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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 27 x^{18} + 52 x^{17} + 302 x^{16} - 552 x^{15} - 1820 x^{14} + 3090 x^{13} + 6449 x^{12} - 9852 x^{11} - 13797 x^{10} + 18080 x^{9} + 17721 x^{8} - 18446 x^{7} + \cdots + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.845808\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.845808 | −0.598076 | −0.299038 | − | 0.954241i | \(-0.596666\pi\) | ||||
−0.299038 | + | 0.954241i | \(0.596666\pi\) | |||||||
\(3\) | 0.0216736 | 0.0125133 | 0.00625663 | − | 0.999980i | \(-0.498008\pi\) | ||||
0.00625663 | + | 0.999980i | \(0.498008\pi\) | |||||||
\(4\) | −1.28461 | −0.642305 | ||||||||
\(5\) | −2.12752 | −0.951455 | −0.475728 | − | 0.879593i | \(-0.657815\pi\) | ||||
−0.475728 | + | 0.879593i | \(0.657815\pi\) | |||||||
\(6\) | −0.0183317 | −0.00748388 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.77815 | 0.982224 | ||||||||
\(9\) | −2.99953 | −0.999843 | ||||||||
\(10\) | 1.79947 | 0.569043 | ||||||||
\(11\) | −5.19192 | −1.56542 | −0.782712 | − | 0.622384i | \(-0.786164\pi\) | ||||
−0.782712 | + | 0.622384i | \(0.786164\pi\) | |||||||
\(12\) | −0.0278421 | −0.00803732 | ||||||||
\(13\) | −3.20762 | −0.889635 | −0.444817 | − | 0.895621i | \(-0.646731\pi\) | ||||
−0.444817 | + | 0.895621i | \(0.646731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0461110 | −0.0119058 | ||||||||
\(16\) | 0.219438 | 0.0548596 | ||||||||
\(17\) | −6.26875 | −1.52040 | −0.760198 | − | 0.649691i | \(-0.774898\pi\) | ||||
−0.760198 | + | 0.649691i | \(0.774898\pi\) | |||||||
\(18\) | 2.53703 | 0.597983 | ||||||||
\(19\) | 1.56448 | 0.358916 | 0.179458 | − | 0.983766i | \(-0.442566\pi\) | ||||
0.179458 | + | 0.983766i | \(0.442566\pi\) | |||||||
\(20\) | 2.73303 | 0.611124 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.39137 | 0.936243 | ||||||||
\(23\) | −4.17962 | −0.871511 | −0.435755 | − | 0.900065i | \(-0.643519\pi\) | ||||
−0.435755 | + | 0.900065i | \(0.643519\pi\) | |||||||
\(24\) | 0.0602125 | 0.0122908 | ||||||||
\(25\) | −0.473663 | −0.0947326 | ||||||||
\(26\) | 2.71303 | 0.532070 | ||||||||
\(27\) | −0.130031 | −0.0250246 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.92688 | 0.729204 | 0.364602 | − | 0.931163i | \(-0.381205\pi\) | ||||
0.364602 | + | 0.931163i | \(0.381205\pi\) | |||||||
\(30\) | 0.0390010 | 0.00712058 | ||||||||
\(31\) | 3.32925 | 0.597951 | 0.298975 | − | 0.954261i | \(-0.403355\pi\) | ||||
0.298975 | + | 0.954261i | \(0.403355\pi\) | |||||||
\(32\) | −5.74190 | −1.01503 | ||||||||
\(33\) | −0.112528 | −0.0195885 | ||||||||
\(34\) | 5.30216 | 0.909313 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.85322 | 0.642204 | ||||||||
\(37\) | 0.150653 | 0.0247672 | 0.0123836 | − | 0.999923i | \(-0.496058\pi\) | ||||
0.0123836 | + | 0.999923i | \(0.496058\pi\) | |||||||
\(38\) | −1.32325 | −0.214659 | ||||||||
\(39\) | −0.0695207 | −0.0111322 | ||||||||
\(40\) | −5.91056 | −0.934542 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.19682 | −0.640009 | −0.320005 | − | 0.947416i | \(-0.603685\pi\) | ||||
−0.320005 | + | 0.947416i | \(0.603685\pi\) | |||||||
\(44\) | 6.66959 | 1.00548 | ||||||||
\(45\) | 6.38156 | 0.951306 | ||||||||
\(46\) | 3.53515 | 0.521230 | ||||||||
\(47\) | −0.154774 | −0.0225761 | −0.0112881 | − | 0.999936i | \(-0.503593\pi\) | ||||
−0.0112881 | + | 0.999936i | \(0.503593\pi\) | |||||||
\(48\) | 0.00475602 | 0.000686472 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.400628 | 0.0566574 | ||||||||
\(51\) | −0.135866 | −0.0190251 | ||||||||
\(52\) | 4.12054 | 0.571417 | ||||||||
\(53\) | −6.90674 | −0.948714 | −0.474357 | − | 0.880333i | \(-0.657319\pi\) | ||||
−0.474357 | + | 0.880333i | \(0.657319\pi\) | |||||||
\(54\) | 0.109982 | 0.0149666 | ||||||||
\(55\) | 11.0459 | 1.48943 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0339078 | 0.00449120 | ||||||||
\(58\) | −3.32139 | −0.436120 | ||||||||
\(59\) | 0.905932 | 0.117942 | 0.0589712 | − | 0.998260i | \(-0.481218\pi\) | ||||
0.0589712 | + | 0.998260i | \(0.481218\pi\) | |||||||
\(60\) | 0.0592346 | 0.00764715 | ||||||||
\(61\) | −7.22479 | −0.925040 | −0.462520 | − | 0.886609i | \(-0.653055\pi\) | ||||
−0.462520 | + | 0.886609i | \(0.653055\pi\) | |||||||
\(62\) | −2.81590 | −0.357620 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.41767 | 0.552208 | ||||||||
\(65\) | 6.82428 | 0.846448 | ||||||||
\(66\) | 0.0951768 | 0.0117154 | ||||||||
\(67\) | −1.72181 | −0.210353 | −0.105176 | − | 0.994454i | \(-0.533541\pi\) | ||||
−0.105176 | + | 0.994454i | \(0.533541\pi\) | |||||||
\(68\) | 8.05290 | 0.976557 | ||||||||
\(69\) | −0.0905874 | −0.0109054 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9514 | −1.53705 | −0.768527 | − | 0.639818i | \(-0.779010\pi\) | ||||
−0.768527 | + | 0.639818i | \(0.779010\pi\) | |||||||
\(72\) | −8.33314 | −0.982070 | ||||||||
\(73\) | 11.0549 | 1.29387 | 0.646937 | − | 0.762543i | \(-0.276050\pi\) | ||||
0.646937 | + | 0.762543i | \(0.276050\pi\) | |||||||
\(74\) | −0.127424 | −0.0148127 | ||||||||
\(75\) | −0.0102660 | −0.00118541 | ||||||||
\(76\) | −2.00974 | −0.230533 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.0588012 | 0.00665792 | ||||||||
\(79\) | 0.331420 | 0.0372877 | 0.0186438 | − | 0.999826i | \(-0.494065\pi\) | ||||
0.0186438 | + | 0.999826i | \(0.494065\pi\) | |||||||
\(80\) | −0.466859 | −0.0521964 | ||||||||
\(81\) | 8.99577 | 0.999530 | ||||||||
\(82\) | −0.845808 | −0.0934039 | ||||||||
\(83\) | −6.16966 | −0.677208 | −0.338604 | − | 0.940929i | \(-0.609955\pi\) | ||||
−0.338604 | + | 0.940929i | \(0.609955\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3369 | 1.44659 | ||||||||
\(86\) | 3.54971 | 0.382775 | ||||||||
\(87\) | 0.0851097 | 0.00912472 | ||||||||
\(88\) | −14.4239 | −1.53760 | ||||||||
\(89\) | −1.82708 | −0.193670 | −0.0968349 | − | 0.995300i | \(-0.530872\pi\) | ||||
−0.0968349 | + | 0.995300i | \(0.530872\pi\) | |||||||
\(90\) | −5.39757 | −0.568954 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.36918 | 0.559775 | ||||||||
\(93\) | 0.0721568 | 0.00748231 | ||||||||
\(94\) | 0.130909 | 0.0135022 | ||||||||
\(95\) | −3.32845 | −0.341492 | ||||||||
\(96\) | −0.124448 | −0.0127014 | ||||||||
\(97\) | 7.73595 | 0.785467 | 0.392733 | − | 0.919652i | \(-0.371529\pi\) | ||||
0.392733 | + | 0.919652i | \(0.371529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.5733 | 1.56518 | ||||||||
\(100\) | 0.608472 | 0.0608472 | ||||||||
\(101\) | 7.56840 | 0.753084 | 0.376542 | − | 0.926400i | \(-0.377113\pi\) | ||||
0.376542 | + | 0.926400i | \(0.377113\pi\) | |||||||
\(102\) | 0.114917 | 0.0113785 | ||||||||
\(103\) | 1.75418 | 0.172844 | 0.0864220 | − | 0.996259i | \(-0.472457\pi\) | ||||
0.0864220 | + | 0.996259i | \(0.472457\pi\) | |||||||
\(104\) | −8.91126 | −0.873821 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.84178 | 0.567403 | ||||||||
\(107\) | −14.3693 | −1.38914 | −0.694568 | − | 0.719427i | \(-0.744404\pi\) | ||||
−0.694568 | + | 0.719427i | \(0.744404\pi\) | |||||||
\(108\) | 0.167039 | 0.0160734 | ||||||||
