Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(17,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.bj (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 593.2 | ||
Character | \(\chi\) | \(=\) | 1440.593 |
Dual form | 1440.2.bj.a.17.2 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −2.23604 | + | 0.0113158i | −0.999987 | + | 0.00506057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.471963 | + | 0.471963i | −0.178385 | + | 0.178385i | −0.790652 | − | 0.612266i | \(-0.790258\pi\) |
0.612266 | + | 0.790652i | \(0.290258\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.335652 | −0.101203 | −0.0506014 | − | 0.998719i | \(-0.516114\pi\) | ||||
−0.0506014 | + | 0.998719i | \(0.516114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.50404 | + | 3.50404i | −0.971846 | + | 0.971846i | −0.999614 | − | 0.0277680i | \(-0.991160\pi\) |
0.0277680 | + | 0.999614i | \(0.491160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.53299 | − | 2.53299i | −0.614340 | − | 0.614340i | 0.329734 | − | 0.944074i | \(-0.393041\pi\) |
−0.944074 | + | 0.329734i | \(0.893041\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.07474 | 0.934809 | 0.467405 | − | 0.884044i | \(-0.345189\pi\) | ||||
0.467405 | + | 0.884044i | \(0.345189\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.20627 | − | 6.20627i | 1.29410 | − | 1.29410i | 0.361868 | − | 0.932229i | \(-0.382139\pi\) |
0.932229 | − | 0.361868i | \(-0.117861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99974 | − | 0.0506050i | 0.999949 | − | 0.0101210i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.42367i | − | 0.450065i | −0.974351 | − | 0.225032i | \(-0.927751\pi\) | ||
0.974351 | − | 0.225032i | \(-0.0722488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.41004 | 1.15128 | 0.575639 | − | 0.817704i | \(-0.304753\pi\) | ||||
0.575639 | + | 0.817704i | \(0.304753\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.04999 | − | 1.06067i | 0.177480 | − | 0.179286i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.24893 | − | 2.24893i | −0.369721 | − | 0.369721i | 0.497654 | − | 0.867375i | \(-0.334195\pi\) |
−0.867375 | + | 0.497654i | \(0.834195\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.80736i | − | 0.906957i | −0.891267 | − | 0.453479i | \(-0.850183\pi\) | ||
0.891267 | − | 0.453479i | \(-0.149817\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.87603 | − | 4.87603i | 0.743588 | − | 0.743588i | −0.229678 | − | 0.973267i | \(-0.573767\pi\) |
0.973267 | + | 0.229678i | \(0.0737675\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.68276 | − | 1.68276i | −0.245455 | − | 0.245455i | 0.573647 | − | 0.819102i | \(-0.305528\pi\) |
−0.819102 | + | 0.573647i | \(0.805528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.55450i | 0.936358i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.05444 | − | 3.05444i | −0.419560 | − | 0.419560i | 0.465492 | − | 0.885052i | \(-0.345877\pi\) |
−0.885052 | + | 0.465492i | \(0.845877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.750530 | − | 0.00379815i | 0.101201 | − | 0.000512143i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.2950i | 1.60067i | 0.599553 | + | 0.800335i | \(0.295345\pi\) | ||||
−0.599553 | + | 0.800335i | \(0.704655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.49787i | − | 0.960004i | −0.877267 | − | 0.480002i | \(-0.840636\pi\) | ||
0.877267 | − | 0.480002i | \(-0.159364\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.79553 | − | 7.87483i | 0.966916 | − | 0.976752i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.55519 | − | 5.55519i | −0.678674 | − | 0.678674i | 0.281026 | − | 0.959700i | \(-0.409325\pi\) |
−0.959700 | + | 0.281026i | \(0.909325\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.4793i | − | 1.59970i | −0.600199 | − | 0.799851i | \(-0.704912\pi\) | ||
0.600199 | − | 0.799851i | \(-0.295088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.05035 | + | 5.05035i | 0.591099 | + | 0.591099i | 0.937928 | − | 0.346830i | \(-0.112742\pi\) |
−0.346830 | + | 0.937928i | \(0.612742\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.158415 | − | 0.158415i | 0.0180531 | − | 0.0180531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.85503i | − | 0.996268i | −0.867100 | − | 0.498134i | \(-0.834019\pi\) | ||
0.867100 | − | 0.498134i | \(-0.165981\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.78510 | − | 4.78510i | −0.525233 | − | 0.525233i | 0.393914 | − | 0.919147i | \(-0.371121\pi\) |
−0.919147 | + | 0.393914i | \(0.871121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.69252 | + | 5.63520i | 0.617441 | + | 0.611223i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.33405 | 0.883408 | 0.441704 | − | 0.897161i | \(-0.354374\pi\) | ||||
0.441704 | + | 0.897161i | \(0.354374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.30755i | − | 0.346726i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.11128 | + | 0.0461088i | −0.934797 | + | 0.00473066i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1367 | − | 10.1367i | 1.02922 | − | 1.02922i | 0.0296647 | − | 0.999560i | \(-0.490556\pi\) |
0.999560 | − | 0.0296647i | \(-0.00944397\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.88830 | 0.983922 | 0.491961 | − | 0.870617i | \(-0.336280\pi\) | ||||
0.491961 | + | 0.870617i | \(0.336280\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0033 | + | 10.0033i | 0.985653 | + | 0.985653i | 0.999899 | − | 0.0142455i | \(-0.00453463\pi\) |
−0.0142455 | + | 0.999899i | \(0.504535\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.2013 | − | 10.2013i | 0.986198 | − | 0.986198i | −0.0137076 | − | 0.999906i | \(-0.504363\pi\) |
0.999906 | + | 0.0137076i | \(0.00436339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0144 | 1.05498 | 0.527492 | − | 0.849560i | \(-0.323133\pi\) | ||||
