Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(215,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.k (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: | \(3.01834519640\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.269 |
Dual form | 378.2.k.a.215.1 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.59808 | − | 1.50000i | −0.783349 | − | 0.452267i | 0.0542666 | − | 0.998526i | \(-0.482718\pi\) |
−0.837616 | + | 0.546259i | \(0.816051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0.866025 | + | 2.50000i | 0.231455 | + | 0.668153i | ||||
\(15\) | 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 | ||||||||
\(22\) | 3.00000 | 0.639602 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 1.73205 | + | 3.00000i | 0.339683 | + | 0.588348i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | − | 9.00000i | − | 1.67126i | −0.549294 | − | 0.835629i | \(-0.685103\pi\) | ||
0.549294 | − | 0.835629i | \(-0.314897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 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 | ||||||||
\(41\) | 10.3923 | 1.62301 | 0.811503 | − | 0.584349i | \(-0.198650\pi\) | ||||
0.811503 | + | 0.584349i | \(0.198650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | −2.59808 | + | 1.50000i | −0.391675 | + | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19615 | − | 9.00000i | −0.757937 | − | 1.31278i | −0.943901 | − | 0.330228i | \(-0.892874\pi\) |
0.185964 | − | 0.982556i | \(-0.440459\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 5.00000i | 0.707107i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | − | 1.73205i | −0.416025 | − | 0.240192i | ||||
\(53\) | 5.19615 | + | 3.00000i | 0.713746 | + | 0.412082i | 0.812447 | − | 0.583036i | \(-0.198135\pi\) |
−0.0987002 | + | 0.995117i | \(0.531468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.59808 | + | 0.500000i | 0.347183 | + | 0.0668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.50000 | + | 7.79423i | 0.590879 | + | 1.02343i | ||||
\(59\) | −2.59808 | + | 4.50000i | −0.338241 | + | 0.585850i | −0.984102 | − | 0.177605i | \(-0.943165\pi\) |
0.645861 | + | 0.763455i | \(0.276498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | + | 6.92820i | −1.53644 | + | 0.887066i | −0.537400 | + | 0.843328i | \(0.680593\pi\) |
−0.999043 | + | 0.0437377i | \(0.986073\pi\) | |||||||
\(62\) | 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 | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | + | 2.59808i | 0.526685 | + | 0.304082i | 0.739666 | − | 0.672975i | \(-0.234984\pi\) |
−0.212980 | + | 0.977056i | \(0.568317\pi\) | |||||||
\(74\) | −6.92820 | − | 4.00000i | −0.805387 | − | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.19615 | + | 6.00000i | −0.592157 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | + | 11.2583i | 0.731307 | + | 1.26666i | 0.956325 | + | 0.292306i | \(0.0944227\pi\) |
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.00000 | + | 5.19615i | −0.993884 | + | 0.573819i | ||||
\(83\) | −5.19615 | −0.570352 | −0.285176 | − | 0.958475i | \(-0.592052\pi\) | ||||
−0.285176 | + | 0.958475i | \(0.592052\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.46410 | + | 2.00000i | −0.373544 | + | 0.215666i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | 5.19615 | + | 9.00000i | 0.550791 | + | 0.953998i | 0.998218 | + | 0.0596775i | \(0.0190072\pi\) |
−0.447427 | + | 0.894321i | \(0.647659\pi\) | |||||||
\(90\) | 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 | ||||||||
\(97\) | 8.66025i | 0.879316i | 0.898165 | + | 0.439658i | \(0.144900\pi\) | ||||
−0.898165 | + | 0.439658i | \(0.855100\pi\) | |||||||
\(98\) | 6.92820 | − | 1.00000i | 0.699854 | − | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.50000 | − | 4.33013i | −0.250000 | − | 0.433013i | ||||
\(101\) | −2.59808 | + | 4.50000i | −0.258518 | + | 0.447767i | −0.965845 | − | 0.259120i | \(-0.916568\pi\) |
0.707327 | + | 0.706887i | \(0.249901\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.0000 | + | 8.66025i | −1.47799 | + | 0.853320i | −0.999691 | − | 0.0248745i | \(-0.992081\pi\) |
−0.478303 | + | 0.878195i | \(0.658748\pi\) | |||||||
\(104\) | 3.46410 | 0.339683 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −10.3923 | + | 6.00000i | −1.00466 | + | 0.580042i | −0.909624 | − | 0.415432i | \(-0.863630\pi\) |
−0.0950377 | + | 0.995474i | \(0.530297\pi\) | |||||||
\(108\) | 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 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | 12.0000i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(114\) | 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 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 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 | ||||||||
\(131\) | −7.79423 | − | 13.5000i | −0.680985 | − | 1.17950i | −0.974681 | − | 0.223602i | \(-0.928219\pi\) |
0.293696 | − | 0.955899i | \(-0.405115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2.00000i | − | 0.172774i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3923 | + | 6.00000i | 0.887875 | + | 0.512615i | 0.873247 | − | 0.487278i | \(-0.162010\pi\) |
0.0146279 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.92820i | − | 0.587643i | −0.955860 | − | 0.293821i | \(-0.905073\pi\) | ||
