Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.05277 | 0.607816 | 0.303908 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.97996 | −0.885466 | −0.442733 | − | 0.896653i | \(-0.645991\pi\) | ||||
−0.442733 | + | 0.896653i | \(0.645991\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.35506 | 1.64606 | 0.823028 | − | 0.568000i | \(-0.192283\pi\) | ||||
0.823028 | + | 0.568000i | \(0.192283\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.89168 | −0.630560 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.68201 | −1.11017 | −0.555083 | − | 0.831795i | \(-0.687314\pi\) | ||||
−0.555083 | + | 0.831795i | \(0.687314\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.40459 | −0.944263 | −0.472131 | − | 0.881528i | \(-0.656515\pi\) | ||||
−0.472131 | + | 0.881528i | \(0.656515\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.08444 | −0.538200 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.913284 | 0.221504 | 0.110752 | − | 0.993848i | \(-0.464674\pi\) | ||||
0.110752 | + | 0.993848i | \(0.464674\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61464 | −0.599840 | −0.299920 | − | 0.953964i | \(-0.596960\pi\) | ||||
−0.299920 | + | 0.953964i | \(0.596960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58486 | 1.00050 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.15857 | 0.658607 | 0.329303 | − | 0.944224i | \(-0.393186\pi\) | ||||
0.329303 | + | 0.944224i | \(0.393186\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.07975 | −0.215950 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.14980 | −0.991080 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.69811 | 1.80089 | 0.900447 | − | 0.434967i | \(-0.143240\pi\) | ||||
0.900447 | + | 0.434967i | \(0.143240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.70856 | 1.38450 | 0.692249 | − | 0.721659i | \(-0.256620\pi\) | ||||
0.692249 | + | 0.721659i | \(0.256620\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.87630 | −0.674777 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.62285 | −1.45753 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.206922 | 0.0340178 | 0.0170089 | − | 0.999855i | \(-0.494586\pi\) | ||||
0.0170089 | + | 0.999855i | \(0.494586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.58424 | −0.573938 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.61588 | 1.34557 | 0.672787 | − | 0.739836i | \(-0.265097\pi\) | ||||
0.672787 | + | 0.739836i | \(0.265097\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.42378 | −0.827118 | −0.413559 | − | 0.910477i | \(-0.635715\pi\) | ||||
−0.413559 | + | 0.910477i | \(0.635715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.74546 | 0.558340 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.71763 | 1.27160 | 0.635799 | − | 0.771855i | \(-0.280671\pi\) | ||||
0.635799 | + | 0.771855i | \(0.280671\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.9665 | 1.70950 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.961476 | 0.134634 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.86324 | −0.393296 | −0.196648 | − | 0.980474i | \(-0.563006\pi\) | ||||
−0.196648 | + | 0.980474i | \(0.563006\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.29023 | 0.983015 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.75261 | −0.364592 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.4512 | 1.49082 | 0.745412 | − | 0.666604i | \(-0.232253\pi\) | ||||
0.745412 | + | 0.666604i | \(0.232253\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9633 | 1.53175 | 0.765873 | − | 0.642992i | \(-0.222307\pi\) | ||||
0.765873 | + | 0.642992i | \(0.222307\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.23837 | −1.03794 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.74096 | 0.836113 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.74197 | −1.19017 | −0.595086 | − | 0.803662i | \(-0.702882\pi\) | ||||
−0.595086 | + | 0.803662i | \(0.702882\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.32524 | 0.400312 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.93633 | −0.229800 | −0.114900 | − | 0.993377i | \(-0.536655\pi\) | ||||
−0.114900 | + | 0.993377i | \(0.536655\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.38898 | 0.864815 | 0.432407 | − | 0.901678i | \(-0.357664\pi\) | ||||
0.432407 | + | 0.901678i | \(0.357664\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.13672 | −0.131258 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.0353 | −1.82740 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.551502 | 0.0620489 | 0.0310244 | − | 0.999519i | \(-0.490123\pi\) | ||||
0.0310244 | + | 0.999519i | \(0.490123\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.253493 | 0.0281659 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.03932 | 0.553137 | 0.276568 | − | 0.960994i | \(-0.410803\pi\) | ||||
0.276568 | + | 0.960994i | \(0.410803\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.80827 | −0.196134 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.2099 | 1.09461 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.7210 | 1.66642 | 0.833209 | − | 0.552958i | \(-0.186501\pi\) | ||||
0.833209 | + | 0.552958i | \(0.186501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.8272 | −1.55431 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.11532 | 0.841520 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.17689 | 0.531138 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.889467 | −0.0903117 | −0.0451559 | − | 0.998980i | \(-0.514378\pi\) | ||||
−0.0451559 | + | 0.998980i | \(0.514378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.96518 | 0.700026 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.8762 | 1.28123 | 0.640614 | − | 0.767863i | \(-0.278680\pi\) | ||||
0.640614 | + | 0.767863i | \(0.278680\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.50928 | 0.247247 | 0.123623 | − | 0.992329i | \(-0.460548\pi\) | ||||
0.123623 | + | 0.992329i | \(0.460548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.07786 | −0.885908 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.87141 | 0.857632 | 0.428816 | − | 0.903392i | \(-0.358931\pi\) | ||||
0.428816 | + | 0.903392i | \(0.358931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.98186 | 0.285611 | 0.142805 | − | 0.989751i | \(-0.454388\pi\) | ||||
