Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.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: | \(77.2951891566\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.45753625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 41x^{2} - 30x - 20 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.444728\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.719585 | −0.415453 | −0.207726 | − | 0.978187i | \(-0.566606\pi\) | ||||
−0.207726 | + | 0.978187i | \(0.566606\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.18418 | 1.58147 | 0.790736 | − | 0.612157i | \(-0.209698\pi\) | ||||
0.790736 | + | 0.612157i | \(0.209698\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.48220 | −0.827399 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.05056 | 1.67812 | 0.839062 | − | 0.544035i | \(-0.183104\pi\) | ||||
0.839062 | + | 0.544035i | \(0.183104\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.719585 | 0.185796 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.52180 | −1.58177 | −0.790885 | − | 0.611965i | \(-0.790379\pi\) | ||||
−0.790885 | + | 0.611965i | \(0.790379\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.739455 | 0.169642 | 0.0848212 | − | 0.996396i | \(-0.472968\pi\) | ||||
0.0848212 | + | 0.996396i | \(0.472968\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.01088 | −0.657027 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.13093 | 1.06987 | 0.534936 | − | 0.844893i | \(-0.320336\pi\) | ||||
0.534936 | + | 0.844893i | \(0.320336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.94491 | 0.759198 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.08036 | −0.386313 | −0.193157 | − | 0.981168i | \(-0.561873\pi\) | ||||
−0.193157 | + | 0.981168i | \(0.561873\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.12698 | 0.202411 | 0.101206 | − | 0.994866i | \(-0.467730\pi\) | ||||
0.101206 | + | 0.994866i | \(0.467730\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.18418 | −0.707256 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.11676 | 1.16999 | 0.584994 | − | 0.811037i | \(-0.301097\pi\) | ||||
0.584994 | + | 0.811037i | \(0.301097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.35390 | −0.697182 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.02170 | 0.628085 | 0.314042 | − | 0.949409i | \(-0.398317\pi\) | ||||
0.314042 | + | 0.949409i | \(0.398317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.29891 | 0.960575 | 0.480288 | − | 0.877111i | \(-0.340532\pi\) | ||||
0.480288 | + | 0.877111i | \(0.340532\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.48220 | 0.370024 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.24147 | −1.34801 | −0.674003 | − | 0.738728i | \(-0.735427\pi\) | ||||
−0.674003 | + | 0.738728i | \(0.735427\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.5074 | 1.50106 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.69299 | 0.657151 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.77015 | 1.06731 | 0.533656 | − | 0.845702i | \(-0.320818\pi\) | ||||
0.533656 | + | 0.845702i | \(0.320818\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.532101 | −0.0704785 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.16416 | −0.802505 | −0.401253 | − | 0.915967i | \(-0.631425\pi\) | ||||
−0.401253 | + | 0.915967i | \(0.631425\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.6869 | −1.88046 | −0.940230 | − | 0.340541i | \(-0.889390\pi\) | ||||
−0.940230 | + | 0.340541i | \(0.889390\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.3860 | −1.30851 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.05056 | −0.750480 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.53268 | 0.675924 | 0.337962 | − | 0.941160i | \(-0.390262\pi\) | ||||
0.337962 | + | 0.941160i | \(0.390262\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.69214 | −0.444481 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.87252 | −1.05297 | −0.526487 | − | 0.850183i | \(-0.676491\pi\) | ||||
−0.526487 | + | 0.850183i | \(0.676491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.09351 | 0.947274 | 0.473637 | − | 0.880720i | \(-0.342941\pi\) | ||||
0.473637 | + | 0.880720i | \(0.342941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.719585 | −0.0830906 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.570482 | −0.0641842 | −0.0320921 | − | 0.999485i | \(-0.510217\pi\) | ||||
−0.0320921 | + | 0.999485i | \(0.510217\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.60789 | 0.511988 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.2224 | −1.67088 | −0.835439 | − | 0.549584i | \(-0.814786\pi\) | ||||
−0.835439 | + | 0.549584i | \(0.814786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.52180 | 0.707389 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.49700 | 0.160495 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.33867 | −0.141899 | −0.0709495 | − | 0.997480i | \(-0.522603\pi\) | ||||
−0.0709495 | + | 0.997480i | \(0.522603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.3167 | 2.65391 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.810957 | −0.0840923 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.739455 | −0.0758664 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.96643 | 1.01194 | 0.505969 | − | 0.862552i | \(-0.331135\pi\) | ||||
0.505969 | + | 0.862552i | \(0.331135\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.8701 | −1.18112 | −0.590562 | − | 0.806992i | \(-0.701094\pi\) | ||||
−0.590562 | + | 0.806992i | \(0.701094\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3935 | 1.02410 | 0.512050 | − | 0.858955i | \(-0.328886\pi\) | ||||
0.512050 | + | 0.858955i | \(0.328886\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.01088 | 0.293832 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.34807 | 0.807039 | 0.403519 | − | 0.914971i | \(-0.367787\pi\) | ||||
0.403519 | + | 0.914971i | \(0.367787\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.25046 | 0.598686 | 0.299343 | − | 0.954146i | \(-0.403233\pi\) | ||||
