Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6024,2,Mod(1,6024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6024 = 2^{3} \cdot 3 \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6024.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: | \(48.1018821776\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - x^{17} - 57 x^{16} + 51 x^{15} + 1328 x^{14} - 1116 x^{13} - 16275 x^{12} + 13699 x^{11} + \cdots + 44032 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.35939\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6024.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.35939 | −0.607936 | −0.303968 | − | 0.952682i | \(-0.598312\pi\) | ||||
−0.303968 | + | 0.952682i | \(0.598312\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0125376 | −0.00473875 | −0.00236938 | − | 0.999997i | \(-0.500754\pi\) | ||||
−0.00236938 | + | 0.999997i | \(0.500754\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.88392 | −0.869534 | −0.434767 | − | 0.900543i | \(-0.643169\pi\) | ||||
−0.434767 | + | 0.900543i | \(0.643169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.96894 | 0.823435 | 0.411717 | − | 0.911312i | \(-0.364929\pi\) | ||||
0.411717 | + | 0.911312i | \(0.364929\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.35939 | −0.350992 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.40219 | −1.06769 | −0.533844 | − | 0.845583i | \(-0.679253\pi\) | ||||
−0.533844 | + | 0.845583i | \(0.679253\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.61716 | −1.74750 | −0.873748 | − | 0.486378i | \(-0.838318\pi\) | ||||
−0.873748 | + | 0.486378i | \(0.838318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0125376 | −0.00273592 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.16709 | 0.868899 | 0.434449 | − | 0.900696i | \(-0.356943\pi\) | ||||
0.434449 | + | 0.900696i | \(0.356943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.15207 | −0.630414 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.4220 | 1.93532 | 0.967658 | − | 0.252266i | \(-0.0811757\pi\) | ||||
0.967658 | + | 0.252266i | \(0.0811757\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.70625 | 0.665663 | 0.332831 | − | 0.942986i | \(-0.391996\pi\) | ||||
0.332831 | + | 0.942986i | \(0.391996\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.88392 | −0.502026 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0170434 | 0.00288086 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.43218 | −0.399848 | −0.199924 | − | 0.979811i | \(-0.564070\pi\) | ||||
−0.199924 | + | 0.979811i | \(0.564070\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.96894 | 0.475410 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.30095 | −0.515521 | −0.257761 | − | 0.966209i | \(-0.582985\pi\) | ||||
−0.257761 | + | 0.966209i | \(0.582985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.1704 | 1.85597 | 0.927984 | − | 0.372621i | \(-0.121541\pi\) | ||||
0.927984 | + | 0.372621i | \(0.121541\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.35939 | −0.202645 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.83060 | 0.558751 | 0.279375 | − | 0.960182i | \(-0.409873\pi\) | ||||
0.279375 | + | 0.960182i | \(0.409873\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99984 | −0.999978 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.40219 | −0.616430 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.362911 | 0.0498496 | 0.0249248 | − | 0.999689i | \(-0.492065\pi\) | ||||
0.0249248 | + | 0.999689i | \(0.492065\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.92036 | 0.528621 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.61716 | −1.00892 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.961715 | 0.125205 | 0.0626023 | − | 0.998039i | \(-0.480060\pi\) | ||||
0.0626023 | + | 0.998039i | \(0.480060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.32742 | −0.682106 | −0.341053 | − | 0.940044i | \(-0.610784\pi\) | ||||
−0.341053 | + | 0.940044i | \(0.610784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0125376 | −0.00157958 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.03593 | −0.500595 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.82978 | 0.467882 | 0.233941 | − | 0.972251i | \(-0.424838\pi\) | ||||
0.233941 | + | 0.972251i | \(0.424838\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.16709 | 0.501659 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.91457 | −0.701930 | −0.350965 | − | 0.936389i | \(-0.614146\pi\) | ||||
−0.350965 | + | 0.936389i | \(0.614146\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5588 | 1.93806 | 0.969030 | − | 0.246944i | \(-0.0794262\pi\) | ||||
0.969030 | + | 0.246944i | \(0.0794262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.15207 | −0.363970 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0361573 | 0.00412051 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4693 | 1.17788 | 0.588941 | − | 0.808176i | \(-0.299545\pi\) | ||||
0.588941 | + | 0.808176i | \(0.299545\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.59889 | 0.834086 | 0.417043 | − | 0.908887i | \(-0.363066\pi\) | ||||
0.417043 | + | 0.908887i | \(0.363066\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.98427 | 0.649085 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.4220 | 1.11736 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0833 | 1.17482 | 0.587412 | − | 0.809288i | \(-0.300147\pi\) | ||||
0.587412 | + | 0.809288i | \(0.300147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0372232 | −0.00390205 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.70625 | 0.384321 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.3547 | 1.06237 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00669 | 0.812956 | 0.406478 | − | 0.913661i | \(-0.366757\pi\) | ||||
0.406478 | + | 0.913661i | \(0.366757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.88392 | −0.289845 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.0721 | −1.49973 | −0.749864 | − | 0.661592i | \(-0.769881\pi\) | ||||
−0.749864 | + | 0.661592i | \(0.769881\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.88744 | 0.678640 | 0.339320 | − | 0.940671i | \(-0.389803\pi\) | ||||
0.339320 | + | 0.940671i | \(0.389803\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0170434 | 0.00166326 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.71794 | −0.456100 | −0.228050 | − | 0.973649i | \(-0.573235\pi\) | ||||
