Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.4 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.c.2591.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.317837i | − 0.142141i | −0.997471 | − | 0.0710706i | \(-0.977358\pi\) | ||||
0.997471 | − | 0.0710706i | \(-0.0226416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.44949 | −1.23407 | −0.617033 | − | 0.786937i | \(-0.711666\pi\) | ||||
−0.617033 | + | 0.786937i | \(0.711666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.97469i | − 1.44908i | −0.689235 | − | 0.724538i | \(-0.742053\pi\) | ||||
0.689235 | − | 0.724538i | \(-0.257947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44949i | 0.561951i | 0.959715 | + | 0.280976i | \(0.0906580\pi\) | ||||
−0.959715 | + | 0.280976i | \(0.909342\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.65685 | −1.17954 | −0.589768 | − | 0.807573i | \(-0.700781\pi\) | ||||
−0.589768 | + | 0.807573i | \(0.700781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | 0.979796 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.51399i | 1.02392i | 0.859009 | + | 0.511961i | \(0.171081\pi\) | ||||
−0.859009 | + | 0.511961i | \(0.828919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 6.44949i | − 1.15836i | −0.815199 | − | 0.579181i | \(-0.803372\pi\) | ||||
0.815199 | − | 0.579181i | \(-0.196628\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.317837 | 0.0537243 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.00000 | 1.47959 | 0.739795 | − | 0.672832i | \(-0.234922\pi\) | ||||
0.739795 | + | 0.672832i | \(0.234922\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.24604i | 1.13164i | 0.824528 | + | 0.565821i | \(0.191441\pi\) | ||||
−0.824528 | + | 0.565821i | \(0.808559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.34847i | 0.968132i | 0.875031 | + | 0.484066i | \(0.160841\pi\) | ||||
−0.875031 | + | 0.484066i | \(0.839159\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.8530 | −1.58307 | −0.791537 | − | 0.611121i | \(-0.790719\pi\) | ||||
−0.791537 | + | 0.611121i | \(0.790719\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.9494i | − 1.64137i | −0.571378 | − | 0.820687i | \(-0.693591\pi\) | ||||
0.571378 | − | 0.820687i | \(-0.306409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.449490i | − 0.0606092i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.83183 | 0.759239 | 0.379620 | − | 0.925143i | \(-0.376055\pi\) | ||||
0.379620 | + | 0.925143i | \(0.376055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4495 | −1.33792 | −0.668960 | − | 0.743298i | \(-0.733260\pi\) | ||||
−0.668960 | + | 0.743298i | \(0.733260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.41421i | 0.175412i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.79796i | 0.708333i | 0.935182 | + | 0.354167i | \(0.115235\pi\) | ||||
−0.935182 | + | 0.354167i | \(0.884765\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.79796 | −1.14676 | −0.573382 | − | 0.819288i | \(-0.694369\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41421i | 0.161165i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3485i | 1.61433i | 0.590327 | + | 0.807164i | \(0.298999\pi\) | ||||
−0.590327 | + | 0.807164i | \(0.701001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.02458 | 0.880812 | 0.440406 | − | 0.897799i | \(-0.354835\pi\) | ||||
0.440406 | + | 0.897799i | \(0.354835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.89898 | −0.205973 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4135i | 1.63383i | 0.576761 | + | 0.816913i | \(0.304316\pi\) | ||||
−0.576761 | + | 0.816913i | \(0.695684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 4.44949i | − 0.466433i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.778539 | 0.0798764 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2474 | −1.44661 | −0.723305 | − | 0.690529i | \(-0.757378\pi\) | ||||
−0.723305 | + | 0.690529i | \(0.757378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.65685i | 0.562878i | 0.959579 | + | 0.281439i | \(0.0908117\pi\) | ||||
−0.959579 | + | 0.281439i | \(0.909188\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.7980i | 1.35955i | 0.733419 | + | 0.679777i | \(0.237923\pi\) | ||||
−0.733419 | + | 0.679777i | \(0.762077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8564 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266391\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.7980 | −1.80052 | −0.900259 | − | 0.435355i | \(-0.856623\pi\) | ||||
−0.900259 | + | 0.435355i | \(0.856623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 3.60697i | − 0.339315i | −0.985503 | − | 0.169657i | \(-0.945734\pi\) | ||||
