Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.53209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.53209 | 1.08335 | 0.541675 | − | 0.840588i | \(-0.317790\pi\) | ||||
0.541675 | + | 0.840588i | \(0.317790\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.347296 | 0.173648 | ||||||||
\(5\) | 0.120615 | 0.0539406 | 0.0269703 | − | 0.999636i | \(-0.491414\pi\) | ||||
0.0269703 | + | 0.999636i | \(0.491414\pi\) | |||||||
\(6\) | 1.53209 | 0.625473 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.53209 | −0.895229 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.184793 | 0.0584365 | ||||||||
\(11\) | 4.57398 | 1.37911 | 0.689553 | − | 0.724235i | \(-0.257807\pi\) | ||||
0.689553 | + | 0.724235i | \(0.257807\pi\) | |||||||
\(12\) | 0.347296 | 0.100256 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.53209 | −0.409468 | ||||||||
\(15\) | 0.120615 | 0.0311426 | ||||||||
\(16\) | −4.57398 | −1.14349 | ||||||||
\(17\) | 4.92127 | 1.19358 | 0.596792 | − | 0.802396i | \(-0.296442\pi\) | ||||
0.596792 | + | 0.802396i | \(0.296442\pi\) | |||||||
\(18\) | 1.53209 | 0.361117 | ||||||||
\(19\) | −0.758770 | −0.174074 | −0.0870369 | − | 0.996205i | \(-0.527740\pi\) | ||||
−0.0870369 | + | 0.996205i | \(0.527740\pi\) | |||||||
\(20\) | 0.0418891 | 0.00936668 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 7.00774 | 1.49406 | ||||||||
\(23\) | −5.47565 | −1.14175 | −0.570876 | − | 0.821036i | \(-0.693396\pi\) | ||||
−0.570876 | + | 0.821036i | \(0.693396\pi\) | |||||||
\(24\) | −2.53209 | −0.516860 | ||||||||
\(25\) | −4.98545 | −0.997090 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.347296 | −0.0656328 | ||||||||
\(29\) | 10.6604 | 1.97959 | 0.989797 | − | 0.142482i | \(-0.0455082\pi\) | ||||
0.989797 | + | 0.142482i | \(0.0455082\pi\) | |||||||
\(30\) | 0.184793 | 0.0337383 | ||||||||
\(31\) | 8.63816 | 1.55146 | 0.775729 | − | 0.631066i | \(-0.217382\pi\) | ||||
0.775729 | + | 0.631066i | \(0.217382\pi\) | |||||||
\(32\) | −1.94356 | −0.343577 | ||||||||
\(33\) | 4.57398 | 0.796227 | ||||||||
\(34\) | 7.53983 | 1.29307 | ||||||||
\(35\) | −0.120615 | −0.0203876 | ||||||||
\(36\) | 0.347296 | 0.0578827 | ||||||||
\(37\) | −4.70233 | −0.773059 | −0.386529 | − | 0.922277i | \(-0.626326\pi\) | ||||
−0.386529 | + | 0.922277i | \(0.626326\pi\) | |||||||
\(38\) | −1.16250 | −0.188583 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.305407 | −0.0482891 | ||||||||
\(41\) | 10.9067 | 1.70334 | 0.851672 | − | 0.524075i | \(-0.175589\pi\) | ||||
0.851672 | + | 0.524075i | \(0.175589\pi\) | |||||||
\(42\) | −1.53209 | −0.236406 | ||||||||
\(43\) | 1.26352 | 0.192685 | 0.0963424 | − | 0.995348i | \(-0.469286\pi\) | ||||
0.0963424 | + | 0.995348i | \(0.469286\pi\) | |||||||
\(44\) | 1.58853 | 0.239479 | ||||||||
\(45\) | 0.120615 | 0.0179802 | ||||||||
\(46\) | −8.38919 | −1.23692 | ||||||||
\(47\) | 5.94356 | 0.866958 | 0.433479 | − | 0.901164i | \(-0.357286\pi\) | ||||