0.955860 | − | 0.293821i | \(-0.0949270\pi\) | |||||||
\(140\) | 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 | ||||||||
\(146\) | −5.19615 | −0.430037 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 12.9904 | − | 7.50000i | 1.06421 | − | 0.614424i | 0.137619 | − | 0.990485i | \(-0.456055\pi\) |
0.926595 | + | 0.376061i | \(0.122722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5000 | − | 19.9186i | 0.935857 | − | 1.62095i | 0.162758 | − | 0.986666i | \(-0.447961\pi\) |
0.773099 | − | 0.634285i | \(-0.218706\pi\) | |||||||
\(152\) | 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 | \(-0.197221\pi\) |
−0.0958404 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(158\) | −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 | \(0.705245\pi\) | |||||||
\(164\) | 5.19615 | − | 9.00000i | 0.405751 | − | 0.702782i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50000 | − | 2.59808i | 0.349268 | − | 0.201650i | ||||
\(167\) | 10.3923 | 0.804181 | 0.402090 | − | 0.915600i | \(-0.368284\pi\) | ||||
0.402090 | + | 0.915600i | \(0.368284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | 12.9904 | + | 22.5000i | 0.987640 | + | 1.71064i | 0.629558 | + | 0.776953i | \(0.283236\pi\) |
0.358082 | + | 0.933690i | \(0.383431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | − | 8.66025i | −0.755929 | − | 0.654654i | ||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.00000 | − | 5.19615i | −0.674579 | − | 0.389468i | ||||
\(179\) | 7.79423 | + | 4.50000i | 0.582568 | + | 0.336346i | 0.762153 | − | 0.647397i | \(-0.224142\pi\) |
−0.179585 | + | 0.983742i | \(0.557476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 20.7846i | − | 1.54491i | −0.635071 | − | 0.772454i | \(-0.719029\pi\) | ||
0.635071 | − | 0.772454i | \(-0.280971\pi\) | |||||||
\(182\) | 8.66025 | − | 3.00000i | 0.641941 | − | 0.222375i | ||||
\(183\) | 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 | −0.300088 | − | 0.953912i | \(-0.597016\pi\) |
0.676068 | + | 0.736839i | \(0.263683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.50000 | − | 9.52628i | 0.395899 | − | 0.685717i | −0.597317 | − | 0.802005i | \(-0.703766\pi\) |
0.993215 | + | 0.116289i | \(0.0370998\pi\) | |||||||
\(194\) | −4.33013 | − | 7.50000i | −0.310885 | − | 0.538469i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.50000 | + | 4.33013i | −0.392857 | + | 0.309295i | ||||
\(197\) | − | 15.0000i | − | 1.06871i | −0.845262 | − | 0.534353i | \(-0.820555\pi\) | ||
0.845262 | − | 0.534353i | \(-0.179445\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 0.866025i | 0.106332 | + | 0.0613909i | 0.552223 | − | 0.833696i | \(-0.313780\pi\) |
−0.445891 | + | 0.895087i | \(0.647113\pi\) | |||||||
\(200\) | 4.33013 | + | 2.50000i | 0.306186 | + | 0.176777i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 5.19615i | − | 0.365600i | ||||||
\(203\) | −23.3827 | − | 4.50000i | −1.64114 | − | 0.315838i | ||||
\(204\) | 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 | ||||||||
\(211\) | −2.00000 | −0.137686 | −0.0688428 | − | 0.997628i | \(-0.521931\pi\) | ||||
−0.0688428 | + | 0.997628i | \(0.521931\pi\) | |||||||
\(212\) | 5.19615 | − | 3.00000i | 0.356873 | − | 0.206041i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | + | 3.46410i | −0.203653 | + | 0.235159i | ||||
\(218\) | 8.00000i | 0.541828i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.19615i | − | 0.347960i | −0.984749 | − | 0.173980i | \(-0.944337\pi\) | ||
0.984749 | − | 0.173980i | \(-0.0556628\pi\) | |||||||
\(224\) | 1.73205 | − | 2.00000i | 0.115728 | − | 0.133631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | − | 10.3923i | −0.399114 | − | 0.691286i | ||||
\(227\) | −12.9904 | + | 22.5000i | −0.862202 | + | 1.49338i | 0.00759708 | + | 0.999971i | \(0.497582\pi\) |
−0.869799 | + | 0.493406i | \(0.835752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.00000 | − | 3.46410i | 0.396491 | − | 0.228914i | −0.288478 | − | 0.957487i | \(-0.593149\pi\) |
0.684969 | + | 0.728572i | \(0.259816\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | 15.5885 | − | 9.00000i | 1.02123 | − | 0.589610i | 0.106773 | − | 0.994283i | \(-0.465948\pi\) |
0.914461 | + | 0.404674i | \(0.132615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.59808 | + | 4.50000i | 0.169120 | + | 0.292925i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000i | 0.776215i | 0.921614 | + | 0.388108i | \(0.126871\pi\) | ||||
−0.921614 | + | 0.388108i | \(0.873129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5000 | − | 6.06218i | −0.676364 | − | 0.390499i | 0.122119 | − | 0.992515i | \(-0.461031\pi\) |
−0.798484 | + | 0.602016i | \(0.794364\pi\) | |||||||
\(242\) | 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 | \(-0.805996\pi\) | ||||
−0.819946 | + | 0.572441i | \(0.805996\pi\) | |||||||
\(252\) | 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 | ||||
\(257\) | −10.3923 | − | 18.0000i | −0.648254 | − | 1.12281i | −0.983540 | − | 0.180693i | \(-0.942166\pi\) |
0.335285 | − | 0.942117i | \(-0.391167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0000 | − | 6.92820i | 1.24274 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.5000 | + | 7.79423i | 0.834033 | + | 0.481529i | ||||
