Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(593,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.t (of order \(6\), degree \(2\), not 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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1025.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1025 |
Dual form | 1134.2.t.a.593.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.00000i | − | 0.904534i | −0.891883 | − | 0.452267i | \(-0.850615\pi\) | ||
0.891883 | − | 0.452267i | \(-0.149385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 1.73205i | 0.832050 | + | 0.480384i | 0.854554 | − | 0.519362i | \(-0.173830\pi\) |
−0.0225039 | + | 0.999747i | \(0.507164\pi\) | |||||||
\(14\) | 2.59808 | + | 0.500000i | 0.694365 | + | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | −1.73205 | − | 3.00000i | −0.339683 | − | 0.588348i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | 7.79423 | − | 4.50000i | 1.44735 | − | 0.835629i | 0.449029 | − | 0.893517i | \(-0.351770\pi\) |
0.998323 | + | 0.0578882i | \(0.0184367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50000 | − | 0.866025i | 0.269408 | − | 0.155543i | −0.359211 | − | 0.933257i | \(-0.616954\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | + | 6.92820i | 0.657596 | + | 1.13899i | 0.981236 | + | 0.192809i | \(0.0617599\pi\) |
−0.323640 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.19615 | − | 9.00000i | 0.811503 | − | 1.40556i | −0.100309 | − | 0.994956i | \(-0.531983\pi\) |
0.911812 | − | 0.410608i | \(-0.134683\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | − | 3.46410i | −0.304997 | − | 0.528271i | 0.672264 | − | 0.740312i | \(-0.265322\pi\) |
−0.977261 | + | 0.212041i | \(0.931989\pi\) | |||||||
\(44\) | 2.59808 | − | 1.50000i | 0.391675 | − | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.19615 | − | 9.00000i | 0.757937 | − | 1.31278i | −0.185964 | − | 0.982556i | \(-0.559541\pi\) |
0.943901 | − | 0.330228i | \(-0.107126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 4.33013 | + | 2.50000i | 0.612372 | + | 0.353553i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.46410i | 0.480384i | ||||||||
\(53\) | −5.19615 | − | 3.00000i | −0.713746 | − | 0.412082i | 0.0987002 | − | 0.995117i | \(-0.468532\pi\) |
−0.812447 | + | 0.583036i | \(0.801865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.866025 | + | 2.50000i | 0.115728 | + | 0.334077i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.00000 | −1.18176 | ||||||||
\(59\) | 2.59808 | + | 4.50000i | 0.338241 | + | 0.585850i | 0.984102 | − | 0.177605i | \(-0.0568349\pi\) |
−0.645861 | + | 0.763455i | \(0.723502\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000 | + | 6.92820i | 1.53644 | + | 0.887066i | 0.999043 | + | 0.0437377i | \(0.0139266\pi\) |
0.537400 | + | 0.843328i | \(0.319407\pi\) | |||||||
\(62\) | −1.73205 | −0.219971 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | + | 2.59808i | 0.526685 | + | 0.304082i | 0.739666 | − | 0.672975i | \(-0.234984\pi\) |
−0.212980 | + | 0.977056i | \(0.568317\pi\) | |||||||
\(74\) | − | 8.00000i | − | 0.929981i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.59808 | + | 7.50000i | 0.296078 | + | 0.854704i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.00000 | + | 5.19615i | −0.993884 | + | 0.573819i | ||||
\(83\) | −2.59808 | − | 4.50000i | −0.285176 | − | 0.493939i | 0.687476 | − | 0.726207i | \(-0.258719\pi\) |
−0.972652 | + | 0.232268i | \(0.925385\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000i | 0.431331i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.00000 | −0.319801 | ||||||||
\(89\) | −5.19615 | − | 9.00000i | −0.550791 | − | 0.953998i | −0.998218 | − | 0.0596775i | \(-0.980993\pi\) |
0.447427 | − | 0.894321i | \(-0.352341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.00000 | − | 1.73205i | −0.943456 | − | 0.181568i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.00000 | + | 5.19615i | −0.928279 | + | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.50000 | − | 4.33013i | 0.761510 | − | 0.439658i | −0.0683279 | − | 0.997663i | \(-0.521766\pi\) |
0.829837 | + | 0.558005i | \(0.188433\pi\) | |||||||
\(98\) | −6.92820 | + | 1.00000i | −0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.50000 | − | 4.33013i | −0.250000 | − | 0.433013i | ||||
\(101\) | −5.19615 | −0.517036 | −0.258518 | − | 0.966006i | \(-0.583234\pi\) | ||||
−0.258518 | + | 0.966006i | \(0.583234\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.3205i | − | 1.70664i | −0.521387 | − | 0.853320i | \(-0.674585\pi\) | ||
0.521387 | − | 0.853320i | \(-0.325415\pi\) | |||||||
\(104\) | 1.73205 | − | 3.00000i | 0.169842 | − | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 10.3923 | − | 6.00000i | 1.00466 | − | 0.580042i | 0.0950377 | − | 0.995474i | \(-0.469703\pi\) |
0.909624 | + | 0.415432i | \(0.136370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | − | 6.92820i | 0.383131 | − | 0.663602i | −0.608377 | − | 0.793648i | \(-0.708179\pi\) |
0.991508 | + | 0.130046i | \(0.0415126\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 10.3923 | + | 6.00000i | 0.977626 | + | 0.564433i | 0.901553 | − | 0.432670i | \(-0.142428\pi\) |
0.0760733 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.79423 | + | 4.50000i | 0.723676 | + | 0.417815i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 5.19615i | − | 0.478345i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.00000 | 0.181818 | ||||||||
\(122\) | −6.92820 | − | 12.0000i | −0.627250 | − | 1.08643i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.50000 | + | 0.866025i | 0.134704 | + | 0.0777714i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.5885 | −1.36197 | −0.680985 | − | 0.732297i | \(-0.738448\pi\) | ||||
−0.680985 | + | 0.732297i | \(0.738448\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.0000i | 1.02523i | 0.858619 | + | 0.512615i | \(0.171323\pi\) | ||||
−0.858619 | + | 0.512615i | \(0.828677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | + | 3.46410i | 0.508913 | + | 0.293821i | 0.732387 | − | 0.680889i | \(-0.238406\pi\) |
−0.223474 | + | 0.974710i | \(0.571740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | − | 10.3923i | 0.503509 | − | 0.872103i | ||||
