Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(109,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("1080.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3x^{18} + 8x^{16} - 24x^{14} + 56x^{12} - 92x^{10} + 224x^{8} - 384x^{6} + 512x^{4} - 768x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(1.37859 - 0.315404i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.109 |
Dual form | 1080.2.d.i.109.2 |
$q$-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 \(\left(\mathbb{Z}/1080\mathbb{Z}\right)^\times\).
\(n\) | \(217\) | \(271\) | \(541\) | \(1001\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.37859 | − | 0.315404i | −0.974813 | − | 0.223024i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.80104 | + | 0.869628i | 0.900520 | + | 0.434814i | ||||
\(5\) | 2.03021 | + | 0.937151i | 0.907937 | + | 0.419107i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.36920i | 1.27344i | 0.771096 | + | 0.636719i | \(0.219709\pi\) | ||||
−0.771096 | + | 0.636719i | \(0.780291\pi\) | |||||||
\(8\) | −2.20862 | − | 1.76692i | −0.780865 | − | 0.624700i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.50325 | − | 1.93229i | −0.791598 | − | 0.611043i | ||||
\(11\) | − | 4.10347i | − | 1.23724i | −0.785689 | − | 0.618622i | \(-0.787691\pi\) | ||
0.785689 | − | 0.618622i | \(-0.212309\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.13592 | −1.70180 | −0.850899 | − | 0.525330i | \(-0.823942\pi\) | ||||
−0.850899 | + | 0.525330i | \(0.823942\pi\) | |||||||
\(14\) | 1.06266 | − | 4.64476i | 0.284008 | − | 1.24136i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.48750 | + | 3.13247i | 0.621874 | + | 0.783117i | ||||
\(17\) | 7.47638i | 1.81329i | 0.421895 | + | 0.906645i | \(0.361365\pi\) | ||||
−0.421895 | + | 0.906645i | \(0.638635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.20559i | 1.42366i | 0.702352 | + | 0.711830i | \(0.252133\pi\) | ||||
−0.702352 | + | 0.711830i | \(0.747867\pi\) | |||||||
\(20\) | 2.84152 | + | 3.45337i | 0.635382 | + | 0.772198i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.29425 | + | 5.65702i | −0.275935 | + | 1.20608i | ||||
\(23\) | − | 3.15814i | − | 0.658518i | −0.944240 | − | 0.329259i | \(-0.893201\pi\) | ||
0.944240 | − | 0.329259i | \(-0.106799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.24349 | + | 3.80523i | 0.648699 | + | 0.761045i | ||||
\(26\) | 8.45894 | + | 1.93529i | 1.65893 | + | 0.379542i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.92995 | + | 6.06807i | −0.553708 | + | 1.14676i | ||||
\(29\) | − | 1.34325i | − | 0.249436i | −0.992192 | − | 0.124718i | \(-0.960197\pi\) | ||
0.992192 | − | 0.124718i | \(-0.0398025\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.229172 | 0.0411605 | 0.0205802 | − | 0.999788i | \(-0.493449\pi\) | ||||
0.0205802 | + | 0.999788i | \(0.493449\pi\) | |||||||
\(32\) | −2.44125 | − | 5.10297i | −0.431557 | − | 0.902086i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.35808 | − | 10.3069i | 0.404408 | − | 1.76762i | ||||
\(35\) | −3.15745 | + | 6.84018i | −0.533707 | + | 1.15620i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.64792 | −0.928512 | −0.464256 | − | 0.885701i | \(-0.653678\pi\) | ||||
−0.464256 | + | 0.885701i | \(0.653678\pi\) | |||||||
\(38\) | 1.95727 | − | 8.55499i | 0.317511 | − | 1.38780i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.82809 | − | 5.65702i | −0.447160 | − | 0.894454i | ||||
\(41\) | −4.52568 | −0.706793 | −0.353397 | − | 0.935474i | \(-0.614973\pi\) | ||||
−0.353397 | + | 0.935474i | \(0.614973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.02966 | −0.309520 | −0.154760 | − | 0.987952i | \(-0.549460\pi\) | ||||
−0.154760 | + | 0.987952i | \(0.549460\pi\) | |||||||
\(44\) | 3.56849 | − | 7.39052i | 0.537971 | − | 1.11416i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.996090 | + | 4.35379i | −0.146865 | + | 0.641932i | ||||
\(47\) | − | 1.67033i | − | 0.243642i | −0.992552 | − | 0.121821i | \(-0.961127\pi\) | ||
0.992552 | − | 0.121821i | \(-0.0388734\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.35151 | −0.621645 | ||||||||
\(50\) | −3.27128 | − | 6.26887i | −0.462629 | − | 0.886552i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.0510 | − | 5.33596i | −1.53250 | − | 0.739965i | ||||
\(53\) | −10.1003 | −1.38738 | −0.693689 | − | 0.720274i | \(-0.744016\pi\) | ||||
−0.693689 | + | 0.720274i | \(0.744016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.84558 | − | 8.33091i | 0.518537 | − | 1.12334i | ||||
\(56\) | 5.95310 | − | 7.44128i | 0.795517 | − | 0.994383i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.423667 | + | 1.85180i | −0.0556302 | + | 0.243153i | ||||
\(59\) | 3.07651i | 0.400527i | 0.979742 | + | 0.200263i | \(0.0641798\pi\) | ||||
−0.979742 | + | 0.200263i | \(0.935820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.762740i | − | 0.0976589i | −0.998807 | − | 0.0488294i | \(-0.984451\pi\) | ||
0.998807 | − | 0.0488294i | \(-0.0155491\pi\) | |||||||
\(62\) | −0.315935 | − | 0.0722817i | −0.0401237 | − | 0.00917978i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.75600 | + | 7.80490i | 0.219500 | + | 0.975613i | ||||
\(65\) | −12.4572 | − | 5.75028i | −1.54512 | − | 0.713235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.8657 | 1.69396 | 0.846980 | − | 0.531625i | \(-0.178418\pi\) | ||||
0.846980 | + | 0.531625i | \(0.178418\pi\) | |||||||
\(68\) | −6.50167 | + | 13.4653i | −0.788443 | + | 1.63290i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.51026 | − | 8.43396i | 0.778125 | − | 1.00805i | ||||
\(71\) | −1.26579 | −0.150222 | −0.0751110 | − | 0.997175i | \(-0.523931\pi\) | ||||
−0.0751110 | + | 0.997175i | \(0.523931\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9347i | 1.63094i | 0.578801 | + | 0.815469i | \(0.303521\pi\) | ||||
−0.578801 | + | 0.815469i | \(0.696479\pi\) | |||||||
\(74\) | 7.78618 | + | 1.78137i | 0.905125 | + | 0.207081i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.39655 | + | 11.1765i | −0.619027 | + | 1.28204i | ||||
\(77\) | 13.8254 | 1.57555 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.245252 | 0.0275930 | 0.0137965 | − | 0.999905i | \(-0.495608\pi\) | ||||
0.0137965 | + | 0.999905i | \(0.495608\pi\) | |||||||
\(80\) | 2.11454 | + | 8.69073i | 0.236412 | + | 0.971653i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.23908 | + | 1.42742i | 0.688991 | + | 0.157632i | ||||
\(83\) | 13.3602 | 1.46647 | 0.733234 | − | 0.679976i | \(-0.238010\pi\) | ||||
0.733234 | + | 0.679976i | \(0.238010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00650 | + | 15.1786i | −0.759962 | + | 1.64635i | ||||
\(86\) | 2.79807 | + | 0.640162i | 0.301724 | + | 0.0690305i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.25050 | + | 9.06301i | −0.772906 | + | 0.966120i | ||||
\(89\) | −8.64631 | −0.916507 | −0.458254 | − | 0.888821i | \(-0.651525\pi\) | ||||
−0.458254 | + | 0.888821i | \(0.651525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20.6731i | − | 2.16713i | ||||||
\(92\) | 2.74641 | − | 5.68794i | 0.286333 | − | 0.593009i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.526827 | + | 2.30270i | −0.0543381 | + | 0.237506i | ||||
\(95\) | −5.81558 | + | 12.5986i | −0.596666 | + | 1.29259i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.2906i | − | 1.24792i | −0.781457 | − | 0.623959i | \(-0.785523\pi\) | ||
0.781457 | − | 0.623959i | \(-0.214477\pi\) | |||||||
\(98\) | 5.99897 | + | 1.37248i | 0.605987 | + | 0.138642i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.53254 | + | 9.67400i | 0.253254 | + | 0.967400i | ||||
\(101\) | 12.9175i | 1.28534i | 0.766142 | + | 0.642672i | \(0.222174\pi\) | ||||
−0.766142 | + | 0.642672i | \(0.777826\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6484i | 1.14776i | 0.818941 | + | 0.573878i | \(0.194561\pi\) | ||||
−0.818941 | + | 0.573878i | \(0.805439\pi\) | |||||||
\(104\) | 13.5519 | + | 10.8417i | 1.32887 | + | 1.06311i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.9242 | + | 3.18566i | 1.35243 | + | 0.309419i | ||||
\(107\) | −5.05116 | −0.488314 | −0.244157 | − | 0.969736i | \(-0.578511\pi\) | ||||
−0.244157 | + | 0.969736i | \(0.578511\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.118695i | 0.0113689i | 0.999984 | + | 0.00568447i | \(0.00180943\pi\) | ||||
−0.999984 | + | 0.00568447i | \(0.998191\pi\) | |||||||
