Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5600,2,Mod(1,5600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5600, 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("5600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5600.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: | \(44.7162251319\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.504568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1120) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.52064\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5600.1 |
$q$-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 | ||||||||
\(3\) | −1.83297 | −1.05827 | −0.529133 | − | 0.848539i | \(-0.677483\pi\) | ||||
−0.529133 | + | 0.848539i | \(0.677483\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.359777 | 0.119926 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.40105 | −1.32697 | −0.663483 | − | 0.748191i | \(-0.730923\pi\) | ||||
−0.663483 | + | 0.748191i | \(0.730923\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.20830 | −0.889823 | −0.444911 | − | 0.895575i | \(-0.646765\pi\) | ||||
−0.444911 | + | 0.895575i | \(0.646765\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.14821 | 0.278482 | 0.139241 | − | 0.990259i | \(-0.455534\pi\) | ||||
0.139241 | + | 0.990259i | \(0.455534\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.72603 | 0.395979 | 0.197990 | − | 0.980204i | \(-0.436559\pi\) | ||||
0.197990 | + | 0.980204i | \(0.436559\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.83297 | −0.399987 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.25284 | 0.678264 | 0.339132 | − | 0.940739i | \(-0.389867\pi\) | ||||
0.339132 | + | 0.940739i | \(0.389867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.83945 | 0.931352 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.18948 | 0.777967 | 0.388983 | − | 0.921245i | \(-0.372826\pi\) | ||||
0.388983 | + | 0.921245i | \(0.372826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.36952 | −0.245973 | −0.122987 | − | 0.992408i | \(-0.539247\pi\) | ||||
−0.122987 | + | 0.992408i | \(0.539247\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.06699 | 1.40428 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.19923 | 0.690348 | 0.345174 | − | 0.938539i | \(-0.387820\pi\) | ||||
0.345174 | + | 0.938539i | \(0.387820\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.88072 | 0.941669 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7485 | 1.83480 | 0.917402 | − | 0.397961i | \(-0.130282\pi\) | ||||
0.917402 | + | 0.397961i | \(0.130282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.64997 | −0.404116 | −0.202058 | − | 0.979374i | \(-0.564763\pi\) | ||||
−0.202058 | + | 0.979374i | \(0.564763\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.106937 | 0.0155983 | 0.00779917 | − | 0.999970i | \(-0.497517\pi\) | ||||
0.00779917 | + | 0.999970i | \(0.497517\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.10463 | −0.294707 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.86516 | 1.08036 | 0.540182 | − | 0.841548i | \(-0.318356\pi\) | ||||
0.540182 | + | 0.841548i | \(0.318356\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.16376 | −0.419051 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.3029 | −1.73189 | −0.865945 | − | 0.500140i | \(-0.833282\pi\) | ||||
−0.865945 | + | 0.500140i | \(0.833282\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0224 | −1.28324 | −0.641622 | − | 0.767021i | \(-0.721738\pi\) | ||||
−0.641622 | + | 0.767021i | \(0.721738\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.359777 | 0.0453276 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.28045 | 0.156431 | 0.0782157 | − | 0.996936i | \(-0.475078\pi\) | ||||
0.0782157 | + | 0.996936i | \(0.475078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.96236 | −0.717783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1616 | −1.68067 | −0.840335 | − | 0.542067i | \(-0.817642\pi\) | ||||
−0.840335 | + | 0.542067i | \(0.817642\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8652 | 1.38871 | 0.694356 | − | 0.719631i | \(-0.255689\pi\) | ||||
0.694356 | + | 0.719631i | \(0.255689\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.40105 | −0.501546 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.48227 | −0.616804 | −0.308402 | − | 0.951256i | \(-0.599794\pi\) | ||||
−0.308402 | + | 0.951256i | \(0.599794\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.94989 | −1.10554 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.1586 | −1.88340 | −0.941701 | − | 0.336451i | \(-0.890773\pi\) | ||||
−0.941701 | + | 0.336451i | \(0.890773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.67919 | −0.823296 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.31591 | 0.457485 | 0.228743 | − | 0.973487i | \(-0.426539\pi\) | ||||
0.228743 | + | 0.973487i | \(0.426539\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.20830 | −0.336321 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.51029 | 0.260305 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.65389 | 0.777135 | 0.388567 | − | 0.921420i | \(-0.372970\pi\) | ||||
0.388567 | + | 0.921420i | \(0.372970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.58340 | −0.159137 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.25581 | −0.224462 | −0.112231 | − | 0.993682i | \(-0.535800\pi\) | ||||
−0.112231 | + | 0.993682i | \(0.535800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.61262 | 0.651560 | 0.325780 | − | 0.945446i | \(-0.394373\pi\) | ||||
0.325780 | + | 0.945446i | \(0.394373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.83756 | 0.564338 | 0.282169 | − | 0.959365i | \(-0.408946\pi\) | ||||
