Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 18 x^{8} - 220 x^{7} + 61 x^{6} + 330 x^{5} - 145 x^{4} + \cdots - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.36377\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36377 | 1.67144 | 0.835719 | − | 0.549158i | \(-0.185051\pi\) | ||||
0.835719 | + | 0.549158i | \(0.185051\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.58741 | 1.79370 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.36377 | 0.965005 | ||||||||
\(7\) | −1.71423 | −0.647919 | −0.323959 | − | 0.946071i | \(-0.605014\pi\) | ||||
−0.323959 | + | 0.946071i | \(0.605014\pi\) | |||||||
\(8\) | 3.75227 | 1.32663 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.58741 | 1.03560 | ||||||||
\(13\) | −3.53338 | −0.979984 | −0.489992 | − | 0.871727i | \(-0.663000\pi\) | ||||
−0.489992 | + | 0.871727i | \(0.663000\pi\) | |||||||
\(14\) | −4.05205 | −1.08296 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.69468 | 0.423670 | ||||||||
\(17\) | −0.373305 | −0.0905398 | −0.0452699 | − | 0.998975i | \(-0.514415\pi\) | ||||
−0.0452699 | + | 0.998975i | \(0.514415\pi\) | |||||||
\(18\) | 2.36377 | 0.557146 | ||||||||
\(19\) | −5.76794 | −1.32326 | −0.661628 | − | 0.749832i | \(-0.730134\pi\) | ||||
−0.661628 | + | 0.749832i | \(0.730134\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71423 | −0.374076 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.80745 | −0.793907 | −0.396954 | − | 0.917839i | \(-0.629933\pi\) | ||||
−0.396954 | + | 0.917839i | \(0.629933\pi\) | |||||||
\(24\) | 3.75227 | 0.765929 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.35211 | −1.63798 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.14965 | −1.16217 | ||||||||
\(29\) | −3.51670 | −0.653035 | −0.326517 | − | 0.945191i | \(-0.605875\pi\) | ||||
−0.326517 | + | 0.945191i | \(0.605875\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0978 | −1.81362 | −0.906808 | − | 0.421545i | \(-0.861488\pi\) | ||||
−0.906808 | + | 0.421545i | \(0.861488\pi\) | |||||||
\(32\) | −3.49870 | −0.618488 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.882407 | −0.151332 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.58741 | 0.597901 | ||||||||
\(37\) | 11.5420 | 1.89748 | 0.948742 | − | 0.316050i | \(-0.102357\pi\) | ||||
0.948742 | + | 0.316050i | \(0.102357\pi\) | |||||||
\(38\) | −13.6341 | −2.21174 | ||||||||
\(39\) | −3.53338 | −0.565794 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.41898 | −0.377781 | −0.188890 | − | 0.981998i | \(-0.560489\pi\) | ||||
−0.188890 | + | 0.981998i | \(0.560489\pi\) | |||||||
\(42\) | −4.05205 | −0.625245 | ||||||||
\(43\) | −0.224486 | −0.0342338 | −0.0171169 | − | 0.999853i | \(-0.505449\pi\) | ||||
−0.0171169 | + | 0.999853i | \(0.505449\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.99992 | −1.32697 | ||||||||
\(47\) | −4.67637 | −0.682118 | −0.341059 | − | 0.940042i | \(-0.610786\pi\) | ||||
−0.341059 | + | 0.940042i | \(0.610786\pi\) | |||||||
\(48\) | 1.69468 | 0.244606 | ||||||||
\(49\) | −4.06141 | −0.580201 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.373305 | −0.0522732 | ||||||||
\(52\) | −12.6757 | −1.75780 | ||||||||
\(53\) | −2.44417 | −0.335732 | −0.167866 | − | 0.985810i | \(-0.553688\pi\) | ||||
−0.167866 | + | 0.985810i | \(0.553688\pi\) | |||||||
\(54\) | 2.36377 | 0.321668 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.43226 | −0.859547 | ||||||||
\(57\) | −5.76794 | −0.763982 | ||||||||
\(58\) | −8.31267 | −1.09151 | ||||||||
\(59\) | 5.35991 | 0.697800 | 0.348900 | − | 0.937160i | \(-0.386555\pi\) | ||||
0.348900 | + | 0.937160i | \(0.386555\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.40629 | −0.436131 | −0.218066 | − | 0.975934i | \(-0.569975\pi\) | ||||
−0.218066 | + | 0.975934i | \(0.569975\pi\) | |||||||
\(62\) | −23.8688 | −3.03134 | ||||||||
\(63\) | −1.71423 | −0.215973 | ||||||||
\(64\) | −11.6595 | −1.45744 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.08988 | 1.11051 | 0.555253 | − | 0.831682i | \(-0.312621\pi\) | ||||
0.555253 | + | 0.831682i | \(0.312621\pi\) | |||||||
\(68\) | −1.33920 | −0.162402 | ||||||||
\(69\) | −3.80745 | −0.458363 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.77564 | −1.04148 | −0.520738 | − | 0.853716i | \(-0.674343\pi\) | ||||
−0.520738 | + | 0.853716i | \(0.674343\pi\) | |||||||
\(72\) | 3.75227 | 0.442209 | ||||||||
\(73\) | −14.9622 | −1.75120 | −0.875599 | − | 0.483040i | \(-0.839533\pi\) | ||||
−0.875599 | + | 0.483040i | \(0.839533\pi\) | |||||||
\(74\) | 27.2825 | 3.17153 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.6919 | −2.37353 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.35211 | −0.945690 | ||||||||
\(79\) | 8.79204 | 0.989181 | 0.494591 | − | 0.869126i | \(-0.335318\pi\) | ||||
0.494591 | + | 0.869126i | \(0.335318\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.71791 | −0.631437 | ||||||||
\(83\) | 7.44215 | 0.816882 | 0.408441 | − | 0.912785i | \(-0.366073\pi\) | ||||
0.408441 | + | 0.912785i | \(0.366073\pi\) | |||||||
\(84\) | −6.14965 | −0.670982 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.530633 | −0.0572196 | ||||||||
\(87\) | −3.51670 | −0.377030 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.5058 | 1.64361 | 0.821806 | − | 0.569767i | \(-0.192966\pi\) | ||||
0.821806 | + | 0.569767i | \(0.192966\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.05704 | 0.634950 | ||||||||
\(92\) | −13.6589 | −1.42403 | ||||||||
\(93\) | −10.0978 | −1.04709 | ||||||||
\(94\) | −11.0539 | −1.14012 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.49870 | −0.357084 | ||||||||
\(97\) | 14.6637 | 1.48887 | 0.744436 | − | 0.667694i | \(-0.232719\pi\) | ||||
0.744436 | + | 0.667694i | \(0.232719\pi\) | |||||||
\(98\) | −9.60024 | −0.969770 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.13469 | 0.610424 | 0.305212 | − | 0.952284i | \(-0.401273\pi\) | ||||
0.305212 | + | 0.952284i | \(0.401273\pi\) | |||||||
\(102\) | −0.882407 | −0.0873713 | ||||||||
\(103\) | 7.86989 | 0.775443 | 0.387722 | − | 0.921777i | \(-0.373262\pi\) | ||||
0.387722 | + | 0.921777i | \(0.373262\pi\) | |||||||
\(104\) | −13.2582 | −1.30007 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.77745 | −0.561156 | ||||||||
\(107\) | −4.95618 | −0.479132 | −0.239566 | − | 0.970880i | \(-0.577005\pi\) | ||||
−0.239566 | + | 0.970880i | \(0.577005\pi\) | |||||||
\(108\) | 3.58741 | 0.345199 | ||||||||
\(109\) | −2.61667 | −0.250632 | −0.125316 | − | 0.992117i | \(-0.539994\pi\) | ||||
−0.125316 | + | 0.992117i | \(0.539994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.5420 | 1.09551 | ||||||||
\(112\) | −2.90508 | −0.274504 | ||||||||
\(113\) | −2.11658 | −0.199111 | −0.0995554 | − | 0.995032i | \(-0.531742\pi\) | ||||
−0.0995554 | + | 0.995032i | \(0.531742\pi\) | |||||||