0.985503 | − | 0.169657i | \(-0.0542661\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.79796i | 0.167661i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.97469 | 0.547699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 3.14626i | − 0.281410i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4495i | 1.54839i | 0.632946 | + | 0.774196i | \(0.281845\pi\) | ||||
−0.632946 | + | 0.774196i | \(0.718155\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7778 | −1.29114 | −0.645572 | − | 0.763700i | \(-0.723381\pi\) | ||||
−0.645572 | + | 0.763700i | \(0.723381\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44949 | −0.212398 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 15.2706i | − 1.30466i | −0.757936 | − | 0.652329i | \(-0.773792\pi\) | ||||
0.757936 | − | 0.652329i | \(-0.226208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.44949i | − 0.377401i | −0.982035 | − | 0.188700i | \(-0.939572\pi\) | ||||
0.982035 | − | 0.188700i | \(-0.0604275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.29253 | −0.526208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.75255 | 0.145541 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3.32124i | − 0.272086i | −0.990703 | − | 0.136043i | \(-0.956561\pi\) | ||||
0.990703 | − | 0.136043i | \(-0.0434386\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 6.34847i | − 0.516631i | −0.966061 | − | 0.258316i | \(-0.916833\pi\) | ||||
0.966061 | − | 0.258316i | \(-0.0831674\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.04989 | −0.164651 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2474 | 1.13707 | 0.568535 | − | 0.822659i | \(-0.307510\pi\) | ||||
0.568535 | + | 0.822659i | \(0.307510\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 5.65685i | − 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.44949i | 0.426837i | 0.976961 | + | 0.213418i | \(0.0684598\pi\) | ||||
−0.976961 | + | 0.213418i | \(0.931540\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.0458 | −1.00951 | −0.504756 | − | 0.863262i | \(-0.668417\pi\) | ||||
−0.504756 | + | 0.863262i | \(0.668417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.79796 | 0.522920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 14.7778i | − 1.12354i | −0.827295 | − | 0.561768i | \(-0.810121\pi\) | ||||
0.827295 | − | 0.561768i | \(-0.189879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.89898i | 0.370328i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.68556 | −0.200728 | −0.100364 | − | 0.994951i | \(-0.532001\pi\) | ||||
−0.100364 | + | 0.994951i | \(0.532001\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.7980 | −1.17425 | −0.587127 | − | 0.809495i | \(-0.699741\pi\) | ||||
−0.587127 | + | 0.809495i | \(0.699741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 2.86054i | − 0.210311i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 8.44949i | − 0.617888i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.7778 | 1.06928 | 0.534642 | − | 0.845078i | \(-0.320446\pi\) | ||||
0.534642 | + | 0.845078i | \(0.320446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.5959 | −1.33856 | −0.669282 | − | 0.743009i | \(-0.733398\pi\) | ||||
−0.669282 | + | 0.743009i | \(0.733398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 9.89949i | − 0.705310i | −0.935753 | − | 0.352655i | \(-0.885279\pi\) | ||||
0.935753 | − | 0.352655i | \(-0.114721\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.6969i | 1.18361i | 0.806079 | + | 0.591807i | \(0.201585\pi\) | ||||
−0.806079 | + | 0.591807i | \(0.798415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.51399 | −0.387006 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.30306 | 0.160853 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.46410i | 0.239617i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.5959i | 1.48672i | 0.668889 | + | 0.743362i | \(0.266770\pi\) | ||||
−0.668889 | + | 0.743362i | \(0.733230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.01778 | 0.137611 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.44949 | 0.437820 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.5843i | 1.78826i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.75255i | − 0.251289i | −0.992075 | − | 0.125645i | \(-0.959900\pi\) | ||||
0.992075 | − | 0.125645i | \(-0.0400999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.0280 | 0.731953 | 0.365976 | − | 0.930624i | \(-0.380735\pi\) | ||||
0.365976 | + | 0.930624i | \(0.380735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.20204 | 0.277679 | 0.138839 | − | 0.990315i | \(-0.455663\pi\) | ||||
0.138839 | + | 0.990315i | \(0.455663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 7.07107i | − 0.463241i | −0.972806 | − | 0.231621i | \(-0.925597\pi\) | ||||
0.972806 | − | 0.231621i | \(-0.0744028\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.44949i | 0.225020i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.1988 | −1.43592 | −0.717961 | − | 0.696083i | \(-0.754925\pi\) | ||||