−0.228050 | + | 0.973649i | \(0.573235\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.1881 | 1.83789 | 0.918945 | − | 0.394385i | \(-0.129042\pi\) | ||||
0.918945 | + | 0.394385i | \(0.129042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.43218 | −0.230853 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.06327 | 0.570384 | 0.285192 | − | 0.958470i | \(-0.407943\pi\) | ||||
0.285192 | + | 0.958470i | \(0.407943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.66468 | −0.528235 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.96894 | 0.274478 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0551927 | 0.00505951 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.68301 | −0.243910 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.30095 | −0.297636 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0818 | 0.991187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.4833 | 1.01898 | 0.509491 | − | 0.860476i | \(-0.329834\pi\) | ||||
0.509491 | + | 0.860476i | \(0.329834\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.1704 | 1.07154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.8087 | −1.64332 | −0.821662 | − | 0.569976i | \(-0.806953\pi\) | ||||
−0.821662 | + | 0.569976i | \(0.806953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0955006 | 0.00828095 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.35939 | −0.116997 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.98392 | 0.254933 | 0.127467 | − | 0.991843i | \(-0.459315\pi\) | ||||
0.127467 | + | 0.991843i | \(0.459315\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7121 | 1.07823 | 0.539113 | − | 0.842233i | \(-0.318760\pi\) | ||||
0.539113 | + | 0.842233i | \(0.318760\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.83060 | 0.322595 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.56217 | −0.716005 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.1675 | −1.17655 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.99984 | −0.577337 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.8794 | −1.46474 | −0.732370 | − | 0.680907i | \(-0.761586\pi\) | ||||
−0.732370 | + | 0.680907i | \(0.761586\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.83186 | −0.311832 | −0.155916 | − | 0.987770i | \(-0.549833\pi\) | ||||
−0.155916 | + | 0.987770i | \(0.549833\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.40219 | −0.355896 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.03823 | −0.404680 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.3528 | 0.985859 | 0.492930 | − | 0.870069i | \(-0.335926\pi\) | ||||
0.492930 | + | 0.870069i | \(0.335926\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.362911 | 0.0287807 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0522452 | −0.00411750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2932 | 0.962877 | 0.481439 | − | 0.876480i | \(-0.340114\pi\) | ||||
0.481439 | + | 0.876480i | \(0.340114\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.92036 | 0.305199 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.5511 | −1.04862 | −0.524309 | − | 0.851528i | \(-0.675676\pi\) | ||||
−0.524309 | + | 0.851528i | \(0.675676\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.18542 | −0.321955 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.61716 | −0.582499 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.81885 | 0.442399 | 0.221199 | − | 0.975229i | \(-0.429003\pi\) | ||||
0.221199 | + | 0.975229i | \(0.429003\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0395193 | 0.00298738 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.961715 | 0.0722869 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.89163 | −0.739335 | −0.369668 | − | 0.929164i | \(-0.620528\pi\) | ||||
−0.369668 | + | 0.929164i | \(0.620528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.14226 | 0.382222 | 0.191111 | − | 0.981568i | \(-0.438791\pi\) | ||||
0.191111 | + | 0.981568i | \(0.438791\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.32742 | −0.393814 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.30627 | 0.243082 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.6956 | 0.928391 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0125376 | −0.000911973 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.6072 | −1.12930 | −0.564648 | − | 0.825332i | \(-0.690988\pi\) | ||||
−0.564648 | + | 0.825332i | \(0.690988\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.6732 | −1.91998 | −0.959989 | − | 0.280036i | \(-0.909653\pi\) | ||||
−0.959989 | + | 0.280036i | \(0.909653\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.03593 | −0.289019 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4324 | 1.59824 | 0.799122 | − | 0.601169i | \(-0.205298\pi\) | ||||
0.799122 | + | 0.601169i | \(0.205298\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.86788 | 0.486851 | 0.243425 | − | 0.969920i | \(-0.421729\pi\) | ||||
0.243425 | + | 0.969920i | \(0.421729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.82978 | 0.270132 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.130666 | −0.00917098 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.48726 | 0.313404 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.16709 | 0.289633 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.9673 | 1.51951 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8361 | 1.15904 | 0.579521 | − | 0.814957i | \(-0.303240\pi\) | ||||
0.579521 | + | 0.814957i | \(0.303240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.91457 | −0.405259 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.5443 | −1.12831 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0464674 | −0.00315441 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.5588 | 1.11894 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.0698 | −0.879171 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.0527 | 1.87855 | 0.939275 | − | 0.343167i | \(-0.111500\pi\) | ||||
0.939275 | + | 0.343167i | \(0.111500\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.15207 | −0.210138 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.8764 | 1.71748 | 0.858740 | − | 0.512412i | \(-0.171248\pi\) | ||||
0.858740 | + | 0.512412i | \(0.171248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.61570 | −0.569342 | −0.284671 | − | 0.958625i | \(-0.591884\pi\) | ||||
