Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.52625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 24x^{2} + 19x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.55745\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.58059 | −0.597408 | −0.298704 | − | 0.954346i | \(-0.596554\pi\) | ||||
−0.298704 | + | 0.954346i | \(0.596554\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −5.75608 | −1.59645 | −0.798225 | − | 0.602360i | \(-0.794227\pi\) | ||||
−0.798225 | + | 0.602360i | \(0.794227\pi\) | |||||||
\(14\) | −1.58059 | −0.422431 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.17549 | 1.74031 | 0.870156 | − | 0.492777i | \(-0.164018\pi\) | ||||
0.870156 | + | 0.492777i | \(0.164018\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.32139 | 0.303147 | 0.151573 | − | 0.988446i | \(-0.451566\pi\) | ||||
0.151573 | + | 0.988446i | \(0.451566\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −1.58059 | −0.344914 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.358826 | −0.0748205 | −0.0374102 | − | 0.999300i | \(-0.511911\pi\) | ||||
−0.0374102 | + | 0.999300i | \(0.511911\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.75608 | −1.12886 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −1.58059 | −0.298704 | ||||||||
\(29\) | 9.67076 | 1.79582 | 0.897908 | − | 0.440184i | \(-0.145087\pi\) | ||||
0.897908 | + | 0.440184i | \(0.145087\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 7.19863 | 1.29291 | 0.646456 | − | 0.762951i | \(-0.276250\pi\) | ||||
0.646456 | + | 0.762951i | \(0.276250\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.17549 | 1.23059 | ||||||||
\(35\) | 1.58059 | 0.267169 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.73294 | 1.60009 | 0.800043 | − | 0.599943i | \(-0.204810\pi\) | ||||
0.800043 | + | 0.599943i | \(0.204810\pi\) | |||||||
\(38\) | 1.32139 | 0.214357 | ||||||||
\(39\) | −5.75608 | −0.921711 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −12.0064 | −1.87509 | −0.937546 | − | 0.347861i | \(-0.886908\pi\) | ||||
−0.937546 | + | 0.347861i | \(0.886908\pi\) | |||||||
\(42\) | −1.58059 | −0.243891 | ||||||||
\(43\) | −6.41156 | −0.977753 | −0.488877 | − | 0.872353i | \(-0.662593\pi\) | ||||
−0.488877 | + | 0.872353i | \(0.662593\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −0.358826 | −0.0529061 | ||||||||
\(47\) | 6.52001 | 0.951042 | 0.475521 | − | 0.879704i | \(-0.342260\pi\) | ||||
0.475521 | + | 0.879704i | \(0.342260\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.50173 | −0.643104 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 7.17549 | 1.00477 | ||||||||
\(52\) | −5.75608 | −0.798225 | ||||||||
\(53\) | 2.34453 | 0.322045 | 0.161023 | − | 0.986951i | \(-0.448521\pi\) | ||||
0.161023 | + | 0.986951i | \(0.448521\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.58059 | −0.211216 | ||||||||
\(57\) | 1.32139 | 0.175022 | ||||||||
\(58\) | 9.67076 | 1.26983 | ||||||||
\(59\) | 10.3262 | 1.34436 | 0.672181 | − | 0.740387i | \(-0.265358\pi\) | ||||
0.672181 | + | 0.740387i | \(0.265358\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 5.63332 | 0.721273 | 0.360637 | − | 0.932706i | \(-0.382559\pi\) | ||||
0.360637 | + | 0.932706i | \(0.382559\pi\) | |||||||
\(62\) | 7.19863 | 0.914227 | ||||||||
\(63\) | −1.58059 | −0.199136 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.75608 | 0.713954 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.07747 | −0.620311 | −0.310156 | − | 0.950686i | \(-0.600381\pi\) | ||||
−0.310156 | + | 0.950686i | \(0.600381\pi\) | |||||||
\(68\) | 7.17549 | 0.870156 | ||||||||
\(69\) | −0.358826 | −0.0431976 | ||||||||
\(70\) | 1.58059 | 0.188917 | ||||||||
\(71\) | 9.11491 | 1.08174 | 0.540870 | − | 0.841106i | \(-0.318095\pi\) | ||||
0.540870 | + | 0.841106i | \(0.318095\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 6.94427 | 0.812766 | 0.406383 | − | 0.913703i | \(-0.366790\pi\) | ||||
0.406383 | + | 0.913703i | \(0.366790\pi\) | |||||||
\(74\) | 9.73294 | 1.13143 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 1.32139 | 0.151573 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.75608 | −0.651748 | ||||||||
\(79\) | 11.5265 | 1.29683 | 0.648414 | − | 0.761288i | \(-0.275433\pi\) | ||||
0.648414 | + | 0.761288i | \(0.275433\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.0064 | −1.32589 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | −1.58059 | −0.172457 | ||||||||
\(85\) | −7.17549 | −0.778291 | ||||||||
\(86\) | −6.41156 | −0.691376 | ||||||||
\(87\) | 9.67076 | 1.03681 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.16764 | 0.759768 | 0.379884 | − | 0.925034i | \(-0.375964\pi\) | ||||
0.379884 | + | 0.925034i | \(0.375964\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 9.09802 | 0.953732 | ||||||||
\(92\) | −0.358826 | −0.0374102 | ||||||||
\(93\) | 7.19863 | 0.746463 | ||||||||
\(94\) | 6.52001 | 0.672488 | ||||||||
\(95\) | −1.32139 | −0.135571 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.92512 | −0.195466 | −0.0977331 | − | 0.995213i | \(-0.531159\pi\) | ||||
−0.0977331 | + | 0.995213i | \(0.531159\pi\) | |||||||
\(98\) | −4.50173 | −0.454743 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.24092 | −0.820002 | −0.410001 | − | 0.912085i | \(-0.634472\pi\) | ||||
−0.410001 | + | 0.912085i | \(0.634472\pi\) | |||||||
\(102\) | 7.17549 | 0.710479 | ||||||||
\(103\) | −4.90843 | −0.483642 | −0.241821 | − | 0.970321i | \(-0.577745\pi\) | ||||
−0.241821 | + | 0.970321i | \(0.577745\pi\) | |||||||
\(104\) | −5.75608 | −0.564430 | ||||||||
\(105\) | 1.58059 | 0.154250 | ||||||||
\(106\) | 2.34453 | 0.227720 | ||||||||
\(107\) | −1.64903 | −0.159417 | −0.0797086 | − | 0.996818i | \(-0.525399\pi\) | ||||
−0.0797086 | + | 0.996818i | \(0.525399\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.94427 | −0.856706 | −0.428353 | − | 0.903612i | \(-0.640906\pi\) | ||||
−0.428353 | + | 0.903612i | \(0.640906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.73294 | 0.923810 | ||||||||
\(112\) | −1.58059 | −0.149352 | ||||||||
\(113\) | 0.0374409 | 0.00352214 | 0.00176107 | − | 0.999998i | \(-0.499439\pi\) | ||||
0.00176107 | + | 0.999998i | \(0.499439\pi\) | |||||||
\(114\) | 1.32139 | 0.123759 | ||||||||
\(115\) | 0.358826 | 0.0334607 | ||||||||
\(116\) | 9.67076 | 0.897908 | ||||||||
\(117\) | −5.75608 | −0.532150 | ||||||||
\(118\) | 10.3262 | 0.950607 | ||||||||
\(119\) | −11.3415 | −1.03968 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 5.63332 | 0.510017 | ||||||||
\(123\) | −12.0064 | −1.08259 | ||||||||
\(124\) | 7.19863 | 0.646456 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.58059 | −0.140810 | ||||||||
\(127\) | −16.5418 | −1.46784 | −0.733921 | − | 0.679234i | \(-0.762312\pi\) | ||||
−0.733921 | + | 0.679234i | \(0.762312\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.41156 | −0.564506 | ||||||||
