Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4508,2,Mod(1,4508)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4508, 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("4508.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4508 = 2^{2} \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4508.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: | \(35.9965612312\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.6963152.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 644) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.25688\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4508.1 |
$q$-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 | ||||||||
\(3\) | −3.25688 | −1.88036 | −0.940181 | − | 0.340675i | \(-0.889345\pi\) | ||||
−0.940181 | + | 0.340675i | \(0.889345\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.04771 | 1.36298 | 0.681489 | − | 0.731828i | \(-0.261333\pi\) | ||||
0.681489 | + | 0.731828i | \(0.261333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.60729 | 2.53576 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.22523 | 1.57546 | 0.787732 | − | 0.616018i | \(-0.211255\pi\) | ||||
0.787732 | + | 0.616018i | \(0.211255\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.38206 | −0.938016 | −0.469008 | − | 0.883194i | \(-0.655388\pi\) | ||||
−0.469008 | + | 0.883194i | \(0.655388\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.92604 | −2.56289 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.63895 | 0.640039 | 0.320019 | − | 0.947411i | \(-0.396311\pi\) | ||||
0.320019 | + | 0.947411i | \(0.396311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.39461 | −0.778777 | −0.389388 | − | 0.921074i | \(-0.627314\pi\) | ||||
−0.389388 | + | 0.921074i | \(0.627314\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.28854 | 0.857708 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.0054 | −2.88779 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00190 | −0.743134 | −0.371567 | − | 0.928406i | \(-0.621179\pi\) | ||||
−0.371567 | + | 0.928406i | \(0.621179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.97185 | −1.25218 | −0.626091 | − | 0.779750i | \(-0.715346\pi\) | ||||
−0.626091 | + | 0.779750i | \(0.715346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.0180 | −2.96245 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.11916 | −0.841585 | −0.420792 | − | 0.907157i | \(-0.638248\pi\) | ||||
−0.420792 | + | 0.907157i | \(0.638248\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.0150 | 1.76381 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.89583 | 0.920774 | 0.460387 | − | 0.887718i | \(-0.347711\pi\) | ||||
0.460387 | + | 0.887718i | \(0.347711\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.90838 | −1.20602 | −0.603008 | − | 0.797735i | \(-0.706031\pi\) | ||||
−0.603008 | + | 0.797735i | \(0.706031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 23.1848 | 3.45619 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.54893 | −1.39286 | −0.696428 | − | 0.717627i | \(-0.745228\pi\) | ||||
−0.696428 | + | 0.717627i | \(0.745228\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.59475 | −1.20351 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.8200 | −1.62360 | −0.811799 | − | 0.583937i | \(-0.801512\pi\) | ||||
−0.811799 | + | 0.583937i | \(0.801512\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.9250 | 2.14732 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0558 | 1.46438 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.51979 | −0.197860 | −0.0989299 | − | 0.995094i | \(-0.531542\pi\) | ||||
−0.0989299 | + | 0.995094i | \(0.531542\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.13934 | −0.145877 | −0.0729385 | − | 0.997336i | \(-0.523238\pi\) | ||||
−0.0729385 | + | 0.997336i | \(0.523238\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.3076 | −1.27849 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.80688 | −1.07593 | −0.537966 | − | 0.842967i | \(-0.680807\pi\) | ||||
−0.537966 | + | 0.842967i | \(0.680807\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.25688 | 0.392083 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5333 | −1.72479 | −0.862394 | − | 0.506237i | \(-0.831036\pi\) | ||||
−0.862394 | + | 0.506237i | \(0.831036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2271 | 1.54812 | 0.774059 | − | 0.633114i | \(-0.218223\pi\) | ||||
0.774059 | + | 0.633114i | \(0.218223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.9673 | −1.61280 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4398 | 1.62461 | 0.812303 | − | 0.583236i | \(-0.198214\pi\) | ||||
0.812303 | + | 0.583236i | \(0.198214\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 26.0490 | 2.89433 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.693795 | 0.0761538 | 0.0380769 | − | 0.999275i | \(-0.487877\pi\) | ||||
0.0380769 | + | 0.999275i | \(0.487877\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.04275 | 0.872359 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.0337 | 1.39736 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8511 | −1.15021 | −0.575106 | − | 0.818079i | \(-0.695039\pi\) | ||||
−0.575106 | + | 0.818079i | \(0.695039\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.7065 | 2.35456 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.3458 | −1.06146 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.23476 | 0.328440 | 0.164220 | − | 0.986424i | \(-0.447489\pi\) | ||||
0.164220 | + | 0.986424i | \(0.447489\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 39.7498 | 3.99501 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.32672 | 0.828540 | 0.414270 | − | 0.910154i | \(-0.364037\pi\) | ||||
