Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(199,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.5 | ||
Root | \(1.75374 - 1.62986i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.199 |
Dual form | 1170.2.bj.d.829.5 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.40066 | + | 1.74303i | 0.626394 | + | 0.779507i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.763837 | + | 1.32301i | 0.288703 | + | 0.500049i | 0.973501 | − | 0.228685i | \(-0.0734425\pi\) |
−0.684797 | + | 0.728734i | \(0.740109\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.20984 | − | 0.341491i | 0.698812 | − | 0.107989i | ||||
\(11\) | 1.14057 | + | 0.658509i | 0.343895 | + | 0.198548i | 0.661993 | − | 0.749510i | \(-0.269711\pi\) |
−0.318098 | + | 0.948058i | \(0.603044\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.41225 | + | 2.67975i | −0.669037 | + | 0.743229i | ||||
\(14\) | 1.52767 | 0.408288 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.35904 | − | 0.784645i | 0.329617 | − | 0.190304i | −0.326054 | − | 0.945351i | \(-0.605719\pi\) |
0.655671 | + | 0.755047i | \(0.272386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.18063 | + | 2.41369i | −0.959103 | + | 0.553738i | −0.895897 | − | 0.444262i | \(-0.853466\pi\) |
−0.0632058 | + | 0.998001i | \(0.520132\pi\) | |||||||
\(20\) | 0.809179 | − | 2.08452i | 0.180938 | − | 0.466113i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.14057 | − | 0.658509i | 0.243171 | − | 0.140395i | ||||
\(23\) | 7.31172 | + | 4.22143i | 1.52460 | + | 0.880228i | 0.999575 | + | 0.0291412i | \(0.00927724\pi\) |
0.525025 | + | 0.851087i | \(0.324056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.07631 | + | 4.88278i | −0.215262 | + | 0.976556i | ||||
\(26\) | 1.11461 | + | 3.42894i | 0.218593 | + | 0.672471i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.763837 | − | 1.32301i | 0.144352 | − | 0.250025i | ||||
\(29\) | 2.21438 | − | 3.83543i | 0.411201 | − | 0.712221i | −0.583821 | − | 0.811883i | \(-0.698443\pi\) |
0.995021 | + | 0.0996620i | \(0.0317762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.62745i | 0.292299i | 0.989263 | + | 0.146149i | \(0.0466880\pi\) | ||||
−0.989263 | + | 0.146149i | \(0.953312\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.56929i | − | 0.269131i | ||||||
\(35\) | −1.23616 | + | 3.18447i | −0.208950 | + | 0.538274i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.40148 | + | 2.42743i | −0.230402 | + | 0.399067i | −0.957926 | − | 0.287014i | \(-0.907337\pi\) |
0.727525 | + | 0.686081i | \(0.240671\pi\) | |||||||
\(38\) | 4.82738i | 0.783104i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.40066 | − | 1.74303i | −0.221464 | − | 0.275597i | ||||
\(41\) | −1.35904 | − | 0.784645i | −0.212247 | − | 0.122541i | 0.390108 | − | 0.920769i | \(-0.372438\pi\) |
−0.602355 | + | 0.798228i | \(0.705771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.58006 | + | 2.64430i | −0.698452 | + | 0.403252i | −0.806771 | − | 0.590865i | \(-0.798787\pi\) |
0.108318 | + | 0.994116i | \(0.465453\pi\) | |||||||
\(44\) | − | 1.31702i | − | 0.198548i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.31172 | − | 4.22143i | 1.07805 | − | 0.622415i | ||||
\(47\) | −4.94552 | −0.721378 | −0.360689 | − | 0.932686i | \(-0.617458\pi\) | ||||
−0.360689 | + | 0.932686i | \(0.617458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.33310 | − | 4.04106i | 0.333301 | − | 0.577294i | ||||
\(50\) | 3.69046 | + | 3.37350i | 0.521910 | + | 0.477085i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.52686 | + | 0.749192i | 0.489087 | + | 0.103894i | ||||
\(53\) | 13.9161i | 1.91152i | 0.294148 | + | 0.955760i | \(0.404964\pi\) | ||||
−0.294148 | + | 0.955760i | \(0.595036\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.449750 | + | 2.91040i | 0.0606443 | + | 0.392438i | ||||
\(56\) | −0.763837 | − | 1.32301i | −0.102072 | − | 0.176794i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.21438 | − | 3.83543i | −0.290763 | − | 0.503616i | ||||
\(59\) | 9.07005 | − | 5.23660i | 1.18082 | − | 0.681747i | 0.224616 | − | 0.974447i | \(-0.427887\pi\) |
0.956204 | + | 0.292700i | \(0.0945539\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.49134 | + | 4.31513i | 0.318984 | + | 0.552496i | 0.980276 | − | 0.197632i | \(-0.0633252\pi\) |
−0.661293 | + | 0.750128i | \(0.729992\pi\) | |||||||
\(62\) | 1.40941 | + | 0.813725i | 0.178996 | + | 0.103343i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.04962 | − | 0.451203i | −0.998433 | − | 0.0559648i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.38628 | − | 2.40112i | 0.169362 | − | 0.293343i | −0.768834 | − | 0.639448i | \(-0.779163\pi\) |
0.938196 | + | 0.346105i | \(0.112496\pi\) | |||||||
\(68\) | −1.35904 | − | 0.784645i | −0.164808 | − | 0.0951521i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.13975 | + | 2.66278i | 0.255749 | + | 0.318264i | ||||
\(71\) | 12.8513 | − | 7.41968i | 1.52516 | − | 0.880554i | 0.525608 | − | 0.850727i | \(-0.323838\pi\) |
0.999555 | − | 0.0298269i | \(-0.00949560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.98944 | 0.701011 | 0.350505 | − | 0.936561i | \(-0.386010\pi\) | ||||
0.350505 | + | 0.936561i | \(0.386010\pi\) | |||||||
\(74\) | 1.40148 | + | 2.42743i | 0.162919 | + | 0.282183i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.18063 | + | 2.41369i | 0.479551 | + | 0.276869i | ||||
\(77\) | 2.01198i | 0.229286i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.87632 | 0.548629 | 0.274315 | − | 0.961640i | \(-0.411549\pi\) | ||||
0.274315 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(80\) | −2.20984 | + | 0.341491i | −0.247067 | + | 0.0381799i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.35904 | + | 0.784645i | −0.150081 | + | 0.0866495i | ||||
\(83\) | 6.39020 | 0.701416 | 0.350708 | − | 0.936485i | \(-0.385941\pi\) | ||||
0.350708 | + | 0.936485i | \(0.385941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.27122 | + | 1.26984i | 0.354813 | + | 0.137733i | ||||
\(86\) | 5.28860i | 0.570284i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.14057 | − | 0.658509i | −0.121585 | − | 0.0701973i | ||||
\(89\) | −15.9738 | − | 9.22251i | −1.69322 | − | 0.977584i | −0.951886 | − | 0.306452i | \(-0.900858\pi\) |
−0.741338 | − | 0.671131i | \(-0.765809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.38789 | − | 1.14452i | −0.564804 | − | 0.119978i | ||||
\(92\) | − | 8.44285i | − | 0.880228i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.47276 | + | 4.28295i | −0.255046 | + | 0.441752i | ||||
\(95\) | −10.0628 | − | 3.90621i | −1.03242 | − | 0.400769i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.963028 | + | 1.66801i | 0.0977807 | + | 0.169361i | 0.910766 | − | 0.412923i | \(-0.135492\pi\) |
−0.812985 | + | 0.582285i | \(0.802159\pi\) | |||||||
\(98\) | −2.33310 | − | 4.04106i | −0.235679 | − | 0.408208i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.76677 | − | 1.50928i | 0.476677 | − | 0.150928i | ||||
\(101\) | −1.21929 | + | 2.11188i | −0.121324 | + | 0.210140i | −0.920290 | − | 0.391237i | \(-0.872047\pi\) |
0.798966 | + | 0.601376i | \(0.205381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.4300i | − | 1.22477i | −0.790561 | − | 0.612383i | \(-0.790211\pi\) | ||
0.790561 | − | 0.612383i | \(-0.209789\pi\) | |||||||
\(104\) | 2.41225 | − | 2.67975i | 0.236540 | − | 0.262771i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0517 | + | 6.95804i | 1.17056 | + | 0.675824i | ||||
\(107\) | 9.07302 | + | 5.23831i | 0.877122 | + | 0.506407i | 0.869708 | − | 0.493566i | \(-0.164307\pi\) |
0.00741349 | + | 0.999973i | \(0.497640\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.1799i | − | 1.64553i | −0.568379 | − | 0.822767i | \(-0.692429\pi\) | ||
0.568379 | − | 0.822767i | \(-0.307571\pi\) | |||||||
\(110\) | 2.74535 | + | 1.06570i | 0.261759 | + | 0.101611i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.52767 | −0.144352 | ||||||||
\(113\) | −2.25151 | + | 1.29991i | −0.211805 | + | 0.122285i | −0.602150 | − | 0.798383i | \(-0.705689\pi\) |
0.390345 | + | 0.920669i | \(0.372356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.88316 | + | 18.6573i | 0.268856 | + | 1.73981i | ||||
\(116\) | −4.42877 | −0.411201 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 10.4732i | − | 0.964136i | ||||||
\(119\) | 2.07618 | + | 1.19868i | 0.190323 | + | 0.109883i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.63273 | − | 8.02413i | −0.421157 | − | 0.729466i | ||||