−0.717961 | + | 0.696083i | \(0.754925\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.34847 | −0.344525 | −0.172263 | − | 0.985051i | \(-0.555108\pi\) | ||||
−0.172263 | + | 0.985051i | \(0.555108\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.317837i | 0.0203059i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 10.8990i | − 0.693485i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.28913 | 0.207608 | 0.103804 | − | 0.994598i | \(-0.466899\pi\) | ||||
0.103804 | + | 0.994598i | \(0.466899\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1421i | 0.882162i | 0.897467 | + | 0.441081i | \(0.145405\pi\) | ||||
−0.897467 | + | 0.441081i | \(0.854595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.00000i | 0.559233i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.9063 | −0.980824 | −0.490412 | − | 0.871491i | \(-0.663154\pi\) | ||||
−0.490412 | + | 0.871491i | \(0.663154\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.79796 | −0.233307 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.4812i | 1.18779i | 0.804544 | + | 0.593893i | \(0.202410\pi\) | ||||
−0.804544 | + | 0.593893i | \(0.797590\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 20.6969i | − 1.25725i | −0.777709 | − | 0.628625i | \(-0.783618\pi\) | ||||
0.777709 | − | 0.628625i | \(-0.216382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.92820 | 0.417786 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | −0.0600842 | −0.0300421 | − | 0.999549i | \(-0.509564\pi\) | ||||
−0.0300421 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.2419i | 1.08822i | 0.839013 | + | 0.544111i | \(0.183133\pi\) | ||||
−0.839013 | + | 0.544111i | \(0.816867\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3485i | 1.03126i | 0.856812 | + | 0.515630i | \(0.172442\pi\) | ||||
−0.856812 | + | 0.515630i | \(0.827558\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.24604 | −0.427720 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.6969 | −1.09982 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.16744i | 0.477147i | 0.971124 | + | 0.238574i | \(0.0766798\pi\) | ||||
−0.971124 | + | 0.238574i | \(0.923320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 1.85357i | − 0.107919i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.1701 | 1.45563 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.34847 | −0.365920 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.32124i | 0.190173i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 21.7980i | − 1.24408i | −0.782987 | − | 0.622038i | \(-0.786305\pi\) | ||||
0.782987 | − | 0.622038i | \(-0.213695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.3595 | −1.38130 | −0.690649 | − | 0.723190i | \(-0.742675\pi\) | ||||
−0.690649 | + | 0.723190i | \(0.742675\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.27135i | 0.0714061i | 0.999362 | + | 0.0357030i | \(0.0113670\pi\) | ||||
−0.999362 | + | 0.0357030i | \(0.988633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.79796i | 0.436602i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6349 | 0.814310 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.7980 | −1.20913 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 10.8530i | − 0.598346i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.14643i | 0.337838i | 0.985630 | + | 0.168919i | \(0.0540277\pi\) | ||||
−0.985630 | + | 0.168919i | \(0.945972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.84281 | 0.100683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.5959 | 1.01298 | 0.506492 | − | 0.862245i | \(-0.330942\pi\) | ||||
0.506492 | + | 0.862245i | \(0.330942\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 9.12096i | − 0.493927i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.7627 | 1.59775 | 0.798873 | − | 0.601500i | \(-0.205430\pi\) | ||||
0.798873 | + | 0.601500i | \(0.205430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0000 | −0.856460 | −0.428230 | − | 0.903670i | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 8.51739i | − 0.453335i | −0.973972 | − | 0.226667i | \(-0.927217\pi\) | ||||
0.973972 | − | 0.226667i | \(-0.0727831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.79796i | − 0.0954258i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3923 | −0.548485 | −0.274242 | − | 0.961661i | \(-0.588427\pi\) | ||||
−0.274242 | + | 0.961661i | \(0.588427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.11416i | 0.163002i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.8990i | 1.40412i | 0.712120 | + | 0.702058i | \(0.247735\pi\) | ||||
−0.712120 | + | 0.702058i | \(0.752265\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.9494 | 0.620381 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.8990 | −1.13389 | −0.566943 | − | 0.823757i | \(-0.691874\pi\) | ||||
