Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1140) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.60555 | 0.984806 | 0.492403 | − | 0.870367i | \(-0.336119\pi\) | ||||
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.60555 | 1.38863 | 0.694313 | − | 0.719673i | \(-0.255708\pi\) | ||||
0.694313 | + | 0.719673i | \(0.255708\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.60555 | 1.27735 | 0.638675 | − | 0.769477i | \(-0.279483\pi\) | ||||
0.638675 | + | 0.769477i | \(0.279483\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.60555 | 0.568578 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.60555 | 0.483839 | 0.241919 | − | 0.970296i | \(-0.422223\pi\) | ||||
0.241919 | + | 0.970296i | \(0.422223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.60555 | 0.801724 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.60555 | −0.440419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.39445 | 0.558044 | 0.279022 | − | 0.960285i | \(-0.409990\pi\) | ||||
0.279022 | + | 0.960285i | \(0.409990\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.60555 | 0.737478 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.60555 | 1.03161 | 0.515807 | − | 0.856705i | \(-0.327492\pi\) | ||||
0.515807 | + | 0.856705i | \(0.327492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6056 | −1.61733 | −0.808666 | − | 0.588268i | \(-0.799810\pi\) | ||||
−0.808666 | + | 0.588268i | \(0.799810\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.211103 | −0.0301575 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.60555 | −0.621012 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.21110 | −0.678428 | −0.339214 | − | 0.940709i | \(-0.610161\pi\) | ||||
−0.339214 | + | 0.940709i | \(0.610161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.21110 | −0.923287 | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||||
−0.461644 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.60555 | 0.328269 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.60555 | −0.571248 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.21110 | 1.09316 | 0.546578 | − | 0.837408i | \(-0.315930\pi\) | ||||
0.546578 | + | 0.837408i | \(0.315930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0000 | 1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2111 | 1.23058 | 0.615289 | − | 0.788301i | \(-0.289039\pi\) | ||||
0.615289 | + | 0.788301i | \(0.289039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.60555 | 0.279344 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.60555 | 0.700187 | 0.350094 | − | 0.936715i | \(-0.386150\pi\) | ||||
0.350094 | + | 0.936715i | \(0.386150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.00000 | −0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.6056 | 1.68604 | 0.843019 | − | 0.537884i | \(-0.180776\pi\) | ||||
0.843019 | + | 0.537884i | \(0.180776\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.60555 | 0.462875 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.21110 | −0.717532 | −0.358766 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358766 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.4222 | −1.81519 | −0.907597 | − | 0.419843i | \(-0.862085\pi\) | ||||
−0.907597 | + | 0.419843i | \(0.862085\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.60555 | −0.254276 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.4222 | −1.78094 | −0.890471 | − | 0.455040i | \(-0.849625\pi\) | ||||
−0.890471 | + | 0.455040i | \(0.849625\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2111 | −1.07383 | −0.536914 | − | 0.843637i | \(-0.680410\pi\) | ||||
−0.536914 | + | 0.843637i | \(0.680410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.39445 | 0.322187 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.21110 | −0.113931 | −0.0569655 | − | 0.998376i | \(-0.518142\pi\) | ||||
−0.0569655 | + | 0.998376i | \(0.518142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.00000 | −0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.60555 | 0.425783 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.21110 | 0.477701 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2111 | 0.928282 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.60555 | 0.595603 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.4222 | −1.63471 | −0.817353 | − | 0.576137i | \(-0.804559\pi\) | ||||
−0.817353 | + | 0.576137i | \(0.804559\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.6056 | −0.933767 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3944 | 1.34502 | 0.672510 | − | 0.740088i | \(-0.265216\pi\) | ||||
0.672510 | + | 0.740088i | \(0.265216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.60555 | 0.225930 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.4222 | −1.06130 | −0.530650 | − | 0.847591i | \(-0.678052\pi\) | ||||
−0.530650 | + | 0.847591i | \(0.678052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.21110 | −0.781276 | −0.390638 | − | 0.920544i | \(-0.627745\pi\) | ||||
−0.390638 | + | 0.920544i | \(0.627745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.2111 | 1.77376 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.60555 | −0.216379 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.211103 | −0.0174114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.4222 | 1.34536 | 0.672680 | − | 0.739934i | \(-0.265143\pi\) | ||||
