Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(1711,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1711");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.m (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 50 x^{10} - 136 x^{9} + 2215 x^{8} - 5020 x^{7} + 18282 x^{6} - 12094 x^{5} + 48457 x^{4} - 30372 x^{3} + 89392 x^{2} + 9344 x + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1711.6 | ||
Root | \(0.816029 + 1.41340i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1711 |
Dual form | 2736.3.m.f.1711.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.606930 | −0.121386 | −0.0606930 | − | 0.998156i | \(-0.519331\pi\) | ||||
−0.0606930 | + | 0.998156i | \(0.519331\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85501i | 0.407859i | 0.978986 | + | 0.203930i | \(0.0653713\pi\) | ||||
−0.978986 | + | 0.203930i | \(0.934629\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41768i | 0.219789i | 0.993943 | + | 0.109895i | \(0.0350513\pi\) | ||||
−0.993943 | + | 0.109895i | \(0.964949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.3960 | −1.56892 | −0.784460 | − | 0.620180i | \(-0.787060\pi\) | ||||
−0.784460 | + | 0.620180i | \(0.787060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.5054 | −0.794437 | −0.397219 | − | 0.917724i | \(-0.630025\pi\) | ||||
−0.397219 | + | 0.917724i | \(0.630025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.35890i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.0337i | 0.523202i | 0.965176 | + | 0.261601i | \(0.0842505\pi\) | ||||
−0.965176 | + | 0.261601i | \(0.915749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.6316 | −0.985265 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 24.8131 | 0.855624 | 0.427812 | − | 0.903868i | \(-0.359284\pi\) | ||||
0.427812 | + | 0.903868i | \(0.359284\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 18.4137i | − 0.593989i | −0.954879 | − | 0.296995i | \(-0.904016\pi\) | ||||
0.954879 | − | 0.296995i | \(-0.0959844\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.73279i | − 0.0495084i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.16584 | 0.0315091 | 0.0157545 | − | 0.999876i | \(-0.494985\pi\) | ||||
0.0157545 | + | 0.999876i | \(0.494985\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 29.4718 | 0.718824 | 0.359412 | − | 0.933179i | \(-0.382977\pi\) | ||||
0.359412 | + | 0.933179i | \(0.382977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 33.7751i | − 0.785468i | −0.919652 | − | 0.392734i | \(-0.871529\pi\) | ||||
0.919652 | − | 0.392734i | \(-0.128471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 13.7717i | − 0.293015i | −0.989210 | − | 0.146508i | \(-0.953197\pi\) | ||||
0.989210 | − | 0.146508i | \(-0.0468033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.8489 | 0.833651 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 51.7771 | 0.976927 | 0.488464 | − | 0.872584i | \(-0.337558\pi\) | ||||
0.488464 | + | 0.872584i | \(0.337558\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.46736i | − 0.0266793i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17.0618i | 0.289182i | 0.989491 | + | 0.144591i | \(0.0461867\pi\) | ||||
−0.989491 | + | 0.144591i | \(0.953813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 34.7473 | 0.569627 | 0.284814 | − | 0.958583i | \(-0.408068\pi\) | ||||
0.284814 | + | 0.958583i | \(0.408068\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.3789 | 0.190445 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 43.5474i | − 0.649961i | −0.945721 | − | 0.324980i | \(-0.894642\pi\) | ||||
0.945721 | − | 0.324980i | \(-0.105358\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 30.7860i | − 0.433605i | −0.976215 | − | 0.216803i | \(-0.930437\pi\) | ||||
0.976215 | − | 0.216803i | \(-0.0695628\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −64.7947 | −0.887599 | −0.443799 | − | 0.896126i | \(-0.646370\pi\) | ||||
−0.443799 | + | 0.896126i | \(0.646370\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.90251 | −0.0896430 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 80.1630i | − 1.01472i | −0.861734 | − | 0.507361i | \(-0.830621\pi\) | ||||
0.861734 | − | 0.507361i | \(-0.169379\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 128.801i | 1.55182i | 0.630845 | + | 0.775909i | \(0.282709\pi\) | ||||
−0.630845 | + | 0.775909i | \(0.717291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.19686 | 0.0964336 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 163.654 | 1.83881 | 0.919404 | − | 0.393314i | \(-0.128671\pi\) | ||||
0.919404 | + | 0.393314i | \(0.128671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 58.2307i | − 0.639898i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.64555i | 0.0278479i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 25.1439 | 0.259216 | 0.129608 | − | 0.991565i | \(-0.458628\pi\) | ||||
0.129608 | + | 0.991565i | \(0.458628\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 114.079 | 1.12950 | 0.564749 | − | 0.825263i | \(-0.308973\pi\) | ||||
