Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,2,Mod(1,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, 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("2004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.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: | \(16.0020205651\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 31x^{7} + 24x^{6} + 293x^{5} - 101x^{4} - 864x^{3} - 278x^{2} + 24x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(3.25977\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2004.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.25977 | 1.45781 | 0.728906 | − | 0.684613i | \(-0.240029\pi\) | ||||
0.728906 | + | 0.684613i | \(0.240029\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.95900 | 0.740431 | 0.370216 | − | 0.928946i | \(-0.379284\pi\) | ||||
0.370216 | + | 0.928946i | \(0.379284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.86584 | 0.562572 | 0.281286 | − | 0.959624i | \(-0.409239\pi\) | ||||
0.281286 | + | 0.959624i | \(0.409239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.83769 | 1.34173 | 0.670867 | − | 0.741578i | \(-0.265922\pi\) | ||||
0.670867 | + | 0.741578i | \(0.265922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.25977 | −0.841669 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.17274 | −1.01204 | −0.506019 | − | 0.862523i | \(-0.668883\pi\) | ||||
−0.506019 | + | 0.862523i | \(0.668883\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.05426 | 1.15953 | 0.579764 | − | 0.814785i | \(-0.303145\pi\) | ||||
0.579764 | + | 0.814785i | \(0.303145\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.95900 | −0.427488 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.26074 | −0.262883 | −0.131441 | − | 0.991324i | \(-0.541961\pi\) | ||||
−0.131441 | + | 0.991324i | \(0.541961\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.62609 | 1.12522 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.5500 | 1.95909 | 0.979543 | − | 0.201233i | \(-0.0644949\pi\) | ||||
0.979543 | + | 0.201233i | \(0.0644949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.26256 | −1.12479 | −0.562394 | − | 0.826869i | \(-0.690120\pi\) | ||||
−0.562394 | + | 0.826869i | \(0.690120\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.86584 | −0.324801 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.38588 | 1.07941 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.409655 | 0.0673469 | 0.0336734 | − | 0.999433i | \(-0.489279\pi\) | ||||
0.0336734 | + | 0.999433i | \(0.489279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.83769 | −0.774650 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.65442 | −0.414550 | −0.207275 | − | 0.978283i | \(-0.566460\pi\) | ||||
−0.207275 | + | 0.978283i | \(0.566460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.317178 | 0.0483692 | 0.0241846 | − | 0.999708i | \(-0.492301\pi\) | ||||
0.0241846 | + | 0.999708i | \(0.492301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.25977 | 0.485938 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.08939 | −0.596499 | −0.298249 | − | 0.954488i | \(-0.596403\pi\) | ||||
−0.298249 | + | 0.954488i | \(0.596403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.16233 | −0.451761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.17274 | 0.584300 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.15844 | −0.983287 | −0.491644 | − | 0.870796i | \(-0.663604\pi\) | ||||
−0.491644 | + | 0.870796i | \(0.663604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.08221 | 0.820125 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.05426 | −0.669453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.72693 | −1.13615 | −0.568074 | − | 0.822977i | \(-0.692311\pi\) | ||||
−0.568074 | + | 0.822977i | \(0.692311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89631 | 1.26709 | 0.633546 | − | 0.773705i | \(-0.281599\pi\) | ||||
0.633546 | + | 0.773705i | \(0.281599\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.95900 | 0.246810 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.7697 | 1.95600 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.55284 | −0.800557 | −0.400278 | − | 0.916394i | \(-0.631087\pi\) | ||||
−0.400278 | + | 0.916394i | \(0.631087\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.26074 | 0.151775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0764 | −1.19585 | −0.597927 | − | 0.801550i | \(-0.704009\pi\) | ||||
−0.597927 | + | 0.801550i | \(0.704009\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.8701 | −1.38929 | −0.694647 | − | 0.719351i | \(-0.744439\pi\) | ||||
−0.694647 | + | 0.719351i | \(0.744439\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.62609 | −0.649645 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.65518 | 0.416546 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.70687 | −0.304547 | −0.152273 | − | 0.988338i | \(-0.548659\pi\) | ||||
−0.152273 | + | 0.988338i | \(0.548659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.18316 | 0.678690 | 0.339345 | − | 0.940662i | \(-0.389795\pi\) | ||||
0.339345 | + | 0.940662i | \(0.389795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.6022 | −1.47536 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.5500 | −1.13108 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6820 | 1.55629 | 0.778147 | − | 0.628082i | \(-0.216160\pi\) | ||||
0.778147 | + | 0.628082i | \(0.216160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.47702 | 0.993461 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.26256 | 0.649397 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.4757 | 1.69037 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3373 | 1.04959 | 0.524796 | − | 0.851228i | \(-0.324142\pi\) | ||||
0.524796 | + | 0.851228i | \(0.324142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.86584 | 0.187524 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.40969 | 0.737292 | 0.368646 | − | 0.929570i | \(-0.379822\pi\) | ||||
0.368646 | + | 0.929570i | \(0.379822\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.02321 | 0.199353 | 0.0996763 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996763 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.38588 | −0.623198 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1811 | 0.984240 | 0.492120 | − | 0.870527i | \(-0.336222\pi\) | ||||
