Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.a (trivial) |
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: | yes |
Analytic conductor: | \(35.1341768894\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 275) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.30278 | −0.752158 | −0.376079 | − | 0.926588i | \(-0.622728\pi\) | ||||
−0.376079 | + | 0.926588i | \(0.622728\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.30278 | 1.62630 | 0.813148 | − | 0.582057i | \(-0.197752\pi\) | ||||
0.813148 | + | 0.582057i | \(0.197752\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.30278 | −0.434259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.90833 | 0.947909 | 0.473954 | − | 0.880549i | \(-0.342826\pi\) | ||||
0.473954 | + | 0.880549i | \(0.342826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.60555 | −1.22323 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.69722 | −0.770925 | −0.385462 | − | 0.922724i | \(-0.625958\pi\) | ||||
−0.385462 | + | 0.922724i | \(0.625958\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.60555 | 1.07879 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.90833 | −1.83993 | −0.919965 | − | 0.392000i | \(-0.871783\pi\) | ||||
−0.919965 | + | 0.392000i | \(0.871783\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.21110 | 0.756336 | 0.378168 | − | 0.925737i | \(-0.376554\pi\) | ||||
0.378168 | + | 0.925737i | \(0.376554\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.30278 | −0.226784 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.60555 | −1.57914 | −0.789571 | − | 0.613659i | \(-0.789697\pi\) | ||||
−0.789571 | + | 0.613659i | \(0.789697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.51388 | 1.04306 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.60555 | 0.250745 | 0.125372 | − | 0.992110i | \(-0.459987\pi\) | ||||
0.125372 | + | 0.992110i | \(0.459987\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.21110 | −1.09968 | −0.549841 | − | 0.835269i | \(-0.685312\pi\) | ||||
−0.549841 | + | 0.835269i | \(0.685312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | −0.437595 | −0.218797 | − | 0.975770i | \(-0.570213\pi\) | ||||
−0.218797 | + | 0.975770i | \(0.570213\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.5139 | 1.64484 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.09167 | −0.712977 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.30278 | −0.316311 | −0.158155 | − | 0.987414i | \(-0.550555\pi\) | ||||
−0.158155 | + | 0.987414i | \(0.550555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.30278 | −0.172557 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.211103 | −0.0274832 | −0.0137416 | − | 0.999906i | \(-0.504374\pi\) | ||||
−0.0137416 | + | 0.999906i | \(0.504374\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.90833 | 0.372373 | 0.186187 | − | 0.982514i | \(-0.440387\pi\) | ||||
0.186187 | + | 0.982514i | \(0.440387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.60555 | −0.706233 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.81665 | 0.579857 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.60555 | −0.546578 | −0.273289 | − | 0.961932i | \(-0.588112\pi\) | ||||
−0.273289 | + | 0.961932i | \(0.588112\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.90833 | −0.340394 | −0.170197 | − | 0.985410i | \(-0.554440\pi\) | ||||
−0.170197 | + | 0.985410i | \(0.554440\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.30278 | 0.490347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0916731 | 0.0103140 | 0.00515701 | − | 0.999987i | \(-0.498358\pi\) | ||||
0.00515701 | + | 0.999987i | \(0.498358\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.5139 | 1.59311 | 0.796553 | − | 0.604569i | \(-0.206655\pi\) | ||||
0.796553 | + | 0.604569i | \(0.206655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.9083 | 1.38392 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.30278 | 0.562093 | 0.281047 | − | 0.959694i | \(-0.409318\pi\) | ||||
0.281047 | + | 0.959694i | \(0.409318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.5139 | −2.25527 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.48612 | −0.568884 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.6972 | −1.18767 | −0.593837 | − | 0.804586i | \(-0.702387\pi\) | ||||
−0.593837 | + | 0.804586i | \(0.702387\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.30278 | −0.130934 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5139 | 1.74270 | 0.871348 | − | 0.490666i | \(-0.163246\pi\) | ||||
0.871348 | + | 0.490666i | \(0.163246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.90833 | −0.779231 | −0.389615 | − | 0.920978i | \(-0.627392\pi\) | ||||
−0.389615 | + | 0.920978i | \(0.627392\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | −0.290021 | −0.145010 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.51388 | −0.623916 | −0.311958 | − | 0.950096i | \(-0.600985\pi\) | ||||
−0.311958 | + | 0.950096i | \(0.600985\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.5139 | 1.18776 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.8167 | −1.01755 | −0.508773 | − | 0.860901i | \(-0.669901\pi\) | ||||
−0.508773 | + | 0.860901i | \(0.669901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.51388 | 0.602208 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.8167 | 1.54158 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.09167 | −0.188600 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1194 | −1.51910 | −0.759552 | − | 0.650447i | \(-0.774582\pi\) | ||||
