Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3200,2,Mod(1,3200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3200, 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("3200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3200 = 2^{7} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3200.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: | \(25.5521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 640) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3200.1 |
$q$-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 | ||||||||
\(3\) | −2.90321 | −1.67617 | −0.838085 | − | 0.545540i | \(-0.816325\pi\) | ||||
−0.838085 | + | 0.545540i | \(0.816325\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.52543 | 1.33249 | 0.666243 | − | 0.745735i | \(-0.267901\pi\) | ||||
0.666243 | + | 0.745735i | \(0.267901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.42864 | 1.80955 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.80642 | −1.14768 | −0.573840 | − | 0.818967i | \(-0.694547\pi\) | ||||
−0.573840 | + | 0.818967i | \(0.694547\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.62222 | 0.727272 | 0.363636 | − | 0.931541i | \(-0.381535\pi\) | ||||
0.363636 | + | 0.931541i | \(0.381535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.80642 | 1.40826 | 0.704132 | − | 0.710069i | \(-0.251336\pi\) | ||||
0.704132 | + | 0.710069i | \(0.251336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.05086 | 1.15875 | 0.579373 | − | 0.815063i | \(-0.303298\pi\) | ||||
0.579373 | + | 0.815063i | \(0.303298\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.2351 | −2.23347 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.474572 | 0.0989552 | 0.0494776 | − | 0.998775i | \(-0.484244\pi\) | ||||
0.0494776 | + | 0.998775i | \(0.484244\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.05086 | −1.35694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.75557 | −0.494915 | −0.247457 | − | 0.968899i | \(-0.579595\pi\) | ||||
−0.247457 | + | 0.968899i | \(0.579595\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.0509 | 1.92371 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.18421 | 1.18108 | 0.590538 | − | 0.807010i | \(-0.298915\pi\) | ||||
0.590538 | + | 0.807010i | \(0.298915\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.61285 | −1.21903 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.18421 | 0.809637 | 0.404819 | − | 0.914397i | \(-0.367335\pi\) | ||||
0.404819 | + | 0.914397i | \(0.367335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.95407 | 0.297992 | 0.148996 | − | 0.988838i | \(-0.452396\pi\) | ||||
0.148996 | + | 0.988838i | \(0.452396\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.33185 | −0.777730 | −0.388865 | − | 0.921295i | \(-0.627133\pi\) | ||||
−0.388865 | + | 0.921295i | \(0.627133\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.42864 | 0.775520 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8573 | −2.36049 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.37778 | 0.738695 | 0.369348 | − | 0.929291i | \(-0.379581\pi\) | ||||
0.369348 | + | 0.929291i | \(0.379581\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.6637 | −1.94225 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.05086 | −0.657565 | −0.328783 | − | 0.944406i | \(-0.606638\pi\) | ||||
−0.328783 | + | 0.944406i | \(0.606638\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2351 | −1.56654 | −0.783270 | − | 0.621682i | \(-0.786450\pi\) | ||||
−0.783270 | + | 0.621682i | \(0.786450\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.1383 | 2.41120 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.76049 | 0.948095 | 0.474047 | − | 0.880499i | \(-0.342793\pi\) | ||||
0.474047 | + | 0.880499i | \(0.342793\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.37778 | −0.165866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.85728 | −0.576453 | −0.288226 | − | 0.957562i | \(-0.593066\pi\) | ||||
−0.288226 | + | 0.957562i | \(0.593066\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.66370 | −0.779927 | −0.389964 | − | 0.920830i | \(-0.627512\pi\) | ||||
−0.389964 | + | 0.920830i | \(0.627512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.4193 | −1.52927 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.24443 | −0.590045 | −0.295022 | − | 0.955490i | \(-0.595327\pi\) | ||||
−0.295022 | + | 0.955490i | \(0.595327\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.18421 | 0.464912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1476 | −1.33338 | −0.666689 | − | 0.745336i | \(-0.732289\pi\) | ||||
−0.666689 | + | 0.745336i | \(0.732289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.80642 | 0.622514 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1017 | −1.28278 | −0.641389 | − | 0.767216i | \(-0.721642\pi\) | ||||
−0.641389 | + | 0.767216i | \(0.721642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.24443 | 0.969080 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | 0.829561 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8064 | 1.40183 | 0.700915 | − | 0.713245i | \(-0.252775\pi\) | ||||
0.700915 | + | 0.713245i | \(0.252775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −20.6637 | −2.07678 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.7146 | 1.96167 | 0.980836 | − | 0.194836i | \(-0.0624173\pi\) | ||||
0.980836 | + | 0.194836i | \(0.0624173\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.13828 | −0.309223 | −0.154612 | − | 0.987975i | \(-0.549413\pi\) | ||||
−0.154612 | + | 0.987975i | \(0.549413\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.39207 | 0.521272 | 0.260636 | − | 0.965437i | \(-0.416068\pi\) | ||||