\(122\) | 4.98268 | 0.451111 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.40941 | − | 0.813725i | 0.126569 | − | 0.0730747i | ||||
\(125\) | −10.0184 | + | 4.96307i | −0.896071 | + | 0.443911i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.01552 | + | 4.05041i | 0.622527 | + | 0.359416i | 0.777852 | − | 0.628447i | \(-0.216309\pi\) |
−0.155325 | + | 0.987863i | \(0.549643\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.41556 | + | 6.74558i | −0.387271 | + | 0.591626i | ||||
\(131\) | 2.32506 | 0.203141 | 0.101571 | − | 0.994828i | \(-0.467613\pi\) | ||||
0.101571 | + | 0.994828i | \(0.467613\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.38665 | − | 3.68733i | −0.553792 | − | 0.319732i | ||||
\(134\) | −1.38628 | − | 2.40112i | −0.119757 | − | 0.207425i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.35904 | + | 0.784645i | −0.116537 | + | 0.0672827i | ||||
\(137\) | −6.14192 | − | 10.6381i | −0.524740 | − | 0.908876i | −0.999585 | − | 0.0288066i | \(-0.990829\pi\) |
0.474845 | − | 0.880069i | \(-0.342504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.32861 | − | 5.76531i | −0.282329 | − | 0.489008i | 0.689629 | − | 0.724163i | \(-0.257774\pi\) |
−0.971958 | + | 0.235155i | \(0.924440\pi\) | |||||||
\(140\) | 3.37591 | − | 0.521687i | 0.285317 | − | 0.0440906i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 14.8394i | − | 1.24529i | ||||||
\(143\) | −4.51598 | + | 1.46796i | −0.377645 | + | 0.122757i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.78686 | − | 1.51239i | 0.812755 | − | 0.125597i | ||||
\(146\) | 2.99472 | − | 5.18700i | 0.247845 | − | 0.429280i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.80296 | 0.230402 | ||||||||
\(149\) | 2.60768 | − | 1.50554i | 0.213629 | − | 0.123339i | −0.389368 | − | 0.921082i | \(-0.627306\pi\) |
0.602997 | + | 0.797744i | \(0.293973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0149i | 0.977759i | 0.872351 | + | 0.488880i | \(0.162594\pi\) | ||||
−0.872351 | + | 0.488880i | \(0.837406\pi\) | |||||||
\(152\) | 4.18063 | − | 2.41369i | 0.339094 | − | 0.195776i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.74242 | + | 1.00599i | 0.140408 | + | 0.0810648i | ||||
\(155\) | −2.83670 | + | 2.27950i | −0.227849 | + | 0.183094i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.01556i | 0.240668i | 0.992733 | + | 0.120334i | \(0.0383965\pi\) | ||||
−0.992733 | + | 0.120334i | \(0.961604\pi\) | |||||||
\(158\) | 2.43816 | − | 4.22302i | 0.193970 | − | 0.335965i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.809179 | + | 2.08452i | −0.0639712 | + | 0.164796i | ||||
\(161\) | 12.8979i | 1.01650i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.95812 | − | 8.58772i | −0.388350 | − | 0.672642i | 0.603878 | − | 0.797077i | \(-0.293621\pi\) |
−0.992228 | + | 0.124435i | \(0.960288\pi\) | |||||||
\(164\) | 1.56929i | 0.122541i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.19510 | − | 5.53408i | 0.247988 | − | 0.429528i | ||||
\(167\) | 6.49472 | − | 11.2492i | 0.502576 | − | 0.870488i | −0.497419 | − | 0.867510i | \(-0.665719\pi\) |
0.999996 | − | 0.00297754i | \(-0.000947782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.36213 | − | 12.9284i | −0.104779 | − | 0.994496i | ||||
\(170\) | 2.73532 | − | 2.19804i | 0.209789 | − | 0.168582i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.58006 | + | 2.64430i | 0.349226 | + | 0.201626i | ||||
\(173\) | −3.35755 | + | 1.93848i | −0.255270 | + | 0.147380i | −0.622175 | − | 0.782878i | \(-0.713751\pi\) |
0.366905 | + | 0.930258i | \(0.380417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.28207 | + | 2.30569i | −0.550473 | + | 0.174294i | ||||
\(176\) | −1.14057 | + | 0.658509i | −0.0859738 | + | 0.0496370i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.9738 | + | 9.22251i | −1.19729 | + | 0.691256i | ||||
\(179\) | −7.05325 | + | 12.2166i | −0.527185 | + | 0.913111i | 0.472313 | + | 0.881431i | \(0.343419\pi\) |
−0.999498 | + | 0.0316802i | \(0.989914\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.1472 | −1.94351 | −0.971753 | − | 0.236001i | \(-0.924163\pi\) | ||||
−0.971753 | + | 0.236001i | \(0.924163\pi\) | |||||||
\(182\) | −3.68513 | + | 4.09379i | −0.273160 | + | 0.303452i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.31172 | − | 4.22143i | −0.539027 | − | 0.311208i | ||||
\(185\) | −6.19408 | + | 0.957185i | −0.455398 | + | 0.0703736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.06678 | 0.151138 | ||||||||
\(188\) | 2.47276 | + | 4.28295i | 0.180345 | + | 0.312366i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.41426 | + | 6.76151i | −0.610435 | + | 0.490531i | ||||
\(191\) | 9.42713 | + | 16.3283i | 0.682123 | + | 1.18147i | 0.974332 | + | 0.225117i | \(0.0722766\pi\) |
−0.292208 | + | 0.956355i | \(0.594390\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.94600 | + | 15.4949i | −0.643947 | + | 1.11535i | 0.340596 | + | 0.940210i | \(0.389371\pi\) |
−0.984544 | + | 0.175140i | \(0.943962\pi\) | |||||||
\(194\) | 1.92606 | 0.138283 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.66621 | −0.333301 | ||||||||
\(197\) | −0.312928 | + | 0.542008i | −0.0222952 | + | 0.0386165i | −0.876958 | − | 0.480567i | \(-0.840431\pi\) |
0.854663 | + | 0.519184i | \(0.173764\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.84057 | − | 15.3123i | −0.626691 | − | 1.08546i | −0.988211 | − | 0.153097i | \(-0.951075\pi\) |
0.361520 | − | 0.932364i | \(-0.382258\pi\) | |||||||
\(200\) | 1.07631 | − | 4.88278i | 0.0761065 | − | 0.345265i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.21929 | + | 2.11188i | 0.0857891 | + | 0.148591i | ||||
\(203\) | 6.76572 | 0.474860 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.535898 | − | 3.46788i | −0.0374288 | − | 0.242207i | ||||
\(206\) | −10.7647 | − | 6.21501i | −0.750013 | − | 0.433020i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.11461 | − | 3.42894i | −0.0772842 | − | 0.237754i | ||||
\(209\) | −6.35774 | −0.439774 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.62227 | + | 14.9342i | −0.593581 | + | 1.02811i | 0.400164 | + | 0.916443i | \(0.368953\pi\) |
−0.993745 | + | 0.111669i | \(0.964380\pi\) | |||||||
\(212\) | 12.0517 | − | 6.95804i | 0.827712 | − | 0.477880i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.07302 | − | 5.23831i | 0.620219 | − | 0.358083i | ||||
\(215\) | −11.0242 | − | 4.27942i | −0.751844 | − | 0.291854i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.15313 | + | 1.24311i | −0.146164 | + | 0.0843877i | ||||
\(218\) | −14.8782 | − | 8.58994i | −1.00768 | − | 0.581784i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.29560 | − | 1.84469i | 0.154769 | − | 0.124369i | ||||
\(221\) | −1.17570 | + | 5.53466i | −0.0790861 | + | 0.372301i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.44858 | + | 4.24107i | −0.163969 | + | 0.284003i | −0.936289 | − | 0.351231i | \(-0.885763\pi\) |
0.772320 | + | 0.635234i | \(0.219096\pi\) | |||||||
\(224\) | −0.763837 | + | 1.32301i | −0.0510360 | + | 0.0883970i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.59982i | 0.172938i | ||||||||
\(227\) | −5.07567 | − | 8.79132i | −0.336884 | − | 0.583500i | 0.646961 | − | 0.762523i | \(-0.276040\pi\) |
−0.983845 | + | 0.179023i | \(0.942706\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.3959i | − | 1.01739i | −0.860947 | − | 0.508694i | \(-0.830129\pi\) | ||
0.860947 | − | 0.508694i | \(-0.169871\pi\) | |||||||
\(230\) | 17.5993 | + | 6.83178i | 1.16046 | + | 0.450474i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.21438 | + | 3.83543i | −0.145381 | + | 0.251808i | ||||
\(233\) | − | 9.91624i | − | 0.649634i | −0.945777 | − | 0.324817i | \(-0.894697\pi\) | ||
0.945777 | − | 0.324817i | \(-0.105303\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.92699 | − | 8.62019i | −0.451867 | − | 0.562319i | ||||
\(236\) | −9.07005 | − | 5.23660i | −0.590410 | − | 0.340873i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.07618 | − | 1.19868i | 0.134579 | − | 0.0776990i | ||||
\(239\) | 9.46167i | 0.612024i | 0.952028 | + | 0.306012i | \(0.0989948\pi\) | ||||
−0.952028 | + | 0.306012i | \(0.901005\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3482 | − | 6.55189i | 0.731002 | − | 0.422044i | −0.0877865 | − | 0.996139i | \(-0.527979\pi\) |
0.818789 | + | 0.574095i | \(0.194646\pi\) | |||||||
\(242\) | −9.26546 | −0.595607 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.49134 | − | 4.31513i | 0.159492 | − | 0.276248i | ||||