−0.284671 | + | 0.958625i | \(0.591884\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0361573 | 0.00237898 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.6491 | −0.894182 | −0.447091 | − | 0.894488i | \(-0.647540\pi\) | ||||
−0.447091 | + | 0.894488i | \(0.647540\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.20726 | −0.339684 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.4693 | 0.680051 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.5074 | 0.873722 | 0.436861 | − | 0.899529i | \(-0.356090\pi\) | ||||
0.436861 | + | 0.899529i | \(0.356090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7997 | 0.953334 | 0.476667 | − | 0.879084i | \(-0.341845\pi\) | ||||
0.476667 | + | 0.879084i | \(0.341845\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.51548 | 0.607922 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.6149 | −1.43895 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.59889 | 0.481560 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0176 | −0.755537 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.98427 | 0.374750 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.09480 | −0.0682919 | −0.0341460 | − | 0.999417i | \(-0.510871\pi\) | ||||
−0.0341460 | + | 0.999417i | \(0.510871\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0304936 | 0.00189478 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.4220 | 0.645105 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.1165 | −0.808797 | −0.404398 | − | 0.914583i | \(-0.632519\pi\) | ||||
−0.404398 | + | 0.914583i | \(0.632519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.493336 | −0.0303054 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.0833 | 0.678285 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.49924 | 0.396266 | 0.198133 | − | 0.980175i | \(-0.436512\pi\) | ||||
0.198133 | + | 0.980175i | \(0.436512\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.97414 | 0.362903 | 0.181452 | − | 0.983400i | \(-0.441920\pi\) | ||||
0.181452 | + | 0.983400i | \(0.441920\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0372232 | −0.00225285 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.09032 | 0.548167 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.33390 | 0.320483 | 0.160241 | − | 0.987078i | \(-0.448773\pi\) | ||||
0.160241 | + | 0.987078i | \(0.448773\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.70625 | 0.221888 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.50264 | −0.0896399 | −0.0448200 | − | 0.998995i | \(-0.514271\pi\) | ||||
−0.0448200 | + | 0.998995i | \(0.514271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.02928 | −0.0611844 | −0.0305922 | − | 0.999532i | \(-0.509739\pi\) | ||||
−0.0305922 | + | 0.999532i | \(0.509739\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.3547 | 0.613357 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0413858 | 0.00244293 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.37927 | 0.139957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.00669 | 0.469360 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.3215 | −1.47930 | −0.739649 | − | 0.672993i | \(-0.765008\pi\) | ||||
−0.739649 | + | 0.672993i | \(0.765008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.30734 | −0.0761164 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.88392 | −0.167342 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3718 | 0.715481 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.152587 | −0.00879497 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.0721 | −0.865868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.24202 | 0.414677 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2934 | 0.815765 | 0.407883 | − | 0.913034i | \(-0.366267\pi\) | ||||
0.407883 | + | 0.913034i | \(0.366267\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.88744 | 0.391813 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1451 | 0.631982 | 0.315991 | − | 0.948762i | \(-0.397663\pi\) | ||||
0.315991 | + | 0.948762i | \(0.397663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5555 | −0.596630 | −0.298315 | − | 0.954467i | \(-0.596425\pi\) | ||||
−0.298315 | + | 0.954467i | \(0.596425\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0170434 | 0.000960285 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.73648 | 0.378358 | 0.189179 | − | 0.981943i | \(-0.439417\pi\) | ||||
0.189179 | + | 0.981943i | \(0.439417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.0562 | −1.68282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.71794 | −0.263330 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.5322 | 1.86578 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.35830 | −0.519105 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.1881 | 1.06111 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0480264 | −0.00264778 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.5523 | 1.89917 | 0.949583 | − | 0.313515i | \(-0.101507\pi\) | ||||
0.949583 | + | 0.313515i | \(0.101507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.43218 | −0.133283 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.20615 | −0.284442 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7183 | −0.747286 | −0.373643 | − | 0.927573i | \(-0.621891\pi\) | ||||
−0.373643 | + | 0.927573i | \(0.621891\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.06327 | 0.329312 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.6885 | −0.578817 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.175524 | 0.00947740 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.66468 | −0.304976 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.7917 | 0.686697 | 0.343348 | − | 0.939208i | \(-0.388439\pi\) | ||||
0.343348 | + | 0.939208i | \(0.388439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.4764 | 1.57784 | 0.788918 | − | 0.614499i | \(-0.210642\pi\) | ||||
0.788918 | + | 0.614499i | \(0.210642\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.96894 | 0.158470 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.4211 | 0.927229 | 0.463615 | − | 0.886037i | \(-0.346552\pi\) | ||||
0.463615 | + | 0.886037i | \(0.346552\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.04018 | 0.426728 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0551927 | 0.00292111 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.3397 | −1.28460 | −0.642300 | − | 0.766454i | \(-0.722019\pi\) | ||||