0.433479 | + | 0.901164i | \(0.357286\pi\) | |||||||
\(48\) | −4.57398 | −0.660197 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.63816 | −1.08020 | ||||||||
\(51\) | 4.92127 | 0.689116 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.49794 | 1.30464 | 0.652321 | − | 0.757943i | \(-0.273795\pi\) | ||||
0.652321 | + | 0.757943i | \(0.273795\pi\) | |||||||
\(54\) | 1.53209 | 0.208491 | ||||||||
\(55\) | 0.551689 | 0.0743898 | ||||||||
\(56\) | 2.53209 | 0.338365 | ||||||||
\(57\) | −0.758770 | −0.100502 | ||||||||
\(58\) | 16.3327 | 2.14459 | ||||||||
\(59\) | −8.99319 | −1.17081 | −0.585407 | − | 0.810740i | \(-0.699065\pi\) | ||||
−0.585407 | + | 0.810740i | \(0.699065\pi\) | |||||||
\(60\) | 0.0418891 | 0.00540786 | ||||||||
\(61\) | −9.45336 | −1.21038 | −0.605190 | − | 0.796081i | \(-0.706903\pi\) | ||||
−0.605190 | + | 0.796081i | \(0.706903\pi\) | |||||||
\(62\) | 13.2344 | 1.68077 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 6.17024 | 0.771281 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.00774 | 0.862593 | ||||||||
\(67\) | 13.0300 | 1.59187 | 0.795936 | − | 0.605381i | \(-0.206979\pi\) | ||||
0.795936 | + | 0.605381i | \(0.206979\pi\) | |||||||
\(68\) | 1.70914 | 0.207264 | ||||||||
\(69\) | −5.47565 | −0.659191 | ||||||||
\(70\) | −0.184793 | −0.0220869 | ||||||||
\(71\) | 2.47565 | 0.293806 | 0.146903 | − | 0.989151i | \(-0.453070\pi\) | ||||
0.146903 | + | 0.989151i | \(0.453070\pi\) | |||||||
\(72\) | −2.53209 | −0.298410 | ||||||||
\(73\) | 5.89393 | 0.689833 | 0.344916 | − | 0.938633i | \(-0.387907\pi\) | ||||
0.344916 | + | 0.938633i | \(0.387907\pi\) | |||||||
\(74\) | −7.20439 | −0.837494 | ||||||||
\(75\) | −4.98545 | −0.575670 | ||||||||
\(76\) | −0.263518 | −0.0302276 | ||||||||
\(77\) | −4.57398 | −0.521253 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.18479 | −0.920861 | −0.460431 | − | 0.887696i | \(-0.652305\pi\) | ||||
−0.460431 | + | 0.887696i | \(0.652305\pi\) | |||||||
\(80\) | −0.551689 | −0.0616807 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 16.7101 | 1.84532 | ||||||||
\(83\) | 12.2490 | 1.34450 | 0.672250 | − | 0.740325i | \(-0.265328\pi\) | ||||
0.672250 | + | 0.740325i | \(0.265328\pi\) | |||||||
\(84\) | −0.347296 | −0.0378931 | ||||||||
\(85\) | 0.593578 | 0.0643826 | ||||||||
\(86\) | 1.93582 | 0.208745 | ||||||||
\(87\) | 10.6604 | 1.14292 | ||||||||
\(88\) | −11.5817 | −1.23462 | ||||||||
\(89\) | −6.75877 | −0.716428 | −0.358214 | − | 0.933639i | \(-0.616614\pi\) | ||||
−0.358214 | + | 0.933639i | \(0.616614\pi\) | |||||||
\(90\) | 0.184793 | 0.0194788 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.90167 | −0.198263 | ||||||||
\(93\) | 8.63816 | 0.895735 | ||||||||
\(94\) | 9.10607 | 0.939219 | ||||||||
\(95\) | −0.0915189 | −0.00938964 | ||||||||
\(96\) | −1.94356 | −0.198364 | ||||||||
\(97\) | −10.0719 | −1.02265 | −0.511324 | − | 0.859388i | \(-0.670845\pi\) | ||||