0.299343 | + | 0.954146i | \(0.403233\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.12112 | −0.486075 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4937 | 1.55160 | 0.775798 | − | 0.630982i | \(-0.217348\pi\) | ||||
0.775798 | + | 0.630982i | \(0.217348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.13093 | −0.478461 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.0187 | −1.38848 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.2884 | −2.50152 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.89396 | −0.260940 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5082 | 1.46487 | 0.732434 | − | 0.680838i | \(-0.238384\pi\) | ||||
0.732434 | + | 0.680838i | \(0.238384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.53261 | −0.399074 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1354 | 1.06027 | 0.530137 | − | 0.847912i | \(-0.322141\pi\) | ||||
0.530137 | + | 0.847912i | \(0.322141\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.09401 | 0.268285 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.94491 | −0.339524 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.18352 | 0.528294 | 0.264147 | − | 0.964482i | \(-0.414910\pi\) | ||||
0.264147 | + | 0.964482i | \(0.414910\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.20245 | −0.441266 | −0.220633 | − | 0.975357i | \(-0.570812\pi\) | ||||
−0.220633 | + | 0.975357i | \(0.570812\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.65003 | 0.560033 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.08036 | 0.172765 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.56096 | −0.623618 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.2912 | 0.925013 | 0.462506 | − | 0.886616i | \(-0.346950\pi\) | ||||
0.462506 | + | 0.886616i | \(0.346950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.156619 | −0.0127455 | −0.00637275 | − | 0.999980i | \(-0.502029\pi\) | ||||
−0.00637275 | + | 0.999980i | \(0.502029\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.1884 | 1.30875 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.12698 | −0.0905210 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6990 | −1.09330 | −0.546650 | − | 0.837361i | \(-0.684097\pi\) | ||||
−0.546650 | + | 0.837361i | \(0.684097\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.59129 | −0.443418 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 21.4687 | 1.69197 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.85320 | −0.458458 | −0.229229 | − | 0.973372i | \(-0.573621\pi\) | ||||
−0.229229 | + | 0.973372i | \(0.573621\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.2892 | −0.950965 | −0.475483 | − | 0.879725i | \(-0.657727\pi\) | ||||
−0.475483 | + | 0.879725i | \(0.657727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.6093 | 1.81610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.83547 | −0.140362 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.0157 | 1.44574 | 0.722868 | − | 0.690987i | \(-0.242824\pi\) | ||||
0.722868 | + | 0.690987i | \(0.242824\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.18418 | 0.316294 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.43564 | 0.333403 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.166428 | 0.0124394 | 0.00621969 | − | 0.999981i | \(-0.498020\pi\) | ||||
0.00621969 | + | 0.999981i | \(0.498020\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.08469 | 0.303613 | 0.151806 | − | 0.988410i | \(-0.451491\pi\) | ||||
0.151806 | + | 0.988410i | \(0.451491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.5684 | 0.781242 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.11676 | −0.523235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.5062 | 1.20065 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7337 | −1.06609 | −0.533047 | − | 0.846086i | \(-0.678953\pi\) | ||||
−0.533047 | + | 0.846086i | \(0.678953\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.314976 | −0.0226725 | −0.0113362 | − | 0.999936i | \(-0.503609\pi\) | ||||
−0.0113362 | + | 0.999936i | \(0.503609\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.35390 | 0.311789 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.41533 | −0.100838 | −0.0504191 | − | 0.998728i | \(-0.516056\pi\) | ||||
−0.0504191 | + | 0.998728i | \(0.516056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.3049 | −1.58115 | −0.790575 | − | 0.612365i | \(-0.790218\pi\) | ||||
−0.790575 | + | 0.612365i | \(0.790218\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.98124 | −0.280815 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.70461 | −0.610944 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.02170 | −0.280888 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.7360 | −0.885211 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.3488 | −1.67624 | −0.838120 | − | 0.545486i | \(-0.816345\pi\) | ||||
−0.838120 | + | 0.545486i | \(0.816345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.38453 | 0.437461 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.29891 | −0.429582 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.71548 | 0.320108 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.82397 | −0.393547 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.4606 | −2.65441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.22145 | −0.416619 | −0.208310 | − | 0.978063i | \(-0.566796\pi\) | ||||
−0.208310 | + | 0.978063i | \(0.566796\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.48220 | −0.165480 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.0658 | −1.06632 | −0.533162 | − | 0.846013i | \(-0.678996\pi\) | ||||
−0.533162 | + | 0.846013i | \(0.678996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.6832 | −1.03638 | −0.518189 | − | 0.855266i | \(-0.673394\pi\) | ||||
−0.518189 | + | 0.855266i | \(0.673394\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.0236 | 0.918718 | 0.459359 | − | 0.888251i | \(-0.348079\pi\) | ||||
