8262.41i | 0.450951i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12108.4 | 0.658015 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3658.86 | 0.197984 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29732.6 | 1.60198 | 0.800988 | − | 0.598680i | \(-0.204308\pi\) | ||||
0.800988 | + | 0.598680i | \(0.204308\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30054.4 | −1.61241 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 1725.23i | − 0.0921642i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18124.3 | −0.960047 | −0.480023 | − | 0.877256i | \(-0.659372\pi\) | ||||
−0.480023 | + | 0.877256i | \(0.659372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 16398.6i | − 0.864974i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 24840.6i | − 1.30475i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5535.97i | − 0.289557i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32971.2i | 1.71734i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22481.7 | −1.16610 | −0.583050 | − | 0.812436i | \(-0.698141\pi\) | ||||
−0.583050 | + | 0.812436i | \(0.698141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28620.4i | 1.47220i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19651.3 | 1.00666 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27637.9 | 1.40995 | 0.704974 | − | 0.709233i | \(-0.250959\pi\) | ||||
0.704974 | + | 0.709233i | \(0.250959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24489.1 | −1.24417 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30958.3 | −1.56640 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7075.60i | 0.356539i | 0.983982 | + | 0.178270i | \(0.0570499\pi\) | ||||
−0.983982 | + | 0.178270i | \(0.942950\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35879.1 | −1.79325 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29891.3i | 1.48792i | 0.668226 | + | 0.743958i | \(0.267054\pi\) | ||||
−0.668226 | + | 0.743958i | \(0.732946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7891.69i | 0.391240i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11676.8i | 0.576553i | 0.957547 | + | 0.288277i | \(0.0930823\pi\) | ||||
−0.957547 | + | 0.288277i | \(0.906918\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 10811.9i | − 0.531700i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11271.0 | −0.552056 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30942.3i | 1.50346i | 0.659468 | + | 0.751732i | \(0.270782\pi\) | ||||
−0.659468 | + | 0.751732i | \(0.729218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1607.42 | −0.0777923 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3071.34 | −0.148049 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28884.0 | −1.38680 | −0.693399 | − | 0.720554i | \(-0.743888\pi\) | ||||
−0.693399 | + | 0.720554i | \(0.743888\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −52523.7 | −2.51184 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22478.8i | 1.07077i | 0.844608 | + | 0.535385i | \(0.179833\pi\) | ||||
−0.844608 | + | 0.535385i | \(0.820167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38654.8 | −1.82689 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 5380.63i | − 0.253303i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30021.9i | 1.40783i | 0.710287 | + | 0.703913i | \(0.248565\pi\) | ||||
−0.710287 | + | 0.703913i | \(0.751435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6939.19i | 0.324136i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2446.25i | 0.113823i | 0.998379 | + | 0.0569117i | \(0.0181253\pi\) | ||||
−0.998379 | + | 0.0569117i | \(0.981875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17732.1 | 0.821881 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8883.44i | 0.408578i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25486.0 | 1.16769 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −61729.2 | −2.81739 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19008.0 | −0.864234 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2274.33 | 0.103013 | 0.0515064 | − | 0.998673i | \(-0.483598\pi\) | ||||
0.0515064 | + | 0.998673i | \(0.483598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38186.4i | 1.72303i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5911.01 | −0.264699 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20604.3i | 0.919193i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25454.5i | 1.13130i | 0.824646 | + | 0.565649i | \(0.191374\pi\) | ||||
−0.824646 | + | 0.565649i | \(0.808626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2614.82i | 0.115777i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1001.92i | 0.0441963i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −50178.4 | −2.20518 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 63332.4i | − 2.76258i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2042.65 | −0.0887709 | −0.0443855 | − | 0.999014i | \(-0.514133\pi\) | ||||
−0.0443855 | + | 0.999014i | \(0.514133\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33523.4 | 1.45150 | 0.725750 | − | 0.687958i | \(-0.241493\pi\) | ||||
0.725750 | + | 0.687958i | \(0.241493\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36309.2 | −1.56632 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 446.278 | 0.0191809 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 22713.0i | − 0.972614i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28446.0 | 1.20922 | 0.604611 | − | 0.796521i | \(-0.293328\pi\) | ||||
0.604611 | + | 0.796521i | \(0.293328\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3185.80i | − 0.134933i | −0.997722 | − | 0.0674666i | \(-0.978508\pi\) | ||||
0.997722 | − | 0.0674666i | \(-0.0214916\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 37493.4i | − 1.58225i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21966.6i | 0.923644i | 0.886973 | + | 0.461822i | \(0.152804\pi\) | ||||
−0.886973 | + | 0.461822i | \(0.847196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 41832.8i | − 1.75261i | −0.481756 | − | 0.876306i | \(-0.660001\pi\) | ||||
0.481756 | − | 0.876306i | \(-0.339999\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 75125.2 | 3.13606 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 28494.0i | − 1.18093i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −55700.8 | −2.30024 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13093.9 | −0.538799 | −0.269400 | − | 0.963028i | \(-0.586825\pi\) | ||||
−0.269400 | + | 0.963028i | \(0.586825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56470.1 | 2.31539 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9820.23 | −0.401218 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15331.8i | 0.624176i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8202.34 | −0.331571 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 39503.0i | − 1.59124i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23013.9i | 0.923777i | 0.886938 | + | 0.461889i | \(0.152828\pi\) | ||||