\(114\) | −13.6341 | −1.27695 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.6158 | −1.17135 | ||||||||
\(117\) | −3.53338 | −0.326661 | ||||||||
\(118\) | 12.6696 | 1.16633 | ||||||||
\(119\) | 0.639932 | 0.0586624 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.05170 | −0.728966 | ||||||||
\(123\) | −2.41898 | −0.218112 | ||||||||
\(124\) | −36.2249 | −3.25309 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.05205 | −0.360985 | ||||||||
\(127\) | −11.9477 | −1.06018 | −0.530092 | − | 0.847940i | \(-0.677843\pi\) | ||||
−0.530092 | + | 0.847940i | \(0.677843\pi\) | |||||||
\(128\) | −20.5629 | −1.81752 | ||||||||
\(129\) | −0.224486 | −0.0197649 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.3359 | 1.77676 | 0.888380 | − | 0.459110i | \(-0.151831\pi\) | ||||
0.888380 | + | 0.459110i | \(0.151831\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.88758 | 0.857362 | ||||||||
\(134\) | 21.4864 | 1.85614 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.40074 | −0.120113 | ||||||||
\(137\) | −5.31343 | −0.453957 | −0.226979 | − | 0.973900i | \(-0.572885\pi\) | ||||
−0.226979 | + | 0.973900i | \(0.572885\pi\) | |||||||
\(138\) | −8.99992 | −0.766124 | ||||||||
\(139\) | 13.2156 | 1.12093 | 0.560465 | − | 0.828178i | \(-0.310622\pi\) | ||||
0.560465 | + | 0.828178i | \(0.310622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.67637 | −0.393821 | ||||||||
\(142\) | −20.7436 | −1.74076 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.69468 | 0.141223 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −35.3673 | −2.92702 | ||||||||
\(147\) | −4.06141 | −0.334979 | ||||||||
\(148\) | 41.4057 | 3.40353 | ||||||||
\(149\) | −6.06286 | −0.496689 | −0.248344 | − | 0.968672i | \(-0.579886\pi\) | ||||
−0.248344 | + | 0.968672i | \(0.579886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.33491 | −0.596907 | −0.298453 | − | 0.954424i | \(-0.596471\pi\) | ||||
−0.298453 | + | 0.954424i | \(0.596471\pi\) | |||||||
\(152\) | −21.6429 | −1.75547 | ||||||||
\(153\) | −0.373305 | −0.0301799 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.6757 | −1.01487 | ||||||||
\(157\) | −10.5558 | −0.842444 | −0.421222 | − | 0.906958i | \(-0.638399\pi\) | ||||
−0.421222 | + | 0.906958i | \(0.638399\pi\) | |||||||
\(158\) | 20.7824 | 1.65336 | ||||||||
\(159\) | −2.44417 | −0.193835 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.52684 | 0.514387 | ||||||||
\(162\) | 2.36377 | 0.185715 | ||||||||
\(163\) | −10.1070 | −0.791645 | −0.395822 | − | 0.918327i | \(-0.629540\pi\) | ||||
−0.395822 | + | 0.918327i | \(0.629540\pi\) | |||||||
\(164\) | −8.67786 | −0.677627 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.5915 | 1.36537 | ||||||||
\(167\) | −13.3472 | −1.03284 | −0.516419 | − | 0.856336i | \(-0.672735\pi\) | ||||
−0.516419 | + | 0.856336i | \(0.672735\pi\) | |||||||
\(168\) | −6.43226 | −0.496259 | ||||||||
\(169\) | −0.515200 | −0.0396308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.76794 | −0.441085 | ||||||||
\(172\) | −0.805322 | −0.0614052 | ||||||||
\(173\) | −17.8603 | −1.35790 | −0.678948 | − | 0.734187i | \(-0.737564\pi\) | ||||
−0.678948 | + | 0.734187i | \(0.737564\pi\) | |||||||
\(174\) | −8.31267 | −0.630182 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.35991 | 0.402875 | ||||||||
\(178\) | 36.6522 | 2.74720 | ||||||||
\(179\) | −12.7372 | −0.952024 | −0.476012 | − | 0.879439i | \(-0.657918\pi\) | ||||
−0.476012 | + | 0.879439i | \(0.657918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7117 | 1.53949 | 0.769746 | − | 0.638350i | \(-0.220383\pi\) | ||||
0.769746 | + | 0.638350i | \(0.220383\pi\) | |||||||
\(182\) | 14.3174 | 1.06128 | ||||||||
\(183\) | −3.40629 | −0.251801 | ||||||||
\(184\) | −14.2866 | −1.05322 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −23.8688 | −1.75015 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −16.7760 | −1.22352 | ||||||||
\(189\) | −1.71423 | −0.124692 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.19957 | −0.448585 | −0.224293 | − | 0.974522i | \(-0.572007\pi\) | ||||
−0.224293 | + | 0.974522i | \(0.572007\pi\) | |||||||
\(192\) | −11.6595 | −0.841451 | ||||||||
\(193\) | −5.52362 | −0.397599 | −0.198800 | − | 0.980040i | \(-0.563704\pi\) | ||||
−0.198800 | + | 0.980040i | \(0.563704\pi\) | |||||||
\(194\) | 34.6616 | 2.48856 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.5699 | −1.04071 | ||||||||
\(197\) | −12.8524 | −0.915693 | −0.457846 | − | 0.889031i | \(-0.651379\pi\) | ||||
−0.457846 | + | 0.889031i | \(0.651379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.42830 | 0.243026 | 0.121513 | − | 0.992590i | \(-0.461225\pi\) | ||||
0.121513 | + | 0.992590i | \(0.461225\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.08988 | 0.641151 | ||||||||
\(202\) | 14.5010 | 1.02029 | ||||||||
\(203\) | 6.02844 | 0.423113 | ||||||||
\(204\) | −1.33920 | −0.0937626 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.6026 | 1.29610 | ||||||||
\(207\) | −3.80745 | −0.264636 | ||||||||
\(208\) | −5.98796 | −0.415190 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8292 | 1.22741 | 0.613705 | − | 0.789535i | \(-0.289678\pi\) | ||||
0.613705 | + | 0.789535i | \(0.289678\pi\) | |||||||
\(212\) | −8.76823 | −0.602205 | ||||||||
\(213\) | −8.77564 | −0.601297 | ||||||||
\(214\) | −11.7153 | −0.800840 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.75227 | 0.255310 | ||||||||
\(217\) | 17.3099 | 1.17508 | ||||||||
\(218\) | −6.18522 | −0.418916 | ||||||||
\(219\) | −14.9622 | −1.01105 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.31903 | 0.0887276 | ||||||||
\(222\) | 27.2825 | 1.83108 | ||||||||
\(223\) | 4.31709 | 0.289094 | 0.144547 | − | 0.989498i | \(-0.453828\pi\) | ||||
0.144547 | + | 0.989498i | \(0.453828\pi\) | |||||||
\(224\) | 5.99758 | 0.400730 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.00310 | −0.332801 | ||||||||
\(227\) | 25.4363 | 1.68827 | 0.844134 | − | 0.536133i | \(-0.180115\pi\) | ||||
0.844134 | + | 0.536133i | \(0.180115\pi\) | |||||||
\(228\) | −20.6919 | −1.37036 | ||||||||
\(229\) | 14.3934 | 0.951139 | 0.475570 | − | 0.879678i | \(-0.342242\pi\) | ||||
0.475570 | + | 0.879678i | \(0.342242\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.1956 | −0.866333 | ||||||||
\(233\) | −11.9315 | −0.781660 | −0.390830 | − | 0.920463i | \(-0.627812\pi\) | ||||
−0.390830 | + | 0.920463i | \(0.627812\pi\) | |||||||
\(234\) | −8.35211 | −0.545994 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 19.2282 | 1.25165 | ||||||||
\(237\) | 8.79204 | 0.571104 | ||||||||
\(238\) | 1.51265 | 0.0980506 | ||||||||
\(239\) | −8.25748 | −0.534132 | −0.267066 | − | 0.963678i | \(-0.586054\pi\) | ||||
−0.267066 | + | 0.963678i | \(0.586054\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.1487 | −0.718154 | −0.359077 | − | 0.933308i | \(-0.616908\pi\) | ||||