\(110\) | −7.92909 | + | 10.2720i | −0.756009 | + | 0.979400i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.5539 | + | 8.38087i | −0.997251 | + | 0.791918i | ||||
\(113\) | 1.90210i | 0.178934i | 0.995990 | + | 0.0894671i | \(0.0285164\pi\) | ||||
−0.995990 | + | 0.0894671i | \(0.971484\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.95966 | − | 6.41169i | 0.275989 | − | 0.597893i | ||||
\(116\) | 1.16813 | − | 2.41925i | 0.108458 | − | 0.224622i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.970342 | − | 4.24125i | 0.0893272 | − | 0.390439i | ||||
\(119\) | −25.1894 | −2.30911 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.83850 | −0.530773 | ||||||||
\(122\) | −0.240571 | + | 1.05151i | −0.0217803 | + | 0.0951991i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.412748 | + | 0.199294i | 0.0370658 | + | 0.0178971i | ||||
\(125\) | 3.01890 | + | 10.7650i | 0.270019 | + | 0.962855i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 11.2077i | − | 0.994519i | −0.867602 | − | 0.497259i | \(-0.834340\pi\) | ||
0.867602 | − | 0.497259i | \(-0.165660\pi\) | |||||||
\(128\) | 0.0408867 | − | 11.3136i | 0.00361391 | − | 0.999993i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.3597 | + | 11.8564i | 1.34714 | + | 1.03987i | ||||
\(131\) | 5.84987i | 0.511105i | 0.966795 | + | 0.255553i | \(0.0822574\pi\) | ||||
−0.966795 | + | 0.255553i | \(0.917743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.9079 | −1.81294 | ||||||||
\(134\) | −19.1151 | − | 4.37328i | −1.65129 | − | 0.377794i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.2102 | − | 16.5125i | 1.13276 | − | 1.41593i | ||||
\(137\) | 12.2520i | 1.04676i | 0.852101 | + | 0.523378i | \(0.175328\pi\) | ||||
−0.852101 | + | 0.523378i | \(0.824672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.32429i | − | 0.536419i | −0.963361 | − | 0.268209i | \(-0.913568\pi\) | ||
0.963361 | − | 0.268209i | \(-0.0864319\pi\) | |||||||
\(140\) | −11.6351 | + | 9.57364i | −0.983346 | + | 0.809120i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.74501 | + | 0.399236i | 0.146438 | + | 0.0335032i | ||||
\(143\) | 25.1786i | 2.10554i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.25883 | − | 2.72708i | 0.104540 | − | 0.226472i | ||||
\(146\) | 4.39507 | − | 19.2103i | 0.363739 | − | 1.58986i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.1721 | − | 4.91158i | −0.836144 | − | 0.403730i | ||||
\(149\) | 2.50921i | 0.205563i | 0.994704 | + | 0.102781i | \(0.0327742\pi\) | ||||
−0.994704 | + | 0.102781i | \(0.967226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4459 | −1.09421 | −0.547106 | − | 0.837063i | \(-0.684271\pi\) | ||||
−0.547106 | + | 0.837063i | \(0.684271\pi\) | |||||||
\(152\) | 10.9648 | − | 13.7058i | 0.889361 | − | 1.11169i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −19.0596 | − | 4.36059i | −1.53587 | − | 0.351387i | ||||
\(155\) | 0.465266 | + | 0.214769i | 0.0373711 | + | 0.0172506i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2885 | 0.980728 | 0.490364 | − | 0.871518i | \(-0.336864\pi\) | ||||
0.490364 | + | 0.871518i | \(0.336864\pi\) | |||||||
\(158\) | −0.338103 | − | 0.0773534i | −0.0268980 | − | 0.00615391i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.173999 | − | 12.6479i | −0.0137558 | − | 0.999905i | ||||
\(161\) | 10.6404 | 0.838582 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.29583 | 0.649780 | 0.324890 | − | 0.945752i | \(-0.394673\pi\) | ||||
0.324890 | + | 0.945752i | \(0.394673\pi\) | |||||||
\(164\) | −8.15094 | − | 3.93566i | −0.636482 | − | 0.307323i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.4182 | − | 4.21385i | −1.42953 | − | 0.327058i | ||||
\(167\) | − | 12.4726i | − | 0.965158i | −0.875853 | − | 0.482579i | \(-0.839700\pi\) | ||
0.875853 | − | 0.482579i | \(-0.160300\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.6495 | 1.89611 | ||||||||
\(170\) | 14.4465 | − | 18.7153i | 1.10800 | − | 1.43540i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.65550 | − | 1.76505i | −0.278729 | − | 0.134584i | ||||
\(173\) | 8.83448 | 0.671673 | 0.335836 | − | 0.941920i | \(-0.390981\pi\) | ||||
0.335836 | + | 0.941920i | \(0.390981\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.8206 | + | 10.9280i | −0.969144 | + | 0.826078i | ||||
\(176\) | 12.8540 | − | 10.2074i | 0.968907 | − | 0.769410i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.9198 | + | 2.72708i | 0.893423 | + | 0.204403i | ||||
\(179\) | 6.64753i | 0.496860i | 0.968650 | + | 0.248430i | \(0.0799146\pi\) | ||||
−0.968650 | + | 0.248430i | \(0.920085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7088i | 1.39061i | 0.718713 | + | 0.695307i | \(0.244732\pi\) | ||||
−0.718713 | + | 0.695307i | \(0.755268\pi\) | |||||||
\(182\) | −6.52039 | + | 28.4999i | −0.483323 | + | 2.11255i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.58018 | + | 6.97513i | −0.411376 | + | 0.514214i | ||||
\(185\) | −11.4664 | − | 5.29295i | −0.843030 | − | 0.389146i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.6792 | 2.24348 | ||||||||
\(188\) | 1.45256 | − | 3.00833i | 0.105939 | − | 0.219405i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.9910 | − | 15.5342i | 0.869917 | − | 1.12697i | ||||
\(191\) | 16.1381 | 1.16771 | 0.583855 | − | 0.811858i | \(-0.301544\pi\) | ||||
0.583855 | + | 0.811858i | \(0.301544\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.19634i | 0.518004i | 0.965877 | + | 0.259002i | \(0.0833936\pi\) | ||||
−0.965877 | + | 0.259002i | \(0.916606\pi\) | |||||||
\(194\) | −3.87649 | + | 16.9437i | −0.278316 | + | 1.21649i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.83725 | − | 3.78419i | −0.559804 | − | 0.270300i | ||||
\(197\) | −16.3550 | −1.16524 | −0.582621 | − | 0.812744i | \(-0.697973\pi\) | ||||
−0.582621 | + | 0.812744i | \(0.697973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.19894 | 0.439431 | 0.219716 | − | 0.975564i | \(-0.429487\pi\) | ||||
0.219716 | + | 0.975564i | \(0.429487\pi\) | |||||||
\(200\) | −0.440123 | − | 14.1353i | −0.0311214 | − | 0.999516i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.07424 | − | 17.8080i | 0.286663 | − | 1.25297i | ||||
\(203\) | 4.52568 | 0.317641 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.18808 | − | 4.24125i | −0.641724 | − | 0.296222i | ||||
\(206\) | 3.67396 | − | 16.0585i | 0.255977 | − | 1.11885i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.2631 | − | 19.2206i | −1.05830 | − | 1.33271i | ||||
\(209\) | 25.4645 | 1.76142 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5974i | 0.936085i | 0.883706 | + | 0.468043i | \(0.155041\pi\) | ||||
−0.883706 | + | 0.468043i | \(0.844959\pi\) | |||||||
\(212\) | −18.1910 | − | 8.78347i | −1.24936 | − | 0.603251i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.96350 | + | 1.59316i | 0.476015 | + | 0.108906i | ||||
\(215\) | −4.12063 | − | 1.90210i | −0.281025 | − | 0.129722i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.772125i | 0.0524153i | ||||||||
\(218\) | 0.0374369 | − | 0.163632i | 0.00253555 | − | 0.0110826i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.1708 | − | 11.6601i | 0.955397 | − | 0.786123i | ||||
\(221\) | − | 45.8745i | − | 3.08585i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.9367i | − | 0.933268i | −0.884451 | − | 0.466634i | \(-0.845467\pi\) | ||
0.884451 | − | 0.466634i | \(-0.154533\pi\) | |||||||
\(224\) | 17.1929 | − | 8.22507i | 1.14875 | − | 0.549561i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.599929 | − | 2.62222i | 0.0399067 | − | 0.174427i | ||||
\(227\) | −5.23933 | −0.347746 | −0.173873 | − | 0.984768i | \(-0.555628\pi\) | ||||
−0.173873 | + | 0.984768i | \(0.555628\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.41618i | 0.357911i | 0.983857 | + | 0.178956i | \(0.0572718\pi\) | ||||
−0.983857 | + | 0.178956i | \(0.942728\pi\) | |||||||
\(230\) | −6.10243 | + | 7.90562i | −0.402383 | + | 0.521281i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.37342 | + | 2.96673i | −0.155822 | + | 0.194775i | ||||
\(233\) | − | 0.0771732i | − | 0.00505578i | −0.999997 | − | 0.00252789i | \(-0.999195\pi\) | ||
0.999997 | − | 0.00252789i | \(-0.000804654\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.56535 | − | 3.39111i | 0.102112 | − | 0.221212i | ||||
\(236\) | −2.67541 | + | 5.54091i | −0.174155 | + | 0.360683i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 34.7260 | + | 7.94485i | 2.25095 | + | 0.514988i | ||||