\(263\) | 20.7846 | + | 12.0000i | 1.28163 | + | 0.739952i | 0.977147 | − | 0.212565i | \(-0.0681817\pi\) |
0.304487 | + | 0.952517i | \(0.401515\pi\) | |||||||
\(264\) | 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 | −0.999597 | − | 0.0283781i | \(-0.990966\pi\) |
0.524375 | + | 0.851488i | \(0.324299\pi\) | |||||||
\(270\) | 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 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | −12.9904 | + | 7.50000i | −0.783349 | + | 0.452267i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 3.46410 | + | 6.00000i | 0.207763 | + | 0.359856i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.00000 | + | 3.46410i | 0.356663 | + | 0.205919i | 0.667616 | − | 0.744506i | \(-0.267315\pi\) |
−0.310953 | + | 0.950425i | \(0.600648\pi\) | |||||||
\(284\) | −10.3923 | − | 6.00000i | −0.616670 | − | 0.356034i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 10.3923i | − | 0.614510i | ||||||
\(287\) | 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 | ||||||||
\(292\) | 4.50000 | − | 2.59808i | 0.263343 | − | 0.152041i | ||||
\(293\) | 5.19615 | 0.303562 | 0.151781 | − | 0.988414i | \(-0.451499\pi\) | ||||
0.151781 | + | 0.988414i | \(0.451499\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 2.00000 | − | 10.3923i | 0.115278 | − | 0.599002i | ||||
\(302\) | 23.0000i | 1.32350i | ||||||||
\(303\) | 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 | \(0.835437\pi\) | |||||||
\(308\) | 2.59808 | + | 7.50000i | 0.148039 | + | 0.427352i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5885 | − | 27.0000i | 0.883940 | − | 1.53103i | 0.0370169 | − | 0.999315i | \(-0.488214\pi\) |
0.846923 | − | 0.531715i | \(-0.178452\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.0000 | + | 10.3923i | −1.01742 | + | 0.587408i | −0.913356 | − | 0.407163i | \(-0.866518\pi\) |
−0.104065 | + | 0.994571i | \(0.533185\pi\) | |||||||
\(314\) | −10.3923 | −0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0000 | 0.731307 | ||||||||
\(317\) | 7.79423 | − | 4.50000i | 0.437767 | − | 0.252745i | −0.264883 | − | 0.964281i | \(-0.585333\pi\) |
0.702650 | + | 0.711535i | \(0.252000\pi\) | |||||||
\(318\) | 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 | ||||
\(326\) | −8.66025 | − | 5.00000i | −0.479647 | − | 0.276924i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.3923i | 0.573819i | ||||||||
\(329\) | −25.9808 | + | 9.00000i | −1.43237 | + | 0.496186i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | −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 | ||||||||
\(337\) | 13.0000 | 0.708155 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(338\) | −0.866025 | + | 0.500000i | −0.0471056 | + | 0.0271964i | ||||
\(339\) | 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 | ||||
\(344\) | 4.00000i | 0.215666i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.5000 | − | 12.9904i | −1.20961 | − | 0.698367i | ||||
\(347\) | 2.59808 | + | 1.50000i | 0.139472 | + | 0.0805242i | 0.568112 | − | 0.822951i | \(-0.307674\pi\) |
−0.428640 | + | 0.903475i | \(0.641007\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.7128i | 1.48343i | 0.670714 | + | 0.741716i | \(0.265988\pi\) | ||||
−0.670714 | + | 0.741716i | \(0.734012\pi\) | |||||||
\(350\) | 12.9904 | + | 2.50000i | 0.694365 | + | 0.133631i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.50000 | − | 2.59808i | −0.0799503 | − | 0.138478i | ||||
\(353\) | 5.19615 | − | 9.00000i | 0.276563 | − | 0.479022i | −0.693965 | − | 0.720009i | \(-0.744138\pi\) |
0.970528 | + | 0.240987i | \(0.0774711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.3923 | 0.550791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.00000 | −0.475665 | ||||||||
\(359\) | 10.3923 | − | 6.00000i | 0.548485 | − | 0.316668i | −0.200026 | − | 0.979791i | \(-0.564103\pi\) |
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 10.3923 | + | 18.0000i | 0.546207 | + | 0.946059i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.00000 | + | 6.92820i | −0.314485 | + | 0.363137i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.00000 | + | 5.19615i | 0.469796 | + | 0.271237i | 0.716154 | − | 0.697942i | \(-0.245901\pi\) |
−0.246358 | + | 0.969179i | \(0.579234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3923 | − | 12.0000i | 0.539542 | − | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 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 | ||||
\(383\) | −10.3923 | − | 18.0000i | −0.531022 | − | 0.919757i | −0.999345 | − | 0.0361995i | \(-0.988475\pi\) |
0.468323 | − | 0.883558i | \(-0.344859\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.0000i | 0.559885i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.50000 | + | 4.33013i | 0.380755 | + | 0.219829i | ||||
\(389\) | −7.79423 | − | 4.50000i | −0.395183 | − | 0.228159i | 0.289220 | − | 0.957263i | \(-0.406604\pi\) |
−0.684403 | + | 0.729103i | \(0.739937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.59808 | − | 6.50000i | 0.131223 | − | 0.328300i | ||||
\(393\) | 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 | \(0.125103\pi\) | |||||||