\(109\) | 2.69508 | 0.258142 | 0.129071 | − | 0.991635i | \(-0.458801\pi\) | ||||
0.129071 | + | 0.991635i | \(0.458801\pi\) | |||||||
\(110\) | −9.34272 | −0.890794 | ||||||||
\(111\) | 0.00326519 | 0.000309919 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.2788 | 1.71952 | 0.859761 | − | 0.510697i | \(-0.170613\pi\) | ||||
0.859761 | + | 0.510697i | \(0.170613\pi\) | |||||||
\(114\) | −0.0286795 | −0.00268608 | ||||||||
\(115\) | 8.89222 | 0.829204 | ||||||||
\(116\) | −5.04451 | −0.468371 | ||||||||
\(117\) | 9.62137 | 0.889496 | ||||||||
\(118\) | −0.766245 | −0.0705385 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.128103 | −0.0116942 | ||||||||
\(121\) | 15.9561 | 1.45055 | ||||||||
\(122\) | 6.11079 | 0.553245 | ||||||||
\(123\) | 0.0216736 | 0.00195424 | ||||||||
\(124\) | −4.27678 | −0.384066 | ||||||||
\(125\) | 11.6453 | 1.04159 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.85675 | −0.164760 | −0.0823798 | − | 0.996601i | \(-0.526252\pi\) | ||||
−0.0823798 | + | 0.996601i | \(0.526252\pi\) | |||||||
\(128\) | 7.74730 | 0.684771 | ||||||||
\(129\) | −0.0909602 | −0.00800860 | ||||||||
\(130\) | −5.77203 | −0.506241 | ||||||||
\(131\) | 17.1914 | 1.50202 | 0.751011 | − | 0.660290i | \(-0.229567\pi\) | ||||
0.751011 | + | 0.660290i | \(0.229567\pi\) | |||||||
\(132\) | 0.144554 | 0.0125818 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.45632 | 0.125807 | ||||||||
\(135\) | 0.276644 | 0.0238097 | ||||||||
\(136\) | −17.4155 | −1.49337 | ||||||||
\(137\) | −8.53668 | −0.729338 | −0.364669 | − | 0.931137i | \(-0.618818\pi\) | ||||
−0.364669 | + | 0.931137i | \(0.618818\pi\) | |||||||
\(138\) | 0.0766195 | 0.00652228 | ||||||||
\(139\) | 15.0184 | 1.27385 | 0.636923 | − | 0.770928i | \(-0.280207\pi\) | ||||
0.636923 | + | 0.770928i | \(0.280207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.00335451 | −0.000282501 0 | ||||||||
\(142\) | 10.9544 | 0.919275 | ||||||||
\(143\) | 16.6537 | 1.39266 | ||||||||
\(144\) | −0.658212 | −0.0548510 | ||||||||
\(145\) | −8.35452 | −0.693805 | ||||||||
\(146\) | −9.35029 | −0.773836 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.193530 | −0.0159081 | ||||||||
\(149\) | −13.5199 | −1.10760 | −0.553798 | − | 0.832651i | \(-0.686822\pi\) | ||||
−0.553798 | + | 0.832651i | \(0.686822\pi\) | |||||||
\(150\) | 0.00868305 | 0.000708968 0 | ||||||||
\(151\) | 2.98665 | 0.243050 | 0.121525 | − | 0.992588i | \(-0.461222\pi\) | ||||
0.121525 | + | 0.992588i | \(0.461222\pi\) | |||||||
\(152\) | 4.34635 | 0.352535 | ||||||||
\(153\) | 18.8033 | 1.52016 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.08304 | −0.568923 | ||||||||
\(156\) | 0.0893070 | 0.00715028 | ||||||||
\(157\) | 11.7665 | 0.939065 | 0.469533 | − | 0.882915i | \(-0.344422\pi\) | ||||
0.469533 | + | 0.882915i | \(0.344422\pi\) | |||||||
\(158\) | −0.280318 | −0.0223009 | ||||||||
\(159\) | −0.149694 | −0.0118715 | ||||||||
\(160\) | 12.2160 | 0.965760 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.60870 | −0.597796 | ||||||||
\(163\) | −11.1721 | −0.875069 | −0.437535 | − | 0.899202i | \(-0.644148\pi\) | ||||
−0.437535 | + | 0.899202i | \(0.644148\pi\) | |||||||
\(164\) | −1.28461 | −0.100311 | ||||||||
\(165\) | 0.239405 | 0.0186376 | ||||||||
\(166\) | 5.21834 | 0.405022 | ||||||||
\(167\) | 24.8646 | 1.92408 | 0.962041 | − | 0.272904i | \(-0.0879842\pi\) | ||||
0.962041 | + | 0.272904i | \(0.0879842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.71115 | −0.208550 | ||||||||
\(170\) | −11.2804 | −0.865171 | ||||||||
\(171\) | −4.69270 | −0.358859 | ||||||||
\(172\) | 5.39128 | 0.411081 | ||||||||
\(173\) | −9.36733 | −0.712185 | −0.356092 | − | 0.934451i | \(-0.615891\pi\) | ||||
−0.356092 | + | 0.934451i | \(0.615891\pi\) | |||||||
\(174\) | −0.0719865 | −0.00545728 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.13931 | −0.0858785 | ||||||||
\(177\) | 0.0196348 | 0.00147584 | ||||||||
\(178\) | 1.54536 | 0.115829 | ||||||||
\(179\) | 11.0566 | 0.826405 | 0.413203 | − | 0.910639i | \(-0.364410\pi\) | ||||
0.413203 | + | 0.910639i | \(0.364410\pi\) | |||||||
\(180\) | −8.19781 | −0.611028 | ||||||||
\(181\) | −7.84517 | −0.583127 | −0.291564 | − | 0.956551i | \(-0.594175\pi\) | ||||
−0.291564 | + | 0.956551i | \(0.594175\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.156587 | −0.0115753 | ||||||||
\(184\) | −11.6116 | −0.856018 | ||||||||
\(185\) | −0.320517 | −0.0235649 | ||||||||
\(186\) | −0.0610308 | −0.00447499 | ||||||||
\(187\) | 32.5469 | 2.38006 | ||||||||
\(188\) | 0.198824 | 0.0145007 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.81523 | 0.204238 | ||||||||
\(191\) | 17.6747 | 1.27890 | 0.639448 | − | 0.768835i | \(-0.279163\pi\) | ||||
0.639448 | + | 0.768835i | \(0.279163\pi\) | |||||||
\(192\) | 0.0957467 | 0.00690992 | ||||||||
\(193\) | −13.7455 | −0.989422 | −0.494711 | − | 0.869057i | \(-0.664726\pi\) | ||||
−0.494711 | + | 0.869057i | \(0.664726\pi\) | |||||||
\(194\) | −6.54313 | −0.469769 | ||||||||
\(195\) | 0.147907 | 0.0105918 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.6689 | −1.18761 | −0.593807 | − | 0.804608i | \(-0.702376\pi\) | ||||
−0.593807 | + | 0.804608i | \(0.702376\pi\) | |||||||
\(198\) | −13.1720 | −0.936097 | ||||||||
\(199\) | 0.732788 | 0.0519460 | 0.0259730 | − | 0.999663i | \(-0.491732\pi\) | ||||
0.0259730 | + | 0.999663i | \(0.491732\pi\) | |||||||
\(200\) | −1.31591 | −0.0930486 | ||||||||
\(201\) | −0.0373178 | −0.00263220 | ||||||||
\(202\) | −6.40141 | −0.450402 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.174535 | 0.0122199 | ||||||||
\(205\) | −2.12752 | −0.148592 | ||||||||
\(206\) | −1.48370 | −0.103374 | ||||||||
\(207\) | 12.5369 | 0.871374 | ||||||||
\(208\) | −0.703876 | −0.0488050 | ||||||||
\(209\) | −8.12264 | −0.561855 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.1457 | −1.73110 | −0.865551 | − | 0.500821i | \(-0.833031\pi\) | ||||
−0.865551 | + | 0.500821i | \(0.833031\pi\) | |||||||
\(212\) | 8.87246 | 0.609363 | ||||||||
\(213\) | −0.280704 | −0.0192335 | ||||||||
\(214\) | 12.1537 | 0.830810 | ||||||||
\(215\) | 8.92882 | 0.608940 | ||||||||
\(216\) | −0.361246 | −0.0245797 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.27952 | −0.154389 | ||||||||
\(219\) | 0.239599 | 0.0161906 | ||||||||
\(220\) | −14.1897 | −0.956668 | ||||||||
\(221\) | 20.1078 | 1.35260 | ||||||||
\(222\) | −0.00276173 | −0.000185355 0 | ||||||||
\(223\) | −27.2560 | −1.82519 | −0.912597 | − | 0.408859i | \(-0.865927\pi\) | ||||
−0.912597 | + | 0.408859i | \(0.865927\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.42077 | 0.0947178 | ||||||||
\(226\) | −15.4603 | −1.02841 | ||||||||
\(227\) | 13.9987 | 0.929127 | 0.464564 | − | 0.885540i | \(-0.346211\pi\) | ||||
0.464564 | + | 0.885540i | \(0.346211\pi\) | |||||||
\(228\) | −0.0435583 | −0.00288472 | ||||||||
\(229\) | 25.7545 | 1.70190 | 0.850951 | − | 0.525244i | \(-0.176026\pi\) | ||||
0.850951 | + | 0.525244i | \(0.176026\pi\) | |||||||
\(230\) | −7.52111 | −0.495927 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.9095 | 0.716242 | ||||||||