−0.359077 | + | 0.933308i | \(0.616908\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −12.2198 | −0.782291 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.71791 | −0.364561 | ||||||||
\(247\) | 20.3803 | 1.29677 | ||||||||
\(248\) | −37.8896 | −2.40599 | ||||||||
\(249\) | 7.44215 | 0.471627 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.6627 | 1.80918 | 0.904588 | − | 0.426286i | \(-0.140178\pi\) | ||||
0.904588 | + | 0.426286i | \(0.140178\pi\) | |||||||
\(252\) | −6.14965 | −0.387392 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −28.2415 | −1.77203 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −25.2871 | −1.58044 | ||||||||
\(257\) | 2.32004 | 0.144720 | 0.0723601 | − | 0.997379i | \(-0.476947\pi\) | ||||
0.0723601 | + | 0.997379i | \(0.476947\pi\) | |||||||
\(258\) | −0.530633 | −0.0330358 | ||||||||
\(259\) | −19.7856 | −1.22942 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.51670 | −0.217678 | ||||||||
\(262\) | 48.0695 | 2.96974 | ||||||||
\(263\) | −2.92970 | −0.180653 | −0.0903265 | − | 0.995912i | \(-0.528791\pi\) | ||||
−0.0903265 | + | 0.995912i | \(0.528791\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 23.3720 | 1.43303 | ||||||||
\(267\) | 15.5058 | 0.948940 | ||||||||
\(268\) | 32.6091 | 1.99192 | ||||||||
\(269\) | −4.53203 | −0.276323 | −0.138161 | − | 0.990410i | \(-0.544119\pi\) | ||||
−0.138161 | + | 0.990410i | \(0.544119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.1116 | 1.64692 | 0.823458 | − | 0.567378i | \(-0.192042\pi\) | ||||
0.823458 | + | 0.567378i | \(0.192042\pi\) | |||||||
\(272\) | −0.632633 | −0.0383590 | ||||||||
\(273\) | 6.05704 | 0.366589 | ||||||||
\(274\) | −12.5597 | −0.758761 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.6589 | −0.822167 | ||||||||
\(277\) | −13.2514 | −0.796199 | −0.398100 | − | 0.917342i | \(-0.630330\pi\) | ||||
−0.398100 | + | 0.917342i | \(0.630330\pi\) | |||||||
\(278\) | 31.2386 | 1.87356 | ||||||||
\(279\) | −10.0978 | −0.604538 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0716 | −0.660479 | −0.330239 | − | 0.943897i | \(-0.607129\pi\) | ||||
−0.330239 | + | 0.943897i | \(0.607129\pi\) | |||||||
\(282\) | −11.0539 | −0.658247 | ||||||||
\(283\) | −10.0767 | −0.599000 | −0.299500 | − | 0.954096i | \(-0.596820\pi\) | ||||
−0.299500 | + | 0.954096i | \(0.596820\pi\) | |||||||
\(284\) | −31.4818 | −1.86810 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.14669 | 0.244771 | ||||||||
\(288\) | −3.49870 | −0.206163 | ||||||||
\(289\) | −16.8606 | −0.991803 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6637 | 0.859600 | ||||||||
\(292\) | −53.6756 | −3.14113 | ||||||||
\(293\) | −7.84659 | −0.458402 | −0.229201 | − | 0.973379i | \(-0.573611\pi\) | ||||
−0.229201 | + | 0.973379i | \(0.573611\pi\) | |||||||
\(294\) | −9.60024 | −0.559897 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 43.3085 | 2.51725 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.3312 | −0.830184 | ||||||||
\(299\) | 13.4532 | 0.778017 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.384821 | 0.0221807 | ||||||||
\(302\) | −17.3380 | −0.997692 | ||||||||
\(303\) | 6.13469 | 0.352429 | ||||||||
\(304\) | −9.77482 | −0.560624 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.882407 | −0.0504439 | ||||||||
\(307\) | 2.64692 | 0.151068 | 0.0755339 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755339 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.86989 | 0.447702 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.50819 | −0.255636 | −0.127818 | − | 0.991798i | \(-0.540797\pi\) | ||||
−0.127818 | + | 0.991798i | \(0.540797\pi\) | |||||||
\(312\) | −13.2582 | −0.750598 | ||||||||
\(313\) | −9.70923 | −0.548798 | −0.274399 | − | 0.961616i | \(-0.588479\pi\) | ||||
−0.274399 | + | 0.961616i | \(0.588479\pi\) | |||||||
\(314\) | −24.9515 | −1.40809 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 31.5406 | 1.77430 | ||||||||
\(317\) | −17.0757 | −0.959066 | −0.479533 | − | 0.877524i | \(-0.659194\pi\) | ||||
−0.479533 | + | 0.877524i | \(0.659194\pi\) | |||||||
\(318\) | −5.77745 | −0.323984 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.95618 | −0.276627 | ||||||||
\(322\) | 15.4280 | 0.859766 | ||||||||
\(323\) | 2.15320 | 0.119807 | ||||||||
\(324\) | 3.58741 | 0.199300 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.8907 | −1.32319 | ||||||||
\(327\) | −2.61667 | −0.144702 | ||||||||
\(328\) | −9.07666 | −0.501174 | ||||||||
\(329\) | 8.01638 | 0.441957 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.79769 | −0.153775 | −0.0768874 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768874 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(332\) | 26.6980 | 1.46524 | ||||||||
\(333\) | 11.5420 | 0.632495 | ||||||||
\(334\) | −31.5497 | −1.72632 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.90508 | −0.158485 | ||||||||
\(337\) | 9.28778 | 0.505937 | 0.252969 | − | 0.967474i | \(-0.418593\pi\) | ||||
0.252969 | + | 0.967474i | \(0.418593\pi\) | |||||||
\(338\) | −1.21781 | −0.0662404 | ||||||||
\(339\) | −2.11658 | −0.114957 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −13.6341 | −0.737247 | ||||||||
\(343\) | 18.9618 | 1.02384 | ||||||||
\(344\) | −0.842331 | −0.0454154 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −42.2177 | −2.26964 | ||||||||
\(347\) | 9.35525 | 0.502216 | 0.251108 | − | 0.967959i | \(-0.419205\pi\) | ||||
0.251108 | + | 0.967959i | \(0.419205\pi\) | |||||||
\(348\) | −12.6158 | −0.676280 | ||||||||
\(349\) | −1.68796 | −0.0903544 | −0.0451772 | − | 0.998979i | \(-0.514385\pi\) | ||||
−0.0451772 | + | 0.998979i | \(0.514385\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.53338 | −0.188598 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.60028 | 0.510971 | 0.255486 | − | 0.966813i | \(-0.417765\pi\) | ||||
0.255486 | + | 0.966813i | \(0.417765\pi\) | |||||||
\(354\) | 12.6696 | 0.673381 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 55.6257 | 2.94816 | ||||||||
\(357\) | 0.639932 | 0.0338688 | ||||||||
\(358\) | −30.1078 | −1.59125 | ||||||||
\(359\) | −27.1863 | −1.43484 | −0.717420 | − | 0.696641i | \(-0.754677\pi\) | ||||
−0.717420 | + | 0.696641i | \(0.754677\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.2691 | 0.751006 | ||||||||
\(362\) | 48.9578 | 2.57317 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 21.7291 | 1.13891 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.05170 | −0.420869 | ||||||||
\(367\) | 7.71659 | 0.402803 | 0.201401 | − | 0.979509i | \(-0.435450\pi\) | ||||
0.201401 | + | 0.979509i | \(0.435450\pi\) | |||||||
\(368\) | −6.45241 | −0.336355 | ||||||||
\(369\) | −2.41898 | −0.125927 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.18987 | 0.217527 | ||||||||
\(372\) | −36.2249 | −1.87817 | ||||||||