0.142805 | + | 0.989751i | \(0.454388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.217841 | 0.0206765 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.12257 | 0.199674 | 0.0998372 | − | 0.995004i | \(-0.468168\pi\) | ||||
0.0998372 | + | 0.995004i | \(0.468168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.25384 | −0.583174 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.44039 | 0.595414 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.97740 | 0.364608 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.55716 | 0.232469 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.07052 | 0.817861 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0377 | 1.07668 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.68457 | −0.504424 | −0.252212 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252212 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.70998 | −0.502736 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.01810 | 0.263693 | 0.131846 | − | 0.991270i | \(-0.457909\pi\) | ||||
0.131846 | + | 0.991270i | \(0.457909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3869 | −0.987370 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.1964 | 0.877568 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.8429 | −1.86616 | −0.933082 | − | 0.359663i | \(-0.882892\pi\) | ||||
−0.933082 | + | 0.359663i | \(0.882892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3347 | −1.21585 | −0.607927 | − | 0.793993i | \(-0.707999\pi\) | ||||
−0.607927 | + | 0.793993i | \(0.707999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.17764 | 0.772897 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5357 | 1.04829 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.2019 | −1.59463 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.5980 | 1.03906 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.8638 | −1.79115 | −0.895576 | − | 0.444908i | \(-0.853236\pi\) | ||||
−0.895576 | + | 0.444908i | \(0.853236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0819 | 0.901832 | 0.450916 | − | 0.892566i | \(-0.351097\pi\) | ||||
0.450916 | + | 0.892566i | \(0.351097\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.72764 | −0.139672 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.2627 | −1.22593 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.42402 | −0.353075 | −0.176538 | − | 0.984294i | \(-0.556490\pi\) | ||||
−0.176538 | + | 0.984294i | \(0.556490\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.01432 | −0.239051 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.7557 | 1.08410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.9699 | −1.09420 | −0.547102 | − | 0.837066i | \(-0.684269\pi\) | ||||
−0.547102 | + | 0.837066i | \(0.684269\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.67492 | 0.597492 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.9194 | −1.61879 | −0.809397 | − | 0.587262i | \(-0.800206\pi\) | ||||
−0.809397 | + | 0.587262i | \(0.800206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.40878 | −0.108368 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.94606 | 0.378235 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.2827 | −1.84618 | −0.923091 | − | 0.384582i | \(-0.874346\pi\) | ||||
−0.923091 | + | 0.384582i | \(0.874346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.70236 | −0.355465 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0555 | 0.906146 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.27827 | −0.319773 | −0.159886 | − | 0.987135i | \(-0.551113\pi\) | ||||
−0.159886 | + | 0.987135i | \(0.551113\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.5742 | 1.75226 | 0.876129 | − | 0.482076i | \(-0.160117\pi\) | ||||
0.876129 | + | 0.482076i | \(0.160117\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.5946 | 0.931019 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.409698 | −0.0301216 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.36272 | −0.245906 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.4277 | −1.63137 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.82832 | −0.566437 | −0.283219 | − | 0.959055i | \(-0.591402\pi\) | ||||
−0.283219 | + | 0.959055i | \(0.591402\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.99381 | 0.647389 | 0.323694 | − | 0.946162i | \(-0.395075\pi\) | ||||
0.323694 | + | 0.946162i | \(0.395075\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.09666 | 0.508203 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.2216 | −1.08449 | −0.542246 | − | 0.840220i | \(-0.682426\pi\) | ||||
−0.542246 | + | 0.840220i | \(0.682426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.86938 | 0.203405 | 0.101703 | − | 0.994815i | \(-0.467571\pi\) | ||||
0.101703 | + | 0.994815i | \(0.467571\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.2560 | −0.723405 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 42.2358 | 2.96437 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.0591 | −1.19146 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.97500 | −0.415291 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.62712 | 0.665922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3156 | 1.46743 | 0.733714 | − | 0.679459i | \(-0.237785\pi\) | ||||
0.733714 | + | 0.679459i | \(0.237785\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.03851 | −0.139676 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.7389 | 0.732385 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 33.5712 | 2.27896 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.77888 | 0.525648 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.10936 | −0.209158 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.14971 | 0.0769905 | 0.0384952 | − | 0.999259i | \(-0.487744\pi\) | ||||
0.0384952 | + | 0.999259i | \(0.487744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.04254 | 0.136169 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.8190 | 1.71367 | 0.856833 | − | 0.515594i | \(-0.172429\pi\) | ||||
0.856833 | + | 0.515594i | \(0.172429\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3048 | −0.879203 | −0.439601 | − | 0.898193i | \(-0.644880\pi\) | ||||
−0.439601 | + | 0.898193i | \(0.644880\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.8815 | −1.11072 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.91624 | 0.125537 | 0.0627684 | − | 0.998028i | \(-0.480007\pi\) | ||||