\(233\) | −20.9873 | −1.37492 | −0.687462 | − | 0.726220i | \(-0.741275\pi\) | ||||
−0.687462 | + | 0.726220i | \(0.741275\pi\) | |||||||
\(234\) | −8.13783 | −0.531986 | ||||||||
\(235\) | 0.329285 | 0.0214802 | ||||||||
\(236\) | −1.16377 | −0.0757549 | ||||||||
\(237\) | 0.00718306 | 0.000466590 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.0254 | −1.61876 | −0.809380 | − | 0.587285i | \(-0.800197\pi\) | ||||
−0.809380 | + | 0.587285i | \(0.800197\pi\) | |||||||
\(240\) | −0.0101185 | −0.000653147 0 | ||||||||
\(241\) | −8.06559 | −0.519551 | −0.259775 | − | 0.965669i | \(-0.583648\pi\) | ||||
−0.259775 | + | 0.965669i | \(0.583648\pi\) | |||||||
\(242\) | −13.4958 | −0.867541 | ||||||||
\(243\) | 0.585065 | 0.0375319 | ||||||||
\(244\) | 9.28104 | 0.594157 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.0183317 | −0.00116879 | ||||||||
\(247\) | −5.01825 | −0.319304 | ||||||||
\(248\) | 9.24915 | 0.587321 | ||||||||
\(249\) | −0.133719 | −0.00847407 | ||||||||
\(250\) | −9.84971 | −0.622950 | ||||||||
\(251\) | −27.2270 | −1.71856 | −0.859278 | − | 0.511509i | \(-0.829087\pi\) | ||||
−0.859278 | + | 0.511509i | \(0.829087\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.7003 | 1.36428 | ||||||||
\(254\) | 1.57045 | 0.0985388 | ||||||||
\(255\) | 0.289058 | 0.0181015 | ||||||||
\(256\) | −15.3881 | −0.961754 | ||||||||
\(257\) | 14.0475 | 0.876261 | 0.438130 | − | 0.898911i | \(-0.355641\pi\) | ||||
0.438130 | + | 0.898911i | \(0.355641\pi\) | |||||||
\(258\) | 0.0769349 | 0.00478976 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.76653 | −0.543677 | ||||||||
\(261\) | −11.7788 | −0.729090 | ||||||||
\(262\) | −14.5406 | −0.898324 | ||||||||
\(263\) | 8.55511 | 0.527531 | 0.263765 | − | 0.964587i | \(-0.415036\pi\) | ||||
0.263765 | + | 0.964587i | \(0.415036\pi\) | |||||||
\(264\) | −0.312618 | −0.0192403 | ||||||||
\(265\) | 14.6942 | 0.902659 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0395993 | −0.00242344 | ||||||||
\(268\) | 2.21185 | 0.135110 | ||||||||
\(269\) | −30.6009 | −1.86577 | −0.932883 | − | 0.360178i | \(-0.882716\pi\) | ||||
−0.932883 | + | 0.360178i | \(0.882716\pi\) | |||||||
\(270\) | −0.233988 | −0.0142400 | ||||||||
\(271\) | −28.4723 | −1.72957 | −0.864786 | − | 0.502141i | \(-0.832546\pi\) | ||||
−0.864786 | + | 0.502141i | \(0.832546\pi\) | |||||||
\(272\) | −1.37560 | −0.0834083 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.22040 | 0.436200 | ||||||||
\(275\) | 2.45922 | 0.148297 | ||||||||
\(276\) | 0.116369 | 0.00700461 | ||||||||
\(277\) | 21.4231 | 1.28719 | 0.643595 | − | 0.765366i | \(-0.277442\pi\) | ||||
0.643595 | + | 0.765366i | \(0.277442\pi\) | |||||||
\(278\) | −12.7027 | −0.761857 | ||||||||
\(279\) | −9.98618 | −0.597857 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.0553 | 0.957778 | 0.478889 | − | 0.877875i | \(-0.341040\pi\) | ||||
0.478889 | + | 0.877875i | \(0.341040\pi\) | |||||||
\(282\) | 0.00283727 | 0.000168957 0 | ||||||||
\(283\) | −11.3955 | −0.677390 | −0.338695 | − | 0.940896i | \(-0.609985\pi\) | ||||
−0.338695 | + | 0.940896i | \(0.609985\pi\) | |||||||
\(284\) | 16.6375 | 0.987256 | ||||||||
\(285\) | −0.0721396 | −0.00427318 | ||||||||
\(286\) | −14.0859 | −0.832915 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 17.2230 | 1.01488 | ||||||||
\(289\) | 22.2973 | 1.31160 | ||||||||
\(290\) | 7.06632 | 0.414949 | ||||||||
\(291\) | 0.167666 | 0.00982875 | ||||||||
\(292\) | −14.2012 | −0.831061 | ||||||||
\(293\) | −15.7980 | −0.922926 | −0.461463 | − | 0.887159i | \(-0.652675\pi\) | ||||
−0.461463 | + | 0.887159i | \(0.652675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.92739 | −0.112217 | ||||||||
\(296\) | 0.418537 | 0.0243269 | ||||||||
\(297\) | 0.675113 | 0.0391740 | ||||||||
\(298\) | 11.4353 | 0.662427 | ||||||||
\(299\) | 13.4066 | 0.775326 | ||||||||
\(300\) | 0.0131878 | 0.000761396 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.52613 | −0.145362 | ||||||||
\(303\) | 0.164034 | 0.00942353 | ||||||||
\(304\) | 0.343306 | 0.0196900 | ||||||||
\(305\) | 15.3709 | 0.880134 | ||||||||
\(306\) | −15.9040 | −0.909171 | ||||||||
\(307\) | 9.37252 | 0.534918 | 0.267459 | − | 0.963569i | \(-0.413816\pi\) | ||||
0.267459 | + | 0.963569i | \(0.413816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0380193 | 0.00216284 | ||||||||
\(310\) | 5.99089 | 0.340260 | ||||||||
\(311\) | −0.975361 | −0.0553076 | −0.0276538 | − | 0.999618i | \(-0.508804\pi\) | ||||
−0.0276538 | + | 0.999618i | \(0.508804\pi\) | |||||||
\(312\) | −0.193139 | −0.0109343 | ||||||||
\(313\) | 32.2917 | 1.82523 | 0.912616 | − | 0.408817i | \(-0.134059\pi\) | ||||
0.912616 | + | 0.408817i | \(0.134059\pi\) | |||||||
\(314\) | −9.95216 | −0.561633 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.425745 | −0.0239500 | ||||||||
\(317\) | −20.2286 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(318\) | 0.126612 | 0.00710006 | ||||||||
\(319\) | −20.3881 | −1.14151 | ||||||||
\(320\) | −9.39867 | −0.525402 | ||||||||
\(321\) | −0.311435 | −0.0173826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.80732 | −0.545694 | ||||||||
\(324\) | −11.5561 | −0.642003 | ||||||||
\(325\) | 1.51933 | 0.0842774 | ||||||||
\(326\) | 9.44948 | 0.523358 | ||||||||
\(327\) | 0.0584121 | 0.00323020 | ||||||||
\(328\) | 2.77815 | 0.153398 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.202490 | −0.0111467 | ||||||||
\(331\) | 30.2925 | 1.66503 | 0.832514 | − | 0.554004i | \(-0.186901\pi\) | ||||
0.832514 | + | 0.554004i | \(0.186901\pi\) | |||||||
\(332\) | 7.92560 | 0.434974 | ||||||||
\(333\) | −0.451889 | −0.0247633 | ||||||||
\(334\) | −21.0307 | −1.15075 | ||||||||
\(335\) | 3.66318 | 0.200141 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.2607 | −0.722359 | −0.361179 | − | 0.932496i | \(-0.617626\pi\) | ||||
−0.361179 | + | 0.932496i | \(0.617626\pi\) | |||||||
\(338\) | 2.29311 | 0.124729 | ||||||||
\(339\) | 0.396167 | 0.0215168 | ||||||||
\(340\) | −17.1327 | −0.929151 | ||||||||
\(341\) | −17.2852 | −0.936046 | ||||||||
\(342\) | 3.96912 | 0.214625 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.6594 | −0.628632 | ||||||||
\(345\) | 0.192726 | 0.0103760 | ||||||||
\(346\) | 7.92296 | 0.425941 | ||||||||
\(347\) | 25.1449 | 1.34985 | 0.674924 | − | 0.737887i | \(-0.264176\pi\) | ||||
0.674924 | + | 0.737887i | \(0.264176\pi\) | |||||||
\(348\) | −0.109333 | −0.00586085 | ||||||||
\(349\) | 15.9360 | 0.853034 | 0.426517 | − | 0.904480i | \(-0.359740\pi\) | ||||
0.426517 | + | 0.904480i | \(0.359740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.417092 | 0.0222627 | ||||||||
\(352\) | 29.8115 | 1.58896 | ||||||||
\(353\) | −12.5243 | −0.666602 | −0.333301 | − | 0.942820i | \(-0.608163\pi\) | ||||
−0.333301 | + | 0.942820i | \(0.608163\pi\) | |||||||
\(354\) | −0.0166073 | −0.000882667 0 | ||||||||
\(355\) | 27.5544 | 1.46244 | ||||||||
\(356\) | 2.34708 | 0.124395 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.35172 | −0.494254 | ||||||||
