Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(289,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.k (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(-1.38255 + 0.297594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.289 |
Dual form | 1152.2.k.e.865.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.595188 | + | 0.595188i | −0.266176 | + | 0.266176i | −0.827557 | − | 0.561381i | \(-0.810270\pi\) |
0.561381 | + | 0.827557i | \(0.310270\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.64575i | − | 0.622036i | −0.950404 | − | 0.311018i | \(-0.899330\pi\) | ||
0.950404 | − | 0.311018i | \(-0.100670\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.36028 | + | 3.36028i | −1.01316 | + | 1.01316i | −0.0132513 | + | 0.999912i | \(0.504218\pi\) |
−0.999912 | + | 0.0132513i | \(0.995782\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.64575 | − | 2.64575i | −0.733799 | − | 0.733799i | 0.237571 | − | 0.971370i | \(-0.423649\pi\) |
−0.971370 | + | 0.237571i | \(0.923649\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.53019 | 1.34127 | 0.670634 | − | 0.741788i | \(-0.266022\pi\) | ||||
0.670634 | + | 0.741788i | \(0.266022\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.64575 | + | 3.64575i | 0.836393 | + | 0.836393i | 0.988382 | − | 0.151989i | \(-0.0485680\pi\) |
−0.151989 | + | 0.988382i | \(0.548568\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.33981i | 0.904914i | 0.891786 | + | 0.452457i | \(0.149452\pi\) | ||||
−0.891786 | + | 0.452457i | \(0.850548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.29150i | 0.858301i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.12538 | + | 6.12538i | 1.13745 | + | 1.13745i | 0.988905 | + | 0.148549i | \(0.0474603\pi\) |
0.148549 | + | 0.988905i | \(0.452540\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.64575 | −1.01401 | −0.507003 | − | 0.861944i | \(-0.669247\pi\) | ||||
−0.507003 | + | 0.861944i | \(0.669247\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.979531 | + | 0.979531i | 0.165571 | + | 0.165571i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.645751 | − | 0.645751i | 0.106161 | − | 0.106161i | −0.652031 | − | 0.758192i | \(-0.726083\pi\) |
0.758192 | + | 0.652031i | \(0.226083\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.91094i | 1.23548i | 0.786382 | + | 0.617741i | \(0.211952\pi\) | ||||
−0.786382 | + | 0.617741i | \(0.788048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.354249 | − | 0.354249i | 0.0540224 | − | 0.0540224i | −0.679579 | − | 0.733602i | \(-0.737838\pi\) |
0.733602 | + | 0.679579i | \(0.237838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.10132 | −1.32756 | −0.663782 | − | 0.747926i | \(-0.731050\pi\) | ||||
−0.663782 | + | 0.747926i | \(0.731050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29150 | 0.613072 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.93500 | − | 4.93500i | 0.677875 | − | 0.677875i | −0.281644 | − | 0.959519i | \(-0.590880\pi\) |
0.959519 | + | 0.281644i | \(0.0908798\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.00000i | − | 0.539360i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.33981 | + | 4.33981i | −0.564996 | + | 0.564996i | −0.930722 | − | 0.365727i | \(-0.880821\pi\) |
0.365727 | + | 0.930722i | \(0.380821\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.645751 | + | 0.645751i | 0.0826800 | + | 0.0826800i | 0.747237 | − | 0.664557i | \(-0.231380\pi\) |
−0.664557 | + | 0.747237i | \(0.731380\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.14944 | 0.390640 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 4.00000i | −0.488678 | − | 0.488678i | 0.419211 | − | 0.907889i | \(-0.362307\pi\) |
−0.907889 | + | 0.419211i | \(0.862307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.4411i | 1.59517i | 0.603207 | + | 0.797584i | \(0.293889\pi\) | ||||
−0.603207 | + | 0.797584i | \(0.706111\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.29150i | − | 0.385241i | −0.981273 | − | 0.192621i | \(-0.938301\pi\) | ||
0.981273 | − | 0.192621i | \(-0.0616987\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.53019 | + | 5.53019i | 0.630224 | + | 0.630224i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.64575 | 1.08523 | 0.542616 | − | 0.839981i | \(-0.317434\pi\) | ||||
0.542616 | + | 0.839981i | \(0.317434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.36028 | + | 3.36028i | 0.368839 | + | 0.368839i | 0.867054 | − | 0.498215i | \(-0.166011\pi\) |
−0.498215 | + | 0.867054i | \(0.666011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.29150 | + | 3.29150i | −0.357014 | + | 0.357014i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.38075i | 0.252359i | 0.992007 | + | 0.126180i | \(0.0402716\pi\) | ||||
−0.992007 | + | 0.126180i | \(0.959728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.35425 | + | 4.35425i | −0.456449 | + | 0.456449i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.33981 | −0.445256 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5830 | −1.07454 | −0.537271 | − | 0.843410i | \(-0.680545\pi\) | ||||
−0.537271 | + | 0.843410i | \(0.680545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.595188 | + | 0.595188i | −0.0592234 | + | 0.0592234i | −0.736098 | − | 0.676875i | \(-0.763334\pi\) |
0.676875 | + | 0.736098i | \(0.263334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9373i | 1.66888i | 0.551101 | + | 0.834439i | \(0.314208\pi\) | ||||
−0.551101 | + | 0.834439i | \(0.685792\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.38075 | + | 2.38075i | −0.230156 | + | 0.230156i | −0.812758 | − | 0.582602i | \(-0.802035\pi\) |