0.672680 | + | 0.739934i | \(0.265143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2111 | 1.21398 | 0.606989 | − | 0.794710i | \(-0.292377\pi\) | ||||
0.606989 | + | 0.794710i | \(0.292377\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.21110 | 0.410692 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.0278 | 1.33372 | 0.666858 | − | 0.745184i | \(-0.267639\pi\) | ||||
0.666858 | + | 0.745184i | \(0.267639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.60555 | −0.358542 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.78890 | 0.525341 | 0.262670 | − | 0.964886i | \(-0.415397\pi\) | ||||
0.262670 | + | 0.964886i | \(0.415397\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.21110 | 0.631623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.21110 | −0.700307 | −0.350154 | − | 0.936692i | \(-0.613871\pi\) | ||||
−0.350154 | + | 0.936692i | \(0.613871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.60555 | 0.196961 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.21110 | −0.391690 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.2111 | 1.58539 | 0.792696 | − | 0.609617i | \(-0.208677\pi\) | ||||
0.792696 | + | 0.609617i | \(0.208677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.788897 | −0.0586383 | −0.0293191 | − | 0.999570i | \(-0.509334\pi\) | ||||
−0.0293191 | + | 0.999570i | \(0.509334\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.21110 | −0.533060 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.39445 | −0.249565 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.21110 | 0.673583 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.60555 | 0.189526 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.81665 | 0.420878 | 0.210439 | − | 0.977607i | \(-0.432511\pi\) | ||||
0.210439 | + | 0.977607i | \(0.432511\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.605551 | −0.0435885 | −0.0217943 | − | 0.999762i | \(-0.506938\pi\) | ||||
−0.0217943 | + | 0.999762i | \(0.506938\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.60555 | −0.329810 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.0000 | 0.997459 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2111 | −1.22006 | −0.610031 | − | 0.792377i | \(-0.708843\pi\) | ||||
−0.610031 | + | 0.792377i | \(0.708843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.78890 | 0.476487 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.60555 | −0.461352 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.60555 | 0.318573 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.21110 | 0.631134 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.6056 | 0.723293 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4222 | −0.707505 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | 0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.21110 | 0.619606 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.4222 | 0.697922 | 0.348961 | − | 0.937137i | \(-0.386534\pi\) | ||||
0.348961 | + | 0.937137i | \(0.386534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.2111 | 0.876852 | 0.438426 | − | 0.898767i | \(-0.355536\pi\) | ||||
0.438426 | + | 0.898767i | \(0.355536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.21110 | −0.212196 | −0.106098 | − | 0.994356i | \(-0.533836\pi\) | ||||
−0.106098 | + | 0.994356i | \(0.533836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | 0.789542 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.4222 | −1.07585 | −0.537927 | − | 0.842991i | \(-0.680792\pi\) | ||||
−0.537927 | + | 0.842991i | \(0.680792\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.00000 | −0.519656 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.8167 | −1.66994 | −0.834970 | − | 0.550295i | \(-0.814515\pi\) | ||||
−0.834970 | + | 0.550295i | \(0.814515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.211103 | 0.0134868 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.60555 | 0.293044 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.2111 | 0.710475 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.18335 | 0.390289 | 0.195145 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195145 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.21110 | 0.579097 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.78890 | 0.173967 | 0.0869833 | − | 0.996210i | \(-0.472277\pi\) | ||||
0.0869833 | + | 0.996210i | \(0.472277\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.84441 | 0.549565 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.60555 | 0.161280 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.21110 | −0.444656 | −0.222328 | − | 0.974972i | \(-0.571366\pi\) | ||||
−0.222328 | + | 0.974972i | \(0.571366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.60555 | 0.404253 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.3944 | −1.06056 | −0.530279 | − | 0.847823i | \(-0.677913\pi\) | ||||
−0.530279 | + | 0.847823i | \(0.677913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6333 | −0.706673 | −0.353337 | − | 0.935496i | \(-0.614953\pi\) | ||||
−0.353337 | + | 0.935496i | \(0.614953\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.0000 | 0.726273 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.60555 | 0.277725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.2389 | 1.08804 | 0.544020 | − | 0.839073i | \(-0.316902\pi\) | ||||