\(130\) | 5.75608 | 0.504842 | ||||||||
\(131\) | −12.5096 | −1.09297 | −0.546483 | − | 0.837470i | \(-0.684034\pi\) | ||||
−0.546483 | + | 0.837470i | \(0.684034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.08857 | −0.181102 | ||||||||
\(134\) | −5.07747 | −0.438626 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 7.17549 | 0.615293 | ||||||||
\(137\) | −12.3135 | −1.05202 | −0.526008 | − | 0.850480i | \(-0.676312\pi\) | ||||
−0.526008 | + | 0.850480i | \(0.676312\pi\) | |||||||
\(138\) | −0.358826 | −0.0305453 | ||||||||
\(139\) | 12.9970 | 1.10239 | 0.551196 | − | 0.834376i | \(-0.314172\pi\) | ||||
0.551196 | + | 0.834376i | \(0.314172\pi\) | |||||||
\(140\) | 1.58059 | 0.133585 | ||||||||
\(141\) | 6.52001 | 0.549084 | ||||||||
\(142\) | 9.11491 | 0.764906 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −9.67076 | −0.803113 | ||||||||
\(146\) | 6.94427 | 0.574712 | ||||||||
\(147\) | −4.50173 | −0.371296 | ||||||||
\(148\) | 9.73294 | 0.800043 | ||||||||
\(149\) | −1.64762 | −0.134979 | −0.0674893 | − | 0.997720i | \(-0.521499\pi\) | ||||
−0.0674893 | + | 0.997720i | \(0.521499\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 6.74823 | 0.549163 | 0.274582 | − | 0.961564i | \(-0.411461\pi\) | ||||
0.274582 | + | 0.961564i | \(0.411461\pi\) | |||||||
\(152\) | 1.32139 | 0.107179 | ||||||||
\(153\) | 7.17549 | 0.580104 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.19863 | −0.578208 | ||||||||
\(156\) | −5.75608 | −0.460855 | ||||||||
\(157\) | 8.92898 | 0.712610 | 0.356305 | − | 0.934370i | \(-0.384036\pi\) | ||||
0.356305 | + | 0.934370i | \(0.384036\pi\) | |||||||
\(158\) | 11.5265 | 0.916996 | ||||||||
\(159\) | 2.34453 | 0.185933 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0.567158 | 0.0446983 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.72251 | 0.761525 | 0.380763 | − | 0.924673i | \(-0.375661\pi\) | ||||
0.380763 | + | 0.924673i | \(0.375661\pi\) | |||||||
\(164\) | −12.0064 | −0.937546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | −15.4643 | −1.19666 | −0.598331 | − | 0.801249i | \(-0.704169\pi\) | ||||
−0.598331 | + | 0.801249i | \(0.704169\pi\) | |||||||
\(168\) | −1.58059 | −0.121945 | ||||||||
\(169\) | 20.1325 | 1.54865 | ||||||||
\(170\) | −7.17549 | −0.550335 | ||||||||
\(171\) | 1.32139 | 0.101049 | ||||||||
\(172\) | −6.41156 | −0.488877 | ||||||||
\(173\) | 18.4037 | 1.39921 | 0.699604 | − | 0.714531i | \(-0.253360\pi\) | ||||
0.699604 | + | 0.714531i | \(0.253360\pi\) | |||||||
\(174\) | 9.67076 | 0.733139 | ||||||||
\(175\) | −1.58059 | −0.119482 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3262 | 0.776168 | ||||||||
\(178\) | 7.16764 | 0.537237 | ||||||||
\(179\) | −18.5623 | −1.38741 | −0.693706 | − | 0.720258i | \(-0.744023\pi\) | ||||
−0.693706 | + | 0.720258i | \(0.744023\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 9.52786 | 0.708201 | 0.354100 | − | 0.935207i | \(-0.384787\pi\) | ||||
0.354100 | + | 0.935207i | \(0.384787\pi\) | |||||||
\(182\) | 9.09802 | 0.674390 | ||||||||
\(183\) | 5.63332 | 0.416427 | ||||||||
\(184\) | −0.358826 | −0.0264530 | ||||||||
\(185\) | −9.73294 | −0.715580 | ||||||||
\(186\) | 7.19863 | 0.527829 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.52001 | 0.475521 | ||||||||
\(189\) | −1.58059 | −0.114971 | ||||||||
\(190\) | −1.32139 | −0.0958634 | ||||||||
\(191\) | 20.0306 | 1.44936 | 0.724681 | − | 0.689085i | \(-0.241987\pi\) | ||||
0.724681 | + | 0.689085i | \(0.241987\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −7.82937 | −0.563570 | −0.281785 | − | 0.959478i | \(-0.590926\pi\) | ||||
−0.281785 | + | 0.959478i | \(0.590926\pi\) | |||||||
\(194\) | −1.92512 | −0.138215 | ||||||||
\(195\) | 5.75608 | 0.412201 | ||||||||
\(196\) | −4.50173 | −0.321552 | ||||||||
\(197\) | −20.6798 | −1.47337 | −0.736687 | − | 0.676234i | \(-0.763611\pi\) | ||||
−0.736687 | + | 0.676234i | \(0.763611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.12921 | −0.221824 | −0.110912 | − | 0.993830i | \(-0.535377\pi\) | ||||
−0.110912 | + | 0.993830i | \(0.535377\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −5.07747 | −0.358137 | ||||||||
\(202\) | −8.24092 | −0.579829 | ||||||||
\(203\) | −15.2855 | −1.07283 | ||||||||
\(204\) | 7.17549 | 0.502385 | ||||||||
\(205\) | 12.0064 | 0.838567 | ||||||||
\(206\) | −4.90843 | −0.341986 | ||||||||
\(207\) | −0.358826 | −0.0249402 | ||||||||
\(208\) | −5.75608 | −0.399112 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.58059 | 0.109071 | ||||||||
\(211\) | −14.3047 | −0.984776 | −0.492388 | − | 0.870376i | \(-0.663876\pi\) | ||||
−0.492388 | + | 0.870376i | \(0.663876\pi\) | |||||||
\(212\) | 2.34453 | 0.161023 | ||||||||
\(213\) | 9.11491 | 0.624543 | ||||||||
\(214\) | −1.64903 | −0.112725 | ||||||||
\(215\) | 6.41156 | 0.437264 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −11.3781 | −0.772396 | ||||||||
\(218\) | −8.94427 | −0.605783 | ||||||||
\(219\) | 6.94427 | 0.469250 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.3027 | −2.77832 | ||||||||
\(222\) | 9.73294 | 0.653232 | ||||||||
\(223\) | 5.58059 | 0.373704 | 0.186852 | − | 0.982388i | \(-0.440171\pi\) | ||||
0.186852 | + | 0.982388i | \(0.440171\pi\) | |||||||
\(224\) | −1.58059 | −0.105608 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0.0374409 | 0.00249053 | ||||||||
\(227\) | −4.68905 | −0.311223 | −0.155612 | − | 0.987818i | \(-0.549735\pi\) | ||||
−0.155612 | + | 0.987818i | \(0.549735\pi\) | |||||||
\(228\) | 1.32139 | 0.0875109 | ||||||||
\(229\) | 8.39725 | 0.554906 | 0.277453 | − | 0.960739i | \(-0.410510\pi\) | ||||
0.277453 | + | 0.960739i | \(0.410510\pi\) | |||||||
\(230\) | 0.358826 | 0.0236603 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.67076 | 0.634917 | ||||||||
\(233\) | −7.27351 | −0.476503 | −0.238252 | − | 0.971203i | \(-0.576574\pi\) | ||||
−0.238252 | + | 0.971203i | \(0.576574\pi\) | |||||||
\(234\) | −5.75608 | −0.376287 | ||||||||
\(235\) | −6.52001 | −0.425319 | ||||||||
\(236\) | 10.3262 | 0.672181 | ||||||||
\(237\) | 11.5265 | 0.748724 | ||||||||
\(238\) | −11.3415 | −0.735162 | ||||||||
\(239\) | −21.7883 | −1.40937 | −0.704683 | − | 0.709523i | \(-0.748911\pi\) | ||||
−0.704683 | + | 0.709523i | \(0.748911\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −4.54057 | −0.292484 | −0.146242 | − | 0.989249i | \(-0.546718\pi\) | ||||
−0.146242 | + | 0.989249i | \(0.546718\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.63332 | 0.360637 | ||||||||
\(245\) | 4.50173 | 0.287605 | ||||||||
\(246\) | −12.0064 | −0.765503 | ||||||||
\(247\) | −7.60600 | −0.483958 | ||||||||
\(248\) | 7.19863 | 0.457113 | ||||||||
\(249\) | 8.00000 | 0.506979 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 4.20906 | 0.265674 | 0.132837 | − | 0.991138i | \(-0.457591\pi\) | ||||
