Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
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([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.15 | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.f.3025.10 |
$q$-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 | ||||||||
\(5\) | 1.25392i | 0.560770i | 0.959888 | + | 0.280385i | \(0.0904622\pi\) | ||||
−0.959888 | + | 0.280385i | \(0.909538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.55766i | − 0.469653i | −0.972037 | − | 0.234827i | \(-0.924548\pi\) | ||||
0.972037 | − | 0.234827i | \(-0.0754522\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.07281i | − 0.297543i | −0.988872 | − | 0.148771i | \(-0.952468\pi\) | ||||
0.988872 | − | 0.148771i | \(-0.0475319\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0158095 | 0.00383438 | 0.00191719 | − | 0.999998i | \(-0.499390\pi\) | ||||
0.00191719 | + | 0.999998i | \(0.499390\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.35077i | 0.539303i | 0.962958 | + | 0.269651i | \(0.0869085\pi\) | ||||
−0.962958 | + | 0.269651i | \(0.913092\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.95129 | −1.24093 | −0.620465 | − | 0.784235i | \(-0.713056\pi\) | ||||
−0.620465 | + | 0.784235i | \(0.713056\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.42768 | 0.685537 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.469737i | 0.0872279i | 0.999048 | + | 0.0436139i | \(0.0138872\pi\) | ||||
−0.999048 | + | 0.0436139i | \(0.986113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.69031 | −0.303589 | −0.151795 | − | 0.988412i | \(-0.548505\pi\) | ||||
−0.151795 | + | 0.988412i | \(0.548505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.25392i | − 0.211951i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.59800i | − 0.755906i | −0.925825 | − | 0.377953i | \(-0.876628\pi\) | ||||
0.925825 | − | 0.377953i | \(-0.123372\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.2190 | 1.90829 | 0.954143 | − | 0.299350i | \(-0.0967698\pi\) | ||||
0.954143 | + | 0.299350i | \(0.0967698\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.97482i | − 0.301158i | −0.988598 | − | 0.150579i | \(-0.951886\pi\) | ||||
0.988598 | − | 0.150579i | \(-0.0481137\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.12571 | −1.03939 | −0.519696 | − | 0.854351i | \(-0.673955\pi\) | ||||
−0.519696 | + | 0.854351i | \(0.673955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.86735i | 0.256500i | 0.991742 | + | 0.128250i | \(0.0409360\pi\) | ||||
−0.991742 | + | 0.128250i | \(0.959064\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.95319 | 0.263368 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 8.54291i | − 1.11219i | −0.831118 | − | 0.556096i | \(-0.812299\pi\) | ||||
0.831118 | − | 0.556096i | \(-0.187701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 3.92502i | − 0.502547i | −0.967916 | − | 0.251274i | \(-0.919151\pi\) | ||||
0.967916 | − | 0.251274i | \(-0.0808494\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.34521 | 0.166853 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7403i | 1.55647i | 0.627972 | + | 0.778236i | \(0.283885\pi\) | ||||
−0.627972 | + | 0.778236i | \(0.716115\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.22205 | 0.501066 | 0.250533 | − | 0.968108i | \(-0.419394\pi\) | ||||
0.250533 | + | 0.968108i | \(0.419394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.51561 | 0.762595 | 0.381297 | − | 0.924452i | \(-0.375477\pi\) | ||||
0.381297 | + | 0.924452i | \(0.375477\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.55766i | 0.177512i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.15343 | 0.692315 | 0.346158 | − | 0.938176i | \(-0.387486\pi\) | ||||
0.346158 | + | 0.938176i | \(0.387486\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.88604i | − 0.975370i | −0.873020 | − | 0.487685i | \(-0.837842\pi\) | ||||
0.873020 | − | 0.487685i | \(-0.162158\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0198239i | 0.00215021i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.240788 | −0.0255235 | −0.0127618 | − | 0.999919i | \(-0.504062\pi\) | ||||
−0.0127618 | + | 0.999919i | \(0.504062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07281i | 0.112461i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.94767 | −0.302425 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.86131 | 0.595126 | 0.297563 | − | 0.954702i | \(-0.403826\pi\) | ||||
0.297563 | + | 0.954702i | \(0.403826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 3.12870i | − 0.311317i | −0.987811 | − | 0.155659i | \(-0.950250\pi\) | ||||
0.987811 | − | 0.155659i | \(-0.0497500\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.72832 | −0.268830 | −0.134415 | − | 0.990925i | \(-0.542915\pi\) | ||||
−0.134415 | + | 0.990925i | \(0.542915\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.05577i | 0.198738i | 0.995051 | + | 0.0993692i | \(0.0316825\pi\) | ||||
−0.995051 | + | 0.0993692i | \(0.968318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 13.8179i | − 1.32351i | −0.749719 | − | 0.661756i | \(-0.769811\pi\) | ||||