\(373\) | −20.0037 | −1.03575 | −0.517876 | − | 0.855456i | \(-0.673277\pi\) | ||||
−0.517876 | + | 0.855456i | \(0.673277\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.5470 | −0.904916 | ||||||||
\(377\) | 12.4258 | 0.639964 | ||||||||
\(378\) | −4.05205 | −0.208415 | ||||||||
\(379\) | −6.71765 | −0.345063 | −0.172531 | − | 0.985004i | \(-0.555195\pi\) | ||||
−0.172531 | + | 0.985004i | \(0.555195\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.9477 | −0.612097 | ||||||||
\(382\) | −14.6544 | −0.749782 | ||||||||
\(383\) | −11.3494 | −0.579928 | −0.289964 | − | 0.957038i | \(-0.593643\pi\) | ||||
−0.289964 | + | 0.957038i | \(0.593643\pi\) | |||||||
\(384\) | −20.5629 | −1.04935 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.0566 | −0.664562 | ||||||||
\(387\) | −0.224486 | −0.0114113 | ||||||||
\(388\) | 52.6046 | 2.67059 | ||||||||
\(389\) | −5.16601 | −0.261927 | −0.130964 | − | 0.991387i | \(-0.541807\pi\) | ||||
−0.130964 | + | 0.991387i | \(0.541807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.42134 | 0.0718802 | ||||||||
\(392\) | −15.2395 | −0.769711 | ||||||||
\(393\) | 20.3359 | 1.02581 | ||||||||
\(394\) | −30.3800 | −1.53052 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.40026 | −0.371408 | −0.185704 | − | 0.982606i | \(-0.559457\pi\) | ||||
−0.185704 | + | 0.982606i | \(0.559457\pi\) | |||||||
\(398\) | 8.10371 | 0.406202 | ||||||||
\(399\) | 9.88758 | 0.494998 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.7932 | −1.58768 | −0.793839 | − | 0.608129i | \(-0.791921\pi\) | ||||
−0.793839 | + | 0.608129i | \(0.791921\pi\) | |||||||
\(402\) | 21.4864 | 1.07164 | ||||||||
\(403\) | 35.6793 | 1.77731 | ||||||||
\(404\) | 22.0076 | 1.09492 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.2498 | 0.707208 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.40074 | −0.0693470 | ||||||||
\(409\) | 11.9000 | 0.588419 | 0.294210 | − | 0.955741i | \(-0.404944\pi\) | ||||
0.294210 | + | 0.955741i | \(0.404944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.31343 | −0.262092 | ||||||||
\(412\) | 28.2325 | 1.39092 | ||||||||
\(413\) | −9.18812 | −0.452118 | ||||||||
\(414\) | −8.99992 | −0.442322 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.3622 | 0.606109 | ||||||||
\(417\) | 13.2156 | 0.647169 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.57012 | 0.320971 | 0.160486 | − | 0.987038i | \(-0.448694\pi\) | ||||
0.160486 | + | 0.987038i | \(0.448694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.3343 | 1.52714 | 0.763570 | − | 0.645725i | \(-0.223445\pi\) | ||||
0.763570 | + | 0.645725i | \(0.223445\pi\) | |||||||
\(422\) | 42.1441 | 2.05154 | ||||||||
\(423\) | −4.67637 | −0.227373 | ||||||||
\(424\) | −9.17118 | −0.445392 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −20.7436 | −1.00503 | ||||||||
\(427\) | 5.83918 | 0.282578 | ||||||||
\(428\) | −17.7799 | −0.859422 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.5417 | 0.604113 | 0.302057 | − | 0.953290i | \(-0.402327\pi\) | ||||
0.302057 | + | 0.953290i | \(0.402327\pi\) | |||||||
\(432\) | 1.69468 | 0.0815354 | ||||||||
\(433\) | −26.0234 | −1.25060 | −0.625302 | − | 0.780383i | \(-0.715024\pi\) | ||||
−0.625302 | + | 0.780383i | \(0.715024\pi\) | |||||||
\(434\) | 40.9167 | 1.96407 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.38708 | −0.449560 | ||||||||
\(437\) | 21.9611 | 1.05054 | ||||||||
\(438\) | −35.3673 | −1.68991 | ||||||||
\(439\) | −35.0511 | −1.67290 | −0.836450 | − | 0.548044i | \(-0.815373\pi\) | ||||
−0.836450 | + | 0.548044i | \(0.815373\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.06141 | −0.193400 | ||||||||
\(442\) | 3.11788 | 0.148303 | ||||||||
\(443\) | −26.0766 | −1.23894 | −0.619468 | − | 0.785022i | \(-0.712652\pi\) | ||||
−0.619468 | + | 0.785022i | \(0.712652\pi\) | |||||||
\(444\) | 41.4057 | 1.96503 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.2046 | 0.483202 | ||||||||
\(447\) | −6.06286 | −0.286763 | ||||||||
\(448\) | 19.9871 | 0.944300 | ||||||||
\(449\) | −0.713928 | −0.0336923 | −0.0168462 | − | 0.999858i | \(-0.505363\pi\) | ||||
−0.0168462 | + | 0.999858i | \(0.505363\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −7.59303 | −0.357146 | ||||||||
\(453\) | −7.33491 | −0.344624 | ||||||||
\(454\) | 60.1256 | 2.82183 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.6429 | −1.01352 | ||||||||
\(457\) | −29.9979 | −1.40324 | −0.701621 | − | 0.712551i | \(-0.747540\pi\) | ||||
−0.701621 | + | 0.712551i | \(0.747540\pi\) | |||||||
\(458\) | 34.0226 | 1.58977 | ||||||||
\(459\) | −0.373305 | −0.0174244 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.0359281 | 0.00167334 | 0.000836670 | − | 1.00000i | \(-0.499734\pi\) | ||||
0.000836670 | 1.00000i | \(0.499734\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.65474 | −0.169850 | −0.0849251 | − | 0.996387i | \(-0.527065\pi\) | ||||
−0.0849251 | + | 0.996387i | \(0.527065\pi\) | |||||||
\(464\) | −5.95969 | −0.276671 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.2034 | −1.30650 | ||||||||
\(467\) | 15.2379 | 0.705124 | 0.352562 | − | 0.935788i | \(-0.385311\pi\) | ||||
0.352562 | + | 0.935788i | \(0.385311\pi\) | |||||||
\(468\) | −12.6757 | −0.585934 | ||||||||
\(469\) | −15.5822 | −0.719517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5558 | −0.486385 | ||||||||
\(472\) | 20.1118 | 0.925721 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 20.7824 | 0.954565 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.29570 | 0.105223 | ||||||||
\(477\) | −2.44417 | −0.111911 | ||||||||
\(478\) | −19.5188 | −0.892768 | ||||||||
\(479\) | −12.5608 | −0.573918 | −0.286959 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286959 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −40.7821 | −1.85951 | ||||||||
\(482\) | −26.3531 | −1.20035 | ||||||||
\(483\) | 6.52684 | 0.296982 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.36377 | 0.107223 | ||||||||
\(487\) | 1.72235 | 0.0780470 | 0.0390235 | − | 0.999238i | \(-0.487575\pi\) | ||||
0.0390235 | + | 0.999238i | \(0.487575\pi\) | |||||||
\(488\) | −12.7813 | −0.578584 | ||||||||
\(489\) | −10.1070 | −0.457056 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.1226 | 0.908122 | 0.454061 | − | 0.890971i | \(-0.349975\pi\) | ||||
0.454061 | + | 0.890971i | \(0.349975\pi\) | |||||||
\(492\) | −8.67786 | −0.391228 | ||||||||
\(493\) | 1.31280 | 0.0591256 | ||||||||
\(494\) | 48.1744 | 2.16747 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.1125 | −0.768375 | ||||||||
\(497\) | 15.0435 | 0.674792 | ||||||||
\(498\) | 17.5915 | 0.788295 | ||||||||
\(499\) | 17.8863 | 0.800702 | 0.400351 | − | 0.916362i | \(-0.368888\pi\) | ||||
0.400351 | + | 0.916362i | \(0.368888\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.3472 | −0.596309 | ||||||||