0.564749 | + | 0.825263i | \(0.308973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 67.3211i | − 0.653603i | −0.945093 | − | 0.326802i | \(-0.894029\pi\) | ||||
0.945093 | − | 0.326802i | \(-0.105971\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.91899i | 0.0927008i | 0.998925 | + | 0.0463504i | \(0.0147591\pi\) | ||||
−0.998925 | + | 0.0463504i | \(0.985241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −96.3365 | −0.883821 | −0.441911 | − | 0.897059i | \(-0.645699\pi\) | ||||
−0.441911 | + | 0.897059i | \(0.645699\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −116.547 | −1.03139 | −0.515695 | − | 0.856772i | \(-0.672466\pi\) | ||||
−0.515695 | + | 0.856772i | \(0.672466\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.30359i | − 0.0635095i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 38.5582i | − 0.324018i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 115.155 | 0.951693 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 30.1229 | 0.240984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 138.728i | 1.09235i | 0.837672 | + | 0.546173i | \(0.183916\pi\) | ||||
−0.837672 | + | 0.546173i | \(0.816084\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 148.710i | 1.13519i | 0.823308 | + | 0.567595i | \(0.192126\pi\) | ||||
−0.823308 | + | 0.567595i | \(0.807874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.4447 | 0.0935693 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −36.4545 | −0.266091 | −0.133046 | − | 0.991110i | \(-0.542476\pi\) | ||||
−0.133046 | + | 0.991110i | \(0.542476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 87.1292i | 0.626829i | 0.949616 | + | 0.313415i | \(0.101473\pi\) | ||||
−0.949616 | + | 0.313415i | \(0.898527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 49.3109i | − 0.344832i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.0598 | −0.103861 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 158.016 | 1.06051 | 0.530256 | − | 0.847838i | \(-0.322096\pi\) | ||||
0.530256 | + | 0.847838i | \(0.322096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 205.568i | − 1.36138i | −0.732573 | − | 0.680689i | \(-0.761681\pi\) | ||||
0.732573 | − | 0.680689i | \(-0.238319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.1758i | 0.0721020i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26.8308 | 0.170897 | 0.0854484 | − | 0.996343i | \(-0.472768\pi\) | ||||
0.0854484 | + | 0.996343i | \(0.472768\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −34.3563 | −0.213393 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 134.797i | − 0.826973i | −0.910510 | − | 0.413487i | \(-0.864311\pi\) | ||||
0.910510 | − | 0.413487i | \(-0.135689\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 75.0890i | − 0.449635i | −0.974401 | − | 0.224817i | \(-0.927821\pi\) | ||||
0.974401 | − | 0.224817i | \(-0.0721786\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 246.995 | 1.46151 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 217.219 | 1.25560 | 0.627800 | − | 0.778375i | \(-0.283956\pi\) | ||||
0.627800 | + | 0.778375i | \(0.283956\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 70.3236i | − 0.401849i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 46.1045i | − 0.257567i | −0.991673 | − | 0.128784i | \(-0.958893\pi\) | ||||
0.991673 | − | 0.128784i | \(-0.0411072\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −148.682 | −0.821445 | −0.410722 | − | 0.911760i | \(-0.634723\pi\) | ||||
−0.410722 | + | 0.911760i | \(0.634723\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.707582 | −0.00382477 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 32.6518i | − 0.174609i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 300.611i | − 1.57388i | −0.617028 | − | 0.786941i | \(-0.711664\pi\) | ||||
0.617028 | − | 0.786941i | \(-0.288336\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 37.3778 | 0.193667 | 0.0968337 | − | 0.995301i | \(-0.469128\pi\) | ||||
0.0968337 | + | 0.995301i | \(0.469128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 118.570 | 0.601876 | 0.300938 | − | 0.953644i | \(-0.402700\pi\) | ||||
0.300938 | + | 0.953644i | \(0.402700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 117.374i | 0.589821i | 0.955525 | + | 0.294910i | \(0.0952898\pi\) | ||||
−0.955525 | + | 0.294910i | \(0.904710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 70.8418i | 0.348974i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.8873 | −0.0872552 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5384 | 0.0504231 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 289.759i | 1.37326i | 0.727005 | + | 0.686632i | \(0.240912\pi\) | ||||
−0.727005 | + | 0.686632i | \(0.759088\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.4992i | 0.0953449i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 52.5713 | 0.242264 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 275.456 | 1.24641 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 79.9420i | − 0.358484i | −0.983805 | − | 0.179242i | \(-0.942635\pi\) | ||||
0.983805 | − | 0.179242i | \(-0.0573646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 385.250i | − 1.69714i | −0.529085 | − | 0.848569i | \(-0.677465\pi\) | ||||