−0.642300 | + | 0.766454i | \(0.722019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.0212 | 2.05374 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.68301 | −0.140822 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.5098 | −1.17822 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.2274 | −0.847064 | −0.423532 | − | 0.905881i | \(-0.639210\pi\) | ||||
−0.423532 | + | 0.905881i | \(0.639210\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.30095 | −0.171840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.00455001 | −0.000236225 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6394 | 1.01689 | 0.508446 | − | 0.861094i | \(-0.330220\pi\) | ||||
0.508446 | + | 0.861094i | \(0.330220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0818 | 0.572262 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.9422 | 1.59361 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5346 | −1.10616 | −0.553079 | − | 0.833129i | \(-0.686547\pi\) | ||||
−0.553079 | + | 0.833129i | \(0.686547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.4833 | 0.588309 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.8944 | 1.57863 | 0.789314 | − | 0.613989i | \(-0.210436\pi\) | ||||
0.789314 | + | 0.613989i | \(0.210436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0491517 | −0.00250500 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.1704 | 0.618656 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.27008 | −0.317905 | −0.158953 | − | 0.987286i | \(-0.550812\pi\) | ||||
−0.158953 | + | 0.987286i | \(0.550812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.3443 | −0.927712 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.8087 | −0.948773 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.2317 | −0.716077 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.7720 | −1.89572 | −0.947860 | − | 0.318686i | \(-0.896758\pi\) | ||||
−0.947860 | + | 0.318686i | \(0.896758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0955006 | 0.00478101 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.4800 | 0.922845 | 0.461423 | − | 0.887180i | \(-0.347339\pi\) | ||||
0.461423 | + | 0.887180i | \(0.347339\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0036 | 0.548130 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.35939 | −0.0675484 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.01422 | 0.347682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.2303 | 1.84092 | 0.920460 | − | 0.390838i | \(-0.127815\pi\) | ||||
0.920460 | + | 0.390838i | \(0.127815\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.98392 | 0.147186 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.0120576 | −0.000593314 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.3298 | −0.507071 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.7121 | 0.622514 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.7924 | −0.771508 | −0.385754 | − | 0.922602i | \(-0.626059\pi\) | ||||
−0.385754 | + | 0.922602i | \(0.626059\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.0315 | −1.60986 | −0.804928 | − | 0.593373i | \(-0.797796\pi\) | ||||
−0.804928 | + | 0.593373i | \(0.797796\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.83060 | 0.186250 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.8760 | 0.673085 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0667928 | 0.00323233 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.56217 | −0.413386 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5159 | −0.843713 | −0.421856 | − | 0.906663i | \(-0.638621\pi\) | ||||
−0.421856 | + | 0.906663i | \(0.638621\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.6656 | −0.608669 | −0.304334 | − | 0.952565i | \(-0.598434\pi\) | ||||
−0.304334 | + | 0.952565i | \(0.598434\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.1675 | −0.679280 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.7414 | −1.51840 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.53869 | −0.168892 | −0.0844462 | − | 0.996428i | \(-0.526912\pi\) | ||||
−0.0844462 | + | 0.996428i | \(0.526912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.99984 | −0.333326 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.6009 | 0.693711 | 0.346856 | − | 0.937919i | \(-0.387249\pi\) | ||||
0.346856 | + | 0.937919i | \(0.387249\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0664 | −0.714217 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.8794 | −0.845668 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.5321 | −1.20493 | −0.602467 | − | 0.798143i | \(-0.705816\pi\) | ||||
−0.602467 | + | 0.798143i | \(0.705816\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.51966 | 0.448263 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.83186 | −0.180036 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0506007 | 0.00237220 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.21608 | −0.384332 | −0.192166 | − | 0.981362i | \(-0.561551\pi\) | ||||
−0.192166 | + | 0.981362i | \(0.561551\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.40219 | −0.205477 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1279 | −0.658000 | −0.329000 | − | 0.944330i | \(-0.606712\pi\) | ||||
−0.329000 | + | 0.944330i | \(0.606712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.39087 | −0.436431 | −0.218215 | − | 0.975901i | \(-0.570024\pi\) | ||||
−0.218215 | + | 0.975901i | \(0.570024\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.03823 | −0.233642 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.53425 | 0.441193 | 0.220596 | − | 0.975365i | \(-0.429200\pi\) | ||||
0.220596 | + | 0.975365i | \(0.429200\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0480161 | −0.00221718 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.3528 | 0.569186 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.0984 | −1.61383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0098 | 1.10165 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.362911 | 0.0166165 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.0211 | 1.73723 | 0.868615 | − | 0.495487i | \(-0.165010\pi\) | ||||
