Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.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: | \(22.0387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1436.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 11x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.28282\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.78872 | −1.43200 | −0.716000 | − | 0.698100i | \(-0.754029\pi\) | ||||
−0.716000 | + | 0.698100i | \(0.754029\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.07154 | −0.926104 | −0.463052 | − | 0.886331i | \(-0.653246\pi\) | ||||
−0.463052 | + | 0.886331i | \(0.653246\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.07154 | −1.40659 | −0.703296 | − | 0.710897i | \(-0.748289\pi\) | ||||
−0.703296 | + | 0.710897i | \(0.748289\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.28282 | 0.796202 | 0.398101 | − | 0.917342i | \(-0.369669\pi\) | ||||
0.398101 | + | 0.917342i | \(0.369669\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.07154 | 1.16349 | 0.581745 | − | 0.813371i | \(-0.302370\pi\) | ||||
0.581745 | + | 0.813371i | \(0.302370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.78872 | −0.826765 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.28282 | 0.238214 | 0.119107 | − | 0.992881i | \(-0.461997\pi\) | ||||
0.119107 | + | 0.992881i | \(0.461997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.78872 | 0.680473 | 0.340237 | − | 0.940340i | \(-0.389493\pi\) | ||||
0.340237 | + | 0.940340i | \(0.389493\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.07154 | −0.534686 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.78872 | 0.640410 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.22307 | 0.529869 | 0.264935 | − | 0.964266i | \(-0.414650\pi\) | ||||
0.264935 | + | 0.964266i | \(0.414650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.07154 | −0.812096 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.42590 | −1.47208 | −0.736039 | − | 0.676939i | \(-0.763306\pi\) | ||||
−0.736039 | + | 0.676939i | \(0.763306\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.1431 | 1.85180 | 0.925901 | − | 0.377766i | \(-0.123308\pi\) | ||||
0.925901 | + | 0.377766i | \(0.123308\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0833 | 1.47080 | 0.735402 | − | 0.677631i | \(-0.236993\pi\) | ||||
0.735402 | + | 0.677631i | \(0.236993\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.35436 | 1.05062 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.28282 | 0.459687 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.84847 | 0.803349 | 0.401675 | − | 0.915782i | \(-0.368428\pi\) | ||||
0.401675 | + | 0.915782i | \(0.368428\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.07154 | 0.414166 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.07154 | 0.671742 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.29461 | −0.298732 | −0.149366 | − | 0.988782i | \(-0.547723\pi\) | ||||
−0.149366 | + | 0.988782i | \(0.547723\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.07154 | −0.393270 | −0.196635 | − | 0.980477i | \(-0.563001\pi\) | ||||
−0.196635 | + | 0.980477i | \(0.563001\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.78872 | −0.477333 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.07154 | 0.629047 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.22307 | 0.393760 | 0.196880 | − | 0.980428i | \(-0.436919\pi\) | ||||
0.196880 | + | 0.980428i | \(0.436919\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.28282 | 0.864312 | 0.432156 | − | 0.901799i | \(-0.357753\pi\) | ||||
0.432156 | + | 0.901799i | \(0.357753\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.63719 | 1.12795 | 0.563974 | − | 0.825793i | \(-0.309272\pi\) | ||||
0.563974 | + | 0.825793i | \(0.309272\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.6372 | 1.32618 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.71718 | 0.737306 | 0.368653 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368653 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.28282 | −0.356072 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.28282 | 0.137533 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.01178 | 0.531248 | 0.265624 | − | 0.964077i | \(-0.414422\pi\) | ||||
0.265624 | + | 0.964077i | \(0.414422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.2146 | 2.01424 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.78872 | 0.392871 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.07154 | −0.520329 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.13130 | −0.114866 | −0.0574328 | − | 0.998349i | \(-0.518292\pi\) | ||||
−0.0574328 | + | 0.998349i | \(0.518292\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.07154 | −0.308701 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.29461 | −0.626337 | −0.313168 | − | 0.949698i | \(-0.601390\pi\) | ||||
−0.313168 | + | 0.949698i | \(0.601390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7087 | −1.25223 | −0.626114 | − | 0.779732i | \(-0.715356\pi\) | ||||
−0.626114 | + | 0.779732i | \(0.715356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.78872 | 0.369741 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.2946 | 1.76861 | 0.884303 | − | 0.466913i | \(-0.154634\pi\) | ||||
0.884303 | + | 0.466913i | \(0.154634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.50589 | −0.431586 | −0.215793 | − | 0.976439i | \(-0.569234\pi\) | ||||
−0.215793 | + | 0.976439i | \(0.569234\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.22307 | 0.305920 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.71718 | 0.443755 | 0.221877 | − | 0.975075i | \(-0.428782\pi\) | ||||
0.221877 | + | 0.975075i | \(0.428782\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.07154 | −0.468864 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.4377 | −1.14016 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.56565 | −0.142332 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.42590 | −0.849905 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0833 | −1.07222 | −0.536111 | − | 0.844148i | \(-0.680107\pi\) | ||||