\(143\) | 5.19615 | − | 9.00000i | 0.434524 | − | 0.752618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.59808 | − | 4.50000i | −0.215018 | − | 0.372423i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | + | 6.92820i | −0.328798 | + | 0.569495i | ||||
\(149\) | − | 15.0000i | − | 1.22885i | −0.788976 | − | 0.614424i | \(-0.789388\pi\) | ||
0.788976 | − | 0.614424i | \(-0.210612\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.0000 | −1.87171 | −0.935857 | − | 0.352381i | \(-0.885372\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.50000 | − | 7.79423i | 0.120873 | − | 0.628077i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | + | 5.19615i | −0.718278 | + | 0.414698i | −0.814119 | − | 0.580699i | \(-0.802779\pi\) |
0.0958404 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(158\) | −11.2583 | + | 6.50000i | −0.895665 | + | 0.517112i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000 | + | 8.66025i | 0.391630 | + | 0.678323i | 0.992665 | − | 0.120900i | \(-0.0385779\pi\) |
−0.601035 | + | 0.799223i | \(0.705245\pi\) | |||||||
\(164\) | 10.3923 | 0.811503 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.19615i | 0.403300i | ||||||||
\(167\) | 5.19615 | − | 9.00000i | 0.402090 | − | 0.696441i | −0.591888 | − | 0.806020i | \(-0.701617\pi\) |
0.993978 | + | 0.109580i | \(0.0349504\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | −12.9904 | + | 22.5000i | −0.987640 | + | 1.71064i | −0.358082 | + | 0.933690i | \(0.616569\pi\) |
−0.629558 | + | 0.776953i | \(0.716764\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5000 | − | 4.33013i | 0.944911 | − | 0.327327i | ||||
\(176\) | 2.59808 | + | 1.50000i | 0.195837 | + | 0.113067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.3923i | 0.778936i | ||||||||
\(179\) | −7.79423 | − | 4.50000i | −0.582568 | − | 0.336346i | 0.179585 | − | 0.983742i | \(-0.442524\pi\) |
−0.762153 | + | 0.647397i | \(0.775858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.7846i | − | 1.54491i | −0.635071 | − | 0.772454i | \(-0.719029\pi\) | ||
0.635071 | − | 0.772454i | \(-0.280971\pi\) | |||||||
\(182\) | 6.92820 | + | 6.00000i | 0.513553 | + | 0.444750i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.3923 | 0.757937 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.19615 | + | 3.00000i | 0.375980 | + | 0.217072i | 0.676068 | − | 0.736839i | \(-0.263683\pi\) |
−0.300088 | + | 0.953912i | \(0.597016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | −8.66025 | −0.621770 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.50000 | + | 2.59808i | 0.464286 | + | 0.185577i | ||||
\(197\) | 15.0000i | 1.06871i | 0.845262 | + | 0.534353i | \(0.179445\pi\) | ||||
−0.845262 | + | 0.534353i | \(0.820555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 0.866025i | 0.106332 | + | 0.0613909i | 0.552223 | − | 0.833696i | \(-0.313780\pi\) |
−0.445891 | + | 0.895087i | \(0.647113\pi\) | |||||||
\(200\) | 5.00000i | 0.353553i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.50000 | + | 2.59808i | 0.316619 | + | 0.182800i | ||||
\(203\) | −15.5885 | + | 18.0000i | −1.09410 | + | 1.26335i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.66025 | + | 15.0000i | −0.603388 | + | 1.04510i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | + | 1.73205i | −0.208013 | + | 0.120096i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.00000 | − | 1.73205i | 0.0688428 | − | 0.119239i | −0.829549 | − | 0.558433i | \(-0.811403\pi\) |
0.898392 | + | 0.439194i | \(0.144736\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | + | 3.46410i | −0.203653 | + | 0.235159i | ||||
\(218\) | −6.92820 | + | 4.00000i | −0.469237 | + | 0.270914i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.50000 | + | 2.59808i | −0.301342 | + | 0.173980i | −0.643046 | − | 0.765828i | \(-0.722329\pi\) |
0.341703 | + | 0.939808i | \(0.388996\pi\) | |||||||
\(224\) | −1.73205 | + | 2.00000i | −0.115728 | + | 0.133631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | − | 10.3923i | −0.399114 | − | 0.691286i | ||||
\(227\) | −25.9808 | −1.72440 | −0.862202 | − | 0.506565i | \(-0.830915\pi\) | ||||
−0.862202 | + | 0.506565i | \(0.830915\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.92820i | 0.457829i | 0.973447 | + | 0.228914i | \(0.0735176\pi\) | ||||
−0.973447 | + | 0.228914i | \(0.926482\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.50000 | − | 7.79423i | −0.295439 | − | 0.511716i | ||||
\(233\) | −15.5885 | + | 9.00000i | −1.02123 | + | 0.589610i | −0.914461 | − | 0.404674i | \(-0.867385\pi\) |
−0.106773 | + | 0.994283i | \(0.534052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.59808 | + | 4.50000i | −0.169120 | + | 0.292925i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923 | + | 6.00000i | 0.672222 | + | 0.388108i | 0.796918 | − | 0.604087i | \(-0.206462\pi\) |
−0.124696 | + | 0.992195i | \(0.539796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1244i | 0.780998i | 0.920603 | + | 0.390499i | \(0.127698\pi\) | ||||
−0.920603 | + | 0.390499i | \(0.872302\pi\) | |||||||
\(242\) | −1.73205 | − | 1.00000i | −0.111340 | − | 0.0642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8564i | 0.887066i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.866025 | − | 1.50000i | −0.0549927 | − | 0.0952501i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9808 | 1.63989 | 0.819946 | − | 0.572441i | \(-0.194004\pi\) | ||||
0.819946 | + | 0.572441i | \(0.194004\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.92820 | − | 4.00000i | −0.434714 | − | 0.250982i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −20.7846 | −1.29651 | −0.648254 | − | 0.761424i | \(-0.724501\pi\) | ||||
−0.648254 | + | 0.761424i | \(0.724501\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.0000 | − | 13.8564i | −0.994192 | − | 0.860995i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.5000 | + | 7.79423i | 0.834033 | + | 0.481529i | ||||
\(263\) | 24.0000i | 1.47990i | 0.672660 | + | 0.739952i | \(0.265152\pi\) | ||||
−0.672660 | + | 0.739952i | \(0.734848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.00000 | − | 1.73205i | 0.0610847 | − | 0.105802i | ||||
\(269\) | 7.79423 | − | 13.5000i | 0.475223 | − | 0.823110i | −0.524375 | − | 0.851488i | \(-0.675701\pi\) |
0.999597 | + | 0.0283781i | \(0.00903423\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00000 | − | 1.73205i | 0.182237 | − | 0.105215i | −0.406106 | − | 0.913826i | \(-0.633114\pi\) |