0.282169 | + | 0.959365i | \(0.408946\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6952 | −1.02441 | −0.512205 | − | 0.858863i | \(-0.671171\pi\) | ||||
−0.512205 | + | 0.858863i | \(0.671171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.69705 | −0.730572 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.867348 | −0.0815932 | −0.0407966 | − | 0.999167i | \(-0.512990\pi\) | ||||
−0.0407966 | + | 0.999167i | \(0.512990\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.15427 | −0.106713 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.14821 | 0.105256 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.36923 | 0.760839 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.5346 | −1.94171 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6158 | 1.29695 | 0.648473 | − | 0.761238i | \(-0.275408\pi\) | ||||
0.648473 | + | 0.761238i | \(0.275408\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.85731 | 0.427662 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8600 | 1.56044 | 0.780218 | − | 0.625508i | \(-0.215108\pi\) | ||||
0.780218 | + | 0.625508i | \(0.215108\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.72603 | 0.149666 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.22523 | −0.446422 | −0.223211 | − | 0.974770i | \(-0.571654\pi\) | ||||
−0.223211 | + | 0.974770i | \(0.571654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.25800 | −0.445977 | −0.222989 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222989 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.196012 | −0.0165072 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.1199 | 1.18076 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.83297 | −0.151181 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.8928 | −0.974294 | −0.487147 | − | 0.873320i | \(-0.661962\pi\) | ||||
−0.487147 | + | 0.873320i | \(0.661962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.54534 | −0.695410 | −0.347705 | − | 0.937604i | \(-0.613039\pi\) | ||||
−0.347705 | + | 0.937604i | \(0.613039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.413099 | 0.0333971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.36436 | −0.268506 | −0.134253 | − | 0.990947i | \(-0.542863\pi\) | ||||
−0.134253 | + | 0.990947i | \(0.542863\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.4166 | −1.14331 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.25284 | 0.256360 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.8310 | 1.23998 | 0.619991 | − | 0.784609i | \(-0.287136\pi\) | ||||
0.619991 | + | 0.784609i | \(0.287136\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.8843 | −1.61608 | −0.808040 | − | 0.589128i | \(-0.799471\pi\) | ||||
−0.808040 | + | 0.589128i | \(0.799471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70680 | −0.208215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.620986 | 0.0474880 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.94735 | 0.452168 | 0.226084 | − | 0.974108i | \(-0.427408\pi\) | ||||
0.226084 | + | 0.974108i | \(0.427408\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.3838 | 1.83280 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.9041 | −1.71194 | −0.855968 | − | 0.517030i | \(-0.827038\pi\) | ||||
−0.855968 | + | 0.517030i | \(0.827038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.77746 | −0.132118 | −0.0660589 | − | 0.997816i | \(-0.521043\pi\) | ||||
−0.0660589 | + | 0.997816i | \(0.521043\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.3708 | 1.35801 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.05332 | −0.369536 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.83945 | 0.352018 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.7183 | 1.42676 | 0.713382 | − | 0.700775i | \(-0.247162\pi\) | ||||
0.713382 | + | 0.700775i | \(0.247162\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4956 | −1.33135 | −0.665673 | − | 0.746244i | \(-0.731855\pi\) | ||||
−0.665673 | + | 0.746244i | \(0.731855\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.4179 | 1.38347 | 0.691735 | − | 0.722151i | \(-0.256847\pi\) | ||||
0.691735 | + | 0.722151i | \(0.256847\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.7485 | −1.54171 | −0.770855 | − | 0.637011i | \(-0.780170\pi\) | ||||
−0.770855 | + | 0.637011i | \(0.780170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.34702 | −0.165546 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.18948 | 0.294044 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.17030 | 0.0813412 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.59635 | −0.525451 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.2091 | −1.59778 | −0.798890 | − | 0.601477i | \(-0.794579\pi\) | ||||
−0.798890 | + | 0.601477i | \(0.794579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.9577 | 1.77860 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.36952 | −0.0929692 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.7485 | −1.46963 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.68380 | −0.247799 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.784235 | −0.0525163 | −0.0262581 | − | 0.999655i | \(-0.508359\pi\) | ||||
−0.0262581 | + | 0.999655i | \(0.508359\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7257 | −0.778265 | −0.389132 | − | 0.921182i | \(-0.627225\pi\) | ||||
−0.389132 | + | 0.921182i | \(0.627225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.09555 | −0.0723962 | −0.0361981 | − | 0.999345i | \(-0.511525\pi\) | ||||