0.582602 | + | 0.812758i | \(0.302035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.64575 | + | 6.64575i | 0.636548 | + | 0.636548i | 0.949702 | − | 0.313155i | \(-0.101386\pi\) |
−0.313155 | + | 0.949702i | \(0.601386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.58301 | − | 2.58301i | −0.240866 | − | 0.240866i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 9.10132i | − | 0.834316i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.5830i | − | 1.05300i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.53019 | − | 5.53019i | −0.494635 | − | 0.494635i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.937254 | 0.0831678 | 0.0415839 | − | 0.999135i | \(-0.486760\pi\) | ||||
0.0415839 | + | 0.999135i | \(0.486760\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.72057 | − | 6.72057i | −0.587179 | − | 0.587179i | 0.349688 | − | 0.936866i | \(-0.386288\pi\) |
−0.936866 | + | 0.349688i | \(0.886288\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | − | 6.00000i | 0.520266 | − | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.2917i | − | 0.879279i | −0.898174 | − | 0.439639i | \(-0.855106\pi\) | ||
0.898174 | − | 0.439639i | \(-0.144894\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.5830 | − | 14.5830i | 1.23691 | − | 1.23691i | 0.275659 | − | 0.961256i | \(-0.411104\pi\) |
0.961256 | − | 0.275659i | \(-0.0888960\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.7809 | 1.48692 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.29150 | −0.605526 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.6556 | + | 11.6556i | −0.954861 | + | 0.954861i | −0.999024 | − | 0.0441630i | \(-0.985938\pi\) |
0.0441630 | + | 0.999024i | \(0.485938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.3542i | − | 0.842617i | −0.906917 | − | 0.421308i | \(-0.861571\pi\) | ||
0.906917 | − | 0.421308i | \(-0.138429\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.36028 | − | 3.36028i | 0.269904 | − | 0.269904i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.64575 | + | 6.64575i | 0.530389 | + | 0.530389i | 0.920688 | − | 0.390299i | \(-0.127628\pi\) |
−0.390299 | + | 0.920688i | \(0.627628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.14226 | 0.562889 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.6458 | − | 11.6458i | −0.912166 | − | 0.912166i | 0.0842767 | − | 0.996442i | \(-0.473142\pi\) |
−0.996442 | + | 0.0842767i | \(0.973142\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.7809i | − | 1.37593i | −0.725743 | − | 0.687965i | \(-0.758504\pi\) | ||
0.725743 | − | 0.687965i | \(-0.241496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.93500 | − | 4.93500i | −0.375201 | − | 0.375201i | 0.494166 | − | 0.869367i | \(-0.335473\pi\) |
−0.869367 | + | 0.494166i | \(0.835473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.06275 | 0.533893 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.38075 | + | 2.38075i | 0.177946 | + | 0.177946i | 0.790460 | − | 0.612514i | \(-0.209842\pi\) |
−0.612514 | + | 0.790460i | \(0.709842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.645751 | − | 0.645751i | 0.0479983 | − | 0.0479983i | −0.682700 | − | 0.730699i | \(-0.739195\pi\) |
0.730699 | + | 0.682700i | \(0.239195\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.768687i | 0.0565150i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.5830 | + | 18.5830i | −1.35892 | + | 1.35892i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.10132 | 0.658548 | 0.329274 | − | 0.944234i | \(-0.393196\pi\) | ||||
0.329274 | + | 0.944234i | \(0.393196\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8745 | 0.854746 | 0.427373 | − | 0.904075i | \(-0.359439\pi\) | ||||
0.427373 | + | 0.904075i | \(0.359439\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.50613 | − | 8.50613i | 0.606037 | − | 0.606037i | −0.335871 | − | 0.941908i | \(-0.609031\pi\) |
0.941908 | + | 0.335871i | \(0.109031\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6458i | 0.967322i | 0.875256 | + | 0.483661i | \(0.160693\pi\) | ||||
−0.875256 | + | 0.483661i | \(0.839307\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.0808 | − | 10.0808i | 0.707537 | − | 0.707537i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.70850 | − | 4.70850i | −0.328856 | − | 0.328856i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.5015 | −1.69481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5830 | + | 14.5830i | 1.00394 | + | 1.00394i | 0.999992 | + | 0.00394326i | \(0.00125518\pi\) |
0.00394326 | + | 0.999992i | \(0.498745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.421689i | 0.0287590i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.29150i | 0.630748i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.6315 | − | 14.6315i | −0.984222 | − | 0.984222i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.3542 | −0.961232 | −0.480616 | − | 0.876931i | \(-0.659587\pi\) | ||||
−0.480616 | + | 0.876931i | \(0.659587\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.40122 | + | 1.40122i | 0.0930023 | + | 0.0930023i | 0.752077 | − | 0.659075i | \(-0.229052\pi\) |
−0.659075 | + | 0.752077i | \(0.729052\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.9373 | + | 17.9373i | −1.18533 | + | 1.18533i | −0.206982 | + | 0.978345i | \(0.566364\pi\) |
−0.978345 | + | 0.206982i | \(0.933636\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 19.7400i | − | 1.29321i | −0.762825 | − | 0.646606i | \(-0.776188\pi\) | ||
0.762825 | − | 0.646606i | \(-0.223812\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.41699 | − | 5.41699i | 0.353366 | − | 0.353366i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.0194 | −0.842158 | −0.421079 | − | 0.907024i | \(-0.638348\pi\) | ||||