\(398\) | −1.73205 | −0.0868199 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 25.9808 | − | 15.0000i | 1.29742 | − | 0.749064i | 0.317460 | − | 0.948272i | \(-0.397170\pi\) |
0.979957 | + | 0.199207i | \(0.0638367\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | + | 5.19615i | −0.149441 | + | 0.258839i | ||||
\(404\) | 2.59808 | + | 4.50000i | 0.129259 | + | 0.223883i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.5000 | − | 7.79423i | 1.11666 | − | 0.386821i | ||||
\(407\) | − | 24.0000i | − | 1.18964i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | + | 3.46410i | 0.296681 | + | 0.171289i | 0.640951 | − | 0.767582i | \(-0.278540\pi\) |
−0.344270 | + | 0.938871i | \(0.611874\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.3205i | 0.853320i | ||||||||
\(413\) | 10.3923 | + | 9.00000i | 0.511372 | + | 0.442861i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.73205 | − | 3.00000i | 0.0849208 | − | 0.147087i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1769 | 1.52309 | 0.761546 | − | 0.648111i | \(-0.224441\pi\) | ||||
0.761546 | + | 0.648111i | \(0.224441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | 12.0000 | + | 34.6410i | 0.580721 | + | 1.67640i | ||||
\(428\) | 12.0000i | 0.580042i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5885 | + | 9.00000i | 0.750870 | + | 0.433515i | 0.826008 | − | 0.563658i | \(-0.190607\pi\) |
−0.0751385 | + | 0.997173i | \(0.523940\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.1244i | − | 0.582659i | −0.956623 | − | 0.291330i | \(-0.905902\pi\) | ||
0.956623 | − | 0.291330i | \(-0.0940977\pi\) | |||||||
\(434\) | 0.866025 | − | 4.50000i | 0.0415705 | − | 0.216007i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | − | 6.92820i | −0.191565 | − | 0.331801i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.5000 | − | 7.79423i | 0.644320 | − | 0.371998i | −0.141957 | − | 0.989873i | \(-0.545339\pi\) |
0.786277 | + | 0.617875i | \(0.212006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.3827 | + | 13.5000i | −1.11094 | + | 0.641404i | −0.939074 | − | 0.343715i | \(-0.888315\pi\) |
−0.171871 | + | 0.985119i | \(0.554981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.59808 | + | 4.50000i | 0.123022 | + | 0.213081i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | + | 2.59808i | −0.0236228 | + | 0.122748i | ||||
\(449\) | − | 30.0000i | − | 1.41579i | −0.706319 | − | 0.707894i | \(-0.749646\pi\) | ||
0.706319 | − | 0.707894i | \(-0.250354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.0000 | − | 15.5885i | −1.27138 | − | 0.734032i | ||||
\(452\) | 10.3923 | + | 6.00000i | 0.488813 | + | 0.282216i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 25.9808i | − | 1.21934i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0000 | − | 19.0526i | −0.514558 | − | 0.891241i | −0.999857 | − | 0.0168929i | \(-0.994623\pi\) |
0.485299 | − | 0.874348i | \(-0.338711\pi\) | |||||||
\(458\) | −3.46410 | + | 6.00000i | −0.161867 | + | 0.280362i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.5885 | −0.726027 | −0.363013 | − | 0.931784i | \(-0.618252\pi\) | ||||
−0.363013 | + | 0.931784i | \(0.618252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.00000 | 0.232370 | 0.116185 | − | 0.993228i | \(-0.462933\pi\) | ||||
0.116185 | + | 0.993228i | \(0.462933\pi\) | |||||||
\(464\) | −7.79423 | + | 4.50000i | −0.361838 | + | 0.208907i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | −2.59808 | − | 4.50000i | −0.120225 | − | 0.208235i | 0.799632 | − | 0.600491i | \(-0.205028\pi\) |
−0.919856 | + | 0.392256i | \(0.871695\pi\) | |||||||
\(468\) | 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 | ||||
\(479\) | 5.19615 | − | 9.00000i | 0.237418 | − | 0.411220i | −0.722554 | − | 0.691314i | \(-0.757032\pi\) |
0.959973 | + | 0.280094i | \(0.0903655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0000 | − | 13.8564i | 1.09431 | − | 0.631798i | ||||
\(482\) | 12.1244 | 0.552249 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 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 | ||||||||
\(491\) | 36.0000i | 1.62466i | 0.583200 | + | 0.812329i | \(0.301800\pi\) | ||||
−0.583200 | + | 0.812329i | \(0.698200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73205i | 0.0777714i | ||||||||
\(497\) | −31.1769 | − | 6.00000i | −1.39848 | − | 0.269137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | − | 13.8564i | −0.358129 | − | 0.620298i | 0.629519 | − | 0.776985i | \(-0.283252\pi\) |
−0.987648 | + | 0.156687i | \(0.949919\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.5000 | − | 12.9904i | 1.00422 | − | 0.579789i | ||||
\(503\) | 31.1769 | 1.39011 | 0.695055 | − | 0.718957i | \(-0.255380\pi\) | ||||
0.695055 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.00000 | − | 6.92820i | 0.177471 | − | 0.307389i | ||||
\(509\) | 2.59808 | + | 4.50000i | 0.115158 | + | 0.199459i | 0.917843 | − | 0.396944i | \(-0.129929\pi\) |
−0.802685 | + | 0.596403i | \(0.796596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.00000 | − | 10.3923i | 0.398137 | − | 0.459728i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.0000 | + | 10.3923i | 0.793946 | + | 0.458385i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.1769i | 1.37116i | ||||||||
