Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1053,2,Mod(649,1053)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1053, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1053.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1053 = 3^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1053.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.40824733284\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{10} + 16x^{8} + 91x^{6} + 222x^{4} + 228x^{2} + 81 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 117) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.5 | ||
Root | \(-0.905597i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1053.649 |
Dual form | 1053.2.b.j.649.6 |
$q$-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 \(\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(730\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.905597i | − | 0.640353i | −0.947358 | − | 0.320177i | \(-0.896258\pi\) | ||
0.947358 | − | 0.320177i | \(-0.103742\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.17989 | 0.589947 | ||||||||
\(5\) | − | 2.24306i | − | 1.00313i | −0.865121 | − | 0.501563i | \(-0.832759\pi\) | ||
0.865121 | − | 0.501563i | \(-0.167241\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.43611i | − | 1.29873i | −0.760478 | − | 0.649364i | \(-0.775035\pi\) | ||
0.760478 | − | 0.649364i | \(-0.224965\pi\) | |||||||
\(8\) | − | 2.87970i | − | 1.01813i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.03130 | −0.642355 | ||||||||
\(11\) | 3.69657i | 1.11456i | 0.830325 | + | 0.557279i | \(0.188155\pi\) | ||||
−0.830325 | + | 0.557279i | \(0.811845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.93184 | − | 2.09865i | 0.813145 | − | 0.582061i | ||||
\(14\) | −3.11173 | −0.831645 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.248059 | −0.0620147 | ||||||||
\(17\) | −4.21120 | −1.02137 | −0.510683 | − | 0.859769i | \(-0.670607\pi\) | ||||
−0.510683 | + | 0.859769i | \(0.670607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.25298i | − | 0.975701i | −0.872927 | − | 0.487851i | \(-0.837781\pi\) | ||
0.872927 | − | 0.487851i | \(-0.162219\pi\) | |||||||
\(20\) | − | 2.64657i | − | 0.591791i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.34760 | 0.713712 | ||||||||
\(23\) | −3.78325 | −0.788861 | −0.394431 | − | 0.918926i | \(-0.629058\pi\) | ||||
−0.394431 | + | 0.918926i | \(0.629058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0313048 | −0.00626096 | ||||||||
\(26\) | −1.90053 | − | 2.65506i | −0.372725 | − | 0.520700i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 4.05425i | − | 0.766181i | ||||||
\(29\) | 2.37891 | 0.441752 | 0.220876 | − | 0.975302i | \(-0.429108\pi\) | ||||
0.220876 | + | 0.975302i | \(0.429108\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.35733i | 1.32141i | 0.750644 | + | 0.660707i | \(0.229744\pi\) | ||||
−0.750644 | + | 0.660707i | \(0.770256\pi\) | |||||||
\(32\) | − | 5.53476i | − | 0.978417i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.81365i | 0.654035i | ||||||||
\(35\) | −7.70739 | −1.30279 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.49928i | 0.904076i | 0.891999 | + | 0.452038i | \(0.149303\pi\) | ||||
−0.891999 | + | 0.452038i | \(0.850697\pi\) | |||||||
\(38\) | −3.85149 | −0.624794 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.45934 | −1.02131 | ||||||||
\(41\) | 7.92223i | 1.23724i | 0.785689 | + | 0.618622i | \(0.212309\pi\) | ||||
−0.785689 | + | 0.618622i | \(0.787691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.900531 | 0.137330 | 0.0686649 | − | 0.997640i | \(-0.478126\pi\) | ||||
0.0686649 | + | 0.997640i | \(0.478126\pi\) | |||||||
\(44\) | 4.36157i | 0.657531i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.42609i | 0.505150i | ||||||||
\(47\) | − | 5.54325i | − | 0.808566i | −0.914634 | − | 0.404283i | \(-0.867521\pi\) | ||
0.914634 | − | 0.404283i | \(-0.132479\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.80686 | −0.686695 | ||||||||
\(50\) | 0.0283495i | 0.00400923i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.45926 | − | 2.47619i | 0.479713 | − | 0.343385i | ||||
\(53\) | 7.59566 | 1.04334 | 0.521672 | − | 0.853146i | \(-0.325308\pi\) | ||||
0.521672 | + | 0.853146i | \(0.325308\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.29163 | 1.11804 | ||||||||
\(56\) | −9.89498 | −1.32227 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.15433i | − | 0.282878i | ||||||
\(59\) | − | 5.13125i | − | 0.668032i | −0.942567 | − | 0.334016i | \(-0.891596\pi\) | ||
0.942567 | − | 0.334016i | \(-0.108404\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0181 | −1.66680 | −0.833401 | − | 0.552669i | \(-0.813609\pi\) | ||||
−0.833401 | + | 0.552669i | \(0.813609\pi\) | |||||||
\(62\) | 6.66277 | 0.846173 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.50838 | −0.688547 | ||||||||
\(65\) | −4.70739 | − | 6.57628i | −0.583880 | − | 0.815687i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.5102i | − | 1.65054i | −0.564741 | − | 0.825269i | \(-0.691024\pi\) | ||
0.564741 | − | 0.825269i | \(-0.308976\pi\) | |||||||
\(68\) | −4.96877 | −0.602552 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.97979i | 0.834244i | ||||||||
\(71\) | − | 2.65506i | − | 0.315098i | −0.987511 | − | 0.157549i | \(-0.949641\pi\) | ||
0.987511 | − | 0.157549i | \(-0.0503592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.45741i | 0.638741i | 0.947630 | + | 0.319371i | \(0.103472\pi\) | ||||
−0.947630 | + | 0.319371i | \(0.896528\pi\) | |||||||
\(74\) | 4.98013 | 0.578928 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 5.01807i | − | 0.575612i | ||||||
\(77\) | 12.7018 | 1.44751 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9377 | 1.23059 | 0.615294 | − | 0.788297i | \(-0.289037\pi\) | ||||
0.615294 | + | 0.788297i | \(0.289037\pi\) | |||||||
\(80\) | 0.556410i | 0.0622085i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.17434 | 0.792273 | ||||||||
\(83\) | 0.537568i | 0.0590057i | 0.999565 | + | 0.0295029i | \(0.00939241\pi\) | ||||
−0.999565 | + | 0.0295029i | \(0.990608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.44596i | 1.02456i | ||||||||
\(86\) | − | 0.815518i | − | 0.0879396i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.6450 | 1.13476 | ||||||||
\(89\) | − | 5.75227i | − | 0.609739i | −0.952394 | − | 0.304870i | \(-0.901387\pi\) | ||
0.952394 | − | 0.304870i | \(-0.0986129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.21120 | − | 10.0741i | −0.755939 | − | 1.05605i | ||||
\(92\) | −4.46383 | −0.465387 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.01995 | −0.517768 | ||||||||
\(95\) | −9.53968 | −0.978751 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.78485i | − | 0.688897i | −0.938805 | − | 0.344449i | \(-0.888066\pi\) | ||
0.938805 | − | 0.344449i | \(-0.111934\pi\) | |||||||
\(98\) | 4.35308i | 0.439727i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.0369364 | −0.00369364 | ||||||||
\(101\) | −4.96231 | −0.493768 | −0.246884 | − | 0.969045i | \(-0.579407\pi\) | ||||
−0.246884 | + | 0.969045i | \(0.579407\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.11173 | 0.208075 | 0.104038 | − | 0.994573i | \(-0.466824\pi\) | ||||