−0.566943 | + | 0.823757i | \(0.691874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 24.5344i | − 1.26359i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.0454i | 1.69743i | 0.528852 | + | 0.848714i | \(0.322623\pi\) | ||||
−0.528852 | + | 0.848714i | \(0.677377\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.36773 | 0.120985 | 0.0604926 | − | 0.998169i | \(-0.480733\pi\) | ||||
0.0604926 | + | 0.998169i | \(0.480733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.449490 | 0.0229081 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5.16404i | − 0.261827i | −0.991394 | − | 0.130914i | \(-0.958209\pi\) | ||||
0.991394 | − | 0.130914i | \(-0.0417911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.7980i | 1.70924i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.56048 | 0.229463 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.20204 | 0.110517 | 0.0552586 | − | 0.998472i | \(-0.482402\pi\) | ||||
0.0552586 | + | 0.998472i | \(0.482402\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.1195i | 1.85366i | 0.375482 | + | 0.926830i | \(0.377477\pi\) | ||||
−0.375482 | + | 0.926830i | \(0.622523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.6969i | 1.42950i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.7279 | 0.630900 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7980 | −0.682265 | −0.341133 | − | 0.940015i | \(-0.610811\pi\) | ||||
−0.341133 | + | 0.940015i | \(0.610811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.83183i | 0.286965i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 2.55051i | − 0.125200i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.02458 | 0.392026 | 0.196013 | − | 0.980601i | \(-0.437200\pi\) | ||||
0.196013 | + | 0.980601i | \(0.437200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1010 | 1.12587 | 0.562937 | − | 0.826500i | \(-0.309671\pi\) | ||||
0.562937 | + | 0.826500i | \(0.309671\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 29.2699i | − 1.41980i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10.4495i | − 0.505686i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.92820 | 0.333720 | 0.166860 | − | 0.985981i | \(-0.446637\pi\) | ||||
0.166860 | + | 0.985981i | \(0.446637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.5505 | 1.03565 | 0.517826 | − | 0.855486i | \(-0.326742\pi\) | ||||
0.517826 | + | 0.855486i | \(0.326742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 13.8564i | − 0.662842i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.8990i | 0.711089i | 0.934659 | + | 0.355545i | \(0.115705\pi\) | ||||
−0.934659 | + | 0.355545i | \(0.884295\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.8194 | −1.84437 | −0.922184 | − | 0.386752i | \(-0.873597\pi\) | ||||
−0.922184 | + | 0.386752i | \(0.873597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.89898 | 0.232234 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.12848i | 0.0532565i | 0.999645 | + | 0.0266282i | \(0.00847703\pi\) | ||||
−0.999645 | + | 0.0266282i | \(0.991523\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.2474i | 0.482534i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.41421 | −0.0662994 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.5959 | −1.29088 | −0.645441 | − | 0.763810i | \(-0.723327\pi\) | ||||
−0.645441 | + | 0.763810i | \(0.723327\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6.26042i | − 0.291577i | −0.989316 | − | 0.145788i | \(-0.953428\pi\) | ||||
0.989316 | − | 0.145788i | \(-0.0465719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 6.75255i | − 0.313818i | −0.987613 | − | 0.156909i | \(-0.949847\pi\) | ||||
0.987613 | − | 0.156909i | \(-0.0501529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.1981 | 1.67505 | 0.837524 | − | 0.546401i | \(-0.184002\pi\) | ||||
0.837524 | + | 0.546401i | \(0.184002\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.79796 | −0.267725 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.97809i | 0.412813i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000i | 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.9951 | −1.14206 | −0.571029 | − | 0.820930i | \(-0.693455\pi\) | ||||
−0.571029 | + | 0.820930i | \(0.693455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.0454 | −1.82591 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.52837i | 0.205623i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5959i | 0.887976i | 0.896033 | + | 0.443988i | \(0.146437\pi\) | ||||
−0.896033 | + | 0.443988i | \(0.853563\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.32124 | 0.149885 | 0.0749427 | − | 0.997188i | \(-0.476123\pi\) | ||||
0.0749427 | + | 0.997188i | \(0.476123\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.9444 | 1.48374 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.65685i | 0.253745i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.752551i | 0.0336888i | 0.999858 | + | 0.0168444i | \(0.00536200\pi\) | ||||