0.544020 | + | 0.839073i | \(0.316902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.6056 | 1.10599 | 0.552993 | − | 0.833186i | \(-0.313486\pi\) | ||||
0.552993 | + | 0.833186i | \(0.313486\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.2111 | 1.01594 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.6056 | 0.973435 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.6333 | 1.14699 | 0.573495 | − | 0.819209i | \(-0.305587\pi\) | ||||
0.573495 | + | 0.819209i | \(0.305587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.21110 | 0.303402 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.60555 | 0.267241 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.21110 | 0.532692 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.6333 | −1.59276 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.21110 | −0.414267 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.21110 | 0.412907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.6333 | 0.663948 | 0.331974 | − | 0.943289i | \(-0.392285\pi\) | ||||
0.331974 | + | 0.943289i | \(0.392285\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4222 | −1.04800 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.6056 | −0.941614 | −0.470807 | − | 0.882236i | \(-0.656037\pi\) | ||||
−0.470807 | + | 0.882236i | \(0.656037\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.788897 | 0.0445911 | 0.0222956 | − | 0.999751i | \(-0.492903\pi\) | ||||
0.0222956 | + | 0.999751i | \(0.492903\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.60555 | −0.146806 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.42221 | −0.360707 | −0.180353 | − | 0.983602i | \(-0.557724\pi\) | ||||
−0.180353 | + | 0.983602i | \(0.557724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.4222 | −1.02823 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | 0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.60555 | 0.255470 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.2111 | −0.619975 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.6333 | −0.861892 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.39445 | 0.186015 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.02776 | 0.164932 | 0.0824662 | − | 0.996594i | \(-0.473720\pi\) | ||||
0.0824662 | + | 0.996594i | \(0.473720\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.21110 | −0.0657781 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.4222 | −0.997618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7889 | −1.01451 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.00000 | −0.107676 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.6333 | −1.16134 | −0.580668 | − | 0.814140i | \(-0.697209\pi\) | ||||
−0.580668 | + | 0.814140i | \(0.697209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.8444 | 1.86518 | 0.932589 | − | 0.360939i | \(-0.117544\pi\) | ||||
0.932589 | + | 0.360939i | \(0.117544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.60555 | 0.245826 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.422205 | 0.0224717 | 0.0112359 | − | 0.999937i | \(-0.496423\pi\) | ||||
0.0112359 | + | 0.999937i | \(0.496423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.21110 | −0.488875 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.21110 | 0.275801 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.8167 | 0.729215 | 0.364608 | − | 0.931161i | \(-0.381203\pi\) | ||||
0.364608 | + | 0.931161i | \(0.381203\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.2111 | 0.535944 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.0278 | −1.30644 | −0.653219 | − | 0.757169i | \(-0.726582\pi\) | ||||
−0.653219 | + | 0.757169i | \(0.726582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.60555 | 0.343871 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.6056 | 0.859803 | 0.429901 | − | 0.902876i | \(-0.358548\pi\) | ||||
0.429901 | + | 0.902876i | \(0.358548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.4222 | −1.35722 | −0.678609 | − | 0.734500i | \(-0.737417\pi\) | ||||
−0.678609 | + | 0.734500i | \(0.737417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.4222 | −0.943798 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | 0.613171 | 0.306586 | − | 0.951843i | \(-0.400813\pi\) | ||||
0.306586 | + | 0.951843i | \(0.400813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | −0.611577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.6056 | −0.539110 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.4222 | 1.84668 | 0.923340 | − | 0.383984i | \(-0.125448\pi\) | ||||
0.923340 | + | 0.383984i | \(0.125448\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.3944 | 0.776547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.57779 | −0.380319 | −0.190159 | − | 0.981753i | \(-0.560900\pi\) | ||||
−0.190159 | + | 0.981753i | \(0.560900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.60555 | 0.130441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.3944 | 1.26814 | 0.634069 | − | 0.773276i | \(-0.281383\pi\) | ||||
0.634069 | + | 0.773276i | \(0.281383\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.4222 | −0.917675 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.6333 | 0.774914 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.7889 | −0.632370 | −0.316185 | − | 0.948698i | \(-0.602402\pi\) | ||||