−0.759552 | + | 0.650447i | \(0.774582\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.39445 | 0.827135 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.908327 | −0.0793609 | −0.0396804 | − | 0.999212i | \(-0.512634\pi\) | ||||
−0.0396804 | + | 0.999212i | \(0.512634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.30278 | 0.373098 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.09167 | 0.178704 | 0.0893518 | − | 0.996000i | \(-0.471520\pi\) | ||||
0.0893518 | + | 0.996000i | \(0.471520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.21110 | −0.696457 | −0.348228 | − | 0.937410i | \(-0.613217\pi\) | ||||
−0.348228 | + | 0.937410i | \(0.613217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.90833 | 0.329141 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.00000 | −0.418121 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.0000 | −1.23718 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.78890 | 0.228475 | 0.114238 | − | 0.993453i | \(-0.463557\pi\) | ||||
0.114238 | + | 0.993453i | \(0.463557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.8167 | 1.69404 | 0.847018 | − | 0.531565i | \(-0.178396\pi\) | ||||
0.847018 | + | 0.531565i | \(0.178396\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.09167 | −0.411637 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.78890 | −0.382196 | −0.191098 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191098 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.9083 | −1.25375 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.69722 | 0.446241 | 0.223121 | − | 0.974791i | \(-0.428376\pi\) | ||||
0.223121 | + | 0.974791i | \(0.428376\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.4222 | −1.19341 | −0.596703 | − | 0.802462i | \(-0.703523\pi\) | ||||
−0.596703 | + | 0.802462i | \(0.703523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.30278 | −0.0996257 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.8167 | −1.27855 | −0.639273 | − | 0.768980i | \(-0.720765\pi\) | ||||
−0.639273 | + | 0.768980i | \(0.720765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.275019 | 0.0206717 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.51388 | 0.412127 | 0.206063 | − | 0.978539i | \(-0.433935\pi\) | ||||
0.206063 | + | 0.978539i | \(0.433935\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.09167 | −0.675779 | −0.337889 | − | 0.941186i | \(-0.609713\pi\) | ||||
−0.337889 | + | 0.941186i | \(0.609713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.78890 | −0.280083 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.90833 | 0.285805 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 24.1194 | 1.75443 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.69722 | −0.484594 | −0.242297 | − | 0.970202i | \(-0.577901\pi\) | ||||
−0.242297 | + | 0.970202i | \(0.577901\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.21110 | 0.0871771 | 0.0435885 | − | 0.999050i | \(-0.486121\pi\) | ||||
0.0435885 | + | 0.999050i | \(0.486121\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.69722 | −0.690899 | −0.345449 | − | 0.938437i | \(-0.612273\pi\) | ||||
−0.345449 | + | 0.938437i | \(0.612273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.5139 | 1.73774 | 0.868871 | − | 0.495038i | \(-0.164846\pi\) | ||||
0.868871 | + | 0.495038i | \(0.164846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.21110 | 0.367563 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −42.6333 | −2.99227 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.81665 | 0.334781 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.2389 | −1.73751 | −0.868757 | − | 0.495238i | \(-0.835081\pi\) | ||||
−0.868757 | + | 0.495238i | \(0.835081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.1194 | 1.23003 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.78890 | 0.256030 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.5416 | −1.31451 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.6333 | 1.38171 | 0.690854 | − | 0.722994i | \(-0.257235\pi\) | ||||
0.690854 | + | 0.722994i | \(0.257235\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.30278 | 0.351958 | 0.175979 | − | 0.984394i | \(-0.443691\pi\) | ||||
0.175979 | + | 0.984394i | \(0.443691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.7250 | 0.906972 | 0.453486 | − | 0.891263i | \(-0.350180\pi\) | ||||
0.453486 | + | 0.891263i | \(0.350180\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.60555 | −0.368818 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.09167 | −0.333567 | −0.166783 | − | 0.985994i | \(-0.553338\pi\) | ||||
−0.166783 | + | 0.985994i | \(0.553338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.119429 | −0.00775778 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.11943 | 0.266464 | 0.133232 | − | 0.991085i | \(-0.457465\pi\) | ||||
0.133232 | + | 0.991085i | \(0.457465\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9361 | −1.60627 | −0.803137 | − | 0.595794i | \(-0.796837\pi\) | ||||