0.492120 | + | 0.870527i | \(0.336222\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0121 | 1.62946 | 0.814730 | − | 0.579840i | \(-0.196885\pi\) | ||||
0.814730 | + | 0.579840i | \(0.196885\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.409655 | −0.0388827 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.94341 | 0.276892 | 0.138446 | − | 0.990370i | \(-0.455789\pi\) | ||||
0.138446 | + | 0.990370i | \(0.455789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.10973 | −0.383234 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.83769 | 0.447244 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.17438 | −0.749344 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.51863 | −0.683512 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.65442 | 0.239341 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.04091 | 0.182545 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1274 | −1.25360 | −0.626802 | − | 0.779179i | \(-0.715636\pi\) | ||||
−0.626802 | + | 0.779179i | \(0.715636\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.317178 | −0.0279260 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.26678 | −0.722272 | −0.361136 | − | 0.932513i | \(-0.617611\pi\) | ||||
−0.361136 | + | 0.932513i | \(0.617611\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.90129 | 0.858550 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.25977 | −0.280556 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.27285 | −0.535926 | −0.267963 | − | 0.963429i | \(-0.586350\pi\) | ||||
−0.267963 | + | 0.963429i | \(0.586350\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3243 | 1.38461 | 0.692304 | − | 0.721606i | \(-0.256596\pi\) | ||||
0.692304 | + | 0.721606i | \(0.256596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.08939 | 0.344389 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.02636 | 0.754822 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.3906 | 2.85598 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.16233 | 0.260825 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.806495 | −0.0660707 | −0.0330353 | − | 0.999454i | \(-0.510517\pi\) | ||||
−0.0330353 | + | 0.999454i | \(0.510517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6840 | −1.19496 | −0.597482 | − | 0.801882i | \(-0.703832\pi\) | ||||
−0.597482 | + | 0.801882i | \(0.703832\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.17274 | −0.337346 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.4145 | −1.63973 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8590 | 1.18588 | 0.592938 | − | 0.805248i | \(-0.297968\pi\) | ||||
0.592938 | + | 0.805248i | \(0.297968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.15844 | 0.567701 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.46979 | −0.194647 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6684 | 0.913942 | 0.456971 | − | 0.889482i | \(-0.348934\pi\) | ||||
0.456971 | + | 0.889482i | \(0.348934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.08221 | −0.473500 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4032 | 0.800248 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.05426 | 0.386509 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.8278 | −1.88763 | −0.943813 | − | 0.330481i | \(-0.892789\pi\) | ||||
−0.943813 | + | 0.330481i | \(0.892789\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.0215 | 0.833147 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.72693 | 0.655956 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.8021 | −1.62957 | −0.814783 | − | 0.579766i | \(-0.803144\pi\) | ||||
−0.814783 | + | 0.579766i | \(0.803144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5477 | 1.37864 | 0.689320 | − | 0.724457i | \(-0.257909\pi\) | ||||
0.689320 | + | 0.724457i | \(0.257909\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.89631 | −0.731556 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.33538 | 0.0981792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.78566 | −0.569344 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.95900 | −0.142496 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.90014 | −0.643992 | −0.321996 | − | 0.946741i | \(-0.604354\pi\) | ||||
−0.321996 | + | 0.946741i | \(0.604354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.4480 | 1.61584 | 0.807921 | − | 0.589291i | \(-0.200593\pi\) | ||||
0.807921 | + | 0.589291i | \(0.200593\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.7697 | −1.12929 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.49823 | −0.605474 | −0.302737 | − | 0.953074i | \(-0.597900\pi\) | ||||
−0.302737 | + | 0.953074i | \(0.597900\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.02067 | 0.214129 | 0.107065 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107065 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.55284 | 0.462202 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.6674 | 1.45057 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.65279 | −0.604337 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.26074 | −0.0876276 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.43045 | 0.652318 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8920 | 1.16289 | 0.581447 | − | 0.813584i | \(-0.302487\pi\) | ||||
0.581447 | + | 0.813584i | \(0.302487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.0764 | 0.690427 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.03393 | 0.0705132 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.2683 | −0.832829 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.8701 | 0.802109 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.1864 | −1.35788 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.393347 | 0.0263405 | 0.0131702 | − | 0.999913i | \(-0.495808\pi\) | ||||
0.0131702 | + | 0.999913i | \(0.495808\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.62609 | 0.375073 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.13362 | 0.606220 | 0.303110 | − | 0.952956i | \(-0.401975\pi\) | ||||
0.303110 | + | 0.952956i | \(0.401975\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.86675 | −0.387686 | −0.193843 | − | 0.981033i | \(-0.562095\pi\) | ||||
−0.193843 | + | 0.981033i | \(0.562095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.65518 | −0.240493 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.0755 | 0.856605 | 0.428302 | − | 0.903635i | \(-0.359112\pi\) | ||||