0.414270 | + | 0.910154i | \(0.364037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.418345 | −0.0412208 | −0.0206104 | − | 0.999788i | \(-0.506561\pi\) | ||||
−0.0206104 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9084 | −1.15123 | −0.575613 | − | 0.817722i | \(-0.695237\pi\) | ||||
−0.575613 | + | 0.817722i | \(0.695237\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.9154 | 1.71598 | 0.857992 | − | 0.513663i | \(-0.171712\pi\) | ||||
0.857992 | + | 0.513663i | \(0.171712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.6725 | 1.58248 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.6375 | −1.18884 | −0.594418 | − | 0.804156i | \(-0.702617\pi\) | ||||
−0.594418 | + | 0.804156i | \(0.702617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.04771 | −0.284201 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −25.7283 | −2.37859 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.3030 | 1.48209 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.2020 | −1.73139 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.16832 | −0.193940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.22333 | −0.286024 | −0.143012 | − | 0.989721i | \(-0.545679\pi\) | ||||
−0.143012 | + | 0.989721i | \(0.545679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.7567 | 2.26775 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.0910 | 1.23114 | 0.615569 | − | 0.788083i | \(-0.288926\pi\) | ||||
0.615569 | + | 0.788083i | \(0.288926\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −45.7321 | −3.93600 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.67250 | 0.228327 | 0.114164 | − | 0.993462i | \(-0.463581\pi\) | ||||
0.114164 | + | 0.993462i | \(0.463581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.23315 | −0.528689 | −0.264344 | − | 0.964428i | \(-0.585156\pi\) | ||||
−0.264344 | + | 0.964428i | \(0.585156\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31.0998 | 2.61907 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.6721 | −1.47781 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.1966 | −1.01287 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.58165 | −0.457267 | −0.228633 | − | 0.973513i | \(-0.573426\pi\) | ||||
−0.228633 | + | 0.973513i | \(0.573426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8325 | −0.962916 | −0.481458 | − | 0.876469i | \(-0.659893\pi\) | ||||
−0.481458 | + | 0.876469i | \(0.659893\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.0752 | 1.62299 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.2482 | −1.70670 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3015 | −1.38081 | −0.690406 | − | 0.723422i | \(-0.742568\pi\) | ||||
−0.690406 | + | 0.723422i | \(0.742568\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 38.4963 | 3.05295 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.3212 | 1.12172 | 0.560861 | − | 0.827910i | \(-0.310470\pi\) | ||||
0.560861 | + | 0.827910i | \(0.310470\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −51.8658 | −4.03775 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.28358 | −0.486238 | −0.243119 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243119 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.56164 | −0.120126 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.8238 | −1.97479 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.60539 | 0.198084 | 0.0990421 | − | 0.995083i | \(-0.468422\pi\) | ||||
0.0990421 | + | 0.995083i | \(0.468422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.94978 | 0.372048 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.2341 | 1.88609 | 0.943044 | − | 0.332667i | \(-0.107949\pi\) | ||||
0.943044 | + | 0.332667i | \(0.107949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.36485 | 0.101448 | 0.0507242 | − | 0.998713i | \(-0.483847\pi\) | ||||
0.0507242 | + | 0.998713i | \(0.483847\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.71068 | 0.274302 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.6017 | −1.14706 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.7891 | 1.00836 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1467 | −1.60248 | −0.801239 | − | 0.598344i | \(-0.795826\pi\) | ||||
−0.801239 | + | 0.598344i | \(0.795826\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3653 | 1.32197 | 0.660983 | − | 0.750401i | \(-0.270139\pi\) | ||||
0.660983 | + | 0.750401i | \(0.270139\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 33.5705 | 2.40403 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.07831 | −0.0768261 | −0.0384131 | − | 0.999262i | \(-0.512230\pi\) | ||||
−0.0384131 | + | 0.999262i | \(0.512230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.55335 | 0.393666 | 0.196833 | − | 0.980437i | \(-0.436934\pi\) | ||||
0.196833 | + | 0.980437i | \(0.436934\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 28.6830 | 2.02314 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.9688 | 1.25499 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.60729 | −0.528743 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.7376 | −1.22693 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3543 | −1.33240 | −0.666201 | − | 0.745772i | \(-0.732081\pi\) | ||||
−0.666201 | + | 0.745772i | \(0.732081\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 47.3334 | 3.24323 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.1024 | −1.64377 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43.0792 | −2.91102 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.92509 | −0.600367 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.69234 | 0.180293 | 0.0901464 | − | 0.995929i | \(-0.471267\pi\) | ||||
0.0901464 | + | 0.995929i | \(0.471267\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 32.6242 | 2.17495 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.26663 | 0.548675 | 0.274338 | − | 0.961633i | \(-0.411541\pi\) | ||||