0.749719 | − | 0.661756i | \(-0.230189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.72061 | −0.350005 | −0.175003 | − | 0.984568i | \(-0.555993\pi\) | ||||
−0.175003 | + | 0.984568i | \(0.555993\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.46244i | − 0.695876i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0158095 | −0.00144926 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.57368 | 0.779426 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.5676i | 0.945199i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8627 | 1.76253 | 0.881264 | − | 0.472625i | \(-0.156693\pi\) | ||||
0.881264 | + | 0.472625i | \(0.156693\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 7.24798i | − 0.633259i | −0.948549 | − | 0.316629i | \(-0.897449\pi\) | ||||
0.948549 | − | 0.316629i | \(-0.102551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.35077i | − 0.203837i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.1526 | −1.12371 | −0.561853 | − | 0.827237i | \(-0.689911\pi\) | ||||
−0.561853 | + | 0.827237i | \(0.689911\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 5.29486i | − 0.449104i | −0.974462 | − | 0.224552i | \(-0.927908\pi\) | ||||
0.974462 | − | 0.224552i | \(-0.0720919\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.67107 | −0.139742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.589012 | −0.0489148 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.59368i | 0.540175i | 0.962836 | + | 0.270088i | \(0.0870526\pi\) | ||||
−0.962836 | + | 0.270088i | \(0.912947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.51585 | 0.774389 | 0.387195 | − | 0.921998i | \(-0.373444\pi\) | ||||
0.387195 | + | 0.921998i | \(0.373444\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.11952i | − 0.170244i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 16.0109i | − 1.27781i | −0.769285 | − | 0.638905i | \(-0.779388\pi\) | ||||
0.769285 | − | 0.638905i | \(-0.220612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.95129 | 0.469027 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 12.5751i | − 0.984959i | −0.870324 | − | 0.492480i | \(-0.836091\pi\) | ||||
0.870324 | − | 0.492480i | \(-0.163909\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.2841 | −1.33748 | −0.668741 | − | 0.743495i | \(-0.733166\pi\) | ||||
−0.668741 | + | 0.743495i | \(0.733166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8491 | 0.911468 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 8.78719i | − 0.668078i | −0.942559 | − | 0.334039i | \(-0.891588\pi\) | ||||
0.942559 | − | 0.334039i | \(-0.108412\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.42768 | −0.259109 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.6964i | 0.874233i | 0.899405 | + | 0.437117i | \(0.144000\pi\) | ||||
−0.899405 | + | 0.437117i | \(0.856000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.2624i | 1.80341i | 0.432351 | + | 0.901705i | \(0.357684\pi\) | ||||
−0.432351 | + | 0.901705i | \(0.642316\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.76552 | 0.423890 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 0.0246260i | − 0.00180083i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4850 | 0.758665 | 0.379333 | − | 0.925260i | \(-0.376154\pi\) | ||||
0.379333 | + | 0.925260i | \(0.376154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7092 | 0.914832 | 0.457416 | − | 0.889253i | \(-0.348775\pi\) | ||||
0.457416 | + | 0.889253i | \(0.348775\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0117i | 1.14079i | 0.821372 | + | 0.570394i | \(0.193209\pi\) | ||||
−0.821372 | + | 0.570394i | \(0.806791\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.1888 | 0.793156 | 0.396578 | − | 0.918001i | \(-0.370198\pi\) | ||||
0.396578 | + | 0.918001i | \(0.370198\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.469737i | − 0.0329690i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.3217i | 1.07011i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.66170 | 0.253285 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 20.1657i | − 1.38827i | −0.719847 | − | 0.694133i | \(-0.755788\pi\) | ||||
0.719847 | − | 0.694133i | \(-0.244212\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.47627 | 0.168880 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.69031 | 0.114746 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.0169606i | − 0.00114089i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1501 | 0.746663 | 0.373332 | − | 0.927698i | \(-0.378215\pi\) | ||||
0.373332 | + | 0.927698i | \(0.378215\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 18.7414i | − 1.24391i | −0.783053 | − | 0.621955i | \(-0.786338\pi\) | ||||
0.783053 | − | 0.621955i | \(-0.213662\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 13.5444i | − 0.895038i | −0.894274 | − | 0.447519i | \(-0.852308\pi\) | ||||
0.894274 | − | 0.447519i | \(-0.147692\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0070 | 0.721094 | 0.360547 | − | 0.932741i | \(-0.382590\pi\) | ||||
