Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + 3251 x^{9} - 12183 x^{8} - 4259 x^{7} + 19567 x^{6} + 2029 x^{5} - 16136 x^{4} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.381923\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381923 | 0.270061 | 0.135030 | − | 0.990841i | \(-0.456887\pi\) | ||||
0.135030 | + | 0.990841i | \(0.456887\pi\) | |||||||
\(3\) | 0.350486 | 0.202353 | 0.101177 | − | 0.994868i | \(-0.467739\pi\) | ||||
0.101177 | + | 0.994868i | \(0.467739\pi\) | |||||||
\(4\) | −1.85413 | −0.927067 | ||||||||
\(5\) | 2.79025 | 1.24784 | 0.623918 | − | 0.781490i | \(-0.285540\pi\) | ||||
0.623918 | + | 0.781490i | \(0.285540\pi\) | |||||||
\(6\) | 0.133859 | 0.0546476 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.47198 | −0.520425 | ||||||||
\(9\) | −2.87716 | −0.959053 | ||||||||
\(10\) | 1.06566 | 0.336991 | ||||||||
\(11\) | 2.56629 | 0.773767 | 0.386883 | − | 0.922129i | \(-0.373552\pi\) | ||||
0.386883 | + | 0.922129i | \(0.373552\pi\) | |||||||
\(12\) | −0.649848 | −0.187595 | ||||||||
\(13\) | 2.81325 | 0.780256 | 0.390128 | − | 0.920761i | \(-0.372431\pi\) | ||||
0.390128 | + | 0.920761i | \(0.372431\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.977941 | 0.252503 | ||||||||
\(16\) | 3.14608 | 0.786521 | ||||||||
\(17\) | 6.65325 | 1.61365 | 0.806825 | − | 0.590790i | \(-0.201184\pi\) | ||||
0.806825 | + | 0.590790i | \(0.201184\pi\) | |||||||
\(18\) | −1.09885 | −0.259003 | ||||||||
\(19\) | −2.30819 | −0.529535 | −0.264767 | − | 0.964312i | \(-0.585295\pi\) | ||||
−0.264767 | + | 0.964312i | \(0.585295\pi\) | |||||||
\(20\) | −5.17349 | −1.15683 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.980128 | 0.208964 | ||||||||
\(23\) | −4.36622 | −0.910420 | −0.455210 | − | 0.890384i | \(-0.650436\pi\) | ||||
−0.455210 | + | 0.890384i | \(0.650436\pi\) | |||||||
\(24\) | −0.515909 | −0.105310 | ||||||||
\(25\) | 2.78547 | 0.557095 | ||||||||
\(26\) | 1.07445 | 0.210716 | ||||||||
\(27\) | −2.05986 | −0.396420 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.00821 | −1.67278 | −0.836392 | − | 0.548132i | \(-0.815339\pi\) | ||||
−0.836392 | + | 0.548132i | \(0.815339\pi\) | |||||||
\(30\) | 0.373499 | 0.0681912 | ||||||||
\(31\) | 7.12027 | 1.27884 | 0.639419 | − | 0.768858i | \(-0.279175\pi\) | ||||
0.639419 | + | 0.768858i | \(0.279175\pi\) | |||||||
\(32\) | 4.14553 | 0.732833 | ||||||||
\(33\) | 0.899449 | 0.156574 | ||||||||
\(34\) | 2.54103 | 0.435783 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.33464 | 0.889107 | ||||||||
\(37\) | 11.1900 | 1.83963 | 0.919816 | − | 0.392349i | \(-0.128338\pi\) | ||||
0.919816 | + | 0.392349i | \(0.128338\pi\) | |||||||
\(38\) | −0.881551 | −0.143006 | ||||||||
\(39\) | 0.986005 | 0.157887 | ||||||||
\(40\) | −4.10720 | −0.649405 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.740251 | 0.112887 | 0.0564436 | − | 0.998406i | \(-0.482024\pi\) | ||||
0.0564436 | + | 0.998406i | \(0.482024\pi\) | |||||||
\(44\) | −4.75825 | −0.717334 | ||||||||
\(45\) | −8.02798 | −1.19674 | ||||||||
\(46\) | −1.66756 | −0.245869 | ||||||||
\(47\) | −0.437347 | −0.0637936 | −0.0318968 | − | 0.999491i | \(-0.510155\pi\) | ||||
−0.0318968 | + | 0.999491i | \(0.510155\pi\) | |||||||
\(48\) | 1.10266 | 0.159155 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.06384 | 0.150449 | ||||||||
\(51\) | 2.33187 | 0.326527 | ||||||||
\(52\) | −5.21615 | −0.723350 | ||||||||
\(53\) | 9.64657 | 1.32506 | 0.662529 | − | 0.749036i | \(-0.269483\pi\) | ||||
0.662529 | + | 0.749036i | \(0.269483\pi\) | |||||||
\(54\) | −0.786709 | −0.107058 | ||||||||
\(55\) | 7.16059 | 0.965534 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.808987 | −0.107153 | ||||||||
\(58\) | −3.44045 | −0.451753 | ||||||||
\(59\) | 10.8160 | 1.40812 | 0.704062 | − | 0.710139i | \(-0.251368\pi\) | ||||
0.704062 | + | 0.710139i | \(0.251368\pi\) | |||||||
\(60\) | −1.81324 | −0.234088 | ||||||||
\(61\) | −10.6452 | −1.36298 | −0.681491 | − | 0.731827i | \(-0.738668\pi\) | ||||
−0.681491 | + | 0.731827i | \(0.738668\pi\) | |||||||
\(62\) | 2.71940 | 0.345364 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.70889 | −0.588612 | ||||||||
\(65\) | 7.84967 | 0.973631 | ||||||||
\(66\) | 0.343521 | 0.0422845 | ||||||||
\(67\) | 13.5898 | 1.66026 | 0.830130 | − | 0.557569i | \(-0.188266\pi\) | ||||
0.830130 | + | 0.557569i | \(0.188266\pi\) | |||||||
\(68\) | −12.3360 | −1.49596 | ||||||||
\(69\) | −1.53030 | −0.184226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9653 | 1.65738 | 0.828691 | − | 0.559707i | \(-0.189086\pi\) | ||||
0.828691 | + | 0.559707i | \(0.189086\pi\) | |||||||
\(72\) | 4.23513 | 0.499115 | ||||||||
\(73\) | −8.32207 | −0.974025 | −0.487012 | − | 0.873395i | \(-0.661913\pi\) | ||||
−0.487012 | + | 0.873395i | \(0.661913\pi\) | |||||||
\(74\) | 4.27374 | 0.496812 | ||||||||
\(75\) | 0.976269 | 0.112730 | ||||||||
\(76\) | 4.27969 | 0.490914 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.376578 | 0.0426391 | ||||||||
\(79\) | 5.09976 | 0.573768 | 0.286884 | − | 0.957965i | \(-0.407381\pi\) | ||||
0.286884 | + | 0.957965i | \(0.407381\pi\) | |||||||
\(80\) | 8.77835 | 0.981449 | ||||||||
\(81\) | 7.90953 | 0.878836 | ||||||||
\(82\) | −0.381923 | −0.0421764 | ||||||||
\(83\) | 5.83272 | 0.640224 | 0.320112 | − | 0.947380i | \(-0.396279\pi\) | ||||
0.320112 | + | 0.947380i | \(0.396279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.5642 | 2.01357 | ||||||||
\(86\) | 0.282719 | 0.0304864 | ||||||||
\(87\) | −3.15725 | −0.338493 | ||||||||
\(88\) | −3.77754 | −0.402688 | ||||||||
\(89\) | −4.07202 | −0.431633 | −0.215817 | − | 0.976434i | \(-0.569241\pi\) | ||||
−0.215817 | + | 0.976434i | \(0.569241\pi\) | |||||||
\(90\) | −3.06607 | −0.323193 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.09556 | 0.844021 | ||||||||
\(93\) | 2.49555 | 0.258777 | ||||||||
\(94\) | −0.167033 | −0.0172281 | ||||||||
\(95\) | −6.44041 | −0.660772 | ||||||||
\(96\) | 1.45295 | 0.148291 | ||||||||
\(97\) | 9.55210 | 0.969869 | 0.484935 | − | 0.874550i | \(-0.338843\pi\) | ||||
0.484935 | + | 0.874550i | \(0.338843\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.38364 | −0.742084 | ||||||||
\(100\) | −5.16464 | −0.516464 | ||||||||
\(101\) | −9.23725 | −0.919141 | −0.459571 | − | 0.888141i | \(-0.651997\pi\) | ||||
−0.459571 | + | 0.888141i | \(0.651997\pi\) | |||||||
\(102\) | 0.890596 | 0.0881821 | ||||||||
\(103\) | 10.8162 | 1.06576 | 0.532878 | − | 0.846192i | \(-0.321111\pi\) | ||||
0.532878 | + | 0.846192i | \(0.321111\pi\) | |||||||
\(104\) | −4.14106 | −0.406065 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.68425 | 0.357846 | ||||||||
\(107\) | −10.2115 | −0.987185 | −0.493592 | − | 0.869693i | \(-0.664316\pi\) | ||||
−0.493592 | + | 0.869693i | \(0.664316\pi\) | |||||||
\(108\) | 3.81926 | 0.367508 | ||||||||
\(109\) | −15.4796 | −1.48267 | −0.741336 | − | 0.671134i | \(-0.765808\pi\) | ||||
−0.741336 | + | 0.671134i | \(0.765808\pi\) | |||||||
\(110\) | 2.73480 | 0.260753 | ||||||||