0.588343 | + | 0.808611i | \(0.299780\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | − | 10.3923i | 0.362473 | − | 0.627822i | ||||
\(275\) | 15.0000i | 0.904534i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | 0.841178 | 0.420589 | − | 0.907251i | \(-0.361823\pi\) | ||||
0.420589 | + | 0.907251i | \(0.361823\pi\) | |||||||
\(278\) | −3.46410 | − | 6.00000i | −0.207763 | − | 0.359856i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.19615 | + | 3.00000i | −0.309976 | + | 0.178965i | −0.646916 | − | 0.762561i | \(-0.723942\pi\) |
0.336939 | + | 0.941526i | \(0.390608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | + | 3.46410i | −0.356663 | + | 0.205919i | −0.667616 | − | 0.744506i | \(-0.732685\pi\) |
0.310953 | + | 0.950425i | \(0.399352\pi\) | |||||||
\(284\) | −10.3923 | + | 6.00000i | −0.616670 | + | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.00000 | + | 5.19615i | −0.532181 | + | 0.307255i | ||||
\(287\) | −5.19615 | + | 27.0000i | −0.306719 | + | 1.59376i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.19615i | 0.304082i | ||||||||
\(293\) | 2.59808 | − | 4.50000i | 0.151781 | − | 0.262893i | −0.780101 | − | 0.625653i | \(-0.784832\pi\) |
0.931882 | + | 0.362761i | \(0.118166\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820 | − | 4.00000i | 0.402694 | − | 0.232495i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.50000 | + | 12.9904i | −0.434463 | + | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | + | 6.92820i | 0.461112 | + | 0.399335i | ||||
\(302\) | 19.9186 | + | 11.5000i | 1.14619 | + | 0.661751i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3205i | 0.988534i | 0.869310 | + | 0.494267i | \(0.164563\pi\) | ||||
−0.869310 | + | 0.494267i | \(0.835437\pi\) | |||||||
\(308\) | −5.19615 | + | 6.00000i | −0.296078 | + | 0.341882i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5885 | − | 27.0000i | −0.883940 | − | 1.53103i | −0.846923 | − | 0.531715i | \(-0.821548\pi\) |
−0.0370169 | − | 0.999315i | \(-0.511786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0000 | + | 10.3923i | 1.01742 | + | 0.587408i | 0.913356 | − | 0.407163i | \(-0.133482\pi\) |
0.104065 | + | 0.994571i | \(0.466815\pi\) | |||||||
\(314\) | 10.3923 | 0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0000 | 0.731307 | ||||||||
\(317\) | 7.79423 | + | 4.50000i | 0.437767 | + | 0.252745i | 0.702650 | − | 0.711535i | \(-0.252000\pi\) |
−0.264883 | + | 0.964281i | \(0.585333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.5000 | − | 23.3827i | −0.755855 | − | 1.30918i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0000 | − | 8.66025i | −0.832050 | − | 0.480384i | ||||
\(326\) | − | 10.0000i | − | 0.553849i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.00000 | − | 5.19615i | −0.496942 | − | 0.286910i | ||||
\(329\) | −5.19615 | + | 27.0000i | −0.286473 | + | 1.48856i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | + | 24.2487i | −0.769510 | + | 1.33283i | 0.168320 | + | 0.985732i | \(0.446166\pi\) |
−0.937829 | + | 0.347097i | \(0.887167\pi\) | |||||||
\(332\) | 2.59808 | − | 4.50000i | 0.142588 | − | 0.246970i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.00000 | + | 5.19615i | −0.492458 | + | 0.284321i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.50000 | + | 11.2583i | −0.354078 | + | 0.613280i | −0.986960 | − | 0.160968i | \(-0.948538\pi\) |
0.632882 | + | 0.774248i | \(0.281872\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.59808 | − | 4.50000i | −0.140694 | − | 0.243689i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −3.46410 | + | 2.00000i | −0.186772 | + | 0.107833i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.5000 | − | 12.9904i | 1.20961 | − | 0.698367i | ||||
\(347\) | 2.59808 | − | 1.50000i | 0.139472 | − | 0.0805242i | −0.428640 | − | 0.903475i | \(-0.641007\pi\) |
0.568112 | + | 0.822951i | \(0.307674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0000 | − | 13.8564i | 1.28469 | − | 0.741716i | 0.306988 | − | 0.951713i | \(-0.400679\pi\) |
0.977702 | + | 0.209997i | \(0.0673454\pi\) | |||||||
\(350\) | −12.9904 | − | 2.50000i | −0.694365 | − | 0.133631i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | 10.3923 | 0.553127 | 0.276563 | − | 0.960996i | \(-0.410804\pi\) | ||||
0.276563 | + | 0.960996i | \(0.410804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.19615 | − | 9.00000i | 0.275396 | − | 0.476999i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.50000 | + | 7.79423i | 0.237832 | + | 0.411938i | ||||
\(359\) | −10.3923 | + | 6.00000i | −0.548485 | + | 0.316668i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | −10.3923 | + | 18.0000i | −0.546207 | + | 0.946059i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | − | 8.66025i | −0.157243 | − | 0.453921i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10.3923i | − | 0.542474i | −0.962513 | − | 0.271237i | \(-0.912567\pi\) | ||
0.962513 | − | 0.271237i | \(-0.0874327\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.5885 | + | 3.00000i | 0.809312 | + | 0.155752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | −0.207112 | −0.103556 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103556 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | − | 5.19615i | −0.464140 | − | 0.267971i | ||||
\(377\) | 31.1769 | 1.60569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.00000 | − | 5.19615i | −0.153493 | − | 0.265858i | ||||
\(383\) | −20.7846 | −1.06204 | −0.531022 | − | 0.847358i | \(-0.678192\pi\) | ||||
−0.531022 | + | 0.847358i | \(0.678192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11.0000i | − | 0.559885i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.50000 | + | 4.33013i | 0.380755 | + | 0.219829i | ||||
\(389\) | − | 9.00000i | − | 0.456318i | −0.973624 | − | 0.228159i | \(-0.926729\pi\) | ||
0.973624 | − | 0.228159i | \(-0.0732706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.33013 | − | 5.50000i | −0.218704 | − | 0.277792i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.50000 | − | 12.9904i | 0.377845 | − | 0.654446i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.0000 | − | 12.1244i | 1.05396 | − | 0.608504i | 0.130204 | − | 0.991487i | \(-0.458437\pi\) |
0.923755 | + | 0.382983i | \(0.125103\pi\) | |||||||
\(398\) | −0.866025 | − | 1.50000i | −0.0434099 | − | 0.0751882i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.50000 | − | 4.33013i | 0.125000 | − | 0.216506i | ||||