0.104038 | + | 0.994573i | \(0.466824\pi\) | |||||||
\(104\) | −6.04349 | − | 8.44281i | −0.592613 | − | 0.827886i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 6.87861i | − | 0.668109i | ||||||
\(107\) | −8.07404 | −0.780547 | −0.390274 | − | 0.920699i | \(-0.627620\pi\) | ||||
−0.390274 | + | 0.920699i | \(0.627620\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0020i | 0.958021i | 0.877809 | + | 0.479011i | \(0.159004\pi\) | ||||
−0.877809 | + | 0.479011i | \(0.840996\pi\) | |||||||
\(110\) | − | 7.50887i | − | 0.715942i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.852357i | 0.0805402i | ||||||||
\(113\) | 19.4347 | 1.82826 | 0.914130 | − | 0.405422i | \(-0.132875\pi\) | ||||
0.914130 | + | 0.405422i | \(0.132875\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.48604i | 0.791327i | ||||||||
\(116\) | 2.80686 | 0.260611 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.64684 | −0.427776 | ||||||||
\(119\) | 14.4702i | 1.32648i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66466 | −0.242242 | ||||||||
\(122\) | 11.7892i | 1.06734i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.68087i | 0.779565i | ||||||||
\(125\) | − | 11.1451i | − | 0.996845i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.76413 | −0.156541 | −0.0782704 | − | 0.996932i | \(-0.524940\pi\) | ||||
−0.0782704 | + | 0.996932i | \(0.524940\pi\) | |||||||
\(128\) | − | 6.08116i | − | 0.537503i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.95545 | + | 4.26300i | −0.522328 | + | 0.373890i | ||||
\(131\) | −7.12979 | −0.622933 | −0.311466 | − | 0.950257i | \(-0.600820\pi\) | ||||
−0.311466 | + | 0.950257i | \(0.600820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.6137 | −1.26717 | ||||||||
\(134\) | −12.2348 | −1.05693 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.1270i | 1.03988i | ||||||||
\(137\) | 4.52058i | 0.386219i | 0.981177 | + | 0.193110i | \(0.0618573\pi\) | ||||
−0.981177 | + | 0.193110i | \(0.938143\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1099 | 1.19679 | 0.598394 | − | 0.801202i | \(-0.295806\pi\) | ||||
0.598394 | + | 0.801202i | \(0.295806\pi\) | |||||||
\(140\) | −9.09391 | −0.768576 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.40441 | −0.201774 | ||||||||
\(143\) | 7.75782 | + | 10.8377i | 0.648741 | + | 0.906298i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 5.33603i | − | 0.443133i | ||||||
\(146\) | 4.94221 | 0.409020 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.48857i | 0.533357i | ||||||||
\(149\) | 5.80236i | 0.475348i | 0.971345 | + | 0.237674i | \(0.0763850\pi\) | ||||
−0.971345 | + | 0.237674i | \(0.923615\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.74588i | 0.793108i | 0.918011 | + | 0.396554i | \(0.129794\pi\) | ||||
−0.918011 | + | 0.396554i | \(0.870206\pi\) | |||||||
\(152\) | −12.2473 | −0.993389 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 11.5027i | − | 0.926917i | ||||||
\(155\) | 16.5029 | 1.32555 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.07960 | −0.0861611 | −0.0430806 | − | 0.999072i | \(-0.513717\pi\) | ||||
−0.0430806 | + | 0.999072i | \(0.513717\pi\) | |||||||
\(158\) | − | 9.90516i | − | 0.788012i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.4148 | −0.981475 | ||||||||
\(161\) | 12.9997i | 1.02452i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.54857i | − | 0.434598i | −0.976105 | − | 0.217299i | \(-0.930275\pi\) | ||
0.976105 | − | 0.217299i | \(-0.0697247\pi\) | |||||||
\(164\) | 9.34739i | 0.729909i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.486819 | 0.0377845 | ||||||||
\(167\) | 13.3385i | 1.03216i | 0.856539 | + | 0.516082i | \(0.172610\pi\) | ||||
−0.856539 | + | 0.516082i | \(0.827390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.19133 | − | 12.3058i | 0.322410 | − | 0.946600i | ||||
\(170\) | 8.55423 | 0.656079 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.06253 | 0.0810173 | ||||||||
\(173\) | 7.44160 | 0.565774 | 0.282887 | − | 0.959153i | \(-0.408708\pi\) | ||||
0.282887 | + | 0.959153i | \(0.408708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.107567i | 0.00813129i | ||||||||
\(176\) | − | 0.916967i | − | 0.0691190i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.20923 | −0.390449 | ||||||||
\(179\) | 23.2047 | 1.73440 | 0.867202 | − | 0.497957i | \(-0.165916\pi\) | ||||
0.867202 | + | 0.497957i | \(0.165916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.18439 | 0.385353 | 0.192676 | − | 0.981262i | \(-0.438283\pi\) | ||||
0.192676 | + | 0.981262i | \(0.438283\pi\) | |||||||
\(182\) | −9.12309 | + | 6.53044i | −0.676248 | + | 0.484068i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.8946i | 0.803162i | ||||||||
\(185\) | 12.3352 | 0.906901 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 15.5670i | − | 1.13837i | ||||||
\(188\) | − | 6.54045i | − | 0.477012i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.63911i | 0.626747i | ||||||||
\(191\) | 16.1411 | 1.16793 | 0.583966 | − | 0.811778i | \(-0.301500\pi\) | ||||
0.583966 | + | 0.811778i | \(0.301500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.27925i | 0.236045i | 0.993011 | + | 0.118023i | \(0.0376556\pi\) | ||||
−0.993011 | + | 0.118023i | \(0.962344\pi\) | |||||||
\(194\) | −6.14434 | −0.441138 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.67159 | −0.405114 | ||||||||
\(197\) | 7.11249i | 0.506744i | 0.967369 | + | 0.253372i | \(0.0815396\pi\) | ||||
−0.967369 | + | 0.253372i | \(0.918460\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8449 | −0.981437 | −0.490719 | − | 0.871318i | \(-0.663266\pi\) | ||||
−0.490719 | + | 0.871318i | \(0.663266\pi\) | |||||||
\(200\) | 0.0901485i | 0.00637446i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.49385i | 0.316186i | ||||||||
\(203\) | − | 8.17420i | − | 0.573716i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.7700 | 1.24111 | ||||||||
\(206\) | − | 1.91238i | − | 0.133242i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.727267 | + | 0.520589i | −0.0504269 | + | 0.0360963i | ||||
\(209\) | 15.7215 | 1.08748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4339 | 0.993671 | 0.496836 | − | 0.867845i | \(-0.334495\pi\) | ||||
0.496836 | + | 0.867845i | \(0.334495\pi\) | |||||||
\(212\) | 8.96208 | 0.615518 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.31182i | 0.499826i | ||||||||
\(215\) | − | 2.01994i | − | 0.137759i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.2806 | 1.71616 | ||||||||
\(218\) | 9.05781 | 0.613472 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.78325 | 0.659586 | ||||||||
\(221\) | −12.3465 | + | 8.83784i | −0.830519 | + | 0.594497i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 11.0038i | − | 0.736871i | −0.929653 | − | 0.368435i | \(-0.879894\pi\) | ||
0.929653 | − | 0.368435i | \(-0.120106\pi\) | |||||||
\(224\) | −19.0181 | −1.27070 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 17.6000i | − | 1.17073i | ||||||
\(227\) | 8.11818i | 0.538823i | 0.963025 | + | 0.269411i | \(0.0868291\pi\) | ||||
−0.963025 | + | 0.269411i | \(0.913171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.37790i | − | 0.355382i | −0.984086 | − | 0.177691i | \(-0.943137\pi\) | ||