\(502\) | 67.7521 | 3.02393 | ||||||||
\(503\) | 16.3835 | 0.730504 | 0.365252 | − | 0.930909i | \(-0.380983\pi\) | ||||
0.365252 | + | 0.930909i | \(0.380983\pi\) | |||||||
\(504\) | −6.43226 | −0.286516 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.515200 | −0.0228808 | ||||||||
\(508\) | −42.8611 | −1.90166 | ||||||||
\(509\) | 0.140642 | 0.00623384 | 0.00311692 | − | 0.999995i | \(-0.499008\pi\) | ||||
0.00311692 | + | 0.999995i | \(0.499008\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.6487 | 1.13463 | ||||||||
\(512\) | −18.6470 | −0.824088 | ||||||||
\(513\) | −5.76794 | −0.254661 | ||||||||
\(514\) | 5.48404 | 0.241891 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.805322 | −0.0354523 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −46.7686 | −2.05489 | ||||||||
\(519\) | −17.8603 | −0.783981 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.91589 | 0.259180 | 0.129590 | − | 0.991568i | \(-0.458634\pi\) | ||||
0.129590 | + | 0.991568i | \(0.458634\pi\) | |||||||
\(522\) | −8.31267 | −0.363836 | ||||||||
\(523\) | −18.9759 | −0.829759 | −0.414879 | − | 0.909876i | \(-0.636176\pi\) | ||||
−0.414879 | + | 0.909876i | \(0.636176\pi\) | |||||||
\(524\) | 72.9533 | 3.18698 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.92513 | −0.301950 | ||||||||
\(527\) | 3.76955 | 0.164204 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.50336 | −0.369711 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.35991 | 0.232600 | ||||||||
\(532\) | 35.4708 | 1.53785 | ||||||||
\(533\) | 8.54718 | 0.370219 | ||||||||
\(534\) | 36.6522 | 1.58609 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 34.1077 | 1.47323 | ||||||||
\(537\) | −12.7372 | −0.549651 | ||||||||
\(538\) | −10.7127 | −0.461856 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.3241 | 0.787813 | 0.393907 | − | 0.919150i | \(-0.371123\pi\) | ||||
0.393907 | + | 0.919150i | \(0.371123\pi\) | |||||||
\(542\) | 64.0857 | 2.75272 | ||||||||
\(543\) | 20.7117 | 0.888826 | ||||||||
\(544\) | 1.30608 | 0.0559978 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.3174 | 0.612730 | ||||||||
\(547\) | 30.8579 | 1.31939 | 0.659694 | − | 0.751534i | \(-0.270686\pi\) | ||||
0.659694 | + | 0.751534i | \(0.270686\pi\) | |||||||
\(548\) | −19.0615 | −0.814265 | ||||||||
\(549\) | −3.40629 | −0.145377 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.2841 | 0.864132 | ||||||||
\(552\) | −14.2866 | −0.608076 | ||||||||
\(553\) | −15.0716 | −0.640909 | ||||||||
\(554\) | −31.3232 | −1.33080 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 47.4096 | 2.01062 | ||||||||
\(557\) | −37.2863 | −1.57987 | −0.789936 | − | 0.613190i | \(-0.789886\pi\) | ||||
−0.789936 | + | 0.613190i | \(0.789886\pi\) | |||||||
\(558\) | −23.8688 | −1.01045 | ||||||||
\(559\) | 0.793194 | 0.0335485 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.1708 | −1.10395 | ||||||||
\(563\) | 18.4747 | 0.778614 | 0.389307 | − | 0.921108i | \(-0.372715\pi\) | ||||
0.389307 | + | 0.921108i | \(0.372715\pi\) | |||||||
\(564\) | −16.7760 | −0.706398 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −23.8191 | −1.00119 | ||||||||
\(567\) | −1.71423 | −0.0719910 | ||||||||
\(568\) | −32.9285 | −1.38165 | ||||||||
\(569\) | −41.9737 | −1.75963 | −0.879814 | − | 0.475318i | \(-0.842333\pi\) | ||||
−0.879814 | + | 0.475318i | \(0.842333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.70741 | −0.406243 | −0.203121 | − | 0.979154i | \(-0.565109\pi\) | ||||
−0.203121 | + | 0.979154i | \(0.565109\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.19957 | −0.258991 | ||||||||
\(574\) | 9.80182 | 0.409120 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.6595 | −0.485812 | ||||||||
\(577\) | 13.0307 | 0.542475 | 0.271237 | − | 0.962513i | \(-0.412567\pi\) | ||||
0.271237 | + | 0.962513i | \(0.412567\pi\) | |||||||
\(578\) | −39.8547 | −1.65774 | ||||||||
\(579\) | −5.52362 | −0.229554 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.7576 | −0.529273 | ||||||||
\(582\) | 34.6616 | 1.43677 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −56.1423 | −2.32319 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.5475 | −0.766191 | ||||||||
\(587\) | −43.2385 | −1.78464 | −0.892321 | − | 0.451401i | \(-0.850925\pi\) | ||||
−0.892321 | + | 0.451401i | \(0.850925\pi\) | |||||||
\(588\) | −14.5699 | −0.600854 | ||||||||
\(589\) | 58.2434 | 2.39988 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8524 | −0.528675 | ||||||||
\(592\) | 19.5599 | 0.803908 | ||||||||
\(593\) | 34.9632 | 1.43576 | 0.717882 | − | 0.696164i | \(-0.245112\pi\) | ||||
0.717882 | + | 0.696164i | \(0.245112\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.7499 | −0.890912 | ||||||||
\(597\) | 3.42830 | 0.140311 | ||||||||
\(598\) | 31.8002 | 1.30041 | ||||||||
\(599\) | 22.5431 | 0.921086 | 0.460543 | − | 0.887637i | \(-0.347655\pi\) | ||||
0.460543 | + | 0.887637i | \(0.347655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.9404 | −0.813388 | −0.406694 | − | 0.913564i | \(-0.633318\pi\) | ||||
−0.406694 | + | 0.913564i | \(0.633318\pi\) | |||||||
\(602\) | 0.909628 | 0.0370737 | ||||||||
\(603\) | 9.08988 | 0.370169 | ||||||||
\(604\) | −26.3133 | −1.07067 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.5010 | 0.589063 | ||||||||
\(607\) | 16.4084 | 0.665997 | 0.332999 | − | 0.942927i | \(-0.391940\pi\) | ||||
0.332999 | + | 0.942927i | \(0.391940\pi\) | |||||||
\(608\) | 20.1803 | 0.818418 | ||||||||
\(609\) | 6.02844 | 0.244285 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.5234 | 0.668465 | ||||||||
\(612\) | −1.33920 | −0.0541339 | ||||||||
\(613\) | 37.2802 | 1.50573 | 0.752866 | − | 0.658174i | \(-0.228671\pi\) | ||||
0.752866 | + | 0.658174i | \(0.228671\pi\) | |||||||
\(614\) | 6.25672 | 0.252501 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.7965 | −1.15930 | −0.579651 | − | 0.814865i | \(-0.696811\pi\) | ||||
−0.579651 | + | 0.814865i | \(0.696811\pi\) | |||||||
\(618\) | 18.6026 | 0.748306 | ||||||||
\(619\) | 8.36974 | 0.336408 | 0.168204 | − | 0.985752i | \(-0.446203\pi\) | ||||
0.168204 | + | 0.985752i | \(0.446203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.80745 | −0.152788 | ||||||||
\(622\) | −10.6563 | −0.427280 | ||||||||
\(623\) | −26.5806 | −1.06493 | ||||||||
\(624\) | −5.98796 | −0.239710 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.9504 | −0.917282 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −37.8679 | −1.51109 | ||||||||
\(629\) | −4.30867 | −0.171798 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.9307 | −1.19152 | −0.595762 | − | 0.803161i | \(-0.703150\pi\) | ||||
−0.595762 | + | 0.803161i | \(0.703150\pi\) | |||||||
\(632\) | 32.9901 | 1.31227 | ||||||||
\(633\) | 17.8292 | 0.708646 | ||||||||
\(634\) | −40.3630 | −1.60302 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.76823 | −0.347683 | ||||||||