\(401\) | − | 30.0000i | − | 1.49813i | −0.662497 | − | 0.749064i | \(-0.730503\pi\) | ||
0.662497 | − | 0.749064i | \(-0.269497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | −2.59808 | − | 4.50000i | −0.129259 | − | 0.223883i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.5000 | − | 7.79423i | 1.11666 | − | 0.386821i | ||||
\(407\) | 20.7846 | − | 12.0000i | 1.03025 | − | 0.594818i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | + | 3.46410i | −0.296681 | + | 0.171289i | −0.640951 | − | 0.767582i | \(-0.721460\pi\) |
0.344270 | + | 0.938871i | \(0.388126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.0000 | − | 8.66025i | 0.738997 | − | 0.426660i | ||||
\(413\) | −10.3923 | − | 9.00000i | −0.511372 | − | 0.442861i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.46410 | 0.169842 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.5885 | − | 27.0000i | 0.761546 | − | 1.31904i | −0.180508 | − | 0.983574i | \(-0.557774\pi\) |
0.942053 | − | 0.335463i | \(-0.108893\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.00000 | + | 8.66025i | 0.243685 | + | 0.422075i | 0.961761 | − | 0.273890i | \(-0.0883103\pi\) |
−0.718076 | + | 0.695965i | \(0.754977\pi\) | |||||||
\(422\) | −1.73205 | + | 1.00000i | −0.0843149 | + | 0.0486792i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.0000 | − | 6.92820i | −1.74216 | − | 0.335279i | ||||
\(428\) | 10.3923 | + | 6.00000i | 0.502331 | + | 0.290021i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5885 | − | 9.00000i | −0.750870 | − | 0.433515i | 0.0751385 | − | 0.997173i | \(-0.476060\pi\) |
−0.826008 | + | 0.563658i | \(0.809393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.1244i | − | 0.582659i | −0.956623 | − | 0.291330i | \(-0.905902\pi\) | ||
0.956623 | − | 0.291330i | \(-0.0940977\pi\) | |||||||
\(434\) | 4.33013 | − | 1.50000i | 0.207853 | − | 0.0720023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5000 | − | 7.79423i | −0.644320 | − | 0.371998i | 0.141957 | − | 0.989873i | \(-0.454661\pi\) |
−0.786277 | + | 0.617875i | \(0.787994\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.3827 | − | 13.5000i | −1.11094 | − | 0.641404i | −0.171871 | − | 0.985119i | \(-0.554981\pi\) |
−0.939074 | + | 0.343715i | \(0.888315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.19615 | 0.246045 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | 30.0000i | 1.41579i | 0.706319 | + | 0.707894i | \(0.250354\pi\) | ||||
−0.706319 | + | 0.707894i | \(0.749646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.0000 | − | 15.5885i | −1.27138 | − | 0.734032i | ||||
\(452\) | 12.0000i | 0.564433i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.5000 | + | 12.9904i | 1.05598 | + | 0.609669i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | + | 19.0526i | −0.514558 | + | 0.891241i | 0.485299 | + | 0.874348i | \(0.338711\pi\) |
−0.999857 | + | 0.0168929i | \(0.994623\pi\) | |||||||
\(458\) | 3.46410 | − | 6.00000i | 0.161867 | − | 0.280362i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.79423 | − | 13.5000i | −0.363013 | − | 0.628758i | 0.625442 | − | 0.780271i | \(-0.284919\pi\) |
−0.988455 | + | 0.151513i | \(0.951585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.50000 | + | 4.33013i | −0.116185 | + | 0.201238i | −0.918253 | − | 0.395995i | \(-0.870400\pi\) |
0.802068 | + | 0.597233i | \(0.203733\pi\) | |||||||
\(464\) | 9.00000i | 0.417815i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.0000 | 0.833834 | ||||||||
\(467\) | 2.59808 | + | 4.50000i | 0.120225 | + | 0.208235i | 0.919856 | − | 0.392256i | \(-0.128305\pi\) |
−0.799632 | + | 0.600491i | \(0.794972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | + | 3.46410i | 0.184703 | + | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.50000 | − | 2.59808i | 0.207129 | − | 0.119586i | ||||
\(473\) | −10.3923 | + | 6.00000i | −0.477839 | + | 0.275880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.00000 | − | 10.3923i | −0.274434 | − | 0.475333i | ||||
\(479\) | 10.3923 | 0.474837 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7128i | 1.26360i | ||||||||
\(482\) | 6.06218 | − | 10.5000i | 0.276125 | − | 0.478262i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.50000 | − | 9.52628i | 0.249229 | − | 0.431677i | −0.714083 | − | 0.700061i | \(-0.753156\pi\) |
0.963312 | + | 0.268384i | \(0.0864896\pi\) | |||||||
\(488\) | 6.92820 | − | 12.0000i | 0.313625 | − | 0.543214i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.1769 | + | 18.0000i | 1.40699 | + | 0.812329i | 0.995097 | − | 0.0989017i | \(-0.0315329\pi\) |
0.411897 | + | 0.911230i | \(0.364866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | −10.3923 | − | 30.0000i | −0.466159 | − | 1.34568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0000 | 0.716258 | 0.358129 | − | 0.933672i | \(-0.383415\pi\) | ||||
0.358129 | + | 0.933672i | \(0.383415\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.5000 | − | 12.9904i | −1.00422 | − | 0.579789i | ||||
\(503\) | −31.1769 | −1.39011 | −0.695055 | − | 0.718957i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718957i | \(0.744620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.00000 | + | 6.92820i | 0.177471 | + | 0.307389i | ||||
\(509\) | 5.19615 | 0.230315 | 0.115158 | − | 0.993347i | \(-0.463263\pi\) | ||||
0.115158 | + | 0.993347i | \(0.463263\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.5000 | − | 2.59808i | −0.597205 | − | 0.114932i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0000 | + | 10.3923i | 0.793946 | + | 0.458385i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.0000 | − | 15.5885i | −1.18746 | − | 0.685580i | ||||
\(518\) | 6.92820 | + | 20.0000i | 0.304408 | + | 0.878750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.3923 | − | 18.0000i | 0.455295 | − | 0.788594i | −0.543410 | − | 0.839467i | \(-0.682867\pi\) |
0.998705 | + | 0.0508731i | \(0.0162004\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0000 | − | 19.0526i | 1.44299 | − | 0.833110i | 0.444941 | − | 0.895560i | \(-0.353225\pi\) |
0.998048 | + | 0.0624496i | \(0.0198913\pi\) | |||||||