−0.536111 | + | 0.844148i | \(0.680107\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.1431 | 1.06914 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.1313 | 1.49677 | 0.748384 | − | 0.663266i | \(-0.230830\pi\) | ||||
0.748384 | + | 0.663266i | \(0.230830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.2146 | −1.66612 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.70873 | −0.231422 | −0.115711 | − | 0.993283i | \(-0.536915\pi\) | ||||
−0.115711 | + | 0.993283i | \(0.536915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.211285 | −0.0179209 | −0.00896047 | − | 0.999960i | \(-0.502852\pi\) | ||||
−0.00896047 | + | 0.999960i | \(0.502852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0833 | 0.849169 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5774 | 1.30265 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.28282 | −0.106533 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.35436 | 0.606578 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.6372 | −1.44489 | −0.722447 | − | 0.691426i | \(-0.756983\pi\) | ||||
−0.722447 | + | 0.691426i | \(0.756983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.7205 | −1.11656 | −0.558280 | − | 0.829653i | \(-0.688538\pi\) | ||||
−0.558280 | + | 0.829653i | \(0.688538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.28282 | 0.265401 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.78872 | −0.304317 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.4857 | 1.07627 | 0.538136 | − | 0.842858i | \(-0.319129\pi\) | ||||
0.538136 | + | 0.842858i | \(0.319129\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.84847 | 0.463814 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.78872 | −0.298593 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.57743 | −0.593510 | −0.296755 | − | 0.954954i | \(-0.595904\pi\) | ||||
−0.296755 | + | 0.954954i | \(0.595904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.07154 | 0.239119 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.2028 | 1.09905 | 0.549524 | − | 0.835478i | \(-0.314809\pi\) | ||||
0.549524 | + | 0.835478i | \(0.314809\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7205 | 0.978501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.07154 | 0.387830 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.57743 | 0.424044 | 0.212022 | − | 0.977265i | \(-0.431995\pi\) | ||||
0.212022 | + | 0.977265i | \(0.431995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.78872 | −0.286400 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.29461 | −0.172473 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.8518 | −1.11008 | −0.555038 | − | 0.831825i | \(-0.687296\pi\) | ||||
−0.555038 | + | 0.831825i | \(0.687296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8518 | 1.54990 | 0.774951 | − | 0.632021i | \(-0.217774\pi\) | ||||
0.774951 | + | 0.632021i | \(0.217774\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.07154 | −0.227055 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.22307 | −0.236965 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0833 | −0.737366 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.78872 | −0.275588 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.0951 | 1.38167 | 0.690837 | − | 0.723011i | \(-0.257242\pi\) | ||||
0.690837 | + | 0.723011i | \(0.257242\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.56565 | −0.616569 | −0.308284 | − | 0.951294i | \(-0.599755\pi\) | ||||
−0.308284 | + | 0.951294i | \(0.599755\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.07154 | 0.363180 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.01178 | 0.214581 | 0.107290 | − | 0.994228i | \(-0.465783\pi\) | ||||
0.107290 | + | 0.994228i | \(0.465783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.8518 | −1.61992 | −0.809961 | − | 0.586484i | \(-0.800512\pi\) | ||||
−0.809961 | + | 0.586484i | \(0.800512\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.22307 | 0.227338 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.86025 | −0.341123 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.42590 | 0.658334 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.5774 | −1.07751 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.21128 | 0.565288 | 0.282644 | − | 0.959225i | \(-0.408788\pi\) | ||||
0.282644 | + | 0.959225i | \(0.408788\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.28282 | 0.499011 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.1431 | −0.828151 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.3544 | −0.974438 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.63719 | 0.651221 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.6490 | −1.11993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2862 | 0.688812 | 0.344406 | − | 0.938821i | \(-0.388080\pi\) | ||||
0.344406 | + | 0.938821i | \(0.388080\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.1549 | 1.53684 | 0.768421 | − | 0.639945i | \(-0.221043\pi\) | ||||
0.768421 | + | 0.639945i | \(0.221043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7205 | −1.56750 | −0.783748 | − | 0.621079i | \(-0.786694\pi\) | ||||
−0.783748 | + | 0.621079i | \(0.786694\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.6372 | 0.765671 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.70873 | 0.177455 | 0.0887273 | − | 0.996056i | \(-0.471720\pi\) | ||||
0.0887273 | + | 0.996056i | \(0.471720\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.0833 | −0.657763 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0033 | 1.09985 | 0.549927 | − | 0.835213i | \(-0.314656\pi\) | ||||
0.549927 | + | 0.835213i | \(0.314656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.36281 | −0.152202 | −0.0761011 | − | 0.997100i | \(-0.524247\pi\) | ||||
−0.0761011 | + | 0.997100i | \(0.524247\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.35436 | −0.469853 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.7205 | −1.63656 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.71718 | 0.425684 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.1313 | 1.46003 | 0.730017 | − | 0.683429i | \(-0.239512\pi\) | ||||