\(245\) | 10.3116 | − | 1.59347i | 0.658782 | − | 0.101803i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.61663 | − | 17.0255i | 0.230121 | − | 1.08330i | ||||
\(248\) | − | 1.62745i | − | 0.103343i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.711042 | + | 11.1577i | −0.0449702 | + | 0.705675i | ||||
\(251\) | −11.5822 | − | 20.0610i | −0.731062 | − | 1.26624i | −0.956430 | − | 0.291963i | \(-0.905692\pi\) |
0.225367 | − | 0.974274i | \(-0.427642\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.55969 | + | 9.62967i | 0.349535 | + | 0.605412i | ||||
\(254\) | 7.01552 | − | 4.05041i | 0.440193 | − | 0.254146i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.32895 | − | 1.92197i | −0.207654 | − | 0.119889i | 0.392566 | − | 0.919724i | \(-0.371587\pi\) |
−0.600221 | + | 0.799834i | \(0.704921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.28201 | −0.266071 | ||||||||
\(260\) | 3.63406 | + | 7.19678i | 0.225375 | + | 0.446325i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.16253 | − | 2.01356i | 0.0718213 | − | 0.124398i | ||||
\(263\) | 26.5060 | + | 15.3032i | 1.63443 | + | 0.943638i | 0.982704 | + | 0.185184i | \(0.0592880\pi\) |
0.651726 | + | 0.758455i | \(0.274045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.2561 | + | 19.4917i | −1.49004 | + | 1.19736i | ||||
\(266\) | −6.38665 | + | 3.68733i | −0.391590 | + | 0.226085i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.77257 | −0.169362 | ||||||||
\(269\) | −9.04370 | − | 15.6641i | −0.551404 | − | 0.955060i | −0.998174 | − | 0.0604109i | \(-0.980759\pi\) |
0.446769 | − | 0.894649i | \(-0.352574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2869 | + | 7.09382i | 0.746373 | + | 0.430919i | 0.824382 | − | 0.566034i | \(-0.191523\pi\) |
−0.0780089 | + | 0.996953i | \(0.524856\pi\) | |||||||
\(272\) | 1.56929i | 0.0951521i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.2838 | −0.742094 | ||||||||
\(275\) | −4.44296 | + | 4.86040i | −0.267921 | + | 0.293093i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5855 | + | 8.42097i | −0.876360 | + | 0.505967i | −0.869457 | − | 0.494009i | \(-0.835531\pi\) |
−0.00690380 | + | 0.999976i | \(0.502198\pi\) | |||||||
\(278\) | −6.65721 | −0.399273 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.23616 | − | 3.18447i | 0.0738748 | − | 0.190309i | ||||
\(281\) | − | 8.61535i | − | 0.513949i | −0.966418 | − | 0.256974i | \(-0.917274\pi\) | ||
0.966418 | − | 0.256974i | \(-0.0827256\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.9192 | + | 13.8098i | 1.42185 | + | 0.820905i | 0.996457 | − | 0.0841040i | \(-0.0268028\pi\) |
0.425392 | + | 0.905009i | \(0.360136\pi\) | |||||||
\(284\) | −12.8513 | − | 7.41968i | −0.762582 | − | 0.440277i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.986699 | + | 4.64493i | −0.0583447 | + | 0.274661i | ||||
\(287\) | − | 2.39736i | − | 0.141512i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.26867 | + | 12.5897i | −0.427569 | + | 0.740570i | ||||
\(290\) | 3.58367 | − | 9.23186i | 0.210440 | − | 0.542114i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.99472 | − | 5.18700i | −0.175253 | − | 0.303546i | ||||
\(293\) | −15.1250 | − | 26.1973i | −0.883614 | − | 1.53046i | −0.847294 | − | 0.531125i | \(-0.821770\pi\) |
−0.0363205 | − | 0.999340i | \(-0.511564\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.8316 | + | 8.47469i | 1.27108 | + | 0.493415i | ||||
\(296\) | 1.40148 | − | 2.42743i | 0.0814593 | − | 0.141092i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 3.01108i | − | 0.174427i | ||||||
\(299\) | −28.9501 | + | 9.41048i | −1.67422 | + | 0.544222i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.99684 | − | 4.03963i | −0.403291 | − | 0.232840i | ||||
\(302\) | 10.4052 | + | 6.00745i | 0.598753 | + | 0.345690i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 4.82738i | − | 0.276869i | ||||||
\(305\) | −4.03188 | + | 10.3865i | −0.230865 | + | 0.594730i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1392 | 0.806966 | 0.403483 | − | 0.914987i | \(-0.367799\pi\) | ||||
0.403483 | + | 0.914987i | \(0.367799\pi\) | |||||||
\(308\) | 1.74242 | − | 1.00599i | 0.0992837 | − | 0.0573215i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.555760 | + | 3.59640i | 0.0315650 | + | 0.204262i | ||||
\(311\) | 9.97427 | 0.565589 | 0.282794 | − | 0.959181i | \(-0.408739\pi\) | ||||
0.282794 | + | 0.959181i | \(0.408739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.08460i | 0.174352i | 0.996193 | + | 0.0871760i | \(0.0277843\pi\) | ||||
−0.996193 | + | 0.0871760i | \(0.972216\pi\) | |||||||
\(314\) | 2.61155 | + | 1.50778i | 0.147378 | + | 0.0850888i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.43816 | − | 4.22302i | −0.137157 | − | 0.237563i | ||||
\(317\) | 14.2980 | 0.803054 | 0.401527 | − | 0.915847i | \(-0.368480\pi\) | ||||
0.401527 | + | 0.915847i | \(0.368480\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.05132 | − | 2.91638i | 0.282820 | − | 0.163286i | ||||
\(320\) | 1.40066 | + | 1.74303i | 0.0782992 | + | 0.0974384i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.1699 | + | 6.44897i | 0.622476 | + | 0.359387i | ||||
\(323\) | −3.78778 | + | 6.56062i | −0.210757 | + | 0.365043i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4883 | − | 14.6627i | −0.581787 | − | 0.813341i | ||||
\(326\) | −9.91624 | −0.549210 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.35904 | + | 0.784645i | 0.0750407 | + | 0.0433248i | ||||
\(329\) | −3.77757 | − | 6.54295i | −0.208264 | − | 0.360724i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.89017 | + | 5.71009i | −0.543613 | + | 0.313855i | −0.746542 | − | 0.665338i | \(-0.768287\pi\) |
0.202929 | + | 0.979193i | \(0.434954\pi\) | |||||||
\(332\) | −3.19510 | − | 5.53408i | −0.175354 | − | 0.303722i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.49472 | − | 11.2492i | −0.355375 | − | 0.615528i | ||||
\(335\) | 6.12693 | − | 0.946808i | 0.334750 | − | 0.0517296i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.53208i | − | 0.301352i | −0.988583 | − | 0.150676i | \(-0.951855\pi\) | ||
0.988583 | − | 0.150676i | \(-0.0481450\pi\) | |||||||
\(338\) | −11.8774 | − | 5.28458i | −0.646047 | − | 0.287443i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.535898 | − | 3.46788i | −0.0290632 | − | 0.188072i | ||||
\(341\) | −1.07169 | + | 1.85622i | −0.0580353 | + | 0.100520i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8222 | 0.962307 | ||||||||
\(344\) | 4.58006 | − | 2.64430i | 0.246940 | − | 0.142571i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.87696i | 0.208427i | ||||||||
\(347\) | −2.44226 | + | 1.41004i | −0.131107 | + | 0.0756949i | −0.564119 | − | 0.825693i | \(-0.690784\pi\) |
0.433012 | + | 0.901388i | \(0.357451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0704 | + | 13.3197i | 1.23493 | + | 0.712986i | 0.968053 | − | 0.250745i | \(-0.0806757\pi\) |
0.266875 | + | 0.963731i | \(0.414009\pi\) | |||||||
\(350\) | −1.64425 | + | 7.45930i | −0.0878889 | + | 0.398717i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.31702i | 0.0701973i | ||||||||
\(353\) | 6.61308 | − | 11.4542i | 0.351979 | − | 0.609645i | −0.634617 | − | 0.772826i | \(-0.718842\pi\) |
0.986596 | + | 0.163182i | \(0.0521757\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.9329 | + | 12.0077i | 1.64175 | + | 0.637302i | ||||
\(356\) | 18.4450i | 0.977584i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.05325 | + | 12.2166i | 0.372776 | + | 0.645667i | ||||
\(359\) | − | 12.3827i | − | 0.653532i | −0.945105 | − | 0.326766i | \(-0.894041\pi\) | ||
0.945105 | − | 0.326766i | \(-0.105959\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.15178 | − | 3.72700i | 0.113252 | − | 0.196158i | ||||
\(362\) | −13.0736 | + | 22.6441i | −0.687133 | + | 1.19015i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.70276 | + | 5.23831i | 0.0892489 | + | 0.274562i | ||||
\(365\) | 8.38916 | + | 10.4398i | 0.439109 | + | 0.546443i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.14226 | − | 3.54624i | −0.320623 | − | 0.185112i | 0.331047 | − | 0.943614i | \(-0.392598\pi\) |
−0.651670 | + | 0.758502i | \(0.725931\pi\) | |||||||
\(368\) | −7.31172 | + | 4.22143i | −0.381150 | + | 0.220057i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.26809 | + | 5.84282i | −0.117913 | + | 0.303754i | ||||
\(371\) | −18.4110 | + | 10.6296i | −0.955854 | + | 0.551862i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.0259 | − | 18.4902i | 1.65824 | − | 0.957384i | 0.684709 | − | 0.728816i | \(-0.259929\pi\) |