0.360547 | + | 0.932741i | \(0.382590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.93508i | − 0.582860i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4366 | 0.998509 | 0.499255 | − | 0.866455i | \(-0.333607\pi\) | ||||
0.499255 | + | 0.866455i | \(0.333607\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0354 | 1.03293 | 0.516466 | − | 0.856308i | \(-0.327247\pi\) | ||||
0.516466 | + | 0.856308i | \(0.327247\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.25392i | 0.0801100i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.52192 | 0.160466 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4441i | 0.722343i | 0.932499 | + | 0.361172i | \(0.117623\pi\) | ||||
−0.932499 | + | 0.361172i | \(0.882377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.27010i | 0.582806i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.7447 | 0.670236 | 0.335118 | − | 0.942176i | \(-0.391224\pi\) | ||||
0.335118 | + | 0.942176i | \(0.391224\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.59800i | 0.285706i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.6747 | 0.904878 | 0.452439 | − | 0.891795i | \(-0.350554\pi\) | ||||
0.452439 | + | 0.891795i | \(0.350554\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.34151 | −0.143838 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.93110i | 0.300655i | 0.988636 | + | 0.150327i | \(0.0480328\pi\) | ||||
−0.988636 | + | 0.150327i | \(0.951967\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.6605 | 1.37652 | 0.688262 | − | 0.725462i | \(-0.258374\pi\) | ||||
0.688262 | + | 0.725462i | \(0.258374\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 5.33918i | − 0.321965i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.99172i | − 0.360008i | −0.983666 | − | 0.180004i | \(-0.942389\pi\) | ||||
0.983666 | − | 0.180004i | \(-0.0576110\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.92544 | −0.114862 | −0.0574309 | − | 0.998349i | \(-0.518291\pi\) | ||||
−0.0574309 | + | 0.998349i | \(0.518291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.2195i | 1.67747i | 0.544537 | + | 0.838737i | \(0.316705\pi\) | ||||
−0.544537 | + | 0.838737i | \(0.683295\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.2190 | −0.721265 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9998 | −0.999985 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.0957i | 1.69979i | 0.526955 | + | 0.849893i | \(0.323334\pi\) | ||||
−0.526955 | + | 0.849893i | \(0.676666\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7121 | 0.623685 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.38458i | 0.369230i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.97482i | 0.113827i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.92166 | 0.281814 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 15.8372i | − 0.903879i | −0.892049 | − | 0.451940i | \(-0.850732\pi\) | ||||
0.892049 | − | 0.451940i | \(-0.149268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.5620 | −0.825737 | −0.412869 | − | 0.910791i | \(-0.635473\pi\) | ||||
−0.412869 | + | 0.910791i | \(0.635473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.47077 | 0.365749 | 0.182875 | − | 0.983136i | \(-0.441460\pi\) | ||||
0.182875 | + | 0.983136i | \(0.441460\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 11.9823i | − 0.672994i | −0.941685 | − | 0.336497i | \(-0.890758\pi\) | ||||
0.941685 | − | 0.336497i | \(-0.109242\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.731691 | 0.0409669 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0371646i | 0.00206789i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.67724i | − 0.203977i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.12571 | 0.392853 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 21.9422i | − 1.20605i | −0.797720 | − | 0.603027i | \(-0.793961\pi\) | ||||
0.797720 | − | 0.603027i | \(-0.206039\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.9753 | −0.872823 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3150 | 1.21558 | 0.607788 | − | 0.794100i | \(-0.292057\pi\) | ||||
0.607788 | + | 0.794100i | \(0.292057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63294i | 0.142582i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.5806i | 1.31956i | 0.751460 | + | 0.659779i | \(0.229350\pi\) | ||||
−0.751460 | + | 0.659779i | \(0.770650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 12.5930i | − 0.674089i | −0.941489 | − | 0.337045i | \(-0.890573\pi\) | ||||
0.941489 | − | 0.337045i | \(-0.109427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.1946 | −0.861953 | −0.430977 | − | 0.902363i | \(-0.641831\pi\) | ||||
−0.430977 | + | 0.902363i | \(0.641831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.29412i | 0.280983i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.1809 | −0.537329 | −0.268665 | − | 0.963234i | \(-0.586582\pi\) | ||||