0.529085 | − | 0.848569i | \(-0.322535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 37.4194 | 0.163404 | 0.0817018 | − | 0.996657i | \(-0.473964\pi\) | ||||
0.0817018 | + | 0.996657i | \(0.473964\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 36.0574 | 0.154753 | 0.0773764 | − | 0.997002i | \(-0.475346\pi\) | ||||
0.0773764 | + | 0.997002i | \(0.475346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.35848i | 0.0355680i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 463.070i | − 1.93753i | −0.247979 | − | 0.968765i | \(-0.579766\pi\) | ||||
0.247979 | − | 0.968765i | \(-0.420234\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 429.839 | 1.78356 | 0.891781 | − | 0.452467i | \(-0.149456\pi\) | ||||
0.891781 | + | 0.452467i | \(0.149456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.7924 | −0.101194 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 88.9039i | 0.359935i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 490.672i | − 1.95487i | −0.211239 | − | 0.977434i | \(-0.567750\pi\) | ||||
0.211239 | − | 0.977434i | \(-0.432250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.0935 | −0.114994 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 189.622 | 0.737828 | 0.368914 | − | 0.929463i | \(-0.379730\pi\) | ||||
0.368914 | + | 0.929463i | \(0.379730\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.32848i | 0.0128513i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 232.128i | 0.882615i | 0.897356 | + | 0.441307i | \(0.145485\pi\) | ||||
−0.897356 | + | 0.441307i | \(0.854515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.4251 | −0.118585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 95.0653 | 0.353402 | 0.176701 | − | 0.984265i | \(-0.443457\pi\) | ||||
0.176701 | + | 0.984265i | \(0.443457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 110.876i | 0.409137i | 0.978852 | + | 0.204569i | \(0.0655791\pi\) | ||||
−0.978852 | + | 0.204569i | \(0.934421\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 59.5514i | − 0.216551i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 119.874 | 0.432760 | 0.216380 | − | 0.976309i | \(-0.430575\pi\) | ||||
0.216380 | + | 0.976309i | \(0.430575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 120.062 | 0.427266 | 0.213633 | − | 0.976914i | \(-0.431470\pi\) | ||||
0.213633 | + | 0.976914i | \(0.431470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 26.4929i | − 0.0936144i | −0.998904 | − | 0.0468072i | \(-0.985095\pi\) | ||||
0.998904 | − | 0.0468072i | \(-0.0149046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 84.1424i | 0.293179i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −106.603 | −0.368869 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.7148 | 0.0741120 | 0.0370560 | − | 0.999313i | \(-0.488202\pi\) | ||||
0.0370560 | + | 0.999313i | \(0.488202\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 10.3553i | − 0.0351027i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 245.438i | − 0.820863i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 96.4285 | 0.320360 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.0892 | −0.0691448 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 58.6798i | − 0.191139i | −0.995423 | − | 0.0955697i | \(-0.969533\pi\) | ||||
0.995423 | − | 0.0955697i | \(-0.0304673\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 73.7996i | 0.237298i | 0.992936 | + | 0.118649i | \(0.0378563\pi\) | ||||
−0.992936 | + | 0.118649i | \(0.962144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 160.115 | 0.511551 | 0.255776 | − | 0.966736i | \(-0.417669\pi\) | ||||
0.255776 | + | 0.966736i | \(0.417669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −75.2978 | −0.237532 | −0.118766 | − | 0.992922i | \(-0.537894\pi\) | ||||
−0.118766 | + | 0.992922i | \(0.537894\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 59.9902i | 0.188057i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 58.8688i | 0.182256i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 502.386 | 1.54580 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.3185 | 0.119509 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 116.291i | 0.351333i | 0.984450 | + | 0.175666i | \(0.0562080\pi\) | ||||
−0.984450 | + | 0.175666i | \(0.943792\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.4302i | 0.0788962i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 166.131 | 0.492971 | 0.246485 | − | 0.969147i | \(-0.420724\pi\) | ||||
0.246485 | + | 0.969147i | \(0.420724\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 44.5184 | 0.130552 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 256.520i | 0.747871i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 180.801i | − 0.521040i | −0.965468 | − | 0.260520i | \(-0.916106\pi\) | ||||
0.965468 | − | 0.260520i | \(-0.0838940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −55.9774 | −0.160394 | −0.0801968 | − | 0.996779i | \(-0.525555\pi\) | ||||