\(359\) | 5.54354 | 0.292577 | 0.146288 | − | 0.989242i | \(-0.453267\pi\) | ||||
0.146288 | + | 0.989242i | \(0.453267\pi\) | |||||||
\(360\) | 17.7289 | 0.934396 | ||||||||
\(361\) | −16.5524 | −0.871180 | ||||||||
\(362\) | 6.63551 | 0.348755 | ||||||||
\(363\) | 0.345825 | 0.0181511 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.5194 | −1.23106 | ||||||||
\(366\) | 0.132443 | 0.00692289 | ||||||||
\(367\) | −2.95894 | −0.154455 | −0.0772277 | − | 0.997013i | \(-0.524607\pi\) | ||||
−0.0772277 | + | 0.997013i | \(0.524607\pi\) | |||||||
\(368\) | −0.917168 | −0.0478107 | ||||||||
\(369\) | −2.99953 | −0.156149 | ||||||||
\(370\) | 0.271096 | 0.0140936 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0926933 | −0.00480592 | ||||||||
\(373\) | 11.1625 | 0.577971 | 0.288986 | − | 0.957333i | \(-0.406682\pi\) | ||||
0.288986 | + | 0.957333i | \(0.406682\pi\) | |||||||
\(374\) | −27.5284 | −1.42346 | ||||||||
\(375\) | 0.252396 | 0.0130337 | ||||||||
\(376\) | −0.429985 | −0.0221748 | ||||||||
\(377\) | −12.5960 | −0.648725 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4510 | −0.690933 | −0.345467 | − | 0.938431i | \(-0.612279\pi\) | ||||
−0.345467 | + | 0.938431i | \(0.612279\pi\) | |||||||
\(380\) | 4.27576 | 0.219342 | ||||||||
\(381\) | −0.0402424 | −0.00206168 | ||||||||
\(382\) | −14.9494 | −0.764877 | ||||||||
\(383\) | −33.5431 | −1.71397 | −0.856987 | − | 0.515338i | \(-0.827666\pi\) | ||||
−0.856987 | + | 0.515338i | \(0.827666\pi\) | |||||||
\(384\) | 0.167912 | 0.00856872 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.6260 | 0.591750 | ||||||||
\(387\) | 12.5885 | 0.639909 | ||||||||
\(388\) | −9.93767 | −0.504509 | ||||||||
\(389\) | 36.6850 | 1.86000 | 0.930001 | − | 0.367558i | \(-0.119806\pi\) | ||||
0.930001 | + | 0.367558i | \(0.119806\pi\) | |||||||
\(390\) | −0.125101 | −0.00633472 | ||||||||
\(391\) | 26.2010 | 1.32504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.372600 | 0.0187952 | ||||||||
\(394\) | 14.0987 | 0.710283 | ||||||||
\(395\) | −0.705102 | −0.0354776 | ||||||||
\(396\) | −20.0056 | −1.00532 | ||||||||
\(397\) | −20.8915 | −1.04851 | −0.524256 | − | 0.851560i | \(-0.675657\pi\) | ||||
−0.524256 | + | 0.851560i | \(0.675657\pi\) | |||||||
\(398\) | −0.619798 | −0.0310677 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.103940 | −0.00519699 | ||||||||
\(401\) | −18.5820 | −0.927939 | −0.463969 | − | 0.885851i | \(-0.653575\pi\) | ||||
−0.463969 | + | 0.885851i | \(0.653575\pi\) | |||||||
\(402\) | 0.0315637 | 0.00157425 | ||||||||
\(403\) | −10.6790 | −0.531958 | ||||||||
\(404\) | −9.72243 | −0.483709 | ||||||||
\(405\) | −19.1387 | −0.951008 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.782179 | −0.0387712 | ||||||||
\(408\) | −0.377457 | −0.0186869 | ||||||||
\(409\) | 28.9182 | 1.42992 | 0.714958 | − | 0.699168i | \(-0.246446\pi\) | ||||
0.714958 | + | 0.699168i | \(0.246446\pi\) | |||||||
\(410\) | 1.79947 | 0.0888696 | ||||||||
\(411\) | −0.185021 | −0.00912640 | ||||||||
\(412\) | −2.25343 | −0.111018 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −10.6038 | −0.521148 | ||||||||
\(415\) | 13.1261 | 0.644333 | ||||||||
\(416\) | 18.4179 | 0.903010 | ||||||||
\(417\) | 0.325503 | 0.0159399 | ||||||||
\(418\) | 6.87020 | 0.336032 | ||||||||
\(419\) | −30.7335 | −1.50143 | −0.750715 | − | 0.660626i | \(-0.770291\pi\) | ||||
−0.750715 | + | 0.660626i | \(0.770291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.2914 | −0.891470 | −0.445735 | − | 0.895165i | \(-0.647058\pi\) | ||||
−0.445735 | + | 0.895165i | \(0.647058\pi\) | |||||||
\(422\) | 21.2684 | 1.03533 | ||||||||
\(423\) | 0.464249 | 0.0225726 | ||||||||
\(424\) | −19.1880 | −0.931849 | ||||||||
\(425\) | 2.96928 | 0.144031 | ||||||||
\(426\) | 0.237422 | 0.0115031 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 18.4590 | 0.892248 | ||||||||
\(429\) | 0.360946 | 0.0174267 | ||||||||
\(430\) | −7.55207 | −0.364193 | ||||||||
\(431\) | 6.26079 | 0.301572 | 0.150786 | − | 0.988566i | \(-0.451820\pi\) | ||||
0.150786 | + | 0.988566i | \(0.451820\pi\) | |||||||
\(432\) | −0.0285339 | −0.00137284 | ||||||||
\(433\) | 17.7835 | 0.854622 | 0.427311 | − | 0.904105i | \(-0.359461\pi\) | ||||
0.427311 | + | 0.904105i | \(0.359461\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.181073 | −0.00868176 | ||||||||
\(436\) | −3.46212 | −0.165806 | ||||||||
\(437\) | −6.53892 | −0.312799 | ||||||||
\(438\) | −0.202654 | −0.00968320 | ||||||||
\(439\) | 21.0267 | 1.00355 | 0.501774 | − | 0.864999i | \(-0.332681\pi\) | ||||
0.501774 | + | 0.864999i | \(0.332681\pi\) | |||||||
\(440\) | 30.6872 | 1.46295 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.0073 | −0.808957 | ||||||||
\(443\) | 14.2736 | 0.678158 | 0.339079 | − | 0.940758i | \(-0.389885\pi\) | ||||
0.339079 | + | 0.940758i | \(0.389885\pi\) | |||||||
\(444\) | −0.00419450 | −0.000199062 0 | ||||||||
\(445\) | 3.88714 | 0.184268 | ||||||||
\(446\) | 23.0533 | 1.09161 | ||||||||
\(447\) | −0.293025 | −0.0138596 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.6951 | −1.11824 | −0.559122 | − | 0.829086i | \(-0.688862\pi\) | ||||
−0.559122 | + | 0.829086i | \(0.688862\pi\) | |||||||
\(450\) | −1.20170 | −0.0566485 | ||||||||
\(451\) | −5.19192 | −0.244478 | ||||||||
\(452\) | −23.4811 | −1.10446 | ||||||||
\(453\) | 0.0647314 | 0.00304135 | ||||||||
\(454\) | −11.8402 | −0.555689 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0942010 | 0.00441137 | ||||||||
\(457\) | −2.48464 | −0.116226 | −0.0581132 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581132 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(458\) | −21.7833 | −1.01787 | ||||||||
\(459\) | 0.815135 | 0.0380472 | ||||||||
\(460\) | −11.4230 | −0.532601 | ||||||||
\(461\) | −25.8203 | −1.20257 | −0.601285 | − | 0.799035i | \(-0.705344\pi\) | ||||
−0.601285 | + | 0.799035i | \(0.705344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.2725 | 1.17451 | 0.587256 | − | 0.809401i | \(-0.300208\pi\) | ||||
0.587256 | + | 0.809401i | \(0.300208\pi\) | |||||||
\(464\) | 0.861709 | 0.0400038 | ||||||||
\(465\) | −0.153515 | −0.00711908 | ||||||||
\(466\) | 17.7512 | 0.822310 | ||||||||
\(467\) | 33.2250 | 1.53747 | 0.768734 | − | 0.639569i | \(-0.220887\pi\) | ||||
0.768734 | + | 0.639569i | \(0.220887\pi\) | |||||||
\(468\) | −12.3597 | −0.571327 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.278512 | −0.0128468 | ||||||||
\(471\) | 0.255021 | 0.0117508 | ||||||||
\(472\) | 2.51681 | 0.115846 | ||||||||
\(473\) | 21.7896 | 1.00189 | ||||||||
\(474\) | −0.00607549 | −0.000279057 0 | ||||||||
\(475\) | −0.741035 | −0.0340010 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.7170 | 0.948565 | ||||||||
\(478\) | 21.1667 | 0.968142 | ||||||||
\(479\) | −18.0657 | −0.825442 | −0.412721 | − | 0.910857i | \(-0.635422\pi\) | ||||
−0.412721 | + | 0.910857i | \(0.635422\pi\) | |||||||
\(480\) | 0.264765 | 0.0120848 | ||||||||
\(481\) | −0.483239 | −0.0220338 | ||||||||
\(482\) | 6.82194 | 0.310731 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −20.4973 | −0.931696 | ||||||||