0.260636 | + | 0.965437i | \(0.416068\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.62222 | 0.825858 | 0.412929 | − | 0.910763i | \(-0.364506\pi\) | ||||
0.412929 | + | 0.910763i | \(0.364506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.8573 | −1.97969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.51114 | 0.518444 | 0.259222 | − | 0.965818i | \(-0.416534\pi\) | ||||
0.259222 | + | 0.965818i | \(0.416534\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.2351 | 1.31603 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.4701 | 1.87649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.48886 | 0.317169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.0509 | −1.35709 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2810 | 0.912291 | 0.456145 | − | 0.889905i | \(-0.349230\pi\) | ||||
0.456145 | + | 0.889905i | \(0.349230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.67307 | −0.499486 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.66370 | 0.407470 | 0.203735 | − | 0.979026i | \(-0.434692\pi\) | ||||
0.203735 | + | 0.979026i | \(0.434692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.8064 | 1.54401 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3461 | 0.969366 | 0.484683 | − | 0.874690i | \(-0.338935\pi\) | ||||
0.484683 | + | 0.874690i | \(0.338935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8064 | 1.00141 | 0.500704 | − | 0.865619i | \(-0.333075\pi\) | ||||
0.500704 | + | 0.865619i | \(0.333075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.4795 | 1.30361 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.98126 | −0.834675 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.7605 | −1.29990 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.47949 | −0.448898 | −0.224449 | − | 0.974486i | \(-0.572058\pi\) | ||||
−0.224449 | + | 0.974486i | \(0.572058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.6128 | 1.92159 | 0.960793 | − | 0.277266i | \(-0.0894284\pi\) | ||||
0.960793 | + | 0.277266i | \(0.0894284\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 31.5210 | 2.54832 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.815792 | 0.0651073 | 0.0325536 | − | 0.999470i | \(-0.489636\pi\) | ||||
0.0325536 | + | 0.999470i | \(0.489636\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.6128 | −1.23818 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.67307 | 0.131856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.9032 | −0.854005 | −0.427003 | − | 0.904250i | \(-0.640431\pi\) | ||||
−0.427003 | + | 0.904250i | \(0.640431\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.57628 | −0.508888 | −0.254444 | − | 0.967088i | \(-0.581892\pi\) | ||||
−0.254444 | + | 0.967088i | \(0.581892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.12399 | −0.471076 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 27.4193 | 2.09680 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5303 | −0.800608 | −0.400304 | − | 0.916382i | \(-0.631095\pi\) | ||||
−0.400304 | + | 0.916382i | \(0.631095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.6637 | 1.10219 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.29529 | −0.470532 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.488863 | −0.0363369 | −0.0181684 | − | 0.999835i | \(-0.505784\pi\) | ||||
−0.0181684 | + | 0.999835i | \(0.505784\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.5210 | 2.62579 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.1017 | −1.61624 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −24.8573 | −1.80810 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4889 | −0.758947 | −0.379474 | − | 0.925203i | \(-0.623895\pi\) | ||||
−0.379474 | + | 0.925203i | \(0.623895\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8064 | 0.993808 | 0.496904 | − | 0.867805i | \(-0.334470\pi\) | ||||
0.496904 | + | 0.867805i | \(0.334470\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.7239 | 1.19153 | 0.595765 | − | 0.803159i | \(-0.296849\pi\) | ||||
0.595765 | + | 0.803159i | \(0.296849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.8573 | 1.47853 | 0.739267 | − | 0.673413i | \(-0.235172\pi\) | ||||
0.739267 | + | 0.673413i | \(0.235172\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.5303 | −1.58917 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.05086 | −0.494873 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.57628 | 0.179064 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.2257 | −1.32987 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.66370 | 0.321063 | 0.160531 | − | 0.987031i | \(-0.448679\pi\) | ||||
0.160531 | + | 0.987031i | \(0.448679\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.1017 | 0.966233 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.71456 | −0.659467 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.3461 | 1.30729 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.2257 | 1.02419 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.4558 | 1.77161 | 0.885807 | − | 0.464054i | \(-0.153606\pi\) | ||||
0.885807 | + | 0.464054i | \(0.153606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.3225 | −0.817872 | −0.408936 | − | 0.912563i | \(-0.634100\pi\) | ||||
−0.408936 | + | 0.912563i | \(0.634100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.2257 | 0.873979 | 0.436989 | − | 0.899467i | \(-0.356045\pi\) | ||||
0.436989 | + | 0.899467i | \(0.356045\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 38.9590 | 2.56331 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.66370 | −0.436554 | −0.218277 | − | 0.975887i | \(-0.570044\pi\) | ||||
−0.218277 | + | 0.975887i | \(0.570044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.2257 | 0.989015 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.9590 | 1.48509 | 0.742547 | − | 0.669794i | \(-0.233618\pi\) | ||||