0.459359 | + | 0.888251i | \(0.348079\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.24147 | 0.602847 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.410510 | 0.0266655 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.8094 | 0.699200 | 0.349600 | − | 0.936899i | \(-0.386317\pi\) | ||||
0.349600 | + | 0.936899i | \(0.386317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.7912 | −1.27486 | −0.637431 | − | 0.770507i | \(-0.720003\pi\) | ||||
−0.637431 | + | 0.770507i | \(0.720003\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1505 | −0.971905 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.5074 | −0.671292 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.47412 | 0.284681 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.9538 | 0.694171 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.82947 | −0.241714 | −0.120857 | − | 0.992670i | \(-0.538564\pi\) | ||||
−0.120857 | + | 0.992670i | \(0.538564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.69299 | −0.293887 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.0304 | 1.18709 | 0.593543 | − | 0.804802i | \(-0.297729\pi\) | ||||
0.593543 | + | 0.804802i | \(0.297729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.7778 | 1.85030 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.16387 | 0.319635 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.6567 | 1.64372 | 0.821862 | − | 0.569686i | \(-0.192935\pi\) | ||||
0.821862 | + | 0.569686i | \(0.192935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.77015 | −0.477317 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.963290 | 0.0589524 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.454544 | 0.0277141 | 0.0138570 | − | 0.999904i | \(-0.495589\pi\) | ||||
0.0138570 | + | 0.999904i | \(0.495589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.2608 | 0.987771 | 0.493885 | − | 0.869527i | \(-0.335576\pi\) | ||||
0.493885 | + | 0.869527i | \(0.335576\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.2175 | −1.10257 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4338 | 0.686989 | 0.343495 | − | 0.939155i | \(-0.388389\pi\) | ||||
0.343495 | + | 0.939155i | \(0.388389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.79738 | −0.167475 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.69217 | 0.339566 | 0.169783 | − | 0.985481i | \(-0.445693\pi\) | ||||
0.169783 | + | 0.985481i | \(0.445693\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.580914 | −0.0345318 | −0.0172659 | − | 0.999851i | \(-0.505496\pi\) | ||||
−0.0172659 | + | 0.999851i | \(0.505496\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.532101 | 0.0315189 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.8275 | 0.993298 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.5339 | 1.50199 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.17170 | −0.420413 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.17741 | 0.0687850 | 0.0343925 | − | 0.999408i | \(-0.489050\pi\) | ||||
0.0343925 | + | 0.999408i | \(0.489050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.16416 | 0.358891 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.0450 | 1.79538 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3558 | 1.51912 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.54158 | 0.490701 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.6869 | 0.840967 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.1615 | −1.09360 | −0.546802 | − | 0.837262i | \(-0.684155\pi\) | ||||
−0.546802 | + | 0.837262i | \(0.684155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.47900 | −0.425466 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.6728 | −1.05884 | −0.529419 | − | 0.848361i | \(-0.677590\pi\) | ||||
−0.529419 | + | 0.848361i | \(0.677590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.58974 | −0.202904 | −0.101452 | − | 0.994840i | \(-0.532349\pi\) | ||||
−0.101452 | + | 0.994840i | \(0.532349\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.3860 | 0.585183 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.50027 | 0.140429 | 0.0702146 | − | 0.997532i | \(-0.477632\pi\) | ||||
0.0702146 | + | 0.997532i | \(0.477632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.00715 | −0.335287 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.82258 | −0.268335 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.05056 | 0.335625 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.49774 | −0.248726 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −38.6680 | −2.13184 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.58629 | 0.362015 | 0.181008 | − | 0.983482i | \(-0.442064\pi\) | ||||
0.181008 | + | 0.983482i | \(0.442064\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.6652 | −0.968047 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.53268 | −0.302283 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2151 | 0.828821 | 0.414410 | − | 0.910090i | \(-0.363988\pi\) | ||||
0.414410 | + | 0.910090i | \(0.363988\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.8686 | −0.644615 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.6755 | 0.792405 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.69214 | 0.198778 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.66135 | 0.411283 | 0.205641 | − | 0.978627i | \(-0.434072\pi\) | ||||
0.205641 | + | 0.978627i | \(0.434072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.99401 | 0.481438 | 0.240719 | − | 0.970595i | \(-0.422617\pi\) | ||||
0.240719 | + | 0.970595i | \(0.422617\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.8689 | 1.27403 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3310 | 0.549862 | 0.274931 | − | 0.961464i | \(-0.411345\pi\) | ||||
0.274931 | + | 0.961464i | \(0.411345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.87252 | 0.470904 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.6363 | 1.03927 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.2627 | 0.858310 | 0.429155 | − | 0.903231i | \(-0.358811\pi\) | ||||