\(524\) | −7.79423 | − | 13.5000i | −0.340492 | − | 0.589750i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | − | 20.7846i | 0.523225 | − | 0.906252i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.1769 | − | 18.0000i | 1.35042 | − | 0.779667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.73205 | + | 1.00000i | −0.0748132 | + | 0.0431934i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.5000 | + | 7.79423i | −0.582026 | + | 0.336033i | ||||
\(539\) | −12.9904 | − | 16.5000i | −0.559535 | − | 0.710705i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0000 | − | 32.9090i | −0.816874 | − | 1.41487i | −0.907975 | − | 0.419025i | \(-0.862372\pi\) |
0.0911008 | − | 0.995842i | \(-0.470961\pi\) | |||||||
\(542\) | −3.46410 | −0.148796 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.00000 | − | 12.1244i | −0.299298 | − | 0.518400i | 0.676677 | − | 0.736280i | \(-0.263419\pi\) |
−0.975976 | + | 0.217880i | \(0.930086\pi\) | |||||||
\(548\) | −10.3923 | + | 6.00000i | −0.443937 | + | 0.256307i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.50000 | − | 12.9904i | 0.319801 | − | 0.553912i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.50000 | + | 33.7750i | −0.276408 | + | 1.43626i | ||||
\(554\) | −12.1244 | − | 7.00000i | −0.515115 | − | 0.297402i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.92820i | 0.293821i | ||||||||
\(557\) | 18.1865 | + | 10.5000i | 0.770588 | + | 0.444899i | 0.833084 | − | 0.553146i | \(-0.186573\pi\) |
−0.0624962 | + | 0.998045i | \(0.519906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.8564i | − | 0.586064i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 15.5885 | + | 27.0000i | 0.656975 | + | 1.13791i | 0.981395 | + | 0.192001i | \(0.0614977\pi\) |
−0.324420 | + | 0.945913i | \(0.605169\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.92820 | 0.291214 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000 | 0.503509 | ||||||||
\(569\) | 10.3923 | + | 6.00000i | 0.435668 | + | 0.251533i | 0.701758 | − | 0.712415i | \(-0.252399\pi\) |
−0.266090 | + | 0.963948i | \(0.585732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | + | 3.46410i | 0.0836974 | + | 0.144968i | 0.904835 | − | 0.425762i | \(-0.139994\pi\) |
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(572\) | 10.3923 | 0.434524 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 18.0000 | − | 20.7846i | 0.751305 | − | 0.867533i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.50000 | − | 4.33013i | −0.312229 | − | 0.180266i | 0.335694 | − | 0.941971i | \(-0.391029\pi\) |
−0.647924 | + | 0.761705i | \(0.724362\pi\) | |||||||
\(578\) | − | 17.0000i | − | 0.707107i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3923 | + | 9.00000i | 0.431145 | + | 0.373383i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | + | 15.5885i | −0.372742 | + | 0.645608i | ||||
\(584\) | 2.59808 | − | 4.50000i | 0.107509 | − | 0.186211i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | + | 2.59808i | −0.185893 | + | 0.107326i | ||||
\(587\) | −5.19615 | − | 9.00000i | −0.214468 | − | 0.371470i | 0.738640 | − | 0.674100i | \(-0.235468\pi\) |
−0.953108 | + | 0.302631i | \(0.902135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.00000 | −0.328798 | ||||||||
\(593\) | −10.3923 | − | 18.0000i | −0.426761 | − | 0.739171i | 0.569822 | − | 0.821768i | \(-0.307012\pi\) |
−0.996583 | + | 0.0825966i | \(0.973679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.9904 | − | 7.50000i | 0.532107 | − | 0.307212i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9808 | − | 15.0000i | 1.06155 | − | 0.612883i | 0.135686 | − | 0.990752i | \(-0.456676\pi\) |
0.925859 | + | 0.377869i | \(0.123343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0000 | + | 17.3205i | −1.22373 | + | 0.706518i | −0.965710 | − | 0.259623i | \(-0.916402\pi\) |
−0.258015 | + | 0.966141i | \(0.583069\pi\) | |||||||
\(602\) | −3.46410 | − | 10.0000i | −0.141186 | − | 0.407570i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.5000 | − | 19.9186i | −0.467928 | − | 0.810476i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.19615i | − | 0.210905i | −0.994424 | − | 0.105453i | \(-0.966371\pi\) | ||
0.994424 | − | 0.105453i | \(-0.0336291\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.1769 | − | 18.0000i | 1.26128 | − | 0.728202i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.00000 | − | 8.66025i | 0.201948 | − | 0.349784i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
0.949156 | + | 0.314806i | \(0.101939\pi\) | |||||||
\(614\) | 8.66025 | − | 15.0000i | 0.349499 | − | 0.605351i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.50000 | − | 2.59808i | 0.302184 | − | 0.104679i | ||||
\(617\) | 15.5885 | + | 9.00000i | 0.627568 | + | 0.362326i | 0.779809 | − | 0.626017i | \(-0.215316\pi\) |
−0.152242 | + | 0.988343i | \(0.548649\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 34.6410i | − | 1.39234i | −0.717877 | − | 0.696170i | \(-0.754886\pi\) | ||
0.717877 | − | 0.696170i | \(-0.245114\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.1769i | 1.25008i | ||||||||
\(623\) | 20.7846 | + | 18.0000i | 0.832718 | + | 0.721155i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −10.3923 | − | 18.0000i | −0.415360 | − | 0.719425i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.00000 | − | 5.19615i | −0.359139 | − | 0.207349i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0000 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(632\) | −11.2583 | − | 6.50000i | −0.447832 | − | 0.258556i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.50000 | − | 7.79423i | −0.178718 | − | 0.309548i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | − | 3.46410i | 0.950915 | − | 0.137253i | ||||
\(638\) | 27.0000i | 1.06894i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 42.0000i | − | 1.65890i | −0.558581 | − | 0.829450i | \(-0.688654\pi\) | ||
0.558581 | − | 0.829450i | \(-0.311346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.00000 | − | 1.73205i | −0.118308 | − | 0.0683054i | 0.439678 | − | 0.898155i | \(-0.355093\pi\) |
−0.557986 | + | 0.829850i | \(0.688426\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.19615 | − | 9.00000i | 0.204282 | − | 0.353827i | −0.745622 | − | 0.666369i | \(-0.767847\pi\) |
0.949904 | + | 0.312543i | \(0.101181\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | − | 7.79423i | 0.529921 | − | 0.305950i | ||||
\(650\) | 8.66025 | + | 15.0000i | 0.339683 | + | 0.588348i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.00000 | + | 8.66025i | −0.195815 | + | 0.339162i | ||||