0.527492 | + | 0.849560i | \(0.323133\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.45369 | + | 2.45369i | −0.230823 | + | 0.230823i | −0.813036 | − | 0.582213i | \(-0.802187\pi\) |
0.582213 | + | 0.813036i | \(0.302187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.8072 | + | 13.9477i | −1.28753 | + | 1.30063i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.39095 | 0.219178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8873 | −0.989758 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1791 | + | 0.169731i | −0.999885 | + | 0.0151812i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.00329 | + | 6.00329i | −0.532705 | + | 0.532705i | −0.921377 | − | 0.388671i | \(-0.872934\pi\) |
0.388671 | + | 0.921377i | \(0.372934\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3345 | −0.990301 | −0.495151 | − | 0.868807i | \(-0.664887\pi\) | ||||
−0.495151 | + | 0.868807i | \(0.664887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.92312 | + | 1.92312i | −0.166756 | + | 0.166756i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.8670 | − | 10.8670i | −0.928434 | − | 0.928434i | 0.0691711 | − | 0.997605i | \(-0.477965\pi\) |
−0.997605 | + | 0.0691711i | \(0.977965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3432 | 1.13176 | 0.565878 | − | 0.824489i | \(-0.308537\pi\) | ||||
0.565878 | + | 0.824489i | \(0.308537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.17614 | − | 1.17614i | 0.0983535 | − | 0.0983535i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0274257 | + | 5.41943i | 0.00227758 | + | 0.450059i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.5961i | 1.11384i | 0.830566 | + | 0.556919i | \(0.188017\pi\) | ||||
−0.830566 | + | 0.556919i | \(0.811983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.64289 | 0.784727 | 0.392364 | − | 0.919810i | \(-0.371657\pi\) | ||||
0.392364 | + | 0.919810i | \(0.371657\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.3331 | + | 0.0725345i | −1.15126 | + | 0.00582611i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.62403 | − | 7.62403i | −0.608464 | − | 0.608464i | 0.334080 | − | 0.942545i | \(-0.391574\pi\) |
−0.942545 | + | 0.334080i | \(0.891574\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.85826i | 0.461695i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2490 | + | 16.2490i | −1.27272 | + | 1.27272i | −0.328065 | + | 0.944655i | \(0.606397\pi\) |
−0.944655 | + | 0.328065i | \(0.893603\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.7067 | + | 13.7067i | 1.06066 | + | 1.06066i | 0.998037 | + | 0.0626204i | \(0.0199458\pi\) |
0.0626204 | + | 0.998037i | \(0.480054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.5566i | − | 0.888971i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.35678 | + | 3.35678i | 0.255211 | + | 0.255211i | 0.823103 | − | 0.567892i | \(-0.192241\pi\) |
−0.567892 | + | 0.823103i | \(0.692241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.33581 | + | 2.38358i | −0.176571 | + | 0.180181i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 10.7537i | − | 0.803772i | −0.915690 | − | 0.401886i | \(-0.868355\pi\) | ||
0.915690 | − | 0.401886i | \(-0.131645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.1290i | − | 0.752883i | −0.926440 | − | 0.376441i | \(-0.877148\pi\) | ||
0.926440 | − | 0.376441i | \(-0.122852\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.05414 | + | 5.00324i | 0.371587 | + | 0.367845i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.850201 | + | 0.850201i | 0.0621728 | + | 0.0621728i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.32194i | 0.312725i | 0.987700 | + | 0.156362i | \(0.0499768\pi\) | ||||
−0.987700 | + | 0.156362i | \(0.950023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.97419 | − | 7.97419i | −0.573995 | − | 0.573995i | 0.359248 | − | 0.933242i | \(-0.383033\pi\) |
−0.933242 | + | 0.359248i | \(0.883033\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.30206 | + | 4.30206i | −0.306509 | + | 0.306509i | −0.843554 | − | 0.537045i | \(-0.819541\pi\) |
0.537045 | + | 0.843554i | \(0.319541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.02113i | 0.214162i | 0.994250 | + | 0.107081i | \(0.0341505\pi\) | ||||
−0.994250 | + | 0.107081i | \(0.965850\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.14388 | + | 1.14388i | 0.0802849 | + | 0.0802849i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0657147 | + | 12.9855i | 0.00458972 | + | 0.906946i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.36769 | −0.0946052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.87754i | − | 0.611155i | −0.952167 | − | 0.305577i | \(-0.901151\pi\) | ||
0.952167 | − | 0.305577i | \(-0.0988495\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8478 | + | 10.9582i | −0.739816 | + | 0.747342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.02530 | + | 3.02530i | −0.205371 | + | 0.205371i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.7514 | 1.19409 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.93808 | − | 9.93808i | −0.665503 | − | 0.665503i | 0.291169 | − | 0.956672i | \(-0.405956\pi\) |
−0.956672 | + | 0.291169i | \(0.905956\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.21442 | − | 7.21442i | 0.478838 | − | 0.478838i | −0.425922 | − | 0.904760i | \(-0.640050\pi\) |
0.904760 | + | 0.425922i | \(0.140050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.8687 | 1.44512 | 0.722562 | − | 0.691306i | \(-0.242965\pi\) | ||||
0.722562 | + | 0.691306i | \(0.242965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.78300 | + | 6.78300i | −0.444369 | + | 0.444369i | −0.893477 | − | 0.449108i | \(-0.851742\pi\) |
0.449108 | + | 0.893477i | \(0.351742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.78175 | + | 3.74367i | 0.246694 | + | 0.244210i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.63287 | −0.299676 | −0.149838 | − | 0.988711i | \(-0.547875\pi\) | ||||