0.984086 | − | 0.177691i | \(-0.0568627\pi\) | |||||||
\(230\) | 7.68493 | 0.506729 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.85055i | − | 0.449761i | ||||||
\(233\) | 20.0992 | 1.31675 | 0.658373 | − | 0.752692i | \(-0.271245\pi\) | ||||
0.658373 | + | 0.752692i | \(0.271245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.4338 | −0.811094 | ||||||||
\(236\) | − | 6.05433i | − | 0.394104i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.1041 | 0.849414 | ||||||||
\(239\) | − | 14.1607i | − | 0.915979i | −0.888958 | − | 0.457989i | \(-0.848570\pi\) | ||
0.888958 | − | 0.457989i | \(-0.151430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.2578i | 1.94908i | 0.224217 | + | 0.974539i | \(0.428018\pi\) | ||||
−0.224217 | + | 0.974539i | \(0.571982\pi\) | |||||||
\(242\) | 2.41310i | 0.155120i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −15.3600 | −0.983326 | ||||||||
\(245\) | 10.7821i | 0.688841i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.92553 | − | 12.4691i | −0.567918 | − | 0.793387i | ||||
\(248\) | 21.1869 | 1.34537 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.0929 | −0.638333 | ||||||||
\(251\) | −17.5085 | −1.10512 | −0.552562 | − | 0.833472i | \(-0.686350\pi\) | ||||
−0.552562 | + | 0.833472i | \(0.686350\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.9850i | − | 0.879232i | ||||||
\(254\) | 1.59759i | 0.100242i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.5238 | −1.03274 | ||||||||
\(257\) | 18.3042 | 1.14179 | 0.570893 | − | 0.821025i | \(-0.306597\pi\) | ||||
0.570893 | + | 0.821025i | \(0.306597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.8961 | 1.17415 | ||||||||
\(260\) | −5.55423 | − | 7.75931i | −0.344459 | − | 0.481212i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.45672i | 0.398897i | ||||||||
\(263\) | −8.39323 | −0.517549 | −0.258774 | − | 0.965938i | \(-0.583319\pi\) | ||||
−0.258774 | + | 0.965938i | \(0.583319\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.0375i | − | 1.04661i | ||||||
\(266\) | 13.2341i | 0.811437i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 15.9406i | − | 0.973730i | ||||||
\(269\) | 21.3238 | 1.30014 | 0.650069 | − | 0.759875i | \(-0.274740\pi\) | ||||
0.650069 | + | 0.759875i | \(0.274740\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4587i | 1.12129i | 0.828057 | + | 0.560643i | \(0.189446\pi\) | ||||
−0.828057 | + | 0.560643i | \(0.810554\pi\) | |||||||
\(272\) | 1.04462 | 0.0633397 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.09382 | 0.247317 | ||||||||
\(275\) | − | 0.115721i | − | 0.00697821i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.62780 | −0.518394 | −0.259197 | − | 0.965824i | \(-0.583458\pi\) | ||||
−0.259197 | + | 0.965824i | \(0.583458\pi\) | |||||||
\(278\) | − | 12.7779i | − | 0.766367i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 22.1950i | 1.32640i | ||||||||
\(281\) | − | 3.47481i | − | 0.207290i | −0.994614 | − | 0.103645i | \(-0.966949\pi\) | ||
0.994614 | − | 0.103645i | \(-0.0330506\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7836 | −0.819348 | −0.409674 | − | 0.912232i | \(-0.634358\pi\) | ||||
−0.409674 | + | 0.912232i | \(0.634358\pi\) | |||||||
\(284\) | − | 3.13269i | − | 0.185891i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.81463 | − | 7.02545i | 0.580351 | − | 0.415424i | ||||
\(287\) | 27.2217 | 1.60684 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.734202 | 0.0431884 | ||||||||
\(290\) | −4.83229 | −0.283762 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.43917i | 0.376824i | ||||||||
\(293\) | 28.5108i | 1.66562i | 0.553559 | + | 0.832810i | \(0.313269\pi\) | ||||
−0.553559 | + | 0.832810i | \(0.686731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.5097 | −0.670120 | ||||||||
\(296\) | 15.8363 | 0.920465 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.25460 | 0.304391 | ||||||||
\(299\) | −11.0919 | + | 7.93971i | −0.641459 | + | 0.459166i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 3.09433i | − | 0.178354i | ||||||
\(302\) | 8.82583 | 0.507870 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.05499i | 0.0605078i | ||||||||
\(305\) | 29.2004i | 1.67201i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.8137i | − | 1.24497i | −0.782631 | − | 0.622486i | \(-0.786123\pi\) | ||
0.782631 | − | 0.622486i | \(-0.213877\pi\) | |||||||
\(308\) | 14.9868 | 0.853954 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 14.9450i | − | 0.848817i | ||||||
\(311\) | −6.96322 | −0.394848 | −0.197424 | − | 0.980318i | \(-0.563258\pi\) | ||||
−0.197424 | + | 0.980318i | \(0.563258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.4506 | 1.26898 | 0.634491 | − | 0.772930i | \(-0.281210\pi\) | ||||
0.634491 | + | 0.772930i | \(0.281210\pi\) | |||||||
\(314\) | 0.977678i | 0.0551736i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.9054 | 0.725983 | ||||||||
\(317\) | 10.2161i | 0.573792i | 0.957962 | + | 0.286896i | \(0.0926235\pi\) | ||||
−0.957962 | + | 0.286896i | \(0.907377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.79381i | 0.492359i | ||||||||
\(320\) | 12.3556i | 0.690700i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.7724 | 0.656053 | ||||||||
\(323\) | 17.9102i | 0.996548i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0917806 | + | 0.0656979i | −0.00509107 | + | 0.00364426i | ||||
\(326\) | −5.02477 | −0.278296 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22.8136 | 1.25967 | ||||||||
\(329\) | −19.0472 | −1.05011 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.40162i | 0.296900i | 0.988920 | + | 0.148450i | \(0.0474284\pi\) | ||||
−0.988920 | + | 0.148450i | \(0.952572\pi\) | |||||||
\(332\) | 0.634273i | 0.0348103i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.0793 | 0.660949 | ||||||||
\(335\) | −30.3042 | −1.65570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.9242 | −1.79350 | −0.896749 | − | 0.442540i | \(-0.854078\pi\) | ||||
−0.896749 | + | 0.442540i | \(0.854078\pi\) | |||||||
\(338\) | −11.1441 | − | 3.79565i | −0.606159 | − | 0.206456i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.1452i | 0.604436i | ||||||||
\(341\) | −27.1969 | −1.47279 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.53586i | − | 0.406898i | ||||||
\(344\) | − | 2.59326i | − | 0.139819i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 6.73908i | − | 0.362295i | ||||||
\(347\) | 13.6278 | 0.731579 | 0.365789 | − | 0.930698i | \(-0.380799\pi\) | ||||
0.365789 | + | 0.930698i | \(0.380799\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2746i | 0.603518i | 0.953384 | + | 0.301759i | \(0.0975738\pi\) | ||||
−0.953384 | + | 0.301759i | \(0.902426\pi\) | |||||||
\(350\) | 0.0974121 | 0.00520690 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.4597 | 1.09050 | ||||||||
\(353\) | − | 26.6308i | − | 1.41741i | −0.705504 | − | 0.708706i | \(-0.749279\pi\) | ||
0.705504 | − | 0.708706i | \(-0.250721\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.95545 | −0.316083 | ||||||||
\(356\) | − | 6.78707i | − | 0.359714i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 21.0141i | − | 1.11063i | ||||||