\(239\) | −19.5280 | −1.26316 | −0.631580 | − | 0.775311i | \(-0.717593\pi\) | ||||
−0.631580 | + | 0.775311i | \(0.717593\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7282 | 1.01314 | 0.506570 | − | 0.862199i | \(-0.330913\pi\) | ||||
0.506570 | + | 0.862199i | \(0.330913\pi\) | |||||||
\(242\) | 8.04892 | + | 1.84149i | 0.517404 | + | 0.118375i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.663300 | − | 1.37373i | 0.0424634 | − | 0.0879438i | ||||
\(245\) | −8.83448 | − | 4.07803i | −0.564414 | − | 0.260535i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 38.0770i | − | 2.42278i | ||||||
\(248\) | −0.506153 | − | 0.404928i | −0.0321408 | − | 0.0257129i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.766498 | − | 15.7928i | −0.0484776 | − | 0.998824i | ||||
\(251\) | − | 10.9286i | − | 0.689806i | −0.938638 | − | 0.344903i | \(-0.887912\pi\) | ||
0.938638 | − | 0.344903i | \(-0.112088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.9594 | −0.814747 | ||||||||
\(254\) | −3.53494 | + | 15.4508i | −0.221802 | + | 0.969470i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.62473 | + | 15.5840i | −0.226546 | + | 0.974001i | ||||
\(257\) | − | 15.8487i | − | 0.988616i | −0.869287 | − | 0.494308i | \(-0.835421\pi\) | ||
0.869287 | − | 0.494308i | \(-0.164579\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19.0290i | − | 1.18240i | ||||||
\(260\) | −17.4353 | − | 21.1896i | −1.08129 | − | 1.31412i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.84507 | − | 8.06459i | 0.113989 | − | 0.498232i | ||||
\(263\) | − | 14.1353i | − | 0.871623i | −0.900038 | − | 0.435811i | \(-0.856461\pi\) | ||
0.900038 | − | 0.435811i | \(-0.143539\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.5057 | − | 9.46548i | −1.25965 | − | 0.581460i | ||||
\(266\) | 28.8235 | + | 6.59443i | 1.76728 | + | 0.404330i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.9726 | + | 12.0580i | 1.52545 | + | 0.736557i | ||||
\(269\) | 17.9902i | 1.09688i | 0.836190 | + | 0.548440i | \(0.184778\pi\) | ||||
−0.836190 | + | 0.548440i | \(0.815222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.9198 | 0.845565 | 0.422782 | − | 0.906231i | \(-0.361053\pi\) | ||||
0.422782 | + | 0.906231i | \(0.361053\pi\) | |||||||
\(272\) | −23.4195 | + | 18.5975i | −1.42002 | + | 1.12764i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.86432 | − | 16.8905i | 0.233452 | − | 1.02039i | ||||
\(275\) | 15.6146 | − | 13.3096i | 0.941599 | − | 0.802599i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.765167 | −0.0459744 | −0.0229872 | − | 0.999736i | \(-0.507318\pi\) | ||||
−0.0229872 | + | 0.999736i | \(0.507318\pi\) | |||||||
\(278\) | −1.99470 | + | 8.71862i | −0.119634 | + | 0.522908i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.0596 | − | 9.52840i | 1.13903 | − | 0.569431i | ||||
\(281\) | −0.550096 | −0.0328160 | −0.0164080 | − | 0.999865i | \(-0.505223\pi\) | ||||
−0.0164080 | + | 0.999865i | \(0.505223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2958 | 0.671468 | 0.335734 | − | 0.941957i | \(-0.391016\pi\) | ||||
0.335734 | + | 0.941957i | \(0.391016\pi\) | |||||||
\(284\) | −2.27975 | − | 1.10077i | −0.135278 | − | 0.0653186i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.94142 | − | 34.7110i | 0.469586 | − | 2.05251i | ||||
\(287\) | − | 15.2479i | − | 0.900057i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −38.8963 | −2.28802 | ||||||||
\(290\) | −2.59555 | + | 3.36250i | −0.152416 | + | 0.197453i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.1180 | + | 25.0970i | −0.709154 | + | 1.46869i | ||||
\(293\) | 15.4265 | 0.901225 | 0.450612 | − | 0.892720i | \(-0.351206\pi\) | ||||
0.450612 | + | 0.892720i | \(0.351206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.88315 | + | 6.24595i | −0.167864 | + | 0.363653i | ||||
\(296\) | 12.4741 | + | 9.97941i | 0.725042 | + | 0.580041i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.791415 | − | 3.45918i | 0.0458455 | − | 0.200385i | ||||
\(299\) | 19.3781i | 1.12066i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 6.83833i | − | 0.394155i | ||||||
\(302\) | 18.5364 | + | 4.24089i | 1.06665 | + | 0.244036i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −19.4388 | + | 15.4364i | −1.11489 | + | 0.885337i | ||||
\(305\) | 0.714803 | − | 1.54852i | 0.0409295 | − | 0.0886681i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.4900 | 1.68308 | 0.841542 | − | 0.540192i | \(-0.181648\pi\) | ||||
0.841542 | + | 0.540192i | \(0.181648\pi\) | |||||||
\(308\) | 24.9002 | + | 12.0230i | 1.41882 | + | 0.685072i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.573674 | − | 0.442825i | −0.0325825 | − | 0.0251508i | ||||
\(311\) | 24.6393 | 1.39717 | 0.698584 | − | 0.715528i | \(-0.253814\pi\) | ||||
0.698584 | + | 0.715528i | \(0.253814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.8011i | − | 1.11922i | −0.828755 | − | 0.559612i | \(-0.810950\pi\) | ||
0.828755 | − | 0.559612i | \(-0.189050\pi\) | |||||||
\(314\) | −16.9408 | − | 3.87584i | −0.956026 | − | 0.218726i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.441709 | + | 0.213278i | 0.0248481 | + | 0.0119978i | ||||
\(317\) | −8.83448 | −0.496194 | −0.248097 | − | 0.968735i | \(-0.579805\pi\) | ||||
−0.248097 | + | 0.968735i | \(0.579805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.51200 | −0.308613 | ||||||||
\(320\) | −3.74933 | + | 17.4912i | −0.209594 | + | 0.977789i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.6688 | − | 3.35603i | −0.817460 | − | 0.187024i | ||||
\(323\) | −46.3954 | −2.58151 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.9018 | − | 23.3486i | −1.10395 | − | 1.29514i | ||||
\(326\) | −11.4366 | − | 2.61654i | −0.633414 | − | 0.144917i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.99551 | + | 7.99651i | 0.551910 | + | 0.441534i | ||||
\(329\) | 5.62766 | 0.310263 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.94044i | 0.491411i | 0.969345 | + | 0.245705i | \(0.0790196\pi\) | ||||
−0.969345 | + | 0.245705i | \(0.920980\pi\) | |||||||
\(332\) | 24.0622 | + | 11.6184i | 1.32058 | + | 0.637641i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.93390 | + | 17.1946i | −0.215254 | + | 0.940848i | ||||
\(335\) | 28.1502 | + | 12.9942i | 1.53801 | + | 0.709950i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.1273i | 1.42324i | 0.702562 | + | 0.711622i | \(0.252039\pi\) | ||||
−0.702562 | + | 0.711622i | \(0.747961\pi\) | |||||||
\(338\) | −33.9816 | − | 7.77455i | −1.84836 | − | 0.422880i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −25.8187 | + | 21.2443i | −1.40022 | + | 1.15213i | ||||
\(341\) | − | 0.940400i | − | 0.0509255i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.92329i | 0.481812i | ||||||||
\(344\) | 4.48274 | + | 3.58624i | 0.241693 | + | 0.193357i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.1792 | − | 2.78643i | −0.654755 | − | 0.149799i | ||||
\(347\) | 13.6975 | 0.735319 | 0.367660 | − | 0.929960i | \(-0.380159\pi\) | ||||
0.367660 | + | 0.929960i | \(0.380159\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9.36394i | − | 0.501240i | −0.968086 | − | 0.250620i | \(-0.919366\pi\) | ||
0.968086 | − | 0.250620i | \(-0.0806345\pi\) | |||||||
\(350\) | 21.1211 | − | 11.0216i | 1.12897 | − | 0.589129i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.9399 | + | 10.0176i | −1.11610 | + | 0.533941i | ||||
\(353\) | − | 27.4608i | − | 1.46159i | −0.682595 | − | 0.730796i | \(-0.739149\pi\) | ||
0.682595 | − | 0.730796i | \(-0.260851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.56982 | − | 1.18624i | −0.136392 | − | 0.0629591i | ||||
\(356\) | −15.5724 | − | 7.51907i | −0.825334 | − | 0.398510i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.09666 | − | 9.16425i | 0.110812 | − | 0.484345i | ||||
\(359\) | −0.111235 | −0.00587078 | −0.00293539 | − | 0.999996i | \(-0.500934\pi\) | ||||
−0.00293539 | + | 0.999996i | \(0.500934\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.5094 | −1.02681 | ||||||||
\(362\) | 5.90083 | − | 25.7918i | 0.310141 | − | 1.35559i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.9779 | − | 37.2332i | 0.942300 | − | 1.95155i | ||||
\(365\) | −13.0590 | + | 28.2904i | −0.683537 | + | 1.48079i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5485i | 0.602828i | 0.953493 | + | 0.301414i | \(0.0974586\pi\) | ||||