0.730017 | + | 0.683429i | \(0.239512\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.07154 | −0.193106 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.28282 | −0.205578 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.505891 | −0.0315566 | −0.0157783 | − | 0.999876i | \(-0.505023\pi\) | ||||
−0.0157783 | + | 0.999876i | \(0.505023\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.2113 | −0.758772 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.28282 | 0.0794048 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.99155 | 0.122804 | 0.0614021 | − | 0.998113i | \(-0.480443\pi\) | ||||
0.0614021 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.84847 | −0.359269 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.01178 | 0.306716 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.13975 | −0.191434 | −0.0957168 | − | 0.995409i | \(-0.530514\pi\) | ||||
−0.0957168 | + | 0.995409i | \(0.530514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9318 | 1.33226 | 0.666131 | − | 0.745835i | \(-0.267949\pi\) | ||||
0.666131 | + | 0.745835i | \(0.267949\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.2146 | 1.16292 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.07154 | −0.185221 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8636 | 0.953151 | 0.476575 | − | 0.879134i | \(-0.341878\pi\) | ||||
0.476575 | + | 0.879134i | \(0.341878\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.78872 | 0.226824 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.37460 | −0.0820015 | −0.0410008 | − | 0.999159i | \(-0.513055\pi\) | ||||
−0.0410008 | + | 0.999159i | \(0.513055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.3544 | 0.734391 | 0.367195 | − | 0.930144i | \(-0.380318\pi\) | ||||
0.367195 | + | 0.930144i | \(0.380318\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.07154 | −0.300412 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.7121 | 2.10802 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.22307 | −0.366063 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.13130 | −0.0663177 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.7121 | −1.73580 | −0.867898 | − | 0.496742i | \(-0.834530\pi\) | ||||
−0.867898 | + | 0.496742i | \(0.834530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.29461 | 0.133597 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.07154 | −0.178229 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.07154 | −0.293295 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46.0067 | −2.65178 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.29461 | −0.361616 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.07154 | 0.175876 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.4890 | −1.74010 | −0.870049 | − | 0.492965i | \(-0.835913\pi\) | ||||
−0.870049 | + | 0.492965i | \(0.835913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.7087 | −0.722974 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.44613 | 0.252117 | 0.126059 | − | 0.992023i | \(-0.459767\pi\) | ||||
0.126059 | + | 0.992023i | \(0.459767\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.35436 | 0.359170 | 0.179585 | − | 0.983742i | \(-0.442525\pi\) | ||||
0.179585 | + | 0.983742i | \(0.442525\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.78872 | 0.213470 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.64897 | 0.148781 | 0.0743905 | − | 0.997229i | \(-0.476299\pi\) | ||||
0.0743905 | + | 0.997229i | \(0.476299\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.94024 | −0.220611 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.2946 | 1.02111 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.6490 | 0.926373 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.07154 | −0.281318 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.50589 | −0.249176 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −38.2028 | −2.10619 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.80050 | 0.263859 | 0.131930 | − | 0.991259i | \(-0.457883\pi\) | ||||
0.131930 | + | 0.991259i | \(0.457883\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.22307 | 0.176623 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.22307 | −0.176095 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7323 | −0.802519 | −0.401260 | − | 0.915964i | \(-0.631427\pi\) | ||||
−0.401260 | + | 0.915964i | \(0.631427\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.71718 | 0.256202 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6372 | −0.630189 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.34258 | −0.0724925 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.5841 | −1.80289 | −0.901444 | − | 0.432895i | \(-0.857492\pi\) | ||||
−0.901444 | + | 0.432895i | \(0.857492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.92001 | −0.370420 | −0.185210 | − | 0.982699i | \(-0.559296\pi\) | ||||
−0.185210 | + | 0.982699i | \(0.559296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.07154 | −0.270699 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.38638 | 0.446362 | 0.223181 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223181 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.28282 | −0.386532 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.4377 | −0.658272 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.2146 | 1.01411 | 0.507054 | − | 0.861914i | \(-0.330734\pi\) | ||||
0.507054 | + | 0.861914i | \(0.330734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.72051 | 0.353711 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.56565 | −0.0821752 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.63719 | −0.504433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4974 | 0.861159 | 0.430580 | − | 0.902553i | \(-0.358309\pi\) | ||||
0.430580 | + | 0.902553i | \(0.358309\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.42590 | −0.490693 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.1582 | −1.15040 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.45792 | −0.282600 | −0.141300 | − | 0.989967i | \(-0.545128\pi\) | ||||