\(111\) | 3.92195 | 0.372255 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.39660 | 0.507670 | 0.253835 | − | 0.967248i | \(-0.418308\pi\) | ||||
0.253835 | + | 0.967248i | \(0.418308\pi\) | |||||||
\(114\) | −0.308971 | −0.0289378 | ||||||||
\(115\) | −12.1828 | −1.13605 | ||||||||
\(116\) | 16.7024 | 1.55078 | ||||||||
\(117\) | −8.09418 | −0.748307 | ||||||||
\(118\) | 4.13088 | 0.380279 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.43951 | −0.131409 | ||||||||
\(121\) | −4.41414 | −0.401285 | ||||||||
\(122\) | −4.06566 | −0.368087 | ||||||||
\(123\) | −0.350486 | −0.0316022 | ||||||||
\(124\) | −13.2019 | −1.18557 | ||||||||
\(125\) | −6.17907 | −0.552673 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.53912 | 0.402782 | 0.201391 | − | 0.979511i | \(-0.435454\pi\) | ||||
0.201391 | + | 0.979511i | \(0.435454\pi\) | |||||||
\(128\) | −10.0895 | −0.891794 | ||||||||
\(129\) | 0.259447 | 0.0228431 | ||||||||
\(130\) | 2.99797 | 0.262939 | ||||||||
\(131\) | 12.1667 | 1.06301 | 0.531503 | − | 0.847057i | \(-0.321628\pi\) | ||||
0.531503 | + | 0.847057i | \(0.321628\pi\) | |||||||
\(132\) | −1.66770 | −0.145155 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.19027 | 0.448371 | ||||||||
\(135\) | −5.74752 | −0.494668 | ||||||||
\(136\) | −9.79348 | −0.839784 | ||||||||
\(137\) | 1.28517 | 0.109800 | 0.0548999 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0548999 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(138\) | −0.584457 | −0.0497523 | ||||||||
\(139\) | −12.1515 | −1.03068 | −0.515339 | − | 0.856986i | \(-0.672334\pi\) | ||||
−0.515339 | + | 0.856986i | \(0.672334\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.153284 | −0.0129088 | ||||||||
\(142\) | 5.33369 | 0.447593 | ||||||||
\(143\) | 7.21963 | 0.603736 | ||||||||
\(144\) | −9.05179 | −0.754316 | ||||||||
\(145\) | −25.1351 | −2.08736 | ||||||||
\(146\) | −3.17839 | −0.263046 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −20.7479 | −1.70546 | ||||||||
\(149\) | 15.2610 | 1.25023 | 0.625113 | − | 0.780534i | \(-0.285053\pi\) | ||||
0.625113 | + | 0.780534i | \(0.285053\pi\) | |||||||
\(150\) | 0.372860 | 0.0304439 | ||||||||
\(151\) | −4.51478 | −0.367407 | −0.183704 | − | 0.982982i | \(-0.558809\pi\) | ||||
−0.183704 | + | 0.982982i | \(0.558809\pi\) | |||||||
\(152\) | 3.39762 | 0.275583 | ||||||||
\(153\) | −19.1425 | −1.54758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.8673 | 1.59578 | ||||||||
\(156\) | −1.82819 | −0.146372 | ||||||||
\(157\) | 15.5519 | 1.24118 | 0.620589 | − | 0.784136i | \(-0.286893\pi\) | ||||
0.620589 | + | 0.784136i | \(0.286893\pi\) | |||||||
\(158\) | 1.94772 | 0.154952 | ||||||||
\(159\) | 3.38099 | 0.268130 | ||||||||
\(160\) | 11.5671 | 0.914456 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.02083 | 0.237339 | ||||||||
\(163\) | 1.61931 | 0.126834 | 0.0634172 | − | 0.997987i | \(-0.479800\pi\) | ||||
0.0634172 | + | 0.997987i | \(0.479800\pi\) | |||||||
\(164\) | 1.85413 | 0.144784 | ||||||||
\(165\) | 2.50969 | 0.195379 | ||||||||
\(166\) | 2.22765 | 0.172899 | ||||||||
\(167\) | 20.8888 | 1.61643 | 0.808214 | − | 0.588890i | \(-0.200435\pi\) | ||||
0.808214 | + | 0.588890i | \(0.200435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.08561 | −0.391201 | ||||||||
\(170\) | 7.09011 | 0.543786 | ||||||||
\(171\) | 6.64103 | 0.507852 | ||||||||
\(172\) | −1.37252 | −0.104654 | ||||||||
\(173\) | −7.19393 | −0.546944 | −0.273472 | − | 0.961880i | \(-0.588172\pi\) | ||||
−0.273472 | + | 0.961880i | \(0.588172\pi\) | |||||||
\(174\) | −1.20583 | −0.0914136 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.07378 | 0.608584 | ||||||||
\(177\) | 3.79085 | 0.284938 | ||||||||
\(178\) | −1.55520 | −0.116567 | ||||||||
\(179\) | 1.36999 | 0.102398 | 0.0511991 | − | 0.998688i | \(-0.483696\pi\) | ||||
0.0511991 | + | 0.998688i | \(0.483696\pi\) | |||||||
\(180\) | 14.8850 | 1.10946 | ||||||||
\(181\) | −8.57407 | −0.637306 | −0.318653 | − | 0.947872i | \(-0.603230\pi\) | ||||
−0.318653 | + | 0.947872i | \(0.603230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.73100 | −0.275803 | ||||||||
\(184\) | 6.42701 | 0.473805 | ||||||||
\(185\) | 31.2230 | 2.29556 | ||||||||
\(186\) | 0.953110 | 0.0698854 | ||||||||
\(187\) | 17.0742 | 1.24859 | ||||||||
\(188\) | 0.810900 | 0.0591410 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.45974 | −0.178449 | ||||||||
\(191\) | 2.48778 | 0.180009 | 0.0900046 | − | 0.995941i | \(-0.471312\pi\) | ||||
0.0900046 | + | 0.995941i | \(0.471312\pi\) | |||||||
\(192\) | −1.65040 | −0.119107 | ||||||||
\(193\) | 4.18984 | 0.301592 | 0.150796 | − | 0.988565i | \(-0.451816\pi\) | ||||
0.150796 | + | 0.988565i | \(0.451816\pi\) | |||||||
\(194\) | 3.64817 | 0.261923 | ||||||||
\(195\) | 2.75120 | 0.197017 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.70173 | −0.619972 | −0.309986 | − | 0.950741i | \(-0.600324\pi\) | ||||
−0.309986 | + | 0.950741i | \(0.600324\pi\) | |||||||
\(198\) | −2.81998 | −0.200408 | ||||||||
\(199\) | −3.29100 | −0.233293 | −0.116646 | − | 0.993174i | \(-0.537214\pi\) | ||||
−0.116646 | + | 0.993174i | \(0.537214\pi\) | |||||||
\(200\) | −4.10017 | −0.289926 | ||||||||
\(201\) | 4.76304 | 0.335959 | ||||||||
\(202\) | −3.52792 | −0.248224 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.32360 | −0.302713 | ||||||||
\(205\) | −2.79025 | −0.194879 | ||||||||
\(206\) | 4.13097 | 0.287818 | ||||||||
\(207\) | 12.5623 | 0.873141 | ||||||||
\(208\) | 8.85073 | 0.613688 | ||||||||
\(209\) | −5.92349 | −0.409736 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.2898 | −0.914905 | −0.457452 | − | 0.889234i | \(-0.651238\pi\) | ||||
−0.457452 | + | 0.889234i | \(0.651238\pi\) | |||||||
\(212\) | −17.8860 | −1.22842 | ||||||||
\(213\) | 4.89465 | 0.335376 | ||||||||
\(214\) | −3.90002 | −0.266600 | ||||||||
\(215\) | 2.06548 | 0.140865 | ||||||||
\(216\) | 3.03208 | 0.206307 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.91200 | −0.400411 | ||||||||
\(219\) | −2.91677 | −0.197097 | ||||||||
\(220\) | −13.2767 | −0.895115 | ||||||||
\(221\) | 18.7173 | 1.25906 | ||||||||
\(222\) | 1.49789 | 0.100531 | ||||||||
\(223\) | −0.947240 | −0.0634319 | −0.0317159 | − | 0.999497i | \(-0.510097\pi\) | ||||
−0.0317159 | + | 0.999497i | \(0.510097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.01425 | −0.534284 | ||||||||
\(226\) | 2.06109 | 0.137102 | ||||||||
\(227\) | −0.0180577 | −0.00119853 | −0.000599267 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000599267 | 1.00000i | \(0.500191\pi\) | ||||||||
\(228\) | 1.49997 | 0.0993380 | ||||||||
\(229\) | −3.88646 | −0.256824 | −0.128412 | − | 0.991721i | \(-0.540988\pi\) | ||||
−0.128412 | + | 0.991721i | \(0.540988\pi\) | |||||||
\(230\) | −4.65291 | −0.306804 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.2599 | 0.870558 | ||||||||
\(233\) | −14.5343 | −0.952171 | −0.476085 | − | 0.879399i | \(-0.657945\pi\) | ||||
−0.476085 | + | 0.879399i | \(0.657945\pi\) | |||||||