−0.803137 | + | 0.595794i | \(0.796837\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.3944 | −0.795104 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | −0.318142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.9083 | −1.19827 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.90833 | 0.246691 | 0.123346 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123346 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.69722 | −0.232443 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41.3305 | −2.56815 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.9083 | 0.799005 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.18335 | −0.0729683 | −0.0364841 | − | 0.999334i | \(-0.511616\pi\) | ||||
−0.0364841 | + | 0.999334i | \(0.511616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.90833 | −0.422783 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.7250 | −1.44654 | −0.723269 | − | 0.690567i | \(-0.757361\pi\) | ||||
−0.723269 | + | 0.690567i | \(0.757361\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.2111 | −0.863263 | −0.431632 | − | 0.902050i | \(-0.642062\pi\) | ||||
−0.431632 | + | 0.902050i | \(0.642062\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 28.0278 | 1.69632 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.6056 | −1.29815 | −0.649076 | − | 0.760724i | \(-0.724844\pi\) | ||||
−0.649076 | + | 0.760724i | \(0.724844\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.48612 | −0.328446 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8167 | −1.36113 | −0.680564 | − | 0.732689i | \(-0.738265\pi\) | ||||
−0.680564 | + | 0.732689i | \(0.738265\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.69722 | 0.160333 | 0.0801667 | − | 0.996781i | \(-0.474455\pi\) | ||||
0.0801667 | + | 0.996781i | \(0.474455\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.90833 | 0.407786 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.72498 | −0.101469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.2389 | 0.893318 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.2111 | −0.888642 | −0.444321 | − | 0.895868i | \(-0.646555\pi\) | ||||
−0.444321 | + | 0.895868i | \(0.646555\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.60555 | 0.325267 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.4861 | 1.06908 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.0278 | −1.78841 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.8167 | −1.31078 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.09167 | −0.347670 | −0.173835 | − | 0.984775i | \(-0.555616\pi\) | ||||
−0.173835 | + | 0.984775i | \(0.555616\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.3028 | 0.586104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.8167 | 0.953585 | 0.476792 | − | 0.879016i | \(-0.341799\pi\) | ||||
0.476792 | + | 0.879016i | \(0.341799\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.8167 | −1.23315 | −0.616575 | − | 0.787296i | \(-0.711480\pi\) | ||||
−0.616575 | + | 0.787296i | \(0.711480\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.90833 | −0.556507 | −0.278254 | − | 0.960508i | \(-0.589756\pi\) | ||||
−0.278254 | + | 0.960508i | \(0.589756\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.90833 | −0.554760 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.90833 | 0.218142 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.90833 | 0.217465 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.48612 | 0.469284 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.9083 | −0.711659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3944 | 0.791190 | 0.395595 | − | 0.918425i | \(-0.370538\pi\) | ||||
0.395595 | + | 0.918425i | \(0.370538\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.5139 | 0.685756 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.8444 | −1.46231 | −0.731154 | − | 0.682212i | \(-0.761018\pi\) | ||||
−0.731154 | + | 0.682212i | \(0.761018\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.0917 | 0.765355 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.21110 | 0.228044 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4222 | 1.04870 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.51388 | 0.296000 | 0.148000 | − | 0.988987i | \(-0.452716\pi\) | ||||
0.148000 | + | 0.988987i | \(0.452716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.8167 | −1.43546 | −0.717731 | − | 0.696320i | \(-0.754819\pi\) | ||||
−0.717731 | + | 0.696320i | \(0.754819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.0278 | −1.49601 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.6333 | 1.31110 | 0.655549 | − | 0.755152i | \(-0.272437\pi\) | ||||
0.655549 | + | 0.755152i | \(0.272437\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.9083 | −1.15951 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2111 | −0.802811 | −0.401406 | − | 0.915900i | \(-0.631478\pi\) | ||||
−0.401406 | + | 0.915900i | \(0.631478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.30278 | −0.0683780 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3028 | −1.26859 | −0.634297 | − | 0.773089i | \(-0.718710\pi\) | ||||
−0.634297 | + | 0.773089i | \(0.718710\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.09167 | −0.108888 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.90833 | −0.514415 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.42221 | 0.0736390 | 0.0368195 | − | 0.999322i | \(-0.488277\pi\) | ||||
0.0368195 | + | 0.999322i | \(0.488277\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 49.5416 | 2.55152 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.8167 | −1.27475 | −0.637373 | − | 0.770555i | \(-0.719979\pi\) | ||||