\(637\) | 14.3505 | 0.568588 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.77564 | −0.347159 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.11788 | 0.0836513 | 0.0418257 | − | 0.999125i | \(-0.486683\pi\) | ||||
0.0418257 | + | 0.999125i | \(0.486683\pi\) | |||||||
\(642\) | −11.7153 | −0.462365 | ||||||||
\(643\) | 19.3340 | 0.762457 | 0.381228 | − | 0.924481i | \(-0.375501\pi\) | ||||
0.381228 | + | 0.924481i | \(0.375501\pi\) | |||||||
\(644\) | 23.4145 | 0.922659 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.08967 | 0.200250 | ||||||||
\(647\) | −2.10369 | −0.0827045 | −0.0413523 | − | 0.999145i | \(-0.513167\pi\) | ||||
−0.0413523 | + | 0.999145i | \(0.513167\pi\) | |||||||
\(648\) | 3.75227 | 0.147403 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.3099 | 0.678430 | ||||||||
\(652\) | −36.2581 | −1.41998 | ||||||||
\(653\) | 2.62234 | 0.102620 | 0.0513100 | − | 0.998683i | \(-0.483660\pi\) | ||||
0.0513100 | + | 0.998683i | \(0.483660\pi\) | |||||||
\(654\) | −6.18522 | −0.241861 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.09940 | −0.160055 | ||||||||
\(657\) | −14.9622 | −0.583732 | ||||||||
\(658\) | 18.9489 | 0.738704 | ||||||||
\(659\) | 36.2473 | 1.41199 | 0.705997 | − | 0.708215i | \(-0.250499\pi\) | ||||
0.705997 | + | 0.708215i | \(0.250499\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.6488 | 0.880937 | 0.440469 | − | 0.897768i | \(-0.354812\pi\) | ||||
0.440469 | + | 0.897768i | \(0.354812\pi\) | |||||||
\(662\) | −6.61309 | −0.257025 | ||||||||
\(663\) | 1.31903 | 0.0512269 | ||||||||
\(664\) | 27.9249 | 1.08370 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.2825 | 1.05718 | ||||||||
\(667\) | 13.3896 | 0.518449 | ||||||||
\(668\) | −47.8819 | −1.85261 | ||||||||
\(669\) | 4.31709 | 0.166908 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.99758 | 0.231362 | ||||||||
\(673\) | −37.0125 | −1.42673 | −0.713364 | − | 0.700793i | \(-0.752829\pi\) | ||||
−0.713364 | + | 0.700793i | \(0.752829\pi\) | |||||||
\(674\) | 21.9542 | 0.845643 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.84823 | −0.0710859 | ||||||||
\(677\) | −29.7163 | −1.14209 | −0.571044 | − | 0.820919i | \(-0.693462\pi\) | ||||
−0.571044 | + | 0.820919i | \(0.693462\pi\) | |||||||
\(678\) | −5.00310 | −0.192143 | ||||||||
\(679\) | −25.1370 | −0.964668 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.4363 | 0.974722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.06173 | 0.0788899 | 0.0394450 | − | 0.999222i | \(-0.487441\pi\) | ||||
0.0394450 | + | 0.999222i | \(0.487441\pi\) | |||||||
\(684\) | −20.6919 | −0.791176 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 44.8214 | 1.71129 | ||||||||
\(687\) | 14.3934 | 0.549141 | ||||||||
\(688\) | −0.380432 | −0.0145038 | ||||||||
\(689\) | 8.63619 | 0.329013 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.97575 | 0.113203 | 0.0566015 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0566015 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(692\) | −64.0723 | −2.43566 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.1137 | 0.839423 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.1956 | −0.500178 | ||||||||
\(697\) | 0.903017 | 0.0342042 | ||||||||
\(698\) | −3.98995 | −0.151022 | ||||||||
\(699\) | −11.9315 | −0.451291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.6095 | 1.60934 | 0.804669 | − | 0.593724i | \(-0.202343\pi\) | ||||
0.804669 | + | 0.593724i | \(0.202343\pi\) | |||||||
\(702\) | −8.35211 | −0.315230 | ||||||||
\(703\) | −66.5733 | −2.51086 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.6928 | 0.854056 | ||||||||
\(707\) | −10.5163 | −0.395505 | ||||||||
\(708\) | 19.2282 | 0.722639 | ||||||||
\(709\) | −41.6111 | −1.56274 | −0.781370 | − | 0.624069i | \(-0.785479\pi\) | ||||
−0.781370 | + | 0.624069i | \(0.785479\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.79204 | 0.329727 | ||||||||
\(712\) | 58.1820 | 2.18046 | ||||||||
\(713\) | 38.4468 | 1.43984 | ||||||||
\(714\) | 1.51265 | 0.0566095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −45.6936 | −1.70765 | ||||||||
\(717\) | −8.25748 | −0.308381 | ||||||||
\(718\) | −64.2622 | −2.39824 | ||||||||
\(719\) | 4.90277 | 0.182843 | 0.0914213 | − | 0.995812i | \(-0.470859\pi\) | ||||
0.0914213 | + | 0.995812i | \(0.470859\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4908 | −0.502424 | ||||||||
\(722\) | 33.7289 | 1.25526 | ||||||||
\(723\) | −11.1487 | −0.414626 | ||||||||
\(724\) | 74.3015 | 2.76139 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.26283 | −0.343539 | −0.171770 | − | 0.985137i | \(-0.554948\pi\) | ||||
−0.171770 | + | 0.985137i | \(0.554948\pi\) | |||||||
\(728\) | 22.7276 | 0.842342 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0838017 | 0.00309952 | ||||||||
\(732\) | −12.2198 | −0.451656 | ||||||||
\(733\) | 13.6525 | 0.504268 | 0.252134 | − | 0.967692i | \(-0.418868\pi\) | ||||
0.252134 | + | 0.967692i | \(0.418868\pi\) | |||||||
\(734\) | 18.2403 | 0.673260 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.3211 | 0.491022 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −5.71791 | −0.210479 | ||||||||
\(739\) | −44.1335 | −1.62348 | −0.811739 | − | 0.584020i | \(-0.801479\pi\) | ||||
−0.811739 | + | 0.584020i | \(0.801479\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.3803 | 0.748690 | ||||||||
\(742\) | 9.90390 | 0.363583 | ||||||||
\(743\) | 14.8496 | 0.544780 | 0.272390 | − | 0.962187i | \(-0.412186\pi\) | ||||
0.272390 | + | 0.962187i | \(0.412186\pi\) | |||||||
\(744\) | −37.8896 | −1.38910 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −47.2841 | −1.73120 | ||||||||
\(747\) | 7.44215 | 0.272294 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.49605 | 0.310439 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.79939 | −0.138642 | −0.0693208 | − | 0.997594i | \(-0.522083\pi\) | ||||
−0.0693208 | + | 0.997594i | \(0.522083\pi\) | |||||||
\(752\) | −7.92495 | −0.288993 | ||||||||
\(753\) | 28.6627 | 1.04453 | ||||||||
\(754\) | 29.3718 | 1.06966 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.14965 | −0.223661 | ||||||||
\(757\) | 7.11918 | 0.258751 | 0.129376 | − | 0.991596i | \(-0.458703\pi\) | ||||
0.129376 | + | 0.991596i | \(0.458703\pi\) | |||||||
\(758\) | −15.8790 | −0.576751 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.47697 | 0.198540 | 0.0992699 | − | 0.995061i | \(-0.468349\pi\) | ||||
0.0992699 | + | 0.995061i | \(0.468349\pi\) | |||||||
\(762\) | −28.2415 | −1.02308 | ||||||||
\(763\) | 4.48559 | 0.162389 | ||||||||
\(764\) | −22.2404 | −0.804629 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.8274 | −0.969313 | ||||||||
\(767\) | −18.9386 | −0.683833 | ||||||||
\(768\) | −25.2871 | −0.912469 | ||||||||