\(359\) | 34.9036i | 1.84214i | 0.389396 | + | 0.921071i | \(0.372684\pi\) | ||||
−0.389396 | + | 0.921071i | \(0.627316\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.912132 | 0.0480069 | ||||||||
\(362\) | − | 4.69497i | − | 0.246762i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.50846 | − | 11.8864i | −0.445964 | − | 0.623017i | ||||
\(365\) | 12.2413 | 0.640738 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.71433 | −0.141687 | −0.0708434 | − | 0.997487i | \(-0.522569\pi\) | ||||
−0.0708434 | + | 0.997487i | \(0.522569\pi\) | |||||||
\(368\) | 0.938467 | 0.0489210 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 11.1707i | − | 0.580737i | ||||||
\(371\) | − | 26.0995i | − | 1.35502i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.75096 | −0.0906613 | −0.0453307 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453307 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(374\) | −14.0974 | −0.728961 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.9629 | −0.823224 | ||||||||
\(377\) | 6.97457 | − | 4.99250i | 0.359209 | − | 0.257127i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.90941i | − | 0.149446i | −0.997204 | − | 0.0747231i | \(-0.976193\pi\) | ||
0.997204 | − | 0.0747231i | \(-0.0238073\pi\) | |||||||
\(380\) | −11.2558 | −0.577412 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 14.6174i | − | 0.747890i | ||||||
\(383\) | − | 20.4457i | − | 1.04473i | −0.852723 | − | 0.522363i | \(-0.825050\pi\) | ||
0.852723 | − | 0.522363i | \(-0.174950\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 28.4910i | − | 1.45203i | ||||||
\(386\) | 2.96968 | 0.151152 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 8.00541i | − | 0.406413i | ||||||
\(389\) | 12.9632 | 0.657261 | 0.328631 | − | 0.944459i | \(-0.393413\pi\) | ||||
0.328631 | + | 0.944459i | \(0.393413\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9320 | 0.805716 | ||||||||
\(392\) | 13.8423i | 0.699143i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.44105 | 0.324495 | ||||||||
\(395\) | − | 24.5339i | − | 1.23444i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.1809i | 1.46455i | 0.681010 | + | 0.732274i | \(0.261541\pi\) | ||||
−0.681010 | + | 0.732274i | \(0.738459\pi\) | |||||||
\(398\) | 12.5379i | 0.628467i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.00776543 | 0.000388271 | ||||||||
\(401\) | − | 22.1724i | − | 1.10723i | −0.832771 | − | 0.553617i | \(-0.813247\pi\) | ||
0.832771 | − | 0.553617i | \(-0.186753\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.4405 | + | 21.5705i | 0.769144 | + | 1.07450i | ||||
\(404\) | −5.85500 | −0.291297 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.40253 | −0.367381 | ||||||||
\(407\) | −20.3285 | −1.00765 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.09865i | 0.103772i | 0.998653 | + | 0.0518858i | \(0.0165232\pi\) | ||||
−0.998653 | + | 0.0518858i | \(0.983477\pi\) | |||||||
\(410\) | − | 16.0925i | − | 0.794750i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.49162 | 0.122753 | ||||||||
\(413\) | −17.6315 | −0.867591 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.20579 | 0.0591901 | ||||||||
\(416\) | −11.6155 | − | 16.2270i | −0.569499 | − | 0.795595i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 14.2373i | − | 0.696369i | ||||||
\(419\) | 0.391399 | 0.0191211 | 0.00956053 | − | 0.999954i | \(-0.496957\pi\) | ||||
0.00956053 | + | 0.999954i | \(0.496957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.0850i | 0.540249i | 0.962825 | + | 0.270124i | \(0.0870648\pi\) | ||||
−0.962825 | + | 0.270124i | \(0.912935\pi\) | |||||||
\(422\) | − | 13.0713i | − | 0.636301i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 21.8732i | − | 1.06226i | ||||||
\(425\) | 0.131831 | 0.00639473 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 44.7318i | 2.16472i | ||||||||
\(428\) | −9.52652 | −0.460482 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.82925 | −0.0882144 | ||||||||
\(431\) | − | 36.4573i | − | 1.75609i | −0.478580 | − | 0.878044i | \(-0.658848\pi\) | ||
0.478580 | − | 0.878044i | \(-0.341152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.82757 | 0.424226 | 0.212113 | − | 0.977245i | \(-0.431966\pi\) | ||||
0.212113 | + | 0.977245i | \(0.431966\pi\) | |||||||
\(434\) | − | 22.8940i | − | 1.09895i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.8013i | 0.565182i | ||||||||
\(437\) | 16.0901i | 0.769693i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.1344 | −1.67688 | −0.838438 | − | 0.544997i | \(-0.816531\pi\) | ||||
−0.838438 | + | 0.544997i | \(0.816531\pi\) | |||||||
\(440\) | − | 23.8774i | − | 1.13831i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.00352 | + | 11.1810i | 0.380688 | + | 0.531826i | ||||
\(443\) | 23.9052 | 1.13577 | 0.567885 | − | 0.823108i | \(-0.307762\pi\) | ||||
0.567885 | + | 0.823108i | \(0.307762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.9027 | −0.611645 | ||||||||
\(446\) | −9.96503 | −0.471858 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.9274i | 0.894236i | ||||||||
\(449\) | − | 13.9683i | − | 0.659206i | −0.944120 | − | 0.329603i | \(-0.893085\pi\) | ||
0.944120 | − | 0.329603i | \(-0.106915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.2851 | −1.37898 | ||||||||
\(452\) | 22.9309 | 1.07858 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.35180 | 0.345037 | ||||||||
\(455\) | −22.5968 | + | 16.1751i | −1.05936 | + | 0.758302i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4212i | 0.814927i | 0.913221 | + | 0.407464i | \(0.133587\pi\) | ||||
−0.913221 | + | 0.407464i | \(0.866413\pi\) | |||||||
\(458\) | −4.87021 | −0.227570 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.0126i | 0.466841i | ||||||||
\(461\) | 23.8667i | 1.11158i | 0.831322 | + | 0.555791i | \(0.187584\pi\) | ||||
−0.831322 | + | 0.555791i | \(0.812416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5373i | 0.489709i | 0.969560 | + | 0.244854i | \(0.0787402\pi\) | ||||
−0.969560 | + | 0.244854i | \(0.921260\pi\) | |||||||
\(464\) | −0.590109 | −0.0273951 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 18.2018i | − | 0.843182i | ||||||
\(467\) | −8.40923 | −0.389133 | −0.194566 | − | 0.980889i | \(-0.562330\pi\) | ||||
−0.194566 | + | 0.980889i | \(0.562330\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −46.4227 | −2.14360 | ||||||||
\(470\) | 11.2600i | 0.519387i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.7765 | −0.680142 | ||||||||
\(473\) | 3.32888i | 0.153062i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.133139i | 0.00610883i | ||||||||
\(476\) | 17.0733i | 0.782551i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.8239 | −0.586550 | ||||||||
\(479\) | − | 15.7068i | − | 0.717660i | −0.933403 | − | 0.358830i | \(-0.883176\pi\) | ||
0.933403 | − | 0.358830i | \(-0.116824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.5411 | + | 16.1230i | 0.526227 | + | 0.735145i | ||||
\(482\) | 27.4014 | 1.24810 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.14402 | −0.142910 | ||||||||
\(485\) | −15.2188 | −0.691051 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.8948i | 1.71718i | 0.512666 | + | 0.858588i | \(0.328658\pi\) | ||||