0.0627684 | + | 0.998028i | \(0.480007\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.2606 | −1.12596 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.580604 | 0.0377143 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.5241 | 0.874804 | 0.437402 | − | 0.899266i | \(-0.355899\pi\) | ||||
0.437402 | + | 0.899266i | \(0.355899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9682 | 0.706525 | 0.353262 | − | 0.935524i | \(-0.385072\pi\) | ||||
0.353262 | + | 0.935524i | \(0.385072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.7163 | 1.00820 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −23.6933 | −1.51371 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.90177 | 0.566406 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.30523 | 0.336205 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3993 | 0.971998 | 0.485999 | − | 0.873959i | \(-0.338456\pi\) | ||||
0.485999 | + | 0.873959i | \(0.338456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.6299 | −0.731163 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.90369 | −0.119213 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.7850 | 1.42129 | 0.710646 | − | 0.703550i | \(-0.248403\pi\) | ||||
0.710646 | + | 0.703550i | \(0.248403\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.901157 | 0.0559952 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.3457 | −1.13557 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.6623 | 1.15077 | 0.575383 | − | 0.817884i | \(-0.304853\pi\) | ||||
0.575383 | + | 0.817884i | \(0.304853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.66910 | 0.348250 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.5505 | 1.01288 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.9824 | 1.64515 | 0.822573 | − | 0.568660i | \(-0.192538\pi\) | ||||
0.822573 | + | 0.568660i | \(0.192538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.58380 | 0.217700 | 0.108850 | − | 0.994058i | \(-0.465283\pi\) | ||||
0.108850 | + | 0.994058i | \(0.465283\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.6096 | −0.944734 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.97564 | 0.239740 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.8115 | −1.31053 | −0.655263 | − | 0.755401i | \(-0.727442\pi\) | ||||
−0.655263 | + | 0.755401i | \(0.727442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.5821 | −0.873009 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3217 | 1.03333 | 0.516664 | − | 0.856188i | \(-0.327173\pi\) | ||||
0.516664 | + | 0.856188i | \(0.327173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.9307 | −0.887535 | −0.443768 | − | 0.896142i | \(-0.646358\pi\) | ||||
−0.443768 | + | 0.896142i | \(0.646358\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.45006 | 0.322834 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.5226 | 2.21489 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1659 | −0.950936 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.936402 | −0.0548929 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.36735 | 0.196723 | 0.0983613 | − | 0.995151i | \(-0.468640\pi\) | ||||
0.0983613 | + | 0.995151i | \(0.468640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.6730 | −1.32007 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9616 | 1.10026 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.7536 | −0.621898 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.6209 | −1.36148 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.5556 | 0.778751 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.6869 | −1.35631 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7459 | −0.784518 | −0.392259 | − | 0.919855i | \(-0.628306\pi\) | ||||
−0.392259 | + | 0.919855i | \(0.628306\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.64169 | 0.150281 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.9073 | 1.58248 | 0.791238 | − | 0.611508i | \(-0.209437\pi\) | ||||
0.791238 | + | 0.611508i | \(0.209437\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.0834 | −1.58737 | −0.793684 | − | 0.608330i | \(-0.791840\pi\) | ||||
−0.793684 | + | 0.608330i | \(0.791840\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.3117 | 0.919059 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.5432 | 1.60315 | 0.801573 | − | 0.597897i | \(-0.203997\pi\) | ||||
0.801573 | + | 0.597897i | \(0.203997\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.7085 | −1.99929 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.33954 | 0.521282 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.38791 | −0.132867 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.67610 | 0.203913 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.13921 | 0.173599 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 37.9658 | 2.09312 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.3785 | 1.50486 | 0.752428 | − | 0.658674i | \(-0.228882\pi\) | ||||
0.752428 | + | 0.658674i | \(0.228882\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.391430 | −0.0214502 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.2887 | 1.05386 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.33938 | −0.290854 | −0.145427 | − | 0.989369i | \(-0.546456\pi\) | ||||
−0.145427 | + | 0.989369i | \(0.546456\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.23457 | 0.121365 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.3830 | −1.53702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 21.6295 | 1.16788 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.58385 | −0.354462 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.7963 | 1.54587 | 0.772933 | − | 0.634488i | \(-0.218789\pi\) | ||||
0.772933 | + | 0.634488i | \(0.218789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −36.3942 | −1.94814 | −0.974069 | − | 0.226253i | \(-0.927352\pi\) | ||||
−0.974069 | + | 0.226253i | \(0.927352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.5330 | 0.935840 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.3860 | −1.56406 | −0.782029 | − | 0.623242i | \(-0.785815\pi\) | ||||
−0.782029 | + | 0.623242i | \(0.785815\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.83386 | 0.203480 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.18728 | 0.221615 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.20141 | 0.0634081 | 0.0317041 | − | 0.999497i | \(-0.489907\pi\) | ||||