\(485\) | −16.4584 | −0.747337 | ||||||||
\(486\) | −0.494852 | −0.0224470 | ||||||||
\(487\) | 10.3071 | 0.467060 | 0.233530 | − | 0.972350i | \(-0.424972\pi\) | ||||
0.233530 | + | 0.972350i | \(0.424972\pi\) | |||||||
\(488\) | −20.0716 | −0.908596 | ||||||||
\(489\) | −0.242140 | −0.0109500 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2743 | −0.824709 | −0.412354 | − | 0.911023i | \(-0.635293\pi\) | ||||
−0.412354 | + | 0.911023i | \(0.635293\pi\) | |||||||
\(492\) | −0.0278421 | −0.00125522 | ||||||||
\(493\) | −24.6167 | −1.10868 | ||||||||
\(494\) | 4.24448 | 0.190968 | ||||||||
\(495\) | −33.1326 | −1.48920 | ||||||||
\(496\) | 0.730565 | 0.0328033 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.113100 | 0.00506814 | ||||||||
\(499\) | 18.8781 | 0.845101 | 0.422550 | − | 0.906339i | \(-0.361135\pi\) | ||||
0.422550 | + | 0.906339i | \(0.361135\pi\) | |||||||
\(500\) | −14.9597 | −0.669017 | ||||||||
\(501\) | 0.538906 | 0.0240765 | ||||||||
\(502\) | 23.0288 | 1.02783 | ||||||||
\(503\) | −32.4514 | −1.44694 | −0.723469 | − | 0.690357i | \(-0.757454\pi\) | ||||
−0.723469 | + | 0.690357i | \(0.757454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1019 | −0.716526 | ||||||||
\(506\) | −18.3542 | −0.815946 | ||||||||
\(507\) | −0.0587603 | −0.00260964 | ||||||||
\(508\) | 2.38519 | 0.105826 | ||||||||
\(509\) | 3.87039 | 0.171552 | 0.0857760 | − | 0.996314i | \(-0.472663\pi\) | ||||
0.0857760 | + | 0.996314i | \(0.472663\pi\) | |||||||
\(510\) | −0.244488 | −0.0108261 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.47926 | −0.109569 | ||||||||
\(513\) | −0.203431 | −0.00898170 | ||||||||
\(514\) | −11.8815 | −0.524071 | ||||||||
\(515\) | −3.73204 | −0.164453 | ||||||||
\(516\) | 0.116848 | 0.00514396 | ||||||||
\(517\) | 0.803575 | 0.0353412 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.203024 | −0.00891175 | ||||||||
\(520\) | 18.9589 | 0.831401 | ||||||||
\(521\) | −43.4935 | −1.90549 | −0.952743 | − | 0.303777i | \(-0.901752\pi\) | ||||
−0.952743 | + | 0.303777i | \(0.901752\pi\) | |||||||
\(522\) | 9.96261 | 0.436052 | ||||||||
\(523\) | −22.7651 | −0.995450 | −0.497725 | − | 0.867335i | \(-0.665831\pi\) | ||||
−0.497725 | + | 0.867335i | \(0.665831\pi\) | |||||||
\(524\) | −22.0843 | −0.964755 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.23598 | −0.315504 | ||||||||
\(527\) | −20.8702 | −0.909122 | ||||||||
\(528\) | −0.0246929 | −0.00107462 | ||||||||
\(529\) | −5.53079 | −0.240469 | ||||||||
\(530\) | −12.4285 | −0.539859 | ||||||||
\(531\) | −2.71737 | −0.117924 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.20762 | −0.138938 | ||||||||
\(534\) | 0.0334934 | 0.00144940 | ||||||||
\(535\) | 30.5710 | 1.32170 | ||||||||
\(536\) | −4.78344 | −0.206613 | ||||||||
\(537\) | 0.239635 | 0.0103410 | ||||||||
\(538\) | 25.8824 | 1.11587 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.355380 | −0.0152931 | ||||||||
\(541\) | −15.7172 | −0.675736 | −0.337868 | − | 0.941193i | \(-0.609706\pi\) | ||||
−0.337868 | + | 0.941193i | \(0.609706\pi\) | |||||||
\(542\) | 24.0821 | 1.03442 | ||||||||
\(543\) | −0.170033 | −0.00729682 | ||||||||
\(544\) | 35.9946 | 1.54325 | ||||||||
\(545\) | −5.73384 | −0.245611 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.590413 | −0.0252442 | −0.0126221 | − | 0.999920i | \(-0.504018\pi\) | ||||
−0.0126221 | + | 0.999920i | \(0.504018\pi\) | |||||||
\(548\) | 10.9663 | 0.468457 | ||||||||
\(549\) | 21.6710 | 0.924895 | ||||||||
\(550\) | −2.08003 | −0.0886928 | ||||||||
\(551\) | 6.14352 | 0.261723 | ||||||||
\(552\) | −0.251665 | −0.0107116 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.1198 | −0.769838 | ||||||||
\(555\) | −0.00694676 | −0.000294874 0 | ||||||||
\(556\) | −19.2928 | −0.818196 | ||||||||
\(557\) | 33.4498 | 1.41732 | 0.708658 | − | 0.705553i | \(-0.249301\pi\) | ||||
0.708658 | + | 0.705553i | \(0.249301\pi\) | |||||||
\(558\) | 8.44639 | 0.357564 | ||||||||
\(559\) | 13.4618 | 0.569375 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.705408 | 0.0297823 | ||||||||
\(562\) | −13.5797 | −0.572824 | ||||||||
\(563\) | −40.5522 | −1.70907 | −0.854536 | − | 0.519392i | \(-0.826158\pi\) | ||||
−0.854536 | + | 0.519392i | \(0.826158\pi\) | |||||||
\(564\) | 0.00430923 | 0.000181451 0 | ||||||||
\(565\) | −38.8884 | −1.63605 | ||||||||
\(566\) | 9.63837 | 0.405131 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −35.9810 | −1.50973 | ||||||||
\(569\) | −2.35745 | −0.0988296 | −0.0494148 | − | 0.998778i | \(-0.515736\pi\) | ||||
−0.0494148 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(570\) | 0.0610162 | 0.00255569 | ||||||||
\(571\) | 6.02445 | 0.252115 | 0.126058 | − | 0.992023i | \(-0.459768\pi\) | ||||
0.126058 | + | 0.992023i | \(0.459768\pi\) | |||||||
\(572\) | −21.3935 | −0.894509 | ||||||||
\(573\) | 0.383074 | 0.0160031 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.97973 | 0.0825605 | ||||||||
\(576\) | −13.2509 | −0.552122 | ||||||||
\(577\) | −14.4100 | −0.599895 | −0.299947 | − | 0.953956i | \(-0.596969\pi\) | ||||
−0.299947 | + | 0.953956i | \(0.596969\pi\) | |||||||
\(578\) | −18.8592 | −0.784440 | ||||||||
\(579\) | −0.297914 | −0.0123809 | ||||||||
\(580\) | 10.7323 | 0.445634 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.141813 | −0.00587834 | ||||||||
\(583\) | 35.8593 | 1.48514 | ||||||||
\(584\) | 30.7121 | 1.27087 | ||||||||
\(585\) | −20.4696 | −0.846315 | ||||||||
\(586\) | 13.3620 | 0.551981 | ||||||||
\(587\) | 0.234221 | 0.00966735 | 0.00483367 | − | 0.999988i | \(-0.498461\pi\) | ||||
0.00483367 | + | 0.999988i | \(0.498461\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.20853 | 0.214614 | ||||||||
\(590\) | 1.63020 | 0.0671143 | ||||||||
\(591\) | −0.361276 | −0.0148609 | ||||||||
\(592\) | 0.0330591 | 0.00135872 | ||||||||
\(593\) | −28.6508 | −1.17655 | −0.588274 | − | 0.808661i | \(-0.700193\pi\) | ||||
−0.588274 | + | 0.808661i | \(0.700193\pi\) | |||||||
\(594\) | −0.571016 | −0.0234291 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.3678 | 0.711413 | ||||||||
\(597\) | 0.0158822 | 0.000650013 0 | ||||||||
\(598\) | −11.3394 | −0.463704 | ||||||||
\(599\) | −25.7299 | −1.05129 | −0.525647 | − | 0.850703i | \(-0.676177\pi\) | ||||
−0.525647 | + | 0.850703i | \(0.676177\pi\) | |||||||
\(600\) | −0.0285204 | −0.00116434 | ||||||||
\(601\) | −25.8320 | −1.05371 | −0.526855 | − | 0.849955i | \(-0.676629\pi\) | ||||
−0.526855 | + | 0.849955i | \(0.676629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.16462 | 0.210320 | ||||||||
\(604\) | −3.83668 | −0.156112 | ||||||||
\(605\) | −33.9468 | −1.38013 | ||||||||
\(606\) | −0.138742 | −0.00563599 | ||||||||
\(607\) | 14.6431 | 0.594346 | 0.297173 | − | 0.954824i | \(-0.403956\pi\) | ||||
0.297173 | + | 0.954824i | \(0.403956\pi\) | |||||||
\(608\) | −8.98307 | −0.364312 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.0008 | −0.526388 | ||||||||
\(611\) | 0.496457 | 0.0200845 | ||||||||
\(612\) | −24.1549 | −0.976404 | ||||||||
