Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.27648.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.33441\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.33441 | −1.65068 | −0.825340 | − | 0.564636i | \(-0.809017\pi\) | ||||
−0.825340 | + | 0.564636i | \(0.809017\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.44949 | 1.72474 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.04930 | −0.396596 | −0.198298 | − | 0.980142i | \(-0.563541\pi\) | ||||
−0.198298 | + | 0.980142i | \(0.563541\pi\) | |||||||
\(8\) | −3.38371 | −1.19632 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.33441 | 0.738207 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.71812 | 1.58592 | 0.792961 | − | 0.609272i | \(-0.208538\pi\) | ||||
0.792961 | + | 0.609272i | \(0.208538\pi\) | |||||||
\(14\) | 2.44949 | 0.654654 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.04930 | 0.254491 | 0.127246 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127246 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.66883 | 1.07110 | 0.535551 | − | 0.844503i | \(-0.320104\pi\) | ||||
0.535551 | + | 0.844503i | \(0.320104\pi\) | |||||||
\(20\) | −3.44949 | −0.771329 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.89898 | −1.02151 | −0.510754 | − | 0.859727i | \(-0.670634\pi\) | ||||
−0.510754 | + | 0.859727i | \(0.670634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −13.3485 | −2.61785 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.61953 | −0.684027 | ||||||||
\(29\) | −2.57024 | −0.477281 | −0.238641 | − | 0.971108i | \(-0.576702\pi\) | ||||
−0.238641 | + | 0.971108i | \(0.576702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 4.43300 | 0.783652 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.44949 | −0.420084 | ||||||||
\(35\) | 1.04930 | 0.177363 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.89898 | −1.13419 | −0.567093 | − | 0.823654i | \(-0.691932\pi\) | ||||
−0.567093 | + | 0.823654i | \(0.691932\pi\) | |||||||
\(38\) | −10.8990 | −1.76805 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.38371 | 0.535011 | ||||||||
\(41\) | −6.76742 | −1.05689 | −0.528447 | − | 0.848967i | \(-0.677225\pi\) | ||||
−0.528447 | + | 0.848967i | \(0.677225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.04930 | 0.160016 | 0.0800080 | − | 0.996794i | \(-0.474505\pi\) | ||||
0.0800080 | + | 0.996794i | \(0.474505\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.4362 | 1.68618 | ||||||||
\(47\) | 9.79796 | 1.42918 | 0.714590 | − | 0.699544i | \(-0.246613\pi\) | ||||
0.714590 | + | 0.699544i | \(0.246613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.89898 | −0.842711 | ||||||||
\(50\) | −2.33441 | −0.330136 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.7246 | 2.73531 | ||||||||
\(53\) | −10.8990 | −1.49709 | −0.748545 | − | 0.663084i | \(-0.769247\pi\) | ||||
−0.748545 | + | 0.663084i | \(0.769247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.55051 | 0.474457 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −10.8990 | −1.41893 | −0.709463 | − | 0.704743i | \(-0.751063\pi\) | ||||
−0.709463 | + | 0.704743i | \(0.751063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.23907 | −0.926867 | −0.463434 | − | 0.886132i | \(-0.653383\pi\) | ||||
−0.463434 | + | 0.886132i | \(0.653383\pi\) | |||||||
\(62\) | 4.66883 | 0.592942 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.3485 | −1.54356 | ||||||||
\(65\) | −5.71812 | −0.709246 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.89898 | 1.08718 | 0.543592 | − | 0.839350i | \(-0.317064\pi\) | ||||
0.543592 | + | 0.839350i | \(0.317064\pi\) | |||||||
\(68\) | 3.61953 | 0.438933 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.44949 | −0.292770 | ||||||||
\(71\) | −1.10102 | −0.130667 | −0.0653335 | − | 0.997863i | \(-0.520811\pi\) | ||||
−0.0653335 | + | 0.997863i | \(0.520811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.52094 | 0.178013 | 0.0890064 | − | 0.996031i | \(-0.471631\pi\) | ||||
0.0890064 | + | 0.996031i | \(0.471631\pi\) | |||||||
\(74\) | 16.1051 | 1.87218 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.1051 | 1.84738 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.80930 | 1.10363 | 0.551816 | − | 0.833966i | \(-0.313935\pi\) | ||||
0.551816 | + | 0.833966i | \(0.313935\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.7980 | 1.74459 | ||||||||
\(83\) | 3.61953 | 0.397295 | 0.198648 | − | 0.980071i | \(-0.436345\pi\) | ||||
0.198648 | + | 0.980071i | \(0.436345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.04930 | −0.113812 | ||||||||
\(86\) | −2.44949 | −0.264135 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.79796 | −0.402583 | −0.201291 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | −0.628971 | ||||||||
\(92\) | −16.8990 | −1.76184 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22.8725 | −2.35912 | ||||||||
\(95\) | −4.66883 | −0.479012 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.6969 | 1.69532 | 0.847659 | − | 0.530542i | \(-0.178012\pi\) | ||||
0.847659 | + | 0.530542i | \(0.178012\pi\) | |||||||
\(98\) | 13.7707 | 1.39105 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.44949 | 0.344949 | ||||||||
\(101\) | 18.2037 | 1.81133 | 0.905666 | − | 0.423991i | \(-0.139371\pi\) | ||||
0.905666 | + | 0.423991i | \(0.139371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8990 | 1.27097 | 0.635487 | − | 0.772111i | \(-0.280799\pi\) | ||||
0.635487 | + | 0.772111i | \(0.280799\pi\) | |||||||
\(104\) | −19.3485 | −1.89727 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 25.4427 | 2.47122 | ||||||||
\(107\) | 7.81671 | 0.755670 | 0.377835 | − | 0.925873i | \(-0.376669\pi\) | ||||
0.377835 | + | 0.925873i | \(0.376669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5348 | −1.29640 | −0.648201 | − | 0.761469i | \(-0.724478\pi\) | ||||
−0.648201 | + | 0.761469i | \(0.724478\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.04930 | −0.0991491 | ||||||||
\(113\) | −1.10102 | −0.103575 | −0.0517876 | − | 0.998658i | \(-0.516492\pi\) | ||||