−0.637373 | + | 0.770555i | \(0.719979\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.3028 | 1.14261 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6333 | −1.10541 | −0.552705 | − | 0.833377i | \(-0.686404\pi\) | ||||
−0.552705 | + | 0.833377i | \(0.686404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.39445 | 0.477547 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | 0.608424 | 0.304212 | − | 0.952604i | \(-0.401607\pi\) | ||||
0.304212 | + | 0.952604i | \(0.401607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.4500 | −0.730766 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.18335 | 0.0596919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.3028 | −1.26991 | −0.634955 | − | 0.772549i | \(-0.718981\pi\) | ||||
−0.634955 | + | 0.772549i | \(0.718981\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.60555 | −0.280629 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.2111 | −1.35886 | −0.679429 | − | 0.733741i | \(-0.737772\pi\) | ||||
−0.679429 | + | 0.733741i | \(0.737772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.0555 | −1.04885 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.60555 | −0.476129 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.21110 | 0.406013 | 0.203006 | − | 0.979177i | \(-0.434929\pi\) | ||||
0.203006 | + | 0.979177i | \(0.434929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.72498 | −0.134413 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.908327 | −0.0446958 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.6972 | 0.523845 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.6056 | −0.664675 | −0.332337 | − | 0.943161i | \(-0.607837\pi\) | ||||
−0.332337 | + | 0.943161i | \(0.607837\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.30278 | 0.209704 | 0.104852 | − | 0.994488i | \(-0.466563\pi\) | ||||
0.104852 | + | 0.994488i | \(0.466563\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.90833 | 0.190029 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.5139 | 0.605589 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.51388 | 0.314493 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.0000 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00000 | −0.240285 | −0.120142 | − | 0.992757i | \(-0.538335\pi\) | ||||
−0.120142 | + | 0.992757i | \(0.538335\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.69722 | −0.176862 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.6972 | −0.987825 | −0.493912 | − | 0.869512i | \(-0.664434\pi\) | ||||
−0.493912 | + | 0.869512i | \(0.664434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.39445 | −0.0662523 | −0.0331261 | − | 0.999451i | \(-0.510546\pi\) | ||||
−0.0331261 | + | 0.999451i | \(0.510546\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.63331 | −0.171850 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.5139 | 1.95916 | 0.979581 | − | 0.201052i | \(-0.0644361\pi\) | ||||
0.979581 | + | 0.201052i | \(0.0644361\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.60555 | 0.0756025 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.1194 | −1.27418 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.3028 | 1.13684 | 0.568418 | − | 0.822740i | \(-0.307556\pi\) | ||||
0.568418 | + | 0.822740i | \(0.307556\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.9083 | 1.02259 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.7889 | 0.828512 | 0.414256 | − | 0.910161i | \(-0.364042\pi\) | ||||
0.414256 | + | 0.910161i | \(0.364042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.2111 | 1.21813 | 0.609067 | − | 0.793119i | \(-0.291544\pi\) | ||||
0.609067 | + | 0.793119i | \(0.291544\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.6333 | 1.13989 | 0.569947 | − | 0.821682i | \(-0.306964\pi\) | ||||
0.569947 | + | 0.821682i | \(0.306964\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.2111 | −0.794735 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.23886 | 0.287471 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.21110 | −0.331567 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.1833 | 0.602362 | 0.301181 | − | 0.953567i | \(-0.402619\pi\) | ||||
0.301181 | + | 0.953567i | \(0.402619\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.0278 | 2.18988 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.7250 | 0.943019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.2111 | −0.462709 | −0.231355 | − | 0.972869i | \(-0.574316\pi\) | ||||
−0.231355 | + | 0.972869i | \(0.574316\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.42221 | −0.335644 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2111 | 1.09263 | 0.546316 | − | 0.837579i | \(-0.316030\pi\) | ||||
0.546316 | + | 0.837579i | \(0.316030\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.7250 | −1.74409 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.8167 | −0.888898 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.5139 | 0.963093 | 0.481547 | − | 0.876420i | \(-0.340075\pi\) | ||||
0.481547 | + | 0.876420i | \(0.340075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.0917 | 0.897630 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.6056 | 0.740405 | 0.370202 | − | 0.928951i | \(-0.379288\pi\) | ||||
0.370202 | + | 0.928951i | \(0.379288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.6333 | −0.694300 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.3028 | −1.16585 | −0.582925 | − | 0.812526i | \(-0.698092\pi\) | ||||
