Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5776,2,Mod(1,5776)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5776, 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("5776.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5776 = 2^{4} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5776.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: | \(46.1215922075\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 722) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.90211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5776.1 |
$q$-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 | ||||||||
\(3\) | −0.442463 | −0.255456 | −0.127728 | − | 0.991809i | \(-0.540769\pi\) | ||||
−0.127728 | + | 0.991809i | \(0.540769\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.891491 | −0.398687 | −0.199344 | − | 0.979930i | \(-0.563881\pi\) | ||||
−0.199344 | + | 0.979930i | \(0.563881\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.52015 | −0.952526 | −0.476263 | − | 0.879303i | \(-0.658009\pi\) | ||||
−0.476263 | + | 0.879303i | \(0.658009\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.80423 | −0.934742 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.95199 | −0.588547 | −0.294273 | − | 0.955721i | \(-0.595078\pi\) | ||||
−0.294273 | + | 0.955721i | \(0.595078\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.45965 | 1.79158 | 0.895792 | − | 0.444473i | \(-0.146609\pi\) | ||||
0.895792 | + | 0.444473i | \(0.146609\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.394452 | 0.101847 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.42226 | −0.830020 | −0.415010 | − | 0.909817i | \(-0.636222\pi\) | ||||
−0.415010 | + | 0.909817i | \(0.636222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.11507 | 0.243329 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.18504 | −1.70670 | −0.853349 | − | 0.521339i | \(-0.825433\pi\) | ||||
−0.853349 | + | 0.521339i | \(0.825433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.20524 | −0.841049 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.56816 | 0.494242 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.58064 | −0.850604 | −0.425302 | − | 0.905051i | \(-0.639832\pi\) | ||||
−0.425302 | + | 0.905051i | \(0.639832\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.79360 | −1.57938 | −0.789689 | − | 0.613507i | \(-0.789758\pi\) | ||||
−0.789689 | + | 0.613507i | \(0.789758\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.863684 | 0.150348 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.24669 | 0.379760 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.97980 | 0.983073 | 0.491536 | − | 0.870857i | \(-0.336436\pi\) | ||||
0.491536 | + | 0.870857i | \(0.336436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.85816 | −0.457672 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.48932 | 0.544941 | 0.272470 | − | 0.962164i | \(-0.412159\pi\) | ||||
0.272470 | + | 0.962164i | \(0.412159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.24669 | 0.952611 | 0.476306 | − | 0.879280i | \(-0.341976\pi\) | ||||
0.476306 | + | 0.879280i | \(0.341976\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.49994 | 0.372670 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.5498 | 1.53885 | 0.769425 | − | 0.638738i | \(-0.220543\pi\) | ||||
0.769425 | + | 0.638738i | \(0.220543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.648859 | −0.0926941 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.51423 | 0.212034 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.76278 | −0.516858 | −0.258429 | − | 0.966030i | \(-0.583205\pi\) | ||||
−0.258429 | + | 0.966030i | \(0.583205\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.74018 | 0.234646 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.84162 | 0.369947 | 0.184973 | − | 0.982744i | \(-0.440780\pi\) | ||||
0.184973 | + | 0.982744i | \(0.440780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.45495 | −0.314324 | −0.157162 | − | 0.987573i | \(-0.550235\pi\) | ||||
−0.157162 | + | 0.987573i | \(0.550235\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.06706 | 0.890366 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.75872 | −0.714282 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.67261 | −0.326511 | −0.163256 | − | 0.986584i | \(-0.552200\pi\) | ||||
−0.163256 | + | 0.986584i | \(0.552200\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.62158 | 0.435987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0564404 | 0.00669824 | 0.00334912 | − | 0.999994i | \(-0.498934\pi\) | ||||
0.00334912 | + | 0.999994i | \(0.498934\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.96917 | −0.815680 | −0.407840 | − | 0.913053i | \(-0.633718\pi\) | ||||
−0.407840 | + | 0.913053i | \(0.633718\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.86067 | 0.214851 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.91930 | 0.560606 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.13162 | −1.02739 | −0.513694 | − | 0.857974i | \(-0.671723\pi\) | ||||
−0.513694 | + | 0.857974i | \(0.671723\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.27636 | 0.808485 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1239 | 1.55030 | 0.775150 | − | 0.631778i | \(-0.217674\pi\) | ||||
0.775150 | + | 0.631778i | \(0.217674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.05092 | 0.330918 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.02677 | 0.217292 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.86774 | −0.197980 | −0.0989901 | − | 0.995088i | \(-0.531561\pi\) | ||||
−0.0989901 | + | 0.995088i | \(0.531561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.2793 | −1.70653 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.89085 | 0.403462 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.82432 | −0.794439 | −0.397219 | − | 0.917724i | \(-0.630025\pi\) | ||||
−0.397219 | + | 0.917724i | \(0.630025\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.47382 | 0.550139 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.38487 | −0.535815 | −0.267907 | − | 0.963445i | \(-0.586332\pi\) | ||||
−0.267907 | + | 0.963445i | \(0.586332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.69468 | −0.462580 | −0.231290 | − | 0.972885i | \(-0.574295\pi\) | ||||
−0.231290 | + | 0.972885i | \(0.574295\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.994078 | −0.0970121 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0373 | 1.55038 | 0.775191 | − | 0.631727i | \(-0.217654\pi\) | ||||