−0.511324 | + | 0.859388i | \(0.670845\pi\) | |||||||
\(98\) | 1.53209 | 0.154764 | ||||||||
\(99\) | 4.57398 | 0.459702 | ||||||||
\(100\) | −1.73143 | −0.173143 | ||||||||
\(101\) | −5.95811 | −0.592854 | −0.296427 | − | 0.955055i | \(-0.595795\pi\) | ||||
−0.296427 | + | 0.955055i | \(0.595795\pi\) | |||||||
\(102\) | 7.53983 | 0.746554 | ||||||||
\(103\) | −2.75877 | −0.271830 | −0.135915 | − | 0.990721i | \(-0.543397\pi\) | ||||
−0.135915 | + | 0.990721i | \(0.543397\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.120615 | −0.0117708 | ||||||||
\(106\) | 14.5517 | 1.41339 | ||||||||
\(107\) | −3.86484 | −0.373628 | −0.186814 | − | 0.982395i | \(-0.559816\pi\) | ||||
−0.186814 | + | 0.982395i | \(0.559816\pi\) | |||||||
\(108\) | 0.347296 | 0.0334186 | ||||||||
\(109\) | −12.0496 | −1.15415 | −0.577073 | − | 0.816693i | \(-0.695805\pi\) | ||||
−0.577073 | + | 0.816693i | \(0.695805\pi\) | |||||||
\(110\) | 0.845237 | 0.0805902 | ||||||||
\(111\) | −4.70233 | −0.446326 | ||||||||
\(112\) | 4.57398 | 0.432200 | ||||||||
\(113\) | 7.57398 | 0.712500 | 0.356250 | − | 0.934391i | \(-0.384055\pi\) | ||||
0.356250 | + | 0.934391i | \(0.384055\pi\) | |||||||
\(114\) | −1.16250 | −0.108878 | ||||||||
\(115\) | −0.660444 | −0.0615868 | ||||||||
\(116\) | 3.70233 | 0.343753 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.7784 | −1.26840 | ||||||||
\(119\) | −4.92127 | −0.451132 | ||||||||
\(120\) | −0.305407 | −0.0278797 | ||||||||
\(121\) | 9.92127 | 0.901934 | ||||||||
\(122\) | −14.4834 | −1.31126 | ||||||||
\(123\) | 10.9067 | 0.983426 | ||||||||
\(124\) | 3.00000 | 0.269408 | ||||||||
\(125\) | −1.20439 | −0.107724 | ||||||||
\(126\) | −1.53209 | −0.136489 | ||||||||
\(127\) | −9.87939 | −0.876654 | −0.438327 | − | 0.898816i | \(-0.644429\pi\) | ||||
−0.438327 | + | 0.898816i | \(0.644429\pi\) | |||||||
\(128\) | 13.3405 | 1.17914 | ||||||||
\(129\) | 1.26352 | 0.111247 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5253 | 1.35645 | 0.678225 | − | 0.734854i | \(-0.262749\pi\) | ||||
0.678225 | + | 0.734854i | \(0.262749\pi\) | |||||||
\(132\) | 1.58853 | 0.138263 | ||||||||
\(133\) | 0.758770 | 0.0657937 | ||||||||
\(134\) | 19.9632 | 1.72455 | ||||||||
\(135\) | 0.120615 | 0.0103809 | ||||||||
\(136\) | −12.4611 | −1.06853 | ||||||||
\(137\) | −1.56624 | −0.133813 | −0.0669063 | − | 0.997759i | \(-0.521313\pi\) | ||||
−0.0669063 | + | 0.997759i | \(0.521313\pi\) | |||||||
\(138\) | −8.38919 | −0.714135 | ||||||||
\(139\) | 10.5030 | 0.890852 | 0.445426 | − | 0.895319i | \(-0.353052\pi\) | ||||
0.445426 | + | 0.895319i | \(0.353052\pi\) | |||||||
\(140\) | −0.0418891 | −0.00354027 | ||||||||
\(141\) | 5.94356 | 0.500538 | ||||||||
\(142\) | 3.79292 | 0.318295 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.57398 | −0.381165 | ||||||||
\(145\) | 1.28581 | 0.106780 | ||||||||
\(146\) | 9.03003 | 0.747331 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −1.63310 | −0.134240 | ||||||||