−0.268665 | + | 0.963234i | \(0.586582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.4739 | 0.709152 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.17006i | 0.427640i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3939 | 0.646955 | 0.323478 | − | 0.946236i | \(-0.395148\pi\) | ||||
0.323478 | + | 0.946236i | \(0.395148\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.86735i | − 0.0969480i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.57921i | 0.392437i | 0.980560 | + | 0.196218i | \(0.0628661\pi\) | ||||
−0.980560 | + | 0.196218i | \(0.937134\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.503936 | 0.0259540 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 14.1179i | − 0.725187i | −0.931947 | − | 0.362594i | \(-0.881891\pi\) | ||||
0.931947 | − | 0.362594i | \(-0.118109\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.28678 | −0.0657512 | −0.0328756 | − | 0.999459i | \(-0.510467\pi\) | ||||
−0.0328756 | + | 0.999459i | \(0.510467\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.95319 | −0.0995436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 33.3310i | − 1.68995i | −0.534806 | − | 0.844975i | \(-0.679615\pi\) | ||||
0.534806 | − | 0.844975i | \(-0.320385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.0940872 | −0.00475819 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.71591i | 0.388230i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7770i | 1.04277i | 0.853322 | + | 0.521385i | \(0.174584\pi\) | ||||
−0.853322 | + | 0.521385i | \(0.825416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.38157 | −0.368618 | −0.184309 | − | 0.982868i | \(-0.559005\pi\) | ||||
−0.184309 | + | 0.982868i | \(0.559005\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.81338i | 0.0903308i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.16213 | −0.355014 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.9846 | 1.58154 | 0.790769 | − | 0.612114i | \(-0.209681\pi\) | ||||
0.790769 | + | 0.612114i | \(0.209681\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.54291i | 0.420369i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.1424 | 0.546958 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 14.6646i | − 0.716413i | −0.933642 | − | 0.358207i | \(-0.883388\pi\) | ||||
0.933642 | − | 0.358207i | \(-0.116612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 28.4958i | − 1.38880i | −0.719589 | − | 0.694400i | \(-0.755670\pi\) | ||||
0.719589 | − | 0.694400i | \(-0.244330\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0541901 | 0.00262861 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.92502i | 0.189945i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.4443 | 1.70729 | 0.853645 | − | 0.520855i | \(-0.174387\pi\) | ||||
0.853645 | + | 0.520855i | \(0.174387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.5907 | −1.51815 | −0.759077 | − | 0.651001i | \(-0.774349\pi\) | ||||
−0.759077 | + | 0.651001i | \(0.774349\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 13.9901i | − 0.669237i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.3732 | −1.11554 | −0.557771 | − | 0.829995i | \(-0.688343\pi\) | ||||
−0.557771 | + | 0.829995i | \(0.688343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 3.52932i | − 0.167683i | −0.996479 | − | 0.0838416i | \(-0.973281\pi\) | ||||
0.996479 | − | 0.0838416i | \(-0.0267190\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 0.301929i | − 0.0143128i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.94601 | 0.139031 | 0.0695154 | − | 0.997581i | \(-0.477855\pi\) | ||||
0.0695154 | + | 0.997581i | \(0.477855\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 19.0331i | − 0.896233i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.34521 | −0.0630646 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.1796 | −1.03752 | −0.518758 | − | 0.854921i | \(-0.673605\pi\) | ||||
−0.518758 | + | 0.854921i | \(0.673605\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 23.4545i | − 1.09238i | −0.837660 | − | 0.546192i | \(-0.816077\pi\) | ||||
0.837660 | − | 0.546192i | \(-0.183923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2354 | 1.35868 | 0.679342 | − | 0.733822i | \(-0.262265\pi\) | ||||
0.679342 | + | 0.733822i | \(0.262265\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.43057i | 0.251297i | 0.992075 | + | 0.125648i | \(0.0401011\pi\) | ||||
−0.992075 | + | 0.125648i | \(0.959899\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 12.7403i | − 0.588291i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.07611 | −0.141440 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.05768i | 0.369712i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.07525 | −0.231894 | −0.115947 | − | 0.993255i | \(-0.536990\pi\) | ||||
−0.115947 | + | 0.993255i | \(0.536990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.93276 | −0.224914 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.34962i | 0.333729i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.23366 | 0.146531 | 0.0732656 | − | 0.997312i | \(-0.476658\pi\) | ||||