\(518\) | −13.8564 | + | 16.0000i | −0.608816 | + | 0.703000i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3923 | + | 18.0000i | −0.455295 | + | 0.788594i | −0.998705 | − | 0.0508731i | \(-0.983800\pi\) |
0.543410 | + | 0.839467i | \(0.317133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0000 | − | 19.0526i | 1.44299 | − | 0.833110i | 0.444941 | − | 0.895560i | \(-0.353225\pi\) |
0.998048 | + | 0.0624496i | \(0.0198913\pi\) | |||||||
\(524\) | −15.5885 | −0.680985 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 36.0000i | − | 1.55933i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.73205 | − | 1.00000i | −0.0748132 | − | 0.0431934i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 15.5885i | − | 0.672066i | ||||||
\(539\) | 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 | \(-0.470961\pi\) | |||||||
\(542\) | −1.73205 | + | 3.00000i | −0.0743980 | + | 0.128861i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | 0.598597 | 0.299298 | − | 0.954160i | \(-0.403247\pi\) | ||||
0.299298 | + | 0.954160i | \(0.403247\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 32.5000 | − | 11.2583i | 1.38204 | − | 0.478753i | ||||
\(554\) | − | 14.0000i | − | 0.594803i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.00000 | − | 3.46410i | −0.254457 | − | 0.146911i | ||||
\(557\) | −18.1865 | − | 10.5000i | −0.770588 | − | 0.444899i | 0.0624962 | − | 0.998045i | \(-0.480094\pi\) |
−0.833084 | + | 0.553146i | \(0.813427\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.8564i | − | 0.586064i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | −15.5885 | + | 27.0000i | −0.656975 | + | 1.13791i | 0.324420 | + | 0.945913i | \(0.394831\pi\) |
−0.981395 | + | 0.192001i | \(0.938502\pi\) | |||||||
\(564\) | 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 | −0.266090 | − | 0.963948i | \(-0.585732\pi\) |
0.701758 | + | 0.712415i | \(0.252399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | − | 3.46410i | 0.0836974 | − | 0.144968i | −0.821138 | − | 0.570730i | \(-0.806660\pi\) |
0.904835 | + | 0.425762i | \(0.139994\pi\) | |||||||
\(572\) | 5.19615 | + | 9.00000i | 0.217262 | + | 0.376309i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.00000 | + | 25.9808i | 0.375653 | + | 1.08442i | ||||
\(575\) | 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 | \(0.724362\pi\) | |||||||
\(578\) | −14.7224 | − | 8.50000i | −0.612372 | − | 0.353553i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.59808 | + | 13.5000i | −0.107786 | + | 0.560074i | ||||
\(582\) | 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 | ||||
\(587\) | −10.3923 | −0.428936 | −0.214468 | − | 0.976731i | \(-0.568802\pi\) | ||||
−0.214468 | + | 0.976731i | \(0.568802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.00000 | − | 6.92820i | 0.164399 | − | 0.284747i | ||||
\(593\) | 10.3923 | + | 18.0000i | 0.426761 | + | 0.739171i | 0.996583 | − | 0.0825966i | \(-0.0263213\pi\) |
−0.569822 | + | 0.821768i | \(0.692988\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 15.0000i | − | 0.614424i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9808 | + | 15.0000i | 1.06155 | + | 0.612883i | 0.925859 | − | 0.377869i | \(-0.123343\pi\) |
0.135686 | + | 0.990752i | \(0.456676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.6410i | − | 1.41304i | −0.707695 | − | 0.706518i | \(-0.750265\pi\) | ||
0.707695 | − | 0.706518i | \(-0.249735\pi\) | |||||||
\(602\) | 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 | ||||||||
\(607\) | −4.50000 | + | 2.59808i | −0.182649 | + | 0.105453i | −0.588537 | − | 0.808470i | \(-0.700296\pi\) |
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | 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 | ||||||||
\(616\) | −6.00000 | − | 5.19615i | −0.241747 | − | 0.209359i | ||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.0000 | + | 17.3205i | 1.20580 | + | 0.696170i | 0.961839 | − | 0.273615i | \(-0.0882193\pi\) |
0.243962 | + | 0.969785i | \(0.421553\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 31.1769i | 1.25008i | ||||||||
\(623\) | 25.9808 | − | 9.00000i | 1.04090 | − | 0.360577i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | 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 | ||||||||
\(637\) | −9.00000 | + | 22.5167i | −0.356593 | + | 0.892143i | ||||
\(638\) | − | 27.0000i | − | 1.06894i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.3731 | − | 21.0000i | −1.43665 | − | 0.829450i | −0.439034 | − | 0.898470i | \(-0.644679\pi\) |
−0.997615 | + | 0.0690201i | \(0.978013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.46410i | 0.136611i | 0.997664 | + | 0.0683054i | \(0.0217592\pi\) | ||||
−0.997664 | + | 0.0683054i | \(0.978241\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.19615 | + | 9.00000i | −0.204282 | + | 0.353827i | −0.949904 | − | 0.312543i | \(-0.898819\pi\) |
0.745622 | + | 0.666369i | \(0.232153\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | − | 7.79423i | 0.529921 | − | 0.305950i | ||||
\(650\) | 17.3205 | 0.679366 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | −25.9808 | + | 15.0000i | −1.01671 | + | 0.586995i | −0.913148 | − | 0.407628i | \(-0.866356\pi\) |