−0.141300 | + | 0.989967i | \(0.545128\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.50589 | −0.335070 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.4175 | 1.30561 | 0.652803 | − | 0.757527i | \(-0.273593\pi\) | ||||
0.652803 | + | 0.757527i | \(0.273593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.0833 | −0.619047 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.7121 | 1.41602 | 0.708010 | − | 0.706202i | \(-0.249593\pi\) | ||||
0.708010 | + | 0.706202i | \(0.249593\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.6372 | −0.593086 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.1431 | 0.617267 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 38.4528 | 1.94963 | 0.974817 | − | 0.223006i | \(-0.0715868\pi\) | ||||
0.974817 | + | 0.223006i | \(0.0715868\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.28282 | 0.166020 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.1313 | 0.864160 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.28616 | 0.415870 | 0.207935 | − | 0.978143i | \(-0.433326\pi\) | ||||
0.207935 | + | 0.978143i | \(0.433326\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.2146 | −0.961934 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.72051 | 0.285669 | 0.142834 | − | 0.989747i | \(-0.454378\pi\) | ||||
0.142834 | + | 0.989747i | \(0.454378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.2146 | −0.957148 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.89978 | −0.490714 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.4974 | −1.31021 | −0.655107 | − | 0.755536i | \(-0.727376\pi\) | ||||
−0.655107 | + | 0.755536i | \(0.727376\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.70873 | −0.133612 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.69361 | 0.427785 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.71718 | −0.329733 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.211285 | −0.0103467 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.2264 | 1.08583 | 0.542915 | − | 0.839787i | \(-0.317320\pi\) | ||||
0.542915 | + | 0.839787i | \(0.317320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9351 | 0.922842 | 0.461421 | − | 0.887181i | \(-0.347340\pi\) | ||||
0.461421 | + | 0.887181i | \(0.347340\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.0833 | 0.490268 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.28282 | 0.159240 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.6372 | 0.563163 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.5774 | 0.752085 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.9882 | 0.529284 | 0.264642 | − | 0.964347i | \(-0.414746\pi\) | ||||
0.264642 | + | 0.964347i | \(0.414746\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.3544 | 0.882054 | 0.441027 | − | 0.897494i | \(-0.354614\pi\) | ||||
0.441027 | + | 0.897494i | \(0.354614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.28282 | −0.0615067 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.07154 | 0.242605 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.0184 | 1.48043 | 0.740215 | − | 0.672370i | \(-0.234724\pi\) | ||||
0.740215 | + | 0.672370i | \(0.234724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.35436 | 0.350208 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.09510 | 0.337099 | 0.168549 | − | 0.985693i | \(-0.446092\pi\) | ||||
0.168549 | + | 0.985693i | \(0.446092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.01178 | −0.237581 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.6372 | −0.834210 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.4326 | 1.67217 | 0.836083 | − | 0.548603i | \(-0.184840\pi\) | ||||
0.836083 | + | 0.548603i | \(0.184840\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9520 | 1.36330 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.7205 | −0.644646 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.2146 | −0.900795 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.514342 | −0.0240599 | −0.0120299 | − | 0.999928i | \(-0.503829\pi\) | ||||
−0.0120299 | + | 0.999928i | \(0.503829\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.28282 | 0.153229 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.5892 | −0.772637 | −0.386318 | − | 0.922366i | \(-0.626253\pi\) | ||||
−0.386318 | + | 0.922366i | \(0.626253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.6725 | 1.14663 | 0.573315 | − | 0.819335i | \(-0.305657\pi\) | ||||
0.573315 | + | 0.819335i | \(0.305657\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.78872 | −0.175697 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.4259 | 0.898924 | 0.449462 | − | 0.893300i | \(-0.351616\pi\) | ||||
0.449462 | + | 0.893300i | \(0.351616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2113 | −0.563865 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4857 | 0.621386 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37.2979 | −1.71496 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.07154 | 0.232698 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.84847 | 0.267783 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2146 | −0.877938 | −0.438969 | − | 0.898502i | \(-0.644656\pi\) | ||||
−0.438969 | + | 0.898502i | \(0.644656\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.3459 | −0.745309 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.78872 | −0.172393 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.13130 | 0.0513695 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −43.5243 | −1.97228 | −0.986138 | − | 0.165927i | \(-0.946938\pi\) | ||||
−0.986138 | + | 0.165927i | \(0.946938\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.57743 | −0.342663 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.82491 | 0.0823569 | 0.0411784 | − | 0.999152i | \(-0.486889\pi\) | ||||
0.0411784 | + | 0.999152i | \(0.486889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.21128 | 0.189667 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.07154 | 0.138055 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.5925 | −1.23769 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6405 | 0.655400 | 0.327700 | − | 0.944782i | \(-0.393727\pi\) | ||||
