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 | 269.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.269 |
Dual form | 378.2.k.a.215.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 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 | \(0.314897\pi\) | ||||
−0.549294 | + | 0.835629i | \(0.685103\pi\) | |||||||
\(30\) | 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 | \(-0.801350\pi\) | ||||
−0.811503 | + | 0.584349i | \(0.801350\pi\) | |||||||
\(42\) | 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 | \(0.107126\pi\) |
−0.185964 | + | 0.982556i | \(0.559541\pi\) | |||||||
\(48\) | 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 | 0.0987002 | − | 0.995117i | \(-0.468532\pi\) |
−0.812447 | + | 0.583036i | \(0.801865\pi\) | |||||||
\(54\) | 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 | −0.645861 | − | 0.763455i | \(-0.723502\pi\) |
0.984102 | + | 0.177605i | \(0.0568349\pi\) | |||||||
\(60\) | 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 | \(0.252242\pi\) | ||||
−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 | \(0.568317\pi\) | |||||||
\(74\) | 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 | \(-0.407948\pi\) | ||||
0.285176 | + | 0.958475i | \(0.407948\pi\) | |||||||
\(84\) | 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 | \(-0.980993\pi\) |
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 | ||||||||
\(97\) | 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 | −0.707327 | − | 0.706887i | \(-0.750099\pi\) |
0.965845 | + | 0.259120i | \(0.0834325\pi\) | |||||||
\(102\) | 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 | 0.0950377 | − | 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 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | − | 12.0000i | − | 1.12887i | −0.825479 | − | 0.564433i | \(-0.809095\pi\) | ||
0.825479 | − | 0.564433i | \(-0.190905\pi\) | |||||||
\(114\) | 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 | \(0.0717814\pi\) |
−0.293696 | + | 0.955899i | \(0.594885\pi\) | |||||||
\(132\) | 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 | −0.0146279 | − | 0.999893i | \(-0.504656\pi\) |
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(138\) | 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 | −0.926595 | − | 0.376061i | \(-0.877278\pi\) |
−0.137619 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(150\) | 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 | \(-0.631716\pi\) | ||||
−0.402090 | + | 0.915600i | \(0.631716\pi\) | |||||||
\(168\) | 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 | \(-0.716764\pi\) |
−0.358082 | − | 0.933690i | \(-0.616569\pi\) | |||||||
\(174\) | 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 | 0.179585 | − | 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 | \(-0.280971\pi\) | |||||||
\(182\) | −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 | −0.676068 | − | 0.736839i | \(-0.736317\pi\) |
0.300088 | + | 0.953912i | \(0.402984\pi\) | |||||||
\(192\) | 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 | \(0.179445\pi\) | ||||
−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 | \(0.647113\pi\) | |||||||
\(200\) | −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 | \(-0.502418\pi\) |
0.869799 | − | 0.493406i | \(-0.164248\pi\) | |||||||
\(228\) | 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 | −0.914461 | − | 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 | ||||||||
\(239\) | − | 12.0000i | − | 0.776215i | −0.921614 | − | 0.388108i | \(-0.873129\pi\) | ||
0.921614 | − | 0.388108i | \(-0.126871\pi\) | |||||||
\(240\) | 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 | \(-0.194004\pi\) | ||||
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 | ||||
\(257\) | 10.3923 | + | 18.0000i | 0.648254 | + | 1.12281i | 0.983540 | + | 0.180693i | \(0.0578339\pi\) |
−0.335285 | + | 0.942117i | \(0.608833\pi\) | |||||||
\(258\) | 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 | −0.304487 | − | 0.952517i | \(-0.598485\pi\) |
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(264\) | 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 | ||||||||
\(274\) | −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 | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 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 | \(-0.548501\pi\) | ||||
−0.151781 | + | 0.988414i | \(0.548501\pi\) | |||||||
\(294\) | 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 | \(0.511786\pi\) |
−0.846923 | + | 0.531715i | \(0.821548\pi\) | |||||||
\(312\) | 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 | −0.702650 | − | 0.711535i | \(-0.748000\pi\) |
0.264883 | + | 0.964281i | \(0.414667\pi\) | |||||||
\(318\) | 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 | 0.428640 | − | 0.903475i | \(-0.358993\pi\) |
−0.568112 | + | 0.822951i | \(0.692326\pi\) | |||||||