−0.0361981 | + | 0.999345i | \(0.511525\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.06699 | 0.530769 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.3345 | −1.65972 | −0.829860 | − | 0.557972i | \(-0.811580\pi\) | ||||
−0.829860 | + | 0.557972i | \(0.811580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0488 | 0.652742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −28.8886 | −1.86865 | −0.934323 | − | 0.356427i | \(-0.883995\pi\) | ||||
−0.934323 | + | 0.356427i | \(0.883995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2542 | 0.660529 | 0.330264 | − | 0.943888i | \(-0.392862\pi\) | ||||
0.330264 | + | 0.943888i | \(0.392862\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.71950 | 0.238606 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.53763 | −0.352351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.4512 | 1.99314 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.5389 | 1.73824 | 0.869120 | − | 0.494601i | \(-0.164686\pi\) | ||||
0.869120 | + | 0.494601i | \(0.164686\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.3159 | −0.900033 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.2636 | −0.764983 | −0.382492 | − | 0.923959i | \(-0.624934\pi\) | ||||
−0.382492 | + | 0.923959i | \(0.624934\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.19923 | 0.260927 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.50728 | 0.0932982 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.8928 | 1.10332 | 0.551658 | − | 0.834071i | \(-0.313995\pi\) | ||||
0.551658 | + | 0.834071i | \(0.313995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.91092 | −0.484141 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.2295 | 1.53827 | 0.769136 | − | 0.639085i | \(-0.220687\pi\) | ||||
0.769136 | + | 0.639085i | \(0.220687\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.65999 | −0.586803 | −0.293401 | − | 0.955989i | \(-0.594787\pi\) | ||||
−0.293401 | + | 0.955989i | \(0.594787\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.88072 | 0.355917 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.1970 | −1.39378 | −0.696888 | − | 0.717180i | \(-0.745432\pi\) | ||||
−0.696888 | + | 0.717180i | \(0.745432\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.492722 | −0.0294985 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.9734 | 1.60910 | 0.804550 | − | 0.593885i | \(-0.202407\pi\) | ||||
0.804550 | + | 0.593885i | \(0.202407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.2119 | −1.32036 | −0.660181 | − | 0.751106i | \(-0.729520\pi\) | ||||
−0.660181 | + | 0.751106i | \(0.729520\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.7485 | 0.693491 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6816 | −0.922448 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0293 | −0.822415 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.8756 | −1.21956 | −0.609782 | − | 0.792569i | \(-0.708743\pi\) | ||||
−0.609782 | + | 0.792569i | \(0.708743\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.2986 | −1.23587 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4361 | −0.603535 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.64997 | −0.152742 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.13484 | 0.237540 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.97374 | 0.169720 | 0.0848601 | − | 0.996393i | \(-0.472956\pi\) | ||||
0.0848601 | + | 0.996393i | \(0.472956\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.1207 | −0.689524 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.04007 | −0.0589770 | −0.0294885 | − | 0.999565i | \(-0.509388\pi\) | ||||
−0.0294885 | + | 0.999565i | \(0.509388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.12411 | 0.515725 | 0.257863 | − | 0.966182i | \(-0.416982\pi\) | ||||
0.257863 | + | 0.966182i | \(0.416982\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.74255 | 0.266368 | 0.133184 | − | 0.991091i | \(-0.457480\pi\) | ||||
0.133184 | + | 0.991091i | \(0.457480\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.4381 | −1.03234 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.7001 | −0.597219 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.98185 | 0.110273 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.6039 | 1.08410 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.106937 | 0.00589562 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.38114 | −0.515634 | −0.257817 | − | 0.966194i | \(-0.583003\pi\) | ||||
−0.257817 | + | 0.966194i | \(0.583003\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.51078 | 0.0827904 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.4797 | −0.952178 | −0.476089 | − | 0.879397i | \(-0.657946\pi\) | ||||
−0.476089 | + | 0.879397i | \(0.657946\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.58982 | 0.0863472 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.02733 | 0.326398 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.2623 | −1.03405 | −0.517027 | − | 0.855969i | \(-0.672961\pi\) | ||||
−0.517027 | + | 0.855969i | \(0.672961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.5730 | 1.52948 | 0.764740 | − | 0.644339i | \(-0.222868\pi\) | ||||
0.764740 | + | 0.644339i | \(0.222868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.5264 | −0.828739 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.8293 | 1.26831 | 0.634153 | − | 0.773208i | \(-0.281349\pi\) | ||||
0.634153 | + | 0.773208i | \(0.281349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.10463 | −0.111389 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.03194 | 0.107242 | 0.0536209 | − | 0.998561i | \(-0.482924\pi\) | ||||