−0.0801968 | + | 0.996779i | \(0.525555\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −543.098 | −1.53852 | −0.769260 | − | 0.638936i | \(-0.779375\pi\) | ||||
−0.769260 | + | 0.638936i | \(0.779375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.6849i | 0.0526336i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 127.591i | − 0.355408i | −0.984084 | − | 0.177704i | \(-0.943133\pi\) | ||||
0.984084 | − | 0.177704i | \(-0.0568669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.3259 | 0.107742 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 60.1583i | − 0.163919i | −0.996636 | − | 0.0819595i | \(-0.973882\pi\) | ||||
0.996636 | − | 0.0819595i | \(-0.0261178\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 147.824i | 0.398449i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −192.929 | −0.517235 | −0.258617 | − | 0.965980i | \(-0.583267\pi\) | ||||
−0.258617 | + | 0.965980i | \(0.583267\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −506.087 | −1.34241 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4601i | 0.0328763i | 0.999865 | + | 0.0164381i | \(0.00523265\pi\) | ||||
−0.999865 | + | 0.0164381i | \(0.994767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 586.965i | − 1.53255i | −0.642515 | − | 0.766273i | \(-0.722109\pi\) | ||||
0.642515 | − | 0.766273i | \(-0.277891\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.18934 | 0.0108814 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 164.796 | 0.423640 | 0.211820 | − | 0.977309i | \(-0.432061\pi\) | ||||
0.211820 | + | 0.977309i | \(0.432061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 162.520i | − 0.415652i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 48.6534i | 0.123173i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −278.595 | −0.701751 | −0.350876 | − | 0.936422i | \(-0.614116\pi\) | ||||
−0.350876 | + | 0.936422i | \(0.614116\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −343.429 | −0.856431 | −0.428215 | − | 0.903677i | \(-0.640858\pi\) | ||||
−0.428215 | + | 0.903677i | \(0.640858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 375.564i | 0.931922i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.81862i | 0.00692536i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 688.882 | 1.68431 | 0.842154 | − | 0.539236i | \(-0.181287\pi\) | ||||
0.842154 | + | 0.539236i | \(0.181287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −48.7115 | −0.117946 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 78.1732i | − 0.188369i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 65.0291i | − 0.155201i | −0.996985 | − | 0.0776004i | \(-0.975274\pi\) | ||||
0.996985 | − | 0.0776004i | \(-0.0247258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −306.543 | −0.728130 | −0.364065 | − | 0.931374i | \(-0.618611\pi\) | ||||
−0.364065 | + | 0.931374i | \(0.618611\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 332.661 | 0.782732 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 99.2039i | 0.232328i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 521.933i | 1.21098i | 0.795853 | + | 0.605491i | \(0.207023\pi\) | ||||
−0.795853 | + | 0.605491i | \(0.792977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 123.944 | 0.286244 | 0.143122 | − | 0.989705i | \(-0.454286\pi\) | ||||
0.143122 | + | 0.989705i | \(0.454286\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 52.4535 | 0.120031 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 513.303i | − 1.16925i | −0.811302 | − | 0.584627i | \(-0.801241\pi\) | ||||
0.811302 | − | 0.584627i | \(-0.198759\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 105.258i | 0.237602i | 0.992918 | + | 0.118801i | \(0.0379051\pi\) | ||||
−0.992918 | + | 0.118801i | \(0.962095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −99.3266 | −0.223206 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 346.829 | 0.772448 | 0.386224 | − | 0.922405i | \(-0.373779\pi\) | ||||
0.386224 | + | 0.922405i | \(0.373779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 71.2534i | 0.157990i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 35.3420i | 0.0776747i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −294.201 | −0.643765 | −0.321883 | − | 0.946780i | \(-0.604316\pi\) | ||||
−0.321883 | + | 0.946780i | \(0.604316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 692.974 | 1.50320 | 0.751598 | − | 0.659621i | \(-0.229283\pi\) | ||||
0.751598 | + | 0.659621i | \(0.229283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 469.144i | − 1.01327i | −0.862161 | − | 0.506635i | \(-0.830889\pi\) | ||||
0.862161 | − | 0.506635i | \(-0.169111\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 445.537i | 0.954041i | 0.878892 | + | 0.477020i | \(0.158283\pi\) | ||||
−0.878892 | + | 0.477020i | \(0.841717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 124.328 | 0.265092 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 81.6575 | 0.172637 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 107.367i | 0.226035i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 783.725i | − 1.63617i | −0.575097 | − | 0.818085i | \(-0.695036\pi\) | ||||