−0.421079 | + | 0.907024i | \(0.638348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.29150 | −0.0831930 | −0.0415965 | − | 0.999134i | \(-0.513244\pi\) | ||||
−0.0415965 | + | 0.999134i | \(0.513244\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.55425 | + | 2.55425i | −0.163185 | + | 0.163185i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.2915i | − | 1.22749i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7605 | − | 18.7605i | 1.18415 | − | 1.18415i | 0.205492 | − | 0.978659i | \(-0.434121\pi\) |
0.978659 | − | 0.205492i | \(-0.0658795\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.5830 | − | 14.5830i | −0.916826 | − | 0.916826i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.2630 | −1.82538 | −0.912688 | − | 0.408656i | \(-0.865998\pi\) | ||||
−0.912688 | + | 0.408656i | \(0.865998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.06275 | − | 1.06275i | −0.0660358 | − | 0.0660358i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.67963i | − | 0.535209i | −0.963529 | − | 0.267604i | \(-0.913768\pi\) | ||
0.963529 | − | 0.267604i | \(-0.0862320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.87451i | 0.360868i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.4652 | − | 10.4652i | −0.638074 | − | 0.638074i | 0.312006 | − | 0.950080i | \(-0.398999\pi\) |
−0.950080 | + | 0.312006i | \(0.898999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.35425 | 0.385993 | 0.192997 | − | 0.981199i | \(-0.438179\pi\) | ||||
0.192997 | + | 0.981199i | \(0.438179\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.4207 | − | 14.4207i | −0.869599 | − | 0.869599i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.5203 | − | 16.5203i | 0.992606 | − | 0.992606i | −0.00736669 | − | 0.999973i | \(-0.502345\pi\) |
0.999973 | + | 0.00736669i | \(0.00234491\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.38075i | 0.142024i | 0.997475 | + | 0.0710119i | \(0.0226228\pi\) | ||||
−0.997475 | + | 0.0710119i | \(0.977377\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.58301 | − | 2.58301i | 0.153544 | − | 0.153544i | −0.626155 | − | 0.779699i | \(-0.715372\pi\) |
0.779699 | + | 0.626155i | \(0.215372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.0194 | 0.768513 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5830 | 0.799000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.55425 | + | 2.55425i | −0.149221 | + | 0.149221i | −0.777770 | − | 0.628549i | \(-0.783649\pi\) |
0.628549 | + | 0.777770i | \(0.283649\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.16601i | − | 0.300777i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.4821 | − | 11.4821i | 0.664025 | − | 0.664025i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.583005 | − | 0.583005i | −0.0336039 | − | 0.0336039i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.768687 | −0.0440149 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | + | 20.0000i | 1.14146 | + | 1.14146i | 0.988183 | + | 0.153277i | \(0.0489827\pi\) |
0.153277 | + | 0.988183i | \(0.451017\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.67963i | − | 0.492177i | −0.969247 | − | 0.246088i | \(-0.920855\pi\) | ||
0.969247 | − | 0.246088i | \(-0.0791453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.29150i | 0.525187i | 0.964907 | + | 0.262593i | \(0.0845778\pi\) | ||||
−0.964907 | + | 0.262593i | \(0.915422\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.595188 | + | 0.595188i | 0.0334291 | + | 0.0334291i | 0.723624 | − | 0.690195i | \(-0.242475\pi\) |
−0.690195 | + | 0.723624i | \(0.742475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.1660 | −2.30485 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.1617 | + | 20.1617i | 1.12183 | + | 1.12183i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3542 | − | 11.3542i | 0.629820 | − | 0.629820i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.9785i | 0.825792i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | − | 8.00000i | 0.439720 | − | 0.439720i | −0.452198 | − | 0.891918i | \(-0.649360\pi\) |
0.891918 | + | 0.452198i | \(0.149360\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.76150 | 0.260149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.70850 | 0.256488 | 0.128244 | − | 0.991743i | \(-0.459066\pi\) | ||||
0.128244 | + | 0.991743i | \(0.459066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.9713 | − | 18.9713i | 1.02735 | − | 1.02735i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 18.5830i | − | 1.00339i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.36028 | + | 3.36028i | −0.180389 | + | 0.180389i | −0.791526 | − | 0.611136i | \(-0.790713\pi\) |
0.611136 | + | 0.791526i | \(0.290713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.22876 | − | 3.22876i | −0.172831 | − | 0.172831i | 0.615391 | − | 0.788222i | \(-0.288998\pi\) |
−0.788222 | + | 0.615391i | \(0.788998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.14226 | 0.380144 | 0.190072 | − | 0.981770i | \(-0.439128\pi\) | ||||
0.190072 | + | 0.981770i | \(0.439128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | − | 8.00000i | −0.424596 | − | 0.424596i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.76150i | − | 0.251303i | −0.992074 | − | 0.125651i | \(-0.959898\pi\) | ||
0.992074 | − | 0.125651i | \(-0.0401020\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.58301i | 0.399106i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.95906 | + | 1.95906i | 0.102542 | + | 0.102542i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.8118 | 1.81716 | 0.908580 | − | 0.417712i | \(-0.137168\pi\) | ||||