0.0536209 | + | 0.998561i | \(0.482924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0208 | −0.843201 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.3405 | −0.805170 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6965 | 1.18475 | 0.592374 | − | 0.805663i | \(-0.298191\pi\) | ||||
0.592374 | + | 0.805663i | \(0.298191\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.22683 | 0.220040 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.86516 | 0.408339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.2909 | −1.56841 | −0.784203 | − | 0.620505i | \(-0.786928\pi\) | ||||
−0.784203 | + | 0.620505i | \(0.786928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.4411 | −0.692253 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9783 | −0.769385 | −0.384692 | − | 0.923045i | \(-0.625693\pi\) | ||||
−0.384692 | + | 0.923045i | \(0.625693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.7904 | −1.37251 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.37413 | 0.274605 | 0.137303 | − | 0.990529i | \(-0.456157\pi\) | ||||
0.137303 | + | 0.990529i | \(0.456157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.953397 | −0.0484639 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.87331 | −0.145683 | −0.0728413 | − | 0.997344i | \(-0.523207\pi\) | ||||
−0.0728413 | + | 0.997344i | \(0.523207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.73494 | 0.188884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.7368 | −1.65136 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.2887 | −1.21901 | −0.609507 | − | 0.792781i | \(-0.708632\pi\) | ||||
−0.609507 | + | 0.792781i | \(0.708632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.16376 | −0.158386 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7274 | 0.635575 | 0.317787 | − | 0.948162i | \(-0.397060\pi\) | ||||
0.317787 | + | 0.948162i | \(0.397060\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.39384 | 0.218873 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.4810 | −0.916069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0455 | −0.496717 | −0.248359 | − | 0.968668i | \(-0.579891\pi\) | ||||
−0.248359 | + | 0.968668i | \(0.579891\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.57769 | 0.472433 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.3029 | −0.654593 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.63775 | 0.471962 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.2433 | −0.793539 | −0.396769 | − | 0.917918i | \(-0.629869\pi\) | ||||
−0.396769 | + | 0.917918i | \(0.629869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.8066 | −1.55016 | −0.775080 | − | 0.631863i | \(-0.782291\pi\) | ||||
−0.775080 | + | 0.631863i | \(0.782291\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.0384734 | 0.00187064 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0224 | −0.485020 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −25.8813 | −1.24956 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.8177 | 0.906414 | 0.453207 | − | 0.891405i | \(-0.350280\pi\) | ||||
0.453207 | + | 0.891405i | \(0.350280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.5825 | −1.03719 | −0.518595 | − | 0.855020i | \(-0.673545\pi\) | ||||
−0.518595 | + | 0.855020i | \(0.673545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.61451 | 0.268578 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.69487 | 0.128619 | 0.0643095 | − | 0.997930i | \(-0.479516\pi\) | ||||
0.0643095 | + | 0.997930i | \(0.479516\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.359777 | 0.0171322 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.5368 | −0.880710 | −0.440355 | − | 0.897824i | \(-0.645147\pi\) | ||||
−0.440355 | + | 0.897824i | \(0.645147\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.7991 | 1.03106 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.6816 | −0.598483 | −0.299241 | − | 0.954177i | \(-0.596734\pi\) | ||||
−0.299241 | + | 0.954177i | \(0.596734\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −51.7056 | −2.43472 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.6633 | 0.735928 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5381 | 0.913954 | 0.456977 | − | 0.889478i | \(-0.348932\pi\) | ||||
0.456977 | + | 0.889478i | \(0.348932\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.55670 | 0.259364 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.9929 | 0.698291 | 0.349145 | − | 0.937069i | \(-0.386472\pi\) | ||||
0.349145 | + | 0.937069i | \(0.386472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.9309 | −1.15864 | −0.579318 | − | 0.815102i | \(-0.696681\pi\) | ||||
−0.579318 | + | 0.815102i | \(0.696681\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.4350 | −1.40836 | −0.704181 | − | 0.710020i | \(-0.748686\pi\) | ||||
−0.704181 | + | 0.710020i | \(0.748686\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.28045 | 0.0591255 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.16678 | 0.284150 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6626 | 0.536249 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.82970 | 0.129563 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.9694 | 0.821041 | 0.410521 | − | 0.911851i | \(-0.365347\pi\) | ||||
0.410521 | + | 0.911851i | \(0.365347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.4724 | −0.614288 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.96236 | −0.271297 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.51295 | 0.431073 | 0.215536 | − | 0.976496i | \(-0.430850\pi\) | ||||
0.215536 | + | 0.976496i | \(0.430850\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.0178 | −1.31223 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.0466 | −0.949822 | −0.474911 | − | 0.880034i | \(-0.657520\pi\) | ||||