0.868615 | + | 0.495487i | \(0.165010\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.22100 | −0.329249 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0522452 | −0.00237724 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.8842 | −0.494225 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5691 | 1.29459 | 0.647294 | − | 0.762240i | \(-0.275901\pi\) | ||||
0.647294 | + | 0.762240i | \(0.275901\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2932 | 0.555917 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.7097 | 1.52130 | 0.760649 | − | 0.649163i | \(-0.224881\pi\) | ||||
0.760649 | + | 0.649163i | \(0.224881\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −45.8796 | −2.06631 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.92036 | 0.176207 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0741542 | 0.00332627 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.8939 | −1.65160 | −0.825799 | − | 0.563964i | \(-0.809276\pi\) | ||||
−0.825799 | + | 0.563964i | \(0.809276\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.5511 | −0.605420 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.19638 | 0.187107 | 0.0935537 | − | 0.995614i | \(-0.470177\pi\) | ||||
0.0935537 | + | 0.995614i | \(0.470177\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.4888 | 0.911738 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.18542 | −0.185881 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4929 | 0.775358 | 0.387679 | − | 0.921794i | \(-0.373277\pi\) | ||||
0.387679 | + | 0.921794i | \(0.373277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.207607 | −0.00918398 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.61716 | −0.336306 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.36269 | −0.412569 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.0471 | −0.485853 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.81885 | 0.255419 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.4574 | −1.15912 | −0.579559 | − | 0.814930i | \(-0.696775\pi\) | ||||
−0.579559 | + | 0.814930i | \(0.696775\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.62984 | 0.333630 | 0.166815 | − | 0.985988i | \(-0.446652\pi\) | ||||
0.166815 | + | 0.985988i | \(0.446652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0395193 | 0.00172476 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.3156 | −0.710720 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.63535 | −0.245015 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.961715 | 0.0417349 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.80030 | −0.424498 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.41349 | 0.277280 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.89163 | −0.426855 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.1870 | 0.869515 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.68728 | −0.115535 | −0.0577676 | − | 0.998330i | \(-0.518398\pi\) | ||||
−0.0577676 | + | 0.998330i | \(0.518398\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.14226 | 0.220676 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −26.0841 | −1.11732 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.5651 | 0.580001 | 0.290000 | − | 0.957027i | \(-0.406345\pi\) | ||||
0.290000 | + | 0.957027i | \(0.406345\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.32742 | −0.227369 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −79.3860 | −3.38196 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.131259 | −0.00558169 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.30627 | 0.140344 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.15779 | 0.0490572 | 0.0245286 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245286 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.1331 | 1.52827 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.6956 | 0.536007 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.5340 | 1.49758 | 0.748791 | − | 0.662807i | \(-0.230635\pi\) | ||||
0.748791 | + | 0.662807i | \(0.230635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.24232 | −0.346757 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.0125376 | −0.000526528 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.53486 | −0.106267 | −0.0531334 | − | 0.998587i | \(-0.516921\pi\) | ||||
−0.0531334 | + | 0.998587i | \(0.516921\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.79986 | −0.326414 | −0.163207 | − | 0.986592i | \(-0.552184\pi\) | ||||
−0.163207 | + | 0.986592i | \(0.552184\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.6072 | −0.651999 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.1350 | −0.547766 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.8004 | 1.44876 | 0.724381 | − | 0.689400i | \(-0.242126\pi\) | ||||
0.724381 | + | 0.689400i | \(0.242126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.6732 | −1.10850 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.0952715 | −0.00395253 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.04661 | −0.0433460 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.03593 | −0.166865 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.7656 | 0.898360 | 0.449180 | − | 0.893441i | \(-0.351716\pi\) | ||||
0.449180 | + | 0.893441i | \(0.351716\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.2311 | −1.16324 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4324 | 0.922746 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.0640 | −1.19352 | −0.596758 | − | 0.802421i | \(-0.703545\pi\) | ||||
−0.596758 | + | 0.802421i | \(0.703545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0750282 | −0.00307585 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.86788 | 0.281083 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.1781 | −1.15133 | −0.575663 | − | 0.817687i | \(-0.695256\pi\) | ||||
−0.575663 | + | 0.817687i | \(0.695256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.10769 | −0.0859745 | −0.0429873 | − | 0.999076i | \(-0.513687\pi\) | ||||
−0.0429873 | + | 0.999076i | \(0.513687\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.82978 | 0.155961 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.64725 | 0.148282 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.0017 | −1.17714 | −0.588571 | − | 0.808445i | \(-0.700309\pi\) | ||||
−0.588571 | + | 0.808445i | \(0.700309\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.130666 | −0.00529487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.3728 | 0.460095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.4389 | 1.10824 | 0.554122 | − | 0.832435i | \(-0.313054\pi\) | ||||