0.742547 | + | 0.669794i | \(0.233618\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0415 | −0.904492 | −0.452246 | − | 0.891893i | \(-0.649377\pi\) | ||||
−0.452246 | + | 0.891893i | \(0.649377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.00492 | 0.577666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.2444 | 0.842723 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 35.2672 | 2.23497 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9304 | 1.57359 | 0.786797 | − | 0.617212i | \(-0.211738\pi\) | ||||
0.786797 | + | 0.617212i | \(0.211738\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80642 | −0.113569 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.7146 | −1.60403 | −0.802015 | − | 0.597304i | \(-0.796239\pi\) | ||||
−0.802015 | + | 0.597304i | \(0.796239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.3274 | 1.57377 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.8573 | −0.672049 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.57628 | 0.158860 | 0.0794302 | − | 0.996840i | \(-0.474690\pi\) | ||||
0.0794302 | + | 0.996840i | \(0.474690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.1338 | 2.15016 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.7462 | 1.56977 | 0.784887 | − | 0.619639i | \(-0.212721\pi\) | ||||
0.784887 | + | 0.619639i | \(0.212721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.1847 | 1.83359 | 0.916795 | − | 0.399359i | \(-0.130767\pi\) | ||||
0.916795 | + | 0.399359i | \(0.130767\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.8385 | −1.62434 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.5303 | −0.632707 | −0.316354 | − | 0.948641i | \(-0.602459\pi\) | ||||
−0.316354 | + | 0.948641i | \(0.602459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.9590 | −0.895571 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.93978 | −0.473647 | −0.236824 | − | 0.971553i | \(-0.576106\pi\) | ||||
−0.236824 | + | 0.971553i | \(0.576106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9032 | −0.648129 | −0.324064 | − | 0.946035i | \(-0.605049\pi\) | ||||
−0.324064 | + | 0.946035i | \(0.605049\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.2766 | 1.07883 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7146 | 0.983209 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −40.0830 | −2.34971 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.42864 | 0.258724 | 0.129362 | − | 0.991597i | \(-0.458707\pi\) | ||||
0.129362 | + | 0.991597i | \(0.458707\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.8385 | 1.55733 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.24443 | 0.0719673 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.88892 | 0.397071 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −57.2355 | −3.28810 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.27163 | 0.300868 | 0.150434 | − | 0.988620i | \(-0.451933\pi\) | ||||
0.150434 | + | 0.988620i | \(0.451933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.11108 | 0.518311 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.387152 | 0.0219534 | 0.0109767 | − | 0.999940i | \(-0.496506\pi\) | ||||
0.0109767 | + | 0.999940i | \(0.496506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.3461 | 0.641322 | 0.320661 | − | 0.947194i | \(-0.396095\pi\) | ||||
0.320661 | + | 0.947194i | \(0.396095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7239 | −0.939309 | −0.469655 | − | 0.882850i | \(-0.655622\pi\) | ||||
−0.469655 | + | 0.882850i | \(0.655622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.61285 | 0.426238 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.6543 | −0.873740 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.3274 | 1.63182 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.0321 | −1.38428 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.7971 | −1.03632 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.33630 | 0.183379 | 0.0916897 | − | 0.995788i | \(-0.470773\pi\) | ||||
0.0916897 | + | 0.995788i | \(0.470773\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 39.0005 | 2.13721 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.61285 | −0.196804 | −0.0984022 | − | 0.995147i | \(-0.531373\pi\) | ||||
−0.0984022 | + | 0.995147i | \(0.531373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.0000 | −0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4889 | 0.568004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.53972 | −0.299117 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.7605 | 0.846067 | 0.423034 | − | 0.906114i | \(-0.360965\pi\) | ||||
0.423034 | + | 0.906114i | \(0.360965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.285442 | −0.0152794 | −0.00763968 | − | 0.999971i | \(-0.502432\pi\) | ||||
−0.00763968 | + | 0.999971i | \(0.502432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.4889 | −0.986862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.38715 | −0.233505 | −0.116752 | − | 0.993161i | \(-0.537248\pi\) | ||||
−0.116752 | + | 0.993161i | \(0.537248\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −59.4291 | −3.14532 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5906 | −1.08673 | −0.543364 | − | 0.839497i | \(-0.682850\pi\) | ||||
−0.543364 | + | 0.839497i | \(0.682850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.51114 | 0.342691 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.1289 | −0.531630 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.5575 | −0.864297 | −0.432148 | − | 0.901802i | \(-0.642244\pi\) | ||||