−0.512666 | + | 0.858588i | \(0.671342\pi\) | |||||||
\(488\) | 37.4884i | 1.69702i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.76420 | 0.441102 | ||||||||
\(491\) | −3.76054 | −0.169711 | −0.0848553 | − | 0.996393i | \(-0.527043\pi\) | ||||
−0.0848553 | + | 0.996393i | \(0.527043\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0181 | −0.451191 | ||||||||
\(494\) | −11.2919 | + | 8.08293i | −0.508048 | + | 0.363668i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.82505i | − | 0.0819471i | ||||||
\(497\) | −9.12309 | −0.409226 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.26147i | 0.369834i | 0.982754 | + | 0.184917i | \(0.0592016\pi\) | ||||
−0.982754 | + | 0.184917i | \(0.940798\pi\) | |||||||
\(500\) | − | 13.1500i | − | 0.588086i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.8556i | 0.707670i | ||||||||
\(503\) | −12.9954 | −0.579434 | −0.289717 | − | 0.957112i | \(-0.593561\pi\) | ||||
−0.289717 | + | 0.957112i | \(0.593561\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1307i | 0.495312i | ||||||||
\(506\) | −12.6648 | −0.563020 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.08148 | −0.0923509 | ||||||||
\(509\) | − | 26.8713i | − | 1.19105i | −0.803338 | − | 0.595524i | \(-0.796945\pi\) | ||
0.803338 | − | 0.595524i | \(-0.203055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.7523 | 0.829551 | ||||||||
\(512\) | 2.80162i | 0.123815i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 16.5762i | − | 0.731146i | ||||||
\(515\) | − | 4.73673i | − | 0.208725i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.4910 | 0.901195 | ||||||||
\(518\) | − | 17.1123i | − | 0.751870i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.9377 | + | 13.5559i | −0.830474 | + | 0.594465i | ||||
\(521\) | 14.2080 | 0.622464 | 0.311232 | − | 0.950334i | \(-0.399258\pi\) | ||||
0.311232 | + | 0.950334i | \(0.399258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.07846 | 0.309519 | 0.154760 | − | 0.987952i | \(-0.450540\pi\) | ||||
0.154760 | + | 0.987952i | \(0.450540\pi\) | |||||||
\(524\) | −8.41241 | −0.367498 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.60088i | 0.331414i | ||||||||
\(527\) | − | 30.9832i | − | 1.34965i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.68705 | −0.377698 | ||||||||
\(530\) | −15.4291 | −0.670198 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.2427 | −0.747564 | ||||||||
\(533\) | 16.6260 | + | 23.2267i | 0.720151 | + | 1.00606i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.1105i | 0.782987i | ||||||||
\(536\) | −38.9054 | −1.68046 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 19.3108i | − | 0.832548i | ||||||
\(539\) | − | 17.7689i | − | 0.765362i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 7.18897i | − | 0.309078i | −0.987987 | − | 0.154539i | \(-0.950611\pi\) | ||
0.987987 | − | 0.154539i | \(-0.0493892\pi\) | |||||||
\(542\) | 16.7161 | 0.718020 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.3080i | 0.999322i | ||||||||
\(545\) | 22.4351 | 0.961016 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.7775 | −1.35871 | −0.679353 | − | 0.733811i | \(-0.737740\pi\) | ||||
−0.679353 | + | 0.733811i | \(0.737740\pi\) | |||||||
\(548\) | 5.33381i | 0.227849i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.104796 | −0.00446852 | ||||||||
\(551\) | − | 10.1175i | − | 0.431018i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 37.5832i | − | 1.59820i | ||||||
\(554\) | 7.81331i | 0.331956i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.6482 | 0.706042 | ||||||||
\(557\) | 32.2223i | 1.36530i | 0.730745 | + | 0.682650i | \(0.239173\pi\) | ||||
−0.730745 | + | 0.682650i | \(0.760827\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.64021 | − | 1.88990i | 0.111669 | − | 0.0799343i | ||||
\(560\) | 1.91189 | 0.0807919 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.14678 | −0.132739 | ||||||||
\(563\) | −33.6514 | −1.41824 | −0.709119 | − | 0.705089i | \(-0.750907\pi\) | ||||
−0.709119 | + | 0.705089i | \(0.750907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 43.5931i | − | 1.83397i | ||||||
\(566\) | 12.4824i | 0.524672i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.64578 | −0.320810 | ||||||||
\(569\) | −11.3359 | −0.475224 | −0.237612 | − | 0.971360i | \(-0.576365\pi\) | ||||
−0.237612 | + | 0.971360i | \(0.576365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.254521 | −0.0106514 | −0.00532568 | − | 0.999986i | \(-0.501695\pi\) | ||||
−0.00532568 | + | 0.999986i | \(0.501695\pi\) | |||||||
\(572\) | 9.15341 | + | 12.7874i | 0.382723 | + | 0.534668i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 24.6518i | − | 1.02895i | ||||||
\(575\) | 0.118434 | 0.00493903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.91400i | 0.0796807i | 0.999206 | + | 0.0398403i | \(0.0126849\pi\) | ||||
−0.999206 | + | 0.0398403i | \(0.987315\pi\) | |||||||
\(578\) | − | 0.664891i | − | 0.0276558i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 6.29595i | − | 0.261425i | ||||||
\(581\) | 1.84714 | 0.0766324 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.0779i | 1.16287i | ||||||||
\(584\) | 15.7157 | 0.650321 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.8193 | 1.06659 | ||||||||
\(587\) | − | 8.88440i | − | 0.366699i | −0.983048 | − | 0.183349i | \(-0.941306\pi\) | ||
0.983048 | − | 0.183349i | \(-0.0586939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.2906 | 1.28931 | ||||||||
\(590\) | 10.4231i | 0.429113i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.36414i | − | 0.0560659i | ||||||
\(593\) | − | 43.1136i | − | 1.77046i | −0.465152 | − | 0.885231i | \(-0.654000\pi\) | ||
0.465152 | − | 0.885231i | \(-0.346000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32.4574 | 1.33062 | ||||||||
\(596\) | 6.84618i | 0.280430i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.19018 | + | 10.0447i | 0.294028 | + | 0.410760i | ||||
\(599\) | −11.1974 | −0.457512 | −0.228756 | − | 0.973484i | \(-0.573466\pi\) | ||||
−0.228756 | + | 0.973484i | \(0.573466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.92545 | 0.241704 | 0.120852 | − | 0.992671i | \(-0.461437\pi\) | ||||
0.120852 | + | 0.992671i | \(0.461437\pi\) | |||||||
\(602\) | −2.80221 | −0.114210 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.4991i | 0.467892i | ||||||||
\(605\) | 5.97698i | 0.242999i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.06940 | 0.205760 | 0.102880 | − | 0.994694i | \(-0.467194\pi\) | ||||
0.102880 | + | 0.994694i | \(0.467194\pi\) | |||||||
\(608\) | −23.5393 | −0.954643 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.4438 | 1.07068 | ||||||||
\(611\) | −11.6334 | − | 16.2519i | −0.470635 | − | 0.657482i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.6393i | − | 0.995173i | −0.867414 | − | 0.497587i | \(-0.834220\pi\) | ||
0.867414 | − | 0.497587i | \(-0.165780\pi\) | |||||||
\(614\) | −19.7544 | −0.797222 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 36.5775i | − | 1.47375i | ||||||
\(617\) | 43.9864i | 1.77083i | 0.464806 | + | 0.885413i | \(0.346124\pi\) | ||||