−0.149838 | + | 0.988711i | \(0.547875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.72150 | −0.626217 | −0.313109 | − | 0.949717i | \(-0.601370\pi\) | ||||
−0.313109 | + | 0.949717i | \(0.601370\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.0741692 | − | 14.6561i | −0.00473850 | − | 0.936346i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.2781 | + | 14.2781i | −0.908491 | + | 0.908491i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.6190 | 1.93265 | 0.966327 | − | 0.257316i | \(-0.0828382\pi\) | ||||
0.966327 | + | 0.257316i | \(0.0828382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.08314 | + | 2.08314i | −0.130966 | + | 0.130966i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.63773 | − | 1.63773i | −0.102158 | − | 0.102158i | 0.654180 | − | 0.756339i | \(-0.273014\pi\) |
−0.756339 | + | 0.654180i | \(0.773014\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.12282 | 0.131905 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.77099 | + | 7.77099i | −0.479180 | + | 0.479180i | −0.904869 | − | 0.425689i | \(-0.860032\pi\) |
0.425689 | + | 0.904869i | \(0.360032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.86441 | + | 6.79529i | 0.421678 | + | 0.417431i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.1341i | 0.983714i | 0.870676 | + | 0.491857i | \(0.163682\pi\) | ||||
−0.870676 | + | 0.491857i | \(0.836318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8474 | −1.02341 | −0.511704 | − | 0.859162i | \(-0.670986\pi\) | ||||
−0.511704 | + | 0.859162i | \(0.670986\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.67817 | + | 0.0169856i | −0.101198 | + | 0.00102427i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3206 | − | 16.3206i | −0.980611 | − | 0.980611i | 0.0192042 | − | 0.999816i | \(-0.493887\pi\) |
−0.999816 | + | 0.0192042i | \(0.993887\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.2898i | 1.86659i | 0.359106 | + | 0.933297i | \(0.383082\pi\) | ||||
−0.359106 | + | 0.933297i | \(0.616918\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.97554 | − | 9.97554i | 0.592984 | − | 0.592984i | −0.345452 | − | 0.938436i | \(-0.612274\pi\) |
0.938436 | + | 0.345452i | \(0.112274\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.74086 | + | 2.74086i | 0.161788 | + | 0.161788i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 4.16795i | − | 0.245174i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.26253 | − | 5.26253i | −0.307440 | − | 0.307440i | 0.536476 | − | 0.843916i | \(-0.319755\pi\) |
−0.843916 | + | 0.536476i | \(0.819755\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.139127 | − | 27.4921i | −0.00810030 | − | 1.60065i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 43.4941i | 2.51533i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.60261i | 0.265290i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.0848442 | + | 16.7655i | 0.00485816 | + | 0.959992i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.54586 | − | 9.54586i | −0.544811 | − | 0.544811i | 0.380124 | − | 0.924935i | \(-0.375881\pi\) |
−0.924935 | + | 0.380124i | \(0.875881\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.08587i | 0.231688i | 0.993267 | + | 0.115844i | \(0.0369573\pi\) | ||||
−0.993267 | + | 0.115844i | \(0.963043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4004 | − | 14.4004i | −0.813958 | − | 0.813958i | 0.171266 | − | 0.985225i | \(-0.445214\pi\) |
−0.985225 | + | 0.171266i | \(0.945214\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0841 | − | 12.0841i | 0.678710 | − | 0.678710i | −0.280998 | − | 0.959708i | \(-0.590666\pi\) |
0.959708 | + | 0.280998i | \(0.0906656\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.813510i | 0.0455478i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3213 | − | 10.3213i | −0.574290 | − | 0.574290i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.3420 | + | 17.6966i | −0.961961 | + | 0.981633i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.58840 | 0.0875711 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 33.6119i | − | 1.84747i | −0.383027 | − | 0.923737i | \(-0.625118\pi\) | ||
0.383027 | − | 0.923737i | \(-0.374882\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4845 | + | 12.3588i | 0.682100 | + | 0.675231i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2142 | + | 20.2142i | −1.10114 | + | 1.10114i | −0.106864 | + | 0.994274i | \(0.534081\pi\) |
−0.994274 | + | 0.106864i | \(0.965919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.15154 | −0.116512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.39722 | − | 6.39722i | −0.345417 | − | 0.345417i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.443163 | + | 0.443163i | −0.0237903 | + | 0.0237903i | −0.718902 | − | 0.695112i | \(-0.755355\pi\) |
0.695112 | + | 0.718902i | \(0.255355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8766 | 0.582212 | 0.291106 | − | 0.956691i | \(-0.405977\pi\) | ||||
0.291106 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0437 | + | 10.0437i | −0.534572 | + | 0.534572i | −0.921930 | − | 0.387357i | \(-0.873388\pi\) |
0.387357 | + | 0.921930i | \(0.373388\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.152529 | + | 30.1403i | 0.00809540 | + | 1.59968i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.6724 | −1.03827 | −0.519136 | − | 0.854692i | \(-0.673746\pi\) | ||||
−0.519136 | + | 0.854692i | \(0.673746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.39651 | −0.126132 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.3499 | − | 11.2356i | −0.594082 | − | 0.588100i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.86005 | − | 9.86005i | 0.514690 | − | 0.514690i | −0.401270 | − | 0.915960i | \(-0.631431\pi\) |