−0.0517876 | + | 0.998658i | \(0.516492\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.89898 | 0.456832 | ||||||||
\(116\) | −8.86601 | −0.823188 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 25.4427 | 2.34219 | ||||||||
\(119\) | −1.10102 | −0.100930 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 16.8990 | 1.52996 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.89898 | −0.619547 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.7246 | −1.75028 | −0.875138 | − | 0.483873i | \(-0.839230\pi\) | ||||
−0.875138 | + | 0.483873i | \(0.839230\pi\) | |||||||
\(128\) | 19.9604 | 1.76427 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.3485 | 1.17074 | ||||||||
\(131\) | −15.6334 | −1.36590 | −0.682949 | − | 0.730466i | \(-0.739303\pi\) | ||||
−0.682949 | + | 0.730466i | \(0.739303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.89898 | −0.424795 | ||||||||
\(134\) | −20.7739 | −1.79459 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.55051 | −0.304454 | ||||||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9646 | 0.930005 | 0.465003 | − | 0.885309i | \(-0.346053\pi\) | ||||
0.465003 | + | 0.885309i | \(0.346053\pi\) | |||||||
\(140\) | 3.61953 | 0.305906 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.57024 | 0.215690 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.57024 | 0.213447 | ||||||||
\(146\) | −3.55051 | −0.293842 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.7980 | −1.95618 | ||||||||
\(149\) | −0.471647 | −0.0386389 | −0.0193194 | − | 0.999813i | \(-0.506150\pi\) | ||||
−0.0193194 | + | 0.999813i | \(0.506150\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.471647 | 0.0383821 | 0.0191911 | − | 0.999816i | \(-0.493891\pi\) | ||||
0.0191911 | + | 0.999816i | \(0.493891\pi\) | |||||||
\(152\) | −15.7980 | −1.28138 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.79796 | 0.622345 | 0.311172 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311172 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(158\) | −22.8990 | −1.82174 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.43300 | −0.350460 | ||||||||
\(161\) | 5.14048 | 0.405126 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.69694 | −0.524545 | −0.262272 | − | 0.964994i | \(-0.584472\pi\) | ||||
−0.262272 | + | 0.964994i | \(0.584472\pi\) | |||||||
\(164\) | −23.3441 | −1.82287 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.44949 | −0.655808 | ||||||||
\(167\) | −12.0139 | −0.929663 | −0.464832 | − | 0.885399i | \(-0.653885\pi\) | ||||
−0.464832 | + | 0.885399i | \(0.653885\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.6969 | 1.51515 | ||||||||
\(170\) | 2.44949 | 0.187867 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.61953 | 0.275987 | ||||||||
\(173\) | −13.4288 | −1.02098 | −0.510488 | − | 0.859885i | \(-0.670535\pi\) | ||||
−0.510488 | + | 0.859885i | \(0.670535\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.04930 | −0.0793193 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.86601 | 0.664536 | ||||||||
\(179\) | −21.7980 | −1.62926 | −0.814628 | − | 0.579984i | \(-0.803059\pi\) | ||||
−0.814628 | + | 0.579984i | \(0.803059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.10102 | 0.230497 | 0.115249 | − | 0.993337i | \(-0.463234\pi\) | ||||
0.115249 | + | 0.993337i | \(0.463234\pi\) | |||||||
\(182\) | 14.0065 | 1.03823 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.5767 | 1.22205 | ||||||||
\(185\) | 6.89898 | 0.507223 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 33.7980 | 2.46497 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.8990 | 0.790695 | ||||||||
\(191\) | 19.5959 | 1.41791 | 0.708955 | − | 0.705253i | \(-0.249167\pi\) | ||||
0.708955 | + | 0.705253i | \(0.249167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.1963 | −1.45376 | −0.726879 | − | 0.686765i | \(-0.759030\pi\) | ||||
−0.726879 | + | 0.686765i | \(0.759030\pi\) | |||||||
\(194\) | −38.9776 | −2.79843 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20.3485 | −1.45346 | ||||||||
\(197\) | 19.7246 | 1.40532 | 0.702660 | − | 0.711526i | \(-0.251995\pi\) | ||||
0.702660 | + | 0.711526i | \(0.251995\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.7980 | −1.26166 | −0.630832 | − | 0.775920i | \(-0.717286\pi\) | ||||
−0.630832 | + | 0.775920i | \(0.717286\pi\) | |||||||
\(200\) | −3.38371 | −0.239264 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −42.4949 | −2.98993 | ||||||||
\(203\) | 2.69694 | 0.189288 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.76742 | 0.472657 | ||||||||
\(206\) | −30.1116 | −2.09797 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.71812 | 0.396481 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0065 | 0.964246 | 0.482123 | − | 0.876103i | \(-0.339866\pi\) | ||||
0.482123 | + | 0.876103i | \(0.339866\pi\) | |||||||
\(212\) | −37.5959 | −2.58210 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.2474 | −1.24737 | ||||||||
\(215\) | −1.04930 | −0.0715613 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.09859 | 0.142462 | ||||||||
\(218\) | 31.5959 | 2.13995 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.79796 | −0.120400 | −0.0602001 | − | 0.998186i | \(-0.519174\pi\) | ||||
−0.0602001 | + | 0.998186i | \(0.519174\pi\) | |||||||
\(224\) | −4.65153 | −0.310793 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.57024 | 0.170970 | ||||||||
\(227\) | −1.52094 | −0.100949 | −0.0504743 | − | 0.998725i | \(-0.516073\pi\) | ||||
−0.0504743 | + | 0.998725i | \(0.516073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.5959 | −1.42710 | −0.713549 | − | 0.700605i | \(-0.752913\pi\) | ||||
−0.713549 | + | 0.700605i | \(0.752913\pi\) | |||||||
\(230\) | −11.4362 | −0.754084 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.69694 | 0.570982 | ||||||||
\(233\) | 10.3870 | 0.680472 | 0.340236 | − | 0.940340i | \(-0.389493\pi\) | ||||
0.340236 | + | 0.940340i | \(0.389493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.79796 | −0.639148 | ||||||||
\(236\) | −37.5959 | −2.44729 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.57024 | 0.166604 | ||||||||