0.428302 | + | 0.903635i | \(0.359112\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.3305 | −0.869584 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.70687 | 0.175830 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4797 | 1.00130 | 0.500648 | − | 0.865651i | \(-0.333095\pi\) | ||||
0.500648 | + | 0.865651i | \(0.333095\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.96592 | 0.641962 | 0.320981 | − | 0.947086i | \(-0.395988\pi\) | ||||
0.320981 | + | 0.947086i | \(0.395988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.3085 | −0.658584 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.4509 | 1.55578 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.18316 | −0.391842 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1882 | −0.769310 | −0.384655 | − | 0.923060i | \(-0.625680\pi\) | ||||
−0.384655 | + | 0.923060i | \(0.625680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.35234 | −0.147891 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.6022 | 0.851800 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.91332 | −0.493619 | −0.246810 | − | 0.969064i | \(-0.579382\pi\) | ||||
−0.246810 | + | 0.969064i | \(0.579382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.802513 | 0.0498658 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5500 | 0.653029 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.615803 | 0.0379721 | 0.0189860 | − | 0.999820i | \(-0.493956\pi\) | ||||
0.0189860 | + | 0.999820i | \(0.493956\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.3349 | −1.43345 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.6820 | −0.898527 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.5177 | −1.49487 | −0.747436 | − | 0.664334i | \(-0.768715\pi\) | ||||
−0.747436 | + | 0.664334i | \(0.768715\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4785 | 1.60846 | 0.804228 | − | 0.594321i | \(-0.202579\pi\) | ||||
0.804228 | + | 0.594321i | \(0.202579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.47702 | −0.573575 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.4974 | 0.633017 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.05737 | −0.303868 | −0.151934 | − | 0.988391i | \(-0.548550\pi\) | ||||
−0.151934 | + | 0.988391i | \(0.548550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.26256 | −0.374929 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1625 | 1.56073 | 0.780363 | − | 0.625326i | \(-0.215034\pi\) | ||||
0.780363 | + | 0.625326i | \(0.215034\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.9055 | −1.71826 | −0.859128 | − | 0.511761i | \(-0.828993\pi\) | ||||
−0.859128 | + | 0.511761i | \(0.828993\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.4757 | −0.975938 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.20000 | −0.306946 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.411724 | 0.0242191 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.3373 | −0.605982 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.3626 | −1.24802 | −0.624009 | − | 0.781417i | \(-0.714497\pi\) | ||||
−0.624009 | + | 0.781417i | \(0.714497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.4478 | −1.65629 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.86584 | −0.108267 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.09907 | −0.352719 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.621351 | 0.0358141 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.40969 | −0.425676 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.2597 | 1.84718 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.5731 | 1.28832 | 0.644158 | − | 0.764892i | \(-0.277208\pi\) | ||||
0.644158 | + | 0.764892i | \(0.277208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.02321 | −0.115096 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.9825 | −1.01969 | −0.509846 | − | 0.860266i | \(-0.670298\pi\) | ||||
−0.509846 | + | 0.860266i | \(0.670298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.05074 | −0.0593913 | −0.0296957 | − | 0.999559i | \(-0.509454\pi\) | ||||
−0.0296957 | + | 0.999559i | \(0.509454\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.38588 | 0.359803 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.29356 | −0.0726537 | −0.0363269 | − | 0.999340i | \(-0.511566\pi\) | ||||
−0.0363269 | + | 0.999340i | \(0.511566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.6846 | 1.10213 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.1811 | −0.568251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.0901 | −1.17348 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.2173 | 1.50974 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.0121 | −0.940769 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.01110 | −0.441666 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.42036 | −0.133035 | −0.0665175 | − | 0.997785i | \(-0.521189\pi\) | ||||
−0.0665175 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.409655 | 0.0224490 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.3607 | −1.16706 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.02901 | −0.491842 | −0.245921 | − | 0.969290i | \(-0.579090\pi\) | ||||
−0.245921 | + | 0.969290i | \(0.579090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.94341 | −0.159864 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6849 | −0.632775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9080 | −1.07493 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.10973 | 0.221260 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.0918 | 1.07858 | 0.539292 | − | 0.842119i | \(-0.318692\pi\) | ||||
0.539292 | + | 0.842119i | \(0.318692\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.7445 | −0.842782 | −0.421391 | − | 0.906879i | \(-0.638458\pi\) | ||||
−0.421391 | + | 0.906879i | \(0.638458\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.83769 | −0.258217 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8715 | −0.844757 | −0.422379 | − | 0.906419i | \(-0.638805\pi\) | ||||
−0.422379 | + | 0.906419i | \(0.638805\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −32.8469 | −1.74333 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.17438 | 0.432634 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.1278 | −1.48453 | −0.742265 | − | 0.670107i | \(-0.766248\pi\) | ||||