0.915960 | + | 0.401270i | \(0.131431\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.88316 | 0.149686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6526 | + | 12.6526i | −0.655127 | + | 0.655127i | −0.954223 | − | 0.299096i | \(-0.903315\pi\) |
0.299096 | + | 0.954223i | \(0.403315\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.49265 | + | 8.49265i | 0.437394 | + | 0.437394i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.9577 | 1.94975 | 0.974877 | − | 0.222743i | \(-0.0715010\pi\) | ||||
0.974877 | + | 0.222743i | \(0.0715010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.18320 | + | 9.18320i | −0.469240 | + | 0.469240i | −0.901668 | − | 0.432428i | \(-0.857657\pi\) |
0.432428 | + | 0.901668i | \(0.357657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.352429 | + | 0.356015i | −0.0179615 | + | 0.0181442i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 4.22258i | − | 0.214093i | −0.994254 | − | 0.107047i | \(-0.965861\pi\) | ||
0.994254 | − | 0.107047i | \(-0.0341394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.4408 | −1.59003 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.100201 | + | 19.8002i | 0.00504168 | + | 0.996256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.27679 | + | 1.27679i | 0.0640801 | + | 0.0640801i | 0.738421 | − | 0.674340i | \(-0.235572\pi\) |
−0.674340 | + | 0.738421i | \(0.735572\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.899990i | 0.0449434i | 0.999747 | + | 0.0224717i | \(0.00715356\pi\) | ||||
−0.999747 | + | 0.0224717i | \(0.992846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.4611 | + | 22.4611i | −1.11886 | + | 1.11886i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.754855 | + | 0.754855i | 0.0374168 | + | 0.0374168i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.1722i | 1.19524i | 0.801781 | + | 0.597618i | \(0.203886\pi\) | ||||
−0.801781 | + | 0.597618i | \(0.796114\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.80277 | − | 5.80277i | −0.285536 | − | 0.285536i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.7538 | + | 10.6455i | 0.527884 | + | 0.522568i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8.45513i | − | 0.413060i | −0.978440 | − | 0.206530i | \(-0.933783\pi\) | ||
0.978440 | − | 0.206530i | \(-0.0662171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8561i | 0.675307i | 0.941270 | + | 0.337654i | \(0.109633\pi\) | ||||
−0.941270 | + | 0.337654i | \(0.890367\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.7925 | − | 12.5361i | −0.620526 | − | 0.608090i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.53872 | + | 3.53872i | 0.171250 | + | 0.171250i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.84351i | 0.281472i | 0.990047 | + | 0.140736i | \(0.0449469\pi\) | ||||
−0.990047 | + | 0.140736i | \(0.955053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0632 | + | 10.0632i | 0.483605 | + | 0.483605i | 0.906281 | − | 0.422676i | \(-0.138909\pi\) |
−0.422676 | + | 0.906281i | \(0.638909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.2889 | − | 25.2889i | 1.20973 | − | 1.20973i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 34.0222i | − | 1.62379i | −0.583802 | − | 0.811896i | \(-0.698436\pi\) | ||
0.583802 | − | 0.811896i | \(-0.301564\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.45259 | + | 6.45259i | 0.306572 | + | 0.306572i | 0.843578 | − | 0.537006i | \(-0.180445\pi\) |
−0.537006 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.6353 | + | 0.0943062i | −0.883396 | + | 0.00447054i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.72541 | 0.270199 | 0.135099 | − | 0.990832i | \(-0.456865\pi\) | ||||
0.135099 | + | 0.990832i | \(0.456865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.94925i | 0.0917866i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0374275 | + | 7.39582i | 0.00175463 | + | 0.346721i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9718 | − | 14.9718i | 0.700352 | − | 0.700352i | −0.264134 | − | 0.964486i | \(-0.585086\pi\) |
0.964486 | + | 0.264134i | \(0.0850862\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.8187 | −1.20250 | −0.601249 | − | 0.799062i | \(-0.705330\pi\) | ||||
−0.601249 | + | 0.799062i | \(0.705330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5140 | + | 20.5140i | 0.953368 | + | 0.953368i | 0.998960 | − | 0.0455925i | \(-0.0145176\pi\) |
−0.0455925 | + | 0.998960i | \(0.514518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.07112 | − | 3.07112i | 0.142114 | − | 0.142114i | −0.632470 | − | 0.774585i | \(-0.717959\pi\) |
0.774585 | + | 0.632470i | \(0.217959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.24368 | 0.242131 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.63665 | + | 1.63665i | −0.0752532 | + | 0.0752532i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.3726 | − | 0.206202i | 0.934761 | − | 0.00946120i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.2621 | 1.51979 | 0.759893 | − | 0.650049i | \(-0.225252\pi\) | ||||
0.759893 | + | 0.650049i | \(0.225252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7607 | 0.718624 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.5513 | + | 22.7807i | −1.02400 | + | 1.03442i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.39322 | + | 1.39322i | −0.0631329 | + | 0.0631329i | −0.737968 | − | 0.674835i | \(-0.764215\pi\) |
0.674835 | + | 0.737968i | \(0.264215\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4709 | 0.653061 | 0.326530 | − | 0.945187i | \(-0.394120\pi\) | ||||
0.326530 | + | 0.945187i | \(0.394120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.13913 | + | 6.13913i | −0.276493 | + | 0.276493i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.36174 | + | 6.36174i | 0.285363 | + | 0.285363i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.4107 | −0.913710 | −0.456855 | − | 0.889541i | \(-0.651024\pi\) | ||||