−0.999858 | + | 0.0168444i | \(0.994638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.7600 | −0.568942 | −0.284471 | − | 0.958685i | \(-0.591818\pi\) | ||||
−0.284471 | + | 0.958685i | \(0.591818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.79796 | 0.0800081 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.2672i | 0.543735i | 0.962335 | + | 0.271867i | \(0.0876412\pi\) | ||||
−0.962335 | + | 0.271867i | \(0.912359\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 9.79796i | − 0.433436i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.38551 | 0.193248 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.3485 | −0.675025 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 25.4880i | − 1.11665i | −0.829623 | − | 0.558324i | \(-0.811445\pi\) | ||||
0.829623 | − | 0.558324i | \(-0.188555\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.0454i | 1.40125i | 0.713531 | + | 0.700624i | \(0.247095\pi\) | ||||
−0.713531 | + | 0.700624i | \(0.752905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −38.5337 | −1.67855 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 32.2412i | − 1.39652i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.40408i | − 0.190405i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.41421 | −0.0609145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0000 | −1.24681 | −0.623404 | − | 0.781900i | \(-0.714251\pi\) | ||||
−0.623404 | + | 0.781900i | \(0.714251\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.97469i | 0.255928i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 34.1464i | − 1.46000i | −0.683449 | − | 0.729998i | \(-0.739521\pi\) | ||||
0.683449 | − | 0.729998i | \(-0.260479\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.5065 | −0.575395 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.3485 | −0.610159 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.7128i | 1.17423i | 0.809504 | + | 0.587115i | \(0.199736\pi\) | ||||
−0.809504 | + | 0.587115i | \(0.800264\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 28.2474i | − 1.19474i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −46.5262 | −1.96084 | −0.980422 | − | 0.196906i | \(-0.936911\pi\) | ||||
−0.980422 | + | 0.196906i | \(0.936911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.14643 | −0.0482306 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 18.2419i | − 0.764741i | −0.924009 | − | 0.382370i | \(-0.875108\pi\) | ||||
0.924009 | − | 0.382370i | \(-0.124892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.348469i | 0.0145830i | 0.999973 | + | 0.00729149i | \(0.00232097\pi\) | ||||
−0.999973 | + | 0.00729149i | \(0.997679\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.7128 | −1.15570 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.5959 | 1.56514 | 0.782569 | − | 0.622564i | \(-0.213909\pi\) | ||||
0.782569 | + | 0.622564i | \(0.213909\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.02458i | 0.332916i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 16.8990i | − 0.699884i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.5412 | 1.26057 | 0.630286 | − | 0.776363i | \(-0.282938\pi\) | ||||
0.630286 | + | 0.776363i | \(0.282938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.7980 | 0.650944 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 24.8523i | − 1.02056i | −0.860008 | − | 0.510280i | \(-0.829542\pi\) | ||||
0.860008 | − | 0.510280i | \(-0.170458\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.89898i | − 0.0778506i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.2986 | −1.07453 | −0.537266 | − | 0.843413i | \(-0.680543\pi\) | ||||
−0.537266 | + | 0.843413i | \(0.680543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7423 | −1.09084 | −0.545422 | − | 0.838162i | \(-0.683630\pi\) | ||||
−0.545422 | + | 0.838162i | \(0.683630\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.86054i | 0.116297i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 26.2474i | − 1.06535i | −0.846320 | − | 0.532676i | \(-0.821187\pi\) | ||||
0.846320 | − | 0.532676i | \(-0.178813\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.2903 | 1.95362 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3939 | 0.702532 | 0.351266 | − | 0.936276i | \(-0.385751\pi\) | ||||
0.351266 | + | 0.936276i | \(0.385751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.2419i | 0.734392i | 0.930144 | + | 0.367196i | \(0.119682\pi\) | ||||
−0.930144 | + | 0.367196i | \(0.880318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 15.8434i | − 0.636799i | −0.947957 | − | 0.318399i | \(-0.896855\pi\) | ||||