\(239\) | 25.9144 | 1.67626 | 0.838131 | − | 0.545469i | \(-0.183648\pi\) | ||||
0.838131 | + | 0.545469i | \(0.183648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.5767 | −1.06780 | −0.533900 | − | 0.845547i | \(-0.679274\pi\) | ||||
−0.533900 | + | 0.845547i | \(0.679274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −24.9711 | −1.59861 | ||||||||
\(245\) | 5.89898 | 0.376872 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.6969 | 1.69869 | ||||||||
\(248\) | 6.76742 | 0.429732 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.33441 | 0.147641 | ||||||||
\(251\) | −13.1010 | −0.826929 | −0.413465 | − | 0.910520i | \(-0.635681\pi\) | ||||
−0.413465 | + | 0.910520i | \(0.635681\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 46.0454 | 2.88915 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −21.8990 | −1.36869 | ||||||||
\(257\) | 25.5959 | 1.59663 | 0.798315 | − | 0.602240i | \(-0.205725\pi\) | ||||
0.798315 | + | 0.602240i | \(0.205725\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.23907 | 0.449814 | ||||||||
\(260\) | −19.7246 | −1.22327 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 36.4949 | 2.25466 | ||||||||
\(263\) | 20.1963 | 1.24535 | 0.622677 | − | 0.782479i | \(-0.286045\pi\) | ||||
0.622677 | + | 0.782479i | \(0.286045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.8990 | 0.669519 | ||||||||
\(266\) | 11.4362 | 0.701201 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 30.6969 | 1.87511 | ||||||||
\(269\) | 7.59592 | 0.463131 | 0.231566 | − | 0.972819i | \(-0.425615\pi\) | ||||
0.231566 | + | 0.972819i | \(0.425615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.4008 | −1.36075 | −0.680377 | − | 0.732862i | \(-0.738184\pi\) | ||||
−0.680377 | + | 0.732862i | \(0.738184\pi\) | |||||||
\(272\) | 1.04930 | 0.0636229 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 42.0195 | 2.53849 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.4920 | 1.59175 | 0.795876 | − | 0.605460i | \(-0.207011\pi\) | ||||
0.795876 | + | 0.605460i | \(0.207011\pi\) | |||||||
\(278\) | −25.5959 | −1.53514 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.55051 | −0.212184 | ||||||||
\(281\) | 6.76742 | 0.403710 | 0.201855 | − | 0.979415i | \(-0.435303\pi\) | ||||
0.201855 | + | 0.979415i | \(0.435303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.0623 | −1.72757 | −0.863786 | − | 0.503859i | \(-0.831913\pi\) | ||||
−0.863786 | + | 0.503859i | \(0.831913\pi\) | |||||||
\(284\) | −3.79796 | −0.225367 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.10102 | 0.419160 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8990 | −0.935234 | ||||||||
\(290\) | −6.00000 | −0.352332 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.24648 | 0.307027 | ||||||||
\(293\) | 29.0623 | 1.69784 | 0.848918 | − | 0.528525i | \(-0.177255\pi\) | ||||
0.848918 | + | 0.528525i | \(0.177255\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8990 | 0.634563 | ||||||||
\(296\) | 23.3441 | 1.35685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.10102 | 0.0637804 | ||||||||
\(299\) | −28.0130 | −1.62003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.10102 | −0.0634618 | ||||||||
\(302\) | −1.10102 | −0.0633566 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.66883 | 0.267776 | ||||||||
\(305\) | 7.23907 | 0.414508 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5274 | −0.886197 | −0.443099 | − | 0.896473i | \(-0.646121\pi\) | ||||
−0.443099 | + | 0.896473i | \(0.646121\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.66883 | −0.265172 | ||||||||
\(311\) | −22.8990 | −1.29848 | −0.649241 | − | 0.760583i | \(-0.724913\pi\) | ||||
−0.649241 | + | 0.760583i | \(0.724913\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.1010 | −1.19270 | −0.596350 | − | 0.802724i | \(-0.703383\pi\) | ||||
−0.596350 | + | 0.802724i | \(0.703383\pi\) | |||||||
\(314\) | −18.2037 | −1.02729 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.8371 | 1.90349 | ||||||||
\(317\) | 8.69694 | 0.488469 | 0.244234 | − | 0.969716i | \(-0.421463\pi\) | ||||
0.244234 | + | 0.969716i | \(0.421463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 12.3485 | 0.690300 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | −0.668734 | ||||||||
\(323\) | 4.89898 | 0.272587 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.71812 | 0.317184 | ||||||||
\(326\) | 15.6334 | 0.865856 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22.8990 | 1.26438 | ||||||||
\(329\) | −10.2810 | −0.566807 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | −0.549650 | −0.274825 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274825 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(332\) | 12.4855 | 0.685233 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 28.0454 | 1.53458 | ||||||||
\(335\) | −8.89898 | −0.486203 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.8586 | −0.591506 | −0.295753 | − | 0.955265i | \(-0.595570\pi\) | ||||
−0.295753 | + | 0.955265i | \(0.595570\pi\) | |||||||
\(338\) | −45.9808 | −2.50103 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.61953 | −0.196297 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.5348 | 0.730813 | ||||||||
\(344\) | −3.55051 | −0.191431 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.3485 | 1.68530 | ||||||||
\(347\) | −12.9572 | −0.695578 | −0.347789 | − | 0.937573i | \(-0.613068\pi\) | ||||
−0.347789 | + | 0.937573i | \(0.613068\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.23907 | −0.387498 | −0.193749 | − | 0.981051i | \(-0.562065\pi\) | ||||
−0.193749 | + | 0.981051i | \(0.562065\pi\) | |||||||
\(350\) | 2.44949 | 0.130931 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.8990 | 0.580094 | 0.290047 | − | 0.957012i | \(-0.406329\pi\) | ||||
0.290047 | + | 0.957012i | \(0.406329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.10102 | 0.0584361 | ||||||||
\(356\) | −13.1010 | −0.694353 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 50.8855 | 2.68938 | ||||||||
\(359\) | −31.0549 | −1.63901 | −0.819506 | − | 0.573070i | \(-0.805752\pi\) | ||||