0.775191 | + | 0.631727i | \(0.217654\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.1008 | −1.35061 | −0.675305 | − | 0.737538i | \(-0.735988\pi\) | ||||
−0.675305 | + | 0.737538i | \(0.735988\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.64584 | −0.251132 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7224 | 1.19682 | 0.598410 | − | 0.801190i | \(-0.295799\pi\) | ||||
0.598410 | + | 0.801190i | \(0.295799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.29689 | 0.680439 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.1143 | −1.67467 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.62460 | 0.790616 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.18974 | −0.653613 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.54390 | −0.139209 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.20640 | 0.734002 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.17442 | 0.636627 | 0.318313 | − | 0.947986i | \(-0.396884\pi\) | ||||
0.318313 | + | 0.947986i | \(0.396884\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.76393 | −0.243351 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.52265 | 0.307776 | 0.153888 | − | 0.988088i | \(-0.450821\pi\) | ||||
0.153888 | + | 0.988088i | \(0.450821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.28949 | −0.197048 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0035 | −0.940096 | −0.470048 | − | 0.882641i | \(-0.655763\pi\) | ||||
−0.470048 | + | 0.882641i | \(0.655763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.7586 | −1.84554 | −0.922771 | − | 0.385350i | \(-0.874081\pi\) | ||||
−0.922771 | + | 0.385350i | \(0.874081\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.66791 | −0.393109 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.6092 | −1.05443 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.08361 | 0.339125 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.287096 | 0.0236793 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.3896 | 1.17884 | 0.589420 | − | 0.807827i | \(-0.299356\pi\) | ||||
0.589420 | + | 0.807827i | \(0.299356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.4068 | 1.00965 | 0.504824 | − | 0.863222i | \(-0.331557\pi\) | ||||
0.504824 | + | 0.863222i | \(0.331557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.59679 | 0.775855 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.83942 | 0.629678 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.451220 | −0.0360113 | −0.0180056 | − | 0.999838i | \(-0.505732\pi\) | ||||
−0.0180056 | + | 0.999838i | \(0.505732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.66489 | 0.132035 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.6275 | 1.62567 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0692542 | 0.00542441 | 0.00271220 | − | 0.999996i | \(-0.499137\pi\) | ||||
0.00271220 | + | 0.999996i | \(0.499137\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.769967 | −0.0599418 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.17371 | 0.168206 | 0.0841032 | − | 0.996457i | \(-0.473197\pi\) | ||||
0.0841032 | + | 0.996457i | \(0.473197\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.7271 | 2.20977 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8493 | 1.28103 | 0.640514 | − | 0.767947i | \(-0.278721\pi\) | ||||
0.640514 | + | 0.767947i | \(0.278721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.5978 | 0.801121 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.25731 | −0.0945053 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9655 | 1.41755 | 0.708775 | − | 0.705435i | \(-0.249248\pi\) | ||||
0.708775 | + | 0.705435i | \(0.249248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.98687 | 0.147683 | 0.0738415 | − | 0.997270i | \(-0.476474\pi\) | ||||
0.0738415 | + | 0.997270i | \(0.476474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.08623 | 0.0802961 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.33094 | −0.391938 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.68021 | 0.488506 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.47214 | −0.470779 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9259 | 1.51415 | 0.757074 | − | 0.653329i | \(-0.226628\pi\) | ||||
0.757074 | + | 0.653329i | \(0.226628\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.78879 | −0.560650 | −0.280325 | − | 0.959905i | \(-0.590442\pi\) | ||||
−0.280325 | + | 0.959905i | \(0.590442\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.54802 | 0.182468 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.82514 | 0.130036 | 0.0650180 | − | 0.997884i | \(-0.479290\pi\) | ||||
0.0650180 | + | 0.997884i | \(0.479290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.35926 | −0.167243 | −0.0836216 | − | 0.996498i | \(-0.526649\pi\) | ||||
−0.0836216 | + | 0.996498i | \(0.526649\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.18253 | 0.0834094 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.5439 | 0.810223 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.11070 | −0.217261 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.9527 | 1.59532 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.361050 | −0.0248557 | −0.0124279 | − | 0.999923i | \(-0.503956\pi\) | ||||
−0.0124279 | + | 0.999923i | \(0.503956\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0249728 | −0.00171111 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.56887 | −0.379794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.1612 | 1.50440 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.08361 | 0.208371 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.1066 | −1.48705 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0486 | 1.20862 | 0.604312 | − | 0.796748i | \(-0.293448\pi\) | ||||
0.604312 | + | 0.796748i | \(0.293448\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.7925 | 0.786163 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.2845 | 0.815349 | 0.407675 | − | 0.913127i | \(-0.366340\pi\) | ||||
0.407675 | + | 0.913127i | \(0.366340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.79174 | 0.448811 | 0.224405 | − | 0.974496i | \(-0.427956\pi\) | ||||
0.224405 | + | 0.974496i | \(0.427956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.17661 | −0.143210 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.4294 | 1.40388 | 0.701942 | − | 0.712234i | \(-0.252317\pi\) | ||||