−0.456855 | + | 0.889541i | \(0.651024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.54697 | − | 2.54697i | 0.113564 | − | 0.113564i | −0.648041 | − | 0.761605i | \(-0.724412\pi\) |
0.761605 | + | 0.648041i | \(0.224412\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.1106 | + | 0.111894i | −0.983910 | + | 0.00497920i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.5045i | 0.598575i | 0.954163 | + | 0.299288i | \(0.0967490\pi\) | ||||
−0.954163 | + | 0.299288i | \(0.903251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.76715 | −0.210886 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.4809 | − | 22.2545i | −0.990628 | − | 0.980652i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.564820 | + | 0.564820i | 0.0248407 | + | 0.0248407i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.5151i | − | 0.592108i | −0.955171 | − | 0.296054i | \(-0.904329\pi\) | ||
0.955171 | − | 0.296054i | \(-0.0956708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.6641 | − | 12.6641i | 0.553760 | − | 0.553760i | −0.373764 | − | 0.927524i | \(-0.621933\pi\) |
0.927524 | + | 0.373764i | \(0.121933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.2365 | − | 16.2365i | −0.707275 | − | 0.707275i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 54.0356i | − | 2.34938i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.3492 | + | 20.3492i | 0.881423 | + | 0.881423i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.6951 | + | 22.9260i | −0.981195 | + | 0.991177i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 2.20003i | − | 0.0947619i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 17.1804i | − | 0.738644i | −0.929301 | − | 0.369322i | \(-0.879590\pi\) | ||
0.929301 | − | 0.369322i | \(-0.120410\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.6285 | + | 0.124636i | −1.05497 | + | 0.00533881i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4105 | − | 17.4105i | −0.744417 | − | 0.744417i | 0.229007 | − | 0.973425i | \(-0.426452\pi\) |
−0.973425 | + | 0.229007i | \(0.926452\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 9.87584i | − | 0.420725i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.17924 | + | 4.17924i | 0.177719 | + | 0.177719i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.22732 | + | 9.22732i | −0.390974 | + | 0.390974i | −0.875035 | − | 0.484060i | \(-0.839162\pi\) |
0.484060 | + | 0.875035i | \(0.339162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.1717i | 1.44531i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.8727 | − | 19.8727i | −0.837535 | − | 0.837535i | 0.150999 | − | 0.988534i | \(-0.451751\pi\) |
−0.988534 | + | 0.150999i | \(0.951751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.45877 | − | 5.51430i | 0.229652 | − | 0.231988i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.73031 | −0.198305 | −0.0991524 | − | 0.995072i | \(-0.531613\pi\) | ||||
−0.0991524 | + | 0.995072i | \(0.531613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.54039i | − | 0.231858i | −0.993257 | − | 0.115929i | \(-0.963015\pi\) | ||
0.993257 | − | 0.115929i | \(-0.0369845\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.7157 | − | 31.3438i | 1.28093 | − | 1.30713i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.9105 | + | 12.9105i | −0.537472 | + | 0.537472i | −0.922786 | − | 0.385314i | \(-0.874093\pi\) |
0.385314 | + | 0.922786i | \(0.374093\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.51677 | 0.187387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.02523 | + | 1.02523i | 0.0424606 | + | 0.0424606i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.90309 | + | 1.90309i | −0.0785487 | + | 0.0785487i | −0.745290 | − | 0.666741i | \(-0.767689\pi\) |
0.666741 | + | 0.745290i | \(0.267689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.1192 | 1.07622 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.7312 | − | 11.7312i | 0.481745 | − | 0.481745i | −0.423944 | − | 0.905688i | \(-0.639355\pi\) |
0.905688 | + | 0.423944i | \(0.139355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.34626 | + | 0.0270554i | −0.219175 | + | 0.00110916i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.61594 | −0.106884 | −0.0534422 | − | 0.998571i | \(-0.517019\pi\) | ||||
−0.0534422 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.1722 | 0.822840 | 0.411420 | − | 0.911446i | \(-0.365033\pi\) | ||||
0.411420 | + | 0.911446i | \(0.365033\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.3445 | − | 0.123199i | 0.989745 | − | 0.00500873i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3218 | − | 17.3218i | 0.703069 | − | 0.703069i | −0.261999 | − | 0.965068i | \(-0.584382\pi\) |
0.965068 | + | 0.261999i | \(0.0843819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.7929 | 0.477090 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8299 | − | 16.8299i | 0.679754 | − | 0.679754i | −0.280191 | − | 0.959944i | \(-0.590398\pi\) |
0.959944 | + | 0.280191i | \(0.0903977\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.56139 | − | 2.56139i | −0.103118 | − | 0.103118i | 0.653666 | − | 0.756783i | \(-0.273230\pi\) |
−0.756783 | + | 0.653666i | \(0.773230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9662 | 0.681931 | 0.340965 | − | 0.940076i | \(-0.389246\pi\) | ||||
0.340965 | + | 0.940076i | \(0.389246\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.93336 | + | 3.93336i | −0.157587 | + | 0.157587i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9949 | − | 0.506024i | 0.999795 | − | 0.0202410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.3930i | 0.454269i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.5630 | 1.57498 | 0.787488 | − | 0.616330i | \(-0.211381\pi\) | ||||