0.274338 | + | 0.961633i | \(0.411541\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.2369 | −1.73378 | −0.866891 | − | 0.498499i | \(-0.833885\pi\) | ||||
−0.866891 | + | 0.498499i | \(0.833885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.17735 | 0.0771310 | 0.0385655 | − | 0.999256i | \(-0.487721\pi\) | ||||
0.0385655 | + | 0.999256i | \(0.487721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −29.1024 | −1.89843 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −47.0288 | −3.05485 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.56911 | 0.360236 | 0.180118 | − | 0.983645i | \(-0.442352\pi\) | ||||
0.180118 | + | 0.983645i | \(0.442352\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.12518 | −0.523389 | −0.261694 | − | 0.965151i | \(-0.584281\pi\) | ||||
−0.261694 | + | 0.965151i | \(0.584281\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −39.8223 | −2.55460 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4808 | 0.730505 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.25961 | −0.143197 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.78542 | −0.175814 | −0.0879071 | − | 0.996129i | \(-0.528018\pi\) | ||||
−0.0879071 | + | 0.996129i | \(0.528018\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.22523 | −0.328507 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26.1943 | −1.64035 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.1150 | 1.50425 | 0.752126 | − | 0.659020i | \(-0.229029\pi\) | ||||
0.752126 | + | 0.659020i | \(0.229029\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.4436 | −1.88441 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.40905 | 0.210211 | 0.105106 | − | 0.994461i | \(-0.466482\pi\) | ||||
0.105106 | + | 0.994461i | \(0.466482\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −36.0239 | −2.21293 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.3407 | 2.16282 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.29044 | −0.322564 | −0.161282 | − | 0.986908i | \(-0.551563\pi\) | ||||
−0.161282 | + | 0.986908i | \(0.551563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2206 | −0.985331 | −0.492666 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492666 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.4086 | 1.35129 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.2211 | −1.33513 | −0.667567 | − | 0.744550i | \(-0.732664\pi\) | ||||
−0.667567 | + | 0.744550i | \(0.732664\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −53.0369 | −3.17524 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.74964 | −0.342995 | −0.171497 | − | 0.985185i | \(-0.554860\pi\) | ||||
−0.171497 | + | 0.985185i | \(0.554860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0108 | 0.832857 | 0.416428 | − | 0.909169i | \(-0.363282\pi\) | ||||
0.416428 | + | 0.909169i | \(0.363282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.6950 | 1.99592 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0360 | −0.590350 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.5352 | −0.617586 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.7616 | −0.920801 | −0.460400 | − | 0.887711i | \(-0.652294\pi\) | ||||
−0.460400 | + | 0.887711i | \(0.652294\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.63188 | −0.269678 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −78.4066 | −4.54961 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.38206 | 0.195590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.1192 | −1.55795 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.47237 | −0.198827 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.4944 | −0.656018 | −0.328009 | − | 0.944675i | \(-0.606378\pi\) | ||||
−0.328009 | + | 0.944675i | \(0.606378\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.36250 | 0.0775100 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.41105 | −0.250128 | −0.125064 | − | 0.992149i | \(-0.539914\pi\) | ||||
−0.125064 | + | 0.992149i | \(0.539914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.20154 | 0.350532 | 0.175266 | − | 0.984521i | \(-0.443921\pi\) | ||||
0.175266 | + | 0.984521i | \(0.443921\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.50769 | −0.534005 | −0.267003 | − | 0.963696i | \(-0.586033\pi\) | ||||
−0.267003 | + | 0.963696i | \(0.586033\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.9108 | −1.17078 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.7842 | 2.16472 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.95819 | −0.498447 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.5041 | −0.804544 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −58.3484 | −3.22667 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0087 | 0.550130 | 0.275065 | − | 0.961426i | \(-0.411301\pi\) | ||||
0.275065 | + | 0.961426i | \(0.411301\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −38.9429 | −2.13406 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.8408 | −1.46647 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5389 | 0.900929 | 0.450464 | − | 0.892794i | \(-0.351258\pi\) | ||||
0.450464 | + | 0.892794i | \(0.351258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 41.1589 | 2.23544 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.4295 | −1.97277 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.92604 | 0.534400 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.8917 | 1.87308 | 0.936541 | − | 0.350558i | \(-0.114008\pi\) | ||||
0.936541 | + | 0.350558i | \(0.114008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.92337 | −0.370599 | −0.185300 | − | 0.982682i | \(-0.559326\pi\) | ||||
−0.185300 | + | 0.982682i | \(0.559326\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 50.7493 | 2.70880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.6050 | −1.14992 | −0.574959 | − | 0.818182i | \(-0.694982\pi\) | ||||