0.327700 | + | 0.944782i | \(0.393727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.2028 | 0.634536 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.88382 | −0.306934 | −0.153467 | − | 0.988154i | \(-0.549044\pi\) | ||||
−0.153467 | + | 0.988154i | \(0.549044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.29461 | 0.280106 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.7205 | 0.564938 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.0000 | −1.24108 | −0.620539 | − | 0.784176i | \(-0.713086\pi\) | ||||
−0.620539 | + | 0.784176i | \(0.713086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.5126 | −1.61522 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.07154 | 0.223914 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.7087 | 0.560013 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.9713 | −1.36212 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.57743 | 0.244822 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.9469 | 1.48724 | 0.743621 | − | 0.668602i | \(-0.233107\pi\) | ||||
0.743621 | + | 0.668602i | \(0.233107\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5774 | 0.593700 | 0.296850 | − | 0.954924i | \(-0.404064\pi\) | ||||
0.296850 | + | 0.954924i | \(0.404064\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.78872 | −0.165353 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.4377 | 0.541794 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.29461 | −0.0995774 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.8038 | 2.07061 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.2946 | −0.790945 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.8518 | −0.640903 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.5892 | −0.972986 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6852 | −0.717351 | −0.358676 | − | 0.933462i | \(-0.616772\pi\) | ||||
−0.358676 | + | 0.933462i | \(0.616772\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.8518 | 0.894837 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.50589 | 0.193011 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.4175 | 0.573689 | 0.286844 | − | 0.957977i | \(-0.407394\pi\) | ||||
0.286844 | + | 0.957977i | \(0.407394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.07154 | −0.131090 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.50589 | 0.277160 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.3097 | 1.28890 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.22307 | −0.136812 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.0269 | 1.48414 | 0.742069 | − | 0.670324i | \(-0.233845\pi\) | ||||
0.742069 | + | 0.670324i | \(0.233845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −61.5841 | −2.60473 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.0833 | −0.425718 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.7356 | −1.42179 | −0.710894 | − | 0.703300i | \(-0.751709\pi\) | ||||
−0.710894 | + | 0.703300i | \(0.751709\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.71718 | −0.198453 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.78872 | −0.159111 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.4579 | −0.815718 | −0.407859 | − | 0.913045i | \(-0.633725\pi\) | ||||
−0.407859 | + | 0.913045i | \(0.633725\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.6843 | 1.66074 | 0.830369 | − | 0.557215i | \(-0.188130\pi\) | ||||
0.830369 | + | 0.557215i | \(0.188130\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.0951 | 0.797709 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.8636 | −1.57628 | −0.788141 | − | 0.615495i | \(-0.788956\pi\) | ||||
−0.788141 | + | 0.615495i | \(0.788956\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.56565 | −0.355976 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.4495 | −1.05582 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.9638 | −0.743985 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.07154 | 0.209682 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.55387 | 0.394330 | 0.197165 | − | 0.980370i | \(-0.436826\pi\) | ||||
0.197165 | + | 0.980370i | \(0.436826\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.2146 | 0.791725 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.01178 | 0.123888 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.9351 | −0.941833 | −0.470916 | − | 0.882178i | \(-0.656077\pi\) | ||||
−0.470916 | + | 0.882178i | \(0.656077\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.4377 | 0.509895 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.8518 | −0.935262 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.6969 | −1.04995 | −0.524974 | − | 0.851118i | \(-0.675925\pi\) | ||||
−0.524974 | + | 0.851118i | \(0.675925\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.0800 | −0.696707 | −0.348354 | − | 0.937363i | \(-0.613259\pi\) | ||||
−0.348354 | + | 0.937363i | \(0.613259\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.22307 | 0.131253 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.56565 | 0.0636526 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.2028 | −0.982363 | −0.491181 | − | 0.871057i | \(-0.663435\pi\) | ||||
−0.491181 | + | 0.871057i | \(0.663435\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.86025 | −0.196947 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −51.1380 | −2.06882 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.73741 | 0.150953 | 0.0754763 | − | 0.997148i | \(-0.475952\pi\) | ||||
0.0754763 | + | 0.997148i | \(0.475952\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.42590 | 0.380089 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.3182 | −0.576428 | −0.288214 | − | 0.957566i | \(-0.593061\pi\) | ||||
−0.288214 | + | 0.957566i | \(0.593061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.4175 | −1.50393 | −0.751967 | − | 0.659201i | \(-0.770895\pi\) | ||||