0.908580 | + | 0.417712i | \(0.137168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.12179 | − | 8.12179i | −0.421662 | − | 0.421662i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.9373 | + | 11.9373i | −0.618088 | + | 0.618088i | −0.945041 | − | 0.326953i | \(-0.893978\pi\) |
0.326953 | + | 0.945041i | \(0.393978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 32.4125i | − | 1.66933i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.35425 | + | 8.35425i | −0.429129 | + | 0.429129i | −0.888332 | − | 0.459203i | \(-0.848135\pi\) |
0.459203 | + | 0.888332i | \(0.348135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.10132 | −0.465056 | −0.232528 | − | 0.972590i | \(-0.574700\pi\) | ||||
−0.232528 | + | 0.972590i | \(0.574700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.58301 | −0.335501 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.7569 | + | 20.7569i | −1.05242 | + | 1.05242i | −0.0538679 | + | 0.998548i | \(0.517155\pi\) |
−0.998548 | + | 0.0538679i | \(0.982845\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000i | 1.21373i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.74103 | + | 5.74103i | −0.288863 | + | 0.288863i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.06275 | − | 8.06275i | −0.404658 | − | 0.404658i | 0.475213 | − | 0.879871i | \(-0.342371\pi\) |
−0.879871 | + | 0.475213i | \(0.842371\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5906 | 0.828494 | 0.414247 | − | 0.910165i | \(-0.364045\pi\) | ||||
0.414247 | + | 0.910165i | \(0.364045\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.9373 | + | 14.9373i | 0.744078 | + | 0.744078i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.33981i | 0.215117i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.1660i | − | 1.24438i | −0.782867 | − | 0.622190i | \(-0.786243\pi\) | ||
0.782867 | − | 0.622190i | \(-0.213757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.14226 | + | 7.14226i | 0.351447 | + | 0.351447i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.7605 | − | 18.7605i | −0.916509 | − | 0.916509i | 0.0802643 | − | 0.996774i | \(-0.474424\pi\) |
−0.996774 | + | 0.0802643i | \(0.974424\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3542 | + | 11.3542i | −0.553372 | + | 0.553372i | −0.927412 | − | 0.374040i | \(-0.877972\pi\) |
0.374040 | + | 0.927412i | \(0.377972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.7328i | 1.15121i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.06275 | − | 1.06275i | 0.0514299 | − | 0.0514299i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.2221 | 1.50391 | 0.751957 | − | 0.659212i | \(-0.229110\pi\) | ||||
0.751957 | + | 0.659212i | \(0.229110\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.8219 | + | 15.8219i | −0.756863 | + | 0.756863i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.479741i | − | 0.0228968i | −0.999934 | − | 0.0114484i | \(-0.996356\pi\) | ||
0.999934 | − | 0.0114484i | \(-0.00364422\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.5629 | + | 21.5629i | −1.02449 | + | 1.02449i | −0.0247926 | + | 0.999693i | \(0.507893\pi\) |
−0.999693 | + | 0.0247926i | \(0.992107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.41699 | − | 1.41699i | −0.0671720 | − | 0.0671720i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.44832 | 0.445894 | 0.222947 | − | 0.974831i | \(-0.428432\pi\) | ||||
0.222947 | + | 0.974831i | \(0.428432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.5830 | − | 26.5830i | −1.25174 | − | 1.25174i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 5.18319i | − | 0.242992i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.41699i | 0.253396i | 0.991941 | + | 0.126698i | \(0.0404380\pi\) | ||||
−0.991941 | + | 0.126698i | \(0.959562\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.50613 | − | 8.50613i | −0.396170 | − | 0.396170i | 0.480710 | − | 0.876880i | \(-0.340379\pi\) |
−0.876880 | + | 0.480710i | \(0.840379\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0627 | 0.700025 | 0.350013 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350013 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.4810 | + | 25.4810i | 1.17912 | + | 1.17912i | 0.979968 | + | 0.199154i | \(0.0638194\pi\) |
0.199154 | + | 0.979968i | \(0.436181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.58301 | + | 6.58301i | −0.303975 | + | 0.303975i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.38075i | 0.109467i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.6458 | + | 15.6458i | −0.717876 | + | 0.717876i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.1208 | −1.01072 | −0.505362 | − | 0.862908i | \(-0.668641\pi\) | ||||
−0.505362 | + | 0.862908i | \(0.668641\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.41699 | −0.155802 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.29888 | − | 6.29888i | 0.286017 | − | 0.286017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.22876i | 0.372881i | 0.982466 | + | 0.186440i | \(0.0596951\pi\) | ||||
−0.982466 | + | 0.186440i | \(0.940305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.4002 | + | 15.4002i | −0.695001 | + | 0.695001i | −0.963328 | − | 0.268327i | \(-0.913529\pi\) |
0.268327 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.8745 | + | 33.8745i | 1.52563 | + | 1.52563i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.1208 | 0.992252 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5830 | − | 10.5830i | −0.473760 | − | 0.473760i | 0.429369 | − | 0.903129i | \(-0.358736\pi\) |
−0.903129 | + | 0.429369i | \(0.858736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.6438i | 1.41093i | 0.708747 | + | 0.705463i | \(0.249261\pi\) | ||||