−0.103558 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(654\) | 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 | ||||
\(659\) | 15.0000i | 0.584317i | 0.956370 | + | 0.292159i | \(0.0943735\pi\) | ||||
−0.956370 | + | 0.292159i | \(0.905627\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.00000 | + | 5.19615i | 0.350059 | + | 0.202107i | 0.664711 | − | 0.747100i | \(-0.268554\pi\) |
−0.314652 | + | 0.949207i | \(0.601888\pi\) | |||||||
\(662\) | 24.2487 | + | 14.0000i | 0.942453 | + | 0.544125i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 5.19615i | − | 0.201650i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 5.19615 | − | 9.00000i | 0.201045 | − | 0.348220i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.5692 | 1.60476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0000 | −1.00223 | −0.501113 | − | 0.865382i | \(-0.667076\pi\) | ||||
−0.501113 | + | 0.865382i | \(0.667076\pi\) | |||||||
\(674\) | −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 | \(-0.263505\pi\) |
−0.976035 | + | 0.217616i | \(0.930172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.5000 | + | 4.33013i | 0.863471 | + | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.50000 | − | 2.59808i | −0.172314 | − | 0.0994855i | ||||
\(683\) | 18.1865 | + | 10.5000i | 0.695888 | + | 0.401771i | 0.805814 | − | 0.592168i | \(-0.201728\pi\) |
−0.109926 | + | 0.993940i | \(0.535061\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.866025 | − | 18.5000i | 0.0330650 | − | 0.706333i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | 10.3923 | − | 18.0000i | 0.395915 | − | 0.685745i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000 | − | 6.92820i | 0.456502 | − | 0.263561i | −0.254071 | − | 0.967186i | \(-0.581770\pi\) |
0.710572 | + | 0.703624i | \(0.248436\pi\) | |||||||
\(692\) | 25.9808 | 0.987640 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.00000 | −0.113878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −13.8564 | − | 24.0000i | −0.524473 | − | 0.908413i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.5000 | + | 4.33013i | −0.472456 | + | 0.163663i | ||||
\(701\) | 6.00000i | 0.226617i | 0.993560 | + | 0.113308i | \(0.0361448\pi\) | ||||
−0.993560 | + | 0.113308i | \(0.963855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.59808 | + | 1.50000i | 0.0979187 | + | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.3923i | 0.391120i | ||||||||
\(707\) | 10.3923 | + | 9.00000i | 0.390843 | + | 0.338480i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00000 | − | 3.46410i | −0.0751116 | − | 0.130097i | 0.826023 | − | 0.563636i | \(-0.190598\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.00000 | + | 5.19615i | −0.337289 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.79423 | − | 4.50000i | 0.291284 | − | 0.168173i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.00000 | + | 10.3923i | −0.223918 | + | 0.387837i | ||||
\(719\) | 5.19615 | + | 9.00000i | 0.193784 | + | 0.335643i | 0.946501 | − | 0.322700i | \(-0.104591\pi\) |
−0.752717 | + | 0.658344i | \(0.771257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | + | 43.3013i | 0.558629 | + | 1.61262i | ||||
\(722\) | − | 19.0000i | − | 0.707107i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.0000 | − | 10.3923i | −0.668965 | − | 0.386227i | ||||
\(725\) | −38.9711 | − | 22.5000i | −1.44735 | − | 0.835629i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.2487i | 0.899335i | 0.893196 | + | 0.449667i | \(0.148458\pi\) | ||||
−0.893196 | + | 0.449667i | \(0.851542\pi\) | |||||||
\(728\) | 1.73205 | − | 9.00000i | 0.0641941 | − | 0.333562i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0000 | − | 6.92820i | 0.443230 | − | 0.255899i | −0.261737 | − | 0.965139i | \(-0.584295\pi\) |
0.704967 | + | 0.709240i | \(0.250962\pi\) | |||||||
\(734\) | −10.3923 | −0.383587 | ||||||||
\(735\) | 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 | ||||||||
\(742\) | −3.00000 | + | 15.5885i | −0.110133 | + | 0.572270i | ||||
\(743\) | 6.00000i | 0.220119i | 0.993925 | + | 0.110059i | \(0.0351041\pi\) | ||||
−0.993925 | + | 0.110059i | \(0.964896\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.46410 | − | 2.00000i | −0.126830 | − | 0.0732252i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3923 | + | 30.0000i | 0.379727 | + | 1.09618i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00000 | − | 3.46410i | −0.0729810 | − | 0.126407i | 0.827225 | − | 0.561870i | \(-0.189918\pi\) |
−0.900207 | + | 0.435463i | \(0.856585\pi\) | |||||||
\(752\) | −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 | ||||||||
\(761\) | 20.7846 | + | 36.0000i | 0.753442 | + | 1.30500i | 0.946145 | + | 0.323742i | \(0.104941\pi\) |
−0.192704 | + | 0.981257i | \(0.561726\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.0000 | − | 13.8564i | −0.579239 | − | 0.501636i | ||||
\(764\) | − | 6.00000i | − | 0.217072i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.0000 | + | 10.3923i | 0.650366 | + | 0.375489i | ||||
\(767\) | 15.5885 | + | 9.00000i | 0.562867 | + | 0.324971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5885i | 0.562134i | 0.959688 | + | 0.281067i | \(0.0906883\pi\) | ||||
−0.959688 | + | 0.281067i | \(0.909312\pi\) | |||||||