−0.432148 | + | 0.901802i | \(0.642244\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.1432 | 1.46508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.9590 | 0.984302 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.8988 | −1.28921 | −0.644605 | − | 0.764516i | \(-0.722978\pi\) | ||||
−0.644605 | + | 0.764516i | \(0.722978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.24443 | −0.270102 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.31756 | 0.478611 | 0.239305 | − | 0.970944i | \(-0.423080\pi\) | ||||
0.239305 | + | 0.970944i | \(0.423080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.8479 | −1.52915 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.5575 | 1.66361 | 0.831806 | − | 0.555066i | \(-0.187307\pi\) | ||||
0.831806 | + | 0.555066i | \(0.187307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.6079 | 0.539231 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.9906 | −0.962863 | −0.481432 | − | 0.876484i | \(-0.659883\pi\) | ||||
−0.481432 | + | 0.876484i | \(0.659883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.75557 | 0.139355 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.5397 | −0.682988 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.9906 | 1.65575 | 0.827876 | − | 0.560911i | \(-0.189549\pi\) | ||||
0.827876 | + | 0.560911i | \(0.189549\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −51.6958 | −2.58803 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.1017 | −0.804081 | −0.402041 | − | 0.915622i | \(-0.631699\pi\) | ||||
−0.402041 | + | 0.915622i | \(0.631699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.22570 | −0.359938 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.3461 | −1.35550 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.3876 | −1.65091 | −0.825456 | − | 0.564466i | \(-0.809082\pi\) | ||||
−0.825456 | + | 0.564466i | \(0.809082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.9403 | −1.62482 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.8064 | −0.876197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −34.2766 | −1.67853 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4193 | 1.33952 | 0.669760 | − | 0.742578i | \(-0.266397\pi\) | ||||
0.669760 | + | 0.742578i | \(0.266397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.2351 | −0.596301 | −0.298150 | − | 0.954519i | \(-0.596370\pi\) | ||||
−0.298150 | + | 0.954519i | \(0.596370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.9447 | −1.40734 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.1338 | −2.08739 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.9777 | 1.39906 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4701 | −1.37136 | −0.685679 | − | 0.727904i | \(-0.740495\pi\) | ||||
−0.685679 | + | 0.727904i | \(0.740495\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.0098 | 1.63441 | 0.817204 | − | 0.576348i | \(-0.195523\pi\) | ||||
0.817204 | + | 0.576348i | \(0.195523\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.39700 | 0.114664 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8385 | −0.708205 | −0.354103 | − | 0.935207i | \(-0.615214\pi\) | ||||
−0.354103 | + | 0.935207i | \(0.615214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.4701 | 1.40334 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.0968 | 0.622247 | 0.311124 | − | 0.950369i | \(-0.399295\pi\) | ||||
0.311124 | + | 0.950369i | \(0.399295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.9081 | 0.752429 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.3876 | −1.00934 | −0.504672 | − | 0.863311i | \(-0.668387\pi\) | ||||
−0.504672 | + | 0.863311i | \(0.668387\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.7333 | −0.929205 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −68.5531 | −3.22091 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.9813 | 0.841128 | 0.420564 | − | 0.907263i | \(-0.361832\pi\) | ||||
0.420564 | + | 0.907263i | \(0.361832\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −40.9403 | −1.91093 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.7368 | −0.500064 | −0.250032 | − | 0.968238i | \(-0.580441\pi\) | ||||
−0.250032 | + | 0.968238i | \(0.580441\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.30327 | −0.432360 | −0.216180 | − | 0.976354i | \(-0.569360\pi\) | ||||
−0.216180 | + | 0.976354i | \(0.569360\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.70964 | −0.403034 | −0.201517 | − | 0.979485i | \(-0.564587\pi\) | ||||
−0.201517 | + | 0.979485i | \(0.564587\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.3590 | 1.26332 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.36842 | −0.109131 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.43801 | −0.342000 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.1941 | 1.33670 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.2257 | 1.06121 | 0.530605 | − | 0.847619i | \(-0.321965\pi\) | ||||
0.530605 | + | 0.847619i | \(0.321965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.8385 | 0.858964 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.85728 | −0.221014 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.8528 | 1.48870 | 0.744352 | − | 0.667787i | \(-0.232759\pi\) | ||||
0.744352 | + | 0.667787i | \(0.232759\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.6543 | 1.43146 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.94914 | −0.133093 | −0.0665465 | − | 0.997783i | \(-0.521198\pi\) | ||||
−0.0665465 | + | 0.997783i | \(0.521198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.6128 | −0.523016 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.1240 | −0.768116 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.0321 | −1.56825 | −0.784127 | − | 0.620601i | \(-0.786889\pi\) | ||||