0.575097 | − | 0.818085i | \(-0.304964\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.7784 | −0.0494352 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.2606 | −0.0314652 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 89.5516i | − 0.183884i | −0.995764 | − | 0.0919421i | \(-0.970693\pi\) | ||||
0.995764 | − | 0.0919421i | \(-0.0293075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 877.757i | 1.78769i | 0.448374 | + | 0.893846i | \(0.352003\pi\) | ||||
−0.448374 | + | 0.893846i | \(0.647997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −335.112 | −0.679740 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 87.8943 | 0.176850 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 511.990i | 1.02603i | 0.858379 | + | 0.513016i | \(0.171472\pi\) | ||||
−0.858379 | + | 0.513016i | \(0.828528\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 497.093i | − 0.988256i | −0.869389 | − | 0.494128i | \(-0.835487\pi\) | ||||
0.869389 | − | 0.494128i | \(-0.164513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −69.2382 | −0.137105 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 939.366 | 1.84551 | 0.922756 | − | 0.385384i | \(-0.125931\pi\) | ||||
0.922756 | + | 0.385384i | \(0.125931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 184.990i | − 0.362015i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 40.8592i | 0.0793383i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.2956 | 0.0644016 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 381.461 | 0.732171 | 0.366086 | − | 0.930581i | \(-0.380698\pi\) | ||||
0.366086 | + | 0.930581i | \(0.380698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 535.503i | − 1.02391i | −0.859014 | − | 0.511953i | \(-0.828922\pi\) | ||||
0.859014 | − | 0.511953i | \(-0.171078\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 248.685i | 0.471887i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 384.191 | 0.726259 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −601.105 | −1.12778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 6.02014i | − 0.0112526i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 98.7596i | 0.183227i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −236.065 | −0.436350 | −0.218175 | − | 0.975910i | \(-0.570010\pi\) | ||||
−0.218175 | + | 0.975910i | \(0.570010\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.4696 | 0.107284 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 351.582i | 0.642745i | 0.946953 | + | 0.321373i | \(0.104144\pi\) | ||||
−0.946953 | + | 0.321373i | \(0.895856\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 108.158i | − 0.196294i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 228.866 | 0.413863 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 91.0821 | 0.163523 | 0.0817613 | − | 0.996652i | \(-0.473945\pi\) | ||||
0.0817613 | + | 0.996652i | \(0.473945\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 688.876i | 1.23234i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 278.239i | 0.494207i | 0.968989 | + | 0.247103i | \(0.0794788\pi\) | ||||
−0.968989 | + | 0.247103i | \(0.920521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 70.7360 | 0.125196 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −189.085 | −0.332312 | −0.166156 | − | 0.986100i | \(-0.553135\pi\) | ||||
−0.166156 | + | 0.986100i | \(0.553135\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 590.253i | − 1.03372i | −0.856071 | − | 0.516859i | \(-0.827101\pi\) | ||||
0.856071 | − | 0.516859i | \(-0.172899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 296.409i | − 0.515493i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −266.414 | −0.461723 | −0.230861 | − | 0.972987i | \(-0.574154\pi\) | ||||
−0.230861 | + | 0.972987i | \(0.574154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −367.728 | −0.632923 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 125.181i | 0.214718i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 495.542i | 0.844194i | 0.906551 | + | 0.422097i | \(0.138706\pi\) | ||||
−0.906551 | + | 0.422097i | \(0.861294\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −80.2633 | −0.136270 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −468.331 | −0.789765 | −0.394883 | − | 0.918732i | \(-0.629215\pi\) | ||||
−0.394883 | + | 0.918732i | \(0.629215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.4021i | 0.0393313i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 164.789i | − 0.275107i | −0.990494 | − | 0.137553i | \(-0.956076\pi\) | ||||
0.990494 | − | 0.137553i | \(-0.0439239\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1051.90 | −1.75024 | −0.875121 | − | 0.483904i | \(-0.839218\pi\) | ||||
−0.875121 | + | 0.483904i | \(0.839218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −69.8910 | −0.115522 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 984.361i | − 1.62168i | −0.585267 | − | 0.810841i | \(-0.699010\pi\) | ||||
0.585267 | − | 0.810841i | \(-0.300990\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 280.888i | 0.459718i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −449.217 | −0.732817 | −0.366408 | − | 0.930454i | \(-0.619413\pi\) | ||||