0.787488 | + | 0.616330i | \(0.211381\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.3557 | − | 13.4915i | 0.530003 | − | 0.535394i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.9673 | − | 22.9673i | −0.909996 | − | 0.909996i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 47.3441i | − | 1.86998i | −0.354676 | − | 0.934989i | \(-0.615409\pi\) | ||
0.354676 | − | 0.934989i | \(-0.384591\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.8250 | + | 14.8250i | −0.584639 | + | 0.584639i | −0.936175 | − | 0.351535i | \(-0.885660\pi\) |
0.351535 | + | 0.936175i | \(0.385660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.86574 | − | 4.86574i | −0.191292 | − | 0.191292i | 0.604962 | − | 0.796254i | \(-0.293188\pi\) |
−0.796254 | + | 0.604962i | \(0.793188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.12683i | − | 0.161992i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.8214 | − | 11.8214i | −0.462609 | − | 0.462609i | 0.436901 | − | 0.899510i | \(-0.356076\pi\) |
−0.899510 | + | 0.436901i | \(0.856076\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.3444 | − | 0.128259i | 0.990289 | − | 0.00501149i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.02230i | 0.234595i | 0.993097 | + | 0.117298i | \(0.0374232\pi\) | ||||
−0.993097 | + | 0.117298i | \(0.962577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 37.9790i | − | 1.47721i | −0.674137 | − | 0.738606i | \(-0.735484\pi\) | ||
0.674137 | − | 0.738606i | \(-0.264516\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.27842 | − | 4.32194i | 0.165910 | − | 0.167598i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0420 | − | 15.0420i | −0.582428 | − | 0.582428i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.51667i | 0.0971551i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.99686 | + | 7.99686i | 0.308256 | + | 0.308256i | 0.844233 | − | 0.535977i | \(-0.180057\pi\) |
−0.535977 | + | 0.844233i | \(0.680057\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.11103 | + | 7.11103i | −0.273299 | + | 0.273299i | −0.830427 | − | 0.557128i | \(-0.811903\pi\) |
0.557128 | + | 0.830427i | \(0.311903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.56827i | 0.367197i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.99061 | + | 7.99061i | 0.305752 | + | 0.305752i | 0.843259 | − | 0.537507i | \(-0.180634\pi\) |
−0.537507 | + | 0.843259i | \(0.680634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.4221 | + | 24.1762i | 0.933120 | + | 0.923723i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.4058 | 0.815495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.5931i | 1.23990i | 0.784641 | + | 0.619951i | \(0.212848\pi\) | ||||
−0.784641 | + | 0.619951i | \(0.787152\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.8359 | + | 0.150989i | −1.13174 | + | 0.00572732i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.7100 | + | 14.7100i | −0.557180 | + | 0.557180i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9064 | 1.62055 | 0.810277 | − | 0.586047i | \(-0.199317\pi\) | ||||
0.810277 | + | 0.586047i | \(0.199317\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.16379 | − | 9.16379i | −0.345619 | − | 0.345619i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.66691 | + | 4.66691i | −0.175517 | + | 0.175517i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3299 | 0.387949 | 0.193975 | − | 0.981007i | \(-0.437862\pi\) | ||||
0.193975 | + | 0.981007i | \(0.437862\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.7825 | − | 39.7825i | 1.48986 | − | 1.48986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.61658 | + | 2.64320i | −0.0978545 | + | 0.0988500i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.49219 | 0.242118 | 0.121059 | − | 0.992645i | \(-0.461371\pi\) | ||||
0.121059 | + | 0.992645i | \(0.461371\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.44235 | −0.351652 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.122650 | − | 12.1177i | −0.00455511 | − | 0.450042i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.0479 | − | 11.0479i | 0.409744 | − | 0.409744i | −0.471905 | − | 0.881649i | \(-0.656434\pi\) |
0.881649 | + | 0.471905i | \(0.156434\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.7019 | −0.913631 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5376 | − | 19.5376i | 0.721636 | − | 0.721636i | −0.247302 | − | 0.968938i | \(-0.579544\pi\) |
0.968938 | + | 0.247302i | \(0.0795441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.86461 | + | 1.86461i | 0.0686837 | + | 0.0686837i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.8980 | −0.915890 | −0.457945 | − | 0.888981i | \(-0.651414\pi\) | ||||
−0.457945 | + | 0.888981i | \(0.651414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.8961 | − | 15.8961i | 0.583171 | − | 0.583171i | −0.352602 | − | 0.935773i | \(-0.614703\pi\) |
0.935773 | + | 0.352602i | \(0.114703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.153851 | − | 30.4015i | −0.00563665 | − | 1.11382i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.62928i | 0.351846i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5535 | −0.421594 | −0.210797 | − | 0.977530i | \(-0.567606\pi\) | ||||
−0.210797 | + | 0.977530i | \(0.567606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.5619 | + | 0.109117i | −0.784717 | + | 0.00397116i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8612 | + | 18.8612i | 0.685524 | + | 0.685524i | 0.961239 | − | 0.275716i | \(-0.0889148\pi\) |
−0.275716 | + | 0.961239i | \(0.588915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 33.0567i | − | 1.19830i | −0.800636 | − | 0.599151i | \(-0.795505\pi\) | ||