0.132837 | + | 0.991138i | \(0.457591\pi\) | |||||||
\(252\) | −1.58059 | −0.0995680 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.5418 | −1.03792 | ||||||||
\(255\) | −7.17549 | −0.449346 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.7945 | −0.922856 | −0.461428 | − | 0.887178i | \(-0.652663\pi\) | ||||
−0.461428 | + | 0.887178i | \(0.652663\pi\) | |||||||
\(258\) | −6.41156 | −0.399166 | ||||||||
\(259\) | −15.3838 | −0.955904 | ||||||||
\(260\) | 5.75608 | 0.356977 | ||||||||
\(261\) | 9.67076 | 0.598605 | ||||||||
\(262\) | −12.5096 | −0.772844 | ||||||||
\(263\) | 7.90358 | 0.487355 | 0.243678 | − | 0.969856i | \(-0.421646\pi\) | ||||
0.243678 | + | 0.969856i | \(0.421646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.34453 | −0.144023 | ||||||||
\(266\) | −2.08857 | −0.128059 | ||||||||
\(267\) | 7.16764 | 0.438652 | ||||||||
\(268\) | −5.07747 | −0.310156 | ||||||||
\(269\) | 17.9469 | 1.09424 | 0.547120 | − | 0.837054i | \(-0.315724\pi\) | ||||
0.547120 | + | 0.837054i | \(0.315724\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 5.86454 | 0.356245 | 0.178123 | − | 0.984008i | \(-0.442998\pi\) | ||||
0.178123 | + | 0.984008i | \(0.442998\pi\) | |||||||
\(272\) | 7.17549 | 0.435078 | ||||||||
\(273\) | 9.09802 | 0.550637 | ||||||||
\(274\) | −12.3135 | −0.743888 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.358826 | −0.0215988 | ||||||||
\(277\) | −8.43371 | −0.506732 | −0.253366 | − | 0.967370i | \(-0.581538\pi\) | ||||
−0.253366 | + | 0.967370i | \(0.581538\pi\) | |||||||
\(278\) | 12.9970 | 0.779508 | ||||||||
\(279\) | 7.19863 | 0.430971 | ||||||||
\(280\) | 1.58059 | 0.0944585 | ||||||||
\(281\) | −5.85024 | −0.348996 | −0.174498 | − | 0.984658i | \(-0.555830\pi\) | ||||
−0.174498 | + | 0.984658i | \(0.555830\pi\) | |||||||
\(282\) | 6.52001 | 0.388261 | ||||||||
\(283\) | −11.0312 | −0.655736 | −0.327868 | − | 0.944724i | \(-0.606330\pi\) | ||||
−0.327868 | + | 0.944724i | \(0.606330\pi\) | |||||||
\(284\) | 9.11491 | 0.540870 | ||||||||
\(285\) | −1.32139 | −0.0782721 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9773 | 1.12020 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 34.4876 | 2.02868 | ||||||||
\(290\) | −9.67076 | −0.567887 | ||||||||
\(291\) | −1.92512 | −0.112852 | ||||||||
\(292\) | 6.94427 | 0.406383 | ||||||||
\(293\) | −3.22962 | −0.188676 | −0.0943382 | − | 0.995540i | \(-0.530073\pi\) | ||||
−0.0943382 | + | 0.995540i | \(0.530073\pi\) | |||||||
\(294\) | −4.50173 | −0.262546 | ||||||||
\(295\) | −10.3262 | −0.601217 | ||||||||
\(296\) | 9.73294 | 0.565716 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.64762 | −0.0954443 | ||||||||
\(299\) | 2.06543 | 0.119447 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 10.1341 | 0.584118 | ||||||||
\(302\) | 6.74823 | 0.388317 | ||||||||
\(303\) | −8.24092 | −0.473429 | ||||||||
\(304\) | 1.32139 | 0.0757867 | ||||||||
\(305\) | −5.63332 | −0.322563 | ||||||||
\(306\) | 7.17549 | 0.410195 | ||||||||
\(307\) | 22.9531 | 1.31000 | 0.655002 | − | 0.755627i | \(-0.272668\pi\) | ||||
0.655002 | + | 0.755627i | \(0.272668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.90843 | −0.279231 | ||||||||
\(310\) | −7.19863 | −0.408855 | ||||||||
\(311\) | 4.20121 | 0.238229 | 0.119114 | − | 0.992881i | \(-0.461994\pi\) | ||||
0.119114 | + | 0.992881i | \(0.461994\pi\) | |||||||
\(312\) | −5.75608 | −0.325874 | ||||||||
\(313\) | −18.3816 | −1.03899 | −0.519493 | − | 0.854474i | \(-0.673879\pi\) | ||||
−0.519493 | + | 0.854474i | \(0.673879\pi\) | |||||||
\(314\) | 8.92898 | 0.503892 | ||||||||
\(315\) | 1.58059 | 0.0890563 | ||||||||
\(316\) | 11.5265 | 0.648414 | ||||||||
\(317\) | −25.3311 | −1.42274 | −0.711368 | − | 0.702820i | \(-0.751924\pi\) | ||||
−0.711368 | + | 0.702820i | \(0.751924\pi\) | |||||||
\(318\) | 2.34453 | 0.131474 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −1.64903 | −0.0920396 | ||||||||
\(322\) | 0.567158 | 0.0316065 | ||||||||
\(323\) | 9.48158 | 0.527569 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −5.75608 | −0.319290 | ||||||||
\(326\) | 9.72251 | 0.538480 | ||||||||
\(327\) | −8.94427 | −0.494619 | ||||||||
\(328\) | −12.0064 | −0.662945 | ||||||||
\(329\) | −10.3055 | −0.568160 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1159 | 1.43546 | 0.717730 | − | 0.696322i | \(-0.245181\pi\) | ||||
0.717730 | + | 0.696322i | \(0.245181\pi\) | |||||||
\(332\) | 8.00000 | 0.439057 | ||||||||
\(333\) | 9.73294 | 0.533362 | ||||||||
\(334\) | −15.4643 | −0.846168 | ||||||||
\(335\) | 5.07747 | 0.277412 | ||||||||
\(336\) | −1.58059 | −0.0862284 | ||||||||
\(337\) | 18.2012 | 0.991483 | 0.495742 | − | 0.868470i | \(-0.334896\pi\) | ||||
0.495742 | + | 0.868470i | \(0.334896\pi\) | |||||||
\(338\) | 20.1325 | 1.09506 | ||||||||
\(339\) | 0.0374409 | 0.00203351 | ||||||||
\(340\) | −7.17549 | −0.389145 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.32139 | 0.0714523 | ||||||||
\(343\) | 18.1795 | 0.981603 | ||||||||
\(344\) | −6.41156 | −0.345688 | ||||||||
\(345\) | 0.358826 | 0.0193186 | ||||||||
\(346\) | 18.4037 | 0.989389 | ||||||||
\(347\) | 18.3816 | 0.986773 | 0.493387 | − | 0.869810i | \(-0.335759\pi\) | ||||
0.493387 | + | 0.869810i | \(0.335759\pi\) | |||||||
\(348\) | 9.67076 | 0.518407 | ||||||||
\(349\) | 29.2204 | 1.56413 | 0.782065 | − | 0.623197i | \(-0.214166\pi\) | ||||
0.782065 | + | 0.623197i | \(0.214166\pi\) | |||||||
\(350\) | −1.58059 | −0.0844863 | ||||||||
\(351\) | −5.75608 | −0.307237 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.41156 | −0.234803 | −0.117402 | − | 0.993085i | \(-0.537457\pi\) | ||||
−0.117402 | + | 0.993085i | \(0.537457\pi\) | |||||||
\(354\) | 10.3262 | 0.548833 | ||||||||
\(355\) | −9.11491 | −0.483769 | ||||||||
\(356\) | 7.16764 | 0.379884 | ||||||||
\(357\) | −11.3415 | −0.600257 | ||||||||
\(358\) | −18.5623 | −0.981048 | ||||||||
\(359\) | −22.1803 | −1.17063 | −0.585317 | − | 0.810805i | \(-0.699030\pi\) | ||||
−0.585317 | + | 0.810805i | \(0.699030\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −17.2539 | −0.908102 | ||||||||
\(362\) | 9.52786 | 0.500773 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.09802 | 0.476866 | ||||||||
\(365\) | −6.94427 | −0.363480 | ||||||||
\(366\) | 5.63332 | 0.294458 | ||||||||
\(367\) | −7.49129 | −0.391042 | −0.195521 | − | 0.980700i | \(-0.562640\pi\) | ||||
−0.195521 | + | 0.980700i | \(0.562640\pi\) | |||||||
\(368\) | −0.358826 | −0.0187051 | ||||||||
\(369\) | −12.0064 | −0.625031 | ||||||||
\(370\) | −9.73294 | −0.505991 | ||||||||
\(371\) | −3.70574 | −0.192392 | ||||||||
\(372\) | 7.19863 | 0.373231 | ||||||||
\(373\) | 7.50173 | 0.388425 | 0.194212 | − | 0.980960i | \(-0.437785\pi\) | ||||
0.194212 | + | 0.980960i | \(0.437785\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 6.52001 | 0.336244 | ||||||||
\(377\) | −55.6657 | −2.86693 | ||||||||