0.0317041 | + | 0.999497i | \(0.489907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1637 | −0.640192 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.69210 | 0.141299 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6299 | −0.765764 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.66844 | 0.243691 | 0.121845 | − | 0.992549i | \(-0.461119\pi\) | ||||
0.121845 | + | 0.992549i | \(0.461119\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.2985 | −0.848465 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.4696 | −0.647387 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.1376 | 1.40513 | 0.702567 | − | 0.711618i | \(-0.252037\pi\) | ||||
0.702567 | + | 0.711618i | \(0.252037\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.6729 | 0.654424 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.0181 | −1.70052 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.49478 | −0.333614 | −0.166807 | − | 0.985990i | \(-0.553346\pi\) | ||||
−0.166807 | + | 0.985990i | \(0.553346\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.98453 | −0.306597 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.7309 | −1.00820 | −0.504101 | − | 0.863645i | \(-0.668176\pi\) | ||||
−0.504101 | + | 0.863645i | \(0.668176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.7494 | 1.61810 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.2601 | 0.521548 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.1184 | −1.27356 | −0.636778 | − | 0.771048i | \(-0.719733\pi\) | ||||
−0.636778 | + | 0.771048i | \(0.719733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.88467 | 0.145884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.17736 | 0.160277 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.09195 | −0.0549422 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7938 | 0.893044 | 0.446522 | − | 0.894773i | \(-0.352662\pi\) | ||||
0.446522 | + | 0.894773i | \(0.352662\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.9878 | −0.600139 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.8512 | 1.19107 | 0.595535 | − | 0.803329i | \(-0.296940\pi\) | ||||
0.595535 | + | 0.803329i | \(0.296940\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.2445 | −1.30733 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.501908 | −0.0249400 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.761888 | −0.0377654 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6359 | 1.21817 | 0.609083 | − | 0.793106i | \(-0.291537\pi\) | ||||
0.609083 | + | 0.793106i | \(0.291537\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.9955 | −1.13428 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 49.8708 | 2.45398 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.97766 | −0.489784 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.0911 | −0.739016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.9579 | −0.926152 | −0.463076 | − | 0.886319i | \(-0.653254\pi\) | ||||
−0.463076 | + | 0.886319i | \(0.653254\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.9110 | −1.55525 | −0.777624 | − | 0.628729i | \(-0.783575\pi\) | ||||
−0.777624 | + | 0.628729i | \(0.783575\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.4910 | −0.801818 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.986116 | −0.0478337 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.1009 | 2.52134 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.1972 | 0.637166 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.62592 | −0.463664 | −0.231832 | − | 0.972756i | \(-0.574472\pi\) | ||||
−0.231832 | + | 0.972756i | \(0.574472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0909 | 0.773280 | 0.386640 | − | 0.922231i | \(-0.373636\pi\) | ||||
0.386640 | + | 0.922231i | \(0.373636\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −20.2151 | −0.969241 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.25852 | −0.395058 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7116 | 0.940784 | 0.470392 | − | 0.882458i | \(-0.344113\pi\) | ||||
0.470392 | + | 0.882458i | \(0.344113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.6368 | −1.07794 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.60983 | 0.171508 | 0.0857541 | − | 0.996316i | \(-0.472670\pi\) | ||||
0.0857541 | + | 0.996316i | \(0.472670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.1269 | −1.47556 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.0175 | −1.08869 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.6044 | 1.20835 | 0.604174 | − | 0.796853i | \(-0.293503\pi\) | ||||
0.604174 | + | 0.796853i | \(0.293503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.7237 | −1.49381 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.6667 | 0.548148 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 29.3572 | 1.37629 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.4625 | −1.23786 | −0.618932 | − | 0.785444i | \(-0.712435\pi\) | ||||
−0.618932 | + | 0.785444i | \(0.712435\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.70323 | −0.219528 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.9008 | 0.926871 | 0.463436 | − | 0.886131i | \(-0.346617\pi\) | ||||
0.463436 | + | 0.886131i | \(0.346617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.11723 | −0.284292 | −0.142146 | − | 0.989846i | \(-0.545400\pi\) | ||||
−0.142146 | + | 0.989846i | \(0.545400\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.0680 | −0.745137 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.1853 | 1.53563 | 0.767817 | − | 0.640669i | \(-0.221343\pi\) | ||||
0.767817 | + | 0.640669i | \(0.221343\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.4268 | −1.95909 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.65747 | −0.214605 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.9704 | 0.918239 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.82315 | 0.129535 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.41633 | 0.247997 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.5769 | −1.76262 | −0.881311 | − | 0.472536i | \(-0.843339\pi\) | ||||
−0.881311 | + | 0.472536i | \(0.843339\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.704484 | −0.0321217 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.4816 | 0.658935 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.76111 | 0.0799680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.85394 | −0.446525 | −0.223262 | − | 0.974758i | \(-0.571671\pi\) | ||||