0.0732656 | + | 0.997312i | \(0.476658\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6437i | 1.47319i | 0.676335 | + | 0.736594i | \(0.263567\pi\) | ||||
−0.676335 | + | 0.736594i | \(0.736433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.00742632i | 0 0.000334465i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.22205 | −0.189385 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.77339i | 0.0793877i | 0.999212 | + | 0.0396939i | \(0.0126383\pi\) | ||||
−0.999212 | + | 0.0396939i | \(0.987362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.3666 | 1.13104 | 0.565519 | − | 0.824735i | \(-0.308676\pi\) | ||||
0.565519 | + | 0.824735i | \(0.308676\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.92314 | 0.174578 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 14.3204i | − 0.634739i | −0.948302 | − | 0.317369i | \(-0.897201\pi\) | ||||
0.948302 | − | 0.317369i | \(-0.102799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.51561 | −0.288234 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.42110i | − 0.150752i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0995i | 0.488154i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.72827 | −0.250960 | −0.125480 | − | 0.992096i | \(-0.540047\pi\) | ||||
−0.125480 | + | 0.992096i | \(0.540047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 11.3779i | − 0.497519i | −0.968565 | − | 0.248759i | \(-0.919977\pi\) | ||||
0.968565 | − | 0.248759i | \(-0.0800229\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.0267231 | −0.00116408 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4178 | 0.539905 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13.1086i | − 0.567797i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.57777 | −0.111447 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.55766i | − 0.0670933i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.3953i | 1.86571i | 0.360252 | + | 0.932855i | \(0.382691\pi\) | ||||
−0.360252 | + | 0.932855i | \(0.617309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.3265 | 0.742187 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.5677i | 0.793898i | 0.917841 | + | 0.396949i | \(0.129931\pi\) | ||||
−0.917841 | + | 0.396949i | \(0.870069\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.10424 | −0.0470422 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.15343 | −0.261671 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 17.4689i | − 0.740182i | −0.928996 | − | 0.370091i | \(-0.879327\pi\) | ||||
0.928996 | − | 0.370091i | \(-0.120673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.11860 | −0.0896073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 26.8370i | − 1.13105i | −0.824733 | − | 0.565523i | \(-0.808675\pi\) | ||||
0.824733 | − | 0.565523i | \(-0.191325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.66534i | − 0.196272i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.4375 | −1.35985 | −0.679926 | − | 0.733281i | \(-0.737988\pi\) | ||||
−0.679926 | + | 0.733281i | \(0.737988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 34.0452i | − 1.42475i | −0.701800 | − | 0.712374i | \(-0.747620\pi\) | ||||
0.701800 | − | 0.712374i | \(-0.252380\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.3991 | −0.850702 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.09534 | 0.253752 | 0.126876 | − | 0.991919i | \(-0.459505\pi\) | ||||
0.126876 | + | 0.991919i | \(0.459505\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.88604i | 0.368655i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.90870 | 0.120466 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 10.7735i | − 0.444669i | −0.974970 | − | 0.222334i | \(-0.928632\pi\) | ||||
0.974970 | − | 0.222334i | \(-0.0713677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.97353i | − 0.163727i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.4720 | −0.553230 | −0.276615 | − | 0.960981i | \(-0.589213\pi\) | ||||
−0.276615 | + | 0.960981i | \(0.589213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 0.0198239i | 0 0.000812701i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.4766 | 1.53125 | 0.765626 | − | 0.643285i | \(-0.222429\pi\) | ||||
0.765626 | + | 0.643285i | \(0.222429\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.99803 | −0.163083 | −0.0815415 | − | 0.996670i | \(-0.525984\pi\) | ||||
−0.0815415 | + | 0.996670i | \(0.525984\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.7507i | 0.437079i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.8295 | −1.49486 | −0.747432 | − | 0.664338i | \(-0.768713\pi\) | ||||
−0.747432 | + | 0.664338i | \(0.768713\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.64451i | 0.309264i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.76469i | 0.394392i | 0.980364 | + | 0.197196i | \(0.0631836\pi\) | ||||
−0.980364 | + | 0.197196i | \(0.936816\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.4832 | −0.583070 | −0.291535 | − | 0.956560i | \(-0.594166\pi\) | ||||
−0.291535 | + | 0.956560i | \(0.594166\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.72500i | 0.270301i | 0.990825 | + | 0.135150i | \(0.0431518\pi\) | ||||