−0.784127 | + | 0.620601i | \(0.786889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.0923 | 0.852983 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.2908 | 0.726373 | 0.363186 | − | 0.931717i | \(-0.381689\pi\) | ||||
0.363186 | + | 0.931717i | \(0.381689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.7792 | 0.789603 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.4924 | −1.03924 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.6128 | −1.57235 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2953 | 0.892586 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.5718 | 1.34195 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.7146 | 0.513224 | 0.256612 | − | 0.966514i | \(-0.417394\pi\) | ||||
0.256612 | + | 0.966514i | \(0.417394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.0370 | 1.66324 | 0.831622 | − | 0.555342i | \(-0.187413\pi\) | ||||
0.831622 | + | 0.555342i | \(0.187413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.0000 | −0.696971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7748 | −0.990208 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.4193 | −1.18990 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5941 | 0.588826 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.2766 | 0.788691 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.6637 | −0.890049 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.5111 | −0.494902 | −0.247451 | − | 0.968900i | \(-0.579593\pi\) | ||||
−0.247451 | + | 0.968900i | \(0.579593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.41927 | 0.0609068 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.2208 | −1.29215 | −0.646073 | − | 0.763275i | \(-0.723590\pi\) | ||||
−0.646073 | + | 0.763275i | \(0.723590\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −66.4197 | −2.83473 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.1017 | −0.430347 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.4889 | −0.786226 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.75605 | 0.413377 | 0.206688 | − | 0.978407i | \(-0.433731\pi\) | ||||
0.206688 | + | 0.978407i | \(0.433731\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12399 | 0.216721 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 64.1659 | 2.70909 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.50622 | 0.189914 | 0.0949572 | − | 0.995481i | \(-0.469729\pi\) | ||||
0.0949572 | + | 0.995481i | \(0.469729\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.7511 | 0.619489 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.30465 | 0.222383 | 0.111191 | − | 0.993799i | \(-0.464533\pi\) | ||||
0.111191 | + | 0.993799i | \(0.464533\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.3970 | 0.686193 | 0.343096 | − | 0.939300i | \(-0.388524\pi\) | ||||
0.343096 | + | 0.939300i | \(0.388524\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.4514 | 1.27213 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.8163 | 1.65757 | 0.828786 | − | 0.559565i | \(-0.189032\pi\) | ||||
0.828786 | + | 0.559565i | \(0.189032\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.0830 | −1.66579 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.8256 | −1.77671 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.4701 | −0.847786 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.1699 | 0.626130 | 0.313065 | − | 0.949732i | \(-0.398644\pi\) | ||||
0.313065 | + | 0.949732i | \(0.398644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.9180 | −0.573480 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −48.5531 | −1.99721 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.00000 | −0.328521 | −0.164260 | − | 0.986417i | \(-0.552524\pi\) | ||||
−0.164260 | + | 0.986417i | \(0.552524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −60.5531 | −2.47827 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.83500 | 0.0749762 | 0.0374881 | − | 0.999297i | \(-0.488064\pi\) | ||||
0.0374881 | + | 0.999297i | \(0.488064\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.1432 | −1.47431 | −0.737156 | − | 0.675723i | \(-0.763832\pi\) | ||||
−0.737156 | + | 0.675723i | \(0.763832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 42.1289 | 1.71562 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.5353 | −0.711735 | −0.355867 | − | 0.934536i | \(-0.615815\pi\) | ||||
−0.355867 | + | 0.934536i | \(0.615815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.4701 | 0.829491 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.9813 | −0.565621 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.9309 | 1.37046 | 0.685228 | − | 0.728329i | \(-0.259703\pi\) | ||||
0.685228 | + | 0.728329i | \(0.259703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.68598 | −0.389943 | −0.194971 | − | 0.980809i | \(-0.562461\pi\) | ||||
−0.194971 | + | 0.980809i | \(0.562461\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.4005 | 1.66403 | 0.832014 | − | 0.554755i | \(-0.187188\pi\) | ||||
0.832014 | + | 0.554755i | \(0.187188\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.34614 | −0.134276 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −42.6637 | −1.70929 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 55.8163 | 2.22909 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 41.7146 | 1.66327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.8163 | −1.10735 | −0.553674 | − | 0.832733i | \(-0.686775\pi\) | ||||
−0.553674 | + | 0.832733i | \(0.686775\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.5397 | −0.538155 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.2351 | 0.564014 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.3684 | −1.04312 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.8988 | 1.69440 | 0.847200 | − | 0.531275i | \(-0.178287\pi\) | ||||