−0.751967 | + | 0.659201i | \(0.770895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9882 | −0.760747 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.5774 | −0.622103 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5808 | 0.421883 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6725 | −1.69877 | −0.849383 | − | 0.527776i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527776i | \(0.823026\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.21128 | 0.326369 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0833 | 0.479512 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.2979 | −1.47780 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.28282 | 0.288104 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.39816 | 0.134219 | 0.0671097 | − | 0.997746i | \(-0.478622\pi\) | ||||
0.0671097 | + | 0.997746i | \(0.478622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.5210 | 0.651525 | 0.325762 | − | 0.945452i | \(-0.394379\pi\) | ||||
0.325762 | + | 0.945452i | \(0.394379\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.1431 | −0.478133 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.9469 | −1.49185 | −0.745923 | − | 0.666032i | \(-0.767992\pi\) | ||||
−0.745923 | + | 0.666032i | \(0.767992\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.04797 | 0.276657 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.3544 | −0.562592 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0715 | 0.746327 | 0.373163 | − | 0.927766i | \(-0.378273\pi\) | ||||
0.373163 | + | 0.927766i | \(0.378273\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.1313 | −0.669375 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.63719 | 0.375982 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.5008 | 0.837551 | 0.418776 | − | 0.908090i | \(-0.362459\pi\) | ||||
0.418776 | + | 0.908090i | \(0.362459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.11951 | 0.0824395 | 0.0412197 | − | 0.999150i | \(-0.486876\pi\) | ||||
0.0412197 | + | 0.999150i | \(0.486876\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.6490 | −0.646592 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.2146 | 0.745111 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.28282 | 0.0496711 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.2862 | 0.397686 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.43435 | 0.364209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.03619 | 0.309772 | 0.154886 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154886 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.5690 | 1.05956 | 0.529781 | − | 0.848134i | \(-0.322274\pi\) | ||||
0.529781 | + | 0.848134i | \(0.322274\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.28616 | 0.164488 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.1549 | 0.887296 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.35770 | −0.358062 | −0.179031 | − | 0.983843i | \(-0.557296\pi\) | ||||
−0.179031 | + | 0.983843i | \(0.557296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.70873 | 0.103495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.7205 | −0.904994 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.6608 | −1.12998 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.8754 | −1.70714 | −0.853570 | − | 0.520979i | \(-0.825567\pi\) | ||||
−0.853570 | + | 0.520979i | \(0.825567\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.6372 | 0.442060 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.211285 | 0.00801449 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.9436 | −1.17207 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.70873 | 0.102453 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.9116 | −1.09197 | −0.545987 | − | 0.837793i | \(-0.683845\pi\) | ||||
−0.545987 | + | 0.837793i | \(0.683845\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3459 | 0.616498 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −10.0833 | −0.379760 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 23.8485 | 0.896914 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −52.7751 | −1.98201 | −0.991006 | − | 0.133817i | \(-0.957277\pi\) | ||||
−0.991006 | + | 0.133817i | \(0.957277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.78872 | 0.141888 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.5774 | −0.582563 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.0033 | 0.635001 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.4090 | −1.69347 | −0.846735 | − | 0.532015i | \(-0.821435\pi\) | ||||
−0.846735 | + | 0.532015i | \(0.821435\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.1497 | 1.79319 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.36281 | −0.0878740 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.28282 | 0.0476429 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.2415 | 1.19577 | 0.597886 | − | 0.801581i | \(-0.296008\pi\) | ||||
0.597886 | + | 0.801581i | \(0.296008\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.8636 | 1.47441 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.3897 | 1.45489 | 0.727446 | − | 0.686165i | \(-0.240707\pi\) | ||||
0.727446 | + | 0.686165i | \(0.240707\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.35436 | −0.271270 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.89978 | −0.364663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.4857 | −0.863934 | −0.431967 | − | 0.901889i | \(-0.642180\pi\) | ||||
−0.431967 | + | 0.901889i | \(0.642180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.7205 | −0.944866 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.1313 | −1.36222 | −0.681108 | − | 0.732183i | \(-0.738501\pi\) | ||||
−0.681108 | + | 0.732183i | \(0.738501\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.6372 | 0.646177 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.71718 | 0.245769 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −69.3131 | −2.53264 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0833 | −0.513908 | −0.256954 | − | 0.966424i | \(-0.582719\pi\) | ||||