\(653\) | 30.0000i | 1.17399i | 0.809590 | + | 0.586995i | \(0.199689\pi\) | ||||
−0.809590 | + | 0.586995i | \(0.800311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.19615 | + | 9.00000i | 0.202876 | + | 0.351391i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.0000 | − | 20.7846i | 0.701713 | − | 0.810268i | ||||
\(659\) | −12.9904 | + | 7.50000i | −0.506033 | + | 0.292159i | −0.731202 | − | 0.682161i | \(-0.761040\pi\) |
0.225168 | + | 0.974320i | \(0.427707\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00000 | + | 5.19615i | −0.350059 | + | 0.202107i | −0.664711 | − | 0.747100i | \(-0.731446\pi\) |
0.314652 | + | 0.949207i | \(0.398112\pi\) | |||||||
\(662\) | 24.2487 | − | 14.0000i | 0.942453 | − | 0.544125i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.50000 | + | 2.59808i | −0.174634 | + | 0.100825i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 10.3923 | 0.402090 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.7846 | − | 36.0000i | 0.802381 | − | 1.38976i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0000 | + | 22.5167i | 0.501113 | + | 0.867953i | 0.999999 | + | 0.00128586i | \(0.000409302\pi\) |
−0.498886 | + | 0.866668i | \(0.666257\pi\) | |||||||
\(674\) | 11.2583 | − | 6.50000i | 0.433655 | − | 0.250371i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.500000 | − | 0.866025i | 0.0192308 | − | 0.0333087i | ||||
\(677\) | 7.79423 | − | 13.5000i | 0.299557 | − | 0.518847i | −0.676478 | − | 0.736463i | \(-0.736495\pi\) |
0.976035 | + | 0.217616i | \(0.0698279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0000 | + | 17.3205i | −0.575647 | + | 0.664700i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.19615i | 0.198971i | ||||||||
\(683\) | −18.1865 | − | 10.5000i | −0.695888 | − | 0.401771i | 0.109926 | − | 0.993940i | \(-0.464939\pi\) |
−0.805814 | + | 0.592168i | \(0.798272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.4545 | − | 8.50000i | 0.628235 | − | 0.324532i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000 | 0.152499 | ||||||||
\(689\) | −10.3923 | − | 18.0000i | −0.395915 | − | 0.685745i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | − | 6.92820i | −0.456502 | − | 0.263561i | 0.254071 | − | 0.967186i | \(-0.418230\pi\) |
−0.710572 | + | 0.703624i | \(0.751564\pi\) | |||||||
\(692\) | −25.9808 | −0.987640 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.00000 | −0.113878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −27.7128 | −1.04895 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.0000 | + | 8.66025i | 0.377964 | + | 0.327327i | ||||
\(701\) | − | 6.00000i | − | 0.226617i | −0.993560 | − | 0.113308i | \(-0.963855\pi\) | ||
0.993560 | − | 0.113308i | \(-0.0361448\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 3.00000i | 0.113067i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | − | 5.19615i | −0.338719 | − | 0.195560i | ||||
\(707\) | 12.9904 | − | 4.50000i | 0.488554 | − | 0.169240i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00000 | + | 3.46410i | −0.0751116 | + | 0.130097i | −0.901135 | − | 0.433539i | \(-0.857265\pi\) |
0.826023 | + | 0.563636i | \(0.190598\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.00000 | + | 5.19615i | −0.337289 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 9.00000i | − | 0.336346i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.0000 | 0.447836 | ||||||||
\(719\) | −5.19615 | − | 9.00000i | −0.193784 | − | 0.335643i | 0.752717 | − | 0.658344i | \(-0.228743\pi\) |
−0.946501 | + | 0.322700i | \(0.895409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | + | 43.3013i | 0.558629 | + | 1.61262i | ||||
\(722\) | 16.4545 | − | 9.50000i | 0.612372 | − | 0.353553i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.0000 | − | 10.3923i | 0.668965 | − | 0.386227i | ||||
\(725\) | −38.9711 | + | 22.5000i | −1.44735 | + | 0.835629i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.0000 | − | 12.1244i | 0.778847 | − | 0.449667i | −0.0571746 | − | 0.998364i | \(-0.518209\pi\) |
0.836021 | + | 0.548697i | \(0.184876\pi\) | |||||||
\(728\) | −1.73205 | + | 9.00000i | −0.0641941 | + | 0.333562i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8564i | 0.511798i | 0.966704 | + | 0.255899i | \(0.0823715\pi\) | ||||
−0.966704 | + | 0.255899i | \(0.917629\pi\) | |||||||
\(734\) | −5.19615 | + | 9.00000i | −0.191793 | + | 0.332196i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.19615 | + | 3.00000i | −0.191403 | + | 0.110506i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.0000 | + | 22.5167i | −0.478213 | + | 0.828289i | −0.999688 | − | 0.0249776i | \(-0.992049\pi\) |
0.521475 | + | 0.853266i | \(0.325382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.0000 | − | 10.3923i | −0.440534 | − | 0.381514i | ||||
\(743\) | 5.19615 | + | 3.00000i | 0.190628 | + | 0.110059i | 0.592277 | − | 0.805735i | \(-0.298229\pi\) |
−0.401648 | + | 0.915794i | \(0.631563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.46410 | + | 2.00000i | 0.126830 | + | 0.0732252i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.7846 | + | 24.0000i | −0.759453 | + | 0.876941i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | 5.19615 | + | 9.00000i | 0.189484 | + | 0.328196i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −27.0000 | − | 15.5885i | −0.983282 | − | 0.567698i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 22.5167 | + | 13.0000i | 0.817842 | + | 0.472181i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.5692 | 1.50688 | 0.753442 | − | 0.657515i | \(-0.228392\pi\) | ||||
0.753442 | + | 0.657515i | \(0.228392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.00000 | + | 20.7846i | −0.144810 | + | 0.752453i | ||||
\(764\) | 6.00000i | 0.217072i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | + | 10.3923i | 0.650366 | + | 0.375489i | ||||
\(767\) | 18.0000i | 0.649942i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5000 | − | 7.79423i | −0.486822 | − | 0.281067i | 0.236433 | − | 0.971648i | \(-0.424022\pi\) |
−0.723255 | + | 0.690581i | \(0.757355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.50000 | + | 9.52628i | −0.197949 | + | 0.342858i | ||||
\(773\) | −20.7846 | + | 36.0000i | −0.747570 | + | 1.29483i | 0.201414 | + | 0.979506i | \(0.435446\pi\) |