−0.708747 | + | 0.705463i | \(0.750739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.708497i | − | 0.0315277i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.6750 | + | 24.6750i | 1.09370 | + | 1.09370i | 0.995130 | + | 0.0985706i | \(0.0314270\pi\) |
0.0985706 | + | 0.995130i | \(0.468573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.41699 | −0.239634 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.0808 | − | 10.0808i | −0.444215 | − | 0.444215i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.5830 | − | 30.5830i | 1.34504 | − | 1.34504i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 14.2098i | − | 0.622543i | −0.950321 | − | 0.311272i | \(-0.899245\pi\) | ||
0.950321 | − | 0.311272i | \(-0.100755\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9373 | − | 18.9373i | 0.828068 | − | 0.828068i | −0.159181 | − | 0.987249i | \(-0.550885\pi\) |
0.987249 | + | 0.159181i | \(0.0508854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.2221 | −1.36006 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.16601 | 0.181131 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.9304 | − | 20.9304i | 0.906596 | − | 0.906596i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.83399i | − | 0.122524i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.4207 | + | 14.4207i | −0.621142 | + | 0.621142i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5203 | + | 28.5203i | 1.22618 | + | 1.22618i | 0.965397 | + | 0.260785i | \(0.0839813\pi\) |
0.260785 | + | 0.965397i | \(0.416019\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.91094 | −0.338868 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.9373 | − | 14.9373i | −0.638671 | − | 0.638671i | 0.311557 | − | 0.950228i | \(-0.399150\pi\) |
−0.950228 | + | 0.311557i | \(0.899150\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.6632i | 1.90272i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.8745i | − | 0.675053i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.7978 | + | 18.7978i | 0.796489 | + | 0.796489i | 0.982540 | − | 0.186051i | \(-0.0595689\pi\) |
−0.186051 | + | 0.982540i | \(0.559569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.87451 | −0.0792832 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.31935 | + | 5.31935i | 0.224184 | + | 0.224184i | 0.810258 | − | 0.586074i | \(-0.199327\pi\) |
−0.586074 | + | 0.810258i | \(0.699327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.0921i | 1.72267i | 0.508038 | + | 0.861335i | \(0.330371\pi\) | ||||
−0.508038 | + | 0.861335i | \(0.669629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | + | 4.00000i | −0.167395 | + | 0.167395i | −0.785833 | − | 0.618438i | \(-0.787766\pi\) |
0.618438 | + | 0.785833i | \(0.287766\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.6243 | −0.776688 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.0405 | −1.62528 | −0.812639 | − | 0.582767i | \(-0.801970\pi\) | ||||
−0.812639 | + | 0.582767i | \(0.801970\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.53019 | − | 5.53019i | 0.229431 | − | 0.229431i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.1660i | 1.37360i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.76150 | − | 4.76150i | 0.196528 | − | 0.196528i | −0.601982 | − | 0.798510i | \(-0.705622\pi\) |
0.798510 | + | 0.601982i | \(0.205622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.5830 | − | 20.5830i | −0.848108 | − | 0.848108i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.1208 | 0.908391 | 0.454195 | − | 0.890902i | \(-0.349927\pi\) | ||||
0.454195 | + | 0.890902i | \(0.349927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.41699 | + | 5.41699i | 0.222075 | + | 0.222075i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 13.8628i | − | 0.566420i | −0.959058 | − | 0.283210i | \(-0.908601\pi\) | ||
0.959058 | − | 0.283210i | \(-0.0913993\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.29150i | − | 0.134263i | −0.997744 | − | 0.0671316i | \(-0.978615\pi\) | ||
0.997744 | − | 0.0671316i | \(-0.0213847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.89407 | + | 6.89407i | 0.280284 | + | 0.280284i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1033 | 0.572434 | 0.286217 | − | 0.958165i | \(-0.407602\pi\) | ||||
0.286217 | + | 0.958165i | \(0.407602\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0798 | + | 24.0798i | 0.974165 | + | 0.974165i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.6458 | + | 26.6458i | −1.07621 | + | 1.07621i | −0.0793662 | + | 0.996846i | \(0.525290\pi\) |
−0.996846 | + | 0.0793662i | \(0.974710\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.6438i | 1.27393i | 0.770893 | + | 0.636965i | \(0.219810\pi\) | ||||
−0.770893 | + | 0.636965i | \(0.780190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1660 | − | 21.1660i | 0.850734 | − | 0.850734i | −0.139490 | − | 0.990224i | \(-0.544546\pi\) |
0.990224 | + | 0.139490i | \(0.0445462\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.91813 | 0.156976 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.8745 | −0.594980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.57113 | − | 3.57113i | 0.142390 | − | 0.142390i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.22876i | − | 0.327582i | −0.986495 | − | 0.163791i | \(-0.947628\pi\) | ||
0.986495 | − | 0.163791i | \(-0.0523722\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.557842 | + | 0.557842i | −0.0221373 | + | 0.0221373i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.3542 | − | 11.3542i | −0.449872 | − | 0.449872i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5906 | 0.655288 | 0.327644 | − | 0.944801i | \(-0.393745\pi\) | ||||
0.327644 | + | 0.944801i | \(0.393745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.64575 | + | 3.64575i | 0.143774 | + | 0.143774i | 0.775330 | − | 0.631556i | \(-0.217583\pi\) |