−0.223262 | + | 0.974758i | \(0.571671\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.7070 | −0.665074 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.75897 | 0.214769 | 0.107385 | − | 0.994218i | \(-0.465752\pi\) | ||||
0.107385 | + | 0.994218i | \(0.465752\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.85713 | 0.398905 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.7908 | −0.619850 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.43283 | −0.378264 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.60733 | −0.295785 | −0.147892 | − | 0.989003i | \(-0.547249\pi\) | ||||
−0.147892 | + | 0.989003i | \(0.547249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22.0233 | −0.983928 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.4944 | −1.13448 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.48312 | −0.0658676 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.5716 | 0.956143 | 0.478071 | − | 0.878321i | \(-0.341336\pi\) | ||||
0.478071 | + | 0.878321i | \(0.341336\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.1794 | 1.42353 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.4649 | 0.594489 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.96829 | −0.218929 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.0984 | −1.41168 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.5641 | −1.12214 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.99183 | −0.393939 | −0.196970 | − | 0.980410i | \(-0.563110\pi\) | ||||
−0.196970 | + | 0.980410i | \(0.563110\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3341 | −0.714240 | −0.357120 | − | 0.934059i | \(-0.616241\pi\) | ||||
−0.357120 | + | 0.934059i | \(0.616241\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.95049 | −0.216057 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.04010 | 0.306672 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0235 | −0.566237 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.6621 | −0.940054 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.3335 | −1.27058 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.5651 | −0.759404 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.50402 | −0.194363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −44.0608 | −1.89783 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.2963 | 0.872607 | 0.436304 | − | 0.899800i | \(-0.356287\pi\) | ||||
0.436304 | + | 0.899800i | \(0.356287\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.8182 | 1.06505 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.90397 | −0.252898 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.5263 | 1.47624 | 0.738118 | − | 0.674671i | \(-0.235715\pi\) | ||||
0.738118 | + | 0.674671i | \(0.235715\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.6308 | −0.965857 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.3571 | −1.08025 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.40182 | 0.102136 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.431317 | −0.0183084 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.41718 | −0.356647 | −0.178324 | − | 0.983972i | \(-0.557067\pi\) | ||||
−0.178324 | + | 0.983972i | \(0.557067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.4657 | 0.781017 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.54016 | −0.149466 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.4921 | −1.36938 | −0.684690 | − | 0.728834i | \(-0.740062\pi\) | ||||
−0.684690 | + | 0.728834i | \(0.740062\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.20261 | −0.176805 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.10398 | 0.0463627 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.5526 | −0.484310 | −0.242155 | − | 0.970238i | \(-0.577854\pi\) | ||||
−0.242155 | + | 0.970238i | \(0.577854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.36859 | 0.0991225 | 0.0495612 | − | 0.998771i | \(-0.484218\pi\) | ||||
0.0495612 | + | 0.998771i | \(0.484218\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.24140 | −0.344290 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.41046 | −0.142226 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.77203 | 0.157032 | 0.0785158 | − | 0.996913i | \(-0.474982\pi\) | ||||
0.0785158 | + | 0.996913i | \(0.474982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.46839 | 0.393493 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.9465 | 0.910494 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5425 | 0.436624 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.7517 | −0.527219 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −40.9189 | −1.68891 | −0.844453 | − | 0.535630i | \(-0.820074\pi\) | ||||
−0.844453 | + | 0.535630i | \(0.820074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1551 | −0.830477 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.0248 | −0.659171 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.874959 | 0.0359303 | 0.0179651 | − | 0.999839i | \(-0.494281\pi\) | ||||
0.0179651 | + | 0.999839i | \(0.494281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.87511 | −0.322848 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.02080 | 0.123633 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.7297 | 1.41902 | 0.709509 | − | 0.704696i | \(-0.248917\pi\) | ||||
0.709509 | + | 0.704696i | \(0.248917\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.2268 | 0.865860 | 0.432930 | − | 0.901428i | \(-0.357480\pi\) | ||||
0.432930 | + | 0.901428i | \(0.357480\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.4287 | 0.750475 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.06309 | −0.205844 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.5508 | 1.03707 | 0.518537 | − | 0.855055i | \(-0.326477\pi\) | ||||
0.518537 | + | 0.855055i | \(0.326477\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 44.4645 | 1.80179 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.6799 | −1.20072 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.6830 | 1.11811 | 0.559053 | − | 0.829132i | \(-0.311165\pi\) | ||||