−0.742265 | + | 0.670107i | \(0.766248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.54557 | 0.344504 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.51863 | 0.394626 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38.6939 | −2.02533 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.0328 | −0.993504 | −0.496752 | − | 0.867892i | \(-0.665474\pi\) | ||||
−0.496752 | + | 0.867892i | \(0.665474\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.65442 | −0.138183 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0234 | −0.728057 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6675 | −0.655899 | −0.327949 | − | 0.944695i | \(-0.606358\pi\) | ||||
−0.327949 | + | 0.944695i | \(0.606358\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.04091 | −0.105392 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 51.0376 | 2.62857 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.31841 | 0.427288 | 0.213644 | − | 0.976912i | \(-0.431467\pi\) | ||||
0.213644 | + | 0.976912i | \(0.431467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.1274 | 0.723769 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.2821 | −1.49624 | −0.748122 | − | 0.663561i | \(-0.769044\pi\) | ||||
−0.748122 | + | 0.663561i | \(0.769044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.9150 | 0.607247 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.317178 | 0.0161231 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.3851 | −0.830756 | −0.415378 | − | 0.909649i | \(-0.636351\pi\) | ||||
−0.415378 | + | 0.909649i | \(0.636351\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.26074 | 0.266047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.26678 | 0.417004 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.82378 | −0.443972 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2130 | −0.663140 | −0.331570 | − | 0.943431i | \(-0.607578\pi\) | ||||
−0.331570 | + | 0.943431i | \(0.607578\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.90129 | −0.495684 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.20672 | −0.210074 | −0.105037 | − | 0.994468i | \(-0.533496\pi\) | ||||
−0.105037 | + | 0.994468i | \(0.533496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.2963 | −1.50917 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.25977 | 0.161979 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.764352 | 0.0378875 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6454 | −1.11974 | −0.559871 | − | 0.828580i | \(-0.689149\pi\) | ||||
−0.559871 | + | 0.828580i | \(0.689149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.27285 | 0.309417 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.0960 | −0.841240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.1557 | 0.989404 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.3243 | −0.799404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.1237 | −0.787693 | −0.393846 | − | 0.919176i | \(-0.628856\pi\) | ||||
−0.393846 | + | 0.919176i | \(0.628856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3944 | 0.896487 | 0.448244 | − | 0.893911i | \(-0.352050\pi\) | ||||
0.448244 | + | 0.893911i | \(0.352050\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.08939 | −0.198833 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.4762 | −1.13876 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.3868 | 0.938195 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.02636 | −0.435797 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3846 | 0.885557 | 0.442779 | − | 0.896631i | \(-0.353993\pi\) | ||||
0.442779 | + | 0.896631i | \(0.353993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7250 | 0.755694 | 0.377847 | − | 0.925868i | \(-0.376664\pi\) | ||||
0.377847 | + | 0.925868i | \(0.376664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.3906 | −1.64890 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.37212 | −0.304820 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.49754 | 0.310111 | 0.155055 | − | 0.987906i | \(-0.450444\pi\) | ||||
0.155055 | + | 0.987906i | \(0.450444\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.16233 | −0.150587 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.33495 | 0.396005 | 0.198003 | − | 0.980201i | \(-0.436555\pi\) | ||||
0.198003 | + | 0.980201i | \(0.436555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.8601 | 2.26879 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.806495 | 0.0381459 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.4466 | −1.76721 | −0.883607 | − | 0.468230i | \(-0.844892\pi\) | ||||
−0.883607 | + | 0.468230i | \(0.844892\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.95272 | −0.233215 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.6840 | 0.689913 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 30.8929 | 1.44828 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9246 | −0.838478 | −0.419239 | − | 0.907876i | \(-0.637703\pi\) | ||||
−0.419239 | + | 0.907876i | \(0.637703\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.17274 | 0.194767 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.4054 | 1.78872 | 0.894359 | − | 0.447349i | \(-0.147632\pi\) | ||||
0.894359 | + | 0.447349i | \(0.147632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.3091 | −1.08327 | −0.541633 | − | 0.840615i | \(-0.682194\pi\) | ||||
−0.541633 | + | 0.840615i | \(0.682194\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.4145 | 0.946699 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.1638 | −1.11817 | −0.559084 | − | 0.829111i | \(-0.688847\pi\) | ||||
−0.559084 | + | 0.829111i | \(0.688847\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8370 | −0.592757 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.8590 | −0.684666 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.591804 | 0.0272112 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.4357 | 1.30472 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.15844 | −0.327762 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.6876 | −1.31077 | −0.655384 | − | 0.755296i | \(-0.727493\pi\) | ||||
−0.655384 | + | 0.755296i | \(0.727493\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.98178 | 0.0903616 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.46979 | 0.112379 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.6971 | 1.53011 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.6346 | 1.02567 | 0.512835 | − | 0.858487i | \(-0.328595\pi\) | ||||