\(149\) | 0.248970 | 0.0203964 | 0.0101982 | − | 0.999948i | \(-0.496754\pi\) | ||||
0.0101982 | + | 0.999948i | \(0.496754\pi\) | |||||||
\(150\) | −7.63816 | −0.623653 | ||||||||
\(151\) | 18.9513 | 1.54224 | 0.771118 | − | 0.636693i | \(-0.219698\pi\) | ||||
0.771118 | + | 0.636693i | \(0.219698\pi\) | |||||||
\(152\) | 1.92127 | 0.155836 | ||||||||
\(153\) | 4.92127 | 0.397861 | ||||||||
\(154\) | −7.00774 | −0.564700 | ||||||||
\(155\) | 1.04189 | 0.0836865 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6827 | −1.49104 | −0.745522 | − | 0.666481i | \(-0.767800\pi\) | ||||
−0.745522 | + | 0.666481i | \(0.767800\pi\) | |||||||
\(158\) | −12.5398 | −0.997615 | ||||||||
\(159\) | 9.49794 | 0.753236 | ||||||||
\(160\) | −0.234422 | −0.0185327 | ||||||||
\(161\) | 5.47565 | 0.431542 | ||||||||
\(162\) | 1.53209 | 0.120372 | ||||||||
\(163\) | 20.0351 | 1.56927 | 0.784634 | − | 0.619959i | \(-0.212851\pi\) | ||||
0.784634 | + | 0.619959i | \(0.212851\pi\) | |||||||
\(164\) | 3.78787 | 0.295783 | ||||||||
\(165\) | 0.551689 | 0.0429489 | ||||||||
\(166\) | 18.7665 | 1.45656 | ||||||||
\(167\) | −2.01960 | −0.156281 | −0.0781407 | − | 0.996942i | \(-0.524898\pi\) | ||||
−0.0781407 | + | 0.996942i | \(0.524898\pi\) | |||||||
\(168\) | 2.53209 | 0.195355 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.909415 | 0.0697489 | ||||||||
\(171\) | −0.758770 | −0.0580246 | ||||||||
\(172\) | 0.438815 | 0.0334594 | ||||||||
\(173\) | 2.19934 | 0.167213 | 0.0836064 | − | 0.996499i | \(-0.473356\pi\) | ||||
0.0836064 | + | 0.996499i | \(0.473356\pi\) | |||||||
\(174\) | 16.3327 | 1.23818 | ||||||||
\(175\) | 4.98545 | 0.376865 | ||||||||
\(176\) | −20.9213 | −1.57700 | ||||||||
\(177\) | −8.99319 | −0.675970 | ||||||||
\(178\) | −10.3550 | −0.776143 | ||||||||
\(179\) | −8.57667 | −0.641050 | −0.320525 | − | 0.947240i | \(-0.603859\pi\) | ||||
−0.320525 | + | 0.947240i | \(0.603859\pi\) | |||||||
\(180\) | 0.0418891 | 0.00312223 | ||||||||
\(181\) | 11.8844 | 0.883363 | 0.441682 | − | 0.897172i | \(-0.354382\pi\) | ||||
0.441682 | + | 0.897172i | \(0.354382\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.45336 | −0.698813 | ||||||||
\(184\) | 13.8648 | 1.02213 | ||||||||
\(185\) | −0.567171 | −0.0416992 | ||||||||
\(186\) | 13.2344 | 0.970395 | ||||||||
\(187\) | 22.5098 | 1.64608 | ||||||||
\(188\) | 2.06418 | 0.150546 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.140215 | −0.0101723 | ||||||||
\(191\) | −13.8007 | −0.998581 | −0.499290 | − | 0.866435i | \(-0.666406\pi\) | ||||
−0.499290 | + | 0.866435i | \(0.666406\pi\) | |||||||
\(192\) | 6.17024 | 0.445299 | ||||||||
\(193\) | 18.2148 | 1.31113 | 0.655566 | − | 0.755138i | \(-0.272430\pi\) | ||||
0.655566 | + | 0.755138i | \(0.272430\pi\) | |||||||
\(194\) | −15.4311 | −1.10789 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.347296 | 0.0248069 | ||||||||
\(197\) | 3.56893 | 0.254275 | 0.127138 | − | 0.991885i | \(-0.459421\pi\) | ||||