0.559053 | + | 0.829132i | \(0.311165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.9593 | −0.724188 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.32890 | 0.134016 | 0.0670082 | − | 0.997752i | \(-0.478655\pi\) | ||||
0.0670082 | + | 0.997752i | \(0.478655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3192 | 0.454956 | 0.227478 | − | 0.973783i | \(-0.426952\pi\) | ||||
0.227478 | + | 0.973783i | \(0.426952\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.2660 | −0.652732 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 68.4657 | 2.74302 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.4354 | −0.737416 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.1351 | 0.404758 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.188979 | 0.00753507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7231 | −0.426880 | −0.213440 | − | 0.976956i | \(-0.568467\pi\) | ||||
−0.213440 | + | 0.976956i | \(0.568467\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.4404 | 0.891925 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.2552 | 0.446651 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −40.7411 | −1.61422 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.66292 | 0.144903 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.9439 | −0.827236 | −0.413618 | − | 0.910451i | \(-0.635735\pi\) | ||||
−0.413618 | + | 0.910451i | \(0.635735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7360 | 0.936058 | 0.468029 | − | 0.883713i | \(-0.344964\pi\) | ||||
0.468029 | + | 0.883713i | \(0.344964\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.3055 | 0.445155 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.4441 | −0.921682 | −0.460841 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460841 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42.1635 | −1.65506 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 35.3427 | 1.38519 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.5562 | 1.66535 | 0.832676 | − | 0.553760i | \(-0.186808\pi\) | ||||
0.832676 | + | 0.553760i | \(0.186808\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.97573 | −0.233491 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.9776 | −0.545318 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.8733 | 0.618335 | 0.309168 | − | 0.951008i | \(-0.399950\pi\) | ||||
0.309168 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.9621 | −1.70993 | −0.854963 | − | 0.518689i | \(-0.826420\pi\) | ||||
−0.854963 | + | 0.518689i | \(0.826420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.27343 | −0.127129 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.5456 | 0.874283 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.6321 | 1.18608 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.21038 | 0.0467960 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.0490 | −1.70049 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.1398 | −1.16181 | −0.580903 | − | 0.813973i | \(-0.697300\pi\) | ||||
−0.580903 | + | 0.813973i | \(0.697300\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56049 | 0.214023 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.0426 | −0.731867 | −0.365933 | − | 0.930641i | \(-0.619250\pi\) | ||||
−0.365933 | + | 0.930641i | \(0.619250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.87368 | −0.148658 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.1814 | 1.04159 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.289286 | −0.0110692 | −0.00553462 | − | 0.999985i | \(-0.501762\pi\) | ||||
−0.00553462 | + | 0.999985i | \(0.501762\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.2481 | 1.65243 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0068 | −0.534393 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.74814 | 0.371375 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.9662 | −1.59647 | −0.798235 | − | 0.602346i | \(-0.794233\pi\) | ||||
−0.798235 | + | 0.602346i | \(0.794233\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30.3337 | 1.15228 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.3822 | 1.07660 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.86874 | 0.298050 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.01735 | 0.0763033 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.99274 | −0.188573 | −0.0942866 | − | 0.995545i | \(-0.530057\pi\) | ||||
−0.0942866 | + | 0.995545i | \(0.530057\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.541027 | −0.0204052 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.1714 | −0.684374 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 56.0765 | 2.10897 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.74294 | −0.178125 | −0.0890625 | − | 0.996026i | \(-0.528387\pi\) | ||||
−0.0890625 | + | 0.996026i | \(0.528387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04327 | −0.0391255 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.3480 | 0.911840 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.8202 | −0.928224 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.2378 | 0.531720 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2036 | −0.604294 | −0.302147 | − | 0.953261i | \(-0.597703\pi\) | ||||
−0.302147 | + | 0.953261i | \(0.597703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.9281 | 0.406983 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.5470 | 0.429437 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.4715 | −0.388902 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.4020 | −1.23881 | −0.619405 | − | 0.785072i | \(-0.712626\pi\) | ||||
−0.619405 | + | 0.785072i | \(0.712626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7851 | 0.584634 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.95345 | −0.183210 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.6148 | 1.24159 | 0.620795 | − | 0.783973i | \(-0.286810\pi\) | ||||
0.620795 | + | 0.783973i | \(0.286810\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −24.9435 | −0.920055 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.8700 | 1.32129 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5752 | 0.756872 | 0.378436 | − | 0.925627i | \(-0.376462\pi\) | ||||
0.378436 | + | 0.925627i | \(0.376462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.37150 | 0.344271 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.54970 | 0.0935396 | 0.0467698 | − | 0.998906i | \(-0.485107\pi\) | ||||