−0.948984 | + | 0.315324i | \(0.897887\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.50000 | + | 4.33013i | −0.269408 | + | 0.155543i | ||||
\(776\) | −4.33013 | − | 7.50000i | −0.155443 | − | 0.269234i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.50000 | + | 7.79423i | −0.161333 | + | 0.279437i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.0000 | − | 12.1244i | 0.748569 | − | 0.432187i | −0.0766075 | − | 0.997061i | \(-0.524409\pi\) |
0.825177 | + | 0.564875i | \(0.191076\pi\) | |||||||
\(788\) | −12.9904 | + | 7.50000i | −0.462763 | + | 0.267176i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.1769 | − | 6.00000i | −1.10852 | − | 0.213335i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0000 | + | 41.5692i | 0.852265 | + | 1.47617i | ||||
\(794\) | −24.2487 | −0.860555 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.73205i | 0.0613909i | ||||||||
\(797\) | 7.79423 | − | 13.5000i | 0.276086 | − | 0.478195i | −0.694323 | − | 0.719664i | \(-0.744296\pi\) |
0.970408 | + | 0.241469i | \(0.0776293\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.33013 | + | 2.50000i | −0.153093 | + | 0.0883883i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.0000 | + | 25.9808i | −0.529668 | + | 0.917413i | ||||
\(803\) | 7.79423 | − | 13.5000i | 0.275052 | − | 0.476405i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.19615 | − | 3.00000i | −0.183027 | − | 0.105670i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.19615i | 0.182800i | ||||||||
\(809\) | 5.19615 | + | 3.00000i | 0.182687 | + | 0.105474i | 0.588555 | − | 0.808458i | \(-0.299697\pi\) |
−0.405868 | + | 0.913932i | \(0.633031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3923i | 0.364923i | 0.983213 | + | 0.182462i | \(0.0584065\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | −23.3827 | − | 4.50000i | −0.820571 | − | 0.157919i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.0000 | −0.841200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 6.92820 | 0.242239 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.5788 | − | 16.5000i | −0.997408 | − | 0.575854i | −0.0899279 | − | 0.995948i | \(-0.528664\pi\) |
−0.907480 | + | 0.420094i | \(0.861997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.50000 | − | 9.52628i | −0.191718 | − | 0.332065i | 0.754102 | − | 0.656758i | \(-0.228073\pi\) |
−0.945820 | + | 0.324692i | \(0.894739\pi\) | |||||||
\(824\) | −17.3205 | −0.603388 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.50000 | + | 12.9904i | 0.156575 | + | 0.451993i | ||||
\(827\) | − | 3.00000i | − | 0.104320i | −0.998639 | − | 0.0521601i | \(-0.983389\pi\) | ||
0.998639 | − | 0.0521601i | \(-0.0166106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.0000 | − | 15.5885i | −0.937749 | − | 0.541409i | −0.0484949 | − | 0.998823i | \(-0.515442\pi\) |
−0.889254 | + | 0.457414i | \(0.848776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.00000 | − | 1.73205i | −0.104006 | − | 0.0600481i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.0000 | + | 15.5885i | −0.932700 | + | 0.538494i | ||||
\(839\) | 10.3923 | + | 18.0000i | 0.358782 | + | 0.621429i | 0.987758 | − | 0.155996i | \(-0.0498587\pi\) |
−0.628975 | + | 0.777425i | \(0.716525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0000 | − | 45.0333i | 0.896552 | − | 1.55287i | ||||
\(842\) | − | 10.0000i | − | 0.344623i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.00000 | 0.0688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | + | 1.73205i | −0.171802 | + | 0.0595140i | ||||
\(848\) | 5.19615 | − | 3.00000i | 0.178437 | − | 0.103020i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.00000 | + | 5.19615i | −0.308154 | + | 0.177913i | −0.646100 | − | 0.763253i | \(-0.723601\pi\) |
0.337946 | + | 0.941165i | \(0.390268\pi\) | |||||||
\(854\) | 27.7128 | + | 24.0000i | 0.948313 | + | 0.821263i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −10.3923 | −0.354994 | −0.177497 | − | 0.984121i | \(-0.556800\pi\) | ||||
−0.177497 | + | 0.984121i | \(0.556800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 48.4974i | − | 1.65471i | −0.561679 | − | 0.827355i | \(-0.689844\pi\) | ||
0.561679 | − | 0.827355i | \(-0.310156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.00000 | + | 15.5885i | 0.306541 | + | 0.530945i | ||||
\(863\) | 5.19615 | − | 3.00000i | 0.176879 | − | 0.102121i | −0.408946 | − | 0.912558i | \(-0.634104\pi\) |
0.585826 | + | 0.810437i | \(0.300770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.06218 | + | 10.5000i | −0.206001 | + | 0.356805i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.50000 | − | 0.866025i | −0.152740 | − | 0.0293948i | ||||
\(869\) | −33.7750 | − | 19.5000i | −1.14574 | − | 0.661492i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.92820i | − | 0.234753i | ||||||
\(872\) | −6.92820 | − | 4.00000i | −0.234619 | − | 0.135457i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.00000 | 0.0675352 | 0.0337676 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337676 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(878\) | 7.79423 | + | 13.5000i | 0.263042 | + | 0.455603i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.1769 | 1.05038 | 0.525188 | − | 0.850986i | \(-0.323995\pi\) | ||||
0.525188 | + | 0.850986i | \(0.323995\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.5000 | + | 23.3827i | 0.453541 | + | 0.785557i | ||||
\(887\) | −31.1769 | −1.04682 | −0.523409 | − | 0.852081i | \(-0.675340\pi\) | ||||
−0.523409 | + | 0.852081i | \(0.675340\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | + | 6.92820i | −0.670778 | + | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.50000 | − | 2.59808i | −0.150671 | − | 0.0869900i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.59808 | − | 0.500000i | −0.0867956 | − | 0.0167038i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.0000 | − | 25.9808i | 0.500556 | − | 0.866989i | ||||
\(899\) | 7.79423 | − | 13.5000i | 0.259952 | − | 0.450250i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 15.5885 | + | 27.0000i | 0.519039 | + | 0.899002i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | − | 10.3923i | 0.199557 | − | 0.345643i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0000 | 0.730498 | 0.365249 | − | 0.930910i | \(-0.380984\pi\) | ||||
0.365249 | + | 0.930910i | \(0.380984\pi\) | |||||||