−0.464806 | + | 0.885413i | \(0.653876\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 20.5512i | − | 0.826024i | −0.910726 | − | 0.413012i | \(-0.864477\pi\) | ||
0.910726 | − | 0.413012i | \(-0.135523\pi\) | |||||||
\(620\) | 19.4717 | 0.782002 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.30587i | 0.252842i | ||||||||
\(623\) | −19.7654 | −0.791885 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.1555 | −1.00622 | ||||||||
\(626\) | − | 20.3312i | − | 0.812597i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.27381 | −0.0508305 | ||||||||
\(629\) | − | 23.1586i | − | 0.923392i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 25.1460i | − | 1.00105i | −0.865723 | − | 0.500523i | \(-0.833141\pi\) | ||
0.865723 | − | 0.500523i | \(-0.166859\pi\) | |||||||
\(632\) | − | 31.4974i | − | 1.25290i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.25165 | 0.367430 | ||||||||
\(635\) | 3.95704i | 0.157030i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.0929 | + | 10.0879i | −0.558382 | + | 0.399698i | ||||
\(638\) | 7.96365 | 0.315284 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.6404 | −0.539183 | ||||||||
\(641\) | −33.3421 | −1.31693 | −0.658467 | − | 0.752609i | \(-0.728795\pi\) | ||||
−0.658467 | + | 0.752609i | \(0.728795\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 31.3801i | − | 1.23751i | −0.785585 | − | 0.618754i | \(-0.787638\pi\) | ||
0.785585 | − | 0.618754i | \(-0.212362\pi\) | |||||||
\(644\) | 15.3382i | 0.604411i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.2194 | 0.638143 | ||||||||
\(647\) | −47.5495 | −1.86936 | −0.934681 | − | 0.355486i | \(-0.884315\pi\) | ||||
−0.934681 | + | 0.355486i | \(0.884315\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.9680 | 0.744561 | ||||||||
\(650\) | 0.0594958 | + | 0.0831162i | 0.00233362 | + | 0.00326008i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6.54673i | − | 0.256390i | ||||||
\(653\) | −27.7456 | −1.08577 | −0.542884 | − | 0.839808i | \(-0.682668\pi\) | ||||
−0.542884 | + | 0.839808i | \(0.682668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.9925i | 0.624880i | ||||||||
\(656\) | − | 1.96518i | − | 0.0767273i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.2491i | 0.672440i | ||||||||
\(659\) | 15.6188 | 0.608422 | 0.304211 | − | 0.952605i | \(-0.401607\pi\) | ||||
0.304211 | + | 0.952605i | \(0.401607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9164i | 0.696869i | 0.937333 | + | 0.348434i | \(0.113287\pi\) | ||||
−0.937333 | + | 0.348434i | \(0.886713\pi\) | |||||||
\(662\) | 4.89169 | 0.190121 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.54803 | 0.0600754 | ||||||||
\(665\) | 32.7794i | 1.27113i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | −0.348481 | ||||||||
\(668\) | 15.7380i | 0.608922i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.4434i | 1.06023i | ||||||||
\(671\) | − | 48.1225i | − | 1.85775i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.89919 | −0.227397 | −0.113699 | − | 0.993515i | \(-0.536270\pi\) | ||||
−0.113699 | + | 0.993515i | \(0.536270\pi\) | |||||||
\(674\) | 29.8161i | 1.14847i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.94532 | − | 14.5196i | 0.190205 | − | 0.558444i | ||||
\(677\) | 27.4090 | 1.05341 | 0.526707 | − | 0.850047i | \(-0.323427\pi\) | ||||
0.526707 | + | 0.850047i | \(0.323427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.3135 | −0.894690 | ||||||||
\(680\) | 27.2016 | 1.04313 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.6294i | 0.943109i | ||||||||
\(683\) | − | 16.0989i | − | 0.616006i | −0.951385 | − | 0.308003i | \(-0.900339\pi\) | ||
0.951385 | − | 0.308003i | \(-0.0996607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1399 | 0.387427 | ||||||||
\(686\) | −6.82445 | −0.260559 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.223385 | −0.00851646 | ||||||||
\(689\) | 22.2692 | − | 15.9406i | 0.848390 | − | 0.607290i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 27.6824i | − | 1.05309i | −0.850148 | − | 0.526543i | \(-0.823488\pi\) | ||
0.850148 | − | 0.526543i | \(-0.176512\pi\) | |||||||
\(692\) | 8.78030 | 0.333777 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 12.3413i | − | 0.468469i | ||||||
\(695\) | − | 31.6494i | − | 1.20053i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.3621i | − | 1.26368i | ||||||
\(698\) | 10.2103 | 0.386465 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.126918i | 0.00479703i | ||||||||
\(701\) | −10.0776 | −0.380624 | −0.190312 | − | 0.981724i | \(-0.560950\pi\) | ||||
−0.190312 | + | 0.981724i | \(0.560950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.3883 | 0.882108 | ||||||||
\(704\) | − | 20.3621i | − | 0.767427i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.1167 | −0.907645 | ||||||||
\(707\) | 17.0511i | 0.641271i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 3.22720i | − | 0.121200i | −0.998162 | − | 0.0606000i | \(-0.980699\pi\) | ||
0.998162 | − | 0.0606000i | \(-0.0193014\pi\) | |||||||
\(710\) | 5.39324i | 0.202405i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.5648 | −0.620793 | ||||||||
\(713\) | − | 27.8346i | − | 1.04241i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.3097 | − | 17.4012i | 0.909131 | − | 0.650769i | ||||
\(716\) | 27.3792 | 1.02321 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31.6086 | 1.17962 | ||||||||
\(719\) | −30.0712 | −1.12147 | −0.560733 | − | 0.827996i | \(-0.689481\pi\) | ||||
−0.560733 | + | 0.827996i | \(0.689481\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 7.25614i | − | 0.270233i | ||||||
\(722\) | − | 0.826023i | − | 0.0307414i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.11704 | 0.227338 | ||||||||
\(725\) | −0.0744713 | −0.00276579 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.3772 | −0.718660 | −0.359330 | − | 0.933210i | \(-0.616995\pi\) | ||||
−0.359330 | + | 0.933210i | \(0.616995\pi\) | |||||||
\(728\) | −29.0105 | + | 20.7661i | −1.07520 | + | 0.769643i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 11.0857i | − | 0.410299i | ||||||
\(731\) | −3.79232 | −0.140264 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4725i | 0.903911i | 0.892041 | + | 0.451955i | \(0.149273\pi\) | ||||
−0.892041 | + | 0.451955i | \(0.850727\pi\) | |||||||
\(734\) | 2.45809i | 0.0907297i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.9394i | 0.771835i | ||||||||
\(737\) | 49.9416 | 1.83962 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.30687i | 0.121645i | 0.998149 | + | 0.0608226i | \(0.0193724\pi\) | ||||
−0.998149 | + | 0.0608226i | \(0.980628\pi\) | |||||||
\(740\) | 14.5542 | 0.535024 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.6357 | −0.867692 | ||||||||
\(743\) | 17.4815i | 0.641335i | 0.947192 | + | 0.320667i | \(0.103907\pi\) | ||||
−0.947192 | + | 0.320667i | \(0.896093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.0150 | 0.476834 | ||||||||
\(746\) | 1.58566i | 0.0580553i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 18.3674i | − | 0.671580i | ||||||
\(749\) | 27.7433i | 1.01372i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.5843 | −1.04306 | −0.521528 | − | 0.853234i | \(-0.674638\pi\) | ||||