\(378\) | −1.58059 | −0.0812969 | ||||||||
\(379\) | −22.6589 | −1.16391 | −0.581955 | − | 0.813221i | \(-0.697712\pi\) | ||||
−0.581955 | + | 0.813221i | \(0.697712\pi\) | |||||||
\(380\) | −1.32139 | −0.0677856 | ||||||||
\(381\) | −16.5418 | −0.847460 | ||||||||
\(382\) | 20.0306 | 1.02485 | ||||||||
\(383\) | −6.48742 | −0.331492 | −0.165746 | − | 0.986168i | \(-0.553003\pi\) | ||||
−0.165746 | + | 0.986168i | \(0.553003\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.82937 | −0.398504 | ||||||||
\(387\) | −6.41156 | −0.325918 | ||||||||
\(388\) | −1.92512 | −0.0977331 | ||||||||
\(389\) | 21.5824 | 1.09427 | 0.547137 | − | 0.837043i | \(-0.315718\pi\) | ||||
0.547137 | + | 0.837043i | \(0.315718\pi\) | |||||||
\(390\) | 5.75608 | 0.291470 | ||||||||
\(391\) | −2.57475 | −0.130211 | ||||||||
\(392\) | −4.50173 | −0.227371 | ||||||||
\(393\) | −12.5096 | −0.631025 | ||||||||
\(394\) | −20.6798 | −1.04183 | ||||||||
\(395\) | −11.5265 | −0.579959 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5235 | 0.829289 | 0.414644 | − | 0.909984i | \(-0.363906\pi\) | ||||
0.414644 | + | 0.909984i | \(0.363906\pi\) | |||||||
\(398\) | −3.12921 | −0.156853 | ||||||||
\(399\) | −2.08857 | −0.104559 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 14.5672 | 0.727449 | 0.363725 | − | 0.931507i | \(-0.381505\pi\) | ||||
0.363725 | + | 0.931507i | \(0.381505\pi\) | |||||||
\(402\) | −5.07747 | −0.253241 | ||||||||
\(403\) | −41.4359 | −2.06407 | ||||||||
\(404\) | −8.24092 | −0.410001 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −15.2855 | −0.758609 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.17549 | 0.355240 | ||||||||
\(409\) | −22.6287 | −1.11892 | −0.559458 | − | 0.828859i | \(-0.688991\pi\) | ||||
−0.559458 | + | 0.828859i | \(0.688991\pi\) | |||||||
\(410\) | 12.0064 | 0.592956 | ||||||||
\(411\) | −12.3135 | −0.607382 | ||||||||
\(412\) | −4.90843 | −0.241821 | ||||||||
\(413\) | −16.3216 | −0.803132 | ||||||||
\(414\) | −0.358826 | −0.0176354 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | −5.75608 | −0.282215 | ||||||||
\(417\) | 12.9970 | 0.636466 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.41057 | 0.264324 | 0.132162 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132162 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(420\) | 1.58059 | 0.0771250 | ||||||||
\(421\) | 3.48158 | 0.169682 | 0.0848410 | − | 0.996395i | \(-0.472962\pi\) | ||||
0.0848410 | + | 0.996395i | \(0.472962\pi\) | |||||||
\(422\) | −14.3047 | −0.696342 | ||||||||
\(423\) | 6.52001 | 0.317014 | ||||||||
\(424\) | 2.34453 | 0.113860 | ||||||||
\(425\) | 7.17549 | 0.348062 | ||||||||
\(426\) | 9.11491 | 0.441619 | ||||||||
\(427\) | −8.90399 | −0.430894 | ||||||||
\(428\) | −1.64903 | −0.0797086 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.41156 | 0.309193 | ||||||||
\(431\) | −12.2169 | −0.588468 | −0.294234 | − | 0.955733i | \(-0.595065\pi\) | ||||
−0.294234 | + | 0.955733i | \(0.595065\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 9.48356 | 0.455751 | 0.227875 | − | 0.973690i | \(-0.426822\pi\) | ||||
0.227875 | + | 0.973690i | \(0.426822\pi\) | |||||||
\(434\) | −11.3781 | −0.546166 | ||||||||
\(435\) | −9.67076 | −0.463678 | ||||||||
\(436\) | −8.94427 | −0.428353 | ||||||||
\(437\) | −0.474148 | −0.0226816 | ||||||||
\(438\) | 6.94427 | 0.331810 | ||||||||
\(439\) | 7.54960 | 0.360323 | 0.180161 | − | 0.983637i | \(-0.442338\pi\) | ||||
0.180161 | + | 0.983637i | \(0.442338\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.50173 | −0.214368 | ||||||||
\(442\) | −41.3027 | −1.96457 | ||||||||
\(443\) | −23.5713 | −1.11991 | −0.559954 | − | 0.828524i | \(-0.689181\pi\) | ||||
−0.559954 | + | 0.828524i | \(0.689181\pi\) | |||||||
\(444\) | 9.73294 | 0.461905 | ||||||||
\(445\) | −7.16764 | −0.339779 | ||||||||
\(446\) | 5.58059 | 0.264249 | ||||||||
\(447\) | −1.64762 | −0.0779299 | ||||||||
\(448\) | −1.58059 | −0.0746760 | ||||||||
\(449\) | −1.98956 | −0.0938933 | −0.0469467 | − | 0.998897i | \(-0.514949\pi\) | ||||
−0.0469467 | + | 0.998897i | \(0.514949\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.0374409 | 0.00176107 | ||||||||
\(453\) | 6.74823 | 0.317059 | ||||||||
\(454\) | −4.68905 | −0.220068 | ||||||||
\(455\) | −9.09802 | −0.426522 | ||||||||
\(456\) | 1.32139 | 0.0618795 | ||||||||
\(457\) | −29.9634 | −1.40163 | −0.700815 | − | 0.713343i | \(-0.747180\pi\) | ||||
−0.700815 | + | 0.713343i | \(0.747180\pi\) | |||||||
\(458\) | 8.39725 | 0.392378 | ||||||||
\(459\) | 7.17549 | 0.334923 | ||||||||
\(460\) | 0.358826 | 0.0167304 | ||||||||
\(461\) | −12.0143 | −0.559562 | −0.279781 | − | 0.960064i | \(-0.590262\pi\) | ||||
−0.279781 | + | 0.960064i | \(0.590262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.85895 | 0.225815 | 0.112907 | − | 0.993606i | \(-0.463984\pi\) | ||||
0.112907 | + | 0.993606i | \(0.463984\pi\) | |||||||
\(464\) | 9.67076 | 0.448954 | ||||||||
\(465\) | −7.19863 | −0.333828 | ||||||||
\(466\) | −7.27351 | −0.336939 | ||||||||
\(467\) | −15.3878 | −0.712063 | −0.356031 | − | 0.934474i | \(-0.615870\pi\) | ||||
−0.356031 | + | 0.934474i | \(0.615870\pi\) | |||||||
\(468\) | −5.75608 | −0.266075 | ||||||||
\(469\) | 8.02541 | 0.370579 | ||||||||
\(470\) | −6.52001 | −0.300746 | ||||||||
\(471\) | 8.92898 | 0.411426 | ||||||||
\(472\) | 10.3262 | 0.475304 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 11.5265 | 0.529428 | ||||||||
\(475\) | 1.32139 | 0.0606293 | ||||||||
\(476\) | −11.3415 | −0.519838 | ||||||||
\(477\) | 2.34453 | 0.107348 | ||||||||
\(478\) | −21.7883 | −0.996572 | ||||||||
\(479\) | 3.62362 | 0.165567 | 0.0827836 | − | 0.996568i | \(-0.473619\pi\) | ||||
0.0827836 | + | 0.996568i | \(0.473619\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −56.0236 | −2.55446 | ||||||||
\(482\) | −4.54057 | −0.206817 | ||||||||
\(483\) | 0.567158 | 0.0258066 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.92512 | 0.0874151 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 3.26664 | 0.148026 | 0.0740129 | − | 0.997257i | \(-0.476419\pi\) | ||||
0.0740129 | + | 0.997257i | \(0.476419\pi\) | |||||||
\(488\) | 5.63332 | 0.255009 | ||||||||
\(489\) | 9.72251 | 0.439667 | ||||||||
\(490\) | 4.50173 | 0.203367 | ||||||||
\(491\) | −34.2745 | −1.54679 | −0.773393 | − | 0.633927i | \(-0.781442\pi\) | ||||
−0.773393 | + | 0.633927i | \(0.781442\pi\) | |||||||
\(492\) | −12.0064 | −0.541293 | ||||||||
\(493\) | 69.3924 | 3.12528 | ||||||||
\(494\) | −7.60600 | −0.342210 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.19863 | 0.323228 | ||||||||
\(497\) | −14.4070 | −0.646240 | ||||||||
\(498\) | 8.00000 | 0.358489 | ||||||||
\(499\) | 38.2077 | 1.71041 | 0.855205 | − | 0.518290i | \(-0.173431\pi\) | ||||
0.855205 | + | 0.518290i | \(0.173431\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −15.4643 | −0.690893 | ||||||||