−0.582925 | + | 0.812526i | \(0.698092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5139 | −0.553581 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.60555 | 0.247491 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | −0.131940 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.9083 | 0.961669 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.4500 | 1.02736 | 0.513681 | − | 0.857981i | \(-0.328282\pi\) | ||||
0.513681 | + | 0.857981i | \(0.328282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.57779 | −0.156446 | −0.0782230 | − | 0.996936i | \(-0.524925\pi\) | ||||
−0.0782230 | + | 0.996936i | \(0.524925\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.4584 | 0.716938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.33053 | −0.405675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.275019 | 0.0119348 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.02776 | −0.347721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.18335 | −0.309984 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.5139 | 0.495938 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.72498 | −0.289130 | −0.144565 | − | 0.989495i | \(-0.546178\pi\) | ||||
−0.144565 | + | 0.989495i | \(0.546178\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.8444 | 0.508292 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1194 | 0.774731 | 0.387365 | − | 0.921926i | \(-0.373385\pi\) | ||||
0.387365 | + | 0.921926i | \(0.373385\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.78890 | −0.161706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.90833 | −0.422109 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.394449 | 0.0167737 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.42221 | 0.399232 | 0.199616 | − | 0.979874i | \(-0.436031\pi\) | ||||
0.199616 | + | 0.979874i | \(0.436031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0555 | 1.52499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.09167 | −0.214971 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.9083 | 0.796891 | 0.398445 | − | 0.917192i | \(-0.369550\pi\) | ||||
0.398445 | + | 0.917192i | \(0.369550\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.6056 | −0.613375 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.1472 | 0.635003 | 0.317502 | − | 0.948258i | \(-0.397156\pi\) | ||||
0.317502 | + | 0.948258i | \(0.397156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.3305 | 0.725260 | 0.362630 | − | 0.931933i | \(-0.381879\pi\) | ||||
0.362630 | + | 0.931933i | \(0.381879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.72498 | 0.364491 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.3583 | 1.30546 | 0.652731 | − | 0.757589i | \(-0.273623\pi\) | ||||
0.652731 | + | 0.757589i | \(0.273623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.57779 | −0.0655709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.4500 | 2.59086 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.30278 | −0.0953712 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.5416 | −1.54951 | −0.774755 | − | 0.632262i | \(-0.782127\pi\) | ||||
−0.774755 | + | 0.632262i | \(0.782127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.21110 | 0.173515 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6333 | 0.519665 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.6056 | 0.558713 | 0.279357 | − | 0.960187i | \(-0.409879\pi\) | ||||
0.279357 | + | 0.960187i | \(0.409879\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.9361 | −1.30706 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0917 | 0.575770 | 0.287885 | − | 0.957665i | \(-0.407048\pi\) | ||||
0.287885 | + | 0.957665i | \(0.407048\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.90833 | 0.363378 | 0.181689 | − | 0.983356i | \(-0.441844\pi\) | ||||
0.181689 | + | 0.983356i | \(0.441844\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.21110 | 0.212213 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.21110 | −0.292690 | −0.146345 | − | 0.989234i | \(-0.546751\pi\) | ||||
−0.146345 | + | 0.989234i | \(0.546751\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 55.5416 | 2.25066 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000 | 0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.1194 | 1.66080 | 0.830399 | − | 0.557169i | \(-0.188112\pi\) | ||||
0.830399 | + | 0.557169i | \(0.188112\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.6056 | −0.426963 | −0.213482 | − | 0.976947i | \(-0.568480\pi\) | ||||
−0.213482 | + | 0.976947i | \(0.568480\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.4222 | −0.700258 | −0.350129 | − | 0.936702i | \(-0.613862\pi\) | ||||
−0.350129 | + | 0.936702i | \(0.613862\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.7250 | −0.831665 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.8167 | 0.914130 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.30278 | −0.0520278 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.5416 | −1.49688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.9361 | 1.58983 | 0.794915 | − | 0.606721i | \(-0.207515\pi\) | ||||
0.794915 | + | 0.606721i | \(0.207515\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.8806 | 1.30689 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −57.5694 | −2.28098 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.00000 | 0.237356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.2111 | 1.66724 | 0.833619 | − | 0.552340i | \(-0.186265\pi\) | ||||