\(348\) | 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 | −0.970528 | − | 0.240987i | \(-0.922529\pi\) |
0.693965 | + | 0.720009i | \(0.255862\pi\) | |||||||
\(354\) | 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 | −0.748511 | − | 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 | ||||||||
\(364\) | −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 | \(0.0115252\pi\) |
−0.468323 | + | 0.883558i | \(0.655141\pi\) | |||||||
\(384\) | 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 | 0.684403 | − | 0.729103i | \(-0.260063\pi\) |
−0.289220 | + | 0.957263i | \(0.593396\pi\) | |||||||
\(390\) | 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 | −0.979957 | − | 0.199207i | \(-0.936163\pi\) |
−0.317460 | + | 0.948272i | \(0.602830\pi\) | |||||||
\(402\) | 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 | \(-0.775559\pi\) | ||||
−0.761546 | + | 0.648111i | \(0.775559\pi\) | |||||||
\(420\) | 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 | 0.0751385 | − | 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 | \(-0.0940977\pi\) | |||||||
\(434\) | −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 | 0.171871 | − | 0.985119i | \(-0.445019\pi\) |
0.939074 | + | 0.343715i | \(0.111685\pi\) | |||||||
\(444\) | 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 | \(0.250354\pi\) | ||||
−0.706319 | + | 0.707894i | \(0.749646\pi\) | |||||||
\(450\) | 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 | \(-0.381748\pi\) | ||||
0.363013 | + | 0.931784i | \(0.381748\pi\) | |||||||
\(462\) | 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 | 0.919856 | − | 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 | ||||
\(479\) | −5.19615 | + | 9.00000i | −0.237418 | + | 0.411220i | −0.959973 | − | 0.280094i | \(-0.909635\pi\) |
0.722554 | + | 0.691314i | \(0.242968\pi\) | |||||||
\(480\) | 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 | \(-0.698200\pi\) | ||
0.583200 | − | 0.812329i | \(-0.301800\pi\) | |||||||
\(492\) | 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 | \(-0.744620\pi\) | ||||
−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 | ||||
\(509\) | −2.59808 | − | 4.50000i | −0.115158 | − | 0.199459i | 0.802685 | − | 0.596403i | \(-0.203404\pi\) |
−0.917843 | + | 0.396944i | \(0.870071\pi\) | |||||||
\(510\) | 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 | −0.543410 | − | 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 | \(0.0198913\pi\) | |||||||
\(524\) | 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 | 0.833084 | − | 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 | ||||||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | 15.5885 | − | 27.0000i | 0.656975 | − | 1.13791i | −0.324420 | − | 0.945913i | \(-0.605169\pi\) |
0.981395 | − | 0.192001i | \(-0.0614977\pi\) | |||||||
\(564\) | 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 | \(-0.747601\pi\) |
0.266090 | + | 0.963948i | \(0.414268\pi\) | |||||||
\(570\) | 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 | \(-0.431198\pi\) | ||||
0.214468 | + | 0.976731i | \(0.431198\pi\) | |||||||
\(588\) | 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 | 0.569822 | − | 0.821768i | \(-0.307012\pi\) |
−0.996583 | + | 0.0825966i | \(0.973679\pi\) | |||||||
\(594\) | 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 | −0.135686 | − | 0.990752i | \(-0.543324\pi\) |
−0.925859 | + | 0.377869i | \(0.876657\pi\) | |||||||
\(600\) | 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 | \(-0.881983\pi\) | ||
0.932051 | − | 0.362326i | \(-0.118017\pi\) | |||||||
\(618\) | 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 | 0.997615 | − | 0.0690201i | \(-0.0219873\pi\) |
0.439034 | + | 0.898470i | \(0.355321\pi\) | |||||||
\(642\) | 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 | −0.745622 | − | 0.666369i | \(-0.767847\pi\) |
0.949904 | + | 0.312543i | \(0.101181\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.5000 | − | 7.79423i | 0.529921 | − | 0.305950i | ||||
\(650\) | −17.3205 | −0.679366 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000 | 0.391630 | ||||||||
\(653\) | 25.9808 | − | 15.0000i | 1.01671 | − | 0.586995i | 0.103558 | − | 0.994623i | \(-0.466977\pi\) |
0.913148 | + | 0.407628i | \(0.133644\pi\) | |||||||
\(654\) | 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 | \(-0.905627\pi\) | ||
0.956370 | − | 0.292159i | \(-0.0943735\pi\) | |||||||
\(660\) | 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 | 0.976035 | − | 0.217616i | \(-0.0698279\pi\) |
−0.676478 | + | 0.736463i | \(0.736495\pi\) | |||||||
\(678\) | 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 | 0.109926 | − | 0.993940i | \(-0.464939\pi\) |
−0.805814 | + | 0.592168i | \(0.798272\pi\) | |||||||
\(684\) | 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 | \(-0.963855\pi\) | ||