\(908\) | −12.9904 | − | 22.5000i | −0.431101 | − | 0.746689i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.1769 | + | 18.0000i | −1.03294 | + | 0.596367i | −0.917825 | − | 0.396986i | \(-0.870056\pi\) |
−0.115113 | + | 0.993352i | \(0.536723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5000 | + | 7.79423i | −0.446785 | + | 0.257951i | ||||
\(914\) | 19.0526 | − | 11.0000i | 0.630203 | − | 0.363848i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | + | 3.46410i | −0.198246 | + | 0.114457i | ||||
\(917\) | 38.9711 | − | 13.5000i | 1.28694 | − | 0.445809i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.5000 | + | 30.3109i | 0.577272 | + | 0.999864i | 0.995791 | + | 0.0916559i | \(0.0292160\pi\) |
−0.418519 | + | 0.908208i | \(0.637451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.5885i | 0.513378i | ||||||||
\(923\) | −20.7846 | + | 36.0000i | −0.684134 | + | 1.18495i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.0000 | − | 34.6410i | −0.657596 | − | 1.13899i | ||||
\(926\) | 4.33013 | − | 2.50000i | 0.142297 | − | 0.0821551i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.50000 | − | 7.79423i | 0.147720 | − | 0.255858i | ||||
\(929\) | −20.7846 | + | 36.0000i | −0.681921 | + | 1.18112i | 0.292473 | + | 0.956274i | \(0.405522\pi\) |
−0.974394 | + | 0.224848i | \(0.927811\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.5885 | − | 9.00000i | −0.510617 | − | 0.294805i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 5.19615i | − | 0.170023i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.6410i | 1.13167i | 0.824518 | + | 0.565836i | \(0.191447\pi\) | ||||
−0.824518 | + | 0.565836i | \(0.808553\pi\) | |||||||
\(938\) | −1.73205 | − | 5.00000i | −0.0565535 | − | 0.163256i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.59808 | + | 4.50000i | 0.0846949 | + | 0.146696i | 0.905261 | − | 0.424856i | \(-0.139675\pi\) |
−0.820566 | + | 0.571551i | \(0.806342\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −5.19615 | −0.169120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | −7.79423 | − | 4.50000i | −0.253278 | − | 0.146230i | 0.367986 | − | 0.929831i | \(-0.380047\pi\) |
−0.621264 | + | 0.783601i | \(0.713381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.00000 | + | 15.5885i | 0.292152 | + | 0.506023i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 18.0000i | − | 0.583077i | −0.956559 | − | 0.291539i | \(-0.905833\pi\) | ||
0.956559 | − | 0.291539i | \(-0.0941672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.0000i | 0.388108i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.00000 | − | 5.19615i | −0.290777 | − | 0.167880i | ||||
\(959\) | −10.3923 | − | 30.0000i | −0.335585 | − | 0.968751i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | + | 24.2487i | −0.451613 | + | 0.782216i | ||||
\(962\) | 13.8564 | − | 24.0000i | 0.446748 | − | 0.773791i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.5000 | + | 6.06218i | −0.338182 | + | 0.195250i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0000 | + | 48.4974i | −0.900419 | + | 1.55957i | −0.0734686 | + | 0.997298i | \(0.523407\pi\) |
−0.826951 | + | 0.562274i | \(0.809926\pi\) | |||||||
\(968\) | − | 2.00000i | − | 0.0642824i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.5885 | + | 27.0000i | 0.500257 | + | 0.866471i | 1.00000 | 0.000297246i | \(9.46163e-5\pi\) | |
−0.499743 | + | 0.866174i | \(0.666572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.0000 | − | 3.46410i | −0.577054 | − | 0.111054i | ||||
\(974\) | −9.52628 | + | 5.50000i | −0.305242 | + | 0.176231i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0000 | + | 6.92820i | −0.384111 | + | 0.221766i | ||||
\(977\) | −15.5885 | + | 9.00000i | −0.498719 | + | 0.287936i | −0.728184 | − | 0.685381i | \(-0.759636\pi\) |
0.229465 | + | 0.973317i | \(0.426302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.0000 | + | 15.5885i | −0.862924 | + | 0.498209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.0000 | − | 31.1769i | −0.574403 | − | 0.994895i | ||||
\(983\) | 20.7846 | 0.662926 | 0.331463 | − | 0.943468i | \(-0.392458\pi\) | ||||
0.331463 | + | 0.943468i | \(0.392458\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.00000 | − | 6.92820i | 0.127064 | − | 0.220082i | −0.795474 | − | 0.605988i | \(-0.792778\pi\) |
0.922538 | + | 0.385906i | \(0.126111\pi\) | |||||||
\(992\) | 0.866025 | − | 1.50000i | 0.0274963 | − | 0.0476250i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.00000 | + | 31.1769i | −0.190308 | + | 0.988872i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 38.1051i | − | 1.20680i | −0.797438 | − | 0.603401i | \(-0.793812\pi\) | ||
0.797438 | − | 0.603401i | \(-0.206188\pi\) | |||||||
\(998\) | −13.8564 | − | 8.00000i | −0.438617 | − | 0.253236i | ||||
\(999\) | 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 | 1134.2.t.a.1025.1 | 4 | ||
3.2 | odd | 2 | inner | 1134.2.t.a.1025.2 | 4 | ||
7.5 | odd | 6 | 1134.2.l.d.215.2 | 4 | |||
9.2 | odd | 6 | 1134.2.l.d.269.1 | 4 | |||
9.4 | even | 3 | 378.2.k.a.269.2 | yes | 4 | ||
9.5 | odd | 6 | 378.2.k.a.269.1 | yes | 4 | ||
9.7 | even | 3 | 1134.2.l.d.269.2 | 4 | |||
21.5 | even | 6 | 1134.2.l.d.215.1 | 4 | |||
63.4 | even | 3 | 2646.2.d.c.2645.3 | 4 | |||
63.5 | even | 6 | 378.2.k.a.215.2 | yes | 4 | ||
63.31 | odd | 6 | 2646.2.d.c.2645.4 | 4 | |||
63.32 | odd | 6 | 2646.2.d.c.2645.1 | 4 | |||
63.40 | odd | 6 | 378.2.k.a.215.1 | ✓ | 4 | ||
63.47 | even | 6 | inner | 1134.2.t.a.593.1 | 4 | ||
63.59 | even | 6 | 2646.2.d.c.2645.2 | 4 | |||
63.61 | odd | 6 | inner | 1134.2.t.a.593.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.a.215.1 | ✓ | 4 | 63.40 | odd | 6 | ||
378.2.k.a.215.2 | yes | 4 | 63.5 | even | 6 | ||
378.2.k.a.269.1 | yes | 4 | 9.5 | odd | 6 | ||
378.2.k.a.269.2 | yes | 4 | 9.4 | even | 3 | ||
1134.2.l.d.215.1 | 4 | 21.5 | even | 6 | |||
1134.2.l.d.215.2 | 4 | 7.5 | odd | 6 | |||
1134.2.l.d.269.1 | 4 | 9.2 | odd | 6 | |||
1134.2.l.d.269.2 | 4 | 9.7 | even | 3 | |||
1134.2.t.a.593.1 | 4 | 63.47 | even | 6 | inner | ||
1134.2.t.a.593.2 | 4 | 63.61 | odd | 6 | inner | ||
1134.2.t.a.1025.1 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.t.a.1025.2 | 4 | 3.2 | odd | 2 | inner | ||
2646.2.d.c.2645.1 | 4 | 63.32 | odd | 6 | |||
2646.2.d.c.2645.2 | 4 | 63.59 | even | 6 | |||
2646.2.d.c.2645.3 | 4 | 63.4 | even | 3 | |||
2646.2.d.c.2645.4 | 4 | 63.31 | odd | 6 |