−0.631556 | + | 0.775330i | \(0.717583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.33981i | 0.170616i | 0.996355 | + | 0.0853079i | \(0.0271874\pi\) | ||||
−0.996355 | + | 0.0853079i | \(0.972813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.1660i | − | 1.14487i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.7569 | + | 20.7569i | 0.812280 | + | 0.812280i | 0.984975 | − | 0.172696i | \(-0.0552477\pi\) |
−0.172696 | + | 0.984975i | \(0.555248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000 | 0.312586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.9232 | − | 24.9232i | −0.970870 | − | 0.970870i | 0.0287175 | − | 0.999588i | \(-0.490858\pi\) |
−0.999588 | + | 0.0287175i | \(0.990858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.77124 | − | 2.77124i | 0.107789 | − | 0.107789i | −0.651155 | − | 0.758944i | \(-0.725715\pi\) |
0.758944 | + | 0.651155i | \(0.225715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.14226i | 0.276965i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.5830 | + | 26.5830i | −1.02930 | + | 1.02930i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.33981 | −0.167537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.0000 | 0.770943 | 0.385472 | − | 0.922720i | \(-0.374039\pi\) | ||||
0.385472 | + | 0.922720i | \(0.374039\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.0363 | − | 14.0363i | 0.539460 | − | 0.539460i | −0.383911 | − | 0.923370i | \(-0.625423\pi\) |
0.923370 | + | 0.383911i | \(0.125423\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4170i | 0.668403i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.557842 | − | 0.557842i | 0.0213452 | − | 0.0213452i | −0.696354 | − | 0.717699i | \(-0.745195\pi\) |
0.717699 | + | 0.696354i | \(0.245195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.12549 | + | 6.12549i | 0.234043 | + | 0.234043i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.1136 | −0.994848 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.64575 | + | 3.64575i | 0.138691 | + | 0.138691i | 0.773044 | − | 0.634353i | \(-0.218733\pi\) |
−0.634353 | + | 0.773044i | \(0.718733\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.3593i | 0.658474i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.7490i | 1.65711i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.16632 | + | 4.16632i | 0.157360 | + | 0.157360i | 0.781396 | − | 0.624036i | \(-0.214508\pi\) |
−0.624036 | + | 0.781396i | \(0.714508\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.70850 | 0.177584 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.979531 | + | 0.979531i | 0.0368391 | + | 0.0368391i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.77124 | − | 8.77124i | 0.329411 | − | 0.329411i | −0.522951 | − | 0.852362i | \(-0.675169\pi\) |
0.852362 | + | 0.522951i | \(0.175169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 24.5015i | − | 0.917589i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5830 | + | 10.5830i | −0.395782 | + | 0.395782i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.3234 | −1.50381 | −0.751904 | − | 0.659272i | \(-0.770865\pi\) | ||||
−0.751904 | + | 0.659272i | \(0.770865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.8745 | 1.03810 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.2871 | + | 26.2871i | −0.976278 | + | 0.976278i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.3948i | − | 1.23854i | −0.785177 | − | 0.619272i | \(-0.787428\pi\) | ||
0.785177 | − | 0.619272i | \(-0.212572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.95906 | − | 1.95906i | 0.0724586 | − | 0.0724586i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.6458 | + | 12.6458i | 0.467081 | + | 0.467081i | 0.900968 | − | 0.433886i | \(-0.142858\pi\) |
−0.433886 | + | 0.900968i | \(0.642858\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.8823 | 0.990221 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.16601 | + | 9.16601i | 0.337177 | + | 0.337177i | 0.855304 | − | 0.518127i | \(-0.173370\pi\) |
−0.518127 | + | 0.855304i | \(0.673370\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5425i | 0.827002i | 0.910504 | + | 0.413501i | \(0.135694\pi\) | ||||
−0.910504 | + | 0.413501i | \(0.864306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.8745i | − | 0.508323i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.91813 | + | 3.91813i | 0.143165 | + | 0.143165i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.9373 | 0.472087 | 0.236044 | − | 0.971742i | \(-0.424149\pi\) | ||||
0.236044 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.16272 | + | 6.16272i | 0.224284 | + | 0.224284i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.22876 | − | 7.22876i | 0.262734 | − | 0.262734i | −0.563430 | − | 0.826164i | \(-0.690519\pi\) |
0.826164 | + | 0.563430i | \(0.190519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.91094i | 0.286771i | 0.989667 | + | 0.143386i | \(0.0457989\pi\) | ||||
−0.989667 | + | 0.143386i | \(0.954201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.9373 | − | 10.9373i | 0.395955 | − | 0.395955i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.9641 | 0.829187 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.2915 | 0.623548 | 0.311774 | − | 0.950156i | \(-0.399077\pi\) | ||||
0.311774 | + | 0.950156i | \(0.399077\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.5256 | − | 21.5256i | 0.774221 | − | 0.774221i | −0.204620 | − | 0.978841i | \(-0.565596\pi\) |