0.973528 | − | 0.228568i | \(-0.0734042\pi\) | |||||||
\(374\) | 1.03339 | − | 1.78989i | 0.0534354 | − | 0.0925528i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.94552 | 0.255046 | ||||||||
\(377\) | 4.93634 | + | 15.1860i | 0.254235 | + | 0.782118i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.6252 | − | 17.1041i | −1.52174 | − | 0.878580i | −0.999670 | − | 0.0256802i | \(-0.991825\pi\) |
−0.522075 | − | 0.852900i | \(-0.674842\pi\) | |||||||
\(380\) | 1.64851 | + | 10.6677i | 0.0845666 | + | 0.547243i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.8543 | 0.964668 | ||||||||
\(383\) | −13.0170 | − | 22.5461i | −0.665137 | − | 1.15205i | −0.979248 | − | 0.202665i | \(-0.935040\pi\) |
0.314111 | − | 0.949386i | \(-0.398294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.50693 | + | 2.81809i | −0.178730 | + | 0.143623i | ||||
\(386\) | 8.94600 | + | 15.4949i | 0.455340 | + | 0.788671i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.963028 | − | 1.66801i | 0.0488904 | − | 0.0846806i | ||||
\(389\) | 6.23568 | 0.316162 | 0.158081 | − | 0.987426i | \(-0.449469\pi\) | ||||
0.158081 | + | 0.987426i | \(0.449469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.2493 | 0.670045 | ||||||||
\(392\) | −2.33310 | + | 4.04106i | −0.117840 | + | 0.204104i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.312928 | + | 0.542008i | 0.0157651 | + | 0.0273060i | ||||
\(395\) | 6.83007 | + | 8.49958i | 0.343658 | + | 0.427660i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3498 | − | 31.7827i | −0.920948 | − | 1.59513i | −0.797951 | − | 0.602722i | \(-0.794083\pi\) |
−0.122997 | − | 0.992407i | \(-0.539250\pi\) | |||||||
\(398\) | −17.6811 | −0.886275 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.69046 | − | 3.37350i | −0.184523 | − | 0.168675i | ||||
\(401\) | −24.5044 | − | 14.1476i | −1.22369 | − | 0.706498i | −0.257987 | − | 0.966148i | \(-0.583059\pi\) |
−0.965703 | + | 0.259651i | \(0.916393\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.36116 | − | 3.92581i | −0.217245 | − | 0.195559i | ||||
\(404\) | 2.43859 | 0.121324 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.38286 | − | 5.85928i | 0.167888 | − | 0.290791i | ||||
\(407\) | −3.19697 | + | 1.84577i | −0.158468 | + | 0.0914915i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.2744 | − | 7.66400i | 0.656379 | − | 0.378961i | −0.134517 | − | 0.990911i | \(-0.542948\pi\) |
0.790896 | + | 0.611951i | \(0.209615\pi\) | |||||||
\(410\) | −3.27122 | − | 1.26984i | −0.161554 | − | 0.0627127i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.7647 | + | 6.21501i | −0.530339 | + | 0.306191i | ||||
\(413\) | 13.8561 | + | 7.99982i | 0.681814 | + | 0.393645i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.95050 | + | 11.1383i | 0.439363 | + | 0.546758i | ||||
\(416\) | −3.52686 | − | 0.749192i | −0.172918 | − | 0.0367322i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.17887 | + | 5.50597i | −0.155484 | + | 0.269306i | ||||
\(419\) | 13.4692 | − | 23.3293i | 0.658013 | − | 1.13971i | −0.323116 | − | 0.946359i | \(-0.604730\pi\) |
0.981129 | − | 0.193353i | \(-0.0619362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.5359i | 1.87812i | 0.343747 | + | 0.939062i | \(0.388304\pi\) | ||||
−0.343747 | + | 0.939062i | \(0.611696\pi\) | |||||||
\(422\) | 8.62227 | + | 14.9342i | 0.419725 | + | 0.726986i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 13.9161i | − | 0.675824i | ||||||
\(425\) | 2.36850 | + | 7.48044i | 0.114889 | + | 0.362855i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.80596 | + | 6.59212i | −0.184183 | + | 0.319015i | ||||
\(428\) | − | 10.4766i | − | 0.506407i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.21818 | + | 7.40752i | −0.444540 | + | 0.357222i | ||||
\(431\) | −2.48744 | − | 1.43612i | −0.119816 | − | 0.0691756i | 0.438894 | − | 0.898539i | \(-0.355370\pi\) |
−0.558710 | + | 0.829363i | \(0.688704\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.2344 | + | 6.48619i | −0.539891 | + | 0.311706i | −0.745035 | − | 0.667026i | \(-0.767567\pi\) |
0.205144 | + | 0.978732i | \(0.434234\pi\) | |||||||
\(434\) | 2.48622i | 0.119342i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.8782 | + | 8.58994i | −0.712537 | + | 0.411383i | ||||
\(437\) | −40.7568 | −1.94966 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.02411 | + | 1.77380i | −0.0488779 | + | 0.0846590i | −0.889429 | − | 0.457073i | \(-0.848898\pi\) |
0.840551 | + | 0.541732i | \(0.182231\pi\) | |||||||
\(440\) | −0.449750 | − | 2.91040i | −0.0214410 | − | 0.138748i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.20530 | + | 3.78551i | 0.200026 | + | 0.180059i | ||||
\(443\) | 25.7082i | 1.22143i | 0.791849 | + | 0.610717i | \(0.209119\pi\) | ||||
−0.791849 | + | 0.610717i | \(0.790881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.29881 | − | 40.7605i | −0.298592 | − | 1.93223i | ||||
\(446\) | 2.44858 | + | 4.24107i | 0.115944 | + | 0.200820i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.763837 | + | 1.32301i | 0.0360879 | + | 0.0625061i | ||||
\(449\) | 16.0756 | − | 9.28127i | 0.758656 | − | 0.438010i | −0.0701571 | − | 0.997536i | \(-0.522350\pi\) |
0.828813 | + | 0.559526i | \(0.189017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.03339 | − | 1.78989i | −0.0486605 | − | 0.0842824i | ||||
\(452\) | 2.25151 | + | 1.29991i | 0.105902 | + | 0.0611427i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.1513 | −0.476426 | ||||||||
\(455\) | −5.55166 | − | 10.9943i | −0.260266 | − | 0.515423i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.3213 | + | 21.3412i | −0.576368 | + | 0.998299i | 0.419523 | + | 0.907745i | \(0.362197\pi\) |
−0.995891 | + | 0.0905546i | \(0.971136\pi\) | |||||||
\(458\) | −13.3332 | − | 7.69794i | −0.623020 | − | 0.359701i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.7161 | − | 11.8256i | 0.686144 | − | 0.551369i | ||||
\(461\) | 27.5693 | − | 15.9171i | 1.28403 | − | 0.741334i | 0.306446 | − | 0.951888i | \(-0.400860\pi\) |
0.977582 | + | 0.210554i | \(0.0675268\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.18319 | 0.147936 | 0.0739678 | − | 0.997261i | \(-0.476434\pi\) | ||||
0.0739678 | + | 0.997261i | \(0.476434\pi\) | |||||||
\(464\) | 2.21438 | + | 3.83543i | 0.102800 | + | 0.178055i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.58772 | − | 4.95812i | −0.397818 | − | 0.229680i | ||||
\(467\) | − | 21.6747i | − | 1.00298i | −0.865162 | − | 0.501492i | \(-0.832785\pi\) | ||
0.865162 | − | 0.501492i | \(-0.167215\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.23559 | 0.195581 | ||||||||
\(470\) | −10.9288 | + | 1.68885i | −0.504108 | + | 0.0779009i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.07005 | + | 5.23660i | −0.417483 | + | 0.241034i | ||||
\(473\) | −6.96517 | −0.320259 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.28586 | − | 23.0110i | −0.334298 | − | 1.05582i | ||||
\(476\) | − | 2.39736i | − | 0.109883i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.19404 | + | 4.73083i | 0.374787 | + | 0.216383i | ||||
\(479\) | 25.3765 | + | 14.6511i | 1.15948 | + | 0.669426i | 0.951179 | − | 0.308639i | \(-0.0998735\pi\) |
0.208300 | + | 0.978065i | \(0.433207\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.12420 | − | 9.61118i | −0.142451 | − | 0.438232i | ||||
\(482\) | − | 13.1038i | − | 0.596861i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.63273 | + | 8.02413i | −0.210579 | + | 0.364733i | ||||
\(485\) | −1.55852 | + | 4.01491i | −0.0707690 | + | 0.182308i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.2643 | − | 36.8309i | −0.963579 | − | 1.66897i | −0.713385 | − | 0.700772i | \(-0.752839\pi\) |
−0.250194 | − | 0.968196i | \(-0.580494\pi\) | |||||||
\(488\) | −2.49134 | − | 4.31513i | −0.112778 | − | 0.195337i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.77580 | − | 9.72681i | 0.170573 | − | 0.439413i | ||||
\(491\) | −6.32521 | + | 10.9556i | −0.285453 | + | 0.494418i | −0.972719 | − | 0.231987i | \(-0.925477\pi\) |
0.687266 | + | 0.726406i | \(0.258811\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.95002i | − | 0.313013i | ||||||
\(494\) | −12.9362 | − | 11.6448i | −0.582026 | − | 0.523925i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.40941 | − | 0.813725i | −0.0632845 | − | 0.0365373i | ||||
\(497\) | 19.6325 | + | 11.3349i | 0.880640 | + | 0.508438i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.54007i | 0.203242i | 0.994823 | + | 0.101621i | \(0.0324028\pi\) | ||||