−0.574959 | + | 0.818182i | \(0.694982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.2934 | −2.35085 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.2085 | −1.38323 | −0.691616 | − | 0.722265i | \(-0.743101\pi\) | ||||
−0.691616 | + | 0.722265i | \(0.743101\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.47664 | −0.393507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −53.0969 | −2.78687 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.3124 | 2.11005 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.5650 | −0.864688 | −0.432344 | − | 0.901709i | \(-0.642313\pi\) | ||||
−0.432344 | + | 0.901709i | \(0.642313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 44.8513 | 2.33487 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.6116 | 0.808340 | 0.404170 | − | 0.914684i | \(-0.367560\pi\) | ||||
0.404170 | + | 0.914684i | \(0.367560\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.06197 | 0.364678 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5347 | 0.697071 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.80933 | −0.503871 | −0.251936 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251936 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4980 | 0.537829 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.4925 | 0.944921 | 0.472461 | − | 0.881352i | \(-0.343366\pi\) | ||||
0.472461 | + | 0.881352i | \(0.343366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −60.1613 | −3.05817 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.3030 | 0.573084 | 0.286542 | − | 0.958068i | \(-0.407494\pi\) | ||||
0.286542 | + | 0.958068i | \(0.407494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.63895 | −0.133457 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −45.8928 | −2.31498 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 44.0084 | 2.21430 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.20204 | 0.0603285 | 0.0301643 | − | 0.999545i | \(-0.490397\pi\) | ||||
0.0301643 | + | 0.999545i | \(0.490397\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.01127 | −0.150376 | −0.0751878 | − | 0.997169i | \(-0.523956\pi\) | ||||
−0.0751878 | + | 0.997169i | \(0.523956\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.5793 | 1.17457 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 79.3898 | 3.94491 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.7488 | −1.32589 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.4725 | 1.65511 | 0.827553 | − | 0.561387i | \(-0.189732\pi\) | ||||
0.827553 | + | 0.561387i | \(0.189732\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.70404 | −0.429338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.11449 | 0.103796 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.3006 | 0.994126 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.40028 | 0.312674 | 0.156337 | − | 0.987704i | \(-0.450031\pi\) | ||||
0.156337 | + | 0.987704i | \(0.450031\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.01082 | −0.390423 | −0.195212 | − | 0.980761i | \(-0.562539\pi\) | ||||
−0.195212 | + | 0.980761i | \(0.562539\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −72.6415 | −3.53195 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.3172 | 0.548967 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 57.5558 | 2.77882 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.6084 | −1.32985 | −0.664925 | − | 0.746910i | \(-0.731537\pi\) | ||||
−0.664925 | + | 0.746910i | \(0.731537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8797 | 0.715074 | 0.357537 | − | 0.933899i | \(-0.383617\pi\) | ||||
0.357537 | + | 0.933899i | \(0.383617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39.7230 | 1.90457 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.39461 | 0.162386 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.1931 | 1.72740 | 0.863702 | − | 0.504004i | \(-0.168140\pi\) | ||||
0.863702 | + | 0.504004i | \(0.168140\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5546 | −0.501465 | −0.250733 | − | 0.968056i | \(-0.580671\pi\) | ||||
−0.250733 | + | 0.968056i | \(0.580671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −33.0710 | −1.56771 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.1788 | 0.859828 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.9560 | 1.88564 | 0.942821 | − | 0.333301i | \(-0.108162\pi\) | ||||
0.942821 | + | 0.333301i | \(0.108162\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.8071 | 1.45065 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 38.5371 | 1.81063 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.1870 | 0.476530 | 0.238265 | − | 0.971200i | \(-0.423421\pi\) | ||||
0.238265 | + | 0.971200i | \(0.423421\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −39.5985 | −1.84830 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.70956 | 0.312495 | 0.156248 | − | 0.987718i | \(-0.450060\pi\) | ||||
0.156248 | + | 0.987718i | \(0.450060\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6512 | 0.773848 | 0.386924 | − | 0.922112i | \(-0.373538\pi\) | ||||
0.386924 | + | 0.922112i | \(0.373538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 69.2029 | 3.20921 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.1863 | −1.81332 | −0.906662 | − | 0.421857i | \(-0.861378\pi\) | ||||
−0.906662 | + | 0.421857i | \(0.861378\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 56.3491 | 2.59643 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.3230 | −1.90004 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.5579 | −0.667963 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −89.9180 | −4.11706 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.2704 | 1.65724 | 0.828619 | − | 0.559813i | \(-0.189127\pi\) | ||||