0.978841 | + | 0.204620i | \(0.0655960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 24.2288i | − | 0.870323i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.8413 | + | 28.8413i | −1.03335 | + | 1.03335i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.1660 | − | 45.1660i | −1.61617 | − | 1.61617i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.91094 | −0.282354 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.22876 | − | 6.22876i | −0.222031 | − | 0.222031i | 0.587322 | − | 0.809353i | \(-0.300182\pi\) |
−0.809353 | + | 0.587322i | \(0.800182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.41699i | − | 0.121341i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.5256 | − | 21.5256i | −0.762475 | − | 0.762475i | 0.214294 | − | 0.976769i | \(-0.431255\pi\) |
−0.976769 | + | 0.214294i | \(0.931255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.3320 | −1.78062 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.0604 | + | 11.0604i | 0.390312 | + | 0.390312i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.25098 | + | 4.25098i | −0.149828 | + | 0.149828i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.4339i | − | 0.612945i | −0.951880 | − | 0.306473i | \(-0.900851\pi\) | ||
0.951880 | − | 0.306473i | \(-0.0991488\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.6458 | − | 15.6458i | 0.549397 | − | 0.549397i | −0.376870 | − | 0.926266i | \(-0.623000\pi\) |
0.926266 | + | 0.376870i | \(0.123000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.8628 | 0.485593 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.58301 | 0.0903679 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.73744 | + | 7.73744i | −0.270039 | + | 0.270039i | −0.829116 | − | 0.559077i | \(-0.811156\pi\) |
0.559077 | + | 0.829116i | \(0.311156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.2288i | − | 1.12342i | −0.827333 | − | 0.561712i | \(-0.810143\pi\) | ||
0.827333 | − | 0.561712i | \(-0.189857\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.33981 | + | 4.33981i | −0.150910 | + | 0.150910i | −0.778524 | − | 0.627614i | \(-0.784032\pi\) |
0.627614 | + | 0.778524i | \(0.284032\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.6458 | − | 14.6458i | −0.508668 | − | 0.508668i | 0.405449 | − | 0.914117i | \(-0.367115\pi\) |
−0.914117 | + | 0.405449i | \(0.867115\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.7328 | 0.822294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5830 | + | 10.5830i | 0.366240 | + | 0.366240i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 52.9212i | − | 1.82704i | −0.406793 | − | 0.913521i | \(-0.633353\pi\) | ||
0.406793 | − | 0.913521i | \(-0.366647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.0405i | 1.58760i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.595188 | − | 0.595188i | −0.0204751 | − | 0.0204751i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0627 | −0.655004 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.80244 | + | 2.80244i | 0.0960664 | + | 0.0960664i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.9373 | + | 11.9373i | −0.408724 | + | 0.408724i | −0.881293 | − | 0.472570i | \(-0.843327\pi\) |
0.472570 | + | 0.881293i | \(0.343327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 10.2917i | − | 0.351558i | −0.984430 | − | 0.175779i | \(-0.943756\pi\) | ||
0.984430 | − | 0.175779i | \(-0.0562443\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.77124 | − | 5.77124i | 0.196912 | − | 0.196912i | −0.601763 | − | 0.798675i | \(-0.705535\pi\) |
0.798675 | + | 0.601763i | \(0.205535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.3428 | 1.81581 | 0.907906 | − | 0.419174i | \(-0.137680\pi\) | ||||
0.907906 | + | 0.419174i | \(0.137680\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.87451 | 0.199739 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.4125 | + | 32.4125i | −1.09952 | + | 1.09952i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.1660i | 0.717183i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.10132 | + | 9.10132i | −0.307681 | + | 0.307681i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.9373 | + | 21.9373i | 0.740768 | + | 0.740768i | 0.972726 | − | 0.231957i | \(-0.0745130\pi\) |
−0.231957 | + | 0.972726i | \(0.574513\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.9785 | −0.504639 | −0.252319 | − | 0.967644i | \(-0.581193\pi\) | ||||
−0.252319 | + | 0.967644i | \(0.581193\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.3948 | + | 35.3948i | 1.19113 | + | 1.19113i | 0.976751 | + | 0.214378i | \(0.0687724\pi\) |
0.214378 | + | 0.976751i | \(0.431228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.76150i | − | 0.159876i | −0.996800 | − | 0.0799378i | \(-0.974528\pi\) | ||
0.996800 | − | 0.0799378i | \(-0.0254722\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.54249i | − | 0.0517333i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.1811 | − | 33.1811i | −1.11036 | − | 1.11036i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.83399 | −0.0947298 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.5824 | − | 34.5824i | −1.15339 | − | 1.15339i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.2915 | − | 27.2915i | 0.909212 | − | 0.909212i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.768687i | 0.0255520i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.1033 | + | 16.1033i | −0.534700 | + | 0.534700i | −0.921967 | − | 0.387267i | \(-0.873419\pi\) |
0.387267 | + | 0.921967i | \(0.373419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.18319 | −0.171727 | −0.0858634 | − | 0.996307i | \(-0.527365\pi\) | ||||
−0.0858634 | + | 0.996307i | \(0.527365\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.5830 | −0.747388 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.0604 | + | 11.0604i | −0.365246 | + | 0.365246i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1033i | 1.38886i | 0.719561 | + | 0.694429i | \(0.244343\pi\) | ||||