−0.994823 | + | 0.101621i | \(0.967597\pi\) | |||||||
\(500\) | 9.30734 | + | 6.19463i | 0.416237 | + | 0.277032i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23.1644 | −1.03388 | ||||||||
\(503\) | 17.2476 | − | 9.95791i | 0.769033 | − | 0.444001i | −0.0634967 | − | 0.997982i | \(-0.520225\pi\) |
0.832529 | + | 0.553981i | \(0.186892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.38888 | + | 0.832755i | −0.239802 | + | 0.0370571i | ||||
\(506\) | 11.1194 | 0.494317 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 8.10083i | − | 0.359416i | ||||||
\(509\) | 9.09532 | + | 5.25118i | 0.403143 | + | 0.232755i | 0.687839 | − | 0.725863i | \(-0.258559\pi\) |
−0.284696 | + | 0.958618i | \(0.591893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.57496 | + | 7.92406i | 0.202384 | + | 0.350540i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.32895 | + | 1.92197i | −0.146834 | + | 0.0847746i | ||||
\(515\) | 21.6659 | − | 17.4102i | 0.954713 | − | 0.767185i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.64072 | − | 3.25667i | −0.248078 | − | 0.143228i | ||||
\(518\) | −2.14100 | + | 3.70833i | −0.0940703 | + | 0.162934i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.04962 | + | 0.451203i | 0.352999 | + | 0.0197866i | ||||
\(521\) | 24.5221 | 1.07433 | 0.537166 | − | 0.843477i | \(-0.319495\pi\) | ||||
0.537166 | + | 0.843477i | \(0.319495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.6924 | + | 12.5241i | 0.948541 | + | 0.547641i | 0.892627 | − | 0.450795i | \(-0.148859\pi\) |
0.0559138 | + | 0.998436i | \(0.482193\pi\) | |||||||
\(524\) | −1.16253 | − | 2.01356i | −0.0507853 | − | 0.0879628i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.5060 | − | 15.3032i | 1.15572 | − | 0.667253i | ||||
\(527\) | 1.27697 | + | 2.21178i | 0.0556257 | + | 0.0963466i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.1409 | + | 41.8132i | 1.04960 | + | 1.81797i | ||||
\(530\) | 4.75222 | + | 30.7523i | 0.206423 | + | 1.33579i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.37466i | 0.319732i | ||||||||
\(533\) | 5.38100 | − | 1.74914i | 0.233077 | − | 0.0757638i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.57767 | + | 23.1516i | 0.154676 | + | 1.00093i | ||||
\(536\) | −1.38628 | + | 2.40112i | −0.0598784 | + | 0.103712i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.0874 | −0.779803 | ||||||||
\(539\) | 5.32214 | − | 3.07274i | 0.229241 | − | 0.132352i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 20.6859i | − | 0.889356i | −0.895690 | − | 0.444678i | \(-0.853318\pi\) | ||
0.895690 | − | 0.444678i | \(-0.146682\pi\) | |||||||
\(542\) | 12.2869 | − | 7.09382i | 0.527765 | − | 0.304705i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.35904 | + | 0.784645i | 0.0582686 | + | 0.0336414i | ||||
\(545\) | 29.9450 | − | 24.0631i | 1.28270 | − | 1.03075i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.5960i | 1.73576i | 0.496773 | + | 0.867880i | \(0.334518\pi\) | ||||
−0.496773 | + | 0.867880i | \(0.665482\pi\) | |||||||
\(548\) | −6.14192 | + | 10.6381i | −0.262370 | + | 0.454438i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.98775 | + | 6.27792i | 0.0847579 | + | 0.267691i | ||||
\(551\) | 21.3793i | 0.910790i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.72472 | + | 6.45140i | 0.158391 | + | 0.274342i | ||||
\(554\) | 16.8419i | 0.715545i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.32861 | + | 5.76531i | −0.141164 | + | 0.244504i | ||||
\(557\) | −20.6032 | + | 35.6858i | −0.872985 | + | 1.51205i | −0.0140907 | + | 0.999901i | \(0.504485\pi\) |
−0.858894 | + | 0.512153i | \(0.828848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.96217 | − | 18.6521i | 0.167582 | − | 0.788900i | ||||
\(560\) | −2.13975 | − | 2.66278i | −0.0904210 | − | 0.112523i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.46112 | − | 4.30768i | −0.314728 | − | 0.181708i | ||||
\(563\) | 13.0933 | − | 7.55940i | 0.551815 | − | 0.318591i | −0.198038 | − | 0.980194i | \(-0.563457\pi\) |
0.749854 | + | 0.661603i | \(0.230124\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.41939 | − | 2.10372i | −0.227995 | − | 0.0885043i | ||||
\(566\) | 23.9192 | − | 13.8098i | 1.00540 | − | 0.580468i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.8513 | + | 7.41968i | −0.539227 | + | 0.311323i | ||||
\(569\) | 13.2995 | − | 23.0353i | 0.557542 | − | 0.965692i | −0.440159 | − | 0.897920i | \(-0.645078\pi\) |
0.997701 | − | 0.0677716i | \(-0.0215889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.8452 | 1.33268 | 0.666340 | − | 0.745648i | \(-0.267860\pi\) | ||||
0.666340 | + | 0.745648i | \(0.267860\pi\) | |||||||
\(572\) | 3.52928 | + | 3.17697i | 0.147567 | + | 0.132836i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.07618 | − | 1.19868i | −0.0866580 | − | 0.0500320i | ||||
\(575\) | −28.4820 | + | 31.1580i | −1.18778 | + | 1.29938i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.20258 | −0.0500639 | −0.0250319 | − | 0.999687i | \(-0.507969\pi\) | ||||
−0.0250319 | + | 0.999687i | \(0.507969\pi\) | |||||||
\(578\) | 7.26867 | + | 12.5897i | 0.302337 | + | 0.523662i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.20319 | − | 7.71948i | −0.257574 | − | 0.320534i | ||||
\(581\) | 4.88108 | + | 8.45427i | 0.202501 | + | 0.350742i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.16386 | + | 15.8723i | −0.379528 | + | 0.657362i | ||||
\(584\) | −5.98944 | −0.247845 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.2501 | −1.24962 | ||||||||
\(587\) | 9.53243 | − | 16.5107i | 0.393446 | − | 0.681468i | −0.599456 | − | 0.800408i | \(-0.704616\pi\) |
0.992901 | + | 0.118940i | \(0.0379496\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.92816 | − | 6.80377i | −0.161857 | − | 0.280344i | ||||
\(590\) | 18.2551 | − | 14.6694i | 0.751550 | − | 0.603929i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.40148 | − | 2.42743i | −0.0576004 | − | 0.0997668i | ||||
\(593\) | 11.8496 | 0.486606 | 0.243303 | − | 0.969950i | \(-0.421769\pi\) | ||||
0.243303 | + | 0.969950i | \(0.421769\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.818679 | + | 5.29779i | 0.0335625 | + | 0.217188i | ||||
\(596\) | −2.60768 | − | 1.50554i | −0.106815 | − | 0.0616694i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.32532 | + | 29.7767i | −0.258661 | + | 1.21766i | ||||
\(599\) | −13.1277 | −0.536382 | −0.268191 | − | 0.963366i | \(-0.586426\pi\) | ||||
−0.268191 | + | 0.963366i | \(0.586426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.8125 | − | 30.8522i | 0.726589 | − | 1.25849i | −0.231728 | − | 0.972781i | \(-0.574438\pi\) |
0.958317 | − | 0.285708i | \(-0.0922288\pi\) | |||||||
\(602\) | −6.99684 | + | 4.03963i | −0.285170 | + | 0.164643i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4052 | − | 6.00745i | 0.423382 | − | 0.244440i | ||||
\(605\) | 7.49742 | − | 19.3141i | 0.304813 | − | 0.785228i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.20075 | + | 2.42530i | −0.170503 | + | 0.0984400i | −0.582823 | − | 0.812599i | \(-0.698052\pi\) |
0.412320 | + | 0.911039i | \(0.364719\pi\) | |||||||
\(608\) | −4.18063 | − | 2.41369i | −0.169547 | − | 0.0978880i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.97904 | + | 8.68497i | 0.282573 | + | 0.351644i | ||||
\(611\) | 11.9298 | − | 13.2528i | 0.482629 | − | 0.536149i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7172 | − | 20.2948i | 0.473253 | − | 0.819698i | −0.526279 | − | 0.850312i | \(-0.676413\pi\) |
0.999531 | + | 0.0306146i | \(0.00974646\pi\) | |||||||
\(614\) | 7.06959 | − | 12.2449i | 0.285306 | − | 0.494164i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 2.01198i | − | 0.0810648i | ||||||
\(617\) | 7.01830 | + | 12.1560i | 0.282546 | + | 0.489384i | 0.972011 | − | 0.234935i | \(-0.0754877\pi\) |
−0.689465 | + | 0.724319i | \(0.742154\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16.1470i | − | 0.649002i | −0.945885 | − | 0.324501i | \(-0.894804\pi\) | ||
0.945885 | − | 0.324501i | \(-0.105196\pi\) | |||||||
\(620\) | 3.39246 | + | 1.31690i | 0.136244 | + | 0.0528879i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.98713 | − | 8.63797i | 0.199966 | − | 0.346351i | ||||
\(623\) | − | 28.1780i | − | 1.12893i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.6831 | − | 10.5108i | −0.907325 | − | 0.420431i | ||||