−0.819506 | + | 0.573070i | \(0.805752\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.79796 | 0.147261 | ||||||||
\(362\) | −7.23907 | −0.380477 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20.6969 | −1.08481 | ||||||||
\(365\) | −1.52094 | −0.0796098 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5959 | −1.23170 | −0.615848 | − | 0.787865i | \(-0.711187\pi\) | ||||
−0.615848 | + | 0.787865i | \(0.711187\pi\) | |||||||
\(368\) | −4.89898 | −0.255377 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.1051 | −0.837263 | ||||||||
\(371\) | 11.4362 | 0.593740 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.91530 | 0.513395 | 0.256698 | − | 0.966492i | \(-0.417366\pi\) | ||||
0.256698 | + | 0.966492i | \(0.417366\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.1534 | −1.70976 | ||||||||
\(377\) | −14.6969 | −0.756931 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.5959 | −1.21204 | −0.606020 | − | 0.795449i | \(-0.707235\pi\) | ||||
−0.606020 | + | 0.795449i | \(0.707235\pi\) | |||||||
\(380\) | −16.1051 | −0.826173 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −45.7450 | −2.34052 | ||||||||
\(383\) | −16.8990 | −0.863498 | −0.431749 | − | 0.901994i | \(-0.642103\pi\) | ||||
−0.431749 | + | 0.901994i | \(0.642103\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 47.1464 | 2.39969 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 57.5959 | 2.92399 | ||||||||
\(389\) | 31.5959 | 1.60198 | 0.800988 | − | 0.598680i | \(-0.204308\pi\) | ||||
0.800988 | + | 0.598680i | \(0.204308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.14048 | −0.259965 | ||||||||
\(392\) | 19.9604 | 1.00815 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −46.0454 | −2.31973 | ||||||||
\(395\) | −9.80930 | −0.493560 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.6969 | 1.44026 | 0.720129 | − | 0.693840i | \(-0.244083\pi\) | ||||
0.720129 | + | 0.693840i | \(0.244083\pi\) | |||||||
\(398\) | 41.5478 | 2.08260 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −8.20204 | −0.409590 | −0.204795 | − | 0.978805i | \(-0.565653\pi\) | ||||
−0.204795 | + | 0.978805i | \(0.565653\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.4362 | −0.569680 | ||||||||
\(404\) | 62.7934 | 3.12409 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.29577 | −0.312454 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7320 | 0.876792 | 0.438396 | − | 0.898782i | \(-0.355547\pi\) | ||||
0.438396 | + | 0.898782i | \(0.355547\pi\) | |||||||
\(410\) | −15.7980 | −0.780206 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44.4949 | 2.19211 | ||||||||
\(413\) | 11.4362 | 0.562741 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.61953 | −0.177676 | ||||||||
\(416\) | 25.3485 | 1.24281 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.30306 | −0.258455 | −0.129228 | − | 0.991615i | \(-0.541250\pi\) | ||||
−0.129228 | + | 0.991615i | \(0.541250\pi\) | |||||||
\(422\) | −32.6969 | −1.59166 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 36.8790 | 1.79100 | ||||||||
\(425\) | 1.04930 | 0.0508983 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.59592 | 0.367592 | ||||||||
\(428\) | 26.9637 | 1.30334 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.44949 | 0.118125 | ||||||||
\(431\) | −4.19718 | −0.202171 | −0.101086 | − | 0.994878i | \(-0.532232\pi\) | ||||
−0.101086 | + | 0.994878i | \(0.532232\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.6969 | −0.610176 | −0.305088 | − | 0.952324i | \(-0.598686\pi\) | ||||
−0.305088 | + | 0.952324i | \(0.598686\pi\) | |||||||
\(434\) | −4.89898 | −0.235159 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −46.6883 | −2.23596 | ||||||||
\(437\) | −22.8725 | −1.09414 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.9209 | −1.90532 | −0.952659 | − | 0.304039i | \(-0.901665\pi\) | ||||
−0.952659 | + | 0.304039i | \(0.901665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0065 | −0.666221 | ||||||||
\(443\) | 2.69694 | 0.128135 | 0.0640677 | − | 0.997946i | \(-0.479593\pi\) | ||||
0.0640677 | + | 0.997946i | \(0.479593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.79796 | 0.180041 | ||||||||
\(446\) | 4.19718 | 0.198742 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.9572 | 0.612170 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.79796 | −0.178641 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.55051 | 0.166634 | ||||||||
\(455\) | 6.00000 | 0.281284 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.4353 | 1.28337 | 0.641685 | − | 0.766968i | \(-0.278236\pi\) | ||||
0.641685 | + | 0.766968i | \(0.278236\pi\) | |||||||
\(458\) | 50.4138 | 2.35568 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.8990 | 0.787919 | ||||||||
\(461\) | 13.0632 | 0.608413 | 0.304207 | − | 0.952606i | \(-0.401609\pi\) | ||||
0.304207 | + | 0.952606i | \(0.401609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | −2.57024 | −0.119320 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.2474 | −1.12324 | ||||||||
\(467\) | 4.89898 | 0.226698 | 0.113349 | − | 0.993555i | \(-0.463842\pi\) | ||||
0.113349 | + | 0.993555i | \(0.463842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.33766 | −0.431173 | ||||||||
\(470\) | 22.8725 | 1.05503 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 36.8790 | 1.69749 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.66883 | 0.214221 | ||||||||
\(476\) | −3.79796 | −0.174079 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −60.4949 | −2.76697 | ||||||||
\(479\) | −29.1683 | −1.33273 | −0.666366 | − | 0.745625i | \(-0.732151\pi\) | ||||
−0.666366 | + | 0.745625i | \(0.732151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.4492 | −1.79873 | ||||||||
\(482\) | 38.6969 | 1.76260 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.6969 | −0.758169 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.89898 | 0.403251 | 0.201626 | − | 0.979463i | \(-0.435378\pi\) | ||||
0.201626 | + | 0.979463i | \(0.435378\pi\) | |||||||
\(488\) | 24.4949 | 1.10883 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.7707 | −0.622095 | ||||||||