−0.316185 | + | 0.948698i | \(0.602402\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4222 | −0.612742 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.5778 | −0.668120 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.2111 | −0.550331 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.21110 | −0.451070 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.02776 | 0.343328 | 0.171664 | − | 0.985156i | \(-0.445086\pi\) | ||||
0.171664 | + | 0.985156i | \(0.445086\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.42221 | −0.410473 | −0.205237 | − | 0.978712i | \(-0.565796\pi\) | ||||
−0.205237 | + | 0.978712i | \(0.565796\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.00000 | −0.291730 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.7889 | −0.909258 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.2111 | 1.02408 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.21110 | 0.443683 | 0.221842 | − | 0.975083i | \(-0.428793\pi\) | ||||
0.221842 | + | 0.975083i | \(0.428793\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6056 | −0.798012 | −0.399006 | − | 0.916948i | \(-0.630645\pi\) | ||||
−0.399006 | + | 0.916948i | \(0.630645\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.60555 | −0.124927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | 0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.4222 | −1.64288 | −0.821441 | − | 0.570293i | \(-0.806830\pi\) | ||||
−0.821441 | + | 0.570293i | \(0.806830\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.211103 | −0.0100525 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.8444 | −0.895325 | −0.447662 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447662 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.60555 | −0.313133 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.4222 | 0.776744 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.2389 | −0.860745 | −0.430372 | − | 0.902651i | \(-0.641618\pi\) | ||||
−0.430372 | + | 0.902651i | \(0.641618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.4222 | 1.43253 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0555 | 1.49949 | 0.749747 | − | 0.661725i | \(-0.230175\pi\) | ||||
0.749747 | + | 0.661725i | \(0.230175\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8444 | −1.06397 | −0.531985 | − | 0.846754i | \(-0.678554\pi\) | ||||
−0.531985 | + | 0.846754i | \(0.678554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.0278 | −1.53493 | −0.767465 | − | 0.641091i | \(-0.778482\pi\) | ||||
−0.767465 | + | 0.641091i | \(0.778482\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | 0.185496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.8444 | −1.05711 | −0.528557 | − | 0.848898i | \(-0.677267\pi\) | ||||
−0.528557 | + | 0.848898i | \(0.677267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4222 | −0.481253 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.2111 | 0.700891 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48.8444 | −2.24587 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.6056 | −1.30702 | −0.653510 | − | 0.756917i | \(-0.726704\pi\) | ||||
−0.653510 | + | 0.756917i | \(0.726704\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.6333 | 0.712817 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.21110 | 0.237113 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.6056 | −0.754019 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.366692 | −0.0166164 | −0.00830821 | − | 0.999965i | \(-0.502645\pi\) | ||||
−0.00830821 | + | 0.999965i | \(0.502645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.0278 | 0.770022 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2389 | 0.552332 | 0.276166 | − | 0.961110i | \(-0.410936\pi\) | ||||
0.276166 | + | 0.961110i | \(0.410936\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.21110 | 0.234696 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.60555 | −0.207004 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0000 | 1.07655 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.6333 | 1.23704 | 0.618518 | − | 0.785770i | \(-0.287733\pi\) | ||||
0.618518 | + | 0.785770i | \(0.287733\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.78890 | 0.303306 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.7889 | −0.570229 | −0.285114 | − | 0.958494i | \(-0.592032\pi\) | ||||
−0.285114 | + | 0.958494i | \(0.592032\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.21110 | 0.320890 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.21110 | 0.364668 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.4500 | −1.57129 | −0.785646 | − | 0.618676i | \(-0.787669\pi\) | ||||
−0.785646 | + | 0.618676i | \(0.787669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.6333 | 0.691577 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.4222 | 0.811779 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.6333 | −1.21531 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.21110 | −0.404323 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.18335 | −0.183276 | −0.0916379 | − | 0.995792i | \(-0.529210\pi\) | ||||
−0.0916379 | + | 0.995792i | \(0.529210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.2111 | 1.10240 | 0.551202 | − | 0.834372i | \(-0.314169\pi\) | ||||