−0.990825 | + | 0.135150i | \(0.956848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.240788 | 0.00964698 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.88743 | 0.155497 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 0.0726923i | − 0.00289843i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2251 | 0.924577 | 0.462288 | − | 0.886730i | \(-0.347029\pi\) | ||||
0.462288 | + | 0.886730i | \(0.347029\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.9062i | 0.988373i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.07281i | − 0.0425061i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.3809 | −1.19998 | −0.599988 | − | 0.800009i | \(-0.704828\pi\) | ||||
−0.599988 | + | 0.800009i | \(0.704828\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.74408i | − 0.226524i | −0.993565 | − | 0.113262i | \(-0.963870\pi\) | ||||
0.993565 | − | 0.113262i | \(-0.0361300\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.19948 | 0.165099 | 0.0825494 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825494 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.3070 | −0.522345 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 45.2069i | − 1.76908i | −0.466460 | − | 0.884542i | \(-0.654471\pi\) | ||||
0.466460 | − | 0.884542i | \(-0.345529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.08839 | 0.355113 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 47.0951i | − 1.83456i | −0.398239 | − | 0.917282i | \(-0.630379\pi\) | ||||
0.398239 | − | 0.917282i | \(-0.369621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 41.9805i | − 1.63285i | −0.577449 | − | 0.816427i | \(-0.695952\pi\) | ||||
0.577449 | − | 0.816427i | \(-0.304048\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.94767 | 0.114306 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.79554i | − 0.108244i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.11386 | −0.236023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0898 | 1.15987 | 0.579937 | − | 0.814661i | \(-0.303077\pi\) | ||||
0.579937 | + | 0.814661i | \(0.303077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 40.5494i | − 1.55844i | −0.626749 | − | 0.779221i | \(-0.715615\pi\) | ||||
0.626749 | − | 0.779221i | \(-0.284385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.86131 | −0.224936 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 50.1042i | 1.91718i | 0.284786 | + | 0.958591i | \(0.408077\pi\) | ||||
−0.284786 | + | 0.958591i | \(0.591923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 16.4924i | − 0.630141i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00330 | 0.0763198 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.2174i | 1.64407i | 0.569438 | + | 0.822034i | \(0.307161\pi\) | ||||
−0.569438 | + | 0.822034i | \(0.692839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.63933 | 0.251844 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.193177 | 0.00731709 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.4337i | 0.734002i | 0.930221 | + | 0.367001i | \(0.119615\pi\) | ||||
−0.930221 | + | 0.367001i | \(0.880385\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8088 | 0.407662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.12870i | 0.117667i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0279i | 0.902387i | 0.892426 | + | 0.451194i | \(0.149002\pi\) | ||||
−0.892426 | + | 0.451194i | \(0.850998\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.0595 | 0.376733 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.09539i | − 0.0783631i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.0898 | 1.34592 | 0.672961 | − | 0.739678i | \(-0.265022\pi\) | ||||
0.672961 | + | 0.739678i | \(0.265022\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.72832 | 0.101608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.61011i | 0.0597979i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.3230 | −1.34714 | −0.673572 | − | 0.739122i | \(-0.735241\pi\) | ||||
−0.673572 | + | 0.739122i | \(0.735241\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 0.0312211i | − 0.00115475i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 11.9814i | − 0.442544i | −0.975212 | − | 0.221272i | \(-0.928979\pi\) | ||||
0.975212 | − | 0.221272i | \(-0.0710209\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.8451 | 0.731002 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.7377i | 1.35142i | 0.737169 | + | 0.675708i | \(0.236162\pi\) | ||||
−0.737169 | + | 0.675708i | \(0.763838\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2966 | 0.487805 | 0.243903 | − | 0.969800i | \(-0.421572\pi\) | ||||
0.243903 | + | 0.969800i | \(0.421572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.26795 | −0.302914 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2.05577i | − 0.0751161i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5953 | 0.496101 | 0.248051 | − | 0.968747i | \(-0.420210\pi\) | ||||