−0.474911 | + | 0.880034i | \(0.657520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.81040 | 0.216649 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.1616 | −0.635234 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.4408 | 1.63131 | 0.815656 | − | 0.578537i | \(-0.196376\pi\) | ||||
0.815656 | + | 0.578537i | \(0.196376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.2804 | 1.71024 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.1783 | 1.43476 | 0.717381 | − | 0.696681i | \(-0.245341\pi\) | ||||
0.717381 | + | 0.696681i | \(0.245341\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.96147 | 0.220347 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.06604 | 0.0915756 | 0.0457878 | − | 0.998951i | \(-0.485420\pi\) | ||||
0.0457878 | + | 0.998951i | \(0.485420\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.8652 | 0.524884 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.35305 | 0.368796 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.470634 | −0.0206985 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.9013 | −0.478514 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0609 | −1.01032 | −0.505158 | − | 0.863027i | \(-0.668566\pi\) | ||||
−0.505158 | + | 0.863027i | \(0.668566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.1602 | −1.14391 | −0.571953 | − | 0.820286i | \(-0.693814\pi\) | ||||
−0.571953 | + | 0.820286i | \(0.693814\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.57250 | −0.0684990 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4190 | −0.539958 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.78607 | −0.207698 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −37.6927 | −1.63265 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 41.9826 | 1.81168 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.40105 | −0.189567 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.2094 | 1.77173 | 0.885866 | − | 0.463941i | \(-0.153565\pi\) | ||||
0.885866 | + | 0.463941i | \(0.153565\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.25804 | 0.139816 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.67055 | 0.327969 | 0.163985 | − | 0.986463i | \(-0.447565\pi\) | ||||
0.163985 | + | 0.986463i | \(0.447565\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.60585 | −0.153894 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.23118 | 0.308059 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.48227 | −0.233130 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.8600 | −1.34995 | −0.674975 | − | 0.737841i | \(-0.735846\pi\) | ||||
−0.674975 | + | 0.737841i | \(0.735846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.50190 | 0.359592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.26258 | 0.391067 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.20351 | 0.387882 | 0.193941 | − | 0.981013i | \(-0.437873\pi\) | ||||
0.193941 | + | 0.981013i | \(0.437873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.94989 | −0.417856 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.47615 | 0.355339 | 0.177669 | − | 0.984090i | \(-0.443144\pi\) | ||||
0.177669 | + | 0.984090i | \(0.443144\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.1245 | −0.549245 | −0.274622 | − | 0.961552i | \(-0.588553\pi\) | ||||
−0.274622 | + | 0.961552i | \(0.588553\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.1430 | −1.50990 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.5640 | −0.689567 | −0.344783 | − | 0.938682i | \(-0.612048\pi\) | ||||
−0.344783 | + | 0.938682i | \(0.612048\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.9019 | 1.40892 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.1586 | −0.711859 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.6150 | −1.43361 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.890659 | −0.0367614 | −0.0183807 | − | 0.999831i | \(-0.505851\pi\) | ||||
−0.0183807 | + | 0.999831i | \(0.505851\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.36384 | −0.0974003 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.5925 | −1.46408 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.12654 | −0.333717 | −0.166858 | − | 0.985981i | \(-0.553362\pi\) | ||||
−0.166858 | + | 0.985981i | \(0.553362\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.8643 | 1.63154 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.38288 | −0.383374 | −0.191687 | − | 0.981456i | \(-0.561396\pi\) | ||||
−0.191687 | + | 0.981456i | \(0.561396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.44289 | −0.222020 | −0.111010 | − | 0.993819i | \(-0.535409\pi\) | ||||
−0.111010 | + | 0.993819i | \(0.535409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.460675 | 0.0187601 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.7479 | 1.49155 | 0.745776 | − | 0.666197i | \(-0.232079\pi\) | ||||
0.745776 | + | 0.666197i | \(0.232079\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.67919 | −0.311176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.343086 | −0.0138798 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.8238 | −0.679505 | −0.339753 | − | 0.940515i | \(-0.610343\pi\) | ||||
−0.339753 | + | 0.940515i | \(0.610343\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.67406 | −0.228429 | −0.114214 | − | 0.993456i | \(-0.536435\pi\) | ||||
−0.114214 | + | 0.993456i | \(0.536435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.33702 | 0.174320 | 0.0871598 | − | 0.996194i | \(-0.472221\pi\) | ||||