0.429155 | + | 0.903231i | \(0.358811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4532 | −0.971221 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.09351 | −0.423634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.5427 | 1.80311 | 0.901557 | − | 0.432660i | \(-0.142425\pi\) | ||||
0.901557 | + | 0.432660i | \(0.142425\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.98266 | −0.519676 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.5117 | 1.68792 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.2168 | −1.61634 | −0.808172 | − | 0.588946i | \(-0.799543\pi\) | ||||
−0.808172 | + | 0.588946i | \(0.799543\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.719585 | 0.0371592 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.5874 | −0.648282 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.4663 | 1.71905 | 0.859525 | − | 0.511094i | \(-0.170759\pi\) | ||||
0.859525 | + | 0.511094i | \(0.170759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.8791 | −0.608584 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.134288 | 0.00686178 | 0.00343089 | − | 0.999994i | \(-0.498908\pi\) | ||||
0.00343089 | + | 0.999994i | \(0.498908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.6351 | −0.794779 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.53807 | −0.432897 | −0.216449 | − | 0.976294i | \(-0.569447\pi\) | ||||
−0.216449 | + | 0.976294i | \(0.569447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.4629 | −1.69229 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.73245 | −0.440494 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.570482 | 0.0287040 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.0250 | 1.90842 | 0.954211 | − | 0.299135i | \(-0.0966982\pi\) | ||||
0.954211 | + | 0.299135i | \(0.0966982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.22641 | −0.111460 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.7343 | −0.585982 | −0.292991 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292991 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.81885 | 0.339671 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.60789 | −0.228968 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.9837 | 1.43315 | 0.716575 | − | 0.697510i | \(-0.245709\pi\) | ||||
0.716575 | + | 0.697510i | \(0.245709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.44957 | −0.219481 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.7920 | −1.26914 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.2224 | 0.747239 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.74361 | 0.183325 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.5318 | −0.612221 | −0.306110 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306110 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4281 | −0.556973 | −0.278486 | − | 0.960440i | \(-0.589833\pi\) | ||||
−0.278486 | + | 0.960440i | \(0.589833\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.9391 | 1.11534 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.52180 | −0.316354 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −61.4525 | −2.97389 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.78747 | 0.182436 | 0.0912181 | − | 0.995831i | \(-0.470924\pi\) | ||||
0.0912181 | + | 0.995831i | \(0.470924\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.6848 | 1.23433 | 0.617166 | − | 0.786833i | \(-0.288281\pi\) | ||||
0.617166 | + | 0.786833i | \(0.288281\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.49700 | −0.0717756 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.79409 | 0.181496 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.1218 | 1.38991 | 0.694955 | − | 0.719054i | \(-0.255424\pi\) | ||||
0.694955 | + | 0.719054i | \(0.255424\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −26.0814 | −1.24197 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.1115 | −0.575437 | −0.287718 | − | 0.957715i | \(-0.592897\pi\) | ||||
−0.287718 | + | 0.957715i | \(0.592897\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.33867 | 0.0634592 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.12500 | −0.384299 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.6886 | 1.40109 | 0.700546 | − | 0.713607i | \(-0.252940\pi\) | ||||
0.700546 | + | 0.713607i | \(0.252940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.112701 | 0.00529516 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.3167 | −1.18686 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.751497 | −0.0351535 | −0.0175768 | − | 0.999846i | \(-0.505595\pi\) | ||||
−0.0175768 | + | 0.999846i | \(0.505595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.7279 | −1.20088 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.62920 | 0.448477 | 0.224238 | − | 0.974534i | \(-0.428011\pi\) | ||||
0.224238 | + | 0.974534i | \(0.428011\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.33661 | 0.155065 | 0.0775327 | − | 0.996990i | \(-0.475296\pi\) | ||||
0.0775327 | + | 0.996990i | \(0.475296\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.810957 | 0.0376072 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.69675 | −0.0785161 | −0.0392581 | − | 0.999229i | \(-0.512499\pi\) | ||||
−0.0392581 | + | 0.999229i | \(0.512499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.1497 | 1.06896 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.85761 | 0.454214 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.739455 | 0.0339285 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.2870 | −0.883093 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.1315 | 1.01121 | 0.505607 | − | 0.862764i | \(-0.331269\pi\) | ||||
0.505607 | + | 0.862764i | \(0.331269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.0604 | 1.96339 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.4486 | −0.702935 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.96643 | −0.452552 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.9414 | 0.903631 | 0.451815 | − | 0.892111i | \(-0.350777\pi\) | ||||