−0.521528 | + | 0.853234i | \(0.674638\pi\) | |||||||
\(752\) | 1.37505i | 0.0501430i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.52119 | − | 6.31615i | −0.164652 | − | 0.230021i | ||||
\(755\) | 21.8606 | 0.795587 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.9611 | 0.434733 | 0.217367 | − | 0.976090i | \(-0.430253\pi\) | ||||
0.217367 | + | 0.976090i | \(0.430253\pi\) | |||||||
\(758\) | −2.63475 | −0.0956983 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.4714i | 0.996494i | ||||||||
\(761\) | 2.12842i | 0.0771553i | 0.999256 | + | 0.0385777i | \(0.0122827\pi\) | ||||
−0.999256 | + | 0.0385777i | \(0.987717\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.3681 | 1.24421 | ||||||||
\(764\) | 19.0449 | 0.689019 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.5156 | −0.668994 | ||||||||
\(767\) | −10.7687 | − | 15.0440i | −0.388835 | − | 0.543207i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7.65086i | − | 0.275897i | −0.990439 | − | 0.137949i | \(-0.955949\pi\) | ||
0.990439 | − | 0.137949i | \(-0.0440509\pi\) | |||||||
\(770\) | −25.8013 | −0.929815 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.86917i | 0.139254i | ||||||||
\(773\) | 24.6440i | 0.886383i | 0.896427 | + | 0.443191i | \(0.146154\pi\) | ||||
−0.896427 | + | 0.443191i | \(0.853846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.230320i | − | 0.00827333i | ||||||
\(776\) | −19.5384 | −0.701386 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 11.7394i | − | 0.420880i | ||||||
\(779\) | 33.6931 | 1.20718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.81463 | 0.351195 | ||||||||
\(782\) | − | 14.4280i | − | 0.515943i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.19238 | 0.0425851 | ||||||||
\(785\) | 2.42159i | 0.0864304i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 41.8679i | − | 1.49243i | −0.665706 | − | 0.746214i | \(-0.731869\pi\) | ||
0.665706 | − | 0.746214i | \(-0.268131\pi\) | |||||||
\(788\) | 8.39199i | 0.298952i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.2178 | −0.790475 | ||||||||
\(791\) | − | 66.7797i | − | 2.37441i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.1671 | + | 27.3205i | −1.35535 | + | 0.970181i | ||||
\(794\) | 26.4261 | 0.937828 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.3355 | −0.578996 | ||||||||
\(797\) | −41.7563 | −1.47908 | −0.739541 | − | 0.673111i | \(-0.764957\pi\) | ||||
−0.739541 | + | 0.673111i | \(0.764957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.3437i | 0.825842i | ||||||||
\(800\) | 0.173265i | 0.00612583i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.0792 | −0.709022 | ||||||||
\(803\) | −20.1737 | −0.711915 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.1590 | 1.02772 | ||||||||
\(806\) | 19.5341 | − | 13.9828i | 0.688061 | − | 0.492524i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.2900i | 0.502720i | ||||||||
\(809\) | 45.2476 | 1.59082 | 0.795410 | − | 0.606072i | \(-0.207256\pi\) | ||||
0.795410 | + | 0.606072i | \(0.207256\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.8820i | 1.85694i | 0.371410 | + | 0.928469i | \(0.378874\pi\) | ||||
−0.371410 | + | 0.928469i | \(0.621126\pi\) | |||||||
\(812\) | − | 9.64469i | − | 0.338462i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.4094i | 0.645249i | ||||||||
\(815\) | −12.4458 | −0.435956 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 3.82994i | − | 0.133993i | ||||||
\(818\) | 1.90053 | 0.0664505 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.9667 | 0.732190 | ||||||||
\(821\) | 34.4222i | 1.20134i | 0.799496 | + | 0.600671i | \(0.205100\pi\) | ||||
−0.799496 | + | 0.600671i | \(0.794900\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.9971 | −0.418191 | −0.209096 | − | 0.977895i | \(-0.567052\pi\) | ||||
−0.209096 | + | 0.977895i | \(0.567052\pi\) | |||||||
\(824\) | − | 6.08116i | − | 0.211847i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.9671i | 0.555565i | ||||||||
\(827\) | 4.35092i | 0.151296i | 0.997135 | + | 0.0756482i | \(0.0241026\pi\) | ||||
−0.997135 | + | 0.0756482i | \(0.975897\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.6204 | 1.58446 | 0.792230 | − | 0.610222i | \(-0.208920\pi\) | ||||
0.792230 | + | 0.610222i | \(0.208920\pi\) | |||||||
\(830\) | − | 1.09196i | − | 0.0379026i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.1497 | + | 11.5602i | −0.559889 | + | 0.400777i | ||||
\(833\) | 20.2427 | 0.701367 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 29.9190 | 1.03539 | ||||||||
\(836\) | 18.5497 | 0.641554 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 0.354449i | − | 0.0122442i | ||||||
\(839\) | − | 24.6675i | − | 0.851615i | −0.904814 | − | 0.425808i | \(-0.859990\pi\) | ||
0.904814 | − | 0.425808i | \(-0.140010\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3408 | −0.804855 | ||||||||
\(842\) | 10.0385 | 0.345950 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.0305 | 0.586214 | ||||||||
\(845\) | −27.6026 | − | 9.40138i | −0.949559 | − | 0.323417i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.15606i | 0.314606i | ||||||||
\(848\) | −1.88417 | −0.0647027 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 0.119386i | − | 0.00409489i | ||||||
\(851\) | − | 20.8051i | − | 0.713190i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 26.5198i | − | 0.908021i | −0.890996 | − | 0.454010i | \(-0.849993\pi\) | ||
0.890996 | − | 0.454010i | \(-0.150007\pi\) | |||||||
\(854\) | 40.5089 | 1.38619 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.2508i | 0.794697i | ||||||||
\(857\) | −6.40948 | −0.218944 | −0.109472 | − | 0.993990i | \(-0.534916\pi\) | ||||
−0.109472 | + | 0.993990i | \(0.534916\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5996 | 0.873446 | 0.436723 | − | 0.899596i | \(-0.356139\pi\) | ||||
0.436723 | + | 0.899596i | \(0.356139\pi\) | |||||||
\(860\) | − | 2.38332i | − | 0.0812706i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.0156 | −1.12452 | ||||||||
\(863\) | 48.4823i | 1.65036i | 0.564873 | + | 0.825178i | \(0.308925\pi\) | ||||
−0.564873 | + | 0.825178i | \(0.691075\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 16.6919i | − | 0.567542i | ||||||
\(866\) | − | 7.99421i | − | 0.271654i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 29.8284 | 1.01244 | ||||||||
\(869\) | 40.4321i | 1.37156i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.3533 | − | 39.6098i | −0.960713 | − | 1.34213i | ||||
\(872\) | 28.8029 | 0.975389 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.5711 | 0.492876 | ||||||||
\(875\) | −38.2957 | −1.29463 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.1795i | 1.05286i | 0.850219 | + | 0.526429i | \(0.176469\pi\) | ||||
−0.850219 | + | 0.526429i | \(0.823531\pi\) | |||||||
\(878\) | 31.8176i | 1.07379i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.05681 | −0.0693350 | ||||||||
\(881\) | −49.6614 | −1.67314 | −0.836568 | − | 0.547863i | \(-0.815442\pi\) | ||||
−0.836568 | + | 0.547863i | \(0.815442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.3523 | 1.02144 | 0.510718 | − | 0.859748i | \(-0.329380\pi\) | ||||