0.0871598 | + | 0.996194i | \(0.472221\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.7420 | 0.631703 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.31591 | 0.172913 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.9239 | 0.556066 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.82159 | 0.192249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.9784 | −1.67113 | −0.835567 | − | 0.549389i | \(-0.814860\pi\) | ||||
−0.835567 | + | 0.549389i | \(0.814860\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.5416 | 1.69088 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.20830 | −0.127118 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.09501 | −0.201555 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.4035 | −1.59584 | −0.797922 | − | 0.602761i | \(-0.794067\pi\) | ||||
−0.797922 | + | 0.602761i | \(0.794067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.7826 | 1.13507 | 0.567537 | − | 0.823348i | \(-0.307896\pi\) | ||||
0.567537 | + | 0.823348i | \(0.307896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 50.0475 | 1.96757 | 0.983786 | − | 0.179346i | \(-0.0573983\pi\) | ||||
0.983786 | + | 0.179346i | \(0.0573983\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 58.5467 | 2.29816 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.51029 | 0.0983861 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.5622 | 1.54819 | 0.774095 | − | 0.633070i | \(-0.218205\pi\) | ||||
0.774095 | + | 0.633070i | \(0.218205\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.26881 | 0.166542 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.0994 | −0.393418 | −0.196709 | − | 0.980462i | \(-0.563025\pi\) | ||||
−0.196709 | + | 0.980462i | \(0.563025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.51434 | −0.175588 | −0.0877938 | − | 0.996139i | \(-0.527982\pi\) | ||||
−0.0877938 | + | 0.996139i | \(0.527982\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.75229 | 0.262237 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6277 | 0.527667 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.43748 | 0.0555762 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.1093 | 1.70282 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.62104 | −0.139581 | −0.0697904 | − | 0.997562i | \(-0.522233\pi\) | ||||
−0.0697904 | + | 0.997562i | \(0.522233\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.1617 | −1.35137 | −0.675687 | − | 0.737189i | \(-0.736153\pi\) | ||||
−0.675687 | + | 0.737189i | \(0.736153\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.65389 | 0.293729 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.4929 | 0.823611 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.39058 | 0.168001 | 0.0840005 | − | 0.996466i | \(-0.473230\pi\) | ||||
0.0840005 | + | 0.996466i | \(0.473230\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.00812 | 0.0766144 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.2338 | −0.961332 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.28314 | 0.239022 | 0.119511 | − | 0.992833i | \(-0.461867\pi\) | ||||
0.119511 | + | 0.992833i | \(0.461867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.58340 | −0.0601482 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4897 | 0.510959 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.4374 | 1.75642 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.41413 | 0.204489 | 0.102244 | − | 0.994759i | \(-0.467398\pi\) | ||||
0.102244 | + | 0.994759i | \(0.467398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.24800 | 0.273363 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.25581 | −0.0848386 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5284 | 0.583180 | 0.291590 | − | 0.956543i | \(-0.405816\pi\) | ||||
0.291590 | + | 0.956543i | \(0.405816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.97239 | −0.0739705 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.45483 | −0.166835 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 52.9519 | 1.97752 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.9304 | 0.743279 | 0.371640 | − | 0.928377i | \(-0.378796\pi\) | ||||
0.371640 | + | 0.928377i | \(0.378796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.61262 | 0.246267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.7956 | −0.699015 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0839 | −0.893222 | −0.446611 | − | 0.894728i | \(-0.647369\pi\) | ||||
−0.446611 | + | 0.894728i | \(0.647369\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0319 | 0.853035 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.04272 | −0.112539 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8771 | 1.32515 | 0.662576 | − | 0.748994i | \(-0.269463\pi\) | ||||
0.662576 | + | 0.748994i | \(0.269463\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.63531 | −0.207579 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.29734 | 0.0477233 | 0.0238617 | − | 0.999715i | \(-0.492404\pi\) | ||||
0.0238617 | + | 0.999715i | \(0.492404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.1503 | 0.372881 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.53790 | 0.313225 | 0.156613 | − | 0.987660i | \(-0.449943\pi\) | ||||
0.156613 | + | 0.987660i | \(0.449943\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.17327 | −0.225868 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.83756 | 0.213300 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5930 | −0.641978 | −0.320989 | − | 0.947083i | \(-0.604015\pi\) | ||||
−0.320989 | + | 0.947083i | \(0.604015\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.4780 | −1.83952 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.5195 | −1.21829 | −0.609143 | − | 0.793061i | \(-0.708486\pi\) | ||||