0.701942 | + | 0.712234i | \(0.252317\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.40507 | −0.613519 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.04041 | 0.262453 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8376 | 0.765713 | 0.382856 | − | 0.923808i | \(-0.374940\pi\) | ||||
0.382856 | + | 0.923808i | \(0.374940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.7463 | 1.40080 | 0.700401 | − | 0.713749i | \(-0.253004\pi\) | ||||
0.700401 | + | 0.713749i | \(0.253004\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.9240 | −0.700775 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.578452 | 0.0369560 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.24931 | −0.396034 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.6410 | −1.49221 | −0.746104 | − | 0.665829i | \(-0.768078\pi\) | ||||
−0.746104 | + | 0.665829i | \(0.768078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.9771 | 1.00447 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.34992 | −0.0845352 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.923469 | 0.0576044 | 0.0288022 | − | 0.999585i | \(-0.490831\pi\) | ||||
0.0288022 | + | 0.999585i | \(0.490831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.0700 | −0.936402 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.8452 | 0.795096 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.31967 | −0.266362 | −0.133181 | − | 0.991092i | \(-0.542519\pi\) | ||||
−0.133181 | + | 0.991092i | \(0.542519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.35449 | 0.206064 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.826407 | 0.0505753 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7954 | 0.658205 | 0.329102 | − | 0.944294i | \(-0.393254\pi\) | ||||
0.329102 | + | 0.944294i | \(0.393254\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.807243 | −0.0490365 | −0.0245183 | − | 0.999699i | \(-0.507805\pi\) | ||||
−0.0245183 | + | 0.999699i | \(0.507805\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.20298 | 0.435944 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.20859 | 0.494996 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.14869 | −0.549691 | −0.274846 | − | 0.961488i | \(-0.588627\pi\) | ||||
−0.274846 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.6593 | 1.47631 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.2158 | −1.26563 | −0.632813 | − | 0.774305i | \(-0.718100\pi\) | ||||
−0.632813 | + | 0.774305i | \(0.718100\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.18985 | −0.308505 | −0.154252 | − | 0.988031i | \(-0.549297\pi\) | ||||
−0.154252 | + | 0.988031i | \(0.549297\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.79360 | −0.519070 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.28814 | −0.311067 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.46197 | 0.202945 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.5660 | 1.02621 | 0.513107 | − | 0.858324i | \(-0.328494\pi\) | ||||
0.513107 | + | 0.858324i | \(0.328494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.53328 | −0.147493 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.01302 | −0.290885 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −52.8725 | −3.05769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.7426 | −0.907387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.38261 | 0.136877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.18857 | 0.125317 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.5684 | −1.23097 | −0.615486 | − | 0.788148i | \(-0.711040\pi\) | ||||
−0.615486 | + | 0.788148i | \(0.711040\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.07722 | 0.118169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.57368 | 0.145940 | 0.0729701 | − | 0.997334i | \(-0.476752\pi\) | ||||
0.0729701 | + | 0.997334i | \(0.476752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.18389 | −0.293011 | −0.146505 | − | 0.989210i | \(-0.546803\pi\) | ||||
−0.146505 | + | 0.989210i | \(0.546803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.30023 | −0.354977 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.2562 | 1.13770 | 0.568850 | − | 0.822442i | \(-0.307389\pi\) | ||||
0.568850 | + | 0.822442i | \(0.307389\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.94137 | 0.500620 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.09591 | −0.396055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.1644 | −1.50681 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.23909 | 0.345022 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.5871 | −1.46579 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.3280 | −1.17229 | −0.586146 | − | 0.810205i | \(-0.699356\pi\) | ||||
−0.586146 | + | 0.810205i | \(0.699356\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.7687 | −0.918919 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.38261 | 0.130176 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7275 | 1.23804 | 0.619022 | − | 0.785374i | \(-0.287529\pi\) | ||||
0.619022 | + | 0.785374i | \(0.287529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.62919 | −0.305735 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1650 | 0.929538 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2762 | 1.04082 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.22861 | −0.173822 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.92855 | 0.264579 | 0.132289 | − | 0.991211i | \(-0.457767\pi\) | ||||
0.132289 | + | 0.991211i | \(0.457767\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1615 | 1.40039 | 0.700197 | − | 0.713950i | \(-0.253096\pi\) | ||||
0.700197 | + | 0.713950i | \(0.253096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.5894 | 0.885477 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.70813 | 0.144139 | 0.0720697 | − | 0.997400i | \(-0.477040\pi\) | ||||
0.0720697 | + | 0.997400i | \(0.477040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0503161 | −0.00267050 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.81607 | −0.201968 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.31002 | 0.491364 | 0.245682 | − | 0.969350i | \(-0.420988\pi\) | ||||
0.245682 | + | 0.969350i | \(0.420988\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.18120 | 0.166970 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.21296 | 0.325201 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.75442 | −0.404777 | −0.202389 | − | 0.979305i | \(-0.564870\pi\) | ||||