0.551202 | + | 0.834372i | \(0.314169\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.60555 | 0.113716 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | −0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.21110 | −0.226143 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.4222 | 1.31773 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.4222 | 0.796461 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.2111 | 0.915327 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.972244 | −0.0418775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.788897 | −0.0338548 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2111 | 0.480231 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7889 | 0.974383 | 0.487191 | − | 0.873295i | \(-0.338021\pi\) | ||||
0.487191 | + | 0.873295i | \(0.338021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.21110 | −0.307762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.60555 | 0.111000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.8444 | −0.886394 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.39445 | −0.144086 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.42221 | −0.187375 | −0.0936874 | − | 0.995602i | \(-0.529865\pi\) | ||||
−0.0936874 | + | 0.995602i | \(0.529865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.8444 | −2.06590 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.21110 | 0.388893 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.6333 | −1.33318 | −0.666592 | − | 0.745422i | \(-0.732248\pi\) | ||||
−0.666592 | + | 0.745422i | \(0.732248\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.21110 | 0.0509515 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.60555 | 0.109423 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.4500 | 1.65383 | 0.826914 | − | 0.562328i | \(-0.190094\pi\) | ||||
0.826914 | + | 0.562328i | \(0.190094\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.63331 | −0.319444 | −0.159722 | − | 0.987162i | \(-0.551060\pi\) | ||||
−0.159722 | + | 0.987162i | \(0.551060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.81665 | 0.242994 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.00000 | 0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.2111 | −0.966291 | −0.483145 | − | 0.875540i | \(-0.660506\pi\) | ||||
−0.483145 | + | 0.875540i | \(0.660506\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.605551 | −0.0251659 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.2111 | 1.21188 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.60555 | −0.190416 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.4222 | −0.512719 | −0.256360 | − | 0.966581i | \(-0.582523\pi\) | ||||
−0.256360 | + | 0.966581i | \(0.582523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.0000 | 0.575883 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.57779 | −0.146922 | −0.0734612 | − | 0.997298i | \(-0.523405\pi\) | ||||
−0.0734612 | + | 0.997298i | \(0.523405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.21110 | −0.213634 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.2111 | −0.704404 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.8444 | −1.50542 | −0.752711 | − | 0.658351i | \(-0.771254\pi\) | ||||
−0.752711 | + | 0.658351i | \(0.771254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.78890 | 0.195343 | 0.0976716 | − | 0.995219i | \(-0.468861\pi\) | ||||
0.0976716 | + | 0.995219i | \(0.468861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.2111 | −0.415140 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.6333 | 0.959246 | 0.479623 | − | 0.877475i | \(-0.340773\pi\) | ||||
0.479623 | + | 0.877475i | \(0.340773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.78890 | 0.275100 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.6333 | −1.11792 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.78890 | 0.193422 | 0.0967109 | − | 0.995313i | \(-0.469168\pi\) | ||||
0.0967109 | + | 0.995313i | \(0.469168\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.60555 | −0.266362 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000 | 1.36879 | 0.684394 | − | 0.729112i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729112i | \(0.260067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.36669 | 0.175512 | 0.0877561 | − | 0.996142i | \(-0.472030\pi\) | ||||
0.0877561 | + | 0.996142i | \(0.472030\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | 0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.2111 | 0.689548 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.60555 | 0.183928 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.78890 | 0.270691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.8444 | −1.46675 | −0.733376 | − | 0.679823i | \(-0.762057\pi\) | ||||
−0.733376 | + | 0.679823i | \(0.762057\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.00000 | 0.158986 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 18.4222 | 0.731063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.972244 | −0.0385217 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.21110 | 0.364386 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.4500 | 1.40019 | 0.700095 | − | 0.714050i | \(-0.253141\pi\) | ||||
0.700095 | + | 0.714050i | \(0.253141\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.39445 | −0.212736 | −0.106368 | − | 0.994327i | \(-0.533922\pi\) | ||||