0.833619 | + | 0.552340i | \(0.186265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0000 | −0.867595 | −0.433798 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433798 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2389 | 0.677729 | 0.338865 | − | 0.940835i | \(-0.389957\pi\) | ||||
0.338865 | + | 0.940835i | \(0.389957\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.211103 | −0.00828650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.6056 | −0.925174 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.1194 | 0.748201 | 0.374101 | − | 0.927388i | \(-0.377951\pi\) | ||||
0.374101 | + | 0.927388i | \(0.377951\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.78890 | 0.147819 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0917 | 0.782660 | 0.391330 | − | 0.920250i | \(-0.372015\pi\) | ||||
0.391330 | + | 0.920250i | \(0.372015\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8167 | 0.498510 | 0.249255 | − | 0.968438i | \(-0.419814\pi\) | ||||
0.249255 | + | 0.968438i | \(0.419814\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 25.4584 | 0.988721 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.6333 | 1.41845 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.8806 | −1.03926 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.90833 | 0.112275 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.02776 | 0.232353 | 0.116176 | − | 0.993229i | \(-0.462936\pi\) | ||||
0.116176 | + | 0.993229i | \(0.462936\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.2389 | 1.00844 | 0.504221 | − | 0.863575i | \(-0.331780\pi\) | ||||
0.504221 | + | 0.863575i | \(0.331780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −50.3305 | −1.93151 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.90833 | −0.264728 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.84441 | −0.376686 | −0.188343 | − | 0.982103i | \(-0.560312\pi\) | ||||
−0.188343 | + | 0.982103i | \(0.560312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.8806 | −0.682186 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.5139 | 0.438644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.5416 | 1.00969 | 0.504846 | − | 0.863210i | \(-0.331549\pi\) | ||||
0.504846 | + | 0.863210i | \(0.331549\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.60555 | −0.212937 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.27502 | 0.237683 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.63331 | 0.250895 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.7889 | −1.01180 | −0.505901 | − | 0.862591i | \(-0.668840\pi\) | ||||
−0.505901 | + | 0.862591i | \(0.668840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.60555 | −0.362280 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 75.3583 | 2.83414 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.6333 | 0.436898 | 0.218449 | − | 0.975848i | \(-0.429900\pi\) | ||||
0.218449 | + | 0.975848i | \(0.429900\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.119429 | −0.00447895 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.5694 | −0.583078 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.36669 | −0.200423 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.8167 | −1.07468 | −0.537340 | − | 0.843366i | \(-0.680571\pi\) | ||||
−0.537340 | + | 0.843366i | \(0.680571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.0278 | −1.26726 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.4861 | 1.20817 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.330532 | 0.0122588 | 0.00612938 | − | 0.999981i | \(-0.498049\pi\) | ||||
0.00612938 | + | 0.999981i | \(0.498049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.3305 | 0.975205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.1833 | −1.04240 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.3944 | −0.457799 | −0.228900 | − | 0.973450i | \(-0.573513\pi\) | ||||
−0.228900 | + | 0.973450i | \(0.573513\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.00000 | −0.147342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.88057 | −0.363463 | −0.181731 | − | 0.983348i | \(-0.558170\pi\) | ||||
−0.181731 | + | 0.983348i | \(0.558170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.51388 | 0.239293 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 44.3028 | 1.62531 | 0.812656 | − | 0.582744i | \(-0.198021\pi\) | ||||
0.812656 | + | 0.582744i | \(0.198021\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.9083 | −0.691820 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.9083 | −0.471660 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.66947 | 0.206882 | 0.103441 | − | 0.994636i | \(-0.467015\pi\) | ||||
0.103441 | + | 0.994636i | \(0.467015\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.09167 | −0.185551 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0555 | 0.837967 | 0.418983 | − | 0.907994i | \(-0.362387\pi\) | ||||
0.418983 | + | 0.907994i | \(0.362387\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.81665 | 0.174833 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.4222 | −1.53780 | −0.768902 | − | 0.639367i | \(-0.779197\pi\) | ||||
−0.768902 | + | 0.639367i | \(0.779197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.0278 | −1.01467 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.05551 | 0.0381124 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.8167 | −0.967033 | −0.483517 | − | 0.875335i | \(-0.660641\pi\) | ||||