−0.953493 | + | 0.301414i | \(0.902541\pi\) | |||||||
\(368\) | 9.89278 | − | 7.85586i | 0.515697 | − | 0.409515i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 14.1382 | + | 10.9134i | 0.735008 | + | 0.567360i | ||||
\(371\) | − | 34.0298i | − | 1.76674i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.87709 | −0.407860 | −0.203930 | − | 0.978985i | \(-0.565372\pi\) | ||||
−0.203930 | + | 0.978985i | \(0.565372\pi\) | |||||||
\(374\) | −42.2941 | − | 9.67632i | −2.18697 | − | 0.500351i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.95133 | + | 3.68912i | −0.152203 | + | 0.190252i | ||||
\(377\) | 8.24208i | 0.424489i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.27691i | − | 0.116957i | −0.998289 | − | 0.0584785i | \(-0.981375\pi\) | ||
0.998289 | − | 0.0584785i | \(-0.0186249\pi\) | |||||||
\(380\) | −21.4302 | + | 17.6333i | −1.09935 | + | 0.904569i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −22.2478 | − | 5.09001i | −1.13830 | − | 0.260428i | ||||
\(383\) | − | 1.55010i | − | 0.0792066i | −0.999215 | − | 0.0396033i | \(-0.987391\pi\) | ||
0.999215 | − | 0.0396033i | \(-0.0126094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.0685 | + | 12.9565i | 1.43050 | + | 0.660325i | ||||
\(386\) | 2.26975 | − | 9.92082i | 0.115527 | − | 0.504957i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.6882 | − | 22.1358i | 0.542612 | − | 1.12378i | ||||
\(389\) | − | 19.7789i | − | 1.00283i | −0.865207 | − | 0.501415i | \(-0.832813\pi\) | ||
0.865207 | − | 0.501415i | \(-0.167187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.6115 | 1.19408 | ||||||||
\(392\) | 9.61083 | + | 7.68877i | 0.485420 | + | 0.388341i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 22.5468 | + | 5.15842i | 1.13589 | + | 0.259877i | ||||
\(395\) | 0.497913 | + | 0.229838i | 0.0250527 | + | 0.0115644i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.4891 | 1.48002 | 0.740009 | − | 0.672597i | \(-0.234821\pi\) | ||||
0.740009 | + | 0.672597i | \(0.234821\pi\) | |||||||
\(398\) | −8.54582 | − | 1.95517i | −0.428363 | − | 0.0980038i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.85157 | + | 19.6256i | −0.192579 | + | 0.981282i | ||||
\(401\) | 13.3170 | 0.665021 | 0.332511 | − | 0.943100i | \(-0.392104\pi\) | ||||
0.332511 | + | 0.943100i | \(0.392104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.40618 | −0.0700468 | ||||||||
\(404\) | −11.2334 | + | 23.2650i | −0.558885 | + | 1.15748i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.23908 | − | 1.42742i | −0.309640 | − | 0.0708416i | ||||
\(407\) | 23.1761i | 1.14880i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.7077 | 0.727248 | 0.363624 | − | 0.931546i | \(-0.381539\pi\) | ||||
0.363624 | + | 0.931546i | \(0.381539\pi\) | |||||||
\(410\) | 11.3289 | + | 8.74492i | 0.559496 | + | 0.431881i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.1298 | + | 20.9793i | −0.499060 | + | 1.03358i | ||||
\(413\) | −10.3654 | −0.510046 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 27.1239 | + | 12.5205i | 1.33146 | + | 0.614607i | ||||
\(416\) | 14.9793 | + | 31.3114i | 0.734422 | + | 1.53517i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −35.1052 | − | 8.03160i | −1.71705 | − | 0.392838i | ||||
\(419\) | − | 21.0125i | − | 1.02653i | −0.858231 | − | 0.513263i | \(-0.828436\pi\) | ||
0.858231 | − | 0.513263i | \(-0.171564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.07559i | 0.296106i | 0.988979 | + | 0.148053i | \(0.0473006\pi\) | ||||
−0.988979 | + | 0.148053i | \(0.952699\pi\) | |||||||
\(422\) | 4.28868 | − | 18.7453i | 0.208770 | − | 0.912508i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.3077 | + | 17.8464i | 1.08336 | + | 0.866696i | ||||
\(425\) | −28.4493 | + | 24.2496i | −1.38000 | + | 1.17628i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.56982 | 0.124363 | ||||||||
\(428\) | −9.09735 | − | 4.39263i | −0.439737 | − | 0.212326i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.08075 | + | 3.92188i | 0.245015 | + | 0.189130i | ||||
\(431\) | 32.9750 | 1.58835 | 0.794175 | − | 0.607689i | \(-0.207903\pi\) | ||||
0.794175 | + | 0.607689i | \(0.207903\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.28424i | 0.0617166i | 0.999524 | + | 0.0308583i | \(0.00982406\pi\) | ||||
−0.999524 | + | 0.0308583i | \(0.990176\pi\) | |||||||
\(434\) | 0.243531 | − | 1.06445i | 0.0116899 | − | 0.0510951i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.103221 | + | 0.213775i | −0.00494337 | + | 0.0102380i | ||||
\(437\) | 19.5981 | 0.937506 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.8635 | −1.75940 | −0.879699 | − | 0.475530i | \(-0.842256\pi\) | ||||
−0.879699 | + | 0.475530i | \(0.842256\pi\) | |||||||
\(440\) | −23.2135 | + | 11.6050i | −1.10666 | + | 0.553246i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.4690 | + | 63.2423i | −0.688220 | + | 3.00813i | ||||
\(443\) | −8.33772 | −0.396137 | −0.198069 | − | 0.980188i | \(-0.563467\pi\) | ||||
−0.198069 | + | 0.980188i | \(0.563467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.5538 | − | 8.10290i | −0.832131 | − | 0.384114i | ||||
\(446\) | −4.39568 | + | 19.2130i | −0.208141 | + | 0.909762i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −26.2963 | + | 5.91631i | −1.24238 | + | 0.279520i | ||||
\(449\) | 36.5100 | 1.72301 | 0.861506 | − | 0.507748i | \(-0.169522\pi\) | ||||
0.861506 | + | 0.507748i | \(0.169522\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.5710i | 0.874476i | ||||||||
\(452\) | −1.65412 | + | 3.42575i | −0.0778031 | + | 0.161134i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.22290 | + | 1.65250i | 0.338988 | + | 0.0775559i | ||||
\(455\) | 19.3739 | − | 41.9708i | 0.908261 | − | 1.96762i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 20.7711i | − | 0.971633i | −0.874061 | − | 0.485816i | \(-0.838522\pi\) | ||
0.874061 | − | 0.485816i | \(-0.161478\pi\) | |||||||
\(458\) | 1.70828 | − | 7.46671i | 0.0798229 | − | 0.348896i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.9062 | − | 8.97391i | 0.508506 | − | 0.418411i | ||||
\(461\) | − | 2.53355i | − | 0.117999i | −0.998258 | − | 0.0589997i | \(-0.981209\pi\) | ||
0.998258 | − | 0.0589997i | \(-0.0187911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.0894i | − | 0.608314i | −0.952622 | − | 0.304157i | \(-0.901625\pi\) | ||
0.952622 | − | 0.304157i | \(-0.0983748\pi\) | |||||||
\(464\) | 4.20769 | − | 3.34133i | 0.195337 | − | 0.155117i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.0243407 | + | 0.106390i | −0.00112756 | + | 0.00492844i | ||||
\(467\) | 23.2966 | 1.07804 | 0.539019 | − | 0.842293i | \(-0.318795\pi\) | ||||
0.539019 | + | 0.842293i | \(0.318795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 46.7162i | 2.15715i | ||||||||
\(470\) | −3.22755 | + | 4.18125i | −0.148876 | + | 0.192867i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.43593 | − | 6.79483i | 0.250209 | − | 0.312757i | ||||
\(473\) | 8.32865i | 0.382952i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.6137 | + | 20.1278i | −1.08347 | + | 0.923527i | ||||
\(476\) | −45.3672 | − | 21.9054i | −2.07940 | − | 1.00403i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.9211 | + | 6.15920i | 1.23134 | + | 0.281715i | ||||
\(479\) | −11.0267 | −0.503823 | −0.251911 | − | 0.967750i | \(-0.581059\pi\) | ||||
−0.251911 | + | 0.967750i | \(0.581059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.6552 | 1.58014 | ||||||||
\(482\) | −21.6827 | − | 4.96072i | −0.987622 | − | 0.225955i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5154 | − | 5.07732i | −0.477972 | − | 0.230787i | ||||
\(485\) | 11.5181 | − | 24.9524i | 0.523011 | − | 1.13303i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.19428i | − | 0.280690i | −0.990103 | − | 0.140345i | \(-0.955179\pi\) | ||
0.990103 | − | 0.140345i | \(-0.0448211\pi\) | |||||||
\(488\) | −1.34770 | + | 1.68460i | −0.0610075 | + | 0.0762584i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.8929 | + | 8.40837i | 0.492092 | + | 0.379851i | ||||
\(491\) | 3.80033i | 0.171506i | 0.996316 | + | 0.0857532i | \(0.0273297\pi\) | ||||
−0.996316 | + | 0.0857532i | \(0.972670\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0427 | 0.452299 | ||||||||