−0.202389 | + | 0.979305i | \(0.564870\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.78485 | −0.509379 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.48276 | 0.492320 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.0124 | 1.29509 | 0.647546 | − | 0.762027i | \(-0.275795\pi\) | ||||
0.647546 | + | 0.762027i | \(0.275795\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.63103 | −0.187506 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.5894 | −1.52393 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.1802 | 0.985222 | 0.492611 | − | 0.870250i | \(-0.336043\pi\) | ||||
0.492611 | + | 0.870250i | \(0.336043\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.17442 | −0.162630 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.83319 | −0.246964 | −0.123482 | − | 0.992347i | \(-0.539406\pi\) | ||||
−0.123482 | + | 0.992347i | \(0.539406\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.38551 | −0.223506 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.5171 | −0.890446 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.7291 | 1.10171 | 0.550855 | − | 0.834601i | \(-0.314302\pi\) | ||||
0.550855 | + | 0.834601i | \(0.314302\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.0113 | 1.41659 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.55865 | −0.0786233 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.14076 | 0.409606 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7140 | 0.587909 | 0.293955 | − | 0.955819i | \(-0.405029\pi\) | ||||
0.293955 | + | 0.955819i | \(0.405029\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8123 | 0.589880 | 0.294940 | − | 0.955516i | \(-0.404700\pi\) | ||||
0.294940 | + | 0.955516i | \(0.404700\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −56.8036 | −2.82959 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.48681 | −0.322332 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.6725 | −0.578584 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.2663 | −1.24934 | −0.624668 | − | 0.780890i | \(-0.714766\pi\) | ||||
−0.624668 | + | 0.780890i | \(0.714766\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.86867 | 0.240154 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.16129 | −0.352384 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5913 | −0.618084 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.62739 | 0.471455 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.6143 | −1.54446 | −0.772229 | − | 0.635344i | \(-0.780858\pi\) | ||||
−0.772229 | + | 0.635344i | \(0.780858\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.18972 | 0.106720 | 0.0533602 | − | 0.998575i | \(-0.483007\pi\) | ||||
0.0533602 | + | 0.998575i | \(0.483007\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.5841 | −1.43843 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.3914 | 0.698087 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.18683 | 0.299402 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.57909 | 0.269361 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.80372 | −0.0868819 | −0.0434410 | − | 0.999056i | \(-0.513832\pi\) | ||||
−0.0434410 | + | 0.999056i | \(0.513832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.57233 | 0.315846 | 0.157923 | − | 0.987451i | \(-0.449520\pi\) | ||||
0.157923 | + | 0.987451i | \(0.449520\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.80685 | −0.0866316 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.13060 | −0.435780 | −0.217890 | − | 0.975973i | \(-0.569917\pi\) | ||||
−0.217890 | + | 0.975973i | \(0.569917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.81955 | 0.0866451 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4686 | 1.30507 | 0.652536 | − | 0.757757i | \(-0.273705\pi\) | ||||
0.652536 | + | 0.757757i | \(0.273705\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.66508 | 0.0789321 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.36686 | −0.301142 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.57293 | 0.357389 | 0.178694 | − | 0.983905i | \(-0.442813\pi\) | ||||
0.178694 | + | 0.983905i | \(0.442813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.81112 | −0.320723 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.48954 | −0.257921 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.5128 | 0.680372 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.7675 | −1.01824 | −0.509120 | − | 0.860696i | \(-0.670029\pi\) | ||||
−0.509120 | + | 0.860696i | \(0.670029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.78890 | −0.410231 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.9444 | 0.556305 | 0.278153 | − | 0.960537i | \(-0.410278\pi\) | ||||
0.278153 | + | 0.960537i | \(0.410278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.75371 | 0.406819 | 0.203410 | − | 0.979094i | \(-0.434798\pi\) | ||||
0.203410 | + | 0.979094i | \(0.434798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.46866 | −0.160855 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.3568 | −1.35847 | −0.679236 | − | 0.733920i | \(-0.737689\pi\) | ||||
−0.679236 | + | 0.733920i | \(0.737689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.73537 | 0.311010 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.199648 | 0.00919932 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.1935 | −0.560656 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.5517 | 0.483128 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.8705 | 1.13636 | 0.568180 | − | 0.822904i | \(-0.307648\pi\) | ||||
0.568180 | + | 0.822904i | \(0.307648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.6274 | 1.76126 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.12692 | −0.415289 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.97531 | 0.316733 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.53766 | −0.386878 | −0.193439 | − | 0.981112i | \(-0.561964\pi\) | ||||
−0.193439 | + | 0.981112i | \(0.561964\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0306425 | −0.00138570 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.5397 | 0.520780 | 0.260390 | − | 0.965504i | \(-0.416149\pi\) | ||||
0.260390 | + | 0.965504i | \(0.416149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.6762 | 0.706019 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.87986 | −0.219333 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.142238 | −0.00638025 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.6091 | 1.32548 | 0.662742 | − | 0.748848i | \(-0.269393\pi\) | ||||