−0.256954 | + | 0.966424i | \(0.582719\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.1313 | 0.842951 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.7205 | 0.499340 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.8072 | 1.62854 | 0.814272 | − | 0.580483i | \(-0.197136\pi\) | ||||
0.814272 | + | 0.580483i | \(0.197136\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.07154 | −0.111490 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.56898 | 0.129375 | 0.0646877 | − | 0.997906i | \(-0.479395\pi\) | ||||
0.0646877 | + | 0.997906i | \(0.479395\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.0715 | 0.618031 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.28282 | −0.118691 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.6372 | 0.420194 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.6439 | −1.57384 | −0.786919 | − | 0.617057i | \(-0.788325\pi\) | ||||
−0.786919 | + | 0.617057i | \(0.788325\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.505891 | −0.0182192 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.8805 | 0.499246 | 0.249623 | − | 0.968343i | \(-0.419693\pi\) | ||||
0.249623 | + | 0.968343i | \(0.419693\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.78872 | 0.136095 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.2113 | −0.438077 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.8038 | −1.71275 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3695 | −0.800443 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.28282 | 0.0458444 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.4857 | −0.481324 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.6523 | 1.34216 | 0.671080 | − | 0.741385i | \(-0.265831\pi\) | ||||
0.671080 | + | 0.741385i | \(0.265831\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.99155 | 0.0709010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.8720 | −0.635456 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5774 | 0.553171 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.84847 | −0.207424 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.15153 | 0.0762110 | 0.0381055 | − | 0.999274i | \(-0.487868\pi\) | ||||
0.0381055 | + | 0.999274i | \(0.487868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.1018 | 1.17106 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.01178 | 0.177083 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.6010 | −1.04460 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.78872 | 0.133535 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.13975 | −0.110524 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.5572 | 0.511804 | 0.255902 | − | 0.966703i | \(-0.417628\pi\) | ||||
0.255902 | + | 0.966703i | \(0.417628\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.47388 | 0.0868695 | 0.0434348 | − | 0.999056i | \(-0.486170\pi\) | ||||
0.0434348 | + | 0.999056i | \(0.486170\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9318 | 0.769182 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.57743 | 0.265426 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 61.5841 | 2.15455 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.2146 | 0.671413 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.3333 | 1.12844 | 0.564220 | − | 0.825625i | \(-0.309177\pi\) | ||||
0.564220 | + | 0.825625i | \(0.309177\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.7087 | 0.512714 | 0.256357 | − | 0.966582i | \(-0.417478\pi\) | ||||
0.256357 | + | 0.966582i | \(0.417478\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.07154 | −0.106937 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.5623 | 0.680248 | 0.340124 | − | 0.940381i | \(-0.389531\pi\) | ||||
0.340124 | + | 0.940381i | \(0.389531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5092 | 1.09436 | 0.547180 | − | 0.837015i | \(-0.315701\pi\) | ||||
0.547180 | + | 0.837015i | \(0.315701\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.8636 | 0.550302 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.1431 | 0.836508 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.2028 | −0.491509 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.78872 | 0.130957 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9949 | 0.724824 | 0.362412 | − | 0.932018i | \(-0.381953\pi\) | ||||
0.362412 | + | 0.932018i | \(0.381953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3544 | −0.943254 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.37460 | −0.0473436 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.7205 | −0.437599 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.93179 | 0.203819 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.3544 | 0.424001 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.22307 | 0.110485 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.0067 | −1.71220 | −0.856098 | − | 0.516814i | \(-0.827118\pi\) | ||||
−0.856098 | + | 0.516814i | \(0.827118\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.07154 | −0.173443 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.3939 | −0.457526 | −0.228763 | − | 0.973482i | \(-0.573468\pi\) | ||||
−0.228763 | + | 0.973482i | \(0.573468\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.633854 | −0.0216268 | −0.0108134 | − | 0.999942i | \(-0.503442\pi\) | ||||
−0.0108134 | + | 0.999942i | \(0.503442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.7121 | 1.21706 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.1144 | −0.991066 | −0.495533 | − | 0.868589i | \(-0.665027\pi\) | ||||
−0.495533 | + | 0.868589i | \(0.665027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.57743 | −0.189638 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.22307 | −0.211346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.5723 | 0.833559 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.3459 | −0.553860 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.13130 | −0.0382886 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.78872 | 0.128082 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.3164 | 1.90167 | 0.950835 | − | 0.309699i | \(-0.100228\pi\) | ||||
0.950835 | + | 0.309699i | \(0.100228\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.7121 | −1.00216 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.79717 | −0.0605480 | −0.0302740 | − | 0.999542i | \(-0.509638\pi\) | ||||