\(491\) | 37.3506 | 1.68561 | 0.842805 | − | 0.538219i | \(-0.180903\pi\) | ||||
0.842805 | + | 0.538219i | \(0.180903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.69694 | −0.121464 | ||||||||
\(494\) | −62.3217 | −2.80399 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 1.15530 | 0.0518221 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7980 | 0.617681 | 0.308841 | − | 0.951114i | \(-0.400059\pi\) | ||||
0.308841 | + | 0.951114i | \(0.400059\pi\) | |||||||
\(500\) | −3.44949 | −0.154266 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.5832 | 1.36500 | ||||||||
\(503\) | −24.3934 | −1.08765 | −0.543825 | − | 0.839199i | \(-0.683024\pi\) | ||||
−0.543825 | + | 0.839199i | \(0.683024\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.2037 | −0.810053 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −68.0398 | −3.01878 | ||||||||
\(509\) | 9.79796 | 0.434287 | 0.217143 | − | 0.976140i | \(-0.430326\pi\) | ||||
0.217143 | + | 0.976140i | \(0.430326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.59592 | −0.0705993 | ||||||||
\(512\) | 11.2004 | 0.494993 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −59.7515 | −2.63552 | ||||||||
\(515\) | −12.8990 | −0.568397 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −16.8990 | −0.742499 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.3485 | 0.848487 | ||||||||
\(521\) | −23.3939 | −1.02490 | −0.512452 | − | 0.858716i | \(-0.671263\pi\) | ||||
−0.512452 | + | 0.858716i | \(0.671263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5422 | −0.504707 | −0.252354 | − | 0.967635i | \(-0.581205\pi\) | ||||
−0.252354 | + | 0.967635i | \(0.581205\pi\) | |||||||
\(524\) | −53.9274 | −2.35583 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −47.1464 | −2.05568 | ||||||||
\(527\) | −2.09859 | −0.0914160 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −25.4427 | −1.10516 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.8990 | −0.732664 | ||||||||
\(533\) | −38.6969 | −1.67615 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.81671 | −0.337946 | ||||||||
\(536\) | −30.1116 | −1.30062 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −17.7320 | −0.764482 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.2669 | −1.34427 | −0.672134 | − | 0.740430i | \(-0.734622\pi\) | ||||
−0.672134 | + | 0.740430i | \(0.734622\pi\) | |||||||
\(542\) | 52.2929 | 2.24617 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.65153 | 0.199433 | ||||||||
\(545\) | 13.5348 | 0.579769 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.1042 | −1.37267 | −0.686337 | − | 0.727283i | \(-0.740783\pi\) | ||||
−0.686337 | + | 0.727283i | \(0.740783\pi\) | |||||||
\(548\) | −62.0908 | −2.65239 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.2929 | −0.437697 | ||||||||
\(554\) | −61.8434 | −2.62747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 37.8223 | 1.60402 | ||||||||
\(557\) | −5.24648 | −0.222300 | −0.111150 | − | 0.993804i | \(-0.535453\pi\) | ||||
−0.111150 | + | 0.993804i | \(0.535453\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 1.04930 | 0.0443408 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.7980 | −0.666397 | ||||||||
\(563\) | −6.87342 | −0.289680 | −0.144840 | − | 0.989455i | \(-0.546267\pi\) | ||||
−0.144840 | + | 0.989455i | \(0.546267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.10102 | 0.0463203 | ||||||||
\(566\) | 67.8434 | 2.85167 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.72553 | 0.156320 | ||||||||
\(569\) | 5.61212 | 0.235272 | 0.117636 | − | 0.993057i | \(-0.462468\pi\) | ||||
0.117636 | + | 0.993057i | \(0.462468\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.9646 | −0.458854 | −0.229427 | − | 0.973326i | \(-0.573685\pi\) | ||||
−0.229427 | + | 0.973326i | \(0.573685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.5767 | −0.691899 | ||||||||
\(575\) | −4.89898 | −0.204302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 37.1148 | 1.54377 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.86601 | 0.368141 | ||||||||
\(581\) | −3.79796 | −0.157566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.14643 | −0.212961 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −67.8434 | −2.80258 | ||||||||
\(587\) | −14.6969 | −0.606608 | −0.303304 | − | 0.952894i | \(-0.598090\pi\) | ||||
−0.303304 | + | 0.952894i | \(0.598090\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.33766 | −0.384751 | ||||||||
\(590\) | −25.4427 | −1.04746 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.89898 | −0.283546 | ||||||||
\(593\) | 17.6260 | 0.723814 | 0.361907 | − | 0.932214i | \(-0.382126\pi\) | ||||
0.361907 | + | 0.932214i | \(0.382126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.10102 | 0.0451374 | ||||||||
\(596\) | −1.62694 | −0.0666422 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 65.3939 | 2.67415 | ||||||||
\(599\) | −31.5959 | −1.29097 | −0.645487 | − | 0.763771i | \(-0.723346\pi\) | ||||
−0.645487 | + | 0.763771i | \(0.723346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.04189 | −0.124081 | −0.0620405 | − | 0.998074i | \(-0.519761\pi\) | ||||
−0.0620405 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(602\) | 2.57024 | 0.104755 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.62694 | 0.0661994 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.5274 | −0.630239 | −0.315119 | − | 0.949052i | \(-0.602045\pi\) | ||||
−0.315119 | + | 0.949052i | \(0.602045\pi\) | |||||||
\(608\) | 20.6969 | 0.839372 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.8990 | −0.684220 | ||||||||
\(611\) | 56.0259 | 2.26657 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5339 | −1.19286 | −0.596432 | − | 0.802664i | \(-0.703415\pi\) | ||||
−0.596432 | + | 0.802664i | \(0.703415\pi\) | |||||||
\(614\) | 36.2474 | 1.46283 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1010 | −0.527427 | −0.263714 | − | 0.964601i | \(-0.584947\pi\) | ||||
−0.263714 | + | 0.964601i | \(0.584947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 6.89898 | 0.277070 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 53.4557 | 2.14338 | ||||||||