0.127138 | + | 0.991885i | \(0.459421\pi\) | |||||||
\(198\) | 7.00774 | 0.498018 | ||||||||
\(199\) | −9.73648 | −0.690201 | −0.345100 | − | 0.938566i | \(-0.612155\pi\) | ||||
−0.345100 | + | 0.938566i | \(0.612155\pi\) | |||||||
\(200\) | 12.6236 | 0.892624 | ||||||||
\(201\) | 13.0300 | 0.919067 | ||||||||
\(202\) | −9.12836 | −0.642269 | ||||||||
\(203\) | −10.6604 | −0.748217 | ||||||||
\(204\) | 1.70914 | 0.119664 | ||||||||
\(205\) | 1.31551 | 0.0918794 | ||||||||
\(206\) | −4.22668 | −0.294487 | ||||||||
\(207\) | −5.47565 | −0.380584 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.47060 | −0.240066 | ||||||||
\(210\) | −0.184793 | −0.0127519 | ||||||||
\(211\) | −22.0574 | −1.51849 | −0.759246 | − | 0.650804i | \(-0.774432\pi\) | ||||
−0.759246 | + | 0.650804i | \(0.774432\pi\) | |||||||
\(212\) | 3.29860 | 0.226549 | ||||||||
\(213\) | 2.47565 | 0.169629 | ||||||||
\(214\) | −5.92127 | −0.404770 | ||||||||
\(215\) | 0.152399 | 0.0103935 | ||||||||
\(216\) | −2.53209 | −0.172287 | ||||||||
\(217\) | −8.63816 | −0.586396 | ||||||||
\(218\) | −18.4611 | −1.25034 | ||||||||
\(219\) | 5.89393 | 0.398275 | ||||||||
\(220\) | 0.191600 | 0.0129176 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.20439 | −0.483527 | ||||||||
\(223\) | −3.45336 | −0.231254 | −0.115627 | − | 0.993293i | \(-0.536888\pi\) | ||||
−0.115627 | + | 0.993293i | \(0.536888\pi\) | |||||||
\(224\) | 1.94356 | 0.129860 | ||||||||
\(225\) | −4.98545 | −0.332363 | ||||||||
\(226\) | 11.6040 | 0.771887 | ||||||||
\(227\) | −5.12061 | −0.339867 | −0.169934 | − | 0.985456i | \(-0.554355\pi\) | ||||
−0.169934 | + | 0.985456i | \(0.554355\pi\) | |||||||
\(228\) | −0.263518 | −0.0174519 | ||||||||
\(229\) | −15.3628 | −1.01520 | −0.507600 | − | 0.861593i | \(-0.669467\pi\) | ||||
−0.507600 | + | 0.861593i | \(0.669467\pi\) | |||||||
\(230\) | −1.01186 | −0.0667200 | ||||||||
\(231\) | −4.57398 | −0.300946 | ||||||||
\(232\) | −26.9932 | −1.77219 | ||||||||
\(233\) | 6.23173 | 0.408254 | 0.204127 | − | 0.978944i | \(-0.434564\pi\) | ||||
0.204127 | + | 0.978944i | \(0.434564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.716881 | 0.0467642 | ||||||||
\(236\) | −3.12330 | −0.203310 | ||||||||
\(237\) | −8.18479 | −0.531659 | ||||||||
\(238\) | −7.53983 | −0.488735 | ||||||||
\(239\) | −4.45336 | −0.288064 | −0.144032 | − | 0.989573i | \(-0.546007\pi\) | ||||
−0.144032 | + | 0.989573i | \(0.546007\pi\) | |||||||
\(240\) | −0.551689 | −0.0356114 | ||||||||
\(241\) | −9.04694 | −0.582765 | −0.291382 | − | 0.956607i | \(-0.594115\pi\) | ||||
−0.291382 | + | 0.956607i | \(0.594115\pi\) | |||||||
\(242\) | 15.2003 | 0.977111 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.28312 | −0.210180 | ||||||||
\(245\) | 0.120615 | 0.00770579 | ||||||||
\(246\) | 16.7101 | 1.06540 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −21.8726 | −1.38891 | ||||||||
\(249\) | 12.2490 | 0.776247 | ||||||||