−0.0302740 | + | 0.999542i | \(0.509638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.6843 | −1.60471 | −0.802353 | − | 0.596850i | \(-0.796419\pi\) | ||||
−0.802353 | + | 0.596850i | \(0.796419\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.29461 | 0.0771324 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.87537 | 0.163699 | 0.0818494 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818494 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 45.7803 | 1.53542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.07154 | −0.102900 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 51.1380 | 1.71127 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.8518 | 0.496441 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.07154 | −0.169334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.86025 | 0.162099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.1995 | 0.639628 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −46.0067 | −1.53101 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.8518 | −0.693137 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.6692 | −0.852332 | −0.426166 | − | 0.904645i | \(-0.640136\pi\) | ||||
−0.426166 | + | 0.904645i | \(0.640136\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.29461 | −0.208779 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.9764 | 0.595586 | 0.297793 | − | 0.954630i | \(-0.403750\pi\) | ||||
0.297793 | + | 0.954630i | \(0.403750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.6321 | −0.682822 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.07154 | 0.101542 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −64.9056 | −2.14337 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.0000 | −1.05558 | −0.527791 | − | 0.849374i | \(-0.676980\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.4890 | −1.00465 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.9351 | −1.21573 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.22307 | 0.105974 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.7087 | −0.417409 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.1582 | 0.398897 | 0.199449 | − | 0.979908i | \(-0.436085\pi\) | ||||
0.199449 | + | 0.979908i | \(0.436085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.2979 | 1.22239 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.44613 | 0.145560 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.0833 | 0.329760 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.97643 | −0.325916 | −0.162958 | − | 0.986633i | \(-0.552103\pi\) | ||||
−0.162958 | + | 0.986633i | \(0.552103\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.35436 | 0.207367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.7685 | 0.351042 | 0.175521 | − | 0.984476i | \(-0.443839\pi\) | ||||
0.175521 | + | 0.984476i | \(0.443839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.42590 | −0.306950 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.78872 | 0.123247 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.8569 | 0.580272 | 0.290136 | − | 0.956985i | \(-0.406299\pi\) | ||||
0.290136 | + | 0.956985i | \(0.406299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.8754 | −1.58656 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.64897 | 0.0858987 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.4175 | −0.758566 | −0.379283 | − | 0.925281i | \(-0.623829\pi\) | ||||
−0.379283 | + | 0.925281i | \(0.623829\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.0951 | −0.617903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.94024 | −0.127370 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.2626 | 0.331396 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.6456 | −0.536956 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.2946 | 0.589535 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.56565 | 0.275738 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0833 | −1.03173 | −0.515865 | − | 0.856670i | \(-0.672529\pi\) | ||||
−0.515865 | + | 0.856670i | \(0.672529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.6490 | 0.534842 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.1615 | 1.77022 | 0.885109 | − | 0.465384i | \(-0.154084\pi\) | ||||
0.885109 | + | 0.465384i | \(0.154084\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.800498 | 0.0256628 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.07154 | −0.162419 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.7069 | 1.87820 | 0.939101 | − | 0.343642i | \(-0.111661\pi\) | ||||
0.939101 | + | 0.343642i | \(0.111661\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.3939 | −0.491991 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.50589 | −0.143862 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.5925 | −0.880066 | −0.440033 | − | 0.897982i | \(-0.645033\pi\) | ||||
−0.440033 | + | 0.897982i | \(0.645033\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.01178 | −0.0959634 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38.2028 | −1.21601 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.1431 | 0.386127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.8307 | 1.67822 | 0.839112 | − | 0.543959i | \(-0.183075\pi\) | ||||
0.839112 | + | 0.543959i | \(0.183075\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.80050 | 0.152339 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.8518 | 0.724451 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.4292 | 1.09038 | 0.545192 | − | 0.838311i | \(-0.316457\pi\) | ||||
0.545192 | + | 0.838311i | \(0.316457\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.22307 | 0.101973 |
(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 | 2760.2.a.s.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bn.1.1 | 3 | |||
4.3 | odd | 2 | 5520.2.a.bw.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.s.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5520.2.a.bw.1.3 | 3 | 4.3 | odd | 2 | |||
8280.2.a.bn.1.1 | 3 | 3.2 | odd | 2 |