\(623\) | 3.98518 | 0.159663 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 49.2585 | 1.96877 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 26.8990 | 1.07339 | ||||||||
\(629\) | −7.23907 | −0.288640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3939 | 0.851677 | 0.425838 | − | 0.904799i | \(-0.359979\pi\) | ||||
0.425838 | + | 0.904799i | \(0.359979\pi\) | |||||||
\(632\) | −33.1918 | −1.32030 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.3023 | −0.806306 | ||||||||
\(635\) | 19.7246 | 0.782747 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.7311 | −1.33647 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.9604 | −0.789005 | ||||||||
\(641\) | 37.5959 | 1.48495 | 0.742475 | − | 0.669874i | \(-0.233652\pi\) | ||||
0.742475 | + | 0.669874i | \(0.233652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.49490 | 0.335006 | 0.167503 | − | 0.985872i | \(-0.446430\pi\) | ||||
0.167503 | + | 0.985872i | \(0.446430\pi\) | |||||||
\(644\) | 17.7320 | 0.698739 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.4362 | −0.449953 | ||||||||
\(647\) | −40.8990 | −1.60790 | −0.803952 | − | 0.594694i | \(-0.797273\pi\) | ||||
−0.803952 | + | 0.594694i | \(0.797273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −13.3485 | −0.523570 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.1010 | −0.904706 | ||||||||
\(653\) | −1.59592 | −0.0624531 | −0.0312265 | − | 0.999512i | \(-0.509941\pi\) | ||||
−0.0312265 | + | 0.999512i | \(0.509941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.6334 | 0.610849 | ||||||||
\(656\) | −6.76742 | −0.264223 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.0000 | 0.935617 | ||||||||
\(659\) | −36.4073 | −1.41823 | −0.709114 | − | 0.705094i | \(-0.750905\pi\) | ||||
−0.709114 | + | 0.705094i | \(0.750905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.00000 | −0.0777910 | −0.0388955 | − | 0.999243i | \(-0.512384\pi\) | ||||
−0.0388955 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(662\) | 23.3441 | 0.907296 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.2474 | −0.475293 | ||||||||
\(665\) | 4.89898 | 0.189974 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.5915 | 0.487546 | ||||||||
\(668\) | −41.4418 | −1.60343 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.7739 | 0.802566 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.46424 | 0.0949894 | 0.0474947 | − | 0.998871i | \(-0.484876\pi\) | ||||
0.0474947 | + | 0.998871i | \(0.484876\pi\) | |||||||
\(674\) | 25.3485 | 0.976387 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 67.9444 | 2.61325 | ||||||||
\(677\) | −30.2176 | −1.16136 | −0.580678 | − | 0.814134i | \(-0.697212\pi\) | ||||
−0.580678 | + | 0.814134i | \(0.697212\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.5200 | −0.672357 | ||||||||
\(680\) | 3.55051 | 0.136156 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.5959 | −1.20898 | −0.604492 | − | 0.796611i | \(-0.706624\pi\) | ||||
−0.604492 | + | 0.796611i | \(0.706624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | −31.5959 | −1.20634 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.04930 | 0.0400040 | ||||||||
\(689\) | −62.3217 | −2.37427 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2020 | −0.692438 | −0.346219 | − | 0.938154i | \(-0.612535\pi\) | ||||
−0.346219 | + | 0.938154i | \(0.612535\pi\) | |||||||
\(692\) | −46.3226 | −1.76092 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.2474 | 1.14818 | ||||||||
\(695\) | −10.9646 | −0.415911 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.10102 | −0.268970 | ||||||||
\(698\) | 16.8990 | 0.639636 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.61953 | −0.136805 | ||||||||
\(701\) | 10.0213 | 0.378499 | 0.189250 | − | 0.981929i | \(-0.439394\pi\) | ||||
0.189250 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.2102 | −1.21483 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25.4427 | −0.957550 | ||||||||
\(707\) | −19.1010 | −0.718368 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.69694 | 0.251509 | 0.125754 | − | 0.992061i | \(-0.459865\pi\) | ||||
0.125754 | + | 0.992061i | \(0.459865\pi\) | |||||||
\(710\) | −2.57024 | −0.0964593 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.8512 | 0.481619 | ||||||||
\(713\) | 9.79796 | 0.366936 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −75.1918 | −2.81005 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 72.4949 | 2.70549 | ||||||||
\(719\) | 14.2020 | 0.529647 | 0.264823 | − | 0.964297i | \(-0.414686\pi\) | ||||
0.264823 | + | 0.964297i | \(0.414686\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5348 | −0.504064 | ||||||||
\(722\) | −6.53160 | −0.243081 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.6969 | 0.397549 | ||||||||
\(725\) | −2.57024 | −0.0954562 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 20.3023 | 0.752452 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.55051 | 0.131410 | ||||||||
\(731\) | 1.10102 | 0.0407227 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.5758 | −1.20321 | −0.601607 | − | 0.798792i | \(-0.705473\pi\) | ||||
−0.601607 | + | 0.798792i | \(0.705473\pi\) | |||||||
\(734\) | 55.0826 | 2.03314 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.7172 | −0.800507 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.71071 | −0.283643 | −0.141822 | − | 0.989892i | \(-0.545296\pi\) | ||||
−0.141822 | + | 0.989892i | \(0.545296\pi\) | |||||||
\(740\) | 23.7980 | 0.874830 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.6969 | −0.980075 | ||||||||
\(743\) | −34.8864 | −1.27986 | −0.639929 | − | 0.768434i | \(-0.721036\pi\) | ||||
−0.639929 | + | 0.768434i | \(0.721036\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.471647 | 0.0172798 | ||||||||
\(746\) | −23.1464 | −0.847451 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.20204 | −0.299696 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1918 | 1.13821 | 0.569103 | − | 0.822266i | \(-0.307291\pi\) | ||||
0.569103 | + | 0.822266i | \(0.307291\pi\) | |||||||