\(769\) | 40.9023 | 1.47498 | 0.737488 | − | 0.675360i | \(-0.236012\pi\) | ||||
0.737488 | + | 0.675360i | \(0.236012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.32004 | 0.0835542 | ||||||||
\(772\) | −19.8155 | −0.713175 | ||||||||
\(773\) | 28.2567 | 1.01632 | 0.508161 | − | 0.861262i | \(-0.330326\pi\) | ||||
0.508161 | + | 0.861262i | \(0.330326\pi\) | |||||||
\(774\) | −0.530633 | −0.0190732 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 55.0221 | 1.97518 | ||||||||
\(777\) | −19.7856 | −0.709804 | ||||||||
\(778\) | −12.2113 | −0.437795 | ||||||||
\(779\) | 13.9525 | 0.499901 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 3.35972 | 0.120143 | ||||||||
\(783\) | −3.51670 | −0.125677 | ||||||||
\(784\) | −6.88280 | −0.245814 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 48.0695 | 1.71458 | ||||||||
\(787\) | 12.9583 | 0.461915 | 0.230957 | − | 0.972964i | \(-0.425814\pi\) | ||||
0.230957 | + | 0.972964i | \(0.425814\pi\) | |||||||
\(788\) | −46.1067 | −1.64248 | ||||||||
\(789\) | −2.92970 | −0.104300 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.62830 | 0.129008 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0357 | 0.427402 | ||||||||
\(794\) | −17.4925 | −0.620786 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.2987 | 0.435916 | ||||||||
\(797\) | −25.2703 | −0.895120 | −0.447560 | − | 0.894254i | \(-0.647707\pi\) | ||||
−0.447560 | + | 0.894254i | \(0.647707\pi\) | |||||||
\(798\) | 23.3720 | 0.827359 | ||||||||
\(799\) | 1.74571 | 0.0617588 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.5058 | 0.547871 | ||||||||
\(802\) | −75.1518 | −2.65370 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 32.6091 | 1.15003 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 84.3377 | 2.97067 | ||||||||
\(807\) | −4.53203 | −0.159535 | ||||||||
\(808\) | 23.0190 | 0.809805 | ||||||||
\(809\) | 27.4522 | 0.965167 | 0.482584 | − | 0.875850i | \(-0.339698\pi\) | ||||
0.482584 | + | 0.875850i | \(0.339698\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.8599 | −1.25921 | −0.629605 | − | 0.776915i | \(-0.716783\pi\) | ||||
−0.629605 | + | 0.776915i | \(0.716783\pi\) | |||||||
\(812\) | 21.6265 | 0.758940 | ||||||||
\(813\) | 27.1116 | 0.950847 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.632633 | −0.0221466 | ||||||||
\(817\) | 1.29482 | 0.0453000 | ||||||||
\(818\) | 28.1290 | 0.983506 | ||||||||
\(819\) | 6.05704 | 0.211650 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.2112 | 1.89198 | 0.945992 | − | 0.324190i | \(-0.105092\pi\) | ||||
0.945992 | + | 0.324190i | \(0.105092\pi\) | |||||||
\(822\) | −12.5597 | −0.438071 | ||||||||
\(823\) | −4.75059 | −0.165595 | −0.0827976 | − | 0.996566i | \(-0.526385\pi\) | ||||
−0.0827976 | + | 0.996566i | \(0.526385\pi\) | |||||||
\(824\) | 29.5299 | 1.02872 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.7186 | −0.755687 | ||||||||
\(827\) | −34.6636 | −1.20537 | −0.602685 | − | 0.797979i | \(-0.705903\pi\) | ||||
−0.602685 | + | 0.797979i | \(0.705903\pi\) | |||||||
\(828\) | −13.6589 | −0.474678 | ||||||||
\(829\) | −17.7771 | −0.617424 | −0.308712 | − | 0.951156i | \(-0.599898\pi\) | ||||
−0.308712 | + | 0.951156i | \(0.599898\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.2514 | −0.459686 | ||||||||
\(832\) | 41.1974 | 1.42826 | ||||||||
\(833\) | 1.51614 | 0.0525313 | ||||||||
\(834\) | 31.2386 | 1.08170 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0978 | −0.349030 | ||||||||
\(838\) | 15.5302 | 0.536484 | ||||||||
\(839\) | 41.7363 | 1.44090 | 0.720449 | − | 0.693508i | \(-0.243936\pi\) | ||||
0.720449 | + | 0.693508i | \(0.243936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.6328 | −0.573546 | ||||||||
\(842\) | 74.0671 | 2.55252 | ||||||||
\(843\) | −11.0716 | −0.381328 | ||||||||
\(844\) | 63.9605 | 2.20161 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.0539 | −0.380039 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.14209 | −0.142240 | ||||||||
\(849\) | −10.0767 | −0.345833 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.9453 | −1.50643 | ||||||||
\(852\) | −31.4818 | −1.07855 | ||||||||
\(853\) | −37.3697 | −1.27951 | −0.639756 | − | 0.768578i | \(-0.720965\pi\) | ||||
−0.639756 | + | 0.768578i | \(0.720965\pi\) | |||||||
\(854\) | 13.8025 | 0.472311 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.5969 | −0.635630 | ||||||||
\(857\) | −14.6046 | −0.498884 | −0.249442 | − | 0.968390i | \(-0.580247\pi\) | ||||
−0.249442 | + | 0.968390i | \(0.580247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.27238 | −0.0775325 | −0.0387663 | − | 0.999248i | \(-0.512343\pi\) | ||||
−0.0387663 | + | 0.999248i | \(0.512343\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.14669 | 0.141319 | ||||||||
\(862\) | 29.6457 | 1.00974 | ||||||||
\(863\) | 49.6791 | 1.69110 | 0.845549 | − | 0.533898i | \(-0.179273\pi\) | ||||
0.845549 | + | 0.533898i | \(0.179273\pi\) | |||||||
\(864\) | −3.49870 | −0.119028 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −61.5133 | −2.09031 | ||||||||
\(867\) | −16.8606 | −0.572617 | ||||||||
\(868\) | 62.0978 | 2.10774 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.1180 | −1.08828 | ||||||||
\(872\) | −9.81846 | −0.332495 | ||||||||
\(873\) | 14.6637 | 0.496290 | ||||||||
\(874\) | 51.9110 | 1.75592 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −53.6756 | −1.81353 | ||||||||
\(877\) | −10.3771 | −0.350411 | −0.175205 | − | 0.984532i | \(-0.556059\pi\) | ||||
−0.175205 | + | 0.984532i | \(0.556059\pi\) | |||||||
\(878\) | −82.8528 | −2.79615 | ||||||||
\(879\) | −7.84659 | −0.264659 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.5784 | 1.29974 | 0.649869 | − | 0.760046i | \(-0.274824\pi\) | ||||
0.649869 | + | 0.760046i | \(0.274824\pi\) | |||||||
\(882\) | −9.60024 | −0.323257 | ||||||||
\(883\) | −17.8591 | −0.601007 | −0.300503 | − | 0.953781i | \(-0.597155\pi\) | ||||
−0.300503 | + | 0.953781i | \(0.597155\pi\) | |||||||
\(884\) | 4.73190 | 0.159151 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −61.6391 | −2.07081 | ||||||||
\(887\) | −40.6791 | −1.36587 | −0.682934 | − | 0.730480i | \(-0.739297\pi\) | ||||
−0.682934 | + | 0.730480i | \(0.739297\pi\) | |||||||
\(888\) | 43.3085 | 1.45334 | ||||||||
\(889\) | 20.4811 | 0.686913 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.4872 | 0.518549 | ||||||||
\(893\) | 26.9730 | 0.902617 | ||||||||
\(894\) | −14.3312 | −0.479307 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 35.2496 | 1.17761 | ||||||||
\(897\) | 13.4532 | 0.449188 | ||||||||
\(898\) | −1.68756 | −0.0563146 | ||||||||
\(899\) | 35.5109 | 1.18435 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.912421 | 0.0303971 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.384821 | 0.0128060 | ||||||||
\(904\) | −7.94196 | −0.264146 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17.3380 | −0.576018 | ||||||||