−0.609143 | + | 0.793061i | \(0.708486\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.2406 | 0.952474 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.8063 | −0.935479 | −0.467740 | − | 0.883866i | \(-0.654931\pi\) | ||||
−0.467740 | + | 0.883866i | \(0.654931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.6952 | −0.387191 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.6797 | 1.54108 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.6616 | −0.997502 | −0.498751 | − | 0.866745i | \(-0.666208\pi\) | ||||
−0.498751 | + | 0.866745i | \(0.666208\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4788 | 0.809555 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 49.4294 | 1.77785 | 0.888927 | − | 0.458050i | \(-0.151452\pi\) | ||||
0.888927 | + | 0.458050i | \(0.151452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.69705 | −0.276130 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.2783 | 0.726544 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.3258 | 2.23019 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.2748 | 0.724561 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.2790 | −1.57837 | −0.789187 | − | 0.614153i | \(-0.789498\pi\) | ||||
−0.789187 | + | 0.614153i | \(0.789498\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.7969 | −1.16760 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.867348 | −0.0308393 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.1550 | 1.14186 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.7589 | 0.629052 | 0.314526 | − | 0.949249i | \(-0.398154\pi\) | ||||
0.314526 | + | 0.949249i | \(0.398154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.122786 | 0.00434385 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.55276 | 0.0548642 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.2192 | −1.84277 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −46.2450 | −1.62790 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.2427 | 1.09844 | 0.549218 | − | 0.835679i | \(-0.314926\pi\) | ||||
0.549218 | + | 0.835679i | \(0.314926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.66672 | 0.234100 | 0.117050 | − | 0.993126i | \(-0.462656\pi\) | ||||
0.117050 | + | 0.993126i | \(0.462656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.7065 | 0.620993 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.57393 | −0.160022 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.15427 | −0.0403336 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.2138 | −1.50817 | −0.754086 | − | 0.656776i | \(-0.771920\pi\) | ||||
−0.754086 | + | 0.656776i | \(0.771920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.8129 | 0.620918 | 0.310459 | − | 0.950587i | \(-0.399517\pi\) | ||||
0.310459 | + | 0.950587i | \(0.399517\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.9139 | −0.657702 | −0.328851 | − | 0.944382i | \(-0.606661\pi\) | ||||
−0.328851 | + | 0.944382i | \(0.606661\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.5969 | 1.30579 | 0.652897 | − | 0.757447i | \(-0.273554\pi\) | ||||
0.652897 | + | 0.757447i | \(0.273554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.5195 | 1.47498 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.14821 | 0.0397831 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.62773 | −0.229088 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.2054 | −1.11185 | −0.555927 | − | 0.831231i | \(-0.687636\pi\) | ||||
−0.555927 | + | 0.831231i | \(0.687636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.4483 | −0.394767 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −49.4415 | −1.70285 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.36923 | 0.287570 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40.7138 | 1.39729 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.6594 | 0.468238 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6540 | 0.707179 | 0.353590 | − | 0.935401i | \(-0.384961\pi\) | ||||
0.353590 | + | 0.935401i | \(0.384961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.6561 | 1.45711 | 0.728553 | − | 0.684990i | \(-0.240193\pi\) | ||||
0.728553 | + | 0.684990i | \(0.240193\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.95286 | 0.271348 | 0.135674 | − | 0.990754i | \(-0.456680\pi\) | ||||
0.135674 | + | 0.990754i | \(0.456680\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21.5346 | −0.733897 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.0419 | 0.988597 | 0.494299 | − | 0.869292i | \(-0.335425\pi\) | ||||
0.494299 | + | 0.869292i | \(0.335425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.7439 | 0.976195 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.1277 | 0.818477 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.10806 | −0.139196 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.75369 | 0.0931983 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.1827 | −0.512682 | −0.256341 | − | 0.966586i | \(-0.582517\pi\) | ||||
−0.256341 | + | 0.966586i | \(0.582517\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.2643 | 1.29062 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.3877 | −0.585806 | −0.292903 | − | 0.956142i | \(-0.594621\pi\) | ||||
−0.292903 | + | 0.956142i | \(0.594621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.46587 | −0.284899 | −0.142450 | − | 0.989802i | \(-0.545498\pi\) | ||||
−0.142450 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.8229 | −1.10208 | −0.551042 | − | 0.834477i | \(-0.685770\pi\) | ||||