0.554122 | + | 0.832435i | \(0.313054\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.48726 | 0.180944 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.02277 | 0.282726 | 0.141363 | − | 0.989958i | \(-0.454852\pi\) | ||||
0.141363 | + | 0.989958i | \(0.454852\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.5238 | 0.945502 | 0.472751 | − | 0.881196i | \(-0.343261\pi\) | ||||
0.472751 | + | 0.881196i | \(0.343261\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.16709 | 0.167220 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.138957 | −0.00556720 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.695908 | 0.0278363 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.9673 | 0.877289 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.7069 | 0.426913 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.6879 | 0.544906 | 0.272453 | − | 0.962169i | \(-0.412165\pi\) | ||||
0.272453 | + | 0.962169i | \(0.412165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.8361 | 0.669173 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.6103 | −0.619475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.7821 | −0.823416 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.91457 | −0.233977 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.5181 | −1.32388 | −0.661942 | − | 0.749555i | \(-0.730267\pi\) | ||||
−0.661942 | + | 0.749555i | \(0.730267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.8591 | 1.09865 | 0.549327 | − | 0.835607i | \(-0.314884\pi\) | ||||
0.549327 | + | 0.835607i | \(0.314884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5443 | −0.651429 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.1382 | 0.791714 | 0.395857 | − | 0.918312i | \(-0.370448\pi\) | ||||
0.395857 | + | 0.918312i | \(0.370448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.77351 | −0.108870 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0464674 | −0.00182120 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.1530 | 0.475584 | 0.237792 | − | 0.971316i | \(-0.423576\pi\) | ||||
0.237792 | + | 0.971316i | \(0.423576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.5683 | 0.999035 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.5588 | 0.646020 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.6674 | 0.493451 | 0.246726 | − | 0.969085i | \(-0.420645\pi\) | ||||
0.246726 | + | 0.969085i | \(0.420645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4785 | 0.990999 | 0.495499 | − | 0.868608i | \(-0.334985\pi\) | ||||
0.495499 | + | 0.868608i | \(0.334985\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.0698 | −0.507590 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.129822 | −0.00503429 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 43.4294 | 1.68159 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.0527 | 1.08458 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3638 | 0.593115 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1469 | −0.660964 | −0.330482 | − | 0.943812i | \(-0.607211\pi\) | ||||
−0.330482 | + | 0.943812i | \(0.607211\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.15207 | −0.121323 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.9084 | −1.22634 | −0.613170 | − | 0.789951i | \(-0.710106\pi\) | ||||
−0.613170 | + | 0.789951i | \(0.710106\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.100384 | −0.00385240 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.8764 | 0.991587 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.5770 | −1.66743 | −0.833715 | − | 0.552196i | \(-0.813790\pi\) | ||||
−0.833715 | + | 0.552196i | \(0.813790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.05629 | −0.154983 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.61570 | −0.328710 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.07746 | 0.0410479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.2411 | 0.465674 | 0.232837 | − | 0.972516i | \(-0.425199\pi\) | ||||
0.232837 | + | 0.972516i | \(0.425199\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0361573 | 0.00137350 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.2806 | −0.655492 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5314 | 0.550415 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.6491 | −0.516256 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.60594 | 0.136194 | 0.0680972 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680972 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5263 | 0.698734 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.20726 | −0.196117 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.188967 | 0.00710684 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.6649 | −1.56476 | −0.782379 | − | 0.622803i | \(-0.785994\pi\) | ||||
−0.782379 | + | 0.622803i | \(0.785994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.4693 | 0.392628 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.4443 | 0.578394 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.6393 | 0.435285 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.5074 | 0.504444 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.99845 | 0.223704 | 0.111852 | − | 0.993725i | \(-0.464322\pi\) | ||||
0.111852 | + | 0.993725i | \(0.464322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0863517 | −0.00321590 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.7997 | 0.550408 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −32.8509 | −1.22005 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.0217 | 1.22471 | 0.612354 | − | 0.790584i | \(-0.290223\pi\) | ||||
0.612354 | + | 0.790584i | \(0.290223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.5764 | −1.98159 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.1316 | 1.33455 | 0.667276 | − | 0.744810i | \(-0.267460\pi\) | ||||
0.667276 | + | 0.744810i | \(0.267460\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.51548 | 0.350984 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.0448 | −0.406840 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.2367 | 1.66406 | 0.832029 | − | 0.554732i | \(-0.187179\pi\) | ||||
0.832029 | + | 0.554732i | \(0.187179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.6149 | −0.830778 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.2770 | −0.487085 | −0.243542 | − | 0.969890i | \(-0.578309\pi\) | ||||