\(502\) | 4.20906 | 0.187860 | ||||||||
\(503\) | 20.9173 | 0.932655 | 0.466327 | − | 0.884612i | \(-0.345577\pi\) | ||||
0.466327 | + | 0.884612i | \(0.345577\pi\) | |||||||
\(504\) | −1.58059 | −0.0704052 | ||||||||
\(505\) | 8.24092 | 0.366716 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.1325 | 0.894114 | ||||||||
\(508\) | −16.5418 | −0.733921 | ||||||||
\(509\) | −34.6279 | −1.53486 | −0.767428 | − | 0.641135i | \(-0.778464\pi\) | ||||
−0.767428 | + | 0.641135i | \(0.778464\pi\) | |||||||
\(510\) | −7.17549 | −0.317736 | ||||||||
\(511\) | −10.9761 | −0.485553 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.32139 | 0.0583406 | ||||||||
\(514\) | −14.7945 | −0.652558 | ||||||||
\(515\) | 4.90843 | 0.216291 | ||||||||
\(516\) | −6.41156 | −0.282253 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −15.3838 | −0.675926 | ||||||||
\(519\) | 18.4037 | 0.807833 | ||||||||
\(520\) | 5.75608 | 0.252421 | ||||||||
\(521\) | −14.2077 | −0.622449 | −0.311224 | − | 0.950336i | \(-0.600739\pi\) | ||||
−0.311224 | + | 0.950336i | \(0.600739\pi\) | |||||||
\(522\) | 9.67076 | 0.423278 | ||||||||
\(523\) | 1.54076 | 0.0673729 | 0.0336864 | − | 0.999432i | \(-0.489275\pi\) | ||||
0.0336864 | + | 0.999432i | \(0.489275\pi\) | |||||||
\(524\) | −12.5096 | −0.546483 | ||||||||
\(525\) | −1.58059 | −0.0689827 | ||||||||
\(526\) | 7.90358 | 0.344612 | ||||||||
\(527\) | 51.6537 | 2.25007 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8712 | −0.994402 | ||||||||
\(530\) | −2.34453 | −0.101840 | ||||||||
\(531\) | 10.3262 | 0.448121 | ||||||||
\(532\) | −2.08857 | −0.0905511 | ||||||||
\(533\) | 69.1101 | 2.99349 | ||||||||
\(534\) | 7.16764 | 0.310174 | ||||||||
\(535\) | 1.64903 | 0.0712936 | ||||||||
\(536\) | −5.07747 | −0.219313 | ||||||||
\(537\) | −18.5623 | −0.801023 | ||||||||
\(538\) | 17.9469 | 0.773744 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 21.1644 | 0.909928 | 0.454964 | − | 0.890510i | \(-0.349652\pi\) | ||||
0.454964 | + | 0.890510i | \(0.349652\pi\) | |||||||
\(542\) | 5.86454 | 0.251903 | ||||||||
\(543\) | 9.52786 | 0.408880 | ||||||||
\(544\) | 7.17549 | 0.307646 | ||||||||
\(545\) | 8.94427 | 0.383131 | ||||||||
\(546\) | 9.09802 | 0.389359 | ||||||||
\(547\) | 25.8720 | 1.10621 | 0.553103 | − | 0.833113i | \(-0.313444\pi\) | ||||
0.553103 | + | 0.833113i | \(0.313444\pi\) | |||||||
\(548\) | −12.3135 | −0.526008 | ||||||||
\(549\) | 5.63332 | 0.240424 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.7788 | 0.544395 | ||||||||
\(552\) | −0.358826 | −0.0152727 | ||||||||
\(553\) | −18.2186 | −0.774736 | ||||||||
\(554\) | −8.43371 | −0.358314 | ||||||||
\(555\) | −9.73294 | −0.413140 | ||||||||
\(556\) | 12.9970 | 0.551196 | ||||||||
\(557\) | 9.76811 | 0.413888 | 0.206944 | − | 0.978353i | \(-0.433648\pi\) | ||||
0.206944 | + | 0.978353i | \(0.433648\pi\) | |||||||
\(558\) | 7.19863 | 0.304742 | ||||||||
\(559\) | 36.9054 | 1.56093 | ||||||||
\(560\) | 1.58059 | 0.0667923 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.85024 | −0.246777 | ||||||||
\(563\) | 21.9348 | 0.924443 | 0.462221 | − | 0.886765i | \(-0.347053\pi\) | ||||
0.462221 | + | 0.886765i | \(0.347053\pi\) | |||||||
\(564\) | 6.52001 | 0.274542 | ||||||||
\(565\) | −0.0374409 | −0.00157515 | ||||||||
\(566\) | −11.0312 | −0.463675 | ||||||||
\(567\) | −1.58059 | −0.0663787 | ||||||||
\(568\) | 9.11491 | 0.382453 | ||||||||
\(569\) | 41.7166 | 1.74885 | 0.874426 | − | 0.485159i | \(-0.161238\pi\) | ||||
0.874426 | + | 0.485159i | \(0.161238\pi\) | |||||||
\(570\) | −1.32139 | −0.0553467 | ||||||||
\(571\) | −23.0928 | −0.966402 | −0.483201 | − | 0.875510i | \(-0.660526\pi\) | ||||
−0.483201 | + | 0.875510i | \(0.660526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.0306 | 0.836789 | ||||||||
\(574\) | 18.9773 | 0.792098 | ||||||||
\(575\) | −0.358826 | −0.0149641 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −30.2552 | −1.25954 | −0.629771 | − | 0.776781i | \(-0.716851\pi\) | ||||
−0.629771 | + | 0.776781i | \(0.716851\pi\) | |||||||
\(578\) | 34.4876 | 1.43450 | ||||||||
\(579\) | −7.82937 | −0.325377 | ||||||||
\(580\) | −9.67076 | −0.401557 | ||||||||
\(581\) | −12.6447 | −0.524592 | ||||||||
\(582\) | −1.92512 | −0.0797987 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.94427 | 0.287356 | ||||||||
\(585\) | 5.75608 | 0.237985 | ||||||||
\(586\) | −3.22962 | −0.133414 | ||||||||
\(587\) | 5.40670 | 0.223159 | 0.111579 | − | 0.993756i | \(-0.464409\pi\) | ||||
0.111579 | + | 0.993756i | \(0.464409\pi\) | |||||||
\(588\) | −4.50173 | −0.185648 | ||||||||
\(589\) | 9.51216 | 0.391942 | ||||||||
\(590\) | −10.3262 | −0.425124 | ||||||||
\(591\) | −20.6798 | −0.850653 | ||||||||
\(592\) | 9.73294 | 0.400021 | ||||||||
\(593\) | −33.4413 | −1.37327 | −0.686636 | − | 0.727002i | \(-0.740913\pi\) | ||||
−0.686636 | + | 0.727002i | \(0.740913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.3415 | 0.464957 | ||||||||
\(596\) | −1.64762 | −0.0674893 | ||||||||
\(597\) | −3.12921 | −0.128070 | ||||||||
\(598\) | 2.06543 | 0.0844618 | ||||||||
\(599\) | 6.37638 | 0.260532 | 0.130266 | − | 0.991479i | \(-0.458417\pi\) | ||||
0.130266 | + | 0.991479i | \(0.458417\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −5.76294 | −0.235075 | −0.117538 | − | 0.993068i | \(-0.537500\pi\) | ||||
−0.117538 | + | 0.993068i | \(0.537500\pi\) | |||||||
\(602\) | 10.1341 | 0.413033 | ||||||||
\(603\) | −5.07747 | −0.206770 | ||||||||
\(604\) | 6.74823 | 0.274582 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.24092 | −0.334765 | ||||||||
\(607\) | 45.5427 | 1.84852 | 0.924261 | − | 0.381760i | \(-0.124682\pi\) | ||||
0.924261 | + | 0.381760i | \(0.124682\pi\) | |||||||
\(608\) | 1.32139 | 0.0535893 | ||||||||
\(609\) | −15.2855 | −0.619401 | ||||||||
\(610\) | −5.63332 | −0.228087 | ||||||||
\(611\) | −37.5297 | −1.51829 | ||||||||
\(612\) | 7.17549 | 0.290052 | ||||||||
\(613\) | −31.1552 | −1.25835 | −0.629173 | − | 0.777265i | \(-0.716606\pi\) | ||||
−0.629173 | + | 0.777265i | \(0.716606\pi\) | |||||||
\(614\) | 22.9531 | 0.926312 | ||||||||
\(615\) | 12.0064 | 0.484147 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.2761 | −1.21887 | −0.609435 | − | 0.792836i | \(-0.708604\pi\) | ||||
−0.609435 | + | 0.792836i | \(0.708604\pi\) | |||||||
\(618\) | −4.90843 | −0.197446 | ||||||||
\(619\) | −37.1225 | −1.49208 | −0.746040 | − | 0.665901i | \(-0.768047\pi\) | ||||
−0.746040 | + | 0.665901i | \(0.768047\pi\) | |||||||
\(620\) | −7.19863 | −0.289104 | ||||||||
\(621\) | −0.358826 | −0.0143992 | ||||||||
\(622\) | 4.20121 | 0.168453 | ||||||||
\(623\) | −11.3291 | −0.453891 | ||||||||
\(624\) | −5.75608 | −0.230428 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.3816 | −0.734675 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.92898 | 0.356305 | ||||||||