\(770\) | 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 | \(-0.564554\pi\) |
0.948984 | − | 0.315324i | \(-0.102113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.50000 | + | 4.33013i | −0.269408 | + | 0.155543i | ||||
\(776\) | −8.66025 | −0.310885 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.00000 | 0.322666 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | + | 31.1769i | −0.644091 | + | 1.11560i | ||||
\(782\) | 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 | \(-0.475591\pi\) |
−0.825177 | + | 0.564875i | \(0.808924\pi\) | |||||||
\(788\) | −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 | ||||
\(794\) | −12.1244 | + | 21.0000i | −0.430277 | + | 0.745262i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.50000 | − | 0.866025i | 0.0531661 | − | 0.0306955i | ||||
\(797\) | 15.5885 | 0.552171 | 0.276086 | − | 0.961133i | \(-0.410963\pi\) | ||||
0.276086 | + | 0.961133i | \(0.410963\pi\) | |||||||
\(798\) | 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 | ||||||||
\(806\) | − | 6.00000i | − | 0.211341i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.50000 | − | 2.59808i | −0.158309 | − | 0.0914000i | ||||
\(809\) | −5.19615 | − | 3.00000i | −0.182687 | − | 0.105474i | 0.405868 | − | 0.913932i | \(-0.366969\pi\) |
−0.588555 | + | 0.808458i | \(0.700303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3923i | 0.364923i | 0.983213 | + | 0.182462i | \(0.0584065\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | −15.5885 | + | 18.0000i | −0.547048 | + | 0.631676i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 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 | −0.907480 | − | 0.420094i | \(-0.861997\pi\) |
−0.0899279 | + | 0.995948i | \(0.528664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.50000 | + | 9.52628i | −0.191718 | + | 0.332065i | −0.945820 | − | 0.324692i | \(-0.894739\pi\) |
0.754102 | + | 0.656758i | \(0.228073\pi\) | |||||||
\(824\) | −8.66025 | − | 15.0000i | −0.301694 | − | 0.522550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.5000 | − | 2.59808i | −0.469725 | − | 0.0903986i | ||||
\(827\) | 3.00000i | 0.104320i | 0.998639 | + | 0.0521601i | \(0.0166106\pi\) | ||||
−0.998639 | + | 0.0521601i | \(0.983389\pi\) | |||||||
\(828\) | 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 | ||||||||
\(832\) | 3.46410i | 0.120096i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.0000 | + | 15.5885i | −0.932700 | + | 0.538494i | ||||
\(839\) | 20.7846 | 0.717564 | 0.358782 | − | 0.933421i | \(-0.383192\pi\) | ||||
0.358782 | + | 0.933421i | \(0.383192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −52.0000 | −1.79310 | ||||||||
\(842\) | 8.66025 | − | 5.00000i | 0.298452 | − | 0.172311i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.00000 | + | 1.73205i | −0.0344214 | + | 0.0596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | + | 1.73205i | −0.171802 | + | 0.0595140i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.3923i | − | 0.355826i | −0.984046 | − | 0.177913i | \(-0.943065\pi\) | ||
0.984046 | − | 0.177913i | \(-0.0569345\pi\) | |||||||
\(854\) | −27.7128 | − | 24.0000i | −0.948313 | − | 0.821263i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −5.19615 | + | 9.00000i | −0.177497 | + | 0.307434i | −0.941023 | − | 0.338344i | \(-0.890133\pi\) |
0.763525 | + | 0.645778i | \(0.223467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.0000 | + | 24.2487i | −1.43302 | + | 0.827355i | −0.997350 | − | 0.0727505i | \(-0.976822\pi\) |
−0.435671 | + | 0.900106i | \(0.643489\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.0000 | −0.613082 | ||||||||
\(863\) | −5.19615 | + | 3.00000i | −0.176879 | + | 0.102121i | −0.585826 | − | 0.810437i | \(-0.699230\pi\) |
0.408946 | + | 0.912558i | \(0.365896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.06218 | + | 10.5000i | 0.206001 | + | 0.356805i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.50000 | + | 4.33013i | 0.0509133 | + | 0.146974i | ||||
\(869\) | − | 39.0000i | − | 1.32298i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | + | 3.46410i | 0.203302 | + | 0.117377i | ||||
\(872\) | 6.92820 | + | 4.00000i | 0.234619 | + | 0.135457i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00000 | − | 1.73205i | −0.0337676 | − | 0.0584872i | 0.848648 | − | 0.528958i | \(-0.177417\pi\) |
−0.882415 | + | 0.470471i | \(0.844084\pi\) | |||||||
\(878\) | −7.79423 | + | 13.5000i | −0.263042 | + | 0.455603i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.1769 | −1.05038 | −0.525188 | − | 0.850986i | \(-0.676005\pi\) | ||||
−0.525188 | + | 0.850986i | \(0.676005\pi\) | |||||||
\(882\) | 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 | ||||
\(887\) | −15.5885 | − | 27.0000i | −0.523409 | − | 0.906571i | −0.999629 | − | 0.0272449i | \(-0.991327\pi\) |
0.476220 | − | 0.879326i | \(-0.342007\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.00000 | − | 20.7846i | 0.134156 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.50000 | − | 2.59808i | −0.150671 | − | 0.0869900i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.866025 | − | 2.50000i | −0.0289319 | − | 0.0835191i | ||||
\(897\) | 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 | ||||||||