−0.551042 | + | 0.834477i | \(0.685770\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.6158 | 0.490199 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.7900 | 1.46702 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.184577 | 0.00617662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.1290 | 0.638700 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.73758 | −0.191359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.03085 | 0.300861 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.85731 | 0.161641 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.6260 | −1.81383 | −0.906913 | − | 0.421317i | \(-0.861568\pi\) | ||||
−0.906913 | + | 0.421317i | \(0.861568\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.811589 | −0.0269187 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.21329 | −0.139592 | −0.0697962 | − | 0.997561i | \(-0.522235\pi\) | ||||
−0.0697962 | + | 0.997561i | \(0.522235\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 75.5159 | 2.49921 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.8600 | 0.589789 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.0033 | 0.824784 | 0.412392 | − | 0.911007i | \(-0.364693\pi\) | ||||
0.412392 | + | 0.911007i | \(0.364693\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.45077 | −0.179609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.4346 | 1.49550 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.37907 | 0.0781388 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.5462 | −1.13342 | −0.566712 | − | 0.823916i | \(-0.691785\pi\) | ||||
−0.566712 | + | 0.823916i | \(0.691785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.72603 | 0.0565684 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.90642 | 0.0624134 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.7689 | −0.645821 | −0.322911 | − | 0.946429i | \(-0.604661\pi\) | ||||
−0.322911 | + | 0.946429i | \(0.604661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.7242 | −0.545774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.0820 | 0.752452 | 0.376226 | − | 0.926528i | \(-0.377222\pi\) | ||||
0.376226 | + | 0.926528i | \(0.377222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.2159 | 1.24448 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 60.0386 | 1.95099 | 0.975496 | − | 0.220019i | \(-0.0706119\pi\) | ||||
0.975496 | + | 0.220019i | \(0.0706119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.0670 | −1.23571 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.69295 | −0.281888 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.4188 | −0.369891 | −0.184945 | − | 0.982749i | \(-0.559211\pi\) | ||||
−0.184945 | + | 0.982749i | \(0.559211\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.7965 | 1.09249 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.22523 | −0.168732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1244 | −0.939497 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.10022 | 0.0676786 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.9169 | −0.929903 | −0.464952 | − | 0.885336i | \(-0.653928\pi\) | ||||
−0.464952 | + | 0.885336i | \(0.653928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.63266 | −0.116698 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.1410 | 1.38446 | 0.692230 | − | 0.721677i | \(-0.256629\pi\) | ||||
0.692230 | + | 0.721677i | \(0.256629\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.25800 | −0.168564 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.0221 | −1.21644 | −0.608218 | − | 0.793770i | \(-0.708115\pi\) | ||||
−0.608218 | + | 0.793770i | \(0.708115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.9945 | −0.607067 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.84787 | −0.122853 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.7030 | 0.405164 | 0.202582 | − | 0.979265i | \(-0.435067\pi\) | ||||
0.202582 | + | 0.979265i | \(0.435067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.196012 | −0.00623913 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.61992 | −0.274098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4382 | −0.808073 | −0.404036 | − | 0.914743i | \(-0.632393\pi\) | ||||
−0.404036 | + | 0.914743i | \(0.632393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.1954 | 0.545678 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.5489 | 0.429098 | 0.214549 | − | 0.976713i | \(-0.431172\pi\) | ||||
0.214549 | + | 0.976713i | \(0.431172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.3219 | 0.642958 |
(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 | 5600.2.a.bu.1.2 | 5 | ||
4.3 | odd | 2 | 5600.2.a.bx.1.4 | 5 | |||
5.2 | odd | 4 | 1120.2.g.b.449.8 | yes | 10 | ||
5.3 | odd | 4 | 1120.2.g.b.449.3 | ✓ | 10 | ||
5.4 | even | 2 | 5600.2.a.bw.1.4 | 5 | |||
20.3 | even | 4 | 1120.2.g.c.449.8 | yes | 10 | ||
20.7 | even | 4 | 1120.2.g.c.449.3 | yes | 10 | ||
20.19 | odd | 2 | 5600.2.a.bv.1.2 | 5 | |||
40.3 | even | 4 | 2240.2.g.n.449.3 | 10 | |||
40.13 | odd | 4 | 2240.2.g.o.449.8 | 10 | |||
40.27 | even | 4 | 2240.2.g.n.449.8 | 10 | |||
40.37 | odd | 4 | 2240.2.g.o.449.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.b.449.3 | ✓ | 10 | 5.3 | odd | 4 | ||
1120.2.g.b.449.8 | yes | 10 | 5.2 | odd | 4 | ||
1120.2.g.c.449.3 | yes | 10 | 20.7 | even | 4 | ||
1120.2.g.c.449.8 | yes | 10 | 20.3 | even | 4 | ||
2240.2.g.n.449.3 | 10 | 40.3 | even | 4 | |||
2240.2.g.n.449.8 | 10 | 40.27 | even | 4 | |||
2240.2.g.o.449.3 | 10 | 40.37 | odd | 4 | |||
2240.2.g.o.449.8 | 10 | 40.13 | odd | 4 | |||
5600.2.a.bu.1.2 | 5 | 1.1 | even | 1 | trivial | ||
5600.2.a.bv.1.2 | 5 | 20.19 | odd | 2 | |||
5600.2.a.bw.1.4 | 5 | 5.4 | even | 2 | |||
5600.2.a.bx.1.4 | 5 | 4.3 | odd | 2 |