\(626\) | 2.67134 | + | 1.54230i | 0.106768 | + | 0.0616428i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.61155 | − | 1.50778i | 0.104212 | − | 0.0601669i | ||||
\(629\) | 4.39865i | 0.175386i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.3611 | − | 9.44608i | 0.651325 | − | 0.376043i | −0.137639 | − | 0.990483i | \(-0.543951\pi\) |
0.788964 | + | 0.614440i | \(0.210618\pi\) | |||||||
\(632\) | −4.87632 | −0.193970 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.14899 | − | 12.3824i | 0.283922 | − | 0.491768i | ||||
\(635\) | 2.76636 | + | 17.9015i | 0.109780 | + | 0.710400i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.20100 | + | 16.0002i | 0.206071 | + | 0.633950i | ||||
\(638\) | − | 5.83277i | − | 0.230921i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.20984 | − | 0.341491i | 0.0873515 | − | 0.0134986i | ||||
\(641\) | −3.57648 | − | 6.19465i | −0.141262 | − | 0.244674i | 0.786710 | − | 0.617323i | \(-0.211783\pi\) |
−0.927972 | + | 0.372649i | \(0.878449\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.9623 | + | 34.5756i | 0.787235 | + | 1.36353i | 0.927655 | + | 0.373438i | \(0.121821\pi\) |
−0.140420 | + | 0.990092i | \(0.544845\pi\) | |||||||
\(644\) | 11.1699 | − | 6.44897i | 0.440157 | − | 0.254125i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.78778 | + | 6.56062i | 0.149028 | + | 0.258124i | ||||
\(647\) | −12.0656 | − | 6.96608i | −0.474348 | − | 0.273865i | 0.243710 | − | 0.969848i | \(-0.421635\pi\) |
−0.718058 | + | 0.695983i | \(0.754969\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.7934 | 0.541438 | ||||||||
\(650\) | −17.9424 | + | 1.75179i | −0.703760 | + | 0.0687108i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.95812 | + | 8.58772i | −0.194175 | + | 0.336321i | ||||
\(653\) | 25.7670 | + | 14.8766i | 1.00834 | + | 0.582165i | 0.910705 | − | 0.413058i | \(-0.135539\pi\) |
0.0976340 | + | 0.995222i | \(0.468873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.25662 | + | 4.05265i | 0.127246 | + | 0.158350i | ||||
\(656\) | 1.35904 | − | 0.784645i | 0.0530618 | − | 0.0306352i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.55515 | −0.294530 | ||||||||
\(659\) | 14.6318 | + | 25.3431i | 0.569975 | + | 0.987226i | 0.996568 | + | 0.0827819i | \(0.0263805\pi\) |
−0.426593 | + | 0.904444i | \(0.640286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0903 | − | 17.3726i | −1.17038 | − | 0.675717i | −0.216608 | − | 0.976259i | \(-0.569499\pi\) |
−0.953769 | + | 0.300541i | \(0.902833\pi\) | |||||||
\(662\) | 11.4202i | 0.443858i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.39020 | −0.247988 | ||||||||
\(665\) | −2.51838 | − | 16.2968i | −0.0976587 | − | 0.631963i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.3819 | − | 18.6957i | 1.25383 | − | 0.723901i | ||||
\(668\) | −12.9894 | −0.502576 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.24351 | − | 5.77948i | 0.0866742 | − | 0.223281i | ||||
\(671\) | 6.56228i | 0.253334i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.1953 | − | 16.2786i | −1.08685 | − | 0.627492i | −0.154113 | − | 0.988053i | \(-0.549252\pi\) |
−0.932736 | + | 0.360561i | \(0.882585\pi\) | |||||||
\(674\) | −4.79092 | − | 2.76604i | −0.184539 | − | 0.106544i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.5153 | + | 7.64386i | −0.404434 | + | 0.293995i | ||||
\(677\) | 32.2002i | 1.23756i | 0.785566 | + | 0.618778i | \(0.212372\pi\) | ||||
−0.785566 | + | 0.618778i | \(0.787628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.47119 | + | 2.54818i | −0.0564593 | + | 0.0977903i | ||||
\(680\) | −3.27122 | − | 1.26984i | −0.125445 | − | 0.0486960i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.07169 | + | 1.85622i | 0.0410372 | + | 0.0710784i | ||||
\(683\) | −3.19280 | − | 5.53009i | −0.122169 | − | 0.211603i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.93983 | − | 25.6059i | 0.379781 | − | 0.978352i | ||||
\(686\) | 8.91109 | − | 15.4345i | 0.340227 | − | 0.589290i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 5.28860i | − | 0.201626i | ||||||
\(689\) | −37.2916 | − | 33.5690i | −1.42070 | − | 1.27888i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.6788 | + | 7.89748i | 0.520368 | + | 0.300434i | 0.737085 | − | 0.675800i | \(-0.236202\pi\) |
−0.216717 | + | 0.976234i | \(0.569535\pi\) | |||||||
\(692\) | 3.35755 | + | 1.93848i | 0.127635 | + | 0.0736900i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.82008i | 0.107049i | ||||||||
\(695\) | 5.38688 | − | 13.8771i | 0.204336 | − | 0.526388i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.46267 | −0.0932803 | ||||||||
\(698\) | 23.0704 | − | 13.3197i | 0.873226 | − | 0.504157i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.63782 | + | 5.15361i | 0.213090 | + | 0.194788i | ||||
\(701\) | 43.7481 | 1.65234 | 0.826171 | − | 0.563420i | \(-0.190515\pi\) | ||||
0.826171 | + | 0.563420i | \(0.190515\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.5309i | − | 0.510329i | ||||||
\(704\) | 1.14057 | + | 0.658509i | 0.0429869 | + | 0.0248185i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.61308 | − | 11.4542i | −0.248886 | − | 0.431084i | ||||
\(707\) | −3.72537 | −0.140107 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.0167 | + | 17.3302i | −1.12730 | + | 0.650848i | −0.943255 | − | 0.332070i | \(-0.892253\pi\) |
−0.184046 | + | 0.982918i | \(0.558920\pi\) | |||||||
\(710\) | 25.8654 | − | 20.7849i | 0.970713 | − | 0.780042i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.9738 | + | 9.22251i | 0.598645 | + | 0.345628i | ||||
\(713\) | −6.87016 | + | 11.8995i | −0.257290 | + | 0.445639i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.88404 | − | 5.81538i | −0.332244 | − | 0.217483i | ||||
\(716\) | 14.1065 | 0.527185 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.7237 | − | 6.19133i | −0.400205 | − | 0.231058i | ||||
\(719\) | 21.9251 | + | 37.9755i | 0.817670 | + | 1.41625i | 0.907395 | + | 0.420279i | \(0.138068\pi\) |
−0.0897253 | + | 0.995967i | \(0.528599\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.4450 | − | 9.49451i | 0.612443 | − | 0.353594i | ||||
\(722\) | −2.15178 | − | 3.72700i | −0.0800811 | − | 0.138704i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.0736 | + | 22.6441i | 0.485876 | + | 0.841563i | ||||
\(725\) | 16.3442 | + | 14.9405i | 0.607008 | + | 0.554875i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 17.2599i | − | 0.640136i | −0.947395 | − | 0.320068i | \(-0.896294\pi\) | ||
0.947395 | − | 0.320068i | \(-0.103706\pi\) | |||||||
\(728\) | 5.38789 | + | 1.14452i | 0.199688 | + | 0.0424188i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.2357 | − | 2.04534i | 0.489875 | − | 0.0757014i | ||||
\(731\) | −4.14967 | + | 7.18744i | −0.153481 | + | 0.265837i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.304799 | −0.0112580 | −0.00562900 | − | 0.999984i | \(-0.501792\pi\) | ||||
−0.00562900 | + | 0.999984i | \(0.501792\pi\) | |||||||
\(734\) | −6.14226 | + | 3.54624i | −0.226715 | + | 0.130894i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.44285i | 0.311208i | ||||||||
\(737\) | 3.16231 | − | 1.82576i | 0.116485 | − | 0.0672528i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.14941 | + | 1.81831i | 0.115853 | + | 0.0668877i | 0.556807 | − | 0.830642i | \(-0.312026\pi\) |
−0.440954 | + | 0.897530i | \(0.645360\pi\) | |||||||
\(740\) | 3.92599 | + | 4.88564i | 0.144322 | + | 0.179600i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21.2592i | 0.780451i | ||||||||
\(743\) | −15.1150 | + | 26.1800i | −0.554517 | + | 0.960451i | 0.443424 | + | 0.896312i | \(0.353764\pi\) |
−0.997941 | + | 0.0641394i | \(0.979570\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.27667 | + | 2.43651i | 0.229959 | + | 0.0892667i | ||||
\(746\) | − | 36.9803i | − | 1.35395i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.03339 | − | 1.78989i | −0.0377845 | − | 0.0654447i | ||||
\(749\) | 16.0049i | 0.584805i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.00159080 | + | 0.00275535i | −5.80493e−5 | + | 0.000100544i | −0.866054 | − | 0.499950i | \(-0.833352\pi\) |
0.865996 | + | 0.500050i | \(0.166685\pi\) | |||||||
\(752\) | 2.47276 | − | 4.28295i | 0.0901723 | − | 0.156183i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.6196 | + | 3.31800i | 0.568833 | + | 0.120834i | ||||
\(755\) | −20.9423 | + | 16.8288i | −0.762170 | + | 0.612462i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.4328 | + | 21.0345i | 1.32417 | + | 0.764512i | 0.984392 | − | 0.175992i | \(-0.0563132\pi\) |