\(234\) | −3.09135 | −0.202088 | ||||||||
\(235\) | −1.22031 | −0.0796040 | ||||||||
\(236\) | −20.0543 | −1.30542 | ||||||||
\(237\) | 1.78739 | 0.116104 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.0608 | −0.780145 | −0.390073 | − | 0.920784i | \(-0.627550\pi\) | ||||
−0.390073 | + | 0.920784i | \(0.627550\pi\) | |||||||
\(240\) | 3.07669 | 0.198599 | ||||||||
\(241\) | −2.65986 | −0.171336 | −0.0856682 | − | 0.996324i | \(-0.527302\pi\) | ||||
−0.0856682 | + | 0.996324i | \(0.527302\pi\) | |||||||
\(242\) | −1.68586 | −0.108371 | ||||||||
\(243\) | 8.95176 | 0.574256 | ||||||||
\(244\) | 19.7377 | 1.26358 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.133859 | −0.00853452 | ||||||||
\(247\) | −6.49352 | −0.413172 | ||||||||
\(248\) | −10.4809 | −0.665540 | ||||||||
\(249\) | 2.04429 | 0.129551 | ||||||||
\(250\) | −2.35993 | −0.149255 | ||||||||
\(251\) | −12.4762 | −0.787489 | −0.393744 | − | 0.919220i | \(-0.628820\pi\) | ||||
−0.393744 | + | 0.919220i | \(0.628820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.2050 | −0.704453 | ||||||||
\(254\) | 1.73360 | 0.108775 | ||||||||
\(255\) | 6.50649 | 0.407452 | ||||||||
\(256\) | 5.56437 | 0.347773 | ||||||||
\(257\) | −2.73873 | −0.170838 | −0.0854188 | − | 0.996345i | \(-0.527223\pi\) | ||||
−0.0854188 | + | 0.996345i | \(0.527223\pi\) | |||||||
\(258\) | 0.0990890 | 0.00616901 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −14.5543 | −0.902622 | ||||||||
\(261\) | 25.9181 | 1.60429 | ||||||||
\(262\) | 4.64673 | 0.287076 | ||||||||
\(263\) | −0.230482 | −0.0142121 | −0.00710607 | − | 0.999975i | \(-0.502262\pi\) | ||||
−0.00710607 | + | 0.999975i | \(0.502262\pi\) | |||||||
\(264\) | −1.32398 | −0.0814850 | ||||||||
\(265\) | 26.9163 | 1.65346 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.42719 | −0.0873423 | ||||||||
\(268\) | −25.1974 | −1.53917 | ||||||||
\(269\) | 8.89980 | 0.542630 | 0.271315 | − | 0.962491i | \(-0.412541\pi\) | ||||
0.271315 | + | 0.962491i | \(0.412541\pi\) | |||||||
\(270\) | −2.19511 | −0.133590 | ||||||||
\(271\) | −15.7432 | −0.956329 | −0.478165 | − | 0.878270i | \(-0.658698\pi\) | ||||
−0.478165 | + | 0.878270i | \(0.658698\pi\) | |||||||
\(272\) | 20.9317 | 1.26917 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.490838 | 0.0296526 | ||||||||
\(275\) | 7.14835 | 0.431061 | ||||||||
\(276\) | 2.83738 | 0.170790 | ||||||||
\(277\) | 14.8431 | 0.891833 | 0.445917 | − | 0.895074i | \(-0.352878\pi\) | ||||
0.445917 | + | 0.895074i | \(0.352878\pi\) | |||||||
\(278\) | −4.64095 | −0.278346 | ||||||||
\(279\) | −20.4862 | −1.22647 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.52162 | −0.448702 | −0.224351 | − | 0.974508i | \(-0.572026\pi\) | ||||
−0.224351 | + | 0.974508i | \(0.572026\pi\) | |||||||
\(282\) | −0.0585427 | −0.00348617 | ||||||||
\(283\) | −0.386790 | −0.0229923 | −0.0114961 | − | 0.999934i | \(-0.503659\pi\) | ||||
−0.0114961 | + | 0.999934i | \(0.503659\pi\) | |||||||
\(284\) | −25.8936 | −1.53650 | ||||||||
\(285\) | −2.25727 | −0.133709 | ||||||||
\(286\) | 2.75735 | 0.163045 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −11.9274 | −0.702826 | ||||||||
\(289\) | 27.2658 | 1.60387 | ||||||||
\(290\) | −9.59970 | −0.563714 | ||||||||
\(291\) | 3.34788 | 0.196256 | ||||||||
\(292\) | 15.4302 | 0.902986 | ||||||||
\(293\) | 0.553673 | 0.0323459 | 0.0161729 | − | 0.999869i | \(-0.494852\pi\) | ||||
0.0161729 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.1793 | 1.75711 | ||||||||
\(296\) | −16.4716 | −0.957391 | ||||||||
\(297\) | −5.28621 | −0.306737 | ||||||||
\(298\) | 5.82852 | 0.337637 | ||||||||
\(299\) | −12.2833 | −0.710360 | ||||||||
\(300\) | −1.81013 | −0.104508 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.72430 | −0.0992222 | ||||||||
\(303\) | −3.23753 | −0.185991 | ||||||||
\(304\) | −7.26175 | −0.416490 | ||||||||
\(305\) | −29.7028 | −1.70078 | ||||||||
\(306\) | −7.31096 | −0.417940 | ||||||||
\(307\) | −31.1079 | −1.77542 | −0.887710 | − | 0.460403i | \(-0.847705\pi\) | ||||
−0.887710 | + | 0.460403i | \(0.847705\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.79094 | 0.215659 | ||||||||
\(310\) | 7.58779 | 0.430958 | ||||||||
\(311\) | −22.5749 | −1.28011 | −0.640053 | − | 0.768331i | \(-0.721087\pi\) | ||||
−0.640053 | + | 0.768331i | \(0.721087\pi\) | |||||||
\(312\) | −1.45138 | −0.0821684 | ||||||||
\(313\) | 20.1533 | 1.13913 | 0.569565 | − | 0.821946i | \(-0.307112\pi\) | ||||
0.569565 | + | 0.821946i | \(0.307112\pi\) | |||||||
\(314\) | 5.93964 | 0.335193 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.45564 | −0.531921 | ||||||||
\(317\) | 1.47763 | 0.0829920 | 0.0414960 | − | 0.999139i | \(-0.486788\pi\) | ||||
0.0414960 | + | 0.999139i | \(0.486788\pi\) | |||||||
\(318\) | 1.29128 | 0.0724113 | ||||||||
\(319\) | −23.1177 | −1.29434 | ||||||||
\(320\) | −13.1390 | −0.734491 | ||||||||
\(321\) | −3.57899 | −0.199760 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.3570 | −0.854484 | ||||||||
\(324\) | −14.6653 | −0.814740 | ||||||||
\(325\) | 7.83624 | 0.434676 | ||||||||
\(326\) | 0.618454 | 0.0342530 | ||||||||
\(327\) | −5.42536 | −0.300023 | ||||||||
\(328\) | 1.47198 | 0.0812767 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.958507 | 0.0527641 | ||||||||
\(331\) | −9.90120 | −0.544219 | −0.272110 | − | 0.962266i | \(-0.587721\pi\) | ||||
−0.272110 | + | 0.962266i | \(0.587721\pi\) | |||||||
\(332\) | −10.8146 | −0.593531 | ||||||||
\(333\) | −32.1956 | −1.76431 | ||||||||
\(334\) | 7.97794 | 0.436533 | ||||||||
\(335\) | 37.9189 | 2.07173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.08380 | −0.276932 | −0.138466 | − | 0.990367i | \(-0.544217\pi\) | ||||
−0.138466 | + | 0.990367i | \(0.544217\pi\) | |||||||
\(338\) | −1.94231 | −0.105648 | ||||||||
\(339\) | 1.89143 | 0.102729 | ||||||||
\(340\) | −34.4205 | −1.86672 | ||||||||
\(341\) | 18.2727 | 0.989523 | ||||||||
\(342\) | 2.53636 | 0.137151 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.08964 | −0.0587493 | ||||||||
\(345\) | −4.26991 | −0.229884 | ||||||||
\(346\) | −2.74753 | −0.147708 | ||||||||
\(347\) | 1.43251 | 0.0769011 | 0.0384506 | − | 0.999261i | \(-0.487758\pi\) | ||||
0.0384506 | + | 0.999261i | \(0.487758\pi\) | |||||||
\(348\) | 5.85397 | 0.313806 | ||||||||
\(349\) | −30.5990 | −1.63792 | −0.818962 | − | 0.573847i | \(-0.805450\pi\) | ||||
−0.818962 | + | 0.573847i | \(0.805450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.79491 | −0.309309 | ||||||||
\(352\) | 10.6387 | 0.567042 | ||||||||
\(353\) | −11.6733 | −0.621307 | −0.310653 | − | 0.950523i | \(-0.600548\pi\) | ||||
−0.310653 | + | 0.950523i | \(0.600548\pi\) | |||||||
\(354\) | 1.44782 | 0.0769505 | ||||||||
\(355\) | 38.9667 | 2.06814 | ||||||||
\(356\) | 7.55008 | 0.400153 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.523233 | 0.0276537 | ||||||||
\(359\) | −14.4087 | −0.760462 | −0.380231 | − | 0.924891i | \(-0.624156\pi\) | ||||
−0.380231 | + | 0.924891i | \(0.624156\pi\) | |||||||