\(494\) | −12.0096 | + | 52.4927i | −0.540339 | + | 2.36176i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.570064 | + | 0.717873i | 0.0255966 | + | 0.0322335i | ||||
\(497\) | − | 4.26471i | − | 0.191298i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 19.9217i | − | 0.891818i | −0.895078 | − | 0.445909i | \(-0.852880\pi\) | ||
0.895078 | − | 0.445909i | \(-0.147120\pi\) | |||||||
\(500\) | −3.92442 | + | 22.0136i | −0.175505 | + | 0.984478i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.44692 | + | 15.0661i | −0.153843 | + | 0.672432i | ||||
\(503\) | − | 24.3013i | − | 1.08354i | −0.840526 | − | 0.541772i | \(-0.817754\pi\) | ||
0.840526 | − | 0.541772i | \(-0.182246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.1057 | + | 26.2253i | −0.538696 | + | 1.16701i | ||||
\(506\) | 17.8657 | + | 4.08743i | 0.794226 | + | 0.181708i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.74649 | − | 20.1854i | 0.432430 | − | 0.895584i | ||||
\(509\) | − | 3.72468i | − | 0.165093i | −0.996587 | − | 0.0825467i | \(-0.973695\pi\) | ||
0.996587 | − | 0.0825467i | \(-0.0263054\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −46.9489 | −2.07690 | ||||||||
\(512\) | 9.91229 | − | 20.3408i | 0.438065 | − | 0.898943i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.99875 | + | 21.8489i | −0.220485 | + | 0.963716i | ||||
\(515\) | −10.9164 | + | 23.6488i | −0.481032 | + | 1.04209i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.85414 | −0.301445 | ||||||||
\(518\) | −6.00181 | + | 26.2332i | −0.263704 | + | 1.15262i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.3529 | + | 34.7110i | 0.760976 | + | 1.52218i | ||||
\(521\) | −11.1905 | −0.490265 | −0.245133 | − | 0.969490i | \(-0.578831\pi\) | ||||
−0.245133 | + | 0.969490i | \(0.578831\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.4017 | −0.804648 | −0.402324 | − | 0.915497i | \(-0.631797\pi\) | ||||
−0.402324 | + | 0.915497i | \(0.631797\pi\) | |||||||
\(524\) | −5.08720 | + | 10.5358i | −0.222236 | + | 0.460261i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.45834 | + | 19.4869i | −0.194393 | + | 0.849669i | ||||
\(527\) | 1.71338i | 0.0746358i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0261 | 0.566354 | ||||||||
\(530\) | 25.2835 | + | 19.5166i | 1.09825 | + | 0.847748i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −37.6559 | − | 18.1821i | −1.63259 | − | 0.788293i | ||||
\(533\) | 27.7692 | 1.20282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.2549 | − | 4.73370i | −0.443359 | − | 0.204656i | ||||
\(536\) | −30.6240 | − | 24.4995i | −1.32275 | − | 1.05822i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.67417 | − | 24.8011i | 0.244631 | − | 1.06925i | ||||
\(539\) | 17.8563i | 0.769126i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.1076i | − | 0.434560i | −0.976109 | − | 0.217280i | \(-0.930282\pi\) | ||
0.976109 | − | 0.217280i | \(-0.0697184\pi\) | |||||||
\(542\) | −19.1897 | − | 4.39034i | −0.824267 | − | 0.188581i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 38.1518 | − | 18.2517i | 1.63574 | − | 0.782537i | ||||
\(545\) | −0.111235 | + | 0.240976i | −0.00476480 | + | 0.0103223i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.83837 | −0.420658 | −0.210329 | − | 0.977631i | \(-0.567454\pi\) | ||||
−0.210329 | + | 0.977631i | \(0.567454\pi\) | |||||||
\(548\) | −10.6546 | + | 22.0663i | −0.455144 | + | 0.942625i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25.7241 | + | 13.4236i | −1.09688 | + | 0.572385i | ||||
\(551\) | 8.33567 | 0.355111 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.826303i | 0.0351380i | ||||||||
\(554\) | 1.05485 | + | 0.241337i | 0.0448164 | + | 0.0102534i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.49977 | − | 11.3903i | 0.233242 | − | 0.483056i | ||||
\(557\) | −24.5189 | −1.03890 | −0.519450 | − | 0.854501i | \(-0.673863\pi\) | ||||
−0.519450 | + | 0.854501i | \(0.673863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4538 | 0.526740 | ||||||||
\(560\) | −29.2808 | + | 7.12430i | −1.23734 | + | 0.301057i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.758359 | + | 0.173502i | 0.0319894 | + | 0.00731876i | ||||
\(563\) | 22.3948 | 0.943829 | 0.471914 | − | 0.881644i | \(-0.343563\pi\) | ||||
0.471914 | + | 0.881644i | \(0.343563\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.78255 | + | 3.86165i | −0.0749926 | + | 0.162461i | ||||
\(566\) | −15.5724 | − | 3.56275i | −0.654555 | − | 0.149754i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.79566 | + | 2.23655i | 0.117303 | + | 0.0938437i | ||||
\(569\) | 17.3701 | 0.728191 | 0.364095 | − | 0.931362i | \(-0.381378\pi\) | ||||
0.364095 | + | 0.931362i | \(0.381378\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 43.7980i | − | 1.83289i | −0.400162 | − | 0.916444i | \(-0.631046\pi\) | ||
0.400162 | − | 0.916444i | \(-0.368954\pi\) | |||||||
\(572\) | −21.8960 | + | 45.3477i | −0.915517 | + | 1.89608i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.80926 | + | 21.0207i | −0.200735 | + | 0.877387i | ||||
\(575\) | 12.0174 | − | 10.2434i | 0.501162 | − | 0.427180i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 27.0993i | − | 1.12816i | −0.825721 | − | 0.564079i | \(-0.809231\pi\) | ||
0.825721 | − | 0.564079i | \(-0.190769\pi\) | |||||||
\(578\) | 53.6222 | + | 12.2681i | 2.23039 | + | 0.510284i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.63875 | − | 3.81687i | 0.192614 | − | 0.158487i | ||||
\(581\) | 45.0131i | 1.86746i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.4462i | 1.71653i | ||||||||
\(584\) | 24.6215 | − | 30.7765i | 1.01885 | − | 1.27354i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.2668 | − | 4.86557i | −0.878525 | − | 0.200995i | ||||
\(587\) | −20.0250 | −0.826520 | −0.413260 | − | 0.910613i | \(-0.635610\pi\) | ||||
−0.413260 | + | 0.910613i | \(0.635610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.42215i | 0.0585985i | ||||||||
\(590\) | 5.94469 | − | 7.70127i | 0.244739 | − | 0.317056i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.0492 | − | 17.6919i | −0.577417 | − | 0.727134i | ||||
\(593\) | 32.7272i | 1.34395i | 0.740576 | + | 0.671973i | \(0.234553\pi\) | ||||
−0.740576 | + | 0.671973i | \(0.765447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −51.1398 | − | 23.6063i | −2.09653 | − | 0.967765i | ||||
\(596\) | −2.18208 | + | 4.51919i | −0.0893815 | + | 0.185113i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.11193 | − | 26.7145i | 0.249935 | − | 1.09244i | ||||
\(599\) | −20.0781 | −0.820367 | −0.410184 | − | 0.912003i | \(-0.634535\pi\) | ||||
−0.410184 | + | 0.912003i | \(0.634535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6066 | −0.514235 | −0.257118 | − | 0.966380i | \(-0.582773\pi\) | ||||
−0.257118 | + | 0.966380i | \(0.582773\pi\) | |||||||
\(602\) | −2.15683 | + | 9.42727i | −0.0879060 | + | 0.384227i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.2166 | − | 11.6929i | −0.985360 | − | 0.475778i | ||||
\(605\) | −11.8534 | − | 5.47156i | −0.481908 | − | 0.222451i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.6884i | 1.04266i | 0.853355 | + | 0.521331i | \(0.174564\pi\) | ||||
−0.853355 | + | 0.521331i | \(0.825436\pi\) | |||||||
\(608\) | 31.6669 | − | 15.1494i | 1.28426 | − | 0.614390i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.47383 | + | 1.90933i | −0.0596737 | + | 0.0773065i | ||||
\(611\) | 10.2490i | 0.414630i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.32356 | 0.376575 | 0.188288 | − | 0.982114i | \(-0.439706\pi\) | ||||
0.188288 | + | 0.982114i | \(0.439706\pi\) | |||||||
\(614\) | −40.6548 | − | 9.30127i | −1.64069 | − | 0.375369i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.5351 | − | 24.4284i | −1.23029 | − | 0.984248i | ||||
\(617\) | − | 6.85132i | − | 0.275824i | −0.990445 | − | 0.137912i | \(-0.955961\pi\) | ||
0.990445 | − | 0.137912i | \(-0.0440391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.6662i | 1.47374i | 0.676036 | + | 0.736869i | \(0.263696\pi\) | ||||
−0.676036 | + | 0.736869i | \(0.736304\pi\) | |||||||
\(620\) | 0.651195 | + | 0.791415i | 0.0261526 | + | 0.0317840i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −33.9676 | − | 7.77134i | −1.36198 | − | 0.311603i | ||||
\(623\) | − | 29.1312i | − | 1.16712i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.95948 | + | 24.6845i | −0.158379 | + | 0.987378i | ||||