0.248051 | + | 0.968747i | \(0.420210\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.9321i | 0.434254i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 8.04991i | − 0.292579i | −0.989242 | − | 0.146290i | \(-0.953267\pi\) | ||||
0.989242 | − | 0.146290i | \(-0.0467331\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −53.5813 | −1.94232 | −0.971160 | − | 0.238429i | \(-0.923368\pi\) | ||||
−0.971160 | + | 0.238429i | \(0.923368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8179i | 0.500241i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.16489 | −0.330925 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.40107 | 0.122646 | 0.0613229 | − | 0.998118i | \(-0.480468\pi\) | ||||
0.0613229 | + | 0.998118i | \(0.480468\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.6537i | 0.455123i | 0.973764 | + | 0.227561i | \(0.0730752\pi\) | ||||
−0.973764 | + | 0.227561i | \(0.926925\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.79386 | −0.208122 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.7240i | 1.02914i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 6.57654i | − 0.235327i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.0764 | 0.716558 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.3539i | 1.33152i | 0.746165 | + | 0.665761i | \(0.231893\pi\) | ||||
−0.746165 | + | 0.665761i | \(0.768107\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.72061 | 0.132290 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.21079 | −0.149529 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.3333i | 0.543134i | 0.962420 | + | 0.271567i | \(0.0875418\pi\) | ||||
−0.962420 | + | 0.271567i | \(0.912458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.112654 | −0.00398542 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10.1491i | − 0.358155i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.46244i | 0.263016i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.1700 | −1.69357 | −0.846784 | − | 0.531938i | \(-0.821464\pi\) | ||||
−0.846784 | + | 0.531938i | \(0.821464\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.4720i | 0.753984i | 0.926216 | + | 0.376992i | \(0.123042\pi\) | ||||
−0.926216 | + | 0.376992i | \(0.876958\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.7682 | 0.552336 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.64235 | 0.162415 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 24.2783i | − 0.847318i | −0.905822 | − | 0.423659i | \(-0.860746\pi\) | ||||
0.905822 | − | 0.423659i | \(-0.139254\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7002 | −0.547275 | −0.273637 | − | 0.961833i | \(-0.588227\pi\) | ||||
−0.273637 | + | 0.961833i | \(0.588227\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.47290i | 0.0512177i | 0.999672 | + | 0.0256089i | \(0.00815244\pi\) | ||||
−0.999672 | + | 0.0256089i | \(0.991848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 25.1759i | − 0.874395i | −0.899365 | − | 0.437198i | \(-0.855971\pi\) | ||||
0.899365 | − | 0.437198i | \(-0.144029\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0158095 | 0.000547768 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 21.6729i | − 0.750020i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.4703 | −0.499570 | −0.249785 | − | 0.968301i | \(-0.580360\pi\) | ||||
−0.249785 | + | 0.968301i | \(0.580360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7793 | 0.992391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.8578i | 0.511124i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.57368 | −0.294595 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.3640i | 0.938026i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 0.552410i | − 0.0189142i | −0.999955 | − | 0.00945708i | \(-0.996990\pi\) | ||||
0.999955 | − | 0.00945708i | \(-0.00301033\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.3043 | 1.61588 | 0.807942 | − | 0.589262i | \(-0.200581\pi\) | ||||
0.807942 | + | 0.589262i | \(0.200581\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.9031i | 1.46384i | 0.681393 | + | 0.731918i | \(0.261375\pi\) | ||||
−0.681393 | + | 0.731918i | \(0.738625\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.39600 | 0.0815609 | 0.0407805 | − | 0.999168i | \(-0.487016\pi\) | ||||
0.0407805 | + | 0.999168i | \(0.487016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.0184 | 0.374638 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 9.58498i | − 0.325148i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6678 | 0.463117 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 10.5676i | − 0.357252i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 36.8060i | − 1.24285i | −0.783473 | − | 0.621426i | \(-0.786554\pi\) | ||||
0.783473 | − | 0.621426i | \(-0.213446\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.1322 | −1.52054 | −0.760271 | − | 0.649606i | \(-0.774934\pi\) | ||||
−0.760271 | + | 0.649606i | \(0.774934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 38.0204i | − 1.27949i | −0.768588 | − | 0.639744i | \(-0.779040\pi\) | ||||