−0.366408 | + | 0.930454i | \(0.619413\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 314.644 | 0.509958 | 0.254979 | − | 0.966947i | \(-0.417931\pi\) | ||||
0.254979 | + | 0.966947i | \(0.417931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 132.283i | − 0.213704i | −0.994275 | − | 0.106852i | \(-0.965923\pi\) | ||||
0.994275 | − | 0.106852i | \(-0.0340771\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 467.234i | 0.749975i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 597.508 | 0.956013 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.7451 | −0.0250320 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 521.872i | − 0.827055i | −0.910492 | − | 0.413528i | \(-0.864297\pi\) | ||||
0.910492 | − | 0.413528i | \(-0.135703\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 84.1982i | − 0.132596i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −833.152 | −1.30793 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 514.200 | 0.802184 | 0.401092 | − | 0.916038i | \(-0.368631\pi\) | ||||
0.401092 | + | 0.916038i | \(0.368631\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 216.096i | − 0.336075i | −0.985781 | − | 0.168037i | \(-0.946257\pi\) | ||||
0.985781 | − | 0.168037i | \(-0.0537429\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.2451i | 0.0745674i | 0.999305 | + | 0.0372837i | \(0.0118705\pi\) | ||||
−0.999305 | + | 0.0372837i | \(0.988129\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.2499 | −0.0635591 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −693.988 | −1.06277 | −0.531384 | − | 0.847131i | \(-0.678328\pi\) | ||||
−0.531384 | + | 0.847131i | \(0.678328\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 90.2566i | − 0.137796i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1059.76i | 1.60814i | 0.594537 | + | 0.804068i | \(0.297335\pi\) | ||||
−0.594537 | + | 0.804068i | \(0.702665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −174.231 | −0.263588 | −0.131794 | − | 0.991277i | \(-0.542074\pi\) | ||||
−0.131794 | + | 0.991277i | \(0.542074\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.55307 | −0.0113580 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 298.592i | 0.447665i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 84.0078i | 0.125198i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −512.636 | −0.761718 | −0.380859 | − | 0.924633i | \(-0.624372\pi\) | ||||
−0.380859 | + | 0.924633i | \(0.624372\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 483.929 | 0.714814 | 0.357407 | − | 0.933949i | \(-0.383661\pi\) | ||||
0.357407 | + | 0.933949i | \(0.383661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 71.7862i | 0.105723i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 961.587i | 1.40789i | 0.710256 | + | 0.703944i | \(0.248579\pi\) | ||||
−0.710256 | + | 0.703944i | \(0.751421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.1254 | 0.0322998 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1056.04 | −1.53272 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 98.7795i | 0.142952i | 0.997442 | + | 0.0714758i | \(0.0227709\pi\) | ||||
−0.997442 | + | 0.0714758i | \(0.977229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 52.8814i | − 0.0760883i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −398.029 | −0.571061 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1135.85 | −1.62033 | −0.810166 | − | 0.586201i | \(-0.800623\pi\) | ||||
−0.810166 | + | 0.586201i | \(0.800623\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.08176i | − 0.00722868i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 325.698i | 0.460676i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −494.337 | −0.697232 | −0.348616 | − | 0.937266i | \(-0.613348\pi\) | ||||
−0.348616 | + | 0.937266i | \(0.613348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 221.584 | 0.310777 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.9283i | 0.0418578i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 355.276i | − 0.494126i | −0.968999 | − | 0.247063i | \(-0.920535\pi\) | ||||
0.968999 | − | 0.247063i | \(-0.0794654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 192.203 | 0.266578 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −611.187 | −0.843017 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 596.808i | − 0.820919i | −0.911879 | − | 0.410459i | \(-0.865368\pi\) | ||||
0.911879 | − | 0.410459i | \(-0.134632\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 456.148i | 0.624005i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1042.13 | 1.42173 | 0.710865 | − | 0.703329i | \(-0.248304\pi\) | ||||
0.710865 | + | 0.703329i | \(0.248304\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 105.284 | 0.142854 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 463.422i | − 0.627094i | −0.949573 | − | 0.313547i | \(-0.898483\pi\) | ||||
0.949573 | − | 0.313547i | \(-0.101517\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 516.160i | 0.694697i | 0.937736 | + | 0.347349i | \(0.112918\pi\) | ||||