0.339782 | + | 0.940504i | \(0.389647\pi\) | |||||||
\(758\) | −29.6252 | + | 17.1041i | −1.07604 | + | 0.621250i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.0628 | + | 3.90621i | 0.365015 | + | 0.141693i | ||||
\(761\) | −21.1489 | + | 12.2103i | −0.766646 | + | 0.442623i | −0.831677 | − | 0.555260i | \(-0.812619\pi\) |
0.0650310 | + | 0.997883i | \(0.479285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.7291 | − | 13.1226i | 0.822847 | − | 0.475071i | ||||
\(764\) | 9.42713 | − | 16.3283i | 0.341062 | − | 0.590736i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.0340 | −0.940646 | ||||||||
\(767\) | −7.84643 | + | 36.9374i | −0.283318 | + | 1.33373i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1198 | − | 16.2350i | −1.01403 | − | 0.585449i | −0.101659 | − | 0.994819i | \(-0.532415\pi\) |
−0.912368 | + | 0.409370i | \(0.865748\pi\) | |||||||
\(770\) | 0.687072 | + | 4.44614i | 0.0247603 | + | 0.160228i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.8920 | 0.643947 | ||||||||
\(773\) | 4.13819 | + | 7.16756i | 0.148840 | + | 0.257799i | 0.930799 | − | 0.365531i | \(-0.119113\pi\) |
−0.781959 | + | 0.623330i | \(0.785779\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.94649 | − | 1.75164i | −0.285446 | − | 0.0629208i | ||||
\(776\) | −0.963028 | − | 1.66801i | −0.0345707 | − | 0.0598782i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.11784 | − | 5.40026i | 0.111780 | − | 0.193609i | ||||
\(779\) | 7.57555 | 0.271422 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5437 | 0.699328 | ||||||||
\(782\) | 6.62464 | − | 11.4742i | 0.236897 | − | 0.410317i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.33310 | + | 4.04106i | 0.0833252 | + | 0.144323i | ||||
\(785\) | −5.25620 | + | 4.22376i | −0.187602 | + | 0.150753i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.61500 | − | 2.79726i | −0.0575685 | − | 0.0997115i | 0.835805 | − | 0.549027i | \(-0.185001\pi\) |
−0.893373 | + | 0.449315i | \(0.851668\pi\) | |||||||
\(788\) | 0.625857 | 0.0222952 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.7759 | − | 1.66522i | 0.383389 | − | 0.0592459i | ||||
\(791\) | −3.43958 | − | 1.98584i | −0.122297 | − | 0.0706085i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5732 | − | 3.73299i | −0.624043 | − | 0.132562i | ||||
\(794\) | −36.6995 | −1.30242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.84057 | + | 15.3123i | −0.313346 | + | 0.542731i | ||||
\(797\) | −35.1612 | + | 20.3003i | −1.24547 | + | 0.719075i | −0.970203 | − | 0.242292i | \(-0.922101\pi\) |
−0.275271 | + | 0.961367i | \(0.588768\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.72118 | + | 3.88048i | −0.237778 | + | 0.137281i | ||||
\(800\) | −4.76677 | + | 1.50928i | −0.168531 | + | 0.0533611i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.5044 | + | 14.1476i | −0.865279 | + | 0.499569i | ||||
\(803\) | 6.83138 | + | 3.94410i | 0.241074 | + | 0.139184i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.4815 | + | 18.0656i | −0.792368 | + | 0.636729i | ||||
\(806\) | −5.58043 | + | 1.81397i | −0.196562 | + | 0.0638944i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.21929 | − | 2.11188i | 0.0428946 | − | 0.0742956i | ||||
\(809\) | −0.000840236 | 0.00145533i | −2.95411e−5 | 5.11667e-5i | −0.866040 | − | 0.499974i | \(-0.833343\pi\) | ||
0.866011 | + | 0.500026i | \(0.166676\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.9476i | 1.22718i | 0.789626 | + | 0.613588i | \(0.210274\pi\) | ||||
−0.789626 | + | 0.613588i | \(0.789726\pi\) | |||||||
\(812\) | −3.38286 | − | 5.85928i | −0.118715 | − | 0.205621i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.69154i | 0.129389i | ||||||||
\(815\) | 8.02401 | − | 20.6706i | 0.281069 | − | 0.724060i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.7650 | − | 22.1097i | 0.446592 | − | 0.773519i | ||||
\(818\) | − | 15.3280i | − | 0.535931i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.73532 | + | 2.19804i | −0.0955215 | + | 0.0767589i | ||||
\(821\) | −22.0044 | − | 12.7042i | −0.767957 | − | 0.443380i | 0.0641882 | − | 0.997938i | \(-0.479554\pi\) |
−0.832145 | + | 0.554557i | \(0.812888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9040 | − | 10.9142i | 0.658952 | − | 0.380446i | −0.132926 | − | 0.991126i | \(-0.542437\pi\) |
0.791878 | + | 0.610680i | \(0.209104\pi\) | |||||||
\(824\) | 12.4300i | 0.433020i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.8561 | − | 7.99982i | 0.482115 | − | 0.278349i | ||||
\(827\) | −18.9366 | −0.658492 | −0.329246 | − | 0.944244i | \(-0.606794\pi\) | ||||
−0.329246 | + | 0.944244i | \(0.606794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.304309 | + | 0.527078i | −0.0105691 | + | 0.0183062i | −0.871262 | − | 0.490819i | \(-0.836698\pi\) |
0.860692 | + | 0.509125i | \(0.170031\pi\) | |||||||
\(830\) | 14.1213 | − | 2.18220i | 0.490158 | − | 0.0757452i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.41225 | + | 2.67975i | −0.0836296 | + | 0.0929036i | ||||
\(833\) | − | 7.32263i | − | 0.253714i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.7046 | − | 4.43578i | 0.993362 | − | 0.153506i | ||||
\(836\) | 3.17887 | + | 5.50597i | 0.109944 | + | 0.190428i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.4692 | − | 23.3293i | −0.465286 | − | 0.805898i | ||||
\(839\) | 23.3215 | − | 13.4647i | 0.805148 | − | 0.464853i | −0.0401198 | − | 0.999195i | \(-0.512774\pi\) |
0.845268 | + | 0.534342i | \(0.179441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.69300 | + | 8.12852i | 0.161828 | + | 0.280294i | ||||
\(842\) | 33.3731 | + | 19.2679i | 1.15011 | + | 0.664017i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.2445 | 0.593581 | ||||||||
\(845\) | 20.6268 | − | 20.4826i | 0.709583 | − | 0.704622i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.07731 | − | 12.2583i | 0.243179 | − | 0.421199i | ||||
\(848\) | −12.0517 | − | 6.95804i | −0.413856 | − | 0.238940i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.66250 | + | 1.68904i | 0.262822 | + | 0.0579336i | ||||
\(851\) | −20.4944 | + | 11.8325i | −0.702541 | + | 0.405612i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.3790 | −1.41679 | −0.708394 | − | 0.705817i | \(-0.750580\pi\) | ||||
−0.708394 | + | 0.705817i | \(0.750580\pi\) | |||||||
\(854\) | 3.80596 | + | 6.59212i | 0.130237 | + | 0.225578i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.07302 | − | 5.23831i | −0.310109 | − | 0.179042i | ||||
\(857\) | − | 30.6051i | − | 1.04545i | −0.852501 | − | 0.522726i | \(-0.824915\pi\) | ||
0.852501 | − | 0.522726i | \(-0.175085\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.9385 | 1.05561 | 0.527803 | − | 0.849367i | \(-0.323016\pi\) | ||||
0.527803 | + | 0.849367i | \(0.323016\pi\) | |||||||
\(860\) | 1.80601 | + | 11.6869i | 0.0615844 | + | 0.398521i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.48744 | + | 1.43612i | −0.0847225 | + | 0.0489145i | ||||
\(863\) | 15.1133 | 0.514464 | 0.257232 | − | 0.966350i | \(-0.417190\pi\) | ||||
0.257232 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.08161 | − | 3.13716i | −0.274783 | − | 0.106667i | ||||
\(866\) | 12.9724i | 0.440819i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.15313 | + | 1.24311i | 0.0730819 | + | 0.0421938i | ||||
\(869\) | 5.56179 | + | 3.21110i | 0.188671 | + | 0.108929i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.09033 | + | 9.50698i | 0.104712 | + | 0.322132i | ||||
\(872\) | 17.1799i | 0.581784i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.3784 | + | 35.2964i | −0.689310 | + | 1.19392i | ||||
\(875\) | −14.2186 | − | 9.46339i | −0.480676 | − | 0.319921i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.54757 | − | 9.60868i | −0.187328 | − | 0.324462i | 0.757030 | − | 0.653380i | \(-0.226649\pi\) |
−0.944359 | + | 0.328918i | \(0.893316\pi\) | |||||||
\(878\) | 1.02411 | + | 1.77380i | 0.0345619 | + | 0.0598629i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.74535 | − | 1.06570i | −0.0925458 | − | 0.0359248i | ||||
\(881\) | −22.3598 | + | 38.7283i | −0.753321 | + | 1.30479i | 0.192884 | + | 0.981222i | \(0.438216\pi\) |
−0.946205 | + | 0.323568i | \(0.895117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.9779i | 0.369435i | 0.982792 | + | 0.184718i | \(0.0591371\pi\) | ||||
−0.982792 | + | 0.184718i | \(0.940863\pi\) | |||||||
\(884\) | 5.38100 | − | 1.74914i | 0.180983 | − | 0.0588301i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.2640 | + | 12.8541i | 0.747973 | + | 0.431842i | ||||