0.510718 | + | 0.859748i | \(0.329380\pi\) | |||||||
\(884\) | −14.5676 | + | 10.4277i | −0.489962 | + | 0.350722i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 21.6485i | − | 0.727294i | ||||||
\(887\) | 12.8432 | 0.431233 | 0.215616 | − | 0.976478i | \(-0.430824\pi\) | ||||
0.215616 | + | 0.976478i | \(0.430824\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.06173i | 0.203304i | ||||||||
\(890\) | 11.6846i | 0.391669i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 12.9834i | − | 0.434715i | ||||||
\(893\) | −23.5754 | −0.788919 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 52.0496i | − | 1.73982i | ||||||
\(896\) | −20.8955 | −0.698071 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.6497 | −0.422125 | ||||||||
\(899\) | 17.5024i | 0.583738i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.9869 | −1.06564 | ||||||||
\(902\) | 26.5205i | 0.883035i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 55.9660i | − | 1.86140i | ||||||
\(905\) | − | 11.6289i | − | 0.386557i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.5986 | −0.683965 | −0.341983 | − | 0.939706i | \(-0.611098\pi\) | ||||
−0.341983 | + | 0.939706i | \(0.611098\pi\) | |||||||
\(908\) | 9.57860i | 0.317877i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14.6481 | + | 20.4636i | 0.485581 | + | 0.678362i | ||||
\(911\) | 42.3899 | 1.40444 | 0.702219 | − | 0.711961i | \(-0.252193\pi\) | ||||
0.702219 | + | 0.711961i | \(0.252193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.98716 | −0.0657653 | ||||||||
\(914\) | 15.7765 | 0.521842 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 6.34535i | − | 0.209656i | ||||||
\(917\) | 24.4988i | 0.809021i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.7987 | −1.41180 | −0.705899 | − | 0.708313i | \(-0.749457\pi\) | ||||
−0.705899 | + | 0.708313i | \(0.749457\pi\) | |||||||
\(920\) | 24.4373 | 0.805672 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.6136 | 0.711805 | ||||||||
\(923\) | −5.57205 | − | 7.78420i | −0.183406 | − | 0.256220i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 0.172154i | − | 0.00566038i | ||||||
\(926\) | 9.54253 | 0.313587 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 13.1667i | − | 0.432218i | ||||||
\(929\) | 11.8059i | 0.387340i | 0.981067 | + | 0.193670i | \(0.0620391\pi\) | ||||
−0.981067 | + | 0.193670i | \(0.937961\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.4435i | 0.670009i | ||||||||
\(932\) | 23.7150 | 0.776810 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.61537i | 0.249183i | ||||||||
\(935\) | −34.9177 | −1.14193 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.7925 | 0.809935 | 0.404967 | − | 0.914331i | \(-0.367283\pi\) | ||||
0.404967 | + | 0.914331i | \(0.367283\pi\) | |||||||
\(938\) | 42.0402i | 1.37266i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.6706 | −0.478503 | ||||||||
\(941\) | − | 23.8292i | − | 0.776810i | −0.921489 | − | 0.388405i | \(-0.873026\pi\) | ||
0.921489 | − | 0.388405i | \(-0.126974\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 29.9717i | − | 0.976014i | ||||||
\(944\) | 1.27285i | 0.0414278i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.01462 | 0.0980138 | ||||||||
\(947\) | 49.0208i | 1.59296i | 0.604664 | + | 0.796480i | \(0.293307\pi\) | ||||
−0.604664 | + | 0.796480i | \(0.706693\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.4532 | + | 16.0002i | 0.371786 | + | 0.519389i | ||||
\(950\) | 0.120570 | 0.00391181 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 41.6697 | 1.35052 | ||||||||
\(953\) | 7.78372 | 0.252140 | 0.126070 | − | 0.992021i | \(-0.459764\pi\) | ||||
0.126070 | + | 0.992021i | \(0.459764\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 36.2055i | − | 1.17158i | ||||||
\(956\) | − | 16.7081i | − | 0.540379i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.2240 | −0.459556 | ||||||||
\(959\) | 15.5332 | 0.501594 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.1303 | −0.746137 | ||||||||
\(962\) | 14.6009 | − | 10.4515i | 0.470752 | − | 0.336971i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.7011i | 1.14985i | ||||||||
\(965\) | 7.35554 | 0.236783 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.5960i | 1.20900i | 0.796603 | + | 0.604502i | \(0.206628\pi\) | ||||
−0.796603 | + | 0.604502i | \(0.793372\pi\) | |||||||
\(968\) | 7.67342i | 0.246633i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.7821i | 0.442517i | ||||||||
\(971\) | −9.16512 | −0.294123 | −0.147061 | − | 0.989127i | \(-0.546981\pi\) | ||||
−0.147061 | + | 0.989127i | \(0.546981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 48.4833i | − | 1.55430i | ||||||
\(974\) | 34.3174 | 1.09960 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.22926 | 0.103366 | ||||||||
\(977\) | 47.3477i | 1.51479i | 0.652959 | + | 0.757394i | \(0.273528\pi\) | ||||
−0.652959 | + | 0.757394i | \(0.726472\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.2637 | 0.679590 | ||||||||
\(980\) | 12.7217i | 0.406380i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.40553i | 0.108675i | ||||||||
\(983\) | 16.2390i | 0.517943i | 0.965885 | + | 0.258972i | \(0.0833836\pi\) | ||||
−0.965885 | + | 0.258972i | \(0.916616\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.9537 | 0.508328 | ||||||||
\(986\) | 9.07232i | 0.288922i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.5312 | − | 14.7122i | −0.335042 | − | 0.468056i | ||||
\(989\) | −3.40693 | −0.108334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7634 | −1.19959 | −0.599797 | − | 0.800152i | \(-0.704752\pi\) | ||||
−0.599797 | + | 0.800152i | \(0.704752\pi\) | |||||||
\(992\) | 40.7211 | 1.29289 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.26184i | 0.262049i | ||||||||
\(995\) | 31.0548i | 0.984505i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.6566 | 1.50930 | 0.754649 | − | 0.656128i | \(-0.227807\pi\) | ||||
0.754649 | + | 0.656128i | \(0.227807\pi\) | |||||||
\(998\) | 7.48156 | 0.236824 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1053.2.b.j.649.5 | 10 | ||
3.2 | odd | 2 | 1053.2.b.i.649.6 | 10 | |||
9.2 | odd | 6 | 351.2.t.c.64.6 | 20 | |||
9.4 | even | 3 | 117.2.t.c.25.6 | yes | 20 | ||
9.5 | odd | 6 | 351.2.t.c.181.5 | 20 | |||
9.7 | even | 3 | 117.2.t.c.103.5 | yes | 20 | ||
13.12 | even | 2 | inner | 1053.2.b.j.649.6 | 10 | ||
39.38 | odd | 2 | 1053.2.b.i.649.5 | 10 | |||
117.25 | even | 6 | 117.2.t.c.103.6 | yes | 20 | ||
117.38 | odd | 6 | 351.2.t.c.64.5 | 20 | |||
117.77 | odd | 6 | 351.2.t.c.181.6 | 20 | |||
117.103 | even | 6 | 117.2.t.c.25.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.t.c.25.5 | ✓ | 20 | 117.103 | even | 6 | ||
117.2.t.c.25.6 | yes | 20 | 9.4 | even | 3 | ||
117.2.t.c.103.5 | yes | 20 | 9.7 | even | 3 | ||
117.2.t.c.103.6 | yes | 20 | 117.25 | even | 6 | ||
351.2.t.c.64.5 | 20 | 117.38 | odd | 6 | |||
351.2.t.c.64.6 | 20 | 9.2 | odd | 6 | |||
351.2.t.c.181.5 | 20 | 9.5 | odd | 6 | |||
351.2.t.c.181.6 | 20 | 117.77 | odd | 6 | |||
1053.2.b.i.649.5 | 10 | 39.38 | odd | 2 | |||
1053.2.b.i.649.6 | 10 | 3.2 | odd | 2 | |||
1053.2.b.j.649.5 | 10 | 1.1 | even | 1 | trivial | ||
1053.2.b.j.649.6 | 10 | 13.12 | even | 2 | inner |