0.512835 | + | 0.858487i | \(0.328595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.6684 | −0.527665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.7912 | 0.802905 | 0.401452 | − | 0.915880i | \(-0.368506\pi\) | ||||
0.401452 | + | 0.915880i | \(0.368506\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.0224 | −1.98267 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.08221 | 0.273375 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.7397 | −0.885448 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0860 | 1.03347 | 0.516736 | − | 0.856145i | \(-0.327147\pi\) | ||||
0.516736 | + | 0.856145i | \(0.327147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9514 | 0.845002 | 0.422501 | − | 0.906362i | \(-0.361152\pi\) | ||||
0.422501 | + | 0.906362i | \(0.361152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.1539 | 1.07483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.4032 | −0.462023 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.7388 | −0.741935 | −0.370968 | − | 0.928646i | \(-0.620974\pi\) | ||||
−0.370968 | + | 0.928646i | \(0.620974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.2535 | −1.02868 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.05426 | −0.223151 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.59519 | 0.290619 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.63015 | −0.335574 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.8278 | 1.08982 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.7522 | −1.74157 | −0.870787 | − | 0.491660i | \(-0.836390\pi\) | ||||
−0.870787 | + | 0.491660i | \(0.836390\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.3323 | −1.06398 | −0.531989 | − | 0.846751i | \(-0.678555\pi\) | ||||
−0.531989 | + | 0.846751i | \(0.678555\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.0215 | −0.481018 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.1320 | 1.13833 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.4105 | −0.930893 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.72693 | −0.378716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.8412 | −0.556216 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.1879 | 1.43484 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.8021 | 0.940831 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.90041 | −0.254148 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.4258 | 1.09314 | 0.546570 | − | 0.837413i | \(-0.315933\pi\) | ||||
0.546570 | + | 0.837413i | \(0.315933\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.5477 | −0.795958 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 55.4554 | 2.37545 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2511 | 1.03690 | 0.518450 | − | 0.855108i | \(-0.326509\pi\) | ||||
0.518450 | + | 0.855108i | \(0.326509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.89631 | 0.422364 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 53.3225 | 2.27161 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.30276 | −0.225496 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.33538 | −0.0566838 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.0732 | −0.426813 | −0.213407 | − | 0.976963i | \(-0.568456\pi\) | ||||
−0.213407 | + | 0.976963i | \(0.568456\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.53441 | 0.0648985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.78566 | 0.328711 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.79902 | 0.286545 | 0.143272 | − | 0.989683i | \(-0.454238\pi\) | ||||
0.143272 | + | 0.989683i | \(0.454238\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.59483 | 0.403657 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.95900 | 0.0822702 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.1444 | 0.592966 | 0.296483 | − | 0.955038i | \(-0.404186\pi\) | ||||
0.296483 | + | 0.955038i | \(0.404186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.33250 | −0.348704 | −0.174352 | − | 0.984683i | \(-0.555783\pi\) | ||||
−0.174352 | + | 0.984683i | \(0.555783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.90014 | 0.371809 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.09305 | −0.295801 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.87608 | −0.119733 | −0.0598665 | − | 0.998206i | \(-0.519067\pi\) | ||||
−0.0598665 | + | 0.998206i | \(0.519067\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.4480 | −0.932907 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.1128 | 0.502524 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3565 | −0.553170 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.7697 | 0.651999 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.86013 | −0.241874 | −0.120937 | − | 0.992660i | \(-0.538590\pi\) | ||||
−0.120937 | + | 0.992660i | \(0.538590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.6526 | −1.30422 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.49823 | 0.349571 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.1853 | 1.36276 | 0.681378 | − | 0.731932i | \(-0.261381\pi\) | ||||
0.681378 | + | 0.731932i | \(0.261381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.6466 | −1.09240 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.02067 | −0.123628 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.4862 | −0.510174 | −0.255087 | − | 0.966918i | \(-0.582104\pi\) | ||||
−0.255087 | + | 0.966918i | \(0.582104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1405 | 0.739964 | 0.369982 | − | 0.929039i | \(-0.379364\pi\) | ||||
0.369982 | + | 0.929039i | \(0.379364\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.55284 | −0.266852 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.5090 | −0.996433 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.7416 | 1.89718 | 0.948591 | − | 0.316506i | \(-0.102510\pi\) | ||||
0.948591 | + | 0.316506i | \(0.102510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.6674 | −0.837487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.7832 | −0.800342 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.1419 | −1.05586 | −0.527930 | − | 0.849288i | \(-0.677032\pi\) | ||||