0.828619 | + | 0.559813i | \(0.189127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.3133 | 0.789420 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.85861 | 0.447656 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.7517 | 1.07629 | 0.538146 | − | 0.842851i | \(-0.319125\pi\) | ||||
0.538146 | + | 0.842851i | \(0.319125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −46.6425 | −2.10925 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3752 | −1.00978 | −0.504889 | − | 0.863185i | \(-0.668466\pi\) | ||||
−0.504889 | + | 0.863185i | \(0.668466\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.5608 | −0.475635 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 121.146 | 5.44510 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2296 | 0.726535 | 0.363268 | − | 0.931685i | \(-0.381661\pi\) | ||||
0.363268 | + | 0.931685i | \(0.381661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.4649 | 0.914304 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.57708 | 0.114906 | 0.0574532 | − | 0.998348i | \(-0.481702\pi\) | ||||
0.0574532 | + | 0.998348i | \(0.481702\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.3774 | 1.12928 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.08608 | 0.225881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.4091 | −1.48083 | −0.740417 | − | 0.672148i | \(-0.765372\pi\) | ||||
−0.740417 | + | 0.672148i | \(0.765372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 50.9375 | 2.24894 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.27500 | −0.0561830 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −49.8953 | −2.19439 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.48546 | −0.372470 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.4303 | −0.544580 | −0.272290 | − | 0.962215i | \(-0.587781\pi\) | ||||
−0.272290 | + | 0.962215i | \(0.587781\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.05262 | −0.0460279 | −0.0230140 | − | 0.999735i | \(-0.507326\pi\) | ||||
−0.0230140 | + | 0.999735i | \(0.507326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.3984 | −0.801445 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.5615 | −0.501725 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.9401 | −0.863701 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.2933 | −1.56910 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −82.1847 | −3.54653 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.4265 | 1.26514 | 0.632572 | − | 0.774502i | \(-0.281999\pi\) | ||||
0.632572 | + | 0.774502i | \(0.281999\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.44515 | −0.190760 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 54.6009 | 2.33885 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.3851 | −1.55571 | −0.777857 | − | 0.628441i | \(-0.783693\pi\) | ||||
−0.777857 | + | 0.628441i | \(0.783693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.66726 | −0.369910 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.5849 | 0.578735 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 50.8130 | 2.15689 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.2666 | −0.943467 | −0.471734 | − | 0.881741i | \(-0.656372\pi\) | ||||
−0.471734 | + | 0.881741i | \(0.656372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.7466 | 1.13126 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44.9095 | −1.89608 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.0300 | −0.928453 | −0.464227 | − | 0.885717i | \(-0.653668\pi\) | ||||
−0.464227 | + | 0.885717i | \(0.653668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.5154 | −1.62036 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.9918 | 1.17348 | 0.586738 | − | 0.809777i | \(-0.300412\pi\) | ||||
0.586738 | + | 0.809777i | \(0.300412\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.7000 | 0.824421 | 0.412210 | − | 0.911089i | \(-0.364757\pi\) | ||||
0.412210 | + | 0.911089i | \(0.364757\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 72.1292 | 3.01324 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.28854 | −0.178845 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.9624 | −0.498000 | −0.249000 | − | 0.968503i | \(-0.580102\pi\) | ||||
−0.249000 | + | 0.968503i | \(0.580102\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −59.8138 | −2.48578 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −61.7620 | −2.55792 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −78.4126 | −3.24196 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.3278 | 0.797743 | 0.398872 | − | 0.917007i | \(-0.369402\pi\) | ||||
0.398872 | + | 0.917007i | \(0.369402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.6667 | 0.975170 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.51192 | 0.144461 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.45045 | −0.347018 | −0.173509 | − | 0.984832i | \(-0.555511\pi\) | ||||
−0.173509 | + | 0.984832i | \(0.555511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.0866 | −0.740235 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.56581 | 0.227413 | 0.113706 | − | 0.993514i | \(-0.463728\pi\) | ||||
0.113706 | + | 0.993514i | \(0.463728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.2258 | 0.743445 | 0.371722 | − | 0.928344i | \(-0.378767\pi\) | ||||
0.371722 | + | 0.928344i | \(0.378767\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −66.9965 | −2.72831 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 49.6868 | 2.02005 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.3740 | −1.15166 | −0.575832 | − | 0.817568i | \(-0.695322\pi\) | ||||
−0.575832 | + | 0.817568i | \(0.695322\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.2951 | 1.30652 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.8620 | 0.640660 | 0.320330 | − | 0.947306i | \(-0.396206\pi\) | ||||