0.0467698 | + | 0.998906i | \(0.485107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.2895 | 1.58601 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.53277 | −0.348786 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.6355 | 1.41171 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.3128 | −1.76296 | −0.881480 | − | 0.472221i | \(-0.843452\pi\) | ||||
−0.881480 | + | 0.472221i | \(0.843452\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.2119 | 0.590796 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.9417 | −0.798542 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1383 | 0.550209 | 0.275105 | − | 0.961414i | \(-0.411287\pi\) | ||||
0.275105 | + | 0.961414i | \(0.411287\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.2435 | −0.444412 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.8681 | −1.01022 | −0.505110 | − | 0.863055i | \(-0.668548\pi\) | ||||
−0.505110 | + | 0.863055i | \(0.668548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.9862 | 0.470131 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.42067 | 0.123674 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −38.9867 | −1.40773 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.9273 | −0.394049 | −0.197024 | − | 0.980399i | \(-0.563128\pi\) | ||||
−0.197024 | + | 0.980399i | \(0.563128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.9874 | 0.863884 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.3445 | −1.77480 | −0.887399 | − | 0.461001i | \(-0.847490\pi\) | ||||
−0.887399 | + | 0.461001i | \(0.847490\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.32330 | −0.298982 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.948709 | 0.0340348 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.5274 | −0.807128 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.12958 | 0.255116 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −49.9433 | −1.78483 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.75940 | 0.312636 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.6570 | −0.629404 | −0.314702 | − | 0.949191i | \(-0.601905\pi\) | ||||
−0.314702 | + | 0.949191i | \(0.601905\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.6471 | 0.699454 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.24390 | 0.328675 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.7301 | −1.44637 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.96825 | 0.211672 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.0277 | 0.744838 | 0.372419 | − | 0.928065i | \(-0.378528\pi\) | ||||
0.372419 | + | 0.928065i | \(0.378528\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.96168 | 0.281664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.7390 | −1.05078 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.2063 | −0.960088 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −27.2358 | −0.959937 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.4062 | 0.999945 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.8072 | −1.57534 | −0.787669 | − | 0.616098i | \(-0.788712\pi\) | ||||
−0.787669 | + | 0.616098i | \(0.788712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.30649 | 0.256566 | 0.128283 | − | 0.991738i | \(-0.459053\pi\) | ||||
0.128283 | + | 0.991738i | \(0.459053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.77291 | 0.132322 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.6598 | 0.968880 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.1812 | 0.496138 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.0483 | 0.980086 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6515 | 0.685841 | 0.342921 | − | 0.939364i | \(-0.388584\pi\) | ||||
0.342921 | + | 0.939364i | \(0.388584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.88253 | 0.135336 | 0.0676682 | − | 0.997708i | \(-0.478444\pi\) | ||||
0.0676682 | + | 0.997708i | \(0.478444\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.18542 | 0.145718 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.07211 | 0.0720543 | 0.0360271 | − | 0.999351i | \(-0.488530\pi\) | ||||
0.0360271 | + | 0.999351i | \(0.488530\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.54915 | 0.262193 | 0.131096 | − | 0.991370i | \(-0.458150\pi\) | ||||
0.131096 | + | 0.991370i | \(0.458150\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.9624 | −0.796558 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.9288 | 0.378661 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.4197 | 1.43339 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −39.6976 | −1.37215 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −57.6888 | −1.99164 | −0.995820 | − | 0.0913423i | \(-0.970884\pi\) | ||||
−0.995820 | + | 0.0913423i | \(0.970884\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 65.0533 | 2.24322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.2358 | 0.628074 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.78933 | 0.0959560 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.1366 | 0.382658 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.7185 | −0.539458 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.653577 | 0.0224043 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.8703 | −1.67329 | −0.836644 | − | 0.547748i | \(-0.815485\pi\) | ||||
−0.836644 | + | 0.547748i | \(0.815485\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.79302 | −0.334914 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0704 | −0.890548 | −0.445274 | − | 0.895394i | \(-0.646894\pi\) | ||||
−0.445274 | + | 0.895394i | \(0.646894\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.7263 | 0.809530 | 0.404765 | − | 0.914421i | \(-0.367353\pi\) | ||||
0.404765 | + | 0.914421i | \(0.367353\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.5026 | 1.34625 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.9724 | −0.645828 | −0.322914 | − | 0.946428i | \(-0.604662\pi\) | ||||
−0.322914 | + | 0.946428i | \(0.604662\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.0789 | 1.63473 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0190 | −0.577994 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.03063 | −0.0688846 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.1674 | 1.12383 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.68259 | 0.0569470 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 52.4247 | 1.77228 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4497 | 0.791840 | 0.395920 | − | 0.918285i | \(-0.370426\pi\) | ||||