0.451815 | + | 0.892111i | \(0.350777\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.21188 | 0.190468 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.2451 | 1.18443 | 0.592213 | − | 0.805782i | \(-0.298254\pi\) | ||||
0.592213 | + | 0.805782i | \(0.298254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.5677 | 0.611059 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −37.1242 | −1.66525 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.34480 | 0.373565 | 0.186782 | − | 0.982401i | \(-0.440194\pi\) | ||||
0.186782 | + | 0.982401i | \(0.440194\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.84311 | 0.395081 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.3824 | 1.35469 | 0.677343 | − | 0.735667i | \(-0.263131\pi\) | ||||
0.677343 | + | 0.735667i | \(0.263131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.8701 | 0.528214 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.9889 | −0.754505 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.2197 | 0.763248 | 0.381624 | − | 0.924318i | \(-0.375365\pi\) | ||||
0.381624 | + | 0.924318i | \(0.375365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 33.8647 | 1.49809 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.91708 | 0.128792 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.3935 | −0.457992 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.6834 | −0.600635 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.4975 | −0.941822 | −0.470911 | − | 0.882181i | \(-0.656075\pi\) | ||||
−0.470911 | + | 0.882181i | \(0.656075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0139271 | −0.000608991 0 | −0.000304496 | − | 1.00000i | \(-0.500097\pi\) | ||||
−0.000304496 | 1.00000i | \(0.500097\pi\) | ||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.01088 | −0.131405 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.34993 | −0.320168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.32640 | 0.144626 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.3007 | 0.663992 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.3336 | 1.05400 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.34807 | −0.360919 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.119759 | −0.00516798 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.7268 | 1.83697 | 0.918483 | − | 0.395459i | \(-0.129415\pi\) | ||||
0.918483 | + | 0.395459i | \(0.129415\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.93929 | −0.126137 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.25046 | −0.267740 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8319 | 0.762438 | 0.381219 | − | 0.924485i | \(-0.375504\pi\) | ||||
0.381219 | + | 0.924485i | \(0.375504\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.4557 | 1.55589 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.53833 | −0.0655352 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.38700 | −0.101506 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.12112 | 0.217379 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.8786 | 0.757541 | 0.378771 | − | 0.925491i | \(-0.376347\pi\) | ||||
0.378771 | + | 0.925491i | \(0.376347\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.1120 | 1.61196 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.6011 | −0.446781 | −0.223391 | − | 0.974729i | \(-0.571713\pi\) | ||||
−0.223391 | + | 0.974729i | \(0.571713\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.4937 | −0.693894 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.2803 | 0.809695 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.8718 | 0.958836 | 0.479418 | − | 0.877587i | \(-0.340848\pi\) | ||||
0.479418 | + | 0.877587i | \(0.340848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5139 | −0.858480 | −0.429240 | − | 0.903191i | \(-0.641218\pi\) | ||||
−0.429240 | + | 0.903191i | \(0.641218\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6022 | 0.442912 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.13093 | 0.213974 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.2174 | 1.00819 | 0.504093 | − | 0.863650i | \(-0.331827\pi\) | ||||
0.504093 | + | 0.863650i | \(0.331827\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.226652 | 0.00941935 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −63.6934 | −2.64245 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0187 | 0.620946 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.9904 | 1.32039 | 0.660194 | − | 0.751095i | \(-0.270474\pi\) | ||||
0.660194 | + | 0.751095i | \(0.270474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.833349 | 0.0343375 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.01845 | 0.0418935 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 42.5206 | 1.74611 | 0.873056 | − | 0.487620i | \(-0.162135\pi\) | ||||
0.873056 | + | 0.487620i | \(0.162135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.2884 | 1.11872 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.0503 | 0.656894 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.29039 | 0.175301 | 0.0876503 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876503 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.9972 | −0.815704 | −0.407852 | − | 0.913048i | \(-0.633722\pi\) | ||||
−0.407852 | + | 0.913048i | \(0.633722\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.7332 | −0.559259 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.2114 | −0.942121 | −0.471060 | − | 0.882101i | \(-0.656129\pi\) | ||||
−0.471060 | + | 0.882101i | \(0.656129\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.26371 | 0.253818 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −55.9161 | −2.26212 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.94916 | 0.240284 | 0.120142 | − | 0.992757i | \(-0.461665\pi\) | ||||
0.120142 | + | 0.992757i | \(0.461665\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.89396 | 0.116696 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.7576 | 1.60058 | 0.800291 | − | 0.599612i | \(-0.204678\pi\) | ||||
0.800291 | + | 0.599612i | \(0.204678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8287 | 0.475436 | 0.237718 | − | 0.971334i | \(-0.423601\pi\) | ||||