−0.886938 | + | 0.461889i | \(0.847172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 28359.5i | − 1.13436i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 18808.6i | − 0.749696i | −0.927086 | − | 0.374848i | \(-0.877695\pi\) | ||||
0.927086 | − | 0.374848i | \(-0.122305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24257.3 | −0.963504 | −0.481752 | − | 0.876308i | \(-0.659999\pi\) | ||||
−0.481752 | + | 0.876308i | \(0.659999\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11594.2i | 0.457326i | 0.973506 | + | 0.228663i | \(0.0734354\pi\) | ||||
−0.973506 | + | 0.228663i | \(0.926565\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2457.17 | 0.0965854 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45771.6 | 1.79295 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19497.6 | 0.761116 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7085.61 | −0.275645 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15801.1i | 0.612585i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6641.93 | 0.255738 | 0.127869 | − | 0.991791i | \(-0.459186\pi\) | ||||
0.127869 | + | 0.991791i | \(0.459186\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6205.95i | 0.238136i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13406.2i | 0.512674i | 0.966588 | + | 0.256337i | \(0.0825156\pi\) | ||||
−0.966588 | + | 0.256337i | \(0.917484\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6095.70i | 0.232318i | 0.993231 | + | 0.116159i | \(0.0370582\pi\) | ||||
−0.993231 | + | 0.116159i | \(0.962942\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29472.8i | 1.11945i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23852.8 | 0.902929 | 0.451464 | − | 0.892289i | \(-0.350902\pi\) | ||||
0.451464 | + | 0.892289i | \(0.350902\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32628.0i | 1.22680i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1918.39 | −0.0718885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27273.4 | −1.01860 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10372.7 | −0.386102 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 72962.5 | 2.70683 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 31228.6i | − 1.15469i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33239.3 | 1.22090 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43014.8i | 1.57473i | 0.616485 | + | 0.787367i | \(0.288556\pi\) | ||||
−0.616485 | + | 0.787367i | \(0.711444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 43929.2i | − 1.60290i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 11732.6i | − 0.426694i | −0.976977 | − | 0.213347i | \(-0.931564\pi\) | ||||
0.976977 | − | 0.213347i | \(-0.0684364\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 13401.0i | − 0.485771i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32378.0 | 1.16982 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31129.0i | 1.11736i | 0.829385 | + | 0.558678i | \(0.188691\pi\) | ||||
−0.829385 | + | 0.558678i | \(0.811309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26224.0 | 0.938232 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5033.13 | 0.179488 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28198.7 | 1.00234 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 91711.9 | 3.24942 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32972.4i | 1.16447i | 0.813021 | + | 0.582234i | \(0.197821\pi\) | ||||
−0.813021 | + | 0.582234i | \(0.802179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16024.4 | 0.562290 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 45959.6i | − 1.60753i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43429.1i | 1.51416i | 0.653323 | + | 0.757080i | \(0.273375\pi\) | ||||
−0.653323 | + | 0.757080i | \(0.726625\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40334.5i | 1.40177i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20473.6i | 0.709267i | 0.935005 | + | 0.354634i | \(0.115394\pi\) | ||||
−0.935005 | + | 0.354634i | \(0.884606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11676.2 | −0.403213 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 4525.11i | − 0.155276i | −0.996982 | − | 0.0776379i | \(-0.975262\pi\) | ||||
0.996982 | − | 0.0776379i | \(-0.0247378\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9909.52 | −0.338964 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6476.05 | −0.220821 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11974.9 | −0.407037 | −0.203518 | − | 0.979071i | \(-0.565238\pi\) | ||||
−0.203518 | + | 0.979071i | \(0.565238\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2904.08 | −0.0984018 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 154274.i | − 5.21105i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36046.1 | 1.20997 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28382.9i | 0.949767i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 17670.4i | − 0.589460i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 36345.2i | − 1.20867i | −0.796730 | − | 0.604335i | \(-0.793439\pi\) | ||||
0.796730 | − | 0.604335i | \(-0.206561\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 65516.9i | 2.17204i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45749.3 | −1.51201 | −0.756006 | − | 0.654564i | \(-0.772852\pi\) | ||||
−0.756006 | + | 0.654564i | \(0.772852\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 7404.41i | − 0.243211i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23883.6 | −0.782091 | −0.391045 | − | 0.920371i | \(-0.627886\pi\) | ||||
−0.391045 | + | 0.920371i | \(0.627886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1191.26 | −0.0388896 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 54116.6 | 1.76127 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55247.4 | −1.79259 | −0.896296 | − | 0.443457i | \(-0.853752\pi\) | ||||
−0.896296 | + | 0.443457i | \(0.853752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 9520.45i | − 0.307966i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29853.5 | 0.959843 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 27352.7i | − 0.876779i | −0.898785 | − | 0.438389i | \(-0.855549\pi\) | ||||
0.898785 | − | 0.438389i | \(-0.144451\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 79183.4i | − 2.53052i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6743.62i | − 0.214862i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 26683.5i | − 0.847619i | −0.905751 | − | 0.423809i | \(-0.860693\pi\) | ||||
0.905751 | − | 0.423809i | \(-0.139307\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −88578.6 | −2.80531 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 784.4.f.j.783.1 | ✓ | 24 | |
4.3 | odd | 2 | inner | 784.4.f.j.783.23 | yes | 24 | |
7.6 | odd | 2 | inner | 784.4.f.j.783.24 | yes | 24 | |
28.27 | even | 2 | inner | 784.4.f.j.783.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
784.4.f.j.783.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
784.4.f.j.783.2 | yes | 24 | 28.27 | even | 2 | inner | |
784.4.f.j.783.23 | yes | 24 | 4.3 | odd | 2 | inner | |
784.4.f.j.783.24 | yes | 24 | 7.6 | odd | 2 | inner |