0.395920 | + | 0.918285i | \(0.370426\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.54504 | 0.119571 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.66510 | −0.157171 | −0.0785856 | − | 0.996907i | \(-0.525040\pi\) | ||||
−0.0785856 | + | 0.996907i | \(0.525040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.4860 | −0.386535 | −0.193268 | − | 0.981146i | \(-0.561909\pi\) | ||||
−0.193268 | + | 0.981146i | \(0.561909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.8694 | −0.802362 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.1480 | −0.508621 | −0.254311 | − | 0.967123i | \(-0.581849\pi\) | ||||
−0.254311 | + | 0.967123i | \(0.581849\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.7566 | −0.830311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.933364 | −0.0312689 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.7935 | −0.762754 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.47081 | 0.283148 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.3211 | −0.377999 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 74.7584 | 2.49333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.61495 | −0.0871166 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.8673 | −0.827531 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46.6761 | −1.55157 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.0715 | 1.59619 | 0.798094 | − | 0.602533i | \(-0.205842\pi\) | ||||
0.798094 | + | 0.602533i | \(0.205842\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.3576 | −0.807891 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.6332 | 1.44563 | 0.722817 | − | 0.691040i | \(-0.242847\pi\) | ||||
0.722817 | + | 0.691040i | \(0.242847\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.5548 | −0.614074 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.9368 | −0.824386 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1440 | 0.434053 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.3325 | 0.802654 | 0.401327 | − | 0.915935i | \(-0.368549\pi\) | ||||
0.401327 | + | 0.915935i | \(0.368549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.4712 | −0.476842 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.59241 | 0.216992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.223424 | −0.00734612 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.74676 | −0.155904 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.3363 | 1.68429 | 0.842145 | − | 0.539252i | \(-0.181293\pi\) | ||||
0.842145 | + | 0.539252i | \(0.181293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.2881 | −1.02543 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.3799 | 0.961854 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.65805 | 0.217742 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.9591 | −0.913383 | −0.456692 | − | 0.889625i | \(-0.650966\pi\) | ||||
−0.456692 | + | 0.889625i | \(0.650966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.5653 | −0.964828 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.64175 | −0.216515 | −0.108257 | − | 0.994123i | \(-0.534527\pi\) | ||||
−0.108257 | + | 0.994123i | \(0.534527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.2138 | 0.886204 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 44.4060 | 1.44453 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.9576 | 1.16846 | 0.584232 | − | 0.811587i | \(-0.301396\pi\) | ||||
0.584232 | + | 0.811587i | \(0.301396\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.1564 | −0.816612 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.0494 | 0.974417 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.13451 | −0.0691436 | −0.0345718 | − | 0.999402i | \(-0.511007\pi\) | ||||
−0.0345718 | + | 0.999402i | \(0.511007\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.4998 | 0.501561 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −37.5927 | −1.21520 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −95.1270 | −3.07181 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4219 | 0.916835 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.7819 | −0.540788 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8074 | −0.573241 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.2062 | 0.714104 | 0.357052 | − | 0.934084i | \(-0.383782\pi\) | ||||
0.357052 | + | 0.934084i | \(0.383782\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.51391 | −0.0807586 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.0609 | 0.483328 | 0.241664 | − | 0.970360i | \(-0.422307\pi\) | ||||
0.241664 | + | 0.970360i | \(0.422307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62.4285 | −2.00137 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.87008 | 0.123942 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.2226 | 0.614984 | 0.307492 | − | 0.951551i | \(-0.400510\pi\) | ||||
0.307492 | + | 0.951551i | \(0.400510\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.8847 | −1.85000 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.64073 | −0.180095 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.4859 | 0.653400 | 0.326700 | − | 0.945128i | \(-0.394063\pi\) | ||||
0.326700 | + | 0.945128i | \(0.394063\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.1381 | 0.960281 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.9691 | 1.27223 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.1314 | −0.544746 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0476 | 1.43099 | 0.715493 | − | 0.698620i | \(-0.246202\pi\) | ||||
0.715493 | + | 0.698620i | \(0.246202\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.8232 | 0.914676 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.68128 | −0.180109 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.2108 | −0.735094 | −0.367547 | − | 0.930005i | \(-0.619802\pi\) | ||||
−0.367547 | + | 0.930005i | \(0.619802\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.06561 | −0.0337143 |
(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 | 4024.2.a.g.1.21 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.x.1.13 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.g.1.21 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.x.1.13 | 33 | 4.3 | odd | 2 |