\(629\) | 69.8386 | 2.78465 | ||||||||
\(630\) | 1.58059 | 0.0629723 | ||||||||
\(631\) | −34.9837 | −1.39268 | −0.696339 | − | 0.717713i | \(-0.745189\pi\) | ||||
−0.696339 | + | 0.717713i | \(0.745189\pi\) | |||||||
\(632\) | 11.5265 | 0.458498 | ||||||||
\(633\) | −14.3047 | −0.568561 | ||||||||
\(634\) | −25.3311 | −1.00603 | ||||||||
\(635\) | 16.5418 | 0.656439 | ||||||||
\(636\) | 2.34453 | 0.0929665 | ||||||||
\(637\) | 25.9123 | 1.02668 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.11491 | 0.360580 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 7.87357 | 0.310987 | 0.155494 | − | 0.987837i | \(-0.450303\pi\) | ||||
0.155494 | + | 0.987837i | \(0.450303\pi\) | |||||||
\(642\) | −1.64903 | −0.0650818 | ||||||||
\(643\) | 45.7923 | 1.80587 | 0.902936 | − | 0.429774i | \(-0.141407\pi\) | ||||
0.902936 | + | 0.429774i | \(0.141407\pi\) | |||||||
\(644\) | 0.567158 | 0.0223492 | ||||||||
\(645\) | 6.41156 | 0.252455 | ||||||||
\(646\) | 9.48158 | 0.373048 | ||||||||
\(647\) | −31.0543 | −1.22087 | −0.610436 | − | 0.792066i | \(-0.709006\pi\) | ||||
−0.610436 | + | 0.792066i | \(0.709006\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.75608 | −0.225772 | ||||||||
\(651\) | −11.3781 | −0.445943 | ||||||||
\(652\) | 9.72251 | 0.380763 | ||||||||
\(653\) | −22.9084 | −0.896476 | −0.448238 | − | 0.893914i | \(-0.647948\pi\) | ||||
−0.448238 | + | 0.893914i | \(0.647948\pi\) | |||||||
\(654\) | −8.94427 | −0.349749 | ||||||||
\(655\) | 12.5096 | 0.488790 | ||||||||
\(656\) | −12.0064 | −0.468773 | ||||||||
\(657\) | 6.94427 | 0.270922 | ||||||||
\(658\) | −10.3055 | −0.401750 | ||||||||
\(659\) | −17.9907 | −0.700820 | −0.350410 | − | 0.936596i | \(-0.613958\pi\) | ||||
−0.350410 | + | 0.936596i | \(0.613958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.6576 | −1.42582 | −0.712909 | − | 0.701257i | \(-0.752623\pi\) | ||||
−0.712909 | + | 0.701257i | \(0.752623\pi\) | |||||||
\(662\) | 26.1159 | 1.01502 | ||||||||
\(663\) | −41.3027 | −1.60406 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 2.08857 | 0.0809914 | ||||||||
\(666\) | 9.73294 | 0.377144 | ||||||||
\(667\) | −3.47012 | −0.134364 | ||||||||
\(668\) | −15.4643 | −0.598331 | ||||||||
\(669\) | 5.58059 | 0.215758 | ||||||||
\(670\) | 5.07747 | 0.196160 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.58059 | −0.0609727 | ||||||||
\(673\) | −1.53106 | −0.0590180 | −0.0295090 | − | 0.999565i | \(-0.509394\pi\) | ||||
−0.0295090 | + | 0.999565i | \(0.509394\pi\) | |||||||
\(674\) | 18.2012 | 0.701084 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 20.1325 | 0.774326 | ||||||||
\(677\) | 1.73361 | 0.0666281 | 0.0333141 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333141 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(678\) | 0.0374409 | 0.00143791 | ||||||||
\(679\) | 3.04283 | 0.116773 | ||||||||
\(680\) | −7.17549 | −0.275167 | ||||||||
\(681\) | −4.68905 | −0.179685 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3161 | −0.586055 | −0.293027 | − | 0.956104i | \(-0.594663\pi\) | ||||
−0.293027 | + | 0.956104i | \(0.594663\pi\) | |||||||
\(684\) | 1.32139 | 0.0505244 | ||||||||
\(685\) | 12.3135 | 0.470476 | ||||||||
\(686\) | 18.1795 | 0.694098 | ||||||||
\(687\) | 8.39725 | 0.320375 | ||||||||
\(688\) | −6.41156 | −0.244438 | ||||||||
\(689\) | −13.4953 | −0.514129 | ||||||||
\(690\) | 0.358826 | 0.0136603 | ||||||||
\(691\) | 25.1487 | 0.956703 | 0.478352 | − | 0.878168i | \(-0.341234\pi\) | ||||
0.478352 | + | 0.878168i | \(0.341234\pi\) | |||||||
\(692\) | 18.4037 | 0.699604 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.3816 | 0.697754 | ||||||||
\(695\) | −12.9970 | −0.493004 | ||||||||
\(696\) | 9.67076 | 0.366569 | ||||||||
\(697\) | −86.1521 | −3.26324 | ||||||||
\(698\) | 29.2204 | 1.10601 | ||||||||
\(699\) | −7.27351 | −0.275109 | ||||||||
\(700\) | −1.58059 | −0.0597408 | ||||||||
\(701\) | 22.0129 | 0.831416 | 0.415708 | − | 0.909498i | \(-0.363534\pi\) | ||||
0.415708 | + | 0.909498i | \(0.363534\pi\) | |||||||
\(702\) | −5.75608 | −0.217249 | ||||||||
\(703\) | 12.8610 | 0.485061 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.52001 | −0.245558 | ||||||||
\(706\) | −4.41156 | −0.166031 | ||||||||
\(707\) | 13.0255 | 0.489876 | ||||||||
\(708\) | 10.3262 | 0.388084 | ||||||||
\(709\) | 34.0129 | 1.27738 | 0.638691 | − | 0.769464i | \(-0.279476\pi\) | ||||
0.638691 | + | 0.769464i | \(0.279476\pi\) | |||||||
\(710\) | −9.11491 | −0.342076 | ||||||||
\(711\) | 11.5265 | 0.432276 | ||||||||
\(712\) | 7.16764 | 0.268619 | ||||||||
\(713\) | −2.58306 | −0.0967362 | ||||||||
\(714\) | −11.3415 | −0.424446 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.5623 | −0.693706 | ||||||||
\(717\) | −21.7883 | −0.813697 | ||||||||
\(718\) | −22.1803 | −0.827763 | ||||||||
\(719\) | 37.4450 | 1.39646 | 0.698232 | − | 0.715872i | \(-0.253971\pi\) | ||||
0.698232 | + | 0.715872i | \(0.253971\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 7.75823 | 0.288932 | ||||||||
\(722\) | −17.2539 | −0.642125 | ||||||||
\(723\) | −4.54057 | −0.168866 | ||||||||
\(724\) | 9.52786 | 0.354100 | ||||||||
\(725\) | 9.67076 | 0.359163 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.1119 | −1.33932 | −0.669658 | − | 0.742669i | \(-0.733559\pi\) | ||||
−0.669658 | + | 0.742669i | \(0.733559\pi\) | |||||||
\(728\) | 9.09802 | 0.337195 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.94427 | −0.257019 | ||||||||
\(731\) | −46.0060 | −1.70159 | ||||||||
\(732\) | 5.63332 | 0.208214 | ||||||||
\(733\) | 17.8774 | 0.660318 | 0.330159 | − | 0.943925i | \(-0.392898\pi\) | ||||
0.330159 | + | 0.943925i | \(0.392898\pi\) | |||||||
\(734\) | −7.49129 | −0.276509 | ||||||||
\(735\) | 4.50173 | 0.166049 | ||||||||
\(736\) | −0.358826 | −0.0132265 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.0064 | −0.441964 | ||||||||
\(739\) | 29.8358 | 1.09753 | 0.548764 | − | 0.835977i | \(-0.315099\pi\) | ||||
0.548764 | + | 0.835977i | \(0.315099\pi\) | |||||||
\(740\) | −9.73294 | −0.357790 | ||||||||
\(741\) | −7.60600 | −0.279413 | ||||||||
\(742\) | −3.70574 | −0.136042 | ||||||||
\(743\) | 22.1285 | 0.811815 | 0.405908 | − | 0.913914i | \(-0.366955\pi\) | ||||
0.405908 | + | 0.913914i | \(0.366955\pi\) | |||||||
\(744\) | 7.19863 | 0.263914 | ||||||||
\(745\) | 1.64762 | 0.0603642 | ||||||||
\(746\) | 7.50173 | 0.274658 | ||||||||
\(747\) | 8.00000 | 0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.60644 | 0.0952372 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −13.9334 | −0.508438 | −0.254219 | − | 0.967147i | \(-0.581818\pi\) | ||||
−0.254219 | + | 0.967147i | \(0.581818\pi\) | |||||||
\(752\) | 6.52001 | 0.237760 | ||||||||
\(753\) | 4.20906 | 0.153387 | ||||||||
\(754\) | −55.6657 | −2.02722 | ||||||||
\(755\) | −6.74823 | −0.245593 | ||||||||
\(756\) | −1.58059 | −0.0574856 | ||||||||