\(626\) | −6.24534 | + | 27.2977i | −0.249614 | + | 1.09103i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.1321 | + | 10.6864i | 0.883166 | + | 0.426434i | ||||
\(629\) | − | 42.2260i | − | 1.68366i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1204 | 1.31850 | 0.659251 | − | 0.751923i | \(-0.270873\pi\) | ||||
0.659251 | + | 0.751923i | \(0.270873\pi\) | |||||||
\(632\) | −0.541668 | − | 0.433340i | −0.0215464 | − | 0.0172374i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.1792 | + | 2.78643i | 0.483696 | + | 0.110663i | ||||
\(635\) | 10.5033 | − | 22.7539i | 0.416810 | − | 0.902960i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.7005 | 1.05791 | ||||||||
\(638\) | 7.59881 | + | 1.73851i | 0.300840 | + | 0.0688281i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.6856 | − | 22.9307i | 0.422385 | − | 0.906416i | ||||
\(641\) | 12.0700 | 0.476737 | 0.238369 | − | 0.971175i | \(-0.423387\pi\) | ||||
0.238369 | + | 0.971175i | \(0.423387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.1615 | −1.11058 | −0.555290 | − | 0.831657i | \(-0.687393\pi\) | ||||
−0.555290 | + | 0.831657i | \(0.687393\pi\) | |||||||
\(644\) | 19.1638 | + | 9.25320i | 0.755160 | + | 0.364627i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 63.9604 | + | 14.6333i | 2.51649 | + | 0.575739i | ||||
\(647\) | 44.7175i | 1.75803i | 0.476798 | + | 0.879013i | \(0.341797\pi\) | ||||
−0.476798 | + | 0.879013i | \(0.658203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.6244 | 0.495549 | ||||||||
\(650\) | 20.0723 | + | 38.4653i | 0.787300 | + | 1.50873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.9411 | + | 7.21429i | 0.585140 | + | 0.282533i | ||||
\(653\) | −32.4930 | −1.27155 | −0.635775 | − | 0.771874i | \(-0.719319\pi\) | ||||
−0.635775 | + | 0.771874i | \(0.719319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.48221 | + | 11.8764i | −0.214208 | + | 0.464051i | ||||
\(656\) | −11.2576 | − | 14.1766i | −0.439536 | − | 0.553502i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.75826 | − | 1.77499i | −0.302449 | − | 0.0691962i | ||||
\(659\) | 4.47524i | 0.174331i | 0.996194 | + | 0.0871653i | \(0.0277808\pi\) | ||||
−0.996194 | + | 0.0871653i | \(0.972219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.740119i | − | 0.0287873i | −0.999896 | − | 0.0143936i | \(-0.995418\pi\) | ||
0.999896 | − | 0.0143936i | \(-0.00458180\pi\) | |||||||
\(662\) | 2.81985 | − | 12.3252i | 0.109597 | − | 0.479034i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.5075 | − | 23.6063i | −1.14511 | − | 0.916103i | ||||
\(665\) | −42.4474 | − | 19.5938i | −1.64604 | − | 0.759817i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.24218 | −0.164258 | ||||||||
\(668\) | 10.8465 | − | 22.4636i | 0.419664 | − | 0.869144i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −34.7092 | − | 26.7924i | −1.34093 | − | 1.03508i | ||||
\(671\) | −3.12988 | −0.120828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.4450i | 0.749550i | 0.927116 | + | 0.374775i | \(0.122280\pi\) | ||||
−0.927116 | + | 0.374775i | \(0.877720\pi\) | |||||||
\(674\) | 8.24065 | − | 36.0189i | 0.317418 | − | 1.38740i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 44.3947 | + | 21.4359i | 1.70749 | + | 0.824457i | ||||
\(677\) | 16.3550 | 0.628572 | 0.314286 | − | 0.949328i | \(-0.398235\pi\) | ||||
0.314286 | + | 0.949328i | \(0.398235\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.4094 | 1.58915 | ||||||||
\(680\) | 42.2941 | − | 21.1439i | 1.62190 | − | 0.810831i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.296606 | + | 1.29643i | −0.0113576 | + | 0.0496429i | ||||
\(683\) | −7.93035 | −0.303446 | −0.151723 | − | 0.988423i | \(-0.548482\pi\) | ||||
−0.151723 | + | 0.988423i | \(0.548482\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.4819 | + | 24.8740i | −0.438702 | + | 0.950388i | ||||
\(686\) | 2.81444 | − | 12.3016i | 0.107456 | − | 0.469677i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.04877 | − | 6.35784i | −0.192482 | − | 0.242390i | ||||
\(689\) | 61.9744 | 2.36104 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.1856i | 1.37657i | 0.725443 | + | 0.688283i | \(0.241635\pi\) | ||||
−0.725443 | + | 0.688283i | \(0.758365\pi\) | |||||||
\(692\) | 15.9113 | + | 7.68271i | 0.604855 | + | 0.292053i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.8833 | − | 4.32024i | −0.716799 | − | 0.163994i | ||||
\(695\) | 5.92681 | − | 12.8396i | 0.224817 | − | 0.487035i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.8358i | − | 1.28162i | ||||||
\(698\) | −2.95342 | + | 12.9091i | −0.111789 | + | 0.488615i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −32.5936 | + | 8.53263i | −1.23192 | + | 0.322503i | ||||
\(701\) | 27.8435i | 1.05163i | 0.850598 | + | 0.525817i | \(0.176240\pi\) | ||||
−0.850598 | + | 0.525817i | \(0.823760\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 35.0487i | − | 1.32189i | ||||||
\(704\) | 32.0272 | − | 7.20570i | 1.20707 | − | 0.271575i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.66126 | + | 37.8573i | −0.325971 | + | 1.42478i | ||||
\(707\) | −43.5218 | −1.63680 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 11.0235i | − | 0.413995i | −0.978341 | − | 0.206998i | \(-0.933631\pi\) | ||
0.978341 | − | 0.206998i | \(-0.0663692\pi\) | |||||||
\(710\) | 3.16860 | + | 2.44588i | 0.118915 | + | 0.0917921i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 19.0964 | + | 15.2773i | 0.715668 | + | 0.572542i | ||||
\(713\) | − | 0.723757i | − | 0.0271049i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.5961 | + | 51.1178i | −0.882446 | + | 1.91170i | ||||
\(716\) | −5.78088 | + | 11.9725i | −0.216042 | + | 0.447432i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.153348 | + | 0.0350841i | 0.00572291 | + | 0.00130933i | ||||
\(719\) | −34.3520 | −1.28111 | −0.640557 | − | 0.767910i | \(-0.721297\pi\) | ||||
−0.640557 | + | 0.767910i | \(0.721297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39.2459 | −1.46160 | ||||||||
\(722\) | 26.8955 | + | 6.15333i | 1.00095 | + | 0.229003i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.2697 | + | 33.6953i | −0.604658 | + | 1.25228i | ||||
\(725\) | 5.11138 | − | 4.35683i | 0.189832 | − | 0.161809i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.3286i | 0.976475i | 0.872711 | + | 0.488237i | \(0.162360\pi\) | ||||
−0.872711 | + | 0.488237i | \(0.837640\pi\) | |||||||
\(728\) | −36.5277 | + | 45.6591i | −1.35381 | + | 1.69224i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 26.9259 | − | 34.8822i | 0.996573 | − | 1.29105i | ||||
\(731\) | − | 15.1745i | − | 0.561249i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.3088 | 0.491573 | 0.245787 | − | 0.969324i | \(-0.420954\pi\) | ||||
0.245787 | + | 0.969324i | \(0.420954\pi\) | |||||||
\(734\) | 3.64245 | − | 15.9207i | 0.134445 | − | 0.587644i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.1159 | + | 7.70982i | −0.594040 | + | 0.284188i | ||||
\(737\) | − | 56.8974i | − | 2.09584i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 15.8743i | − | 0.583947i | −0.956426 | − | 0.291973i | \(-0.905688\pi\) | ||
0.956426 | − | 0.291973i | \(-0.0943119\pi\) | |||||||
\(740\) | −16.0486 | − | 19.5044i | −0.589960 | − | 0.716995i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.7331 | + | 46.9133i | −0.394026 | + | 1.72224i | ||||
\(743\) | 23.2285i | 0.852171i | 0.904683 | + | 0.426086i | \(0.140108\pi\) | ||||
−0.904683 | + | 0.426086i | \(0.859892\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.35151 | + | 5.09423i | −0.0861527 | + | 0.186638i | ||||
\(746\) | 10.8593 | + | 2.48446i | 0.397587 | + | 0.0909627i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 55.2544 | + | 26.6794i | 2.02030 | + | 0.975497i | ||||
\(749\) | − | 17.0184i | − | 0.621838i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.8181 | 1.27053 | 0.635265 | − | 0.772294i | \(-0.280891\pi\) | ||||
0.635265 | + | 0.772294i | \(0.280891\pi\) | |||||||
\(752\) | 5.23225 | − | 4.15493i | 0.190800 | − | 0.151515i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.59958 | − | 11.3625i | 0.0946713 | − | 0.413797i | ||||
\(755\) | −27.2980 | − | 12.6008i | −0.993475 | − | 0.458592i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.4089 | 0.850811 | 0.425405 | − | 0.905003i | \(-0.360132\pi\) | ||||
0.425405 | + | 0.905003i | \(0.360132\pi\) | |||||||