\(887\) | −33.2555 | − | 19.2001i | −1.11661 | − | 0.644675i | −0.176076 | − | 0.984377i | \(-0.556341\pi\) |
−0.940533 | + | 0.339702i | \(0.889674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.3754i | 0.415059i | ||||||||
\(890\) | −38.4490 | − | 14.9253i | −1.28881 | − | 0.500298i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.89716 | 0.163969 | ||||||||
\(893\) | 20.6754 | − | 11.9369i | 0.691876 | − | 0.399455i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.1731 | + | 4.81725i | −1.04200 | + | 0.161023i | ||||
\(896\) | 1.52767 | 0.0510360 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 18.5625i | − | 0.619440i | ||||||
\(899\) | 6.24197 | + | 3.60380i | 0.208181 | + | 0.120193i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9192 | + | 18.9126i | 0.363770 | + | 0.630069i | ||||
\(902\) | −2.06678 | −0.0688163 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.25151 | − | 1.29991i | 0.0748842 | − | 0.0432344i | ||||
\(905\) | −36.6233 | − | 45.5754i | −1.21740 | − | 1.51498i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.3953 | + | 19.8581i | 1.14208 | + | 0.659378i | 0.946944 | − | 0.321399i | \(-0.104153\pi\) |
0.195133 | + | 0.980777i | \(0.437486\pi\) | |||||||
\(908\) | −5.07567 | + | 8.79132i | −0.168442 | + | 0.291750i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.2972 | − | 0.689291i | −0.407648 | − | 0.0228498i | ||||
\(911\) | −17.9575 | −0.594959 | −0.297479 | − | 0.954728i | \(-0.596146\pi\) | ||||
−0.297479 | + | 0.954728i | \(0.596146\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.28848 | + | 4.20801i | 0.241213 | + | 0.139265i | ||||
\(914\) | 12.3213 | + | 21.3412i | 0.407554 | + | 0.705904i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.3332 | + | 7.69794i | −0.440542 | + | 0.254347i | ||||
\(917\) | 1.77597 | + | 3.07607i | 0.0586476 | + | 0.101581i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0149 | + | 17.3463i | 0.330361 | + | 0.572203i | 0.982583 | − | 0.185826i | \(-0.0594961\pi\) |
−0.652221 | + | 0.758029i | \(0.726163\pi\) | |||||||
\(920\) | −2.88316 | − | 18.6573i | −0.0950549 | − | 0.615114i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 31.8342i | − | 1.04840i | ||||||
\(923\) | −11.1175 | + | 52.3363i | −0.365938 | + | 1.72267i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.3442 | − | 9.45578i | −0.340115 | − | 0.310904i | ||||
\(926\) | 1.59160 | − | 2.75673i | 0.0523031 | − | 0.0905916i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.42877 | 0.145381 | ||||||||
\(929\) | −35.1451 | + | 20.2910i | −1.15307 | + | 0.665727i | −0.949634 | − | 0.313361i | \(-0.898545\pi\) |
−0.203439 | + | 0.979088i | \(0.565212\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.5255i | 0.738245i | ||||||||
\(932\) | −8.58772 | + | 4.95812i | −0.281300 | + | 0.162409i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −18.7708 | − | 10.8373i | −0.614200 | − | 0.354609i | ||||
\(935\) | 2.89486 | + | 3.60246i | 0.0946719 | + | 0.117813i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.1112i | 1.53905i | 0.638614 | + | 0.769527i | \(0.279508\pi\) | ||||
−0.638614 | + | 0.769527i | \(0.720492\pi\) | |||||||
\(938\) | 2.11779 | − | 3.66812i | 0.0691484 | − | 0.119769i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.00181 | + | 10.3090i | −0.130525 | + | 0.336244i | ||||
\(941\) | − | 4.35101i | − | 0.141839i | −0.997482 | − | 0.0709195i | \(-0.977407\pi\) | ||
0.997482 | − | 0.0709195i | \(-0.0225933\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.62464 | − | 11.4742i | −0.215728 | − | 0.373652i | ||||
\(944\) | 10.4732i | 0.340873i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.48259 | + | 6.03202i | −0.113229 | + | 0.196118i | ||||
\(947\) | 17.4580 | − | 30.2381i | 0.567307 | − | 0.982605i | −0.429524 | − | 0.903056i | \(-0.641319\pi\) |
0.996831 | − | 0.0795494i | \(-0.0253481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.4480 | + | 16.0502i | −0.469002 | + | 0.521011i | ||||
\(950\) | −23.5710 | − | 5.19575i | −0.764745 | − | 0.168572i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.07618 | − | 1.19868i | −0.0672893 | − | 0.0388495i | ||||
\(953\) | 8.39700 | − | 4.84801i | 0.272005 | − | 0.157042i | −0.357793 | − | 0.933801i | \(-0.616471\pi\) |
0.629799 | + | 0.776758i | \(0.283137\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.2565 | + | 39.3021i | −0.493688 | + | 1.27179i | ||||
\(956\) | 8.19404 | − | 4.73083i | 0.265014 | − | 0.153006i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.3765 | − | 14.6511i | 0.819876 | − | 0.473356i | ||||
\(959\) | 9.38286 | − | 16.2516i | 0.302988 | − | 0.524791i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.3514 | 0.914561 | ||||||||
\(962\) | −9.88562 | − | 2.09995i | −0.318725 | − | 0.0677052i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.3482 | − | 6.55189i | −0.365501 | − | 0.211022i | ||||
\(965\) | −39.5384 | + | 6.10996i | −1.27279 | + | 0.196687i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.1715 | −1.16320 | −0.581599 | − | 0.813476i | \(-0.697573\pi\) | ||||
−0.581599 | + | 0.813476i | \(0.697573\pi\) | |||||||
\(968\) | 4.63273 | + | 8.02413i | 0.148902 | + | 0.257905i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.69775 | + | 3.35718i | 0.0866195 | + | 0.107792i | ||||
\(971\) | −0.194688 | − | 0.337209i | −0.00624783 | − | 0.0108216i | 0.862885 | − | 0.505401i | \(-0.168655\pi\) |
−0.869132 | + | 0.494579i | \(0.835322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.08503 | − | 8.80753i | 0.163019 | − | 0.282356i | ||||
\(974\) | −42.5287 | −1.36271 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.98268 | −0.159492 | ||||||||
\(977\) | −2.70086 | + | 4.67802i | −0.0864080 | + | 0.149663i | −0.905990 | − | 0.423298i | \(-0.860872\pi\) |
0.819582 | + | 0.572961i | \(0.194206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.1462 | − | 21.0378i | −0.388194 | − | 0.672372i | ||||
\(980\) | −6.53577 | − | 8.13334i | −0.208777 | − | 0.259810i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.32521 | + | 10.9556i | 0.201845 | + | 0.349607i | ||||
\(983\) | 43.6819 | 1.39324 | 0.696618 | − | 0.717442i | \(-0.254687\pi\) | ||||
0.696618 | + | 0.717442i | \(0.254687\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.38304 | + | 0.213725i | −0.0440674 | + | 0.00680983i | ||||
\(986\) | −6.01889 | − | 3.47501i | −0.191681 | − | 0.110667i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.5528 | + | 5.38064i | −0.526615 | + | 0.171181i | ||||
\(989\) | −44.6508 | −1.41981 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.9427 | − | 48.3981i | 0.887628 | − | 1.53742i | 0.0449569 | − | 0.998989i | \(-0.485685\pi\) |
0.842671 | − | 0.538428i | \(-0.180982\pi\) | |||||||
\(992\) | −1.40941 | + | 0.813725i | −0.0447489 | + | 0.0258358i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.6325 | − | 11.3349i | 0.622706 | − | 0.359520i | ||||
\(995\) | 14.3072 | − | 36.8567i | 0.453569 | − | 1.16844i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.9866 | + | 17.8901i | −0.981357 | + | 0.566587i | −0.902680 | − | 0.430314i | \(-0.858403\pi\) |
−0.0786773 | + | 0.996900i | \(0.525070\pi\) | |||||||
\(998\) | 3.93182 | + | 2.27004i | 0.124460 | + | 0.0718567i | ||||
\(999\) | 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 | 1170.2.bj.d.199.5 | 12 | ||
3.2 | odd | 2 | 390.2.x.a.199.2 | yes | 12 | ||
5.4 | even | 2 | 1170.2.bj.c.199.2 | 12 | |||
13.10 | even | 6 | 1170.2.bj.c.829.2 | 12 | |||
15.2 | even | 4 | 1950.2.bc.i.901.1 | 12 | |||
15.8 | even | 4 | 1950.2.bc.j.901.6 | 12 | |||
15.14 | odd | 2 | 390.2.x.b.199.5 | yes | 12 | ||
39.23 | odd | 6 | 390.2.x.b.49.5 | yes | 12 | ||
65.49 | even | 6 | inner | 1170.2.bj.d.829.5 | 12 | ||
195.23 | even | 12 | 1950.2.bc.j.751.6 | 12 | |||
195.62 | even | 12 | 1950.2.bc.i.751.1 | 12 | |||
195.179 | odd | 6 | 390.2.x.a.49.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.x.a.49.2 | ✓ | 12 | 195.179 | odd | 6 | ||
390.2.x.a.199.2 | yes | 12 | 3.2 | odd | 2 | ||
390.2.x.b.49.5 | yes | 12 | 39.23 | odd | 6 | ||
390.2.x.b.199.5 | yes | 12 | 15.14 | odd | 2 | ||
1170.2.bj.c.199.2 | 12 | 5.4 | even | 2 | |||
1170.2.bj.c.829.2 | 12 | 13.10 | even | 6 | |||
1170.2.bj.d.199.5 | 12 | 1.1 | even | 1 | trivial | ||
1170.2.bj.d.829.5 | 12 | 65.49 | even | 6 | inner | ||
1950.2.bc.i.751.1 | 12 | 195.62 | even | 12 | |||
1950.2.bc.i.901.1 | 12 | 15.2 | even | 4 | |||
1950.2.bc.j.751.6 | 12 | 195.23 | even | 12 | |||
1950.2.bc.j.901.6 | 12 | 15.8 | even | 4 |