0.947957 | − | 0.318399i | \(-0.103145\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.4135 | −0.617528 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4949 | 0.939796 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 53.7722i | − 2.14404i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.7423i | 1.58212i | 0.611740 | + | 0.791059i | \(0.290470\pi\) | ||||
−0.611740 | + | 0.791059i | \(0.709530\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.54610 | 0.220090 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.44949 | 0.176295 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 5.16404i | − 0.203967i | −0.994786 | − | 0.101984i | \(-0.967481\pi\) | ||||
0.994786 | − | 0.101984i | \(-0.0325190\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 10.4949i | − 0.413878i | −0.978354 | − | 0.206939i | \(-0.933650\pi\) | ||||
0.978354 | − | 0.206939i | \(-0.0663502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.3546 | 1.94033 | 0.970165 | − | 0.242446i | \(-0.0779496\pi\) | ||||
0.970165 | + | 0.242446i | \(0.0779496\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.24745 | 0.323741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.3636i | 0.522958i | 0.965209 | + | 0.261479i | \(0.0842102\pi\) | ||||
−0.965209 | + | 0.261479i | \(0.915790\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.69694i | 0.183525i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.0197 | 1.28627 | 0.643133 | − | 0.765755i | \(-0.277634\pi\) | ||||
0.643133 | + | 0.765755i | \(0.277634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.04541 | −0.0795571 | −0.0397786 | − | 0.999209i | \(-0.512665\pi\) | ||||
−0.0397786 | + | 0.999209i | \(0.512665\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.778539i | 0.0301905i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 31.1918i | − 1.20775i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.7778 | −0.570491 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.10102 | −0.119536 | −0.0597678 | − | 0.998212i | \(-0.519036\pi\) | ||||
−0.0597678 | + | 0.998212i | \(0.519036\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.9985i | 1.07607i | 0.842922 | + | 0.538036i | \(0.180833\pi\) | ||||
−0.842922 | + | 0.538036i | \(0.819167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 14.2474i | − 0.546767i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.2344 | 1.00383 | 0.501915 | − | 0.864917i | \(-0.332629\pi\) | ||||
0.501915 | + | 0.864917i | \(0.332629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85357 | −0.185445 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 53.1687i | 2.02556i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 12.9444i | − 0.492428i | −0.969216 | − | 0.246214i | \(-0.920813\pi\) | ||||
0.969216 | − | 0.246214i | \(-0.0791866\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.41421 | −0.0536442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.2929 | 1.63983 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 50.1331i | − 1.89350i | −0.321965 | − | 0.946751i | \(-0.604343\pi\) | ||||
0.321965 | − | 0.946751i | \(-0.395657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.0454i | 0.831458i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.65685 | −0.212748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.39388 | −0.240127 | −0.120064 | − | 0.992766i | \(-0.538310\pi\) | ||||
−0.120064 | + | 0.992766i | \(0.538310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.4838i | 1.36633i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000i | 0.0747958i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.38211 | −0.0515438 | −0.0257719 | − | 0.999668i | \(-0.508204\pi\) | ||||
−0.0257719 | + | 0.999668i | \(0.508204\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.7980 | −0.513863 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 27.0129i | 1.00323i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 18.0454i | − 0.669267i | −0.942348 | − | 0.334634i | \(-0.891387\pi\) | ||||
0.942348 | − | 0.334634i | \(-0.108613\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.9301 | 1.40290 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.5959 | −0.797663 | −0.398832 | − | 0.917024i | \(-0.630584\pi\) | ||||
−0.398832 | + | 0.917024i | \(0.630584\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.19955i | 0.302034i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 20.0000i | − 0.735712i | −0.929883 | − | 0.367856i | \(-0.880092\pi\) | ||||
0.929883 | − | 0.367856i | \(-0.119908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.76416 | 0.0647207 | 0.0323604 | − | 0.999476i | \(-0.489698\pi\) | ||||
0.0323604 | + | 0.999476i | \(0.489698\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.05561 | −0.0386747 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.8564i | 0.506302i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.20204i | 0.226316i | 0.993577 | + | 0.113158i | \(0.0360966\pi\) | ||||