\(758\) | −0.718146 | + | 3.13893i | −0.0260842 | + | 0.114011i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 35.1052 | − | 17.5500i | 1.27340 | − | 0.636604i | ||||
\(761\) | −49.2769 | −1.78629 | −0.893143 | − | 0.449773i | \(-0.851505\pi\) | ||||
−0.893143 | + | 0.449773i | \(0.851505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.399908 | −0.0144776 | ||||||||
\(764\) | 29.0653 | + | 14.0341i | 1.05155 | + | 0.507736i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.488909 | + | 2.13696i | −0.0176650 | + | 0.0772116i | ||||
\(767\) | − | 18.8772i | − | 0.681616i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.0838 | −1.19303 | −0.596517 | − | 0.802601i | \(-0.703449\pi\) | ||||
−0.596517 | + | 0.802601i | \(0.703449\pi\) | |||||||
\(770\) | −34.6085 | − | 26.7147i | −1.24720 | − | 0.962731i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.25813 | + | 12.9609i | −0.225235 | + | 0.466473i | ||||
\(773\) | −17.2906 | −0.621899 | −0.310949 | − | 0.950426i | \(-0.600647\pi\) | ||||
−0.310949 | + | 0.950426i | \(0.600647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.743317 | + | 0.872050i | 0.0267007 | + | 0.0313250i | ||||
\(776\) | −21.7164 | + | 27.1452i | −0.779574 | + | 0.974455i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.23834 | + | 27.2671i | −0.223655 | + | 0.977571i | ||||
\(779\) | − | 28.0845i | − | 1.00623i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.19415i | 0.185861i | ||||||||
\(782\) | −32.5506 | − | 7.44715i | −1.16401 | − | 0.266310i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.8244 | − | 13.6310i | −0.386585 | − | 0.486821i | ||||
\(785\) | 24.9482 | + | 11.5162i | 0.890439 | + | 0.411030i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.1070 | −0.431566 | −0.215783 | − | 0.976441i | \(-0.569230\pi\) | ||||
−0.215783 | + | 0.976441i | \(0.569230\pi\) | |||||||
\(788\) | −29.4559 | − | 14.2227i | −1.04932 | − | 0.506664i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.613928 | − | 0.473897i | −0.0218426 | − | 0.0168605i | ||||
\(791\) | −6.40855 | −0.227862 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.68011i | 0.166196i | ||||||||
\(794\) | −40.6535 | − | 9.30099i | −1.44274 | − | 0.330080i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.1645 | + | 5.39077i | 0.395717 | + | 0.191071i | ||||
\(797\) | −8.12494 | −0.287800 | −0.143900 | − | 0.989592i | \(-0.545964\pi\) | ||||
−0.143900 | + | 0.989592i | \(0.545964\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.4880 | 0.441794 | ||||||||
\(800\) | 11.4998 | − | 25.8410i | 0.406578 | − | 0.913616i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.3588 | − | 4.20025i | −0.648271 | − | 0.148316i | ||||
\(803\) | 57.1808 | 2.01787 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.6023 | + | 9.97168i | 0.761379 | + | 0.351455i | ||||
\(806\) | 1.93855 | + | 0.443514i | 0.0682825 | + | 0.0156221i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.8242 | − | 28.5299i | 0.802954 | − | 1.00368i | ||||
\(809\) | 37.7588 | 1.32753 | 0.663764 | − | 0.747942i | \(-0.268958\pi\) | ||||
0.663764 | + | 0.747942i | \(0.268958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6205i | 0.478282i | 0.970985 | + | 0.239141i | \(0.0768658\pi\) | ||||
−0.970985 | + | 0.239141i | \(0.923134\pi\) | |||||||
\(812\) | 8.15094 | + | 3.93566i | 0.286042 | + | 0.138115i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.30983 | − | 31.9504i | 0.256209 | − | 1.11986i | ||||
\(815\) | 16.8423 | + | 7.77445i | 0.589959 | + | 0.272327i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 12.5952i | − | 0.440651i | ||||||
\(818\) | −20.2759 | − | 4.63886i | −0.708930 | − | 0.162194i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.8598 | − | 15.6289i | −0.449084 | − | 0.545784i | ||||
\(821\) | − | 3.82718i | − | 0.133569i | −0.997767 | − | 0.0667847i | \(-0.978726\pi\) | ||
0.997767 | − | 0.0667847i | \(-0.0212741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 33.6077i | − | 1.17149i | −0.810495 | − | 0.585746i | \(-0.800802\pi\) | ||
0.810495 | − | 0.585746i | \(-0.199198\pi\) | |||||||
\(824\) | 20.5818 | − | 25.7270i | 0.717003 | − | 0.896242i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.2896 | + | 3.26928i | 0.497200 | + | 0.113753i | ||||
\(827\) | 47.5387 | 1.65308 | 0.826541 | − | 0.562876i | \(-0.190305\pi\) | ||||
0.826541 | + | 0.562876i | \(0.190305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.9453i | − | 1.21370i | −0.794816 | − | 0.606851i | \(-0.792433\pi\) | ||
0.794816 | − | 0.606851i | \(-0.207567\pi\) | |||||||
\(830\) | −33.4438 | − | 25.8157i | −1.16085 | − | 0.896075i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.7747 | − | 47.8902i | −0.373544 | − | 1.66029i | ||||
\(833\) | − | 32.5336i | − | 1.12722i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.6887 | − | 25.3220i | 0.404504 | − | 0.876302i | ||||
\(836\) | 45.8626 | + | 22.1446i | 1.58619 | + | 0.765888i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.62741 | + | 28.9677i | −0.228940 | + | 1.00067i | ||||
\(839\) | −3.50113 | −0.120872 | −0.0604362 | − | 0.998172i | \(-0.519249\pi\) | ||||
−0.0604362 | + | 0.998172i | \(0.519249\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1957 | 0.937782 | ||||||||
\(842\) | 1.91626 | − | 8.37576i | 0.0660388 | − | 0.288648i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.8247 | + | 24.4895i | −0.407023 | + | 0.842964i | ||||
\(845\) | 50.0436 | + | 23.1003i | 1.72155 | + | 0.794675i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 19.6711i | − | 0.675906i | ||||||
\(848\) | −25.1244 | − | 31.6388i | −0.862775 | − | 1.08648i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 46.8685 | − | 24.4573i | 1.60758 | − | 0.838880i | ||||
\(851\) | 17.8369i | 0.611442i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.9745 | 1.02631 | 0.513154 | − | 0.858296i | \(-0.328477\pi\) | ||||
0.513154 | + | 0.858296i | \(0.328477\pi\) | |||||||
\(854\) | −3.54274 | − | 0.810533i | −0.121230 | − | 0.0277359i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.1561 | + | 8.92499i | 0.381308 | + | 0.305050i | ||||
\(857\) | − | 48.7191i | − | 1.66421i | −0.554615 | − | 0.832107i | \(-0.687135\pi\) | ||
0.554615 | − | 0.832107i | \(-0.312865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6152i | 1.14694i | 0.819228 | + | 0.573468i | \(0.194402\pi\) | ||||
−0.819228 | + | 0.573468i | \(0.805598\pi\) | |||||||
\(860\) | −5.76731 | − | 7.00917i | −0.196664 | − | 0.239011i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −45.4591 | − | 10.4004i | −1.54834 | − | 0.354241i | ||||
\(863\) | 38.1251i | 1.29779i | 0.760876 | + | 0.648897i | \(0.224769\pi\) | ||||
−0.760876 | + | 0.648897i | \(0.775231\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.9358 | + | 8.27924i | 0.609837 | + | 0.281503i | ||||
\(866\) | 0.405054 | − | 1.77044i | 0.0137643 | − | 0.0601621i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.671462 | + | 1.39063i | −0.0227909 | + | 0.0472010i | ||||
\(869\) | − | 1.00639i | − | 0.0341393i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −85.0785 | −2.88278 | ||||||||
\(872\) | 0.209725 | − | 0.262153i | 0.00710218 | − | 0.00887761i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27.0179 | − | 6.18133i | −0.913893 | − | 0.209087i | ||||
\(875\) | −36.2696 | + | 10.1713i | −1.22614 | + | 0.343852i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.9505 | 1.45034 | 0.725168 | − | 0.688572i | \(-0.241762\pi\) | ||||
0.725168 | + | 0.688572i | \(0.241762\pi\) | |||||||
\(878\) | 50.8198 | + | 11.6269i | 1.71508 | + | 0.392389i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 35.6622 | − | 8.67695i | 1.20217 | − | 0.292500i | ||||
\(881\) | 1.97970 | 0.0666978 | 0.0333489 | − | 0.999444i | \(-0.489383\pi\) | ||||
0.0333489 | + | 0.999444i | \(0.489383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.1386 | −1.04790 | −0.523949 | − | 0.851750i | \(-0.675542\pi\) | ||||
−0.523949 | + | 0.851750i | \(0.675542\pi\) | |||||||
\(884\) | 39.8937 | − | 82.6218i | 1.34177 | − | 2.77887i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.4943 | + | 2.62975i | 0.386160 | + | 0.0883482i | ||||
\(887\) | 58.8602i | 1.97633i | 0.153385 | + | 0.988167i | \(0.450983\pi\) | ||||
−0.153385 | + | 0.988167i | \(0.549017\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.7608 | 1.26646 | ||||||||