\(360\) | 11.8171 | 0.622814 | ||||||||
\(361\) | −13.6723 | −0.719593 | ||||||||
\(362\) | −3.27464 | −0.172111 | ||||||||
\(363\) | −1.54709 | −0.0812012 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.2206 | −1.21542 | ||||||||
\(366\) | −1.42496 | −0.0744836 | ||||||||
\(367\) | −33.8514 | −1.76703 | −0.883513 | − | 0.468406i | \(-0.844828\pi\) | ||||
−0.883513 | + | 0.468406i | \(0.844828\pi\) | |||||||
\(368\) | −13.7365 | −0.716064 | ||||||||
\(369\) | 2.87716 | 0.149779 | ||||||||
\(370\) | 11.9248 | 0.619940 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.62709 | −0.239904 | ||||||||
\(373\) | −14.1001 | −0.730077 | −0.365039 | − | 0.930992i | \(-0.618944\pi\) | ||||
−0.365039 | + | 0.930992i | \(0.618944\pi\) | |||||||
\(374\) | 6.52104 | 0.337195 | ||||||||
\(375\) | −2.16568 | −0.111835 | ||||||||
\(376\) | 0.643768 | 0.0331998 | ||||||||
\(377\) | −25.3424 | −1.30520 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.0376 | 1.69703 | 0.848513 | − | 0.529175i | \(-0.177499\pi\) | ||||
0.848513 | + | 0.529175i | \(0.177499\pi\) | |||||||
\(380\) | 11.9414 | 0.612581 | ||||||||
\(381\) | 1.59090 | 0.0815041 | ||||||||
\(382\) | 0.950140 | 0.0486134 | ||||||||
\(383\) | −6.88197 | −0.351652 | −0.175826 | − | 0.984421i | \(-0.556260\pi\) | ||||
−0.175826 | + | 0.984421i | \(0.556260\pi\) | |||||||
\(384\) | −3.53623 | −0.180457 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.60020 | 0.0814480 | ||||||||
\(387\) | −2.12982 | −0.108265 | ||||||||
\(388\) | −17.7109 | −0.899134 | ||||||||
\(389\) | 27.6030 | 1.39953 | 0.699765 | − | 0.714373i | \(-0.253288\pi\) | ||||
0.699765 | + | 0.714373i | \(0.253288\pi\) | |||||||
\(390\) | 1.05075 | 0.0532066 | ||||||||
\(391\) | −29.0496 | −1.46910 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.26424 | 0.215102 | ||||||||
\(394\) | −3.32339 | −0.167430 | ||||||||
\(395\) | 14.2296 | 0.715968 | ||||||||
\(396\) | 13.6903 | 0.687961 | ||||||||
\(397\) | −25.8854 | −1.29915 | −0.649576 | − | 0.760297i | \(-0.725054\pi\) | ||||
−0.649576 | + | 0.760297i | \(0.725054\pi\) | |||||||
\(398\) | −1.25691 | −0.0630032 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.76334 | 0.438167 | ||||||||
\(401\) | 3.79311 | 0.189419 | 0.0947093 | − | 0.995505i | \(-0.469808\pi\) | ||||
0.0947093 | + | 0.995505i | \(0.469808\pi\) | |||||||
\(402\) | 1.81912 | 0.0907292 | ||||||||
\(403\) | 20.0311 | 0.997821 | ||||||||
\(404\) | 17.1271 | 0.852106 | ||||||||
\(405\) | 22.0695 | 1.09664 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.7170 | 1.42345 | ||||||||
\(408\) | −3.43247 | −0.169933 | ||||||||
\(409\) | 25.0191 | 1.23712 | 0.618558 | − | 0.785739i | \(-0.287717\pi\) | ||||
0.618558 | + | 0.785739i | \(0.287717\pi\) | |||||||
\(410\) | −1.06566 | −0.0526292 | ||||||||
\(411\) | 0.450435 | 0.0222183 | ||||||||
\(412\) | −20.0548 | −0.988027 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.79784 | 0.235801 | ||||||||
\(415\) | 16.2747 | 0.798895 | ||||||||
\(416\) | 11.6624 | 0.571797 | ||||||||
\(417\) | −4.25894 | −0.208561 | ||||||||
\(418\) | −2.26232 | −0.110654 | ||||||||
\(419\) | −23.1834 | −1.13258 | −0.566291 | − | 0.824205i | \(-0.691622\pi\) | ||||
−0.566291 | + | 0.824205i | \(0.691622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00007 | −0.341163 | −0.170581 | − | 0.985344i | \(-0.554565\pi\) | ||||
−0.170581 | + | 0.985344i | \(0.554565\pi\) | |||||||
\(422\) | −5.07567 | −0.247080 | ||||||||
\(423\) | 1.25832 | 0.0611815 | ||||||||
\(424\) | −14.1996 | −0.689594 | ||||||||
\(425\) | 18.5325 | 0.898956 | ||||||||
\(426\) | 1.86938 | 0.0905719 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.9335 | 0.915186 | ||||||||
\(429\) | 2.53038 | 0.122168 | ||||||||
\(430\) | 0.788856 | 0.0380420 | ||||||||
\(431\) | −18.9909 | −0.914759 | −0.457379 | − | 0.889272i | \(-0.651212\pi\) | ||||
−0.457379 | + | 0.889272i | \(0.651212\pi\) | |||||||
\(432\) | −6.48049 | −0.311793 | ||||||||
\(433\) | −1.94264 | −0.0933571 | −0.0466786 | − | 0.998910i | \(-0.514864\pi\) | ||||
−0.0466786 | + | 0.998910i | \(0.514864\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.80951 | −0.422383 | ||||||||
\(436\) | 28.7012 | 1.37454 | ||||||||
\(437\) | 10.0781 | 0.482099 | ||||||||
\(438\) | −1.11398 | −0.0532281 | ||||||||
\(439\) | −20.0057 | −0.954818 | −0.477409 | − | 0.878681i | \(-0.658424\pi\) | ||||
−0.477409 | + | 0.878681i | \(0.658424\pi\) | |||||||
\(440\) | −10.5403 | −0.502488 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.14856 | 0.340023 | ||||||||
\(443\) | −2.61996 | −0.124478 | −0.0622390 | − | 0.998061i | \(-0.519824\pi\) | ||||
−0.0622390 | + | 0.998061i | \(0.519824\pi\) | |||||||
\(444\) | −7.27183 | −0.345106 | ||||||||
\(445\) | −11.3619 | −0.538608 | ||||||||
\(446\) | −0.361773 | −0.0171304 | ||||||||
\(447\) | 5.34875 | 0.252987 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.8631 | −0.701434 | −0.350717 | − | 0.936482i | \(-0.614062\pi\) | ||||
−0.350717 | + | 0.936482i | \(0.614062\pi\) | |||||||
\(450\) | −3.06083 | −0.144289 | ||||||||
\(451\) | −2.56629 | −0.120842 | ||||||||
\(452\) | −10.0060 | −0.470644 | ||||||||
\(453\) | −1.58236 | −0.0743460 | ||||||||
\(454\) | −0.00689667 | −0.000323677 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.19082 | 0.0557651 | ||||||||
\(457\) | −35.4909 | −1.66020 | −0.830098 | − | 0.557618i | \(-0.811715\pi\) | ||||
−0.830098 | + | 0.557618i | \(0.811715\pi\) | |||||||
\(458\) | −1.48433 | −0.0693582 | ||||||||
\(459\) | −13.7048 | −0.639684 | ||||||||
\(460\) | 22.5886 | 1.05320 | ||||||||
\(461\) | −26.2318 | −1.22174 | −0.610868 | − | 0.791733i | \(-0.709179\pi\) | ||||
−0.610868 | + | 0.791733i | \(0.709179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.8514 | 1.52673 | 0.763366 | − | 0.645966i | \(-0.223545\pi\) | ||||
0.763366 | + | 0.645966i | \(0.223545\pi\) | |||||||
\(464\) | −28.3406 | −1.31568 | ||||||||
\(465\) | 6.96321 | 0.322911 | ||||||||
\(466\) | −5.55097 | −0.257144 | ||||||||
\(467\) | 3.27993 | 0.151777 | 0.0758886 | − | 0.997116i | \(-0.475821\pi\) | ||||
0.0758886 | + | 0.997116i | \(0.475821\pi\) | |||||||
\(468\) | 15.0077 | 0.693731 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.466063 | −0.0214979 | ||||||||
\(471\) | 5.45073 | 0.251156 | ||||||||
\(472\) | −15.9210 | −0.732822 | ||||||||
\(473\) | 1.89970 | 0.0873483 | ||||||||
\(474\) | 0.682647 | 0.0313550 | ||||||||
\(475\) | −6.42940 | −0.295001 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.7547 | −1.27080 | ||||||||
\(478\) | −4.60628 | −0.210686 | ||||||||
\(479\) | 6.31527 | 0.288552 | 0.144276 | − | 0.989537i | \(-0.453915\pi\) | ||||
0.144276 | + | 0.989537i | \(0.453915\pi\) | |||||||
\(480\) | 4.05409 | 0.185043 | ||||||||
\(481\) | 31.4804 | 1.43538 | ||||||||
\(482\) | −1.01586 | −0.0462712 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.18440 | 0.372018 | ||||||||
\(485\) | 26.6527 | 1.21024 | ||||||||
\(486\) | 3.41889 | 0.155084 | ||||||||