0.800636 | − | 0.599151i | \(-0.204495\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.19836 | + | 5.19836i | −0.188193 | + | 0.188193i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −43.0821 | − | 43.0821i | −1.55561 | − | 1.55561i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.9240i | 1.62000i | 0.586429 | + | 0.810001i | \(0.300533\pi\) | ||||
−0.586429 | + | 0.810001i | \(0.699467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.3672 | − | 28.3672i | −1.02030 | − | 1.02030i | −0.999790 | − | 0.0205060i | \(-0.993472\pi\) |
−0.0205060 | − | 0.999790i | \(-0.506528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0486 | − | 0.324380i | 1.15122 | − | 0.0116521i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 23.6635i | − | 0.847832i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.52436i | 0.161894i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.1339 | + | 16.9614i | 0.611536 | + | 0.605377i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.79302 | + | 4.79302i | 0.170853 | + | 0.170853i | 0.787354 | − | 0.616501i | \(-0.211450\pi\) |
−0.616501 | + | 0.787354i | \(0.711450\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.31610i | − | 0.0823509i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.2729 | + | 26.2729i | 0.932977 | + | 0.932977i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.30136 | − | 7.30136i | 0.258627 | − | 0.258627i | −0.565868 | − | 0.824496i | \(-0.691459\pi\) |
0.824496 | + | 0.565868i | \(0.191459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.52480i | 0.301586i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.69516 | − | 1.69516i | −0.0598208 | − | 0.0598208i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0662907 | − | 13.0993i | −0.00233644 | − | 0.461689i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.9078 | −0.946026 | −0.473013 | − | 0.881055i | \(-0.656834\pi\) | ||||
−0.473013 | + | 0.881055i | \(0.656834\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.38227i | − | 0.153882i | −0.997036 | − | 0.0769412i | \(-0.975485\pi\) | ||
0.997036 | − | 0.0769412i | \(-0.0245154\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.1495 | − | 36.5173i | 1.26626 | − | 1.27914i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.8686 | − | 19.8686i | 0.695113 | − | 0.695113i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.5890 | −1.20716 | −0.603582 | − | 0.797301i | \(-0.706261\pi\) | ||||
−0.603582 | + | 0.797301i | \(0.706261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.63496 | + | 5.63496i | 0.196422 | + | 0.196422i | 0.798464 | − | 0.602042i | \(-0.205646\pi\) |
−0.602042 | + | 0.798464i | \(0.705646\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.8906 | + | 29.8906i | −1.03940 | + | 1.03940i | −0.0402073 | + | 0.999191i | \(0.512802\pi\) |
−0.999191 | + | 0.0402073i | \(0.987198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.0207 | −1.56363 | −0.781817 | − | 0.623508i | \(-0.785707\pi\) | ||||
−0.781817 | + | 0.623508i | \(0.785707\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.6025 | − | 16.6025i | 0.575241 | − | 0.575241i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.8039 | − | 30.4937i | −1.06601 | − | 1.05528i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.14853 | 0.212271 | 0.106135 | − | 0.994352i | \(-0.466152\pi\) | ||||
0.106135 | + | 0.994352i | \(0.466152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.1258 | 0.797442 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.130772 | + | 25.8411i | 0.00449870 | + | 0.888960i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.13842 | − | 5.13842i | 0.176558 | − | 0.176558i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.9149 | −0.956910 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5962 | + | 11.5962i | −0.397046 | + | 0.397046i | −0.877190 | − | 0.480144i | \(-0.840585\pi\) |
0.480144 | + | 0.877190i | \(0.340585\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.8521 | + | 23.8521i | 0.814772 | + | 0.814772i | 0.985345 | − | 0.170573i | \(-0.0545619\pi\) |
−0.170573 | + | 0.985345i | \(0.554562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.3817 | 1.07073 | 0.535365 | − | 0.844621i | \(-0.320174\pi\) | ||||
0.535365 | + | 0.844621i | \(0.320174\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.4212 | + | 12.4212i | −0.422823 | + | 0.422823i | −0.886175 | − | 0.463351i | \(-0.846647\pi\) |
0.463351 | + | 0.886175i | \(0.346647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.54388 | − | 7.46791i | −0.256500 | − | 0.253917i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.97220i | 0.100825i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.9312 | 1.31913 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.19599 | − | 5.35620i | 0.175656 | − | 0.181073i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0074 | + | 38.0074i | 1.28342 | + | 1.28342i | 0.938710 | + | 0.344708i | \(0.112022\pi\) |
0.344708 | + | 0.938710i | \(0.387978\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.9118i | − | 0.367626i | −0.982961 | − | 0.183813i | \(-0.941156\pi\) | ||
0.982961 | − | 0.183813i | \(-0.0588442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.85770 | + | 1.85770i | −0.0625165 | + | 0.0625165i | −0.737674 | − | 0.675157i | \(-0.764076\pi\) |
0.675157 | + | 0.737674i | \(0.264076\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.17163 | + | 3.17163i | 0.106493 | + | 0.106493i | 0.758346 | − | 0.651853i | \(-0.226008\pi\) |
−0.651853 | + | 0.758346i | \(0.726008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.66665i | − | 0.190053i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.85679 | − | 6.85679i | −0.229454 | − | 0.229454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.121687 | + | 24.0458i | 0.00406754 | + | 0.803762i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 15.5358i | − | 0.518150i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4737i | 0.515504i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.114617 | + | 22.6488i | 0.00381001 | + | 0.752873i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.88501 | + | 5.88501i | 0.195408 | + | 0.195408i | 0.798028 | − | 0.602620i | \(-0.205876\pi\) |