−0.483517 | + | 0.875335i | \(0.660641\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.4500 | −0.844530 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.1194 | 0.795581 | 0.397790 | − | 0.917476i | \(-0.369777\pi\) | ||||
0.397790 | + | 0.917476i | \(0.369777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 53.8444 | 1.93166 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.60555 | 0.0575248 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.60555 | −0.164800 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −55.5416 | −1.98490 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.21110 | −0.150110 | −0.0750548 | − | 0.997179i | \(-0.523913\pi\) | ||||
−0.0750548 | + | 0.997179i | \(0.523913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.54163 | 0.0548836 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.5416 | −1.65483 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.5416 | −0.516389 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.5139 | 0.514108 | 0.257054 | − | 0.966397i | \(-0.417248\pi\) | ||||
0.257054 | + | 0.966397i | \(0.417248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.7250 | −0.414800 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.90833 | −0.244094 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.90833 | −0.102633 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.9083 | 1.08802 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.63331 | −0.127740 | −0.0638701 | − | 0.997958i | \(-0.520344\pi\) | ||||
−0.0638701 | + | 0.997958i | \(0.520344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.8722 | 1.92682 | 0.963411 | − | 0.268028i | \(-0.0863719\pi\) | ||||
0.963411 | + | 0.268028i | \(0.0863719\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.5139 | 0.649310 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.21110 | −0.252285 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.0278 | 0.979369 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0000 | 0.418803 | 0.209401 | − | 0.977830i | \(-0.432848\pi\) | ||||
0.209401 | + | 0.977830i | \(0.432848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.4222 | −0.363295 | −0.181648 | − | 0.983364i | \(-0.558143\pi\) | ||||
−0.181648 | + | 0.983364i | \(0.558143\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.81665 | −0.271812 | −0.135906 | − | 0.990722i | \(-0.543394\pi\) | ||||
−0.135906 | + | 0.990722i | \(0.543394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.7527 | −1.34594 | −0.672969 | − | 0.739671i | \(-0.734981\pi\) | ||||
−0.672969 | + | 0.739671i | \(0.734981\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.1472 | 0.976415 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45.0000 | 1.55916 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.6056 | 0.815927 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.1194 | −0.556505 | −0.278252 | − | 0.960508i | \(-0.589755\pi\) | ||||
−0.278252 | + | 0.960508i | \(0.589755\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 69.1749 | 2.38534 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.7250 | 1.02378 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.30278 | 0.147845 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.51388 | −0.120596 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.5139 | 1.21740 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.7250 | −0.675370 | −0.337685 | − | 0.941259i | \(-0.609644\pi\) | ||||
−0.337685 | + | 0.941259i | \(0.609644\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | 0.102478 | 0.0512390 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512390 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.6056 | −1.65840 | −0.829200 | − | 0.558952i | \(-0.811204\pi\) | ||||
−0.829200 | + | 0.558952i | \(0.811204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.00000 | −0.306719 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.6056 | −0.667381 | −0.333690 | − | 0.942683i | \(-0.608294\pi\) | ||||
−0.333690 | + | 0.942683i | \(0.608294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.24726 | 0.0763210 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0916731 | 0.00310980 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0000 | 0.677674 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.2389 | 0.515757 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0000 | −0.675352 | −0.337676 | − | 0.941262i | \(-0.609641\pi\) | ||||
−0.337676 | + | 0.941262i | \(0.609641\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.8167 | 0.668399 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.5416 | −1.16374 | −0.581869 | − | 0.813283i | \(-0.697678\pi\) | ||||
−0.581869 | + | 0.813283i | \(0.697678\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.4500 | −0.418975 | −0.209487 | − | 0.977811i | \(-0.567179\pi\) | ||||
−0.209487 | + | 0.977811i | \(0.567179\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.2389 | 1.58613 | 0.793063 | − | 0.609140i | \(-0.208485\pi\) | ||||