\(487\) | 13.9699 | 0.633039 | 0.316519 | − | 0.948586i | \(-0.397486\pi\) | ||||
0.316519 | + | 0.948586i | \(0.397486\pi\) | |||||||
\(488\) | 15.6696 | 0.709329 | ||||||||
\(489\) | 0.567546 | 0.0256653 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.9855 | −1.26297 | −0.631484 | − | 0.775389i | \(-0.717554\pi\) | ||||
−0.631484 | + | 0.775389i | \(0.717554\pi\) | |||||||
\(492\) | 0.649848 | 0.0292974 | ||||||||
\(493\) | −59.9339 | −2.69929 | ||||||||
\(494\) | −2.48003 | −0.111582 | ||||||||
\(495\) | −20.6022 | −0.925999 | ||||||||
\(496\) | 22.4010 | 1.00583 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.780760 | 0.0349867 | ||||||||
\(499\) | −6.61178 | −0.295984 | −0.147992 | − | 0.988989i | \(-0.547281\pi\) | ||||
−0.147992 | + | 0.988989i | \(0.547281\pi\) | |||||||
\(500\) | 11.4568 | 0.512365 | ||||||||
\(501\) | 7.32124 | 0.327089 | ||||||||
\(502\) | −4.76494 | −0.212670 | ||||||||
\(503\) | 18.2722 | 0.814717 | 0.407358 | − | 0.913268i | \(-0.366450\pi\) | ||||
0.407358 | + | 0.913268i | \(0.366450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.7742 | −1.14694 | ||||||||
\(506\) | −4.27945 | −0.190245 | ||||||||
\(507\) | −1.78243 | −0.0791607 | ||||||||
\(508\) | −8.41614 | −0.373406 | ||||||||
\(509\) | −0.735146 | −0.0325848 | −0.0162924 | − | 0.999867i | \(-0.505186\pi\) | ||||
−0.0162924 | + | 0.999867i | \(0.505186\pi\) | |||||||
\(510\) | 2.48498 | 0.110037 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.3042 | 0.985714 | ||||||||
\(513\) | 4.75455 | 0.209918 | ||||||||
\(514\) | −1.04599 | −0.0461365 | ||||||||
\(515\) | 30.1800 | 1.32989 | ||||||||
\(516\) | −0.481050 | −0.0211771 | ||||||||
\(517\) | −1.12236 | −0.0493614 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.52137 | −0.110676 | ||||||||
\(520\) | −11.5546 | −0.506702 | ||||||||
\(521\) | −39.6253 | −1.73602 | −0.868008 | − | 0.496550i | \(-0.834600\pi\) | ||||
−0.868008 | + | 0.496550i | \(0.834600\pi\) | |||||||
\(522\) | 9.89872 | 0.433255 | ||||||||
\(523\) | 30.1005 | 1.31620 | 0.658101 | − | 0.752930i | \(-0.271360\pi\) | ||||
0.658101 | + | 0.752930i | \(0.271360\pi\) | |||||||
\(524\) | −22.5586 | −0.985477 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.0880265 | −0.00383814 | ||||||||
\(527\) | 47.3730 | 2.06360 | ||||||||
\(528\) | 2.82974 | 0.123149 | ||||||||
\(529\) | −3.93611 | −0.171135 | ||||||||
\(530\) | 10.2800 | 0.446533 | ||||||||
\(531\) | −31.1194 | −1.35047 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.81325 | −0.121855 | ||||||||
\(534\) | −0.545076 | −0.0235877 | ||||||||
\(535\) | −28.4926 | −1.23184 | ||||||||
\(536\) | −20.0040 | −0.864041 | ||||||||
\(537\) | 0.480163 | 0.0207206 | ||||||||
\(538\) | 3.39904 | 0.146543 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.6567 | 0.458590 | ||||||||
\(541\) | 16.2139 | 0.697088 | 0.348544 | − | 0.937292i | \(-0.386676\pi\) | ||||
0.348544 | + | 0.937292i | \(0.386676\pi\) | |||||||
\(542\) | −6.01268 | −0.258267 | ||||||||
\(543\) | −3.00509 | −0.128961 | ||||||||
\(544\) | 27.5813 | 1.18254 | ||||||||
\(545\) | −43.1918 | −1.85013 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.2961 | 1.72294 | 0.861468 | − | 0.507812i | \(-0.169546\pi\) | ||||
0.861468 | + | 0.507812i | \(0.169546\pi\) | |||||||
\(548\) | −2.38289 | −0.101792 | ||||||||
\(549\) | 30.6280 | 1.30717 | ||||||||
\(550\) | 2.73012 | 0.116413 | ||||||||
\(551\) | 20.7927 | 0.885797 | ||||||||
\(552\) | 2.25257 | 0.0958759 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.66891 | 0.240849 | ||||||||
\(555\) | 10.9432 | 0.464513 | ||||||||
\(556\) | 22.5306 | 0.955509 | ||||||||
\(557\) | −17.3769 | −0.736283 | −0.368141 | − | 0.929770i | \(-0.620006\pi\) | ||||
−0.368141 | + | 0.929770i | \(0.620006\pi\) | |||||||
\(558\) | −7.82414 | −0.331222 | ||||||||
\(559\) | 2.08251 | 0.0880809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.98426 | 0.252656 | ||||||||
\(562\) | −2.87268 | −0.121177 | ||||||||
\(563\) | 25.7302 | 1.08440 | 0.542199 | − | 0.840250i | \(-0.317592\pi\) | ||||
0.542199 | + | 0.840250i | \(0.317592\pi\) | |||||||
\(564\) | 0.284209 | 0.0119674 | ||||||||
\(565\) | 15.0579 | 0.633489 | ||||||||
\(566\) | −0.147724 | −0.00620931 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.5568 | −0.862543 | ||||||||
\(569\) | 19.1948 | 0.804686 | 0.402343 | − | 0.915489i | \(-0.368196\pi\) | ||||
0.402343 | + | 0.915489i | \(0.368196\pi\) | |||||||
\(570\) | −0.862105 | −0.0361096 | ||||||||
\(571\) | 3.03484 | 0.127004 | 0.0635020 | − | 0.997982i | \(-0.479773\pi\) | ||||
0.0635020 | + | 0.997982i | \(0.479773\pi\) | |||||||
\(572\) | −13.3862 | −0.559704 | ||||||||
\(573\) | 0.871931 | 0.0364254 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.1620 | −0.507190 | ||||||||
\(576\) | 13.5482 | 0.564510 | ||||||||
\(577\) | 19.4877 | 0.811282 | 0.405641 | − | 0.914033i | \(-0.367048\pi\) | ||||
0.405641 | + | 0.914033i | \(0.367048\pi\) | |||||||
\(578\) | 10.4134 | 0.433142 | ||||||||
\(579\) | 1.46848 | 0.0610280 | ||||||||
\(580\) | 46.6039 | 1.93512 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.27863 | 0.0530010 | ||||||||
\(583\) | 24.7559 | 1.02529 | ||||||||
\(584\) | 12.2500 | 0.506907 | ||||||||
\(585\) | −22.5847 | −0.933764 | ||||||||
\(586\) | 0.211460 | 0.00873535 | ||||||||
\(587\) | 26.7821 | 1.10541 | 0.552707 | − | 0.833375i | \(-0.313595\pi\) | ||||
0.552707 | + | 0.833375i | \(0.313595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.4349 | −0.677189 | ||||||||
\(590\) | 11.5262 | 0.474525 | ||||||||
\(591\) | −3.04983 | −0.125453 | ||||||||
\(592\) | 35.2048 | 1.44691 | ||||||||
\(593\) | −6.46300 | −0.265403 | −0.132702 | − | 0.991156i | \(-0.542365\pi\) | ||||
−0.132702 | + | 0.991156i | \(0.542365\pi\) | |||||||
\(594\) | −2.01893 | −0.0828376 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.2959 | −1.15904 | ||||||||
\(597\) | −1.15345 | −0.0472075 | ||||||||
\(598\) | −4.69127 | −0.191840 | ||||||||
\(599\) | 12.0599 | 0.492753 | 0.246376 | − | 0.969174i | \(-0.420760\pi\) | ||||
0.246376 | + | 0.969174i | \(0.420760\pi\) | |||||||
\(600\) | −1.43705 | −0.0586674 | ||||||||
\(601\) | 1.73965 | 0.0709620 | 0.0354810 | − | 0.999370i | \(-0.488704\pi\) | ||||
0.0354810 | + | 0.999370i | \(0.488704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −39.1001 | −1.59228 | ||||||||
\(604\) | 8.37100 | 0.340611 | ||||||||
\(605\) | −12.3165 | −0.500738 | ||||||||
\(606\) | −1.23649 | −0.0502288 | ||||||||
\(607\) | −31.4098 | −1.27488 | −0.637442 | − | 0.770498i | \(-0.720008\pi\) | ||||
−0.637442 | + | 0.770498i | \(0.720008\pi\) | |||||||
\(608\) | −9.56867 | −0.388061 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.3442 | −0.459313 | ||||||||
\(611\) | −1.23037 | −0.0497753 | ||||||||
\(612\) | 35.4927 | 1.43471 | ||||||||
\(613\) | 11.1482 | 0.450271 | 0.225135 | − | 0.974327i | \(-0.427718\pi\) | ||||
0.225135 | + | 0.974327i | \(0.427718\pi\) | |||||||
\(614\) | −11.8808 | −0.479471 | ||||||||