−0.937736 | + | 0.347349i | \(0.887082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −95.9049 | −0.128731 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.3188 | −0.0378089 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 141.566i | 0.188504i | 0.995548 | + | 0.0942520i | \(0.0300459\pi\) | ||||
−0.995548 | + | 0.0942520i | \(0.969954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 124.765i | 0.165252i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 714.786 | 0.944235 | 0.472118 | − | 0.881536i | \(-0.343490\pi\) | ||||
0.472118 | + | 0.881536i | \(0.343490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 528.806 | 0.694883 | 0.347442 | − | 0.937702i | \(-0.387050\pi\) | ||||
0.347442 | + | 0.937702i | \(0.387050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 275.042i | − 0.360474i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 347.991i | − 0.453704i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 305.574 | 0.397366 | 0.198683 | − | 0.980064i | \(-0.436334\pi\) | ||||
0.198683 | + | 0.980064i | \(0.436334\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −79.5350 | −0.102891 | −0.0514456 | − | 0.998676i | \(-0.516383\pi\) | ||||
−0.0514456 | + | 0.998676i | \(0.516383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 453.559i | 0.585237i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 128.465i | − 0.164910i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 74.4306 | 0.0953017 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.2844 | −0.0207445 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 333.127i | 0.423287i | 0.977347 | + | 0.211644i | \(0.0678816\pi\) | ||||
−0.977347 | + | 0.211644i | \(0.932118\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 332.744i | − 0.420662i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −708.704 | −0.893699 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1014.86 | −1.27336 | −0.636678 | − | 0.771130i | \(-0.719692\pi\) | ||||
−0.636678 | + | 0.771130i | \(0.719692\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 185.993i | 0.232782i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 156.653i | − 0.195085i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.8519 | 0.0259029 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −423.473 | −0.523452 | −0.261726 | − | 0.965142i | \(-0.584292\pi\) | ||||
−0.261726 | + | 0.965142i | \(0.584292\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 265.825i | 0.327774i | 0.986479 | + | 0.163887i | \(0.0524033\pi\) | ||||
−0.986479 | + | 0.163887i | \(0.947597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 81.8122i | 0.100383i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −147.222 | −0.180199 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −437.207 | −0.532529 | −0.266265 | − | 0.963900i | \(-0.585790\pi\) | ||||
−0.266265 | + | 0.963900i | \(0.585790\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 138.346i | − 0.168100i | −0.996462 | − | 0.0840500i | \(-0.973214\pi\) | ||||
0.996462 | − | 0.0840500i | \(-0.0267855\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 927.025i | 1.12095i | 0.828172 | + | 0.560475i | \(0.189381\pi\) | ||||
−0.828172 | + | 0.560475i | \(0.810619\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1330.94 | −1.60547 | −0.802737 | − | 0.596333i | \(-0.796624\pi\) | ||||
−0.802737 | + | 0.596333i | \(0.796624\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −551.682 | −0.662283 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.5738i | 0.0545794i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 248.602i | − 0.296308i | −0.988964 | − | 0.148154i | \(-0.952667\pi\) | ||||
0.988964 | − | 0.148154i | \(-0.0473331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −225.310 | −0.267907 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −149.909 | −0.177407 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 328.769i | 0.388156i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.0293i | 0.0164856i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 955.871 | 1.12060 | 0.560300 | − | 0.828290i | \(-0.310686\pi\) | ||||
0.560300 | + | 0.828290i | \(0.310686\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −990.079 | −1.15528 | −0.577642 | − | 0.816290i | \(-0.696027\pi\) | ||||
−0.577642 | + | 0.816290i | \(0.696027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 187.142i | 0.217861i | 0.994049 | + | 0.108930i | \(0.0347425\pi\) | ||||
−0.994049 | + | 0.108930i | \(0.965257\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 423.878i | 0.491168i | 0.969375 | + | 0.245584i | \(0.0789797\pi\) | ||||
−0.969375 | + | 0.245584i | \(0.921020\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −131.837 | −0.152412 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 193.809 | 0.223025 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 888.190i | 1.01974i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 86.0014i | 0.0982873i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 510.331 | 0.581906 | 0.290953 | − | 0.956737i | \(-0.406028\pi\) | ||||