−0.993577 | + | 0.113158i | \(0.963903\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.01778 | −0.0734345 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.30306 | −0.156397 | −0.0781987 | − | 0.996938i | \(-0.524917\pi\) | ||||
−0.0781987 | + | 0.996938i | \(0.524917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 5.05329i | − 0.183182i | −0.995797 | − | 0.0915908i | \(-0.970805\pi\) | ||||
0.995797 | − | 0.0915908i | \(-0.0291952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 18.7980i | − 0.680532i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.9487 | −0.936952 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.2020 | 0.584261 | 0.292130 | − | 0.956379i | \(-0.405636\pi\) | ||||
0.292130 | + | 0.956379i | \(0.405636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.8735i | 1.07447i | 0.843431 | + | 0.537237i | \(0.180532\pi\) | ||||
−0.843431 | + | 0.537237i | \(0.819468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 31.5959i | − 1.13496i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.7491 | −0.635928 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 4.52837i | − 0.161624i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.3939i | 0.762609i | 0.924449 | + | 0.381305i | \(0.124525\pi\) | ||||
−0.924449 | + | 0.381305i | \(0.875475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.60697 | 0.128249 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.4949 | 1.65108 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 0.985620i | − 0.0349124i | −0.999848 | − | 0.0174562i | \(-0.994443\pi\) | ||||
0.999848 | − | 0.0174562i | \(-0.00555677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64.8434i | 2.29399i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.8564 | −0.488982 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.79796 | −0.0633697 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 42.7764i | − 1.50394i | −0.659199 | − | 0.751968i | \(-0.729105\pi\) | ||||
0.659199 | − | 0.751968i | \(-0.270895\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0454i | 0.984807i | 0.870367 | + | 0.492404i | \(0.163882\pi\) | ||||
−0.870367 | + | 0.492404i | \(0.836118\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.73205 | 0.0606711 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.5505 | −0.544043 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 47.2261i | − 1.64820i | −0.566443 | − | 0.824101i | \(-0.691681\pi\) | ||||
0.566443 | − | 0.824101i | \(-0.308319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 20.8434i | − 0.726554i | −0.931681 | − | 0.363277i | \(-0.881658\pi\) | ||||
0.931681 | − | 0.363277i | \(-0.118342\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.68556 | 0.0933862 | 0.0466931 | − | 0.998909i | \(-0.485132\pi\) | ||||
0.0466931 | + | 0.998909i | \(0.485132\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.95459 | −0.276274 | −0.138137 | − | 0.990413i | \(-0.544111\pi\) | ||||
−0.138137 | + | 0.990413i | \(0.544111\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.97469i | 0.207011i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.14643i | 0.143493i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.09638 | 0.0378511 | 0.0189256 | − | 0.999821i | \(-0.493975\pi\) | ||||
0.0189256 | + | 0.999821i | \(0.493975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.40408 | −0.0484166 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.16064i | − 0.0743284i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 9.00000i | − 0.309244i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.9117 | −1.74523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.7980 | 1.49961 | 0.749807 | − | 0.661657i | \(-0.230146\pi\) | ||||
0.749807 | + | 0.661657i | \(0.230146\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 28.6021i | − 0.977029i | −0.872556 | − | 0.488515i | \(-0.837539\pi\) | ||||
0.872556 | − | 0.488515i | \(-0.162461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 38.8990i | − 1.32722i | −0.748080 | − | 0.663608i | \(-0.769024\pi\) | ||||
0.748080 | − | 0.663608i | \(-0.230976\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.5065 | 0.459765 | 0.229883 | − | 0.973218i | \(-0.426166\pi\) | ||||
0.229883 | + | 0.973218i | \(0.426166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.69694 | −0.159701 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.2918i | 0.688352i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 25.7980i | − 0.874130i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.14626 | 0.106363 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.595918 | −0.0201227 | −0.0100614 | − | 0.999949i | \(-0.503203\pi\) | ||||
−0.0100614 | + | 0.999949i | \(0.503203\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.4974i | 1.63392i | 0.576695 | + | 0.816960i | \(0.304342\pi\) | ||||