\(613\) | −30.1823 | −1.21905 | −0.609526 | − | 0.792766i | \(-0.708640\pi\) | ||||
−0.609526 | + | 0.792766i | \(0.708640\pi\) | |||||||
\(614\) | −7.92735 | −0.319922 | ||||||||
\(615\) | −0.0461110 | −0.00185937 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5169 | −0.544170 | −0.272085 | − | 0.962273i | \(-0.587713\pi\) | ||||
−0.272085 | + | 0.962273i | \(0.587713\pi\) | |||||||
\(618\) | −0.0321570 | −0.00129354 | ||||||||
\(619\) | −14.2452 | −0.572565 | −0.286282 | − | 0.958145i | \(-0.592420\pi\) | ||||
−0.286282 | + | 0.958145i | \(0.592420\pi\) | |||||||
\(620\) | 9.09894 | 0.365422 | ||||||||
\(621\) | 0.543482 | 0.0218092 | ||||||||
\(622\) | 0.824968 | 0.0330782 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.0152555 | −0.000610709 0 | ||||||||
\(625\) | −22.4073 | −0.896293 | ||||||||
\(626\) | −27.3125 | −1.09163 | ||||||||
\(627\) | −0.176047 | −0.00703064 | ||||||||
\(628\) | −15.1153 | −0.603166 | ||||||||
\(629\) | −0.944407 | −0.0376560 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.1182 | 0.402798 | 0.201399 | − | 0.979509i | \(-0.435451\pi\) | ||||
0.201399 | + | 0.979509i | \(0.435451\pi\) | |||||||
\(632\) | 0.920734 | 0.0366248 | ||||||||
\(633\) | −0.544998 | −0.0216617 | ||||||||
\(634\) | 17.1095 | 0.679504 | ||||||||
\(635\) | 3.95026 | 0.156761 | ||||||||
\(636\) | 0.192298 | 0.00762512 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 17.2444 | 0.682712 | ||||||||
\(639\) | 38.8482 | 1.53681 | ||||||||
\(640\) | −16.4825 | −0.651529 | ||||||||
\(641\) | 48.2183 | 1.90451 | 0.952254 | − | 0.305307i | \(-0.0987592\pi\) | ||||
0.952254 | + | 0.305307i | \(0.0987592\pi\) | |||||||
\(642\) | 0.263414 | 0.0103961 | ||||||||
\(643\) | 20.1040 | 0.792823 | 0.396412 | − | 0.918073i | \(-0.370255\pi\) | ||||
0.396412 | + | 0.918073i | \(0.370255\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.193520 | 0.00761983 | ||||||||
\(646\) | 8.29511 | 0.326367 | ||||||||
\(647\) | 12.0746 | 0.474701 | 0.237350 | − | 0.971424i | \(-0.423721\pi\) | ||||
0.237350 | + | 0.971424i | \(0.423721\pi\) | |||||||
\(648\) | 24.9916 | 0.981762 | ||||||||
\(649\) | −4.70353 | −0.184630 | ||||||||
\(650\) | −1.28506 | −0.0504044 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.3518 | 0.562061 | ||||||||
\(653\) | −22.6661 | −0.886991 | −0.443496 | − | 0.896277i | \(-0.646262\pi\) | ||||
−0.443496 | + | 0.896277i | \(0.646262\pi\) | |||||||
\(654\) | −0.0494054 | −0.00193190 | ||||||||
\(655\) | −36.5751 | −1.42911 | ||||||||
\(656\) | 0.219438 | 0.00856763 | ||||||||
\(657\) | −33.1594 | −1.29367 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.4712 | 0.992217 | 0.496109 | − | 0.868260i | \(-0.334762\pi\) | ||||
0.496109 | + | 0.868260i | \(0.334762\pi\) | |||||||
\(660\) | −0.307541 | −0.0119710 | ||||||||
\(661\) | 47.3837 | 1.84301 | 0.921507 | − | 0.388362i | \(-0.126959\pi\) | ||||
0.921507 | + | 0.388362i | \(0.126959\pi\) | |||||||
\(662\) | −25.6217 | −0.995814 | ||||||||
\(663\) | 0.435808 | 0.0169254 | ||||||||
\(664\) | −17.1402 | −0.665170 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.382211 | 0.0148104 | ||||||||
\(667\) | −16.4129 | −0.635509 | ||||||||
\(668\) | −31.9413 | −1.23585 | ||||||||
\(669\) | −0.590735 | −0.0228391 | ||||||||
\(670\) | −3.09835 | −0.119700 | ||||||||
\(671\) | 37.5106 | 1.44808 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.32956 | −0.128345 | −0.0641726 | − | 0.997939i | \(-0.520441\pi\) | ||||
−0.0641726 | + | 0.997939i | \(0.520441\pi\) | |||||||
\(674\) | 11.2160 | 0.432026 | ||||||||
\(675\) | 0.0615911 | 0.00237064 | ||||||||
\(676\) | 3.48276 | 0.133952 | ||||||||
\(677\) | 4.42275 | 0.169980 | 0.0849901 | − | 0.996382i | \(-0.472914\pi\) | ||||
0.0849901 | + | 0.996382i | \(0.472914\pi\) | |||||||
\(678\) | −0.335081 | −0.0128687 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 37.0519 | 1.42087 | ||||||||
\(681\) | 0.303402 | 0.0116264 | ||||||||
\(682\) | 14.6200 | 0.559827 | ||||||||
\(683\) | −35.3517 | −1.35270 | −0.676348 | − | 0.736583i | \(-0.736438\pi\) | ||||
−0.676348 | + | 0.736583i | \(0.736438\pi\) | |||||||
\(684\) | 6.02828 | 0.230497 | ||||||||
\(685\) | 18.1620 | 0.693933 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.558192 | 0.0212963 | ||||||||
\(688\) | −0.920944 | −0.0351106 | ||||||||
\(689\) | 22.1542 | 0.844009 | ||||||||
\(690\) | −0.163009 | −0.00620566 | ||||||||
\(691\) | 27.4126 | 1.04282 | 0.521412 | − | 0.853305i | \(-0.325405\pi\) | ||||
0.521412 | + | 0.853305i | \(0.325405\pi\) | |||||||
\(692\) | 12.0334 | 0.457439 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.2677 | −0.807312 | ||||||||
\(695\) | −31.9520 | −1.21201 | ||||||||
\(696\) | 0.236447 | 0.00896251 | ||||||||
\(697\) | −6.26875 | −0.237446 | ||||||||
\(698\) | −13.4788 | −0.510180 | ||||||||
\(699\) | −0.454870 | −0.0172048 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.3878 | 1.71427 | 0.857137 | − | 0.515088i | \(-0.172241\pi\) | ||||
0.857137 | + | 0.515088i | \(0.172241\pi\) | |||||||
\(702\) | −0.352780 | −0.0133148 | ||||||||
\(703\) | 0.235693 | 0.00888934 | ||||||||
\(704\) | −22.9362 | −0.864440 | ||||||||
\(705\) | 0.00713678 | 0.000268787 0 | ||||||||
\(706\) | 10.5932 | 0.398679 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.0252230 | −0.000947940 0 | ||||||||
\(709\) | −8.87595 | −0.333343 | −0.166672 | − | 0.986012i | \(-0.553302\pi\) | ||||
−0.166672 | + | 0.986012i | \(0.553302\pi\) | |||||||
\(710\) | −23.3058 | −0.874650 | ||||||||
\(711\) | −0.994105 | −0.0372818 | ||||||||
\(712\) | −5.07589 | −0.190227 | ||||||||
\(713\) | −13.9150 | −0.521120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.4311 | −1.32505 | ||||||||
\(716\) | −14.2033 | −0.530804 | ||||||||
\(717\) | −0.542391 | −0.0202560 | ||||||||
\(718\) | −4.68877 | −0.174983 | ||||||||
\(719\) | 21.2366 | 0.791993 | 0.395997 | − | 0.918252i | \(-0.370399\pi\) | ||||
0.395997 | + | 0.918252i | \(0.370399\pi\) | |||||||
\(720\) | 1.40036 | 0.0521883 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14.0002 | 0.521032 | ||||||||
\(723\) | −0.174810 | −0.00650127 | ||||||||
\(724\) | 10.0780 | 0.374545 | ||||||||
\(725\) | −1.86002 | −0.0690794 | ||||||||
\(726\) | −0.292502 | −0.0108558 | ||||||||
\(727\) | 8.30528 | 0.308026 | 0.154013 | − | 0.988069i | \(-0.450780\pi\) | ||||
0.154013 | + | 0.988069i | \(0.450780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9746 | −0.999061 | ||||||||
\(730\) | 19.8929 | 0.736270 | ||||||||
\(731\) | 26.3088 | 0.973068 | ||||||||
\(732\) | 0.201153 | 0.00743484 | ||||||||
\(733\) | 5.01851 | 0.185363 | 0.0926814 | − | 0.995696i | \(-0.470456\pi\) | ||||
0.0926814 | + | 0.995696i | \(0.470456\pi\) | |||||||
\(734\) | 2.50269 | 0.0923761 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23.9989 | 0.884613 | ||||||||
\(737\) | 8.93950 | 0.329291 | ||||||||
\(738\) | 2.53703 | 0.0933892 | ||||||||
\(739\) | −30.8086 | −1.13331 | −0.566656 | − | 0.823955i | \(-0.691763\pi\) | ||||
−0.566656 | + | 0.823955i | \(0.691763\pi\) | |||||||
\(740\) | 0.411739 | 0.0151358 | ||||||||