0.662742 | + | 0.748848i | \(0.269393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.961785 | −0.0429694 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.86827 | −0.261653 | −0.130827 | − | 0.991405i | \(-0.541763\pi\) | ||||
−0.130827 | + | 0.991405i | \(0.541763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.80057 | 0.213622 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7107 | −0.564501 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.5687 | −1.13331 | −0.566656 | − | 0.823954i | \(-0.691763\pi\) | ||||
−0.566656 | + | 0.823954i | \(0.691763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.5633 | 0.776957 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.18527 | 0.184425 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.5931 | −0.905685 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.45520 | −0.327247 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.0332 | −0.614807 | −0.307403 | − | 0.951579i | \(-0.599460\pi\) | ||||
−0.307403 | + | 0.951579i | \(0.599460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.0784 | −1.35896 | −0.679482 | − | 0.733692i | \(-0.737795\pi\) | ||||
−0.679482 | + | 0.733692i | \(0.737795\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.68915 | −0.204651 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.0940 | 1.31092 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.9949 | 1.91282 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.96853 | −0.345805 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.5398 | 0.976307 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.2971 | −0.618117 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.39155 | −0.362122 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.26657 | 0.0545548 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.89608 | 0.124512 | 0.0622561 | − | 0.998060i | \(-0.480170\pi\) | ||||
0.0622561 | + | 0.998060i | \(0.480170\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.879118 | −0.0377266 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.5707 | 0.538471 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.3861 | −1.29922 | −0.649608 | − | 0.760269i | \(-0.725067\pi\) | ||||
−0.649608 | + | 0.760269i | \(0.725067\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.88423 | 0.293812 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.0130 | 0.978613 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.35875 | 0.100123 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.13412 | −0.259911 | −0.129956 | − | 0.991520i | \(-0.541483\pi\) | ||||
−0.129956 | + | 0.991520i | \(0.541483\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.3514 | 1.70668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.95575 | −0.124792 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.1917 | 1.18814 | 0.594069 | − | 0.804414i | \(-0.297521\pi\) | ||||
0.594069 | + | 0.804414i | \(0.297521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3419 | −0.477157 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.3375 | −0.770103 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.1145 | −1.76553 | −0.882766 | − | 0.469812i | \(-0.844322\pi\) | ||||
−0.882766 | + | 0.469812i | \(0.844322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.166927 | −0.00698566 | −0.00349283 | − | 0.999994i | \(-0.501112\pi\) | ||||
−0.00349283 | + | 0.999994i | \(0.501112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.25896 | −0.386799 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.4201 | 1.43542 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.9631 | −0.831076 | −0.415538 | − | 0.909576i | \(-0.636407\pi\) | ||||
−0.415538 | + | 0.909576i | \(0.636407\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.44626 | 0.143222 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −35.5943 | −1.47670 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.34490 | 0.304195 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.1488 | 0.667669 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.1440 | −0.418689 | −0.209345 | − | 0.977842i | \(-0.567133\pi\) | ||||
−0.209345 | + | 0.977842i | \(0.567133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.807559 | −0.0332185 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.45315 | 0.306064 | 0.153032 | − | 0.988221i | \(-0.451096\pi\) | ||||
0.153032 | + | 0.988221i | \(0.451096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.68876 | −0.315208 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.04388 | 0.0427233 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.37141 | 0.260329 | 0.130164 | − | 0.991492i | \(-0.458449\pi\) | ||||
0.130164 | + | 0.991492i | \(0.458449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.74631 | 0.0712333 | 0.0356166 | − | 0.999366i | \(-0.488660\pi\) | ||||
0.0356166 | + | 0.999366i | \(0.488660\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.49460 | 0.305204 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.40959 | 0.260587 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.1612 | −1.30538 | −0.652691 | − | 0.757624i | \(-0.726360\pi\) | ||||
−0.652691 | + | 0.757624i | \(0.726360\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.10775 | −0.206977 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 68.1481 | 2.75698 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.7645 | 0.515552 | 0.257776 | − | 0.966205i | \(-0.417010\pi\) | ||||
0.257776 | + | 0.966205i | \(0.417010\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.37637 | 0.0555007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.68323 | −0.0677643 | −0.0338822 | − | 0.999426i | \(-0.510787\pi\) | ||||
−0.0338822 | + | 0.999426i | \(0.510787\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.5285 | −1.26724 | −0.633618 | − | 0.773646i | \(-0.718431\pi\) | ||||
−0.633618 | + | 0.773646i | \(0.718431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.0205 | −0.843523 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.70698 | 0.188581 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.7103 | 0.548411 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4644 | −0.815970 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.7662 | 1.26459 | 0.632297 | − | 0.774726i | \(-0.282112\pi\) | ||||