0.793063 | + | 0.609140i | \(0.208485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −73.6611 | −2.47051 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.39445 | −0.113718 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.00000 | −0.100391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0833 | −0.804117 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.7250 | −1.39161 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | −0.299833 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 40.4222 | 1.34517 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.8167 | −0.756781 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.2111 | 1.29912 | 0.649561 | − | 0.760310i | \(-0.274953\pi\) | ||||
0.649561 | + | 0.760310i | \(0.274953\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.5139 | 0.480339 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.90833 | −0.129064 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.2111 | −1.35943 | −0.679714 | − | 0.733477i | \(-0.737896\pi\) | ||||
−0.679714 | + | 0.733477i | \(0.737896\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.93608 | 0.261503 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.0278 | 0.757968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.3028 | 0.338388 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.3944 | 1.52215 | 0.761076 | − | 0.648662i | \(-0.224671\pi\) | ||||
0.761076 | + | 0.648662i | \(0.224671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.5139 | 0.377352 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.9083 | −0.717246 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.21110 | −0.170239 | −0.0851196 | − | 0.996371i | \(-0.527127\pi\) | ||||
−0.0851196 | + | 0.996371i | \(0.527127\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.4222 | 0.927524 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.3944 | 1.70801 | 0.854005 | − | 0.520265i | \(-0.174167\pi\) | ||||
0.854005 | + | 0.520265i | \(0.174167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.93608 | −0.193305 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.6333 | −1.19042 | −0.595211 | − | 0.803569i | \(-0.702932\pi\) | ||||
−0.595211 | + | 0.803569i | \(0.702932\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.5416 | 0.472041 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.9083 | 0.418581 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.2666 | 1.59590 | 0.797951 | − | 0.602722i | \(-0.205917\pi\) | ||||
0.797951 | + | 0.602722i | \(0.205917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.9083 | 0.417267 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000 | 0.290625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.2666 | −0.427955 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.90833 | 0.125944 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.09167 | 0.131579 | 0.0657897 | − | 0.997834i | \(-0.479043\pi\) | ||||
0.0657897 | + | 0.997834i | \(0.479043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.09167 | −0.163568 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.3583 | 0.974244 | 0.487122 | − | 0.873334i | \(-0.338047\pi\) | ||||
0.487122 | + | 0.873334i | \(0.338047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.3305 | −1.13264 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.9722 | 0.510997 | 0.255499 | − | 0.966809i | \(-0.417760\pi\) | ||||
0.255499 | + | 0.966809i | \(0.417760\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.30278 | 0.169477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.48612 | 0.270941 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.8444 | −1.55789 | −0.778947 | − | 0.627089i | \(-0.784246\pi\) | ||||
−0.778947 | + | 0.627089i | \(0.784246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.8167 | 0.535280 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.6611 | 0.847773 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.09167 | 0.193508 | 0.0967542 | − | 0.995308i | \(-0.469154\pi\) | ||||
0.0967542 | + | 0.995308i | \(0.469154\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.7527 | −0.595100 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.2750 | −0.452094 | −0.226047 | − | 0.974116i | \(-0.572580\pi\) | ||||
−0.226047 | + | 0.974116i | \(0.572580\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −53.8444 | −1.70356 |
(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 | 4400.2.a.bs.1.1 | 2 | ||
4.3 | odd | 2 | 275.2.a.e.1.1 | ✓ | 2 | ||
5.2 | odd | 4 | 4400.2.b.y.4049.3 | 4 | |||
5.3 | odd | 4 | 4400.2.b.y.4049.2 | 4 | |||
5.4 | even | 2 | 4400.2.a.bh.1.2 | 2 | |||
12.11 | even | 2 | 2475.2.a.t.1.2 | 2 | |||
20.3 | even | 4 | 275.2.b.c.199.4 | 4 | |||
20.7 | even | 4 | 275.2.b.c.199.1 | 4 | |||
20.19 | odd | 2 | 275.2.a.f.1.2 | yes | 2 | ||
44.43 | even | 2 | 3025.2.a.n.1.2 | 2 | |||
60.23 | odd | 4 | 2475.2.c.k.199.1 | 4 | |||
60.47 | odd | 4 | 2475.2.c.k.199.4 | 4 | |||
60.59 | even | 2 | 2475.2.a.o.1.1 | 2 | |||
220.219 | even | 2 | 3025.2.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.a.e.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
275.2.a.f.1.2 | yes | 2 | 20.19 | odd | 2 | ||
275.2.b.c.199.1 | 4 | 20.7 | even | 4 | |||
275.2.b.c.199.4 | 4 | 20.3 | even | 4 | |||
2475.2.a.o.1.1 | 2 | 60.59 | even | 2 | |||
2475.2.a.t.1.2 | 2 | 12.11 | even | 2 | |||
2475.2.c.k.199.1 | 4 | 60.23 | odd | 4 | |||
2475.2.c.k.199.4 | 4 | 60.47 | odd | 4 | |||
3025.2.a.h.1.1 | 2 | 220.219 | even | 2 | |||
3025.2.a.n.1.2 | 2 | 44.43 | even | 2 | |||
4400.2.a.bh.1.2 | 2 | 5.4 | even | 2 | |||
4400.2.a.bs.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.b.y.4049.2 | 4 | 5.3 | odd | 4 | |||
4400.2.b.y.4049.3 | 4 | 5.2 | odd | 4 |