−0.719561 | + | 0.694429i | \(0.755657\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.5619 | − | 35.5619i | 1.17053 | − | 1.17053i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.77124 | + | 2.77124i | 0.0911179 | + | 0.0911179i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.7328 | −0.778649 | −0.389324 | − | 0.921101i | \(-0.627291\pi\) | ||||
−0.389324 | + | 0.921101i | \(0.627291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.6458 | + | 15.6458i | 0.512769 | + | 0.512769i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 22.1208i | − | 0.723426i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.1660i | 1.01815i | 0.860722 | + | 0.509075i | \(0.170012\pi\) | ||||
−0.860722 | + | 0.509075i | \(0.829988\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.4243 | − | 12.4243i | −0.405019 | − | 0.405019i | 0.474978 | − | 0.879997i | \(-0.342456\pi\) |
−0.879997 | + | 0.474978i | \(0.842456\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.3320 | −1.11800 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.38075 | + | 2.38075i | 0.0773640 | + | 0.0773640i | 0.744730 | − | 0.667366i | \(-0.232578\pi\) |
−0.667366 | + | 0.744730i | \(0.732578\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.70850 | + | 8.70850i | −0.282690 | + | 0.282690i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25.2702i | − | 0.818582i | −0.912404 | − | 0.409291i | \(-0.865776\pi\) | ||
0.912404 | − | 0.409291i | \(-0.134224\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.41699 | + | 5.41699i | −0.175290 | + | 0.175290i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.9376 | −0.546943 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.874508 | 0.0282099 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.06756 | + | 7.06756i | −0.227513 | + | 0.227513i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.3948i | − | 1.45980i | −0.683555 | − | 0.729899i | \(-0.739567\pi\) | ||
0.683555 | − | 0.729899i | \(-0.260433\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.7195 | − | 20.7195i | 0.664922 | − | 0.664922i | −0.291614 | − | 0.956536i | \(-0.594192\pi\) |
0.956536 | + | 0.291614i | \(0.0941924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | − | 24.0000i | −0.769405 | − | 0.769405i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.5087 | −0.656131 | −0.328066 | − | 0.944655i | \(-0.606397\pi\) | ||||
−0.328066 | + | 0.944655i | \(0.606397\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | − | 8.00000i | −0.255681 | − | 0.255681i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 26.8823i | − | 0.857411i | −0.903444 | − | 0.428706i | \(-0.858970\pi\) | ||
0.903444 | − | 0.428706i | \(-0.141030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1255i | 0.322625i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.53737 | + | 1.53737i | 0.0488856 | + | 0.0488856i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.06275 | 0.0972913 | 0.0486457 | − | 0.998816i | \(-0.484509\pi\) | ||||
0.0486457 | + | 0.998816i | \(0.484509\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.12179 | − | 8.12179i | −0.257478 | − | 0.257478i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.5203 | + | 36.5203i | −1.15661 | + | 1.15661i | −0.171408 | + | 0.985200i | \(0.554832\pi\) |
−0.985200 | + | 0.171408i | \(0.945168\pi\) | |||||||
\(998\) | 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 | 1152.2.k.e.289.2 | 8 | ||
3.2 | odd | 2 | inner | 1152.2.k.e.289.3 | 8 | ||
4.3 | odd | 2 | 1152.2.k.d.289.2 | 8 | |||
8.3 | odd | 2 | 576.2.k.c.145.3 | 8 | |||
8.5 | even | 2 | 144.2.k.c.109.1 | yes | 8 | ||
12.11 | even | 2 | 1152.2.k.d.289.3 | 8 | |||
16.3 | odd | 4 | 576.2.k.c.433.3 | 8 | |||
16.5 | even | 4 | inner | 1152.2.k.e.865.2 | 8 | ||
16.11 | odd | 4 | 1152.2.k.d.865.2 | 8 | |||
16.13 | even | 4 | 144.2.k.c.37.1 | ✓ | 8 | ||
24.5 | odd | 2 | 144.2.k.c.109.4 | yes | 8 | ||
24.11 | even | 2 | 576.2.k.c.145.2 | 8 | |||
32.5 | even | 8 | 9216.2.a.bq.1.3 | 8 | |||
32.11 | odd | 8 | 9216.2.a.bt.1.6 | 8 | |||
32.21 | even | 8 | 9216.2.a.bq.1.6 | 8 | |||
32.27 | odd | 8 | 9216.2.a.bt.1.3 | 8 | |||
48.5 | odd | 4 | inner | 1152.2.k.e.865.3 | 8 | ||
48.11 | even | 4 | 1152.2.k.d.865.3 | 8 | |||
48.29 | odd | 4 | 144.2.k.c.37.4 | yes | 8 | ||
48.35 | even | 4 | 576.2.k.c.433.2 | 8 | |||
96.5 | odd | 8 | 9216.2.a.bq.1.5 | 8 | |||
96.11 | even | 8 | 9216.2.a.bt.1.4 | 8 | |||
96.53 | odd | 8 | 9216.2.a.bq.1.4 | 8 | |||
96.59 | even | 8 | 9216.2.a.bt.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.k.c.37.1 | ✓ | 8 | 16.13 | even | 4 | ||
144.2.k.c.37.4 | yes | 8 | 48.29 | odd | 4 | ||
144.2.k.c.109.1 | yes | 8 | 8.5 | even | 2 | ||
144.2.k.c.109.4 | yes | 8 | 24.5 | odd | 2 | ||
576.2.k.c.145.2 | 8 | 24.11 | even | 2 | |||
576.2.k.c.145.3 | 8 | 8.3 | odd | 2 | |||
576.2.k.c.433.2 | 8 | 48.35 | even | 4 | |||
576.2.k.c.433.3 | 8 | 16.3 | odd | 4 | |||
1152.2.k.d.289.2 | 8 | 4.3 | odd | 2 | |||
1152.2.k.d.289.3 | 8 | 12.11 | even | 2 | |||
1152.2.k.d.865.2 | 8 | 16.11 | odd | 4 | |||
1152.2.k.d.865.3 | 8 | 48.11 | even | 4 | |||
1152.2.k.e.289.2 | 8 | 1.1 | even | 1 | trivial | ||
1152.2.k.e.289.3 | 8 | 3.2 | odd | 2 | inner | ||
1152.2.k.e.865.2 | 8 | 16.5 | even | 4 | inner | ||
1152.2.k.e.865.3 | 8 | 48.5 | odd | 4 | inner | ||
9216.2.a.bq.1.3 | 8 | 32.5 | even | 8 | |||
9216.2.a.bq.1.4 | 8 | 96.53 | odd | 8 | |||
9216.2.a.bq.1.5 | 8 | 96.5 | odd | 8 | |||
9216.2.a.bq.1.6 | 8 | 32.21 | even | 8 | |||
9216.2.a.bt.1.3 | 8 | 32.27 | odd | 8 | |||
9216.2.a.bt.1.4 | 8 | 96.11 | even | 8 | |||
9216.2.a.bt.1.5 | 8 | 96.59 | even | 8 | |||
9216.2.a.bt.1.6 | 8 | 32.11 | odd | 8 |