−0.576695 | + | 0.816960i | \(0.695658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 22.3485i | − 0.752086i | −0.926602 | − | 0.376043i | \(-0.877285\pi\) | ||||
0.926602 | − | 0.376043i | \(-0.122715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.2030 | −0.376158 | −0.188079 | − | 0.982154i | \(-0.560226\pi\) | ||||
−0.188079 | + | 0.982154i | \(0.560226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.4495 | −0.585237 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 26.5843i | − 0.889611i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.853572i | 0.0285318i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.5624 | 1.18607 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −71.3939 | −2.37847 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.02118i | 0.166910i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1.24745i | − 0.0414209i | −0.999786 | − | 0.0207104i | \(-0.993407\pi\) | ||||
0.999786 | − | 0.0207104i | \(-0.00659281\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.4989 | 0.712291 | 0.356146 | − | 0.934430i | \(-0.384091\pi\) | ||||
0.356146 | + | 0.934430i | \(0.384091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.3485 | 0.375580 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 14.7778i | − 0.488006i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 34.8434i | − 1.14938i | −0.818372 | − | 0.574688i | \(-0.805123\pi\) | ||||
0.818372 | − | 0.574688i | \(-0.194877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.1701 | −0.828484 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 44.0908 | 1.44970 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.317837i | 0.0104279i | 0.999986 | + | 0.00521395i | \(0.00165966\pi\) | ||||
−0.999986 | + | 0.00521395i | \(0.998340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 2.44949i | − 0.0802788i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.68556 | −0.0878273 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.7423 | −0.612286 | −0.306143 | − | 0.951986i | \(-0.599039\pi\) | ||||
−0.306143 | + | 0.951986i | \(0.599039\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.7449i | 0.904459i | 0.891902 | + | 0.452229i | \(0.149371\pi\) | ||||
−0.891902 | + | 0.452229i | \(0.850629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 40.9898i | − 1.33481i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.84281 | 0.0598832 | 0.0299416 | − | 0.999552i | \(-0.490468\pi\) | ||||
0.0299416 | + | 0.999552i | \(0.490468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.5959 | 1.41518 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 37.7552i | − 1.22301i | −0.791241 | − | 0.611505i | \(-0.790564\pi\) | ||||
0.791241 | − | 0.611505i | \(-0.209436\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 4.69694i | − 0.151989i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.2706 | 0.493114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.5959 | −0.341804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.91048i | 0.190265i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.10102i | 0.0997221i | 0.998756 | + | 0.0498610i | \(0.0158778\pi\) | ||||
−0.998756 | + | 0.0498610i | \(0.984122\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.5446 | −1.07650 | −0.538249 | − | 0.842786i | \(-0.680914\pi\) | ||||
−0.538249 | + | 0.842786i | \(0.680914\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.44949 | 0.142644 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 3.17837i | − 0.101685i | −0.998707 | − | 0.0508426i | \(-0.983809\pi\) | ||||
0.998707 | − | 0.0508426i | \(-0.0161907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.7980i | 0.696666i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0458 | −0.416095 | −0.208048 | − | 0.978119i | \(-0.566711\pi\) | ||||
−0.208048 | + | 0.978119i | \(0.566711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.14643 | −0.100254 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 35.9124i | − 1.14195i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3485i | 0.709923i | 0.934881 | + | 0.354961i | \(0.115506\pi\) | ||||
−0.934881 | + | 0.354961i | \(0.884494\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.30691 | 0.168240 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.8434 | 0.691786 | 0.345893 | − | 0.938274i | \(-0.387576\pi\) | ||||
0.345893 | + | 0.938274i | \(0.387576\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 6048.2.h.c.2591.4 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.c.2591.6 | yes | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.c.2591.3 | ✓ | 8 | |
12.11 | even | 2 | inner | 6048.2.h.c.2591.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.c.2591.3 | ✓ | 8 | 4.3 | odd | 2 | inner | |
6048.2.h.c.2591.4 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.c.2591.5 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.c.2591.6 | yes | 8 | 3.2 | odd | 2 | inner |