\(741\) | −0.108764 | −0.00399553 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.4367 | 1.30005 | 0.650023 | − | 0.759915i | \(-0.274759\pi\) | ||||
0.650023 | + | 0.759915i | \(0.274759\pi\) | |||||||
\(744\) | 0.200462 | 0.00734930 | ||||||||
\(745\) | 28.7639 | 1.05383 | ||||||||
\(746\) | −9.44131 | −0.345671 | ||||||||
\(747\) | 18.5061 | 0.677102 | ||||||||
\(748\) | −41.8100 | −1.52873 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.213479 | −0.00779513 | ||||||||
\(751\) | 7.27823 | 0.265586 | 0.132793 | − | 0.991144i | \(-0.457605\pi\) | ||||
0.132793 | + | 0.991144i | \(0.457605\pi\) | |||||||
\(752\) | −0.0339634 | −0.00123852 | ||||||||
\(753\) | −0.590108 | −0.0215047 | ||||||||
\(754\) | 10.6538 | 0.387987 | ||||||||
\(755\) | −6.35415 | −0.231251 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0166 | 0.909243 | 0.454621 | − | 0.890685i | \(-0.349775\pi\) | ||||
0.454621 | + | 0.890685i | \(0.349775\pi\) | |||||||
\(758\) | 11.3770 | 0.413231 | ||||||||
\(759\) | 0.470323 | 0.0170716 | ||||||||
\(760\) | −9.24694 | −0.335422 | ||||||||
\(761\) | 23.2193 | 0.841701 | 0.420850 | − | 0.907130i | \(-0.361732\pi\) | ||||
0.420850 | + | 0.907130i | \(0.361732\pi\) | |||||||
\(762\) | 0.0340373 | 0.00123304 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −22.7051 | −0.821440 | ||||||||
\(765\) | −40.0044 | −1.44636 | ||||||||
\(766\) | 28.3710 | 1.02509 | ||||||||
\(767\) | −2.90589 | −0.104926 | ||||||||
\(768\) | −0.333515 | −0.0120347 | ||||||||
\(769\) | 40.2927 | 1.45299 | 0.726496 | − | 0.687170i | \(-0.241147\pi\) | ||||
0.726496 | + | 0.687170i | \(0.241147\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.304461 | 0.0109649 | ||||||||
\(772\) | 17.6576 | 0.635510 | ||||||||
\(773\) | −11.5294 | −0.414685 | −0.207343 | − | 0.978268i | \(-0.566481\pi\) | ||||
−0.207343 | + | 0.978268i | \(0.566481\pi\) | |||||||
\(774\) | −10.6474 | −0.382715 | ||||||||
\(775\) | −1.57694 | −0.0566454 | ||||||||
\(776\) | 21.4916 | 0.771504 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.0284 | −1.11242 | ||||||||
\(779\) | 1.56448 | 0.0560532 | ||||||||
\(780\) | −0.190002 | −0.00680317 | ||||||||
\(781\) | 67.2429 | 2.40614 | ||||||||
\(782\) | −22.1610 | −0.792476 | ||||||||
\(783\) | −0.510618 | −0.0182480 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.0334 | −0.893479 | ||||||||
\(786\) | −0.315148 | −0.0112410 | ||||||||
\(787\) | 52.0845 | 1.85661 | 0.928306 | − | 0.371818i | \(-0.121266\pi\) | ||||
0.928306 | + | 0.371818i | \(0.121266\pi\) | |||||||
\(788\) | 21.4131 | 0.762809 | ||||||||
\(789\) | 0.185420 | 0.00660113 | ||||||||
\(790\) | 0.596381 | 0.0212183 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 43.2650 | 1.53736 | ||||||||
\(793\) | 23.1744 | 0.822948 | ||||||||
\(794\) | 17.6702 | 0.627091 | ||||||||
\(795\) | 0.318477 | 0.0112952 | ||||||||
\(796\) | −0.941347 | −0.0333651 | ||||||||
\(797\) | −19.7674 | −0.700197 | −0.350098 | − | 0.936713i | \(-0.613852\pi\) | ||||
−0.350098 | + | 0.936713i | \(0.613852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.970240 | 0.0343246 | ||||||||
\(800\) | 2.71973 | 0.0961568 | ||||||||
\(801\) | 5.48038 | 0.193640 | ||||||||
\(802\) | 15.7168 | 0.554978 | ||||||||
\(803\) | −57.3960 | −2.02546 | ||||||||
\(804\) | 0.0479388 | 0.00169067 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.03236 | 0.318151 | ||||||||
\(807\) | −0.663230 | −0.0233468 | ||||||||
\(808\) | 21.0261 | 0.739697 | ||||||||
\(809\) | 34.1602 | 1.20101 | 0.600504 | − | 0.799621i | \(-0.294967\pi\) | ||||
0.600504 | + | 0.799621i | \(0.294967\pi\) | |||||||
\(810\) | 16.1876 | 0.568776 | ||||||||
\(811\) | 48.6449 | 1.70815 | 0.854077 | − | 0.520147i | \(-0.174123\pi\) | ||||
0.854077 | + | 0.520147i | \(0.174123\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.617098 | −0.0216426 | ||||||||
\(814\) | 0.661573 | 0.0231881 | ||||||||
\(815\) | 23.7689 | 0.832589 | ||||||||
\(816\) | −0.0298143 | −0.00104371 | ||||||||
\(817\) | −6.56583 | −0.229709 | ||||||||
\(818\) | −24.4593 | −0.855199 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.73303 | 0.0954415 | ||||||||
\(821\) | 18.1850 | 0.634659 | 0.317330 | − | 0.948315i | \(-0.397214\pi\) | ||||
0.317330 | + | 0.948315i | \(0.397214\pi\) | |||||||
\(822\) | 0.156492 | 0.00545828 | ||||||||
\(823\) | 11.6225 | 0.405135 | 0.202567 | − | 0.979268i | \(-0.435072\pi\) | ||||
0.202567 | + | 0.979268i | \(0.435072\pi\) | |||||||
\(824\) | 4.87336 | 0.169772 | ||||||||
\(825\) | 0.0533002 | 0.00185567 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.09639 | −0.246766 | −0.123383 | − | 0.992359i | \(-0.539374\pi\) | ||||
−0.123383 | + | 0.992359i | \(0.539374\pi\) | |||||||
\(828\) | −16.1050 | −0.559688 | ||||||||
\(829\) | 8.50362 | 0.295343 | 0.147672 | − | 0.989036i | \(-0.452822\pi\) | ||||
0.147672 | + | 0.989036i | \(0.452822\pi\) | |||||||
\(830\) | −11.1021 | −0.385360 | ||||||||
\(831\) | 0.464316 | 0.0161069 | ||||||||
\(832\) | −14.1702 | −0.491264 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.275313 | −0.00953331 | ||||||||
\(835\) | −52.9000 | −1.83068 | ||||||||
\(836\) | 10.4344 | 0.360882 | ||||||||
\(837\) | −0.432907 | −0.0149634 | ||||||||
\(838\) | 25.9947 | 0.897970 | ||||||||
\(839\) | 39.3940 | 1.36003 | 0.680015 | − | 0.733198i | \(-0.261973\pi\) | ||||
0.680015 | + | 0.733198i | \(0.261973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.5796 | −0.468261 | ||||||||
\(842\) | 15.4710 | 0.533167 | ||||||||
\(843\) | 0.347976 | 0.0119849 | ||||||||
\(844\) | 32.3024 | 1.11189 | ||||||||
\(845\) | 5.76801 | 0.198426 | ||||||||
\(846\) | −0.392666 | −0.0135001 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.51560 | −0.0520460 | ||||||||
\(849\) | −0.246981 | −0.00847635 | ||||||||
\(850\) | −2.51144 | −0.0861416 | ||||||||
\(851\) | −0.629672 | −0.0215849 | ||||||||
\(852\) | 0.360595 | 0.0123538 | ||||||||
\(853\) | −50.8194 | −1.74002 | −0.870012 | − | 0.493031i | \(-0.835889\pi\) | ||||
−0.870012 | + | 0.493031i | \(0.835889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.98380 | 0.341439 | ||||||||
\(856\) | −39.9201 | −1.36444 | ||||||||
\(857\) | −17.4259 | −0.595257 | −0.297628 | − | 0.954682i | \(-0.596196\pi\) | ||||
−0.297628 | + | 0.954682i | \(0.596196\pi\) | |||||||
\(858\) | −0.305291 | −0.0104225 | ||||||||
\(859\) | 14.7578 | 0.503530 | 0.251765 | − | 0.967788i | \(-0.418989\pi\) | ||||
0.251765 | + | 0.967788i | \(0.418989\pi\) | |||||||
\(860\) | −11.4700 | −0.391125 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.29543 | −0.180363 | ||||||||
\(863\) | −10.2274 | −0.348143 | −0.174072 | − | 0.984733i | \(-0.555692\pi\) | ||||
−0.174072 | + | 0.984733i | \(0.555692\pi\) | |||||||
\(864\) | 0.746627 | 0.0254008 | ||||||||
\(865\) | 19.9292 | 0.677612 | ||||||||
\(866\) | −15.0415 | −0.511129 | ||||||||
\(867\) | 0.483262 | 0.0164124 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.72071 | −0.0583710 | ||||||||
\(870\) | 0.153153 | 0.00519236 | ||||||||
\(871\) | 5.52292 | 0.187137 | ||||||||
\(872\) | 7.48733 | 0.253553 | ||||||||