\(757\) | −47.8361 | −1.73863 | −0.869317 | − | 0.494255i | \(-0.835441\pi\) | ||||
−0.869317 | + | 0.494255i | \(0.835441\pi\) | |||||||
\(758\) | −22.6589 | −0.823009 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.32139 | −0.0479317 | ||||||||
\(761\) | −30.7019 | −1.11294 | −0.556472 | − | 0.830866i | \(-0.687846\pi\) | ||||
−0.556472 | + | 0.830866i | \(0.687846\pi\) | |||||||
\(762\) | −16.5418 | −0.599244 | ||||||||
\(763\) | 14.1373 | 0.511803 | ||||||||
\(764\) | 20.0306 | 0.724681 | ||||||||
\(765\) | −7.17549 | −0.259430 | ||||||||
\(766\) | −6.48742 | −0.234400 | ||||||||
\(767\) | −59.4387 | −2.14621 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −7.23993 | −0.261079 | −0.130539 | − | 0.991443i | \(-0.541671\pi\) | ||||
−0.130539 | + | 0.991443i | \(0.541671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.7945 | −0.532811 | ||||||||
\(772\) | −7.82937 | −0.281785 | ||||||||
\(773\) | 52.3755 | 1.88382 | 0.941908 | − | 0.335872i | \(-0.109031\pi\) | ||||
0.941908 | + | 0.335872i | \(0.109031\pi\) | |||||||
\(774\) | −6.41156 | −0.230459 | ||||||||
\(775\) | 7.19863 | 0.258582 | ||||||||
\(776\) | −1.92512 | −0.0691077 | ||||||||
\(777\) | −15.3838 | −0.551891 | ||||||||
\(778\) | 21.5824 | 0.773768 | ||||||||
\(779\) | −15.8651 | −0.568428 | ||||||||
\(780\) | 5.75608 | 0.206101 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.57475 | −0.0920730 | ||||||||
\(783\) | 9.67076 | 0.345605 | ||||||||
\(784\) | −4.50173 | −0.160776 | ||||||||
\(785\) | −8.92898 | −0.318689 | ||||||||
\(786\) | −12.5096 | −0.446202 | ||||||||
\(787\) | 40.2155 | 1.43353 | 0.716764 | − | 0.697316i | \(-0.245622\pi\) | ||||
0.716764 | + | 0.697316i | \(0.245622\pi\) | |||||||
\(788\) | −20.6798 | −0.736687 | ||||||||
\(789\) | 7.90358 | 0.281375 | ||||||||
\(790\) | −11.5265 | −0.410093 | ||||||||
\(791\) | −0.0591788 | −0.00210415 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.4259 | −1.15148 | ||||||||
\(794\) | 16.5235 | 0.586396 | ||||||||
\(795\) | −2.34453 | −0.0831517 | ||||||||
\(796\) | −3.12921 | −0.110912 | ||||||||
\(797\) | 8.24479 | 0.292045 | 0.146023 | − | 0.989281i | \(-0.453353\pi\) | ||||
0.146023 | + | 0.989281i | \(0.453353\pi\) | |||||||
\(798\) | −2.08857 | −0.0739347 | ||||||||
\(799\) | 46.7843 | 1.65511 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 7.16764 | 0.253256 | ||||||||
\(802\) | 14.5672 | 0.514384 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −5.07747 | −0.179068 | ||||||||
\(805\) | −0.567158 | −0.0199897 | ||||||||
\(806\) | −41.4359 | −1.45952 | ||||||||
\(807\) | 17.9469 | 0.631759 | ||||||||
\(808\) | −8.24092 | −0.289915 | ||||||||
\(809\) | 0.436292 | 0.0153392 | 0.00766961 | − | 0.999971i | \(-0.497559\pi\) | ||||
0.00766961 | + | 0.999971i | \(0.497559\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −8.03703 | −0.282218 | −0.141109 | − | 0.989994i | \(-0.545067\pi\) | ||||
−0.141109 | + | 0.989994i | \(0.545067\pi\) | |||||||
\(812\) | −15.2855 | −0.536417 | ||||||||
\(813\) | 5.86454 | 0.205678 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.72251 | −0.340564 | ||||||||
\(816\) | 7.17549 | 0.251192 | ||||||||
\(817\) | −8.47214 | −0.296403 | ||||||||
\(818\) | −22.6287 | −0.791193 | ||||||||
\(819\) | 9.09802 | 0.317911 | ||||||||
\(820\) | 12.0064 | 0.419283 | ||||||||
\(821\) | −10.8726 | −0.379456 | −0.189728 | − | 0.981837i | \(-0.560761\pi\) | ||||
−0.189728 | + | 0.981837i | \(0.560761\pi\) | |||||||
\(822\) | −12.3135 | −0.429484 | ||||||||
\(823\) | 6.87466 | 0.239635 | 0.119818 | − | 0.992796i | \(-0.461769\pi\) | ||||
0.119818 | + | 0.992796i | \(0.461769\pi\) | |||||||
\(824\) | −4.90843 | −0.170993 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3216 | −0.567900 | ||||||||
\(827\) | −7.40070 | −0.257348 | −0.128674 | − | 0.991687i | \(-0.541072\pi\) | ||||
−0.128674 | + | 0.991687i | \(0.541072\pi\) | |||||||
\(828\) | −0.358826 | −0.0124701 | ||||||||
\(829\) | −2.50871 | −0.0871311 | −0.0435656 | − | 0.999051i | \(-0.513872\pi\) | ||||
−0.0435656 | + | 0.999051i | \(0.513872\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | −8.43371 | −0.292562 | ||||||||
\(832\) | −5.75608 | −0.199556 | ||||||||
\(833\) | −32.3021 | −1.11920 | ||||||||
\(834\) | 12.9970 | 0.450049 | ||||||||
\(835\) | 15.4643 | 0.535164 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.19863 | 0.248821 | ||||||||
\(838\) | 5.41057 | 0.186905 | ||||||||
\(839\) | −10.7450 | −0.370960 | −0.185480 | − | 0.982648i | \(-0.559384\pi\) | ||||
−0.185480 | + | 0.982648i | \(0.559384\pi\) | |||||||
\(840\) | 1.58059 | 0.0545356 | ||||||||
\(841\) | 64.5237 | 2.22495 | ||||||||
\(842\) | 3.48158 | 0.119983 | ||||||||
\(843\) | −5.85024 | −0.201493 | ||||||||
\(844\) | −14.3047 | −0.492388 | ||||||||
\(845\) | −20.1325 | −0.692578 | ||||||||
\(846\) | 6.52001 | 0.224163 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.34453 | 0.0805113 | ||||||||
\(849\) | −11.0312 | −0.378589 | ||||||||
\(850\) | 7.17549 | 0.246117 | ||||||||
\(851\) | −3.49244 | −0.119719 | ||||||||
\(852\) | 9.11491 | 0.312272 | ||||||||
\(853\) | −7.70175 | −0.263703 | −0.131852 | − | 0.991269i | \(-0.542092\pi\) | ||||
−0.131852 | + | 0.991269i | \(0.542092\pi\) | |||||||
\(854\) | −8.90399 | −0.304688 | ||||||||
\(855\) | −1.32139 | −0.0451904 | ||||||||
\(856\) | −1.64903 | −0.0563625 | ||||||||
\(857\) | 7.18839 | 0.245551 | 0.122775 | − | 0.992434i | \(-0.460821\pi\) | ||||
0.122775 | + | 0.992434i | \(0.460821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.4661 | 1.38068 | 0.690342 | − | 0.723483i | \(-0.257460\pi\) | ||||
0.690342 | + | 0.723483i | \(0.257460\pi\) | |||||||
\(860\) | 6.41156 | 0.218632 | ||||||||
\(861\) | 18.9773 | 0.646745 | ||||||||
\(862\) | −12.2169 | −0.416110 | ||||||||
\(863\) | −49.6424 | −1.68985 | −0.844923 | − | 0.534888i | \(-0.820354\pi\) | ||||
−0.844923 | + | 0.534888i | \(0.820354\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −18.4037 | −0.625745 | ||||||||
\(866\) | 9.48356 | 0.322264 | ||||||||
\(867\) | 34.4876 | 1.17126 | ||||||||
\(868\) | −11.3781 | −0.386198 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −9.67076 | −0.327870 | ||||||||
\(871\) | 29.2263 | 0.990296 | ||||||||
\(872\) | −8.94427 | −0.302891 | ||||||||
\(873\) | −1.92512 | −0.0651554 | ||||||||
\(874\) | −0.474148 | −0.0160383 | ||||||||
\(875\) | 1.58059 | 0.0534338 | ||||||||
\(876\) | 6.94427 | 0.234625 | ||||||||
\(877\) | −9.08046 | −0.306626 | −0.153313 | − | 0.988178i | \(-0.548994\pi\) | ||||
−0.153313 | + | 0.988178i | \(0.548994\pi\) | |||||||
\(878\) | 7.54960 | 0.254787 | ||||||||
\(879\) | −3.22962 | −0.108932 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.85152 | −0.331906 | −0.165953 | − | 0.986134i | \(-0.553070\pi\) | ||||
−0.165953 | + | 0.986134i | \(0.553070\pi\) | |||||||
\(882\) | −4.50173 | −0.151581 | ||||||||