0.237718 | + | 0.971334i | \(0.423601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.2410 | 0.812245 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.60125 | −0.224410 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −46.4141 | −1.85065 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.8112 | −0.589623 | −0.294812 | − | 0.955555i | \(-0.595257\pi\) | ||||
−0.294812 | + | 0.955555i | \(0.595257\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.5210 | 0.696398 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.5082 | −0.655109 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 63.5756 | 2.51896 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.0233 | 0.871230 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.51035 | −0.336139 | −0.168069 | − | 0.985775i | \(-0.553753\pi\) | ||||
−0.168069 | + | 0.985775i | \(0.553753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.4340 | −1.35794 | −0.678971 | − | 0.734165i | \(-0.737574\pi\) | ||||
−0.678971 | + | 0.734165i | \(0.737574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.53261 | 0.178471 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.32491 | −0.209344 | −0.104672 | − | 0.994507i | \(-0.533379\pi\) | ||||
−0.104672 | + | 0.994507i | \(0.533379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.39319 | −0.132990 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.2099 | 1.10394 | 0.551970 | − | 0.833864i | \(-0.313876\pi\) | ||||
0.551970 | + | 0.833864i | \(0.313876\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1354 | −0.474169 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.0897 | −0.783773 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.9228 | −0.776082 | −0.388041 | − | 0.921642i | \(-0.626848\pi\) | ||||
−0.388041 | + | 0.921642i | \(0.626848\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.6144 | −0.646225 | −0.323112 | − | 0.946361i | \(-0.604729\pi\) | ||||
−0.323112 | + | 0.946361i | \(0.604729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.3953 | 1.10278 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.09401 | −0.119981 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.6742 | −0.413306 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.47687 | 0.173086 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.7246 | −1.26144 | −0.630720 | − | 0.776010i | \(-0.717240\pi\) | ||||
−0.630720 | + | 0.776010i | \(0.717240\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.94491 | 0.151840 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.0308 | −1.57694 | −0.788472 | − | 0.615071i | \(-0.789127\pi\) | ||||
−0.788472 | + | 0.615071i | \(0.789127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.7014 | 1.60035 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.5607 | 0.443007 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.71534 | −0.218691 | −0.109346 | − | 0.994004i | \(-0.534876\pi\) | ||||
−0.109346 | + | 0.994004i | \(0.534876\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.18352 | −0.236260 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.2854 | 0.430566 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 47.0138 | 1.79108 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.8709 | 1.47872 | 0.739358 | − | 0.673312i | \(-0.235129\pi\) | ||||
0.739358 | + | 0.673312i | \(0.235129\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.20245 | 0.197340 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −26.2288 | −0.993485 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0912 | −0.381684 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.37005 | −0.127285 | −0.0636426 | − | 0.997973i | \(-0.520272\pi\) | ||||
−0.0636426 | + | 0.997973i | \(0.520272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.26252 | 0.198480 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.65003 | −0.250455 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.6668 | −1.86791 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.6143 | −0.849300 | −0.424650 | − | 0.905358i | \(-0.639603\pi\) | ||||
−0.424650 | + | 0.905358i | \(0.639603\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.41605 | 0.0531059 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.78244 | 0.216554 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.77827 | −0.290485 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.7071 | 0.697655 | 0.348828 | − | 0.937187i | \(-0.386580\pi\) | ||||
0.348828 | + | 0.937187i | \(0.386580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.4883 | 1.61959 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.2415 | 0.529645 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.08036 | −0.0772627 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.98028 | 0.110532 | 0.0552662 | − | 0.998472i | \(-0.482399\pi\) | ||||
0.0552662 | + | 0.998472i | \(0.482399\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.92160 | −0.108207 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.0803 | −1.51941 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.1444 | 0.744050 | 0.372025 | − | 0.928223i | \(-0.378664\pi\) | ||||
0.372025 | + | 0.928223i | \(0.378664\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.56096 | 0.278890 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.2196 | 0.854146 | 0.427073 | − | 0.904217i | \(-0.359545\pi\) | ||||
0.427073 | + | 0.904217i | \(0.359545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.21951 | −0.118272 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.4412 | 1.15346 | 0.576732 | − | 0.816933i | \(-0.304328\pi\) | ||||
0.576732 | + | 0.816933i | \(0.304328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.2912 | −0.413678 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 37.7850 | 1.38248 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 34.9299 | 1.27631 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.5769 | −1.48067 | −0.740337 | − | 0.672236i | \(-0.765334\pi\) | ||||