−0.527930 | + | 0.849288i | \(0.677032\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.65279 | 0.348914 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.8947 | −0.438606 | −0.219303 | − | 0.975657i | \(-0.570378\pi\) | ||||
−0.219303 | + | 0.975657i | \(0.570378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.3051 | 0.655355 | 0.327678 | − | 0.944790i | \(-0.393734\pi\) | ||||
0.327678 | + | 0.944790i | \(0.393734\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.26074 | 0.0505918 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 28.7621 | 1.15233 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4776 | −0.859102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.43045 | −0.376616 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.70938 | −0.0681576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2613 | −0.926019 | −0.463010 | − | 0.886353i | \(-0.653230\pi\) | ||||
−0.463010 | + | 0.886353i | \(0.653230\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.8920 | −0.671397 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.0520 | −1.82752 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.2984 | −0.606143 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.0764 | −0.398618 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.97779 | −0.236108 | −0.118054 | − | 0.993007i | \(-0.537666\pi\) | ||||
−0.118054 | + | 0.993007i | \(0.537666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.0348 | 0.908403 | 0.454202 | − | 0.890899i | \(-0.349925\pi\) | ||||
0.454202 | + | 0.890899i | \(0.349925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.03393 | −0.0407108 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.539846 | −0.0212235 | −0.0106118 | − | 0.999944i | \(-0.503378\pi\) | ||||
−0.0106118 | + | 0.999944i | \(0.503378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.2831 | −0.639166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.2683 | 0.480834 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.6423 | 0.651262 | 0.325631 | − | 0.945497i | \(-0.394423\pi\) | ||||
0.325631 | + | 0.945497i | \(0.394423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.9478 | −1.05294 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.8701 | −0.463098 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.1742 | 1.33124 | 0.665619 | − | 0.746292i | \(-0.268168\pi\) | ||||
0.665619 | + | 0.746292i | \(0.268168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.8130 | −1.19849 | −0.599243 | − | 0.800567i | \(-0.704532\pi\) | ||||
−0.599243 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.1864 | 0.783975 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.2759 | 1.25161 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.3008 | −0.515010 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.393347 | −0.0152077 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4649 | 0.712831 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.0355 | −0.810859 | −0.405430 | − | 0.914126i | \(-0.632878\pi\) | ||||
−0.405430 | + | 0.914126i | \(0.632878\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.62609 | −0.216548 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.32794 | 0.204769 | 0.102385 | − | 0.994745i | \(-0.467353\pi\) | ||||
0.102385 | + | 0.994745i | \(0.467353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2507 | 0.777151 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.13362 | −0.350001 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.97577 | −0.305185 | −0.152592 | − | 0.988289i | \(-0.548762\pi\) | ||||
−0.152592 | + | 0.988289i | \(0.548762\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.4480 | −0.781279 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.86675 | 0.223831 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.6303 | −1.31931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.54471 | 0.287014 | 0.143507 | − | 0.989649i | \(-0.454162\pi\) | ||||
0.143507 | + | 0.989649i | \(0.454162\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.65518 | 0.138849 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.2134 | 2.01850 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0762 | 0.419540 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.0755 | −0.494561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.7808 | 1.16258 | 0.581288 | − | 0.813698i | \(-0.302549\pi\) | ||||
0.581288 | + | 0.813698i | \(0.302549\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.07050 | 0.0780906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.3305 | 0.502054 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.5156 | 0.545914 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.62232 | 0.0984834 | 0.0492417 | − | 0.998787i | \(-0.484320\pi\) | ||||
0.0492417 | + | 0.998787i | \(0.484320\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.70687 | −0.101516 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.89547 | 0.295688 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.4238 | 1.10039 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.4797 | −0.578098 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.01417 | −0.336172 | −0.168086 | − | 0.985772i | \(-0.553759\pi\) | ||||
−0.168086 | + | 0.985772i | \(0.553759\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.96346 | 0.147607 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.96592 | −0.370637 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 59.3553 | 2.20440 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0515 | −0.817846 | −0.408923 | − | 0.912569i | \(-0.634095\pi\) | ||||
−0.408923 | + | 0.912569i | \(0.634095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.32350 | −0.0489514 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.7621 | 1.91188 | 0.955938 | − | 0.293569i | \(-0.0948429\pi\) | ||||
0.955938 | + | 0.293569i | \(0.0948429\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.3085 | 0.380233 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.2266 | −0.450371 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.4176 | 1.70750 | 0.853749 | − | 0.520684i | \(-0.174323\pi\) | ||||
0.853749 | + | 0.520684i | \(0.174323\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.4509 | −0.898228 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.9648 | −1.53954 | −0.769770 | − | 0.638321i | \(-0.779629\pi\) | ||||