\(902\) | 31.1769 | 1.03808 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.0000 | + | 19.0526i | −0.365249 | + | 0.632630i | −0.988816 | − | 0.149140i | \(-0.952349\pi\) |
0.623567 | + | 0.781770i | \(0.285683\pi\) | |||||||
\(908\) | 12.9904 | + | 22.5000i | 0.431101 | + | 0.746689i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.0000i | 1.19273i | 0.802712 | + | 0.596367i | \(0.203390\pi\) | ||||
−0.802712 | + | 0.596367i | \(0.796610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.5000 | + | 7.79423i | 0.446785 | + | 0.257951i | ||||
\(914\) | 19.0526 | + | 11.0000i | 0.630203 | + | 0.363848i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 6.92820i | − | 0.228914i | ||||||
\(917\) | −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 | ||||||||
\(922\) | 13.5000 | − | 7.79423i | 0.444599 | − | 0.256689i | ||||
\(923\) | −41.5692 | −1.36827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.0000 | 1.31519 | ||||||||
\(926\) | −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 | 0.974394 | + | 0.224848i | \(0.0721885\pi\) |
−0.292473 | + | 0.956274i | \(0.594478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 18.0000i | − | 0.589610i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.50000 | + | 2.59808i | 0.147244 | + | 0.0850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.6410i | 1.13167i | 0.824518 | + | 0.565836i | \(0.191447\pi\) | ||||
−0.824518 | + | 0.565836i | \(0.808553\pi\) | |||||||
\(938\) | −5.19615 | − | 1.00000i | −0.169660 | − | 0.0326512i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.59808 | + | 4.50000i | −0.0846949 | + | 0.146696i | −0.905261 | − | 0.424856i | \(-0.860325\pi\) |
0.820566 | + | 0.571551i | \(0.193658\pi\) | |||||||
\(942\) | 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 | −0.621264 | − | 0.783601i | \(-0.713381\pi\) |
0.367986 | + | 0.929831i | \(0.380047\pi\) | |||||||
\(948\) | 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 | \(0.0941672\pi\) | ||||
−0.956559 | + | 0.291539i | \(0.905833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.3923 | + | 6.00000i | 0.336111 | + | 0.194054i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.3923i | 0.335760i | ||||||||
\(959\) | 20.7846 | − | 24.0000i | 0.671170 | − | 0.775000i | ||||
\(960\) | 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 | ||||||||
\(967\) | 56.0000 | 1.80084 | 0.900419 | − | 0.435023i | \(-0.143260\pi\) | ||||
0.900419 | + | 0.435023i | \(0.143260\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5885 | − | 27.0000i | −0.500257 | − | 0.866471i | −1.00000 | 0.000297246i | \(-0.999905\pi\) | |
0.499743 | − | 0.866174i | \(-0.333428\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.0000 | − | 3.46410i | −0.577054 | − | 0.111054i | ||||
\(974\) | 11.0000i | 0.352463i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.0000 | + | 6.92820i | 0.384111 | + | 0.221766i | ||||
\(977\) | −15.5885 | − | 9.00000i | −0.498719 | − | 0.287936i | 0.229465 | − | 0.973317i | \(-0.426302\pi\) |
−0.728184 | + | 0.685381i | \(0.759636\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.0000 | − | 31.1769i | −0.574403 | − | 0.994895i | ||||
\(983\) | 10.3923 | − | 18.0000i | 0.331463 | − | 0.574111i | −0.651336 | − | 0.758790i | \(-0.725791\pi\) |
0.982799 | + | 0.184679i | \(0.0591244\pi\) | |||||||
\(984\) | 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 | ||||||||
\(994\) | 30.0000 | − | 10.3923i | 0.951542 | − | 0.329624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.0000 | + | 19.0526i | 1.04512 | + | 0.603401i | 0.921279 | − | 0.388901i | \(-0.127145\pi\) |
0.123841 | + | 0.992302i | \(0.460479\pi\) | |||||||
\(998\) | 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 | 378.2.k.a.269.1 | yes | 4 | |
3.2 | odd | 2 | inner | 378.2.k.a.269.2 | yes | 4 | |
7.3 | odd | 6 | 2646.2.d.c.2645.2 | 4 | |||
7.4 | even | 3 | 2646.2.d.c.2645.1 | 4 | |||
7.5 | odd | 6 | inner | 378.2.k.a.215.2 | yes | 4 | |
9.2 | odd | 6 | 1134.2.t.a.1025.1 | 4 | |||
9.4 | even | 3 | 1134.2.l.d.269.1 | 4 | |||
9.5 | odd | 6 | 1134.2.l.d.269.2 | 4 | |||
9.7 | even | 3 | 1134.2.t.a.1025.2 | 4 | |||
21.5 | even | 6 | inner | 378.2.k.a.215.1 | ✓ | 4 | |
21.11 | odd | 6 | 2646.2.d.c.2645.3 | 4 | |||
21.17 | even | 6 | 2646.2.d.c.2645.4 | 4 | |||
63.5 | even | 6 | 1134.2.t.a.593.2 | 4 | |||
63.40 | odd | 6 | 1134.2.t.a.593.1 | 4 | |||
63.47 | even | 6 | 1134.2.l.d.215.2 | 4 | |||
63.61 | odd | 6 | 1134.2.l.d.215.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.a.215.1 | ✓ | 4 | 21.5 | even | 6 | inner | |
378.2.k.a.215.2 | yes | 4 | 7.5 | odd | 6 | inner | |
378.2.k.a.269.1 | yes | 4 | 1.1 | even | 1 | trivial | |
378.2.k.a.269.2 | yes | 4 | 3.2 | odd | 2 | inner | |
1134.2.l.d.215.1 | 4 | 63.61 | odd | 6 | |||
1134.2.l.d.215.2 | 4 | 63.47 | even | 6 | |||
1134.2.l.d.269.1 | 4 | 9.4 | even | 3 | |||
1134.2.l.d.269.2 | 4 | 9.5 | odd | 6 | |||
1134.2.t.a.593.1 | 4 | 63.40 | odd | 6 | |||
1134.2.t.a.593.2 | 4 | 63.5 | even | 6 | |||
1134.2.t.a.1025.1 | 4 | 9.2 | odd | 6 | |||
1134.2.t.a.1025.2 | 4 | 9.7 | even | 3 | |||
2646.2.d.c.2645.1 | 4 | 7.4 | even | 3 | |||
2646.2.d.c.2645.2 | 4 | 7.3 | odd | 6 | |||
2646.2.d.c.2645.3 | 4 | 21.11 | odd | 6 | |||
2646.2.d.c.2645.4 | 4 | 21.17 | even | 6 |