\(615\) | −0.977941 | −0.0394344 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.4284 | −0.540608 | −0.270304 | − | 0.962775i | \(-0.587124\pi\) | ||||
−0.270304 | + | 0.962775i | \(0.587124\pi\) | |||||||
\(618\) | 1.44785 | 0.0582409 | ||||||||
\(619\) | 15.1941 | 0.610700 | 0.305350 | − | 0.952240i | \(-0.401226\pi\) | ||||
0.305350 | + | 0.952240i | \(0.401226\pi\) | |||||||
\(620\) | −36.8367 | −1.47940 | ||||||||
\(621\) | 8.99381 | 0.360909 | ||||||||
\(622\) | −8.62188 | −0.345706 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.10205 | 0.124182 | ||||||||
\(625\) | −31.1685 | −1.24674 | ||||||||
\(626\) | 7.69701 | 0.307634 | ||||||||
\(627\) | −2.07610 | −0.0829114 | ||||||||
\(628\) | −28.8354 | −1.15066 | ||||||||
\(629\) | 74.4502 | 2.96852 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.1970 | 1.24193 | 0.620966 | − | 0.783837i | \(-0.286740\pi\) | ||||
0.620966 | + | 0.783837i | \(0.286740\pi\) | |||||||
\(632\) | −7.50676 | −0.298603 | ||||||||
\(633\) | −4.65787 | −0.185134 | ||||||||
\(634\) | 0.564342 | 0.0224129 | ||||||||
\(635\) | 12.6653 | 0.502606 | ||||||||
\(636\) | −6.26880 | −0.248574 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.82920 | −0.349551 | ||||||||
\(639\) | −40.1805 | −1.58952 | ||||||||
\(640\) | −28.1522 | −1.11281 | ||||||||
\(641\) | 36.0536 | 1.42403 | 0.712016 | − | 0.702163i | \(-0.247782\pi\) | ||||
0.712016 | + | 0.702163i | \(0.247782\pi\) | |||||||
\(642\) | −1.36690 | −0.0539472 | ||||||||
\(643\) | 33.5678 | 1.32378 | 0.661892 | − | 0.749600i | \(-0.269754\pi\) | ||||
0.661892 | + | 0.749600i | \(0.269754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.723922 | 0.0285044 | ||||||||
\(646\) | −5.86518 | −0.230762 | ||||||||
\(647\) | 0.274010 | 0.0107724 | 0.00538621 | − | 0.999985i | \(-0.498286\pi\) | ||||
0.00538621 | + | 0.999985i | \(0.498286\pi\) | |||||||
\(648\) | −11.6427 | −0.457368 | ||||||||
\(649\) | 27.7570 | 1.08956 | ||||||||
\(650\) | 2.99284 | 0.117389 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.00242 | −0.117584 | ||||||||
\(653\) | −0.861511 | −0.0337135 | −0.0168568 | − | 0.999858i | \(-0.505366\pi\) | ||||
−0.0168568 | + | 0.999858i | \(0.505366\pi\) | |||||||
\(654\) | −2.07207 | −0.0810244 | ||||||||
\(655\) | 33.9480 | 1.32646 | ||||||||
\(656\) | −3.14608 | −0.122834 | ||||||||
\(657\) | 23.9439 | 0.934141 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9842 | −0.661609 | −0.330805 | − | 0.943699i | \(-0.607320\pi\) | ||||
−0.330805 | + | 0.943699i | \(0.607320\pi\) | |||||||
\(660\) | −4.65329 | −0.181129 | ||||||||
\(661\) | −19.9732 | −0.776868 | −0.388434 | − | 0.921477i | \(-0.626984\pi\) | ||||
−0.388434 | + | 0.921477i | \(0.626984\pi\) | |||||||
\(662\) | −3.78150 | −0.146972 | ||||||||
\(663\) | 6.56014 | 0.254775 | ||||||||
\(664\) | −8.58567 | −0.333189 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.2962 | −0.476469 | ||||||||
\(667\) | 39.3319 | 1.52294 | ||||||||
\(668\) | −38.7307 | −1.49854 | ||||||||
\(669\) | −0.331994 | −0.0128356 | ||||||||
\(670\) | 14.4821 | 0.559494 | ||||||||
\(671\) | −27.3188 | −1.05463 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.4496 | 0.556992 | 0.278496 | − | 0.960437i | \(-0.410164\pi\) | ||||
0.278496 | + | 0.960437i | \(0.410164\pi\) | |||||||
\(674\) | −1.94162 | −0.0747885 | ||||||||
\(675\) | −5.73769 | −0.220844 | ||||||||
\(676\) | 9.42941 | 0.362670 | ||||||||
\(677\) | 17.6835 | 0.679631 | 0.339815 | − | 0.940492i | \(-0.389635\pi\) | ||||
0.339815 | + | 0.940492i | \(0.389635\pi\) | |||||||
\(678\) | 0.722382 | 0.0277429 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −27.3262 | −1.04791 | ||||||||
\(681\) | −0.00632897 | −0.000242527 0 | ||||||||
\(682\) | 6.97878 | 0.267231 | ||||||||
\(683\) | 1.11202 | 0.0425504 | 0.0212752 | − | 0.999774i | \(-0.493227\pi\) | ||||
0.0212752 | + | 0.999774i | \(0.493227\pi\) | |||||||
\(684\) | −12.3134 | −0.470813 | ||||||||
\(685\) | 3.58595 | 0.137012 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.36215 | −0.0519692 | ||||||||
\(688\) | 2.32889 | 0.0887881 | ||||||||
\(689\) | 27.1382 | 1.03388 | ||||||||
\(690\) | −1.63078 | −0.0620827 | ||||||||
\(691\) | −15.2935 | −0.581794 | −0.290897 | − | 0.956754i | \(-0.593954\pi\) | ||||
−0.290897 | + | 0.956754i | \(0.593954\pi\) | |||||||
\(692\) | 13.3385 | 0.507054 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.547109 | 0.0207680 | ||||||||
\(695\) | −33.9057 | −1.28612 | ||||||||
\(696\) | 4.64742 | 0.176160 | ||||||||
\(697\) | −6.65325 | −0.252010 | ||||||||
\(698\) | −11.6865 | −0.442339 | ||||||||
\(699\) | −5.09405 | −0.192675 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.9453 | −1.43317 | −0.716586 | − | 0.697498i | \(-0.754296\pi\) | ||||
−0.716586 | + | 0.697498i | \(0.754296\pi\) | |||||||
\(702\) | −2.21321 | −0.0835322 | ||||||||
\(703\) | −25.8287 | −0.974149 | ||||||||
\(704\) | −12.0844 | −0.455448 | ||||||||
\(705\) | −0.427700 | −0.0161081 | ||||||||
\(706\) | −4.45830 | −0.167791 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −7.02875 | −0.264157 | ||||||||
\(709\) | −29.2638 | −1.09903 | −0.549513 | − | 0.835485i | \(-0.685187\pi\) | ||||
−0.549513 | + | 0.835485i | \(0.685187\pi\) | |||||||
\(710\) | 14.8823 | 0.558523 | ||||||||
\(711\) | −14.6728 | −0.550274 | ||||||||
\(712\) | 5.99395 | 0.224633 | ||||||||
\(713\) | −31.0887 | −1.16428 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.1446 | 0.753363 | ||||||||
\(716\) | −2.54015 | −0.0949299 | ||||||||
\(717\) | −4.22712 | −0.157865 | ||||||||
\(718\) | −5.50302 | −0.205371 | ||||||||
\(719\) | 24.4954 | 0.913524 | 0.456762 | − | 0.889589i | \(-0.349009\pi\) | ||||
0.456762 | + | 0.889589i | \(0.349009\pi\) | |||||||
\(720\) | −25.2567 | −0.941262 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.22176 | −0.194334 | ||||||||
\(723\) | −0.932241 | −0.0346704 | ||||||||
\(724\) | 15.8975 | 0.590825 | ||||||||
\(725\) | −25.0921 | −0.931899 | ||||||||
\(726\) | −0.590870 | −0.0219293 | ||||||||
\(727\) | −13.8973 | −0.515422 | −0.257711 | − | 0.966222i | \(-0.582968\pi\) | ||||
−0.257711 | + | 0.966222i | \(0.582968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.5911 | −0.762634 | ||||||||
\(730\) | −8.86850 | −0.328238 | ||||||||
\(731\) | 4.92507 | 0.182160 | ||||||||
\(732\) | 6.91777 | 0.255688 | ||||||||
\(733\) | 7.28624 | 0.269123 | 0.134562 | − | 0.990905i | \(-0.457037\pi\) | ||||
0.134562 | + | 0.990905i | \(0.457037\pi\) | |||||||
\(734\) | −12.9286 | −0.477204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.1003 | −0.667186 | ||||||||
\(737\) | 34.8755 | 1.28465 | ||||||||
\(738\) | 1.09885 | 0.0404494 | ||||||||
\(739\) | −3.20790 | −0.118005 | −0.0590023 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590023 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(740\) | −57.8916 | −2.12814 | ||||||||
\(741\) | −2.27588 | −0.0836067 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.42278 | 0.0521967 | 0.0260984 | − | 0.999659i | \(-0.491692\pi\) | ||||
0.0260984 | + | 0.999659i | \(0.491692\pi\) | |||||||