0.768588 | − | 0.639744i | \(-0.220960\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.4326 | 1.02183 | 0.510913 | − | 0.859633i | \(-0.329308\pi\) | ||||
0.510913 | + | 0.859633i | \(0.329308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.8627 | −0.666173 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 16.7509i | − 0.560547i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.6664 | −0.490244 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 0.794002i | − 0.0264814i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0295220i | 0 0.000983519i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.4231 | −1.01130 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8.80211i | − 0.292269i | −0.989265 | − | 0.146135i | \(-0.953317\pi\) | ||||
0.989265 | − | 0.146135i | \(-0.0466833\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.9516 | −1.05860 | −0.529302 | − | 0.848434i | \(-0.677546\pi\) | ||||
−0.529302 | + | 0.848434i | \(0.677546\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.8415 | −0.458086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.24798i | 0.239349i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.5377 | −1.83202 | −0.916009 | − | 0.401157i | \(-0.868608\pi\) | ||||
−0.916009 | + | 0.401157i | \(0.868608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 4.52944i | − 0.149088i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 15.7605i | − 0.518201i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.4706 | −0.737235 | −0.368617 | − | 0.929581i | \(-0.620169\pi\) | ||||
−0.368617 | + | 0.929581i | \(0.620169\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.35077i | 0.0770433i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.0308790 | 0.00100985 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.5975 | −1.55494 | −0.777471 | − | 0.628919i | \(-0.783498\pi\) | ||||
−0.777471 | + | 0.628919i | \(0.783498\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 5.03276i | − 0.164063i | −0.996630 | − | 0.0820317i | \(-0.973859\pi\) | ||||
0.996630 | − | 0.0820317i | \(-0.0261409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −72.7188 | −2.36805 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 18.9034i | − 0.614277i | −0.951665 | − | 0.307138i | \(-0.900629\pi\) | ||||
0.951665 | − | 0.307138i | \(-0.0993714\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 6.98999i | − 0.226905i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 59.5108 | 1.92774 | 0.963872 | − | 0.266365i | \(-0.0858225\pi\) | ||||
0.963872 | + | 0.266365i | \(0.0858225\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.1473i | 0.425437i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.1526 | 0.424721 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.1428 | −0.907834 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.9364i | 0.513010i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.3394 | 0.847018 | 0.423509 | − | 0.905892i | \(-0.360798\pi\) | ||||
0.423509 | + | 0.905892i | \(0.360798\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.9352i | 1.63459i | 0.576222 | + | 0.817293i | \(0.304526\pi\) | ||||
−0.576222 | + | 0.817293i | \(0.695474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.29486i | 0.169745i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23.5022 | −0.751903 | −0.375951 | − | 0.926639i | \(-0.622684\pi\) | ||||
−0.375951 | + | 0.926639i | \(0.622684\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.375067i | 0.0119872i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.3639 | −1.31930 | −0.659651 | − | 0.751572i | \(-0.729296\pi\) | ||||
−0.659651 | + | 0.751572i | \(0.729296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0774 | −0.639720 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.7527i | 0.373715i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.06637 | 0.256237 | 0.128118 | − | 0.991759i | \(-0.459106\pi\) | ||||
0.128118 | + | 0.991759i | \(0.459106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0299i | 0.444778i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.8503i | 1.23040i | 0.788371 | + | 0.615200i | \(0.210925\pi\) | ||||
−0.788371 | + | 0.615200i | \(0.789075\pi\) | |||||||
\(998\) | 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.c.f.3025.15 | 24 | ||
3.2 | odd | 2 | inner | 6048.2.c.f.3025.9 | 24 | ||
4.3 | odd | 2 | 1512.2.c.g.757.15 | yes | 24 | ||
8.3 | odd | 2 | 1512.2.c.g.757.16 | yes | 24 | ||
8.5 | even | 2 | inner | 6048.2.c.f.3025.10 | 24 | ||
12.11 | even | 2 | 1512.2.c.g.757.10 | yes | 24 | ||
24.5 | odd | 2 | inner | 6048.2.c.f.3025.16 | 24 | ||
24.11 | even | 2 | 1512.2.c.g.757.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.9 | ✓ | 24 | 24.11 | even | 2 | ||
1512.2.c.g.757.10 | yes | 24 | 12.11 | even | 2 | ||
1512.2.c.g.757.15 | yes | 24 | 4.3 | odd | 2 | ||
1512.2.c.g.757.16 | yes | 24 | 8.3 | odd | 2 | ||
6048.2.c.f.3025.9 | 24 | 3.2 | odd | 2 | inner | ||
6048.2.c.f.3025.10 | 24 | 8.5 | even | 2 | inner | ||
6048.2.c.f.3025.15 | 24 | 1.1 | even | 1 | trivial | ||
6048.2.c.f.3025.16 | 24 | 24.5 | odd | 2 | inner |