0.632297 | + | 0.774726i | \(0.282112\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.159752 | 0.00634955 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.39593 | −0.253815 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.19140 | −0.166069 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.158272 | −0.00626113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.4437 | −1.59743 | −0.798715 | − | 0.601709i | \(-0.794487\pi\) | ||||
−0.798715 | + | 0.601709i | \(0.794487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.1033 | 1.02941 | 0.514706 | − | 0.857367i | \(-0.327901\pi\) | ||||
0.514706 | + | 0.857367i | \(0.327901\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.46402 | 0.0970208 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.7713 | 1.91740 | 0.958699 | − | 0.284423i | \(-0.0918018\pi\) | ||||
0.958699 | + | 0.284423i | \(0.0918018\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.54680 | −0.217731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.80551 | −0.384308 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.1831 | −1.68988 | −0.844942 | − | 0.534858i | \(-0.820365\pi\) | ||||
−0.844942 | + | 0.534858i | \(0.820365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.14042 | −0.122706 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.5431 | 0.762451 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.2769 | 0.556148 | 0.278074 | − | 0.960560i | \(-0.410304\pi\) | ||||
0.278074 | + | 0.960560i | \(0.410304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.7497 | 1.39050 | 0.695251 | − | 0.718768i | \(-0.255293\pi\) | ||||
0.695251 | + | 0.718768i | \(0.255293\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.78136 | 0.379877 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.4928 | 1.45173 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.98585 | −0.308751 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.79204 | 0.184994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3574 | 0.399248 | 0.199624 | − | 0.979873i | \(-0.436028\pi\) | ||||
0.199624 | + | 0.979873i | \(0.436028\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.7997 | −0.415682 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.7171 | −0.411891 | −0.205945 | − | 0.978564i | \(-0.566027\pi\) | ||||
−0.205945 | + | 0.978564i | \(0.566027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.7184 | 0.756724 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.43543 | −0.208286 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.122930 | −0.00470377 | −0.00235188 | − | 0.999997i | \(-0.500749\pi\) | ||||
−0.00235188 | + | 0.999997i | \(0.500749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.80957 | 0.374804 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.00510 | −0.114652 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.3062 | −0.925994 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2815 | 0.961752 | 0.480876 | − | 0.876789i | \(-0.340319\pi\) | ||||
0.480876 | + | 0.876789i | \(0.340319\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.7948 | −0.524022 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.3976 | 0.735793 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.9414 | −0.452312 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.48171 | −0.358631 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.17287 | −0.195377 | −0.0976883 | − | 0.995217i | \(-0.531145\pi\) | ||||
−0.0976883 | + | 0.995217i | \(0.531145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.16140 | 0.156727 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.5707 | 0.510377 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.9907 | −1.12632 | −0.563162 | − | 0.826346i | \(-0.690415\pi\) | ||||
−0.563162 | + | 0.826346i | \(0.690415\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.6071 | 0.960342 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 71.9760 | 2.69552 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.2410 | 0.420388 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.23772 | −0.195606 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.7033 | 0.846688 | 0.423344 | − | 0.905969i | \(-0.360856\pi\) | ||||
0.423344 | + | 0.905969i | \(0.360856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.8313 | 0.440620 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.62195 | −0.357844 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.2627 | 0.715400 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.5937 | −1.35719 | −0.678593 | − | 0.734514i | \(-0.737410\pi\) | ||||
−0.678593 | + | 0.734514i | \(0.737410\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.9956 | −0.629467 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.3778 | −0.790686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.1522 | 0.781275 | 0.390637 | − | 0.920545i | \(-0.372255\pi\) | ||||
0.390637 | + | 0.920545i | \(0.372255\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.255944 | −0.00944064 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.21690 | 0.192167 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.3066 | −1.77699 | −0.888494 | − | 0.458888i | \(-0.848248\pi\) | ||||
−0.888494 | + | 0.458888i | \(0.848248\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.8598 | −1.16882 | −0.584412 | − | 0.811457i | \(-0.698675\pi\) | ||||
−0.584412 | + | 0.811457i | \(0.698675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.8282 | −0.469988 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −39.6066 | −1.44913 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.4163 | −1.47678 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.9962 | 1.49597 | 0.747987 | − | 0.663713i | \(-0.231020\pi\) | ||||
0.747987 | + | 0.663713i | \(0.231020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.4603 | 0.381194 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.0605 | −0.402533 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8215 | −0.466006 | −0.233003 | − | 0.972476i | \(-0.574855\pi\) | ||||
−0.233003 | + | 0.972476i | \(0.574855\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.06929 | −0.256599 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.6382 | 1.29188 | 0.645942 | − | 0.763386i | \(-0.276465\pi\) | ||||
0.645942 | + | 0.763386i | \(0.276465\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.5361 | 1.28649 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.55546 | −0.309323 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.3558 | 0.662791 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.57401 | −0.201004 | −0.100502 | − | 0.994937i | \(-0.532045\pi\) | ||||