−0.740337 | + | 0.672236i | \(0.765334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.75563 | 0.100421 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.156619 | 0.00569996 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5716 | −0.820378 | −0.410189 | − | 0.912000i | \(-0.634537\pi\) | ||||
−0.410189 | + | 0.912000i | \(0.634537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.9901 | −0.797139 | −0.398570 | − | 0.917138i | \(-0.630493\pi\) | ||||
−0.398570 | + | 0.917138i | \(0.630493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.1531 | 0.946805 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.1884 | −0.585293 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.2966 | −1.34670 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.1834 | 1.48511 | 0.742556 | − | 0.669784i | \(-0.233613\pi\) | ||||
0.742556 | + | 0.669784i | \(0.233613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.6940 | −0.493178 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.8352 | −0.389716 | −0.194858 | − | 0.980831i | \(-0.562425\pi\) | ||||
−0.194858 | + | 0.980831i | \(0.562425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.12698 | 0.0404822 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.4277 | −0.768714 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.97387 | 0.106550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.20684 | −0.293288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.6990 | 0.488938 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.3348 | −1.11696 | −0.558482 | − | 0.829517i | \(-0.688616\pi\) | ||||
−0.558482 | + | 0.829517i | \(0.688616\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.1818 | −0.682890 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 69.0126 | 2.45381 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −88.8638 | −3.15565 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.59129 | 0.198303 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.52077 | −0.337243 | −0.168621 | − | 0.985681i | \(-0.553932\pi\) | ||||
−0.168621 | + | 0.985681i | \(0.553932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.2710 | 2.13224 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.32285 | 0.117407 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.4687 | −0.756673 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.327084 | −0.0115139 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.0902 | 1.02276 | 0.511379 | − | 0.859355i | \(-0.329135\pi\) | ||||
0.511379 | + | 0.859355i | \(0.329135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.6205 | −1.53172 | −0.765862 | − | 0.643005i | \(-0.777687\pi\) | ||||
−0.765862 | + | 0.643005i | \(0.777687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.7010 | −0.410372 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.85320 | 0.205029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.65776 | 0.162954 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −62.8410 | −2.19584 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6375 | −0.929656 | −0.464828 | − | 0.885401i | \(-0.653884\pi\) | ||||
−0.464828 | + | 0.885401i | \(0.653884\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.9584 | −0.695706 | −0.347853 | − | 0.937549i | \(-0.613089\pi\) | ||||
−0.347853 | + | 0.937549i | \(0.613089\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.6819 | 0.927819 | 0.463910 | − | 0.885883i | \(-0.346446\pi\) | ||||
0.463910 | + | 0.885883i | \(0.346446\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.7077 | −1.76115 | −0.880576 | − | 0.473905i | \(-0.842844\pi\) | ||||
−0.880576 | + | 0.473905i | \(0.842844\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.22758 | −0.285412 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −68.5271 | −2.37432 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.2892 | 0.425285 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.44583 | 0.153670 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.69881 | 0.0931733 | 0.0465867 | − | 0.998914i | \(-0.485166\pi\) | ||||
0.0465867 | + | 0.998914i | \(0.485166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6721 | −0.850762 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.09600 | −0.141074 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.6093 | −0.812186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.418017 | 0.0143463 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.5156 | 1.25174 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.6391 | 0.603951 | 0.301976 | − | 0.953316i | \(-0.402354\pi\) | ||||
0.301976 | + | 0.953316i | \(0.402354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.83547 | 0.0627718 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.72254 | 0.297956 | 0.148978 | − | 0.988840i | \(-0.452402\pi\) | ||||
0.148978 | + | 0.988840i | \(0.452402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.2322 | 1.16799 | 0.583993 | − | 0.811759i | \(-0.301490\pi\) | ||||
0.583993 | + | 0.811759i | \(0.301490\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.1089 | −0.412669 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.8286 | 1.38982 | 0.694911 | − | 0.719096i | \(-0.255444\pi\) | ||||
0.694911 | + | 0.719096i | \(0.255444\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.0157 | −0.646552 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.3738 | −0.624008 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.4758 | 1.13429 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −24.7387 | −0.837276 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.18418 | −0.141451 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.01395 | 0.135541 | 0.0677707 | − | 0.997701i | \(-0.478411\pi\) | ||||
0.0677707 | + | 0.997701i | \(0.478411\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.847247 | −0.0285769 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.1713 | 0.713278 | 0.356639 | − | 0.934242i | \(-0.383923\pi\) | ||||
0.356639 | + | 0.934242i | \(0.383923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.66990 | −0.224460 | −0.112230 | − | 0.993682i | \(-0.535799\pi\) | ||||