−0.106368 | + | 0.994327i | \(0.533922\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.6056 | 0.417593 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.36669 | 0.0930443 | 0.0465221 | − | 0.998917i | \(-0.485186\pi\) | ||||
0.0465221 | + | 0.998917i | \(0.485186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.4222 | −0.408478 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.0000 | 1.64359 | 0.821794 | − | 0.569785i | \(-0.192974\pi\) | ||||
0.821794 | + | 0.569785i | \(0.192974\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.3944 | −0.601511 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.2111 | −1.21397 | −0.606986 | − | 0.794713i | \(-0.707621\pi\) | ||||
−0.606986 | + | 0.794713i | \(0.707621\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.21110 | 0.357730 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.60555 | −0.101039 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.21110 | 0.201775 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.4222 | 0.402946 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.2111 | −1.28210 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.6056 | 1.41104 | 0.705520 | − | 0.708690i | \(-0.250713\pi\) | ||||
0.705520 | + | 0.708690i | \(0.250713\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.4222 | 0.400558 | 0.200279 | − | 0.979739i | \(-0.435815\pi\) | ||||
0.200279 | + | 0.979739i | \(0.435815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.2666 | 1.66042 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.2111 | 0.506251 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.0000 | 1.83667 | 0.918334 | − | 0.395805i | \(-0.129534\pi\) | ||||
0.918334 | + | 0.395805i | \(0.129534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.4222 | 0.474628 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.21110 | −0.122511 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.0555 | 1.59987 | 0.799934 | − | 0.600089i | \(-0.204868\pi\) | ||||
0.799934 | + | 0.600089i | \(0.204868\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.0000 | 0.455842 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.21110 | 0.349397 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2111 | 0.500406 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.4222 | −0.621145 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.39445 | 0.128024 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.00000 | 0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.7889 | −0.706629 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.6333 | −0.962679 | −0.481340 | − | 0.876534i | \(-0.659850\pi\) | ||||
−0.481340 | + | 0.876534i | \(0.659850\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.00000 | −0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.2111 | −0.793250 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.8167 | −0.964141 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2389 | −0.605607 | −0.302804 | − | 0.953053i | \(-0.597923\pi\) | ||||
−0.302804 | + | 0.953053i | \(0.597923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.0000 | −1.78761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.0000 | −0.371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.60555 | 0.0967677 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3944 | 0.645124 | 0.322562 | − | 0.946548i | \(-0.395456\pi\) | ||||
0.322562 | + | 0.946548i | \(0.395456\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.2111 | −0.784521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.4222 | −0.902055 | −0.451027 | − | 0.892510i | \(-0.648942\pi\) | ||||
−0.451027 | + | 0.892510i | \(0.648942\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.211103 | 0.00778663 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.4222 | −0.678591 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.4222 | −1.41338 | −0.706692 | − | 0.707521i | \(-0.749813\pi\) | ||||
−0.706692 | + | 0.707521i | \(0.749813\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.60555 | 0.169189 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.0000 | 0.733729 | 0.366864 | − | 0.930274i | \(-0.380431\pi\) | ||||
0.366864 | + | 0.930274i | \(0.380431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.4222 | −0.601663 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2111 | 0.410193 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.0000 | −1.75388 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.8444 | −1.49043 | −0.745217 | − | 0.666822i | \(-0.767654\pi\) | ||||
−0.745217 | + | 0.666822i | \(0.767654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.18335 | 0.225334 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0555 | −1.31046 | −0.655230 | − | 0.755429i | \(-0.727428\pi\) | ||||
−0.655230 | + | 0.755429i | \(0.727428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.21110 | 0.334342 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.2111 | −1.05751 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | −0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.0000 | −0.866590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.4222 | −0.736444 | −0.368222 | − | 0.929738i | \(-0.620033\pi\) | ||||
−0.368222 | + | 0.929738i | \(0.620033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78890 | 0.100440 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.2666 | −1.55619 | −0.778096 | − | 0.628145i | \(-0.783814\pi\) | ||||