−0.602620 | + | 0.798028i | \(0.705876\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3886i | 0.344188i | 0.985080 | + | 0.172094i | \(0.0550534\pi\) | ||||
−0.985080 | + | 0.172094i | \(0.944947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.60613 | + | 1.60613i | 0.0531550 | + | 0.0531550i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.34947 | − | 5.34947i | 0.176655 | − | 0.176655i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5186i | 0.478924i | 0.970906 | + | 0.239462i | \(0.0769710\pi\) | ||||
−0.970906 | + | 0.239462i | \(0.923029\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47.2321 | + | 47.2321i | 1.55466 | + | 1.55466i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.3579 | − | 11.1302i | −0.373444 | − | 0.365960i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.3689 | −1.45570 | −0.727848 | − | 0.685738i | \(-0.759480\pi\) | ||||
−0.727848 | + | 0.685738i | \(0.759480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.7079i | 0.875316i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.91070 | − | 1.89146i | −0.0624867 | − | 0.0618574i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.66665 | + | 2.66665i | −0.0871157 | + | 0.0871157i | −0.749322 | − | 0.662206i | \(-0.769620\pi\) |
0.662206 | + | 0.749322i | \(0.269620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.4675 | −1.35180 | −0.675901 | − | 0.736992i | \(-0.736245\pi\) | ||||
−0.675901 | + | 0.736992i | \(0.736245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0421 | − | 36.0421i | −1.17369 | − | 1.17369i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.3858 | − | 34.3858i | 1.11739 | − | 1.11739i | 0.125264 | − | 0.992123i | \(-0.460022\pi\) |
0.992123 | − | 0.125264i | \(-0.0399779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.3933 | −1.14891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.82947 | + | 5.82947i | −0.188835 | + | 0.188835i | −0.795192 | − | 0.606357i | \(-0.792630\pi\) |
0.606357 | + | 0.795192i | \(0.292630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.0489061 | − | 9.66403i | −0.00158256 | − | 0.312721i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.2577 | 0.331237 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0886 | 0.325439 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.9208 | + | 17.7404i | 0.576892 | + | 0.571083i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.1550 | + | 18.1550i | −0.583826 | + | 0.583826i | −0.935952 | − | 0.352126i | \(-0.885459\pi\) |
0.352126 | + | 0.935952i | \(0.385459\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.87264 | −0.220554 | −0.110277 | − | 0.993901i | \(-0.535174\pi\) | ||||
−0.110277 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.29749 | + | 6.29749i | −0.201888 | + | 0.201888i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.8533 | − | 14.8533i | −0.475200 | − | 0.475200i | 0.428393 | − | 0.903593i | \(-0.359080\pi\) |
−0.903593 | + | 0.428393i | \(0.859080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.79734 | −0.0894033 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.3770 | − | 21.3770i | 0.681822 | − | 0.681822i | −0.278589 | − | 0.960410i | \(-0.589867\pi\) |
0.960410 | + | 0.278589i | \(0.0898667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.57090 | − | 9.66827i | 0.304954 | − | 0.308057i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 60.5240i | − | 1.92455i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.1515 | −0.862497 | −0.431249 | − | 0.902233i | \(-0.641927\pi\) | ||||
−0.431249 | + | 0.902233i | \(0.641927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.0341864 | − | 6.75537i | −0.00108378 | − | 0.214160i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8850 | + | 16.8850i | 0.534754 | + | 0.534754i | 0.921983 | − | 0.387230i | \(-0.126568\pi\) |
−0.387230 | + | 0.921983i | \(0.626568\pi\) | |||||||
\(998\) | 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 | 1440.2.bj.a.593.2 | 48 | ||
3.2 | odd | 2 | inner | 1440.2.bj.a.593.23 | 48 | ||
4.3 | odd | 2 | 360.2.x.a.53.5 | ✓ | 48 | ||
5.2 | odd | 4 | inner | 1440.2.bj.a.17.1 | 48 | ||
8.3 | odd | 2 | 360.2.x.a.53.17 | yes | 48 | ||
8.5 | even | 2 | inner | 1440.2.bj.a.593.24 | 48 | ||
12.11 | even | 2 | 360.2.x.a.53.20 | yes | 48 | ||
15.2 | even | 4 | inner | 1440.2.bj.a.17.24 | 48 | ||
20.7 | even | 4 | 360.2.x.a.197.8 | yes | 48 | ||
24.5 | odd | 2 | inner | 1440.2.bj.a.593.1 | 48 | ||
24.11 | even | 2 | 360.2.x.a.53.8 | yes | 48 | ||
40.27 | even | 4 | 360.2.x.a.197.20 | yes | 48 | ||
40.37 | odd | 4 | inner | 1440.2.bj.a.17.23 | 48 | ||
60.47 | odd | 4 | 360.2.x.a.197.17 | yes | 48 | ||
120.77 | even | 4 | inner | 1440.2.bj.a.17.2 | 48 | ||
120.107 | odd | 4 | 360.2.x.a.197.5 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.5 | ✓ | 48 | 4.3 | odd | 2 | ||
360.2.x.a.53.8 | yes | 48 | 24.11 | even | 2 | ||
360.2.x.a.53.17 | yes | 48 | 8.3 | odd | 2 | ||
360.2.x.a.53.20 | yes | 48 | 12.11 | even | 2 | ||
360.2.x.a.197.5 | yes | 48 | 120.107 | odd | 4 | ||
360.2.x.a.197.8 | yes | 48 | 20.7 | even | 4 | ||
360.2.x.a.197.17 | yes | 48 | 60.47 | odd | 4 | ||
360.2.x.a.197.20 | yes | 48 | 40.27 | even | 4 | ||
1440.2.bj.a.17.1 | 48 | 5.2 | odd | 4 | inner | ||
1440.2.bj.a.17.2 | 48 | 120.77 | even | 4 | inner | ||
1440.2.bj.a.17.23 | 48 | 40.37 | odd | 4 | inner | ||
1440.2.bj.a.17.24 | 48 | 15.2 | even | 4 | inner | ||
1440.2.bj.a.593.1 | 48 | 24.5 | odd | 2 | inner | ||
1440.2.bj.a.593.2 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.bj.a.593.23 | 48 | 3.2 | odd | 2 | inner | ||
1440.2.bj.a.593.24 | 48 | 8.5 | even | 2 | inner |