−0.243542 | + | 0.969890i | \(0.578309\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.3050 | 0.890467 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.59889 | 0.278029 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0591514 | 0.00216135 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.5575 | −1.22453 | −0.612265 | − | 0.790652i | \(-0.709742\pi\) | ||||
−0.612265 | + | 0.790652i | \(0.709742\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.00000 | 0.0364420 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.20897 | 0.189574 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.0326 | −1.67308 | −0.836541 | − | 0.547904i | \(-0.815426\pi\) | ||||
−0.836541 | + | 0.547904i | \(0.815426\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.0176 | −0.436210 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.2409 | −1.27748 | −0.638741 | − | 0.769422i | \(-0.720545\pi\) | ||||
−0.638741 | + | 0.769422i | \(0.720545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.240572 | −0.00870931 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.98427 | 0.216362 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.85527 | 0.103098 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.35636 | 0.301338 | 0.150669 | − | 0.988584i | \(-0.451857\pi\) | ||||
0.150669 | + | 0.988584i | \(0.451857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.09480 | −0.0394284 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.4910 | 0.413301 | 0.206651 | − | 0.978415i | \(-0.433744\pi\) | ||||
0.206651 | + | 0.978415i | \(0.433744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.6824 | −0.419643 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0304936 | 0.00109395 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.1438 | 0.900871 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.0571 | 0.610352 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.4220 | 0.372452 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.7922 | −0.599339 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.7856 | 0.491405 | 0.245703 | − | 0.969345i | \(-0.420981\pi\) | ||||
0.245703 | + | 0.969345i | \(0.420981\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.1165 | −0.466959 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.0760186 | −0.00270291 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.8168 | −0.561670 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.493336 | −0.0174968 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.3981 | 0.474587 | 0.237293 | − | 0.971438i | \(-0.423740\pi\) | ||||
0.237293 | + | 0.971438i | \(0.423740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.8630 | −0.596571 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.0833 | 0.391608 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −47.7542 | −1.68521 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0710213 | 0.00250317 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.49924 | 0.228784 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.3975 | 1.13903 | 0.569517 | − | 0.821979i | \(-0.307130\pi\) | ||||
0.569517 | + | 0.821979i | \(0.307130\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.1421 | 0.637054 | 0.318527 | − | 0.947914i | \(-0.396812\pi\) | ||||
0.318527 | + | 0.947914i | \(0.396812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.97414 | 0.209522 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.7112 | −0.585367 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −92.7038 | −3.24330 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0372232 | −0.00130068 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.6025 | −1.34723 | −0.673617 | − | 0.739080i | \(-0.735260\pi\) | ||||
−0.673617 | + | 0.739080i | \(0.735260\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.6083 | −0.474354 | −0.237177 | − | 0.971466i | \(-0.576222\pi\) | ||||
−0.237177 | + | 0.971466i | \(0.576222\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.09032 | 0.316484 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.3135 | −1.22797 | −0.613985 | − | 0.789318i | \(-0.710434\pi\) | ||||
−0.613985 | + | 0.789318i | \(0.710434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.13227 | 0.282445 | 0.141223 | − | 0.989978i | \(-0.454897\pi\) | ||||
0.141223 | + | 0.989978i | \(0.454897\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.33390 | 0.185031 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.8146 | 1.06766 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.4212 | 0.637492 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.70625 | 0.128107 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.39002 | −0.0479887 | −0.0239944 | − | 0.999712i | \(-0.507638\pi\) | ||||
−0.0239944 | + | 0.999712i | \(0.507638\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 79.6180 | 2.74545 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.50264 | −0.0517536 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.68959 | 0.195728 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.0336384 | 0.00115583 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.02928 | −0.0353248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1351 | −0.347428 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.03654 | −0.206687 | −0.103344 | − | 0.994646i | \(-0.532954\pi\) | ||||
−0.103344 | + | 0.994646i | \(0.532954\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.3547 | 0.354122 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.8433 | −1.53182 | −0.765909 | − | 0.642949i | \(-0.777711\pi\) | ||||
−0.765909 | + | 0.642949i | \(0.777711\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.0647 | −1.12815 | −0.564076 | − | 0.825723i | \(-0.690768\pi\) | ||||
−0.564076 | + | 0.825723i | \(0.690768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0413858 | 0.00141042 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.08434 | −0.241154 | −0.120577 | − | 0.992704i | \(-0.538474\pi\) | ||||
−0.120577 | + | 0.992704i | \(0.538474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.91006 | −0.268950 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.37927 | 0.0808041 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.1925 | −1.02421 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3704 | 0.385271 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.00669 | 0.270985 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.138939 | −0.00469699 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.0915635 | −0.00309188 | −0.00154594 | − | 0.999999i | \(-0.500492\pi\) | ||||