−0.778096 | + | 0.628145i | \(0.783814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.00000 | −0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.84441 | 0.317291 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.60555 | 0.236668 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.4222 | 1.51799 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.60555 | 0.0931148 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.2111 | −0.542908 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.6333 | 0.699852 | 0.349926 | − | 0.936777i | \(-0.386207\pi\) | ||||
0.349926 | + | 0.936777i | \(0.386207\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.21110 | −0.256722 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.15559 | −0.112200 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.2111 | −1.17936 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.2111 | 0.609649 | 0.304824 | − | 0.952409i | \(-0.401402\pi\) | ||||
0.304824 | + | 0.952409i | \(0.401402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.60555 | 0.233396 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.6333 | 0.975158 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.21110 | −0.183667 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.3944 | −0.612314 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −48.4222 | −1.70243 | −0.851217 | − | 0.524814i | \(-0.824135\pi\) | ||||
−0.851217 | + | 0.524814i | \(0.824135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.8444 | 1.43424 | 0.717121 | − | 0.696949i | \(-0.245460\pi\) | ||||
0.717121 | + | 0.696949i | \(0.245460\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.6333 | −0.407998 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.0278 | −0.596456 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.6056 | −0.371041 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0000 | 0.419314 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.2111 | 1.50808 | 0.754039 | − | 0.656830i | \(-0.228103\pi\) | ||||
0.754039 | + | 0.656830i | \(0.228103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.8167 | 1.66678 | 0.833392 | − | 0.552683i | \(-0.186396\pi\) | ||||
0.833392 | + | 0.552683i | \(0.186396\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.60555 | 0.160345 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.6333 | 0.960904 | 0.480452 | − | 0.877021i | \(-0.340473\pi\) | ||||
0.480452 | + | 0.877021i | \(0.340473\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.2111 | 0.528303 | 0.264152 | − | 0.964481i | \(-0.414908\pi\) | ||||
0.264152 | + | 0.964481i | \(0.414908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.422205 | −0.0146285 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.78890 | −0.234939 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.6333 | −0.954008 | −0.477004 | − | 0.878901i | \(-0.658277\pi\) | ||||
−0.477004 | + | 0.878901i | \(0.658277\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2111 | −0.765900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.2389 | 0.628180 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.21110 | −0.282471 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.6056 | 0.914178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.6056 | 0.638541 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.78890 | 0.232720 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6333 | 1.01463 | 0.507313 | − | 0.861762i | \(-0.330639\pi\) | ||||
0.507313 | + | 0.861762i | \(0.330639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.00000 | −0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.42221 | 0.219378 | 0.109689 | − | 0.993966i | \(-0.465014\pi\) | ||||
0.109689 | + | 0.993966i | \(0.465014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.84441 | −0.301767 | −0.150884 | − | 0.988552i | \(-0.548212\pi\) | ||||
−0.150884 | + | 0.988552i | \(0.548212\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.2111 | 0.586553 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.42221 | −0.218614 | −0.109307 | − | 0.994008i | \(-0.534863\pi\) | ||||
−0.109307 | + | 0.994008i | \(0.534863\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.21110 | 0.313187 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.8444 | −1.24986 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.4222 | −0.624213 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.6056 | 0.562013 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.60555 | −0.0880837 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0278 | 0.912662 | 0.456331 | − | 0.889810i | \(-0.349163\pi\) | ||||
0.456331 | + | 0.889810i | \(0.349163\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.6333 | 0.662215 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 59.2111 | 1.99487 | 0.997436 | − | 0.0715590i | \(-0.0227974\pi\) | ||||
0.997436 | + | 0.0715590i | \(0.0227974\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.8167 | −0.936105 | −0.468052 | − | 0.883701i | \(-0.655044\pi\) | ||||
−0.468052 | + | 0.883701i | \(0.655044\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.21110 | 0.175169 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8444 | 0.699887 | 0.349943 | − | 0.936771i | \(-0.386201\pi\) | ||||