\(744\) | −3.67342 | −0.134674 | ||||||||
\(745\) | 42.5818 | 1.56008 | ||||||||
\(746\) | −5.38517 | −0.197165 | ||||||||
\(747\) | −16.7817 | −0.614009 | ||||||||
\(748\) | −31.6579 | −1.15753 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.827123 | −0.0302022 | ||||||||
\(751\) | −28.9997 | −1.05821 | −0.529107 | − | 0.848555i | \(-0.677473\pi\) | ||||
−0.529107 | + | 0.848555i | \(0.677473\pi\) | |||||||
\(752\) | −1.37593 | −0.0501750 | ||||||||
\(753\) | −4.37272 | −0.159351 | ||||||||
\(754\) | −9.67885 | −0.352483 | ||||||||
\(755\) | −12.5973 | −0.458464 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.8833 | 0.940744 | 0.470372 | − | 0.882468i | \(-0.344120\pi\) | ||||
0.470372 | + | 0.882468i | \(0.344120\pi\) | |||||||
\(758\) | 12.6178 | 0.458300 | ||||||||
\(759\) | −3.92720 | −0.142548 | ||||||||
\(760\) | 9.48019 | 0.343882 | ||||||||
\(761\) | −36.0482 | −1.30675 | −0.653374 | − | 0.757036i | \(-0.726647\pi\) | ||||
−0.653374 | + | 0.757036i | \(0.726647\pi\) | |||||||
\(762\) | 0.607601 | 0.0220110 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.61267 | −0.166881 | ||||||||
\(765\) | −53.4122 | −1.93112 | ||||||||
\(766\) | −2.62838 | −0.0949674 | ||||||||
\(767\) | 30.4281 | 1.09870 | ||||||||
\(768\) | 1.95023 | 0.0703729 | ||||||||
\(769\) | −35.4285 | −1.27758 | −0.638791 | − | 0.769380i | \(-0.720565\pi\) | ||||
−0.638791 | + | 0.769380i | \(0.720565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.959887 | −0.0345695 | ||||||||
\(772\) | −7.76854 | −0.279596 | ||||||||
\(773\) | −37.8547 | −1.36154 | −0.680769 | − | 0.732498i | \(-0.738354\pi\) | ||||
−0.680769 | + | 0.732498i | \(0.738354\pi\) | |||||||
\(774\) | −0.813428 | −0.0292381 | ||||||||
\(775\) | 19.8333 | 0.712434 | ||||||||
\(776\) | −14.0605 | −0.504744 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.5422 | 0.377958 | ||||||||
\(779\) | 2.30819 | 0.0826994 | ||||||||
\(780\) | −5.10109 | −0.182648 | ||||||||
\(781\) | 35.8392 | 1.28243 | ||||||||
\(782\) | −11.0947 | −0.396746 | ||||||||
\(783\) | 18.5557 | 0.663125 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.3937 | 1.54879 | ||||||||
\(786\) | 1.62861 | 0.0580907 | ||||||||
\(787\) | 43.7967 | 1.56118 | 0.780592 | − | 0.625041i | \(-0.214918\pi\) | ||||
0.780592 | + | 0.625041i | \(0.214918\pi\) | |||||||
\(788\) | 16.1342 | 0.574756 | ||||||||
\(789\) | −0.0807807 | −0.00287587 | ||||||||
\(790\) | 5.43461 | 0.193355 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.8686 | 0.386199 | ||||||||
\(793\) | −29.9477 | −1.06347 | ||||||||
\(794\) | −9.88625 | −0.350850 | ||||||||
\(795\) | 9.43378 | 0.334582 | ||||||||
\(796\) | 6.10196 | 0.216278 | ||||||||
\(797\) | 5.00505 | 0.177288 | 0.0886439 | − | 0.996063i | \(-0.471747\pi\) | ||||
0.0886439 | + | 0.996063i | \(0.471747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.90978 | −0.102941 | ||||||||
\(800\) | 11.5473 | 0.408258 | ||||||||
\(801\) | 11.7159 | 0.413959 | ||||||||
\(802\) | 1.44868 | 0.0511545 | ||||||||
\(803\) | −21.3569 | −0.753668 | ||||||||
\(804\) | −8.83131 | −0.311456 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.65035 | 0.269472 | ||||||||
\(807\) | 3.11925 | 0.109803 | ||||||||
\(808\) | 13.5971 | 0.478344 | ||||||||
\(809\) | −15.6219 | −0.549236 | −0.274618 | − | 0.961553i | \(-0.588551\pi\) | ||||
−0.274618 | + | 0.961553i | \(0.588551\pi\) | |||||||
\(810\) | 8.42887 | 0.296160 | ||||||||
\(811\) | 30.9054 | 1.08523 | 0.542617 | − | 0.839980i | \(-0.317433\pi\) | ||||
0.542617 | + | 0.839980i | \(0.317433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.51775 | −0.193516 | ||||||||
\(814\) | 10.9677 | 0.384417 | ||||||||
\(815\) | 4.51828 | 0.158269 | ||||||||
\(816\) | 7.33626 | 0.256820 | ||||||||
\(817\) | −1.70864 | −0.0597777 | ||||||||
\(818\) | 9.55539 | 0.334096 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.17349 | 0.180666 | ||||||||
\(821\) | −8.03281 | −0.280347 | −0.140173 | − | 0.990127i | \(-0.544766\pi\) | ||||
−0.140173 | + | 0.990127i | \(0.544766\pi\) | |||||||
\(822\) | 0.172032 | 0.00600030 | ||||||||
\(823\) | −52.6132 | −1.83398 | −0.916991 | − | 0.398908i | \(-0.869389\pi\) | ||||
−0.916991 | + | 0.398908i | \(0.869389\pi\) | |||||||
\(824\) | −15.9213 | −0.554646 | ||||||||
\(825\) | 2.50539 | 0.0872266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.2906 | −0.427385 | −0.213693 | − | 0.976901i | \(-0.568549\pi\) | ||||
−0.213693 | + | 0.976901i | \(0.568549\pi\) | |||||||
\(828\) | −23.2922 | −0.809461 | ||||||||
\(829\) | −21.6800 | −0.752978 | −0.376489 | − | 0.926421i | \(-0.622869\pi\) | ||||
−0.376489 | + | 0.926421i | \(0.622869\pi\) | |||||||
\(830\) | 6.21570 | 0.215750 | ||||||||
\(831\) | 5.20228 | 0.180465 | ||||||||
\(832\) | −13.2473 | −0.459268 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.62659 | −0.0563241 | ||||||||
\(835\) | 58.2850 | 2.01704 | ||||||||
\(836\) | 10.9829 | 0.379853 | ||||||||
\(837\) | −14.6668 | −0.506958 | ||||||||
\(838\) | −8.85428 | −0.305866 | ||||||||
\(839\) | 26.8087 | 0.925540 | 0.462770 | − | 0.886478i | \(-0.346856\pi\) | ||||
0.462770 | + | 0.886478i | \(0.346856\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.1479 | 1.79820 | ||||||||
\(842\) | −2.67349 | −0.0921346 | ||||||||
\(843\) | −2.63622 | −0.0907963 | ||||||||
\(844\) | 24.6410 | 0.848178 | ||||||||
\(845\) | −14.1901 | −0.488155 | ||||||||
\(846\) | 0.480581 | 0.0165227 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.3489 | 1.04219 | ||||||||
\(849\) | −0.135564 | −0.00465255 | ||||||||
\(850\) | 7.07798 | 0.242773 | ||||||||
\(851\) | −48.8582 | −1.67484 | ||||||||
\(852\) | −9.07534 | −0.310916 | ||||||||
\(853\) | 36.5753 | 1.25231 | 0.626157 | − | 0.779697i | \(-0.284627\pi\) | ||||
0.626157 | + | 0.779697i | \(0.284627\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.5301 | 0.633716 | ||||||||
\(856\) | 15.0312 | 0.513755 | ||||||||
\(857\) | 14.1015 | 0.481700 | 0.240850 | − | 0.970562i | \(-0.422574\pi\) | ||||
0.240850 | + | 0.970562i | \(0.422574\pi\) | |||||||
\(858\) | 0.966410 | 0.0329927 | ||||||||
\(859\) | −19.3798 | −0.661232 | −0.330616 | − | 0.943765i | \(-0.607256\pi\) | ||||
−0.330616 | + | 0.943765i | \(0.607256\pi\) | |||||||
\(860\) | −3.82968 | −0.130591 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.25306 | −0.247040 | ||||||||
\(863\) | 36.9877 | 1.25908 | 0.629538 | − | 0.776970i | \(-0.283244\pi\) | ||||
0.629538 | + | 0.776970i | \(0.283244\pi\) | |||||||
\(864\) | −8.53922 | −0.290510 | ||||||||
\(865\) | −20.0728 | −0.682497 | ||||||||
\(866\) | −0.741938 | −0.0252121 | ||||||||
\(867\) | 9.55626 | 0.324548 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.0875 | 0.443962 | ||||||||
\(870\) | −3.36456 | −0.114069 | ||||||||
\(871\) | 38.2316 | 1.29543 | ||||||||
\(872\) | 22.7857 | 0.771620 | ||||||||
\(873\) | −27.4829 | −0.930156 | ||||||||
\(874\) | 3.84905 | 0.130196 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.40808 | 0.182722 | ||||||||