\(752\) | 9.79796 | 0.357295 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.3087 | 1.24945 | ||||||||
\(755\) | −0.471647 | −0.0171650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 55.0826 | 2.00069 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.7980 | 0.573052 | ||||||||
\(761\) | −22.4008 | −0.812030 | −0.406015 | − | 0.913866i | \(-0.633082\pi\) | ||||
−0.406015 | + | 0.913866i | \(0.633082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2020 | 0.514148 | ||||||||
\(764\) | 67.5959 | 2.44553 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 39.4492 | 1.42536 | ||||||||
\(767\) | −62.3217 | −2.25031 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.4362 | 0.412402 | 0.206201 | − | 0.978510i | \(-0.433890\pi\) | ||||
0.206201 | + | 0.978510i | \(0.433890\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −69.6668 | −2.50736 | ||||||||
\(773\) | 20.2020 | 0.726617 | 0.363308 | − | 0.931669i | \(-0.381647\pi\) | ||||
0.363308 | + | 0.931669i | \(0.381647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | −56.4976 | −2.02815 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −73.7580 | −2.64435 | ||||||||
\(779\) | −31.5959 | −1.13204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 12.0000 | 0.429119 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.89898 | −0.210678 | ||||||||
\(785\) | −7.79796 | −0.278321 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.6957 | −1.59323 | −0.796615 | − | 0.604487i | \(-0.793378\pi\) | ||||
−0.796615 | + | 0.604487i | \(0.793378\pi\) | |||||||
\(788\) | 68.0398 | 2.42382 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.8990 | 0.814709 | ||||||||
\(791\) | 1.15530 | 0.0410776 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.3939 | −1.46994 | ||||||||
\(794\) | −66.9905 | −2.37741 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −61.3939 | −2.17605 | ||||||||
\(797\) | −1.10102 | −0.0390001 | −0.0195001 | − | 0.999810i | \(-0.506207\pi\) | ||||
−0.0195001 | + | 0.999810i | \(0.506207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2810 | 0.363714 | ||||||||
\(800\) | 4.43300 | 0.156730 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.1470 | 0.676103 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.14048 | −0.181178 | ||||||||
\(806\) | 26.6969 | 0.940360 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −61.5959 | −2.16694 | ||||||||
\(809\) | −31.5265 | −1.10841 | −0.554206 | − | 0.832379i | \(-0.686978\pi\) | ||||
−0.554206 | + | 0.832379i | \(0.686978\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1051 | −0.565526 | −0.282763 | − | 0.959190i | \(-0.591251\pi\) | ||||
−0.282763 | + | 0.959190i | \(0.591251\pi\) | |||||||
\(812\) | 9.30306 | 0.326473 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.69694 | 0.234584 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.89898 | 0.171394 | ||||||||
\(818\) | −41.3939 | −1.44730 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.3441 | 0.815213 | ||||||||
\(821\) | 39.9209 | 1.39325 | 0.696624 | − | 0.717437i | \(-0.254685\pi\) | ||||
0.696624 | + | 0.717437i | \(0.254685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.1010 | 1.36298 | 0.681488 | − | 0.731829i | \(-0.261333\pi\) | ||||
0.681488 | + | 0.731829i | \(0.261333\pi\) | |||||||
\(824\) | −43.6464 | −1.52049 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −26.6969 | −0.928905 | ||||||||
\(827\) | 43.0688 | 1.49765 | 0.748824 | − | 0.662769i | \(-0.230619\pi\) | ||||
0.748824 | + | 0.662769i | \(0.230619\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.6969 | −1.48293 | −0.741463 | − | 0.670994i | \(-0.765868\pi\) | ||||
−0.741463 | + | 0.670994i | \(0.765868\pi\) | |||||||
\(830\) | 8.44949 | 0.293286 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −70.6101 | −2.44796 | ||||||||
\(833\) | −6.18977 | −0.214463 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0139 | 0.415758 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.0130 | 0.967692 | ||||||||
\(839\) | 30.4949 | 1.05280 | 0.526400 | − | 0.850237i | \(-0.323541\pi\) | ||||
0.526400 | + | 0.850237i | \(0.323541\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3939 | −0.772203 | ||||||||
\(842\) | 12.3795 | 0.426627 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 48.3152 | 1.66308 | ||||||||
\(845\) | −19.6969 | −0.677595 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.8990 | −0.374272 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.44949 | −0.0840168 | ||||||||
\(851\) | 33.7980 | 1.15858 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.9991 | 0.547798 | 0.273899 | − | 0.961758i | \(-0.411687\pi\) | ||||
0.273899 | + | 0.961758i | \(0.411687\pi\) | |||||||
\(854\) | −17.7320 | −0.606777 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.4495 | −0.904025 | ||||||||
\(857\) | 18.5693 | 0.634316 | 0.317158 | − | 0.948373i | \(-0.397272\pi\) | ||||
0.317158 | + | 0.948373i | \(0.397272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.0000 | −1.16007 | −0.580033 | − | 0.814593i | \(-0.696960\pi\) | ||||
−0.580033 | + | 0.814593i | \(0.696960\pi\) | |||||||
\(860\) | −3.61953 | −0.123425 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.79796 | 0.333720 | ||||||||
\(863\) | 21.3031 | 0.725165 | 0.362582 | − | 0.931952i | \(-0.381895\pi\) | ||||
0.362582 | + | 0.931952i | \(0.381895\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.4288 | 0.456594 | ||||||||
\(866\) | 29.6399 | 1.00721 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.23907 | 0.245710 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.8855 | 1.72419 | ||||||||
\(872\) | 45.7980 | 1.55091 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 53.3939 | 1.80607 | ||||||||
\(875\) | 1.04930 | 0.0354727 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.2111 | 0.547409 | 0.273705 | − | 0.961814i | \(-0.411751\pi\) | ||||
0.273705 | + | 0.961814i | \(0.411751\pi\) | |||||||
\(878\) | 93.1918 | 3.14507 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.7980 | −0.734392 | −0.367196 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367196 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.0000 | 0.942275 | 0.471138 | − | 0.882060i | \(-0.343844\pi\) | ||||