0.847200 | + | 0.531275i | \(0.178287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.9639 | −1.10279 | −0.551395 | − | 0.834245i | \(-0.685904\pi\) | ||||
−0.551395 | + | 0.834245i | \(0.685904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.13828 | 0.280635 | 0.140317 | − | 0.990107i | \(-0.455188\pi\) | ||||
0.140317 | + | 0.990107i | \(0.455188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.2257 | 0.754675 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.2034 | 1.10538 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.7649 | −0.695196 | −0.347598 | − | 0.937644i | \(-0.613003\pi\) | ||||
−0.347598 | + | 0.937644i | \(0.613003\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.1748 | −1.41131 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.1936 | 0.786630 | 0.393315 | − | 0.919404i | \(-0.371328\pi\) | ||||
0.393315 | + | 0.919404i | \(0.371328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0701 | 0.858426 | 0.429213 | − | 0.903203i | \(-0.358791\pi\) | ||||
0.429213 | + | 0.903203i | \(0.358791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −44.2034 | −1.71672 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.949145 | −0.0367510 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −76.8069 | −2.96953 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.5718 | 1.79789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0098 | −1.00261 | −0.501303 | − | 0.865272i | \(-0.667146\pi\) | ||||
−0.501303 | + | 0.865272i | \(0.667146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.86665 | −0.302340 | −0.151170 | − | 0.988508i | \(-0.548304\pi\) | ||||
−0.151170 | + | 0.988508i | \(0.548304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.6735 | 1.86792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35.7748 | 1.37089 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.2494 | −0.698292 | −0.349146 | − | 0.937068i | \(-0.613528\pi\) | ||||
−0.349146 | + | 0.937068i | \(0.613528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.3970 | −1.46494 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.1017 | 0.537232 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.2543 | −0.960718 | −0.480359 | − | 0.877072i | \(-0.659494\pi\) | ||||
−0.480359 | + | 0.877072i | \(0.659494\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −72.8484 | −2.76728 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.1017 | 1.14018 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.3461 | 0.731738 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.8069 | 1.31464 | 0.657319 | − | 0.753612i | \(-0.271690\pi\) | ||||
0.657319 | + | 0.753612i | \(0.271690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.2864 | 1.36857 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 69.5022 | 2.61390 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.51114 | −0.282087 | −0.141043 | − | 0.990003i | \(-0.545046\pi\) | ||||
−0.141043 | + | 0.990003i | \(0.545046\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28.4701 | −1.06771 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.30772 | −0.0489744 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −66.6548 | −2.48927 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.7556 | 0.997814 | 0.498907 | − | 0.866655i | \(-0.333735\pi\) | ||||
0.498907 | + | 0.866655i | \(0.333735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.0638 | −0.412036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.7654 | 1.51608 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.6271 | 0.950458 | 0.475229 | − | 0.879862i | \(-0.342365\pi\) | ||||
0.475229 | + | 0.879862i | \(0.342365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6958 | −1.43318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.3461 | 0.419652 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.6543 | −0.725949 | −0.362975 | − | 0.931799i | \(-0.618239\pi\) | ||||
−0.362975 | + | 0.931799i | \(0.618239\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.5397 | −1.08811 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.5433 | −1.19712 | −0.598562 | − | 0.801077i | \(-0.704261\pi\) | ||||
−0.598562 | + | 0.801077i | \(0.704261\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.4514 | −1.41255 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.1383 | −0.848861 | −0.424430 | − | 0.905461i | \(-0.639526\pi\) | ||||
−0.424430 | + | 0.905461i | \(0.639526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −65.9452 | −2.41281 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.0094 | 0.694587 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.48886 | −0.0908199 | −0.0454099 | − | 0.998968i | \(-0.514459\pi\) | ||||
−0.0454099 | + | 0.998968i | \(0.514459\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −72.3783 | −2.63761 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2859 | 0.773650 | 0.386825 | − | 0.922153i | \(-0.373572\pi\) | ||||
0.386825 | + | 0.922153i | \(0.373572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.24443 | 0.190361 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1240 | 0.693244 | 0.346622 | − | 0.938005i | \(-0.387329\pi\) | ||||
0.346622 | + | 0.938005i | \(0.387329\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.3970 | 1.10045 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.2444 | −0.478229 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.9625 | −1.22472 | −0.612360 | − | 0.790579i | \(-0.709780\pi\) | ||||
−0.612360 | + | 0.790579i | \(0.709780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 74.6548 | 2.68863 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.133353 | −0.00479638 | −0.00239819 | − | 0.999997i | \(-0.500763\pi\) | ||||