\(873\) | −23.2042 | −0.785344 | ||||||||
\(874\) | 5.53067 | 0.187078 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.307791 | −0.0103993 | ||||||||
\(877\) | −42.7787 | −1.44453 | −0.722266 | − | 0.691615i | \(-0.756900\pi\) | ||||
−0.722266 | + | 0.691615i | \(0.756900\pi\) | |||||||
\(878\) | −17.7845 | −0.600199 | ||||||||
\(879\) | −0.342399 | −0.0115488 | ||||||||
\(880\) | 2.42390 | 0.0817095 | ||||||||
\(881\) | 0.101554 | 0.00342143 | 0.00171072 | − | 0.999999i | \(-0.499455\pi\) | ||||
0.00171072 | + | 0.999999i | \(0.499455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0311 | −0.573142 | −0.286571 | − | 0.958059i | \(-0.592515\pi\) | ||||
−0.286571 | + | 0.958059i | \(0.592515\pi\) | |||||||
\(884\) | −25.8307 | −0.868779 | ||||||||
\(885\) | −0.0417734 | −0.00140420 | ||||||||
\(886\) | −12.0727 | −0.405590 | ||||||||
\(887\) | −44.0812 | −1.48010 | −0.740051 | − | 0.672550i | \(-0.765199\pi\) | ||||
−0.740051 | + | 0.672550i | \(0.765199\pi\) | |||||||
\(888\) | 0.00907119 | 0.000304409 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.28778 | −0.110207 | ||||||||
\(891\) | −46.7054 | −1.56469 | ||||||||
\(892\) | 35.0133 | 1.17233 | ||||||||
\(893\) | −0.242140 | −0.00810292 | ||||||||
\(894\) | 0.247843 | 0.00828911 | ||||||||
\(895\) | −23.5230 | −0.786288 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.290570 | 0.00970186 | ||||||||
\(898\) | 20.0415 | 0.668795 | ||||||||
\(899\) | 13.0736 | 0.436028 | ||||||||
\(900\) | −1.82513 | −0.0608377 | ||||||||
\(901\) | 43.2967 | 1.44242 | ||||||||
\(902\) | 4.39137 | 0.146217 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 50.7811 | 1.68895 | ||||||||
\(905\) | 16.6908 | 0.554819 | ||||||||
\(906\) | −0.0547503 | −0.00181896 | ||||||||
\(907\) | 6.16615 | 0.204744 | 0.102372 | − | 0.994746i | \(-0.467357\pi\) | ||||
0.102372 | + | 0.994746i | \(0.467357\pi\) | |||||||
\(908\) | −17.9829 | −0.596783 | ||||||||
\(909\) | −22.7016 | −0.752966 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.0446 | 1.26048 | 0.630238 | − | 0.776402i | \(-0.282957\pi\) | ||||
0.630238 | + | 0.776402i | \(0.282957\pi\) | |||||||
\(912\) | 0.00744068 | 0.000246385 0 | ||||||||
\(913\) | 32.0324 | 1.06012 | ||||||||
\(914\) | 2.10153 | 0.0695123 | ||||||||
\(915\) | 0.333142 | 0.0110133 | ||||||||
\(916\) | −33.0844 | −1.09314 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.689447 | −0.0227552 | ||||||||
\(919\) | 47.2627 | 1.55905 | 0.779526 | − | 0.626370i | \(-0.215460\pi\) | ||||
0.779526 | + | 0.626370i | \(0.215460\pi\) | |||||||
\(920\) | 24.7039 | 0.814463 | ||||||||
\(921\) | 0.203136 | 0.00669357 | ||||||||
\(922\) | 21.8390 | 0.719229 | ||||||||
\(923\) | 41.5434 | 1.36742 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0713588 | −0.00234626 | ||||||||
\(926\) | −21.3757 | −0.702448 | ||||||||
\(927\) | −5.26170 | −0.172817 | ||||||||
\(928\) | −22.5478 | −0.740167 | ||||||||
\(929\) | −23.4189 | −0.768349 | −0.384174 | − | 0.923261i | \(-0.625514\pi\) | ||||
−0.384174 | + | 0.923261i | \(0.625514\pi\) | |||||||
\(930\) | 0.129844 | 0.00425776 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 26.9605 | 0.883120 | ||||||||
\(933\) | −0.0211396 | −0.000692078 0 | ||||||||
\(934\) | −28.1019 | −0.919523 | ||||||||
\(935\) | −69.2441 | −2.26452 | ||||||||
\(936\) | 26.7296 | 0.873684 | ||||||||
\(937\) | 38.4910 | 1.25745 | 0.628723 | − | 0.777629i | \(-0.283578\pi\) | ||||
0.628723 | + | 0.777629i | \(0.283578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.699876 | 0.0228396 | ||||||||
\(940\) | −0.423002 | −0.0137968 | ||||||||
\(941\) | 22.3251 | 0.727777 | 0.363889 | − | 0.931442i | \(-0.381449\pi\) | ||||
0.363889 | + | 0.931442i | \(0.381449\pi\) | |||||||
\(942\) | −0.215699 | −0.00702786 | ||||||||
\(943\) | −4.17962 | −0.136107 | ||||||||
\(944\) | 0.198796 | 0.00647027 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.4298 | −0.599204 | ||||||||
\(947\) | −12.6943 | −0.412510 | −0.206255 | − | 0.978498i | \(-0.566128\pi\) | ||||
−0.206255 | + | 0.978498i | \(0.566128\pi\) | |||||||
\(948\) | −0.00922743 | −0.000299693 0 | ||||||||
\(949\) | −35.4599 | −1.15108 | ||||||||
\(950\) | 0.626773 | 0.0203352 | ||||||||
\(951\) | −0.438426 | −0.0142169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.70948 | −0.217341 | −0.108671 | − | 0.994078i | \(-0.534659\pi\) | ||||
−0.108671 | + | 0.994078i | \(0.534659\pi\) | |||||||
\(954\) | −17.5226 | −0.567315 | ||||||||
\(955\) | −37.6032 | −1.21681 | ||||||||
\(956\) | 32.1479 | 1.03974 | ||||||||
\(957\) | −0.441883 | −0.0142840 | ||||||||
\(958\) | 15.2801 | 0.493678 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.203703 | −0.00657448 | ||||||||
\(961\) | −19.9161 | −0.642455 | ||||||||
\(962\) | 0.408727 | 0.0131779 | ||||||||
\(963\) | 43.1013 | 1.38892 | ||||||||
\(964\) | 10.3611 | 0.333710 | ||||||||
\(965\) | 29.2438 | 0.941391 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.1576 | 0.680382 | 0.340191 | − | 0.940356i | \(-0.389508\pi\) | ||||
0.340191 | + | 0.940356i | \(0.389508\pi\) | |||||||
\(968\) | 44.3283 | 1.42477 | ||||||||
\(969\) | −0.212560 | −0.00682841 | ||||||||
\(970\) | 13.9206 | 0.446965 | ||||||||
\(971\) | 15.8074 | 0.507283 | 0.253642 | − | 0.967298i | \(-0.418372\pi\) | ||||
0.253642 | + | 0.967298i | \(0.418372\pi\) | |||||||
\(972\) | −0.751580 | −0.0241069 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.71784 | −0.279338 | ||||||||
\(975\) | 0.0329294 | 0.00105459 | ||||||||
\(976\) | −1.58540 | −0.0507473 | ||||||||
\(977\) | 44.0859 | 1.41043 | 0.705216 | − | 0.708993i | \(-0.250850\pi\) | ||||
0.705216 | + | 0.708993i | \(0.250850\pi\) | |||||||
\(978\) | 0.204804 | 0.00654892 | ||||||||
\(979\) | 9.48605 | 0.303175 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.08398 | −0.258101 | ||||||||
\(982\) | 15.4566 | 0.493239 | ||||||||
\(983\) | 17.4650 | 0.557047 | 0.278523 | − | 0.960429i | \(-0.410155\pi\) | ||||
0.278523 | + | 0.960429i | \(0.410155\pi\) | |||||||
\(984\) | 0.0602125 | 0.00191950 | ||||||||
\(985\) | 35.4635 | 1.12996 | ||||||||
\(986\) | 20.8210 | 0.663075 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.44650 | 0.205090 | ||||||||
\(989\) | 17.5411 | 0.557775 | ||||||||
\(990\) | 28.0238 | 0.890654 | ||||||||
\(991\) | 23.4368 | 0.744495 | 0.372248 | − | 0.928133i | \(-0.378587\pi\) | ||||
0.372248 | + | 0.928133i | \(0.378587\pi\) | |||||||
\(992\) | −19.1162 | −0.606940 | ||||||||
\(993\) | 0.656548 | 0.0208349 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.55902 | −0.0494243 | ||||||||
\(996\) | 0.171776 | 0.00544294 | ||||||||
\(997\) | 14.6814 | 0.464963 | 0.232482 | − | 0.972601i | \(-0.425315\pi\) | ||||
0.232482 | + | 0.972601i | \(0.425315\pi\) | |||||||
\(998\) | −15.9673 | −0.505435 | ||||||||
\(999\) | −0.0195896 | −0.000619789 0 |
(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.u.1.9 | yes | 20 | |
7.6 | odd | 2 | 2009.2.a.t.1.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.2.a.t.1.9 | ✓ | 20 | 7.6 | odd | 2 | ||
2009.2.a.u.1.9 | yes | 20 | 1.1 | even | 1 | trivial |