0.320330 | + | 0.947306i | \(0.396206\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −58.5223 | −2.35985 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9140 | −0.600417 | −0.300208 | − | 0.953874i | \(-0.597056\pi\) | ||||
−0.300208 | + | 0.953874i | \(0.597056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.3397 | −1.29984 | −0.649920 | − | 0.760002i | \(-0.725198\pi\) | ||||
−0.649920 | + | 0.760002i | \(0.725198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0054 | 0.602146 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.0511 | −1.12204 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 57.7693 | 2.30708 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.5092 | −0.538647 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.3840 | −0.612426 | −0.306213 | − | 0.951963i | \(-0.599062\pi\) | ||||
−0.306213 | + | 0.951963i | \(0.599062\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 63.0346 | 2.50540 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.82377 | −0.389844 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −110.559 | −4.37366 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.0193 | 1.46217 | 0.731087 | − | 0.682284i | \(-0.239013\pi\) | ||||
0.731087 | + | 0.682284i | \(0.239013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.7183 | −0.974796 | −0.487398 | − | 0.873180i | \(-0.662054\pi\) | ||||
−0.487398 | + | 0.873180i | \(0.662054\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 78.4988 | 3.09089 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.3207 | 0.798887 | 0.399444 | − | 0.916758i | \(-0.369203\pi\) | ||||
0.399444 | + | 0.916758i | \(0.369203\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.94124 | −0.311721 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.7950 | −0.539839 | −0.269919 | − | 0.962883i | \(-0.586997\pi\) | ||||
−0.269919 | + | 0.962883i | \(0.586997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42.9453 | 1.67801 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 100.623 | 3.92566 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.4316 | 1.53604 | 0.768019 | − | 0.640427i | \(-0.221243\pi\) | ||||
0.768019 | + | 0.640427i | \(0.221243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.9211 | −1.51385 | −0.756927 | − | 0.653499i | \(-0.773300\pi\) | ||||
−0.756927 | + | 0.653499i | \(0.773300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 29.0680 | 1.12891 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00190 | 0.154954 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.76865 | −0.339016 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.95329 | −0.229824 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.7150 | −1.68509 | −0.842544 | − | 0.538627i | \(-0.818943\pi\) | ||||
−0.842544 | + | 0.538627i | \(0.818943\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −64.3513 | −2.47688 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.6777 | −0.640977 | −0.320489 | − | 0.947252i | \(-0.603847\pi\) | ||||
−0.320489 | + | 0.947252i | \(0.603847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.9234 | −1.03171 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.7312 | 1.86465 | 0.932324 | − | 0.361625i | \(-0.117778\pi\) | ||||
0.932324 | + | 0.361625i | \(0.117778\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.14502 | 0.311205 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 85.4504 | 3.26014 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 39.9759 | 1.52296 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.7882 | 1.58970 | 0.794849 | − | 0.606807i | \(-0.207550\pi\) | ||||
0.794849 | + | 0.606807i | \(0.207550\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.9968 | −0.720591 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5588 | 0.589331 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.83450 | −0.145034 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.1499 | −1.06321 | −0.531604 | − | 0.846993i | \(-0.678410\pi\) | ||||
−0.531604 | + | 0.846993i | \(0.678410\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.3775 | 0.655406 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 94.7831 | 3.56974 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.1680 | 0.832536 | 0.416268 | − | 0.909242i | \(-0.363338\pi\) | ||||
0.416268 | + | 0.909242i | \(0.363338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 109.848 | 4.11961 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.97185 | 0.261098 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −53.8593 | −2.01422 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.1379 | −0.677374 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.2623 | 0.830243 | 0.415122 | − | 0.909766i | \(-0.363739\pi\) | ||||
0.415122 | + | 0.909766i | \(0.363739\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.4628 | 0.984161 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.1623 | −0.637392 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6618 | 0.803392 | 0.401696 | − | 0.915773i | \(-0.368421\pi\) | ||||
0.401696 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 51.5497 | 1.90925 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.8698 | −0.771897 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.50596 | 0.166431 | 0.0832156 | − | 0.996532i | \(-0.473481\pi\) | ||||
0.0832156 | + | 0.996532i | \(0.473481\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −46.0179 | −1.69509 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.7692 | −0.580079 | −0.290040 | − | 0.957015i | \(-0.593669\pi\) | ||||
−0.290040 | + | 0.957015i | \(0.593669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.3916 | −1.37361 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.8619 | 1.13222 | 0.566108 | − | 0.824331i | \(-0.308449\pi\) | ||||