−0.00239819 | + | 0.999997i | \(0.500763\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −73.5308 | −2.63790 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.1847 | 0.938164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.4889 | 0.661584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1017 | 0.503954 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.12537 | 0.0401150 | 0.0200575 | − | 0.999799i | \(-0.493615\pi\) | ||||
0.0200575 | + | 0.999799i | \(0.493615\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.47949 | −0.266277 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.4291 | 0.690820 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0830 | −1.13930 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.11108 | −0.181044 | −0.0905218 | − | 0.995894i | \(-0.528853\pi\) | ||||
−0.0905218 | + | 0.995894i | \(0.528853\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.9590 | −1.09525 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −65.6958 | −2.32125 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.3649 | 0.895107 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −74.7467 | −2.63121 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.7368 | 0.658752 | 0.329376 | − | 0.944199i | \(-0.393162\pi\) | ||||
0.329376 | + | 0.944199i | \(0.393162\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.5210 | −1.31754 | −0.658770 | − | 0.752344i | \(-0.728923\pi\) | ||||
−0.658770 | + | 0.752344i | \(0.728923\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −87.6325 | −3.07341 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.86971 | 0.345297 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 50.1847 | 1.75359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.4001 | 0.642166 | 0.321083 | − | 0.947051i | \(-0.395953\pi\) | ||||
0.321083 | + | 0.947051i | \(0.395953\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.649413 | −0.0226371 | −0.0113186 | − | 0.999936i | \(-0.503603\pi\) | ||||
−0.0113186 | + | 0.999936i | \(0.503603\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8622 | 1.03841 | 0.519205 | − | 0.854650i | \(-0.326228\pi\) | ||||
0.519205 | + | 0.854650i | \(0.326228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.1753 | 0.735449 | 0.367725 | − | 0.929935i | \(-0.380137\pi\) | ||||
0.367725 | + | 0.929935i | \(0.380137\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.5718 | 1.06053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.5210 | 1.09214 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.4291 | 0.671568 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.8163 | −1.51271 | −0.756353 | − | 0.654164i | \(-0.773021\pi\) | ||||
−0.756353 | + | 0.654164i | \(0.773021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.0509 | 0.793914 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2997 | 0.422624 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.6543 | 1.08637 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.40943 | 0.116874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7846 | 1.29372 | 0.646860 | − | 0.762608i | \(-0.276082\pi\) | ||||
0.646860 | + | 0.762608i | \(0.276082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.5299 | −0.667128 | −0.333564 | − | 0.942727i | \(-0.608251\pi\) | ||||
−0.333564 | + | 0.942727i | \(0.608251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.2543 | −1.13462 | −0.567311 | − | 0.823504i | \(-0.692016\pi\) | ||||
−0.567311 | + | 0.823504i | \(0.692016\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −53.0607 | −1.80830 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44.9733 | −1.53091 | −0.765454 | − | 0.643490i | \(-0.777486\pi\) | ||||
−0.765454 | + | 0.643490i | \(0.777486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −48.5259 | −1.64803 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.9625 | 0.677182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.3497 | 0.689523 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 74.9501 | 2.53668 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.30819 | −0.280548 | −0.140274 | − | 0.990113i | \(-0.544798\pi\) | ||||
−0.140274 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.8573 | −0.433665 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3689 | −1.32637 | −0.663186 | − | 0.748455i | \(-0.730796\pi\) | ||||
−0.663186 | + | 0.748455i | \(0.730796\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.29036 | −0.245340 | −0.122670 | − | 0.992447i | \(-0.539146\pi\) | ||||
−0.122670 | + | 0.992447i | \(0.539146\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.1097 | −0.373027 | −0.186514 | − | 0.982452i | \(-0.559719\pi\) | ||||
−0.186514 | + | 0.982452i | \(0.559719\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.2449 | 1.21562 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.9269 | −0.533570 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.9304 | −0.901192 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.61285 | −0.120629 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.51114 | 0.183807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.2257 | 1.04028 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.0000 | −0.665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.5383 | 0.582351 | 0.291175 | − | 0.956670i | \(-0.405954\pi\) | ||||
0.291175 | + | 0.956670i | \(0.405954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 107.023 | 3.54974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.4701 | 1.47336 | 0.736681 | − | 0.676241i | \(-0.236392\pi\) | ||||
0.736681 | + | 0.676241i | \(0.236392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46.2391 | 1.53029 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4415 | 0.542948 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.87955 | 0.259922 | 0.129961 | − | 0.991519i | \(-0.458515\pi\) | ||||