−0.769770 | + | 0.638321i | \(0.779629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.62899 | −0.0963187 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.18316 | 0.226230 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.9447 | 0.728762 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.9764 | 1.49525 | 0.747625 | − | 0.664121i | \(-0.231194\pi\) | ||||
0.747625 | + | 0.664121i | \(0.231194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.1882 | 0.444161 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −47.8663 | −1.74203 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.14287 | −0.114230 | −0.0571148 | − | 0.998368i | \(-0.518190\pi\) | ||||
−0.0571148 | + | 0.998368i | \(0.518190\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.35234 | 0.0853847 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9986 | 0.579949 | 0.289974 | − | 0.957034i | \(-0.406353\pi\) | ||||
0.289974 | + | 0.957034i | \(0.406353\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.3266 | 1.20650 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.6022 | −0.491787 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.2181 | −1.52441 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.4686 | −1.24297 | −0.621485 | − | 0.783426i | \(-0.713470\pi\) | ||||
−0.621485 | + | 0.783426i | \(0.713470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.91332 | 0.284991 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.97582 | 0.214935 | 0.107468 | − | 0.994209i | \(-0.465726\pi\) | ||||
0.107468 | + | 0.994209i | \(0.465726\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.2337 | −1.26563 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.802513 | −0.0287900 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.4161 | −0.480682 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.8011 | −0.672755 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.5500 | −0.377026 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.4368 | 1.72878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −48.8368 | −1.74084 | −0.870422 | − | 0.492306i | \(-0.836154\pi\) | ||||
−0.870422 | + | 0.492306i | \(0.836154\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.615803 | −0.0219232 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.76613 | 0.205020 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 47.8753 | 1.70010 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.3349 | 0.827602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.1178 | 1.42105 | 0.710523 | − | 0.703674i | \(-0.248458\pi\) | ||||
0.710523 | + | 0.703674i | \(0.248458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0639 | 0.603679 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.6820 | 0.518765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.1478 | −0.781578 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.05094 | −0.283758 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.5177 | 0.863065 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.67223 | −0.199425 | −0.0997126 | − | 0.995016i | \(-0.531792\pi\) | ||||
−0.0997126 | + | 0.995016i | \(0.531792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.49117 | 0.298165 | 0.149083 | − | 0.988825i | \(-0.452368\pi\) | ||||
0.149083 | + | 0.988825i | \(0.452368\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.4785 | −0.928642 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.0364 | 1.33236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.60310 | 0.0560854 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.47702 | 0.331154 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.01425 | 0.279699 | 0.139850 | − | 0.990173i | \(-0.455338\pi\) | ||||
0.139850 | + | 0.990173i | \(0.455338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.3868 | 1.82609 | 0.913045 | − | 0.407858i | \(-0.133724\pi\) | ||||
0.913045 | + | 0.407858i | \(0.133724\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.4974 | −0.365472 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.346898 | 0.0120628 | 0.00603141 | − | 0.999982i | \(-0.498080\pi\) | ||||
0.00603141 | + | 0.999982i | \(0.498080\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.4031 | 0.778091 | 0.389046 | − | 0.921218i | \(-0.372805\pi\) | ||||
0.389046 | + | 0.921218i | \(0.372805\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.05737 | 0.175438 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.1956 | 0.457199 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.25977 | −0.112809 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.26256 | 0.216466 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.27328 | 0.320149 | 0.160075 | − | 0.987105i | \(-0.448827\pi\) | ||||
0.160075 | + | 0.987105i | \(0.448827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.3026 | 2.83802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.1625 | −0.901086 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.9121 | 1.16661 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.7290 | −0.506094 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.9055 | 0.992035 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.516469 | −0.0177043 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.6268 | −1.08288 | −0.541440 | − | 0.840739i | \(-0.682121\pi\) | ||||
−0.541440 | + | 0.840739i | \(0.682121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.4757 | 0.563458 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0275 | 0.342533 | 0.171267 | − | 0.985225i | \(-0.445214\pi\) | ||||
0.171267 | + | 0.985225i | \(0.445214\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.1534 | −0.824102 | −0.412051 | − | 0.911161i | \(-0.635187\pi\) | ||||
−0.412051 | + | 0.911161i | \(0.635187\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.20000 | 0.177215 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.9292 | −1.32516 | −0.662582 | − | 0.748989i | \(-0.730540\pi\) | ||||
−0.662582 | + | 0.748989i | \(0.730540\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −80.9330 | −2.75180 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.411724 | −0.0139829 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.05059 | −0.171330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.7006 | −1.07413 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.3373 | 0.349864 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.99814 | 0.135162 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.1448 | −1.55820 | −0.779100 | − | 0.626900i | \(-0.784324\pi\) | ||||