0.566108 | + | 0.824331i | \(0.308449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.0113 | −0.623245 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.27790 | 0.193108 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.1808 | 1.39324 | 0.696618 | − | 0.717442i | \(-0.254687\pi\) | ||||
0.696618 | + | 0.717442i | \(0.254687\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.07179 | 0.330594 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.0621 | −1.31243 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.6733 | −0.569655 | −0.284828 | − | 0.958579i | \(-0.591936\pi\) | ||||
−0.284828 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.0180 | 0.617713 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.8363 | −1.51657 | −0.758283 | − | 0.651926i | \(-0.773961\pi\) | ||||
−0.758283 | + | 0.651926i | \(0.773961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 61.1835 | 2.21210 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.14003 | 0.185596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.39928 | −0.194703 | −0.0973515 | − | 0.995250i | \(-0.531037\pi\) | ||||
−0.0973515 | + | 0.995250i | \(0.531037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −78.5397 | −2.82854 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.1956 | −1.33783 | −0.668917 | − | 0.743337i | \(-0.733242\pi\) | ||||
−0.668917 | + | 0.743337i | \(0.733242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.8991 | −1.07401 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.0140 | −0.717077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −75.9399 | −2.71734 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 60.0501 | 2.14602 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −52.7301 | −1.88202 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.9942 | 1.38999 | 0.694997 | − | 0.719013i | \(-0.255406\pi\) | ||||
0.694997 | + | 0.719013i | \(0.255406\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.1029 | −0.395273 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.85331 | 0.136835 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 117.326 | 4.16111 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.8311 | −0.914986 | −0.457493 | − | 0.889213i | \(-0.651253\pi\) | ||||
−0.457493 | + | 0.889213i | \(0.651253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.1991 | −0.891482 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −82.5473 | −2.91667 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 69.1147 | 2.43901 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.2303 | 0.606537 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.7612 | 0.940875 | 0.470437 | − | 0.882433i | \(-0.344096\pi\) | ||||
0.470437 | + | 0.882433i | \(0.344096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.3856 | −1.06698 | −0.533492 | − | 0.845805i | \(-0.679120\pi\) | ||||
−0.533492 | + | 0.845805i | \(0.679120\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 52.8286 | 1.85278 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.6469 | 1.52888 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.8458 | 0.939217 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.5069 | −0.576095 | −0.288048 | − | 0.957616i | \(-0.593006\pi\) | ||||
−0.288048 | + | 0.957616i | \(0.593006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.9562 | −0.695631 | −0.347816 | − | 0.937563i | \(-0.613076\pi\) | ||||
−0.347816 | + | 0.937563i | \(0.613076\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −72.9822 | −2.54091 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.8443 | −1.28120 | −0.640601 | − | 0.767874i | \(-0.721315\pi\) | ||||
−0.640601 | + | 0.767874i | \(0.721315\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.80916 | −0.201760 | −0.100880 | − | 0.994899i | \(-0.532166\pi\) | ||||
−0.100880 | + | 0.994899i | \(0.532166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 72.3714 | 2.51054 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.1505 | −0.662732 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 104.615 | 3.61604 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.2733 | 0.423722 | 0.211861 | − | 0.977300i | \(-0.432048\pi\) | ||||
0.211861 | + | 0.977300i | \(0.432048\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.9848 | −0.447752 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.7259 | 0.644954 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.75942 | −0.163729 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −45.6316 | −1.56607 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.11916 | 0.175483 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2560 | 0.453878 | 0.226939 | − | 0.973909i | \(-0.427128\pi\) | ||||
0.226939 | + | 0.973909i | \(0.427128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −78.7034 | −2.69160 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.1066 | 0.652670 | 0.326335 | − | 0.945254i | \(-0.394186\pi\) | ||||
0.326335 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.1878 | 1.57591 | 0.787953 | − | 0.615735i | \(-0.211141\pi\) | ||||
0.787953 | + | 0.615735i | \(0.211141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.5341 | 0.392625 | 0.196313 | − | 0.980541i | \(-0.437103\pi\) | ||||
0.196313 | + | 0.980541i | \(0.437103\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.94048 | 0.269984 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32.6859 | 1.11007 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 75.4512 | 2.55951 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.7854 | 1.00924 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.6077 | 0.832846 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.9695 | −0.573020 | −0.286510 | − | 0.958077i | \(-0.592495\pi\) | ||||