0.129961 | + | 0.991519i | \(0.458515\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.3047 | −0.504306 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.7368 | −0.419238 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.0366 | −0.559554 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.7560 | 0.516939 | 0.258470 | − | 0.966019i | \(-0.416782\pi\) | ||||
0.258470 | + | 0.966019i | \(0.416782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.4193 | 0.898630 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.12399 | −0.0367976 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2766 | −0.335720 | −0.167860 | − | 0.985811i | \(-0.553686\pi\) | ||||
−0.167860 | + | 0.985811i | \(0.553686\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.9403 | −1.07496 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.53341 | 0.0825869 | 0.0412934 | − | 0.999147i | \(-0.486852\pi\) | ||||
0.0412934 | + | 0.999147i | \(0.486852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.46028 | 0.0801178 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.06821 | 0.0347121 | 0.0173560 | − | 0.999849i | \(-0.494475\pi\) | ||||
0.0173560 | + | 0.999849i | \(0.494475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.4737 | −0.567219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 48.5531 | 1.57444 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.6958 | −1.67459 | −0.837296 | − | 0.546750i | \(-0.815865\pi\) | ||||
−0.837296 | + | 0.546750i | \(0.815865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22.1017 | −0.714447 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 40.0000 | 1.29167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.4068 | −0.755059 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.2716 | 0.943265 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.2623 | 1.68064 | 0.840320 | − | 0.542090i | \(-0.182367\pi\) | ||||
0.840320 | + | 0.542090i | \(0.182367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −85.1437 | −2.73521 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −59.3560 | −1.90482 | −0.952412 | − | 0.304813i | \(-0.901406\pi\) | ||||
−0.952412 | + | 0.304813i | \(0.901406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.6227 | 1.33436 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.8707 | 1.53152 | 0.765759 | − | 0.643128i | \(-0.222363\pi\) | ||||
0.765759 | + | 0.643128i | \(0.222363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 46.0642 | 1.47222 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.8069 | 1.49443 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.01429 | −0.191826 | −0.0959130 | − | 0.995390i | \(-0.530577\pi\) | ||||
−0.0959130 | + | 0.995390i | \(0.530577\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 54.5718 | 1.73704 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.927346 | 0.0294879 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.4291 | −0.617186 | −0.308593 | − | 0.951194i | \(-0.599858\pi\) | ||||
−0.308593 | + | 0.951194i | \(0.599858\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.68598 | −0.307375 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.1334 | 1.01767 | 0.508837 | − | 0.860863i | \(-0.330076\pi\) | ||||
0.508837 | + | 0.860863i | \(0.330076\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −50.6548 | −1.60265 |
(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 | 3200.2.a.br.1.1 | 3 | ||
4.3 | odd | 2 | 3200.2.a.bs.1.3 | 3 | |||
5.2 | odd | 4 | 640.2.c.b.129.6 | yes | 6 | ||
5.3 | odd | 4 | 640.2.c.b.129.1 | yes | 6 | ||
5.4 | even | 2 | 3200.2.a.bt.1.3 | 3 | |||
8.3 | odd | 2 | 3200.2.a.bp.1.1 | 3 | |||
8.5 | even | 2 | 3200.2.a.bu.1.3 | 3 | |||
20.3 | even | 4 | 640.2.c.a.129.6 | yes | 6 | ||
20.7 | even | 4 | 640.2.c.a.129.1 | ✓ | 6 | ||
20.19 | odd | 2 | 3200.2.a.bq.1.1 | 3 | |||
40.3 | even | 4 | 640.2.c.d.129.1 | yes | 6 | ||
40.13 | odd | 4 | 640.2.c.c.129.6 | yes | 6 | ||
40.19 | odd | 2 | 3200.2.a.bv.1.3 | 3 | |||
40.27 | even | 4 | 640.2.c.d.129.6 | yes | 6 | ||
40.29 | even | 2 | 3200.2.a.bo.1.1 | 3 | |||
40.37 | odd | 4 | 640.2.c.c.129.1 | yes | 6 | ||
80.3 | even | 4 | 1280.2.f.i.129.2 | 6 | |||
80.13 | odd | 4 | 1280.2.f.k.129.6 | 6 | |||
80.27 | even | 4 | 1280.2.f.i.129.1 | 6 | |||
80.37 | odd | 4 | 1280.2.f.k.129.5 | 6 | |||
80.43 | even | 4 | 1280.2.f.l.129.5 | 6 | |||
80.53 | odd | 4 | 1280.2.f.j.129.1 | 6 | |||
80.67 | even | 4 | 1280.2.f.l.129.6 | 6 | |||
80.77 | odd | 4 | 1280.2.f.j.129.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.2.c.a.129.1 | ✓ | 6 | 20.7 | even | 4 | ||
640.2.c.a.129.6 | yes | 6 | 20.3 | even | 4 | ||
640.2.c.b.129.1 | yes | 6 | 5.3 | odd | 4 | ||
640.2.c.b.129.6 | yes | 6 | 5.2 | odd | 4 | ||
640.2.c.c.129.1 | yes | 6 | 40.37 | odd | 4 | ||
640.2.c.c.129.6 | yes | 6 | 40.13 | odd | 4 | ||
640.2.c.d.129.1 | yes | 6 | 40.3 | even | 4 | ||
640.2.c.d.129.6 | yes | 6 | 40.27 | even | 4 | ||
1280.2.f.i.129.1 | 6 | 80.27 | even | 4 | |||
1280.2.f.i.129.2 | 6 | 80.3 | even | 4 | |||
1280.2.f.j.129.1 | 6 | 80.53 | odd | 4 | |||
1280.2.f.j.129.2 | 6 | 80.77 | odd | 4 | |||
1280.2.f.k.129.5 | 6 | 80.37 | odd | 4 | |||
1280.2.f.k.129.6 | 6 | 80.13 | odd | 4 | |||
1280.2.f.l.129.5 | 6 | 80.43 | even | 4 | |||
1280.2.f.l.129.6 | 6 | 80.67 | even | 4 | |||
3200.2.a.bo.1.1 | 3 | 40.29 | even | 2 | |||
3200.2.a.bp.1.1 | 3 | 8.3 | odd | 2 | |||
3200.2.a.bq.1.1 | 3 | 20.19 | odd | 2 | |||
3200.2.a.br.1.1 | 3 | 1.1 | even | 1 | trivial | ||
3200.2.a.bs.1.3 | 3 | 4.3 | odd | 2 | |||
3200.2.a.bt.1.3 | 3 | 5.4 | even | 2 | |||
3200.2.a.bu.1.3 | 3 | 8.5 | even | 2 | |||
3200.2.a.bv.1.3 | 3 | 40.19 | odd | 2 |