\(883\) | −18.5456 | −0.624110 | −0.312055 | − | 0.950064i | \(-0.601017\pi\) | ||||
−0.312055 | + | 0.950064i | \(0.601017\pi\) | |||||||
\(884\) | −41.3027 | −1.38916 | ||||||||
\(885\) | −10.3262 | −0.347113 | ||||||||
\(886\) | −23.5713 | −0.791895 | ||||||||
\(887\) | −22.6172 | −0.759413 | −0.379706 | − | 0.925107i | \(-0.623975\pi\) | ||||
−0.379706 | + | 0.925107i | \(0.623975\pi\) | |||||||
\(888\) | 9.73294 | 0.326616 | ||||||||
\(889\) | 26.1458 | 0.876901 | ||||||||
\(890\) | −7.16764 | −0.240260 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.58059 | 0.186852 | ||||||||
\(893\) | 8.61545 | 0.288305 | ||||||||
\(894\) | −1.64762 | −0.0551048 | ||||||||
\(895\) | 18.5623 | 0.620469 | ||||||||
\(896\) | −1.58059 | −0.0528039 | ||||||||
\(897\) | 2.06543 | 0.0689628 | ||||||||
\(898\) | −1.98956 | −0.0663926 | ||||||||
\(899\) | 69.6162 | 2.32183 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 16.8231 | 0.560459 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.1341 | 0.337240 | ||||||||
\(904\) | 0.0374409 | 0.00124526 | ||||||||
\(905\) | −9.52786 | −0.316717 | ||||||||
\(906\) | 6.74823 | 0.224195 | ||||||||
\(907\) | −34.4273 | −1.14314 | −0.571569 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571569 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(908\) | −4.68905 | −0.155612 | ||||||||
\(909\) | −8.24092 | −0.273334 | ||||||||
\(910\) | −9.09802 | −0.301596 | ||||||||
\(911\) | 2.38155 | 0.0789043 | 0.0394522 | − | 0.999221i | \(-0.487439\pi\) | ||||
0.0394522 | + | 0.999221i | \(0.487439\pi\) | |||||||
\(912\) | 1.32139 | 0.0437554 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −29.9634 | −0.991102 | ||||||||
\(915\) | −5.63332 | −0.186232 | ||||||||
\(916\) | 8.39725 | 0.277453 | ||||||||
\(917\) | 19.7726 | 0.652947 | ||||||||
\(918\) | 7.17549 | 0.236826 | ||||||||
\(919\) | −7.11351 | −0.234653 | −0.117326 | − | 0.993093i | \(-0.537432\pi\) | ||||
−0.117326 | + | 0.993093i | \(0.537432\pi\) | |||||||
\(920\) | 0.358826 | 0.0118302 | ||||||||
\(921\) | 22.9531 | 0.756331 | ||||||||
\(922\) | −12.0143 | −0.395670 | ||||||||
\(923\) | −52.4661 | −1.72694 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.73294 | 0.320017 | ||||||||
\(926\) | 4.85895 | 0.159675 | ||||||||
\(927\) | −4.90843 | −0.161214 | ||||||||
\(928\) | 9.67076 | 0.317458 | ||||||||
\(929\) | 6.54057 | 0.214589 | 0.107295 | − | 0.994227i | \(-0.465781\pi\) | ||||
0.107295 | + | 0.994227i | \(0.465781\pi\) | |||||||
\(930\) | −7.19863 | −0.236052 | ||||||||
\(931\) | −5.94851 | −0.194955 | ||||||||
\(932\) | −7.27351 | −0.238252 | ||||||||
\(933\) | 4.20121 | 0.137541 | ||||||||
\(934\) | −15.3878 | −0.503504 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.75608 | −0.188143 | ||||||||
\(937\) | −36.8231 | −1.20296 | −0.601479 | − | 0.798888i | \(-0.705422\pi\) | ||||
−0.601479 | + | 0.798888i | \(0.705422\pi\) | |||||||
\(938\) | 8.02541 | 0.262039 | ||||||||
\(939\) | −18.3816 | −0.599859 | ||||||||
\(940\) | −6.52001 | −0.212659 | ||||||||
\(941\) | 9.59908 | 0.312921 | 0.156460 | − | 0.987684i | \(-0.449992\pi\) | ||||
0.156460 | + | 0.987684i | \(0.449992\pi\) | |||||||
\(942\) | 8.92898 | 0.290922 | ||||||||
\(943\) | 4.30823 | 0.140295 | ||||||||
\(944\) | 10.3262 | 0.336090 | ||||||||
\(945\) | 1.58059 | 0.0514167 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.5427 | −1.15498 | −0.577492 | − | 0.816396i | \(-0.695968\pi\) | ||||
−0.577492 | + | 0.816396i | \(0.695968\pi\) | |||||||
\(948\) | 11.5265 | 0.374362 | ||||||||
\(949\) | −39.9718 | −1.29754 | ||||||||
\(950\) | 1.32139 | 0.0428714 | ||||||||
\(951\) | −25.3311 | −0.821417 | ||||||||
\(952\) | −11.3415 | −0.367581 | ||||||||
\(953\) | −30.5476 | −0.989534 | −0.494767 | − | 0.869026i | \(-0.664747\pi\) | ||||
−0.494767 | + | 0.869026i | \(0.664747\pi\) | |||||||
\(954\) | 2.34453 | 0.0759068 | ||||||||
\(955\) | −20.0306 | −0.648174 | ||||||||
\(956\) | −21.7883 | −0.704683 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.62362 | 0.117074 | ||||||||
\(959\) | 19.4627 | 0.628483 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 20.8202 | 0.671620 | ||||||||
\(962\) | −56.0236 | −1.80627 | ||||||||
\(963\) | −1.64903 | −0.0531391 | ||||||||
\(964\) | −4.54057 | −0.146242 | ||||||||
\(965\) | 7.82937 | 0.252036 | ||||||||
\(966\) | 0.567158 | 0.0182480 | ||||||||
\(967\) | 22.9241 | 0.737190 | 0.368595 | − | 0.929590i | \(-0.379839\pi\) | ||||
0.368595 | + | 0.929590i | \(0.379839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.48158 | 0.304592 | ||||||||
\(970\) | 1.92512 | 0.0618118 | ||||||||
\(971\) | −52.1763 | −1.67442 | −0.837208 | − | 0.546885i | \(-0.815814\pi\) | ||||
−0.837208 | + | 0.546885i | \(0.815814\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −20.5430 | −0.658577 | ||||||||
\(974\) | 3.26664 | 0.104670 | ||||||||
\(975\) | −5.75608 | −0.184342 | ||||||||
\(976\) | 5.63332 | 0.180318 | ||||||||
\(977\) | 7.49646 | 0.239833 | 0.119916 | − | 0.992784i | \(-0.461737\pi\) | ||||
0.119916 | + | 0.992784i | \(0.461737\pi\) | |||||||
\(978\) | 9.72251 | 0.310891 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.50173 | 0.143802 | ||||||||
\(981\) | −8.94427 | −0.285569 | ||||||||
\(982\) | −34.2745 | −1.09374 | ||||||||
\(983\) | −57.8539 | −1.84525 | −0.922626 | − | 0.385695i | \(-0.873962\pi\) | ||||
−0.922626 | + | 0.385695i | \(0.873962\pi\) | |||||||
\(984\) | −12.0064 | −0.382752 | ||||||||
\(985\) | 20.6798 | 0.658913 | ||||||||
\(986\) | 69.3924 | 2.20991 | ||||||||
\(987\) | −10.3055 | −0.328027 | ||||||||
\(988\) | −7.60600 | −0.241979 | ||||||||
\(989\) | 2.30063 | 0.0731559 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.1292 | 0.480595 | 0.240298 | − | 0.970699i | \(-0.422755\pi\) | ||||
0.240298 | + | 0.970699i | \(0.422755\pi\) | |||||||
\(992\) | 7.19863 | 0.228557 | ||||||||
\(993\) | 26.1159 | 0.828763 | ||||||||
\(994\) | −14.4070 | −0.456961 | ||||||||
\(995\) | 3.12921 | 0.0992026 | ||||||||
\(996\) | 8.00000 | 0.253490 | ||||||||
\(997\) | 20.9268 | 0.662758 | 0.331379 | − | 0.943498i | \(-0.392486\pi\) | ||||
0.331379 | + | 0.943498i | \(0.392486\pi\) | |||||||
\(998\) | 38.2077 | 1.20944 | ||||||||
\(999\) | 9.73294 | 0.307937 |
(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 | 3630.2.a.bs.1.2 | 4 | ||
11.7 | odd | 10 | 330.2.m.f.181.1 | yes | 8 | ||
11.8 | odd | 10 | 330.2.m.f.31.1 | ✓ | 8 | ||
11.10 | odd | 2 | 3630.2.a.bq.1.3 | 4 | |||
33.8 | even | 10 | 990.2.n.i.361.1 | 8 | |||
33.29 | even | 10 | 990.2.n.i.181.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.f.31.1 | ✓ | 8 | 11.8 | odd | 10 | ||
330.2.m.f.181.1 | yes | 8 | 11.7 | odd | 10 | ||
990.2.n.i.181.1 | 8 | 33.29 | even | 10 | |||
990.2.n.i.361.1 | 8 | 33.8 | even | 10 | |||
3630.2.a.bq.1.3 | 4 | 11.10 | odd | 2 | |||
3630.2.a.bs.1.2 | 4 | 1.1 | even | 1 | trivial |