−0.286510 | + | 0.958077i | \(0.592495\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 51.3336 | 1.73144 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.4505 | −0.385775 | −0.192888 | − | 0.981221i | \(-0.561785\pi\) | ||||
−0.192888 | + | 0.981221i | \(0.561785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3634 | 0.584325 | 0.292162 | − | 0.956369i | \(-0.405625\pi\) | ||||
0.292162 | + | 0.956369i | \(0.405625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.0855 | 0.507093 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.7378 | −0.763460 | −0.381730 | − | 0.924274i | \(-0.624672\pi\) | ||||
−0.381730 | + | 0.924274i | \(0.624672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 136.112 | 4.55992 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.4149 | 1.08472 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 76.9064 | 2.57070 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.0150 | −0.367780 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.9006 | 0.930539 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.1923 | −1.03917 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.15966 | 0.138272 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.5359 | −1.37918 | −0.689588 | − | 0.724202i | \(-0.742208\pi\) | ||||
−0.689588 | + | 0.724202i | \(0.742208\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 63.3438 | 2.10098 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.92749 | 0.0969921 | 0.0484961 | − | 0.998823i | \(-0.484557\pi\) | ||||
0.0484961 | + | 0.998823i | \(0.484557\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.62523 | 0.119978 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.3091 | 0.373867 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.9648 | 0.460658 | 0.230329 | − | 0.973113i | \(-0.426020\pi\) | ||||
0.230329 | + | 0.973113i | \(0.426020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37.4358 | 1.23355 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 49.1527 | 1.61788 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.9537 | −0.721834 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.18247 | −0.104526 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3541 | 0.766222 | 0.383111 | − | 0.923702i | \(-0.374853\pi\) | ||||
0.383111 | + | 0.923702i | \(0.374853\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.3663 | 0.470331 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.0252 | 1.37437 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1156 | −0.363130 | −0.181565 | − | 0.983379i | \(-0.558116\pi\) | ||||
−0.181565 | + | 0.983379i | \(0.558116\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.1977 | −0.659127 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.13868 | −0.167516 | −0.0837580 | − | 0.996486i | \(-0.526692\pi\) | ||||
−0.0837580 | + | 0.996486i | \(0.526692\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.89583 | −0.191995 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.4147 | 0.955851 | 0.477925 | − | 0.878400i | \(-0.341389\pi\) | ||||
0.477925 | + | 0.878400i | \(0.341389\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.7350 | −1.45216 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.9655 | 1.00412 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.67396 | −0.183797 | −0.0918987 | − | 0.995768i | \(-0.529294\pi\) | ||||
−0.0918987 | + | 0.995768i | \(0.529294\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −67.4967 | −2.18414 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 68.1041 | 2.20149 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.6067 | 0.567959 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −90.5905 | −2.91924 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 55.9723 | 1.80181 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.898731 | −0.0289013 | −0.0144506 | − | 0.999896i | \(-0.504600\pi\) | ||||
−0.0144506 | + | 0.999896i | \(0.504600\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.1758 | 0.937262 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.2084 | −1.09780 | −0.548899 | − | 0.835889i | \(-0.684953\pi\) | ||||
−0.548899 | + | 0.835889i | \(0.684953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 47.2382 | 1.51283 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.19697 | 0.262244 | 0.131122 | − | 0.991366i | \(-0.458142\pi\) | ||||
0.131122 | + | 0.991366i | \(0.458142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.6994 | −1.81212 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 136.288 | 4.35133 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.12997 | 0.0360406 | 0.0180203 | − | 0.999838i | \(-0.494264\pi\) | ||||
0.0180203 | + | 0.999838i | \(0.494264\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.28637 | −0.104712 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.90838 | 0.251472 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.6766 | 0.466218 | 0.233109 | − | 0.972451i | \(-0.425110\pi\) | ||||
0.233109 | + | 0.972451i | \(0.425110\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.5973 | −1.03444 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.9250 | 0.536558 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.64207 | 0.0520049 | 0.0260024 | − | 0.999662i | \(-0.491722\pi\) | ||||
0.0260024 | + | 0.999662i | \(0.491722\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 76.8151 | 2.43032 |
(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 | 4508.2.a.f.1.1 | 5 | ||
7.6 | odd | 2 | 644.2.a.d.1.5 | ✓ | 5 | ||
21.20 | even | 2 | 5796.2.a.t.1.4 | 5 | |||
28.27 | even | 2 | 2576.2.a.bb.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
644.2.a.d.1.5 | ✓ | 5 | 7.6 | odd | 2 | ||
2576.2.a.bb.1.1 | 5 | 28.27 | even | 2 | |||
4508.2.a.f.1.1 | 5 | 1.1 | even | 1 | trivial | ||
5796.2.a.t.1.4 | 5 | 21.20 | even | 2 |