\(907\) | −17.2956 | −0.574289 | −0.287145 | − | 0.957887i | \(-0.592706\pi\) | ||||
−0.287145 | + | 0.957887i | \(0.592706\pi\) | |||||||
\(908\) | 91.2505 | 3.02825 | ||||||||
\(909\) | 6.13469 | 0.203475 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.8317 | 1.55160 | 0.775802 | − | 0.630977i | \(-0.217346\pi\) | ||||
0.775802 | + | 0.630977i | \(0.217346\pi\) | |||||||
\(912\) | −9.77482 | −0.323677 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −70.9081 | −2.34543 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 51.6348 | 1.70606 | ||||||||
\(917\) | −34.8605 | −1.15120 | ||||||||
\(918\) | −0.882407 | −0.0291238 | ||||||||
\(919\) | −42.2482 | −1.39364 | −0.696820 | − | 0.717246i | \(-0.745402\pi\) | ||||
−0.696820 | + | 0.717246i | \(0.745402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.64692 | 0.0872191 | ||||||||
\(922\) | 0.0849258 | 0.00279688 | ||||||||
\(923\) | 31.0077 | 1.02063 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.63897 | −0.283894 | ||||||||
\(927\) | 7.86989 | 0.258481 | ||||||||
\(928\) | 12.3039 | 0.403894 | ||||||||
\(929\) | 11.4317 | 0.375062 | 0.187531 | − | 0.982259i | \(-0.439952\pi\) | ||||
0.187531 | + | 0.982259i | \(0.439952\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.4260 | 0.767755 | ||||||||
\(932\) | −42.8032 | −1.40207 | ||||||||
\(933\) | −4.50819 | −0.147592 | ||||||||
\(934\) | 36.0188 | 1.17857 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.2582 | −0.433358 | ||||||||
\(937\) | −1.46708 | −0.0479275 | −0.0239637 | − | 0.999713i | \(-0.507629\pi\) | ||||
−0.0239637 | + | 0.999713i | \(0.507629\pi\) | |||||||
\(938\) | −36.8326 | −1.20263 | ||||||||
\(939\) | −9.70923 | −0.316849 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.3755 | −0.631623 | −0.315811 | − | 0.948822i | \(-0.602277\pi\) | ||||
−0.315811 | + | 0.948822i | \(0.602277\pi\) | |||||||
\(942\) | −24.9515 | −0.812962 | ||||||||
\(943\) | 9.21013 | 0.299923 | ||||||||
\(944\) | 9.08334 | 0.295637 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.4774 | 0.892895 | 0.446448 | − | 0.894810i | \(-0.352689\pi\) | ||||
0.446448 | + | 0.894810i | \(0.352689\pi\) | |||||||
\(948\) | 31.5406 | 1.02439 | ||||||||
\(949\) | 52.8673 | 1.71615 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.0757 | −0.553717 | ||||||||
\(952\) | 2.40119 | 0.0778232 | ||||||||
\(953\) | −12.9686 | −0.420095 | −0.210048 | − | 0.977691i | \(-0.567362\pi\) | ||||
−0.210048 | + | 0.977691i | \(0.567362\pi\) | |||||||
\(954\) | −5.77745 | −0.187052 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29.6230 | −0.958075 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.6908 | −0.959268 | ||||||||
\(959\) | 9.10846 | 0.294127 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.9652 | 2.28920 | ||||||||
\(962\) | −96.3996 | −3.10805 | ||||||||
\(963\) | −4.95618 | −0.159711 | ||||||||
\(964\) | −39.9951 | −1.28816 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15.4280 | 0.496386 | ||||||||
\(967\) | −48.0563 | −1.54539 | −0.772694 | − | 0.634779i | \(-0.781091\pi\) | ||||
−0.772694 | + | 0.634779i | \(0.781091\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.15320 | 0.0691708 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.7067 | 1.65935 | 0.829674 | − | 0.558249i | \(-0.188527\pi\) | ||||
0.829674 | + | 0.558249i | \(0.188527\pi\) | |||||||
\(972\) | 3.58741 | 0.115066 | ||||||||
\(973\) | −22.6545 | −0.726271 | ||||||||
\(974\) | 4.07123 | 0.130451 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.77259 | −0.184776 | ||||||||
\(977\) | −12.7980 | −0.409444 | −0.204722 | − | 0.978820i | \(-0.565629\pi\) | ||||
−0.204722 | + | 0.978820i | \(0.565629\pi\) | |||||||
\(978\) | −23.8907 | −0.763941 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.61667 | −0.0835440 | ||||||||
\(982\) | 47.5653 | 1.51787 | ||||||||
\(983\) | −13.6790 | −0.436293 | −0.218147 | − | 0.975916i | \(-0.570001\pi\) | ||||
−0.218147 | + | 0.975916i | \(0.570001\pi\) | |||||||
\(984\) | −9.07666 | −0.289353 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.10316 | 0.0988248 | ||||||||
\(987\) | 8.01638 | 0.255164 | ||||||||
\(988\) | 73.1126 | 2.32602 | ||||||||
\(989\) | 0.854717 | 0.0271784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.7067 | 1.10250 | 0.551248 | − | 0.834342i | \(-0.314152\pi\) | ||||
0.551248 | + | 0.834342i | \(0.314152\pi\) | |||||||
\(992\) | 35.3291 | 1.12170 | ||||||||
\(993\) | −2.79769 | −0.0887819 | ||||||||
\(994\) | 35.5593 | 1.12787 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 26.6980 | 0.845959 | ||||||||
\(997\) | −30.9145 | −0.979072 | −0.489536 | − | 0.871983i | \(-0.662834\pi\) | ||||
−0.489536 | + | 0.871983i | \(0.662834\pi\) | |||||||
\(998\) | 42.2791 | 1.33832 | ||||||||
\(999\) | 11.5420 | 0.365171 |
(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 | 9075.2.a.dy.1.12 | 12 | ||
5.2 | odd | 4 | 1815.2.c.j.364.22 | 24 | |||
5.3 | odd | 4 | 1815.2.c.j.364.3 | 24 | |||
5.4 | even | 2 | 9075.2.a.dz.1.1 | 12 | |||
11.5 | even | 5 | 825.2.n.p.751.1 | 24 | |||
11.9 | even | 5 | 825.2.n.p.301.1 | 24 | |||
11.10 | odd | 2 | 9075.2.a.ea.1.1 | 12 | |||
55.9 | even | 10 | 825.2.n.o.301.6 | 24 | |||
55.27 | odd | 20 | 165.2.s.a.124.2 | yes | 48 | ||
55.32 | even | 4 | 1815.2.c.k.364.3 | 24 | |||
55.38 | odd | 20 | 165.2.s.a.124.11 | yes | 48 | ||
55.42 | odd | 20 | 165.2.s.a.4.11 | yes | 48 | ||
55.43 | even | 4 | 1815.2.c.k.364.22 | 24 | |||
55.49 | even | 10 | 825.2.n.o.751.6 | 24 | |||
55.53 | odd | 20 | 165.2.s.a.4.2 | ✓ | 48 | ||
55.54 | odd | 2 | 9075.2.a.dx.1.12 | 12 | |||
165.38 | even | 20 | 495.2.ba.c.289.2 | 48 | |||
165.53 | even | 20 | 495.2.ba.c.334.11 | 48 | |||
165.137 | even | 20 | 495.2.ba.c.289.11 | 48 | |||
165.152 | even | 20 | 495.2.ba.c.334.2 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.s.a.4.2 | ✓ | 48 | 55.53 | odd | 20 | ||
165.2.s.a.4.11 | yes | 48 | 55.42 | odd | 20 | ||
165.2.s.a.124.2 | yes | 48 | 55.27 | odd | 20 | ||
165.2.s.a.124.11 | yes | 48 | 55.38 | odd | 20 | ||
495.2.ba.c.289.2 | 48 | 165.38 | even | 20 | |||
495.2.ba.c.289.11 | 48 | 165.137 | even | 20 | |||
495.2.ba.c.334.2 | 48 | 165.152 | even | 20 | |||
495.2.ba.c.334.11 | 48 | 165.53 | even | 20 | |||
825.2.n.o.301.6 | 24 | 55.9 | even | 10 | |||
825.2.n.o.751.6 | 24 | 55.49 | even | 10 | |||
825.2.n.p.301.1 | 24 | 11.9 | even | 5 | |||
825.2.n.p.751.1 | 24 | 11.5 | even | 5 | |||
1815.2.c.j.364.3 | 24 | 5.3 | odd | 4 | |||
1815.2.c.j.364.22 | 24 | 5.2 | odd | 4 | |||
1815.2.c.k.364.3 | 24 | 55.32 | even | 4 | |||
1815.2.c.k.364.22 | 24 | 55.43 | even | 4 | |||
9075.2.a.dx.1.12 | 12 | 55.54 | odd | 2 | |||
9075.2.a.dy.1.12 | 12 | 1.1 | even | 1 | trivial | ||
9075.2.a.dz.1.1 | 12 | 5.4 | even | 2 | |||
9075.2.a.ea.1.1 | 12 | 11.10 | odd | 2 |