0.290953 | + | 0.956737i | \(0.406028\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −224.398 | −0.254708 | −0.127354 | − | 0.991857i | \(-0.540648\pi\) | ||||
−0.127354 | + | 0.991857i | \(0.540648\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 213.961i | − 0.242312i | −0.992633 | − | 0.121156i | \(-0.961340\pi\) | ||||
0.992633 | − | 0.121156i | \(-0.0386601\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1124.46i | − 1.26771i | −0.773451 | − | 0.633856i | \(-0.781471\pi\) | ||||
0.773451 | − | 0.633856i | \(-0.218529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −396.070 | −0.445523 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −60.0296 | −0.0672224 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.9822i | 0.0312651i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 456.900i | − 0.508232i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −699.273 | −0.776107 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 90.2393 | 0.0997120 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1546.70i | 1.70529i | 0.522489 | + | 0.852646i | \(0.325003\pi\) | ||||
−0.522489 | + | 0.852646i | \(0.674997\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 833.914i | 0.915383i | 0.889111 | + | 0.457692i | \(0.151324\pi\) | ||||
−0.889111 | + | 0.457692i | \(0.848676\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −311.400 | −0.341073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −424.569 | −0.462998 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 931.367i | − 1.01346i | −0.862106 | − | 0.506729i | \(-0.830855\pi\) | ||||
0.862106 | − | 0.506729i | \(-0.169145\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 627.909i | 0.680292i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.7165 | −0.0310448 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1462.78 | −1.57457 | −0.787286 | − | 0.616587i | \(-0.788515\pi\) | ||||
−0.787286 | + | 0.616587i | \(0.788515\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 178.056i | − 0.191253i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.8174i | 0.0211951i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1683.57 | −1.79677 | −0.898383 | − | 0.439212i | \(-0.855258\pi\) | ||||
−0.898383 | + | 0.439212i | \(0.855258\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 415.814 | 0.441885 | 0.220942 | − | 0.975287i | \(-0.429087\pi\) | ||||
0.220942 | + | 0.975287i | \(0.429087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 354.653i | 0.376091i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 987.972i | 1.04327i | 0.853170 | + | 0.521633i | \(0.174677\pi\) | ||||
−0.853170 | + | 0.521633i | \(0.825323\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1321.55 | 1.39257 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 887.756 | 0.931538 | 0.465769 | − | 0.884906i | \(-0.345778\pi\) | ||||
0.465769 | + | 0.884906i | \(0.345778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 182.450i | 0.191047i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 104.078i | − 0.108528i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 621.937 | 0.647177 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.6857 | −0.0235085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1635.00i | − 1.69080i | −0.534136 | − | 0.845399i | \(-0.679363\pi\) | ||||
0.534136 | − | 0.845399i | \(-0.320637\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 549.534i | − 0.565947i | −0.959128 | − | 0.282973i | \(-0.908679\pi\) | ||||
0.959128 | − | 0.282973i | \(-0.0913208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −248.755 | −0.255658 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −527.248 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586967\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586967\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 395.663i | 0.404150i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.1942i | 0.0327509i | 0.999866 | + | 0.0163755i | \(0.00521270\pi\) | ||||
−0.999866 | + | 0.0163755i | \(0.994787\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −71.9635 | −0.0730594 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 406.438 | 0.410959 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1854.35i | 1.87119i | 0.353069 | + | 0.935597i | \(0.385138\pi\) | ||||
−0.353069 | + | 0.935597i | \(0.614862\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 71.2380i | − 0.0715960i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 535.802 | 0.537415 | 0.268707 | − | 0.963222i | \(-0.413404\pi\) | ||||
0.268707 | + | 0.963222i | \(0.413404\pi\) | |||||||
\(998\) | 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 | 2736.3.m.f.1711.6 | 12 | ||
3.2 | odd | 2 | 912.3.m.a.799.10 | yes | 12 | ||
4.3 | odd | 2 | inner | 2736.3.m.f.1711.5 | 12 | ||
12.11 | even | 2 | 912.3.m.a.799.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.3.m.a.799.4 | ✓ | 12 | 12.11 | even | 2 | ||
912.3.m.a.799.10 | yes | 12 | 3.2 | odd | 2 | ||
2736.3.m.f.1711.5 | 12 | 4.3 | odd | 2 | inner | ||
2736.3.m.f.1711.6 | 12 | 1.1 | even | 1 | trivial |