\(877\) | −8.16131 | −0.275588 | −0.137794 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137794 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(878\) | −7.64063 | −0.257859 | ||||||||
\(879\) | 0.194054 | 0.00654529 | ||||||||
\(880\) | 22.5278 | 0.759413 | ||||||||
\(881\) | −54.1517 | −1.82442 | −0.912209 | − | 0.409725i | \(-0.865625\pi\) | ||||
−0.912209 | + | 0.409725i | \(0.865625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.6230 | 1.53533 | 0.767667 | − | 0.640848i | \(-0.221417\pi\) | ||||
0.767667 | + | 0.640848i | \(0.221417\pi\) | |||||||
\(884\) | −34.7043 | −1.16723 | ||||||||
\(885\) | 10.5774 | 0.355556 | ||||||||
\(886\) | −1.00062 | −0.0336166 | ||||||||
\(887\) | −17.8641 | −0.599817 | −0.299908 | − | 0.953968i | \(-0.596956\pi\) | ||||
−0.299908 | + | 0.953968i | \(0.596956\pi\) | |||||||
\(888\) | −5.77305 | −0.193731 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.33939 | −0.145457 | ||||||||
\(891\) | 20.2982 | 0.680014 | ||||||||
\(892\) | 1.75631 | 0.0588056 | ||||||||
\(893\) | 1.00948 | 0.0337809 | ||||||||
\(894\) | 2.04281 | 0.0683219 | ||||||||
\(895\) | 3.82262 | 0.127776 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.30511 | −0.143744 | ||||||||
\(898\) | −5.67657 | −0.189430 | ||||||||
\(899\) | −64.1409 | −2.13922 | ||||||||
\(900\) | 14.8595 | 0.495317 | ||||||||
\(901\) | 64.1811 | 2.13818 | ||||||||
\(902\) | −0.980128 | −0.0326347 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.94372 | −0.264204 | ||||||||
\(905\) | −23.9238 | −0.795253 | ||||||||
\(906\) | −0.604342 | −0.0200779 | ||||||||
\(907\) | 30.9726 | 1.02843 | 0.514214 | − | 0.857662i | \(-0.328084\pi\) | ||||
0.514214 | + | 0.857662i | \(0.328084\pi\) | |||||||
\(908\) | 0.0334814 | 0.00111112 | ||||||||
\(909\) | 26.5771 | 0.881505 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.5068 | 1.27579 | 0.637893 | − | 0.770125i | \(-0.279806\pi\) | ||||
0.637893 | + | 0.770125i | \(0.279806\pi\) | |||||||
\(912\) | −2.54514 | −0.0842780 | ||||||||
\(913\) | 14.9685 | 0.495384 | ||||||||
\(914\) | −13.5548 | −0.448353 | ||||||||
\(915\) | −10.4104 | −0.344157 | ||||||||
\(916\) | 7.20602 | 0.238094 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.23417 | −0.172753 | ||||||||
\(919\) | 53.4161 | 1.76203 | 0.881017 | − | 0.473085i | \(-0.156860\pi\) | ||||
0.881017 | + | 0.473085i | \(0.156860\pi\) | |||||||
\(920\) | 17.9329 | 0.591231 | ||||||||
\(921\) | −10.9029 | −0.359262 | ||||||||
\(922\) | −10.0185 | −0.329943 | ||||||||
\(923\) | 39.2880 | 1.29318 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.1696 | 1.02485 | ||||||||
\(926\) | 12.5467 | 0.412310 | ||||||||
\(927\) | −31.1200 | −1.02212 | ||||||||
\(928\) | −37.3438 | −1.22587 | ||||||||
\(929\) | −32.7404 | −1.07418 | −0.537089 | − | 0.843525i | \(-0.680476\pi\) | ||||
−0.537089 | + | 0.843525i | \(0.680476\pi\) | |||||||
\(930\) | 2.65941 | 0.0872056 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.9485 | 0.882726 | ||||||||
\(933\) | −7.91218 | −0.259033 | ||||||||
\(934\) | 1.25268 | 0.0409890 | ||||||||
\(935\) | 47.6412 | 1.55803 | ||||||||
\(936\) | 11.9145 | 0.389438 | ||||||||
\(937\) | −28.0682 | −0.916948 | −0.458474 | − | 0.888708i | \(-0.651604\pi\) | ||||
−0.458474 | + | 0.888708i | \(0.651604\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.06343 | 0.230506 | ||||||||
\(940\) | 2.26261 | 0.0737983 | ||||||||
\(941\) | 56.3824 | 1.83801 | 0.919006 | − | 0.394243i | \(-0.128993\pi\) | ||||
0.919006 | + | 0.394243i | \(0.128993\pi\) | |||||||
\(942\) | 2.08176 | 0.0678274 | ||||||||
\(943\) | 4.36622 | 0.142184 | ||||||||
\(944\) | 34.0280 | 1.10752 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.725540 | 0.0235893 | ||||||||
\(947\) | −24.5587 | −0.798052 | −0.399026 | − | 0.916940i | \(-0.630652\pi\) | ||||
−0.399026 | + | 0.916940i | \(0.630652\pi\) | |||||||
\(948\) | −3.31407 | −0.107636 | ||||||||
\(949\) | −23.4121 | −0.759988 | ||||||||
\(950\) | −2.45554 | −0.0796682 | ||||||||
\(951\) | 0.517888 | 0.0167937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.4811 | 0.371910 | 0.185955 | − | 0.982558i | \(-0.440462\pi\) | ||||
0.185955 | + | 0.982558i | \(0.440462\pi\) | |||||||
\(954\) | −10.6002 | −0.343194 | ||||||||
\(955\) | 6.94151 | 0.224622 | ||||||||
\(956\) | 22.3623 | 0.723247 | ||||||||
\(957\) | −8.10243 | −0.261914 | ||||||||
\(958\) | 2.41195 | 0.0779266 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.60502 | −0.148626 | ||||||||
\(961\) | 19.6983 | 0.635428 | ||||||||
\(962\) | 12.0231 | 0.387641 | ||||||||
\(963\) | 29.3802 | 0.946763 | ||||||||
\(964\) | 4.93173 | 0.158840 | ||||||||
\(965\) | 11.6907 | 0.376337 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.7786 | −1.79372 | −0.896859 | − | 0.442316i | \(-0.854157\pi\) | ||||
−0.896859 | + | 0.442316i | \(0.854157\pi\) | |||||||
\(968\) | 6.49754 | 0.208839 | ||||||||
\(969\) | −5.38239 | −0.172907 | ||||||||
\(970\) | 10.1793 | 0.326838 | ||||||||
\(971\) | 6.99246 | 0.224399 | 0.112199 | − | 0.993686i | \(-0.464210\pi\) | ||||
0.112199 | + | 0.993686i | \(0.464210\pi\) | |||||||
\(972\) | −16.5978 | −0.532374 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.33545 | 0.170959 | ||||||||
\(975\) | 2.74649 | 0.0879581 | ||||||||
\(976\) | −33.4908 | −1.07201 | ||||||||
\(977\) | −19.6472 | −0.628571 | −0.314285 | − | 0.949329i | \(-0.601765\pi\) | ||||
−0.314285 | + | 0.949329i | \(0.601765\pi\) | |||||||
\(978\) | 0.216759 | 0.00693119 | ||||||||
\(979\) | −10.4500 | −0.333984 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 44.5371 | 1.42196 | ||||||||
\(982\) | −10.6883 | −0.341078 | ||||||||
\(983\) | −28.0238 | −0.893820 | −0.446910 | − | 0.894579i | \(-0.647476\pi\) | ||||
−0.446910 | + | 0.894579i | \(0.647476\pi\) | |||||||
\(984\) | 0.515909 | 0.0164466 | ||||||||
\(985\) | −24.2800 | −0.773624 | ||||||||
\(986\) | −22.8902 | −0.728971 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0399 | 0.383039 | ||||||||
\(989\) | −3.23210 | −0.102775 | ||||||||
\(990\) | −7.86845 | −0.250076 | ||||||||
\(991\) | 35.0606 | 1.11374 | 0.556869 | − | 0.830601i | \(-0.312003\pi\) | ||||
0.556869 | + | 0.830601i | \(0.312003\pi\) | |||||||
\(992\) | 29.5173 | 0.937175 | ||||||||
\(993\) | −3.47023 | −0.110124 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.18270 | −0.291111 | ||||||||
\(996\) | −3.79038 | −0.120103 | ||||||||
\(997\) | −41.7816 | −1.32324 | −0.661619 | − | 0.749841i | \(-0.730130\pi\) | ||||
−0.661619 | + | 0.749841i | \(0.730130\pi\) | |||||||
\(998\) | −2.52519 | −0.0799336 | ||||||||
\(999\) | −23.0499 | −0.729268 |
(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 | 2009.2.a.r.1.9 | 17 | ||
7.3 | odd | 6 | 287.2.e.d.247.9 | yes | 34 | ||
7.5 | odd | 6 | 287.2.e.d.165.9 | ✓ | 34 | ||
7.6 | odd | 2 | 2009.2.a.s.1.9 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.9 | ✓ | 34 | 7.5 | odd | 6 | ||
287.2.e.d.247.9 | yes | 34 | 7.3 | odd | 6 | ||
2009.2.a.r.1.9 | 17 | 1.1 | even | 1 | trivial | ||
2009.2.a.s.1.9 | 17 | 7.6 | odd | 2 |