−0.00154594 | + | 0.999999i | \(0.500492\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.3215 | −0.854073 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.6554 | −0.965427 | −0.482713 | − | 0.875778i | \(-0.660349\pi\) | ||||
−0.482713 | + | 0.875778i | \(0.660349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.4261 | 0.350866 | 0.175433 | − | 0.984491i | \(-0.443867\pi\) | ||||
0.175433 | + | 0.984491i | \(0.443867\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.30734 | −0.0439458 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.18790 | −0.107039 | −0.0535196 | − | 0.998567i | \(-0.517044\pi\) | ||||
−0.0535196 | + | 0.998567i | \(0.517044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.143973 | −0.00482870 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.88392 | −0.0966149 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.1783 | −0.976415 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4465 | 0.449468 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.3718 | 0.413083 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.6266 | 1.28827 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.59760 | −0.0532238 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.152587 | −0.00507778 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.99032 | −0.232366 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.5437 | −0.648936 | −0.324468 | − | 0.945897i | \(-0.605185\pi\) | ||||
−0.324468 | + | 0.945897i | \(0.605185\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.0721 | −0.499909 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8082 | −1.55083 | −0.775413 | − | 0.631454i | \(-0.782458\pi\) | ||||
−0.775413 | + | 0.631454i | \(0.782458\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9146 | −0.725267 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.24202 | 0.239414 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.235815 | 0.00778730 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.4476 | −1.82905 | −0.914523 | − | 0.404533i | \(-0.867434\pi\) | ||||
−0.914523 | + | 0.404533i | \(0.867434\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.2934 | 0.470982 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.5600 | −0.577994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.66641 | 0.252070 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.88744 | 0.226213 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.0616 | 0.822245 | 0.411122 | − | 0.911580i | \(-0.365137\pi\) | ||||
0.411122 | + | 0.911580i | \(0.365137\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53.3189 | 1.74746 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.1451 | 0.364875 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.2582 | −0.564402 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.2328 | −1.44502 | −0.722511 | − | 0.691359i | \(-0.757012\pi\) | ||||
−0.722511 | + | 0.691359i | \(0.757012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.5555 | −0.344465 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.7943 | −0.775673 | −0.387836 | − | 0.921728i | \(-0.626777\pi\) | ||||
−0.387836 | + | 0.921728i | \(0.626777\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.7553 | −0.447936 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.0170434 | 0.000554421 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.603415 | 0.0196083 | 0.00980417 | − | 0.999952i | \(-0.496879\pi\) | ||||
0.00980417 | + | 0.999952i | \(0.496879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.1620 | 1.59587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.73648 | 0.218445 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0133 | 0.453935 | 0.226968 | − | 0.973902i | \(-0.427119\pi\) | ||||
0.226968 | + | 0.973902i | \(0.427119\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.2162 | 0.686539 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.0562 | −0.971579 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0374110 | −0.00120806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.2637 | −0.556893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.71794 | −0.152033 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.2592 | 1.16722 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.2756 | −0.491229 | −0.245615 | − | 0.969368i | \(-0.578990\pi\) | ||||
−0.245615 | + | 0.969368i | \(0.578990\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.5322 | 1.07721 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.0754 | 0.419609 | 0.209805 | − | 0.977743i | \(-0.432717\pi\) | ||||
0.209805 | + | 0.977743i | \(0.432717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.159379 | −0.00510945 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.35830 | −0.299705 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.3538 | 1.38701 | 0.693505 | − | 0.720452i | \(-0.256065\pi\) | ||||
0.693505 | + | 0.720452i | \(0.256065\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.9632 | −1.02155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.1881 | 0.612630 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42.4577 | 1.35419 | 0.677095 | − | 0.735896i | \(-0.263239\pi\) | ||||
0.677095 | + | 0.735896i | \(0.263239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.4943 | −0.971629 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0480264 | −0.00152870 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50.7151 | 1.61265 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.9968 | −1.33407 | −0.667037 | − | 0.745025i | \(-0.732438\pi\) | ||||
−0.667037 | + | 0.745025i | \(0.732438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.5523 | 1.09648 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.33609 | −0.295974 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.5587 | 0.587760 | 0.293880 | − | 0.955842i | \(-0.405053\pi\) | ||||
0.293880 | + | 0.955842i | \(0.405053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.43218 | −0.0769509 |
(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 | 6024.2.a.q.1.7 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6024.2.a.q.1.7 | ✓ | 18 | 1.1 | even | 1 | trivial |