−0.100502 | + | 0.994937i | \(0.532045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.408601 | −0.0147154 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.4119 | −1.30965 | −0.654823 | − | 0.755782i | \(-0.727257\pi\) | ||||
−0.654823 | + | 0.755782i | \(0.727257\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.9792 | 1.32833 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.66791 | 0.239210 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.110171 | −0.00394223 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.7638 | −0.420405 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.402259 | 0.0143572 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.9046 | 1.13728 | 0.568638 | − | 0.822588i | \(-0.307471\pi\) | ||||
0.568638 | + | 0.822588i | \(0.307471\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.91130 | 0.0680440 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.0622 | −1.14000 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.8581 | −0.563138 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.48424 | −0.0526405 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.09165 | 0.0740900 | 0.0370450 | − | 0.999314i | \(-0.488206\pi\) | ||||
0.0370450 | + | 0.999314i | \(0.488206\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.1042 | −1.27728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.23757 | 0.185060 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6038 | 0.480066 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.3892 | −0.648136 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.77655 | −0.168143 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0719 | −1.05727 | −0.528636 | − | 0.848849i | \(-0.677296\pi\) | ||||
−0.528636 | + | 0.848849i | \(0.677296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.823592 | 0.0289202 | 0.0144601 | − | 0.999895i | \(-0.495397\pi\) | ||||
0.0144601 | + | 0.999895i | \(0.495397\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.357176 | 0.0125267 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0617395 | −0.00216264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 45.6507 | 1.59517 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.71124 | 0.269124 | 0.134562 | − | 0.990905i | \(-0.457037\pi\) | ||||
0.134562 | + | 0.990905i | \(0.457037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.8120 | 0.864893 | 0.432447 | − | 0.901660i | \(-0.357650\pi\) | ||||
0.432447 | + | 0.901660i | \(0.357650\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.63200 | −0.126450 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6285 | 0.369588 | 0.184794 | − | 0.982777i | \(-0.440838\pi\) | ||||
0.184794 | + | 0.982777i | \(0.440838\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.4710 | −0.745718 | −0.372859 | − | 0.927888i | \(-0.621623\pi\) | ||||
−0.372859 | + | 0.927888i | \(0.621623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.04796 | 0.140422 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.22056 | 0.0769380 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.93784 | −0.0670617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.5834 | −0.780595 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.8239 | −1.68559 | −0.842794 | − | 0.538237i | \(-0.819091\pi\) | ||||
−0.842794 | + | 0.538237i | \(0.819091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.01770 | −0.276472 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.38720 | 0.323312 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.6099 | −0.881009 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.1192 | 0.622583 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.29632 | 0.0788095 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48.9449 | −1.67781 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0110 | −0.719404 | −0.359702 | − | 0.933067i | \(-0.617122\pi\) | ||||
−0.359702 | + | 0.933067i | \(0.617122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.2392 | −1.10127 | −0.550635 | − | 0.834746i | \(-0.685614\pi\) | ||||
−0.550635 | + | 0.834746i | \(0.685614\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.2274 | 1.40666 | 0.703331 | − | 0.710863i | \(-0.251695\pi\) | ||||
0.703331 | + | 0.710863i | \(0.251695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.89085 | 0.132600 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.0649 | −1.43191 | −0.715953 | − | 0.698148i | \(-0.754008\pi\) | ||||
−0.715953 | + | 0.698148i | \(0.754008\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0210 | −0.510729 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.33981 | 0.0794640 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8248 | 0.604665 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.2641 | −0.584972 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.9412 | 0.742596 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.6813 | −0.699156 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.35551 | 0.0795400 | 0.0397700 | − | 0.999209i | \(-0.487337\pi\) | ||||
0.0397700 | + | 0.999209i | \(0.487337\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.77230 | −0.262153 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.1354 | 0.779450 | 0.389725 | − | 0.920931i | \(-0.372570\pi\) | ||||
0.389725 | + | 0.920931i | \(0.372570\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.01191 | −0.235969 | −0.117985 | − | 0.993015i | \(-0.537643\pi\) | ||||
−0.117985 | + | 0.993015i | \(0.537643\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.12088 | 0.0376780 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.9293 | −1.64289 | −0.821443 | − | 0.570291i | \(-0.806830\pi\) | ||||
−0.821443 | + | 0.570291i | \(0.806830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0806 | −0.606403 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.2034 | −0.475831 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9076 | −0.565159 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.3941 | 0.781108 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.2804 | 1.34343 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.8772 | 0.429002 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.96552 | 0.231798 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.77128 | −0.0588793 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.19304 | 0.0396143 | 0.0198071 | − | 0.999804i | \(-0.493695\pi\) | ||||