−0.779100 | + | 0.626900i | \(0.784324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.3626 | 0.720543 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.41271 | −0.283431 | −0.141716 | − | 0.989907i | \(-0.545262\pi\) | ||||
−0.141716 | + | 0.989907i | \(0.545262\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.4167 | −1.36013 | −0.680065 | − | 0.733152i | \(-0.738048\pi\) | ||||
−0.680065 | + | 0.733152i | \(0.738048\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.4478 | 0.956261 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.8983 | −0.903156 | −0.451578 | − | 0.892232i | \(-0.649139\pi\) | ||||
−0.451578 | + | 0.892232i | \(0.649139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.6755 | −0.928208 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.86584 | 0.0625080 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.6689 | −0.691657 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71.0699 | −2.37560 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.09907 | 0.203642 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −66.0700 | −2.20356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.8703 | 0.995123 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.621351 | −0.0206773 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 60.4612 | 2.00980 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.2510 | −1.17049 | −0.585244 | − | 0.810857i | \(-0.699001\pi\) | ||||
−0.585244 | + | 0.810857i | \(0.699001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.40969 | 0.245764 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.88805 | 0.261343 | 0.130671 | − | 0.991426i | \(-0.458287\pi\) | ||||
0.130671 | + | 0.991426i | \(0.458287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.5368 | 0.381813 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −32.2597 | −1.06647 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.1946 | −0.534793 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.3691 | −0.737887 | −0.368944 | − | 0.929452i | \(-0.620280\pi\) | ||||
−0.368944 | + | 0.929452i | \(0.620280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.5731 | −0.743810 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.7467 | −1.60452 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.30476 | 0.0757799 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.02321 | 0.0664509 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.4881 | 1.39399 | 0.696994 | − | 0.717077i | \(-0.254520\pi\) | ||||
0.696994 | + | 0.717077i | \(0.254520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.9832 | −0.523830 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.9825 | 0.588719 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.3795 | −0.829997 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.4812 | 1.32246 | 0.661232 | − | 0.750181i | \(-0.270034\pi\) | ||||
0.661232 | + | 0.750181i | \(0.270034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.05074 | 0.0342896 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.8361 | 1.42902 | 0.714508 | − | 0.699627i | \(-0.246651\pi\) | ||||
0.714508 | + | 0.699627i | \(0.246651\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.34653 | 0.108978 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.38588 | −0.207733 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.4133 | −1.11828 | −0.559142 | − | 0.829072i | \(-0.688869\pi\) | ||||
−0.559142 | + | 0.829072i | \(0.688869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.4240 | −1.86406 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.29356 | 0.0419466 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.11149 | 0.0683978 | 0.0341989 | − | 0.999415i | \(-0.489112\pi\) | ||||
0.0341989 | + | 0.999415i | \(0.489112\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.0124 | −0.938819 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.6846 | −0.636314 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.2885 | −0.396816 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.21961 | 0.265149 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.1811 | 0.328080 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.1752 | 2.35559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.4443 | 0.786076 | 0.393038 | − | 0.919522i | \(-0.371424\pi\) | ||||
0.393038 | + | 0.919522i | \(0.371424\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.0901 | 0.677512 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.3151 | 0.812401 | 0.406200 | − | 0.913784i | \(-0.366853\pi\) | ||||
0.406200 | + | 0.913784i | \(0.366853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.9792 | 1.02521 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.2173 | −0.871650 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.758388 | 0.0242630 | 0.0121315 | − | 0.999926i | \(-0.496138\pi\) | ||||
0.0121315 | + | 0.999926i | \(0.496138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.3944 | 0.875528 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0121 | 0.543153 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.4057 | 0.427575 | 0.213787 | − | 0.976880i | \(-0.431420\pi\) | ||||
0.213787 | + | 0.976880i | \(0.431420\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.7023 | −0.882668 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.01110 | 0.254996 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.399879 | −0.0127154 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.74067 | 0.277657 | 0.138828 | − | 0.990316i | \(-0.455666\pi\) | ||||
0.138828 | + | 0.990316i | \(0.455666\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.42036 | 0.0768077 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.84667 | 0.312161 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.0544 | −1.71192 | −0.855960 | − | 0.517042i | \(-0.827033\pi\) | ||||
−0.855960 | + | 0.517042i | \(0.827033\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.409655 | −0.0129609 |
(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 | 2004.2.a.c.1.8 | ✓ | 9 | |
3.2 | odd | 2 | 6012.2.a.i.1.2 | 9 | |||
4.3 | odd | 2 | 8016.2.a.bc.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.c.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial | |
6012.2.a.i.1.2 | 9 | 3.2 | odd | 2 | |||
8016.2.a.bc.1.8 | 9 | 4.3 | odd | 2 |