0.349943 | + | 0.936771i | \(0.386201\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.0000 | −1.60987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.60555 | 0.154292 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | −0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.2111 | −0.709009 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.21110 | 0.307550 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.4222 | −0.347600 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.6333 | −0.919579 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.788897 | 0.0262238 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.0555 | −0.997977 | −0.498988 | − | 0.866609i | \(-0.666295\pi\) | ||||
−0.498988 | + | 0.866609i | \(0.666295\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.21110 | −0.239177 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4222 | −0.345303 | −0.172652 | − | 0.984983i | \(-0.555233\pi\) | ||||
−0.172652 | + | 0.984983i | \(0.555233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.6333 | 1.70881 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.21110 | 0.238392 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40.1110 | 1.32458 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.6333 | 0.383331 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.4222 | 1.39634 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.39445 | 0.111609 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.4222 | −0.605065 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.6333 | −1.49718 | −0.748590 | − | 0.663033i | \(-0.769269\pi\) | ||||
−0.748590 | + | 0.663033i | \(0.769269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.211103 | −0.00691861 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.6056 | −0.543641 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.21110 | −0.301235 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.2111 | −0.627599 | −0.313800 | − | 0.949489i | \(-0.601602\pi\) | ||||
−0.313800 | + | 0.949489i | \(0.601602\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.788897 | 0.0257447 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.2389 | −0.985759 | −0.492879 | − | 0.870098i | \(-0.664056\pi\) | ||||
−0.492879 | + | 0.870098i | \(0.664056\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.2111 | 0.430213 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.60555 | −0.0847586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.21110 | 0.234329 | 0.117165 | − | 0.993113i | \(-0.462619\pi\) | ||||
0.117165 | + | 0.993113i | \(0.462619\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.6333 | 0.897015 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.42221 | −0.208254 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.21110 | 0.168804 | 0.0844021 | − | 0.996432i | \(-0.473102\pi\) | ||||
0.0844021 | + | 0.996432i | \(0.473102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.81665 | −0.188222 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0000 | 0.387905 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.3667 | −1.04518 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.4222 | −0.593647 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.605551 | 0.0194934 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.2389 | 0.843785 | 0.421892 | − | 0.906646i | \(-0.361366\pi\) | ||||
0.421892 | + | 0.906646i | \(0.361366\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.00000 | 0.0642493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | −0.769405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.60555 | 0.147496 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.42221 | 0.205465 | 0.102732 | − | 0.994709i | \(-0.467242\pi\) | ||||
0.102732 | + | 0.994709i | \(0.467242\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.4222 | 0.972298 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.2111 | −0.357943 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.21110 | 0.293789 | 0.146894 | − | 0.989152i | \(-0.453072\pi\) | ||||
0.146894 | + | 0.989152i | \(0.453072\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0000 | −0.446077 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15.6333 | −0.497614 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.2111 | −0.674474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.4222 | −1.60171 | −0.800857 | − | 0.598856i | \(-0.795622\pi\) | ||||
−0.800857 | + | 0.598856i | \(0.795622\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.00000 | 0.253872 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.2111 | 0.545629 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −61.6333 | −1.95195 | −0.975973 | − | 0.217891i | \(-0.930082\pi\) | ||||
−0.975973 | + | 0.217891i | \(0.930082\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.39445 | 0.107396 |
(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 | 4560.2.a.bl.1.2 | 2 | ||
4.3 | odd | 2 | 1140.2.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 3420.2.a.i.1.1 | 2 | |||
20.3 | even | 4 | 5700.2.f.n.3649.2 | 4 | |||
20.7 | even | 4 | 5700.2.f.n.3649.3 | 4 | |||
20.19 | odd | 2 | 5700.2.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.e.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
3420.2.a.i.1.1 | 2 | 12.11 | even | 2 | |||
4560.2.a.bl.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5700.2.a.u.1.2 | 2 | 20.19 | odd | 2 | |||
5700.2.f.n.3649.2 | 4 | 20.3 | even | 4 | |||
5700.2.f.n.3649.3 | 4 | 20.7 | even | 4 |