\(890\) | 21.6439 | + | 16.7072i | 0.725505 | + | 0.560025i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.1197 | − | 25.1005i | 0.405798 | − | 0.840427i | ||||
\(893\) | 10.3654 | 0.346864 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.22974 | + | 13.4959i | −0.208237 | + | 0.451117i | ||||
\(896\) | 38.1179 | + | 0.137755i | 1.27343 | + | 0.00460209i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −50.3324 | − | 11.5154i | −1.67961 | − | 0.384273i | ||||
\(899\) | − | 0.307835i | − | 0.0102669i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 75.5135i | − | 2.51572i | ||||||
\(902\) | 5.85737 | − | 25.6019i | 0.195029 | − | 0.852450i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.36085 | − | 4.20101i | 0.111780 | − | 0.139723i | ||||
\(905\) | −17.5330 | + | 37.9828i | −0.582816 | + | 1.26259i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.6822 | 0.520718 | 0.260359 | − | 0.965512i | \(-0.416159\pi\) | ||||
0.260359 | + | 0.965512i | \(0.416159\pi\) | |||||||
\(908\) | −9.43624 | − | 4.55626i | −0.313153 | − | 0.151205i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −39.9464 | + | 51.7501i | −1.32421 | + | 1.71550i | ||||
\(911\) | −38.0864 | −1.26186 | −0.630929 | − | 0.775840i | \(-0.717326\pi\) | ||||
−0.630929 | + | 0.775840i | \(0.717326\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 54.8231i | − | 1.81438i | ||||||
\(914\) | −6.55130 | + | 28.6350i | −0.216698 | + | 0.947160i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.71006 | + | 9.75476i | −0.155625 | + | 0.322306i | ||||
\(917\) | −19.7094 | −0.650861 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.97964 | 0.329198 | 0.164599 | − | 0.986361i | \(-0.447367\pi\) | ||||
0.164599 | + | 0.986361i | \(0.447367\pi\) | |||||||
\(920\) | −17.8657 | + | 8.93150i | −0.589014 | + | 0.294463i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.799093 | + | 3.49274i | −0.0263167 | + | 0.115027i | ||||
\(923\) | 7.76680 | 0.255647 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.3190 | − | 21.4916i | −0.602325 | − | 0.706639i | ||||
\(926\) | −4.12843 | + | 18.0449i | −0.135669 | + | 0.592992i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.85457 | + | 3.27922i | −0.225012 | + | 0.107646i | ||||
\(929\) | 9.06397 | 0.297379 | 0.148690 | − | 0.988884i | \(-0.452494\pi\) | ||||
0.148690 | + | 0.988884i | \(0.452494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 27.0037i | − | 0.885011i | ||||||
\(932\) | 0.0671119 | − | 0.138992i | 0.00219832 | − | 0.00455284i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.1166 | − | 7.34784i | −1.05089 | − | 0.240429i | ||||
\(935\) | 62.2851 | + | 28.7510i | 2.03694 | + | 0.940258i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.7084i | 1.65657i | 0.560306 | + | 0.828286i | \(0.310684\pi\) | ||||
−0.560306 | + | 0.828286i | \(0.689316\pi\) | |||||||
\(938\) | 14.7345 | − | 64.4026i | 0.481097 | − | 2.10282i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.76826 | − | 4.74626i | 0.188140 | − | 0.154806i | ||||
\(941\) | − | 47.8274i | − | 1.55913i | −0.626323 | − | 0.779564i | \(-0.715441\pi\) | ||
0.626323 | − | 0.779564i | \(-0.284559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.2927i | 0.465436i | ||||||||
\(944\) | −9.63706 | + | 7.65279i | −0.313660 | + | 0.249077i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.62689 | − | 11.4818i | 0.0854075 | − | 0.373306i | ||||
\(947\) | 21.3095 | 0.692467 | 0.346234 | − | 0.938148i | \(-0.387460\pi\) | ||||
0.346234 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 85.5024i | − | 2.77553i | ||||||
\(950\) | 38.9020 | − | 20.3002i | 1.26215 | − | 0.658626i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 55.6339 | + | 44.5077i | 1.80310 | + | 1.44250i | ||||
\(953\) | 54.1752i | 1.75491i | 0.479663 | + | 0.877453i | \(0.340759\pi\) | ||||
−0.479663 | + | 0.877453i | \(0.659241\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.7636 | + | 15.1238i | 1.06021 | + | 0.489395i | ||||
\(956\) | −35.1707 | − | 16.9821i | −1.13750 | − | 0.549239i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.2013 | + | 3.47786i | 0.491133 | + | 0.112365i | ||||
\(959\) | −41.2793 | −1.33298 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9475 | −0.998306 | ||||||||
\(962\) | −47.7754 | − | 10.9304i | −1.54034 | − | 0.352409i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28.3270 | + | 13.6776i | 0.912353 | + | 0.440527i | ||||
\(965\) | −6.74406 | + | 14.6101i | −0.217099 | + | 0.470315i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0178i | 0.515097i | 0.966265 | + | 0.257548i | \(0.0829147\pi\) | ||||
−0.966265 | + | 0.257548i | \(0.917085\pi\) | |||||||
\(968\) | 12.8950 | + | 10.3162i | 0.414462 | + | 0.331574i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.7489 | + | 30.7664i | −0.762531 | + | 0.987849i | ||||
\(971\) | 16.1971i | 0.519789i | 0.965637 | + | 0.259894i | \(0.0836878\pi\) | ||||
−0.965637 | + | 0.259894i | \(0.916312\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3078 | 0.683096 | ||||||||
\(974\) | −1.95370 | + | 8.53940i | −0.0626006 | + | 0.273620i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.38926 | − | 1.89731i | 0.0764784 | − | 0.0607315i | ||||
\(977\) | 18.8412i | 0.602784i | 0.953500 | + | 0.301392i | \(0.0974513\pi\) | ||||
−0.953500 | + | 0.301392i | \(0.902549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.4799i | 1.13394i | ||||||||
\(980\) | −12.3649 | − | 15.0274i | −0.394982 | − | 0.480033i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.19864 | − | 5.23911i | 0.0382501 | − | 0.167187i | ||||
\(983\) | 24.3103i | 0.775377i | 0.921790 | + | 0.387688i | \(0.126726\pi\) | ||||
−0.921790 | + | 0.387688i | \(0.873274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.2040 | − | 15.3271i | −1.05797 | − | 0.488361i | ||||
\(986\) | −13.8448 | − | 3.16750i | −0.440907 | − | 0.100874i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.1128 | − | 68.5782i | 1.05346 | − | 2.18176i | ||||
\(989\) | 6.40995i | 0.203824i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.1831 | −0.577606 | −0.288803 | − | 0.957389i | \(-0.593257\pi\) | ||||
−0.288803 | + | 0.957389i | \(0.593257\pi\) | |||||||
\(992\) | −0.559466 | − | 1.16946i | −0.0177631 | − | 0.0371303i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.34511 | + | 5.87930i | −0.0426642 | + | 0.186480i | ||||
\(995\) | 12.5851 | + | 5.80935i | 0.398976 | + | 0.184169i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.1520 | 0.733231 | 0.366615 | − | 0.930373i | \(-0.380516\pi\) | ||||
0.366615 | + | 0.930373i | \(0.380516\pi\) | |||||||
\(998\) | −6.28338 | + | 27.4639i | −0.198897 | + | 0.869356i | ||||
\(999\) | 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 | 1080.2.d.i.109.1 | ✓ | 20 | |
3.2 | odd | 2 | inner | 1080.2.d.i.109.20 | yes | 20 | |
4.3 | odd | 2 | 4320.2.d.i.3889.18 | 20 | |||
5.4 | even | 2 | 1080.2.d.j.109.20 | yes | 20 | ||
8.3 | odd | 2 | 4320.2.d.j.3889.3 | 20 | |||
8.5 | even | 2 | 1080.2.d.j.109.19 | yes | 20 | ||
12.11 | even | 2 | 4320.2.d.i.3889.3 | 20 | |||
15.14 | odd | 2 | 1080.2.d.j.109.1 | yes | 20 | ||
20.19 | odd | 2 | 4320.2.d.j.3889.4 | 20 | |||
24.5 | odd | 2 | 1080.2.d.j.109.2 | yes | 20 | ||
24.11 | even | 2 | 4320.2.d.j.3889.18 | 20 | |||
40.19 | odd | 2 | 4320.2.d.i.3889.17 | 20 | |||
40.29 | even | 2 | inner | 1080.2.d.i.109.2 | yes | 20 | |
60.59 | even | 2 | 4320.2.d.j.3889.17 | 20 | |||
120.29 | odd | 2 | inner | 1080.2.d.i.109.19 | yes | 20 | |
120.59 | even | 2 | 4320.2.d.i.3889.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.d.i.109.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1080.2.d.i.109.2 | yes | 20 | 40.29 | even | 2 | inner | |
1080.2.d.i.109.19 | yes | 20 | 120.29 | odd | 2 | inner | |
1080.2.d.i.109.20 | yes | 20 | 3.2 | odd | 2 | inner | |
1080.2.d.j.109.1 | yes | 20 | 15.14 | odd | 2 | ||
1080.2.d.j.109.2 | yes | 20 | 24.5 | odd | 2 | ||
1080.2.d.j.109.19 | yes | 20 | 8.5 | even | 2 | ||
1080.2.d.j.109.20 | yes | 20 | 5.4 | even | 2 | ||
4320.2.d.i.3889.3 | 20 | 12.11 | even | 2 | |||
4320.2.d.i.3889.4 | 20 | 120.59 | even | 2 | |||
4320.2.d.i.3889.17 | 20 | 40.19 | odd | 2 | |||
4320.2.d.i.3889.18 | 20 | 4.3 | odd | 2 | |||
4320.2.d.j.3889.3 | 20 | 8.3 | odd | 2 | |||
4320.2.d.j.3889.4 | 20 | 20.19 | odd | 2 | |||
4320.2.d.j.3889.17 | 20 | 60.59 | even | 2 | |||
4320.2.d.j.3889.18 | 20 | 24.11 | even | 2 |