−0.112230 | + | 0.993682i | \(0.535799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.43564 | −0.149102 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.53548 | 0.0851332 | 0.0425666 | − | 0.999094i | \(-0.486447\pi\) | ||||
0.0425666 | + | 0.999094i | \(0.486447\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 69.0735 | 2.31665 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.83365 | −0.228679 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.166428 | −0.00556306 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.3395 | −0.745895 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.34452 | −0.0781942 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.6754 | −1.68824 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.9653 | −0.631124 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.08469 | −0.135780 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.3808 | 1.20801 | 0.604003 | − | 0.796982i | \(-0.293572\pi\) | ||||
0.604003 | + | 0.796982i | \(0.293572\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.4640 | 0.977260 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 58.3264 | 1.93244 | 0.966220 | − | 0.257719i | \(-0.0829709\pi\) | ||||
0.966220 | + | 0.257719i | \(0.0829709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.5684 | −0.349382 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 50.7767 | 1.67679 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.7560 | 0.981560 | 0.490780 | − | 0.871283i | \(-0.336712\pi\) | ||||
0.490780 | + | 0.871283i | \(0.336712\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.7883 | 0.454341 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53.6837 | −1.76702 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.11676 | 0.233998 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.7987 | −0.847340 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.0033 | −0.853140 | −0.426570 | − | 0.904455i | \(-0.640278\pi\) | ||||
−0.426570 | + | 0.904455i | \(0.640278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.76973 | 0.254643 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.4367 | 0.439897 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.46058 | 0.211058 | 0.105529 | − | 0.994416i | \(-0.466346\pi\) | ||||
0.105529 | + | 0.994416i | \(0.466346\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.58312 | 0.0842970 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.8484 | 0.973030 | 0.486515 | − | 0.873672i | \(-0.338268\pi\) | ||||
0.486515 | + | 0.873672i | \(0.338268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.6351 | 0.671970 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.5062 | −0.536947 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.1069 | −1.17332 | −0.586658 | − | 0.809834i | \(-0.699557\pi\) | ||||
−0.586658 | + | 0.809834i | \(0.699557\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48.9703 | 1.58964 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.79916 | −0.0583417 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.5190 | 1.11818 | 0.559091 | − | 0.829107i | \(-0.311150\pi\) | ||||
0.559091 | + | 0.829107i | \(0.311150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.7337 | 0.476772 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.8730 | 0.835482 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7299 | −0.959030 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.7216 | −0.667743 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.314976 | 0.0101394 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.4086 | −0.913559 | −0.456780 | − | 0.889580i | \(-0.650997\pi\) | ||||
−0.456780 | + | 0.889580i | \(0.650997\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.47026 | 0.111481 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.9718 | 0.993932 | 0.496966 | − | 0.867770i | \(-0.334447\pi\) | ||||
0.496966 | + | 0.867770i | \(0.334447\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.7680 | −0.697850 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.35390 | −0.139436 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.7235 | −1.23887 | −0.619437 | − | 0.785046i | \(-0.712639\pi\) | ||||
−0.619437 | + | 0.785046i | \(0.712639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.5149 | −0.495352 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.1197 | −0.354663 | −0.177331 | − | 0.984151i | \(-0.556746\pi\) | ||||
−0.177331 | + | 0.984151i | \(0.556746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.41533 | 0.0450962 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.8249 | 0.885677 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.3193 | 1.02769 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.5682 | 0.367475 | 0.183737 | − | 0.982975i | \(-0.441180\pi\) | ||||
0.183737 | + | 0.982975i | \(0.441180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.73940 | −0.150400 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.3049 | 0.707112 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.1683 | −0.892097 | −0.446049 | − | 0.895009i | \(-0.647169\pi\) | ||||
−0.446049 | + | 0.895009i | \(0.647169\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.0750 | 0.888253 |
(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 | 9680.2.a.cy.1.4 | 6 | ||
4.3 | odd | 2 | 4840.2.a.be.1.3 | 6 | |||
11.7 | odd | 10 | 880.2.bo.j.401.2 | 12 | |||
11.8 | odd | 10 | 880.2.bo.j.801.2 | 12 | |||
11.10 | odd | 2 | 9680.2.a.cx.1.4 | 6 | |||
44.7 | even | 10 | 440.2.y.b.401.2 | yes | 12 | ||
44.19 | even | 10 | 440.2.y.b.361.2 | ✓ | 12 | ||
44.43 | even | 2 | 4840.2.a.bf.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.b.361.2 | ✓ | 12 | 44.19 | even | 10 | ||
440.2.y.b.401.2 | yes | 12 | 44.7 | even | 10 | ||
880.2.bo.j.401.2 | 12 | 11.7 | odd | 10 | |||
880.2.bo.j.801.2 | 12 | 11.8 | odd | 10 | |||
4840.2.a.be.1.3 | 6 | 4.3 | odd | 2 | |||
4840.2.a.bf.1.3 | 6 | 44.43 | even | 2 | |||
9680.2.a.cx.1.4 | 6 | 11.10 | odd | 2 | |||
9680.2.a.cy.1.4 | 6 | 1.1 | even | 1 | trivial |