0.0198071 | + | 0.999804i | \(0.493695\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1004 | 0.500848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.6344 | −1.24688 | −0.623442 | − | 0.781870i | \(-0.714266\pi\) | ||||
−0.623442 | + | 0.781870i | \(0.714266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.5697 | −0.912424 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.968361 | −0.0320130 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.87761 | −0.293164 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.9476 | −0.888921 | −0.444460 | − | 0.895799i | \(-0.646605\pi\) | ||||
−0.444460 | + | 0.895799i | \(0.646605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.54321 | 0.314460 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.364585 | 0.0120005 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.1465 | −0.826812 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.1649 | 0.432393 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.8550 | −0.585804 | −0.292902 | − | 0.956142i | \(-0.594621\pi\) | ||||
−0.292902 | + | 0.956142i | \(0.594621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.13876 | −0.0372814 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.95535 | −0.194761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.8326 | −0.778576 | −0.389288 | − | 0.921116i | \(-0.627279\pi\) | ||||
−0.389288 | + | 0.921116i | \(0.627279\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.29368 | 0.0748514 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3651 | 0.663882 | 0.331941 | − | 0.943300i | \(-0.392296\pi\) | ||||
0.331941 | + | 0.943300i | \(0.392296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −28.5602 | −0.930049 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.76985 | 0.187693 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.41590 | 0.111002 | 0.0555009 | − | 0.998459i | \(-0.482324\pi\) | ||||
0.0555009 | + | 0.998459i | \(0.482324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.0184 | −1.46136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.96261 | −0.290633 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.7393 | −0.574634 | −0.287317 | − | 0.957836i | \(-0.592763\pi\) | ||||
−0.287317 | + | 0.957836i | \(0.592763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.6553 | −0.603671 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.95623 | −0.127887 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.7306 | 0.895466 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.3275 | 1.49443 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −44.9721 | −1.44921 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.94364 | 0.223524 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.7551 | 1.37491 | 0.687456 | − | 0.726226i | \(-0.258727\pi\) | ||||
0.687456 | + | 0.726226i | \(0.258727\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.0487 | −1.70241 | −0.851207 | − | 0.524830i | \(-0.824129\pi\) | ||||
−0.851207 | + | 0.524830i | \(0.824129\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.8349 | 1.75793 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12.0193 | 0.384924 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.3264 | −0.394356 | −0.197178 | − | 0.980368i | \(-0.563178\pi\) | ||||
−0.197178 | + | 0.980368i | \(0.563178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.64581 | 0.116521 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 39.5418 | 1.26247 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.2554 | 1.02879 | 0.514394 | − | 0.857554i | \(-0.328017\pi\) | ||||
0.514394 | + | 0.857554i | \(0.328017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.62710 | −0.0518437 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.7638 | 0.374446 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.1294 | −1.62582 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.8366 | −0.884258 | −0.442129 | − | 0.896951i | \(-0.645777\pi\) | ||||
−0.442129 | + | 0.896951i | \(0.645777\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.43686 | 0.299470 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.10326 | 0.0666777 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.3313 | −1.37232 | −0.686159 | − | 0.727452i | \(-0.740704\pi\) | ||||
−0.686159 | + | 0.727452i | \(0.740704\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.3571 | 0.485876 |
(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 | 5776.2.a.bt.1.3 | 4 | ||
4.3 | odd | 2 | 722.2.a.n.1.2 | yes | 4 | ||
12.11 | even | 2 | 6498.2.a.bx.1.2 | 4 | |||
19.18 | odd | 2 | 5776.2.a.bv.1.2 | 4 | |||
76.3 | even | 18 | 722.2.e.s.389.3 | 24 | |||
76.7 | odd | 6 | 722.2.c.m.429.3 | 8 | |||
76.11 | odd | 6 | 722.2.c.m.653.3 | 8 | |||
76.15 | even | 18 | 722.2.e.s.415.2 | 24 | |||
76.23 | odd | 18 | 722.2.e.r.415.3 | 24 | |||
76.27 | even | 6 | 722.2.c.n.653.2 | 8 | |||
76.31 | even | 6 | 722.2.c.n.429.2 | 8 | |||
76.35 | odd | 18 | 722.2.e.r.389.2 | 24 | |||
76.43 | odd | 18 | 722.2.e.r.595.3 | 24 | |||
76.47 | odd | 18 | 722.2.e.r.423.2 | 24 | |||
76.51 | even | 18 | 722.2.e.s.245.3 | 24 | |||
76.55 | odd | 18 | 722.2.e.r.99.2 | 24 | |||
76.59 | even | 18 | 722.2.e.s.99.3 | 24 | |||
76.63 | odd | 18 | 722.2.e.r.245.2 | 24 | |||
76.67 | even | 18 | 722.2.e.s.423.3 | 24 | |||
76.71 | even | 18 | 722.2.e.s.595.2 | 24 | |||
76.75 | even | 2 | 722.2.a.m.1.3 | ✓ | 4 | ||
228.227 | odd | 2 | 6498.2.a.ca.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.m.1.3 | ✓ | 4 | 76.75 | even | 2 | ||
722.2.a.n.1.2 | yes | 4 | 4.3 | odd | 2 | ||
722.2.c.m.429.3 | 8 | 76.7 | odd | 6 | |||
722.2.c.m.653.3 | 8 | 76.11 | odd | 6 | |||
722.2.c.n.429.2 | 8 | 76.31 | even | 6 | |||
722.2.c.n.653.2 | 8 | 76.27 | even | 6 | |||
722.2.e.r.99.2 | 24 | 76.55 | odd | 18 | |||
722.2.e.r.245.2 | 24 | 76.63 | odd | 18 | |||
722.2.e.r.389.2 | 24 | 76.35 | odd | 18 | |||
722.2.e.r.415.3 | 24 | 76.23 | odd | 18 | |||
722.2.e.r.423.2 | 24 | 76.47 | odd | 18 | |||
722.2.e.r.595.3 | 24 | 76.43 | odd | 18 | |||
722.2.e.s.99.3 | 24 | 76.59 | even | 18 | |||
722.2.e.s.245.3 | 24 | 76.51 | even | 18 | |||
722.2.e.s.389.3 | 24 | 76.3 | even | 18 | |||
722.2.e.s.415.2 | 24 | 76.15 | even | 18 | |||
722.2.e.s.423.3 | 24 | 76.67 | even | 18 | |||
722.2.e.s.595.2 | 24 | 76.71 | even | 18 | |||
5776.2.a.bt.1.3 | 4 | 1.1 | even | 1 | trivial | ||
5776.2.a.bv.1.2 | 4 | 19.18 | odd | 2 | |||
6498.2.a.bx.1.2 | 4 | 12.11 | even | 2 | |||
6498.2.a.ca.1.2 | 4 | 228.227 | odd | 2 |