0.993560 | − | 0.113308i | \(-0.0361448\pi\) | |||||||
\(702\) | 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 | 0.752717 | − | 0.658344i | \(-0.228743\pi\) |
−0.946501 | + | 0.322700i | \(0.895409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | + | 43.3013i | 0.558629 | + | 1.61262i | ||||
\(722\) | 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 | \(-0.964896\pi\) | ||
0.993925 | − | 0.110059i | \(-0.0351041\pi\) | |||||||
\(744\) | 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 | \(-0.895059\pi\) |
0.192704 | − | 0.981257i | \(-0.438274\pi\) | |||||||
\(762\) | 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 | \(0.435446\pi\) |
−0.948984 | + | 0.315324i | \(0.897887\pi\) | |||||||
\(774\) | 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 | \(-0.589037\pi\) | ||||
−0.276086 | + | 0.961133i | \(0.589037\pi\) | |||||||
\(798\) | 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 | 0.588555 | − | 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 | \(0.941593\pi\) | |||||||
\(812\) | 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 | 0.0899279 | − | 0.995948i | \(-0.471336\pi\) |
0.907480 | + | 0.420094i | \(0.138003\pi\) | |||||||
\(822\) | 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 | \(-0.983389\pi\) | ||
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 | ||||||||
\(832\) | 3.46410i | 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 | \(-0.616808\pi\) | ||||
−0.358782 | + | 0.933421i | \(0.616808\pi\) | |||||||
\(840\) | 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 | −0.763525 | − | 0.645778i | \(-0.776533\pi\) |
0.941023 | + | 0.338344i | \(0.109867\pi\) | |||||||
\(858\) | 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 | −0.408946 | − | 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 | ||||||||
\(868\) | 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 | \(-0.323995\pi\) | ||||
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 | ||||
\(887\) | 15.5885 | + | 27.0000i | 0.523409 | + | 0.906571i | 0.999629 | + | 0.0272449i | \(0.00867339\pi\) |
−0.476220 | + | 0.879326i | \(0.657993\pi\) | |||||||
\(888\) | 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 | \(-0.796610\pi\) | ||
0.802712 | − | 0.596367i | \(-0.203390\pi\) | |||||||
\(912\) | 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 | \(-0.927811\pi\) |
0.292473 | − | 0.956274i | \(-0.405522\pi\) | |||||||
\(930\) | 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 | −0.820566 | − | 0.571551i | \(-0.806342\pi\) |
0.905261 | + | 0.424856i | \(0.139675\pi\) | |||||||
\(942\) | 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 | \(-0.619953\pi\) |
0.621264 | + | 0.783601i | \(0.286619\pi\) | |||||||
\(948\) | 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 | ||||||||
\(956\) | −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 | \(9.46163e-5\pi\) | |
−0.499743 | + | 0.866174i | \(0.666572\pi\) | |||||||
\(972\) | 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 | 0.728184 | − | 0.685381i | \(-0.240364\pi\) |
−0.229465 | + | 0.973317i | \(0.573698\pi\) | |||||||
\(978\) | 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 | −0.982799 | − | 0.184679i | \(-0.940876\pi\) |
0.651336 | + | 0.758790i | \(0.274209\pi\) | |||||||
\(984\) | 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.269.2 | yes | 4 | |
3.2 | odd | 2 | inner | 378.2.k.a.269.1 | yes | 4 | |
7.3 | odd | 6 | 2646.2.d.c.2645.4 | 4 | |||
7.4 | even | 3 | 2646.2.d.c.2645.3 | 4 | |||
7.5 | odd | 6 | inner | 378.2.k.a.215.1 | ✓ | 4 | |
9.2 | odd | 6 | 1134.2.t.a.1025.2 | 4 | |||
9.4 | even | 3 | 1134.2.l.d.269.2 | 4 | |||
9.5 | odd | 6 | 1134.2.l.d.269.1 | 4 | |||
9.7 | even | 3 | 1134.2.t.a.1025.1 | 4 | |||
21.5 | even | 6 | inner | 378.2.k.a.215.2 | yes | 4 | |
21.11 | odd | 6 | 2646.2.d.c.2645.1 | 4 | |||
21.17 | even | 6 | 2646.2.d.c.2645.2 | 4 | |||
63.5 | even | 6 | 1134.2.t.a.593.1 | 4 | |||
63.40 | odd | 6 | 1134.2.t.a.593.2 | 4 | |||
63.47 | even | 6 | 1134.2.l.d.215.1 | 4 | |||
63.61 | odd | 6 | 1134.2.l.d.215.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.a.215.1 | ✓ | 4 | 7.5 | odd | 6 | inner | |
378.2.k.a.215.2 | yes | 4 | 21.5 | even | 6 | inner | |
378.2.k.a.269.1 | yes | 4 | 3.2 | odd | 2 | inner | |
378.2.k.a.269.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1134.2.l.d.215.1 | 4 | 63.47 | even | 6 | |||
1134.2.l.d.215.2 | 4 | 63.61 | odd | 6 | |||
1134.2.l.d.269.1 | 4 | 9.5 | odd | 6 | |||
1134.2.l.d.269.2 | 4 | 9.4 | even | 3 | |||
1134.2.t.a.593.1 | 4 | 63.5 | even | 6 | |||
1134.2.t.a.593.2 | 4 | 63.40 | odd | 6 | |||
1134.2.t.a.1025.1 | 4 | 9.7 | even | 3 | |||
1134.2.t.a.1025.2 | 4 | 9.2 | odd | 6 | |||
2646.2.d.c.2645.1 | 4 | 21.11 | odd | 6 | |||
2646.2.d.c.2645.2 | 4 | 21.17 | even | 6 | |||
2646.2.d.c.2645.3 | 4 | 7.4 | even | 3 | |||
2646.2.d.c.2645.4 | 4 | 7.3 | odd | 6 |