0.471138 | + | 0.882060i | \(0.343844\pi\) | |||||||
\(884\) | 20.6969 | 0.696113 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.29577 | −0.211511 | ||||||||
\(887\) | −29.5339 | −0.991652 | −0.495826 | − | 0.868422i | \(-0.665135\pi\) | ||||
−0.495826 | + | 0.868422i | \(0.665135\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.6969 | 0.694153 | ||||||||
\(890\) | −8.86601 | −0.297189 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.20204 | −0.207660 | ||||||||
\(893\) | 45.7450 | 1.53080 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.7980 | 0.728625 | ||||||||
\(896\) | −20.9444 | −0.699703 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42.0195 | 1.40221 | ||||||||
\(899\) | 5.14048 | 0.171444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.4362 | −0.380997 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.72553 | 0.123909 | ||||||||
\(905\) | −3.10102 | −0.103081 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.39388 | −0.311919 | −0.155959 | − | 0.987763i | \(-0.549847\pi\) | ||||
−0.155959 | + | 0.987763i | \(0.549847\pi\) | |||||||
\(908\) | −5.24648 | −0.174110 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.0065 | −0.464310 | ||||||||
\(911\) | −14.2020 | −0.470535 | −0.235267 | − | 0.971931i | \(-0.575597\pi\) | ||||
−0.235267 | + | 0.971931i | \(0.575597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −64.0454 | −2.11843 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −74.4949 | −2.46138 | ||||||||
\(917\) | 16.4041 | 0.541711 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3590 | 0.638593 | 0.319297 | − | 0.947655i | \(-0.396553\pi\) | ||||
0.319297 | + | 0.947655i | \(0.396553\pi\) | |||||||
\(920\) | −16.5767 | −0.546518 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.4949 | −1.00430 | ||||||||
\(923\) | −6.29577 | −0.207228 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.89898 | −0.226837 | ||||||||
\(926\) | −18.6753 | −0.613709 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.3939 | −0.374022 | ||||||||
\(929\) | −53.3939 | −1.75180 | −0.875898 | − | 0.482496i | \(-0.839730\pi\) | ||||
−0.875898 | + | 0.482496i | \(0.839730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.5413 | −0.902630 | ||||||||
\(932\) | 35.8297 | 1.17364 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.4362 | −0.374205 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7878 | 1.07113 | 0.535565 | − | 0.844494i | \(-0.320099\pi\) | ||||
0.535565 | + | 0.844494i | \(0.320099\pi\) | |||||||
\(938\) | 21.7980 | 0.711729 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −33.7980 | −1.10237 | ||||||||
\(941\) | 42.9628 | 1.40055 | 0.700273 | − | 0.713875i | \(-0.253062\pi\) | ||||
0.700273 | + | 0.713875i | \(0.253062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.1534 | 1.07962 | ||||||||
\(944\) | −10.8990 | −0.354732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.0000 | −1.55979 | −0.779895 | − | 0.625910i | \(-0.784728\pi\) | ||||
−0.779895 | + | 0.625910i | \(0.784728\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.69694 | 0.282315 | ||||||||
\(950\) | −10.8990 | −0.353610 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.72553 | 0.120745 | ||||||||
\(953\) | −0.106000 | −0.00343369 | −0.00171684 | − | 0.999999i | \(-0.500546\pi\) | ||||
−0.00171684 | + | 0.999999i | \(0.500546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5959 | −0.634109 | ||||||||
\(956\) | 89.3914 | 2.89112 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 68.0908 | 2.19991 | ||||||||
\(959\) | 18.8873 | 0.609903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 92.0908 | 2.96913 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −57.1812 | −1.84168 | ||||||||
\(965\) | 20.1963 | 0.650140 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.1042 | 1.03240 | 0.516200 | − | 0.856468i | \(-0.327346\pi\) | ||||
0.516200 | + | 0.856468i | \(0.327346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38.9776 | 1.25149 | ||||||||
\(971\) | −29.3939 | −0.943294 | −0.471647 | − | 0.881787i | \(-0.656340\pi\) | ||||
−0.471647 | + | 0.881787i | \(0.656340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.5051 | −0.368837 | ||||||||
\(974\) | −20.7739 | −0.665639 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.23907 | −0.231717 | ||||||||
\(977\) | −33.1918 | −1.06190 | −0.530950 | − | 0.847403i | \(-0.678165\pi\) | ||||
−0.530950 | + | 0.847403i | \(0.678165\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 20.3485 | 0.650008 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −87.1918 | −2.78240 | ||||||||
\(983\) | −2.69694 | −0.0860190 | −0.0430095 | − | 0.999075i | \(-0.513695\pi\) | ||||
−0.0430095 | + | 0.999075i | \(0.513695\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.7246 | −0.628478 | ||||||||
\(986\) | 6.29577 | 0.200498 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 92.0908 | 2.92980 | ||||||||
\(989\) | −5.14048 | −0.163458 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.1918 | 0.800245 | 0.400123 | − | 0.916462i | \(-0.368968\pi\) | ||||
0.400123 | + | 0.916462i | \(0.368968\pi\) | |||||||
\(992\) | −8.86601 | −0.281496 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.69694 | −0.0855417 | ||||||||
\(995\) | 17.7980 | 0.564233 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1692 | −0.417072 | −0.208536 | − | 0.978015i | \(-0.566870\pi\) | ||||
−0.208536 | + | 0.978015i | \(0.566870\pi\) | |||||||
\(998\) | −32.2102 | −1.01959 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5445.2.a.bm.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 5445.2.a.bn.1.4 | yes | 4 | ||
11.10 | odd | 2 | inner | 5445.2.a.bm.1.4 | yes | 4 | |
33.32 | even | 2 | 5445.2.a.bn.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5445.2.a.bm.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
5445.2.a.bm.1.4 | yes | 4 | 11.10 | odd | 2 | inner | |
5445.2.a.bn.1.1 | yes | 4 | 33.32 | even | 2 | ||
5445.2.a.bn.1.4 | yes | 4 | 3.2 | odd | 2 |