\(250\) | −1.84524 | −0.116703 | ||||||||
\(251\) | −1.94356 | −0.122677 | −0.0613383 | − | 0.998117i | \(-0.519537\pi\) | ||||
−0.0613383 | + | 0.998117i | \(0.519537\pi\) | |||||||
\(252\) | −0.347296 | −0.0218776 | ||||||||
\(253\) | −25.0455 | −1.57460 | ||||||||
\(254\) | −15.1361 | −0.949723 | ||||||||
\(255\) | 0.593578 | 0.0371713 | ||||||||
\(256\) | 8.09833 | 0.506145 | ||||||||
\(257\) | −20.5594 | −1.28246 | −0.641231 | − | 0.767348i | \(-0.721576\pi\) | ||||
−0.641231 | + | 0.767348i | \(0.721576\pi\) | |||||||
\(258\) | 1.93582 | 0.120519 | ||||||||
\(259\) | 4.70233 | 0.292189 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.6604 | 0.659865 | ||||||||
\(262\) | 23.7861 | 1.46951 | ||||||||
\(263\) | 16.1061 | 0.993143 | 0.496571 | − | 0.867996i | \(-0.334592\pi\) | ||||
0.496571 | + | 0.867996i | \(0.334592\pi\) | |||||||
\(264\) | −11.5817 | −0.712806 | ||||||||
\(265\) | 1.14559 | 0.0703731 | ||||||||
\(266\) | 1.16250 | 0.0712777 | ||||||||
\(267\) | −6.75877 | −0.413630 | ||||||||
\(268\) | 4.52528 | 0.276426 | ||||||||
\(269\) | −4.29767 | −0.262033 | −0.131017 | − | 0.991380i | \(-0.541824\pi\) | ||||
−0.131017 | + | 0.991380i | \(0.541824\pi\) | |||||||
\(270\) | 0.184793 | 0.0112461 | ||||||||
\(271\) | 11.9017 | 0.722975 | 0.361488 | − | 0.932377i | \(-0.382269\pi\) | ||||
0.361488 | + | 0.932377i | \(0.382269\pi\) | |||||||
\(272\) | −22.5098 | −1.36486 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.39961 | −0.144966 | ||||||||
\(275\) | −22.8033 | −1.37509 | ||||||||
\(276\) | −1.90167 | −0.114467 | ||||||||
\(277\) | 10.8229 | 0.650288 | 0.325144 | − | 0.945665i | \(-0.394587\pi\) | ||||
0.325144 | + | 0.945665i | \(0.394587\pi\) | |||||||
\(278\) | 16.0915 | 0.965105 | ||||||||
\(279\) | 8.63816 | 0.517153 | ||||||||
\(280\) | 0.305407 | 0.0182516 | ||||||||
\(281\) | 6.83481 | 0.407730 | 0.203865 | − | 0.978999i | \(-0.434650\pi\) | ||||
0.203865 | + | 0.978999i | \(0.434650\pi\) | |||||||
\(282\) | 9.10607 | 0.542258 | ||||||||
\(283\) | −22.7442 | −1.35200 | −0.676002 | − | 0.736900i | \(-0.736289\pi\) | ||||
−0.676002 | + | 0.736900i | \(0.736289\pi\) | |||||||
\(284\) | 0.859785 | 0.0510188 | ||||||||
\(285\) | −0.0915189 | −0.00542111 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.9067 | −0.643804 | ||||||||
\(288\) | −1.94356 | −0.114526 | ||||||||
\(289\) | 7.21894 | 0.424644 | ||||||||
\(290\) | 1.96997 | 0.115681 | ||||||||
\(291\) | −10.0719 | −0.590426 | ||||||||
\(292\) | 2.04694 | 0.119788 | ||||||||
\(293\) | 20.9982 | 1.22673 | 0.613365 | − | 0.789799i | \(-0.289815\pi\) | ||||
0.613365 | + | 0.789799i | \(0.289815\pi\) | |||||||
\(294\) | 1.53209 | 0.0893532 | ||||||||
\(295\) | −1.08471 | −0.0631544 | ||||||||
\(296\) | 11.9067 | 0.692064 | ||||||||
\(297\) | 4.57398 | 0.265409 | ||||||||
\(298\) | 0.381445 | 0.0220965 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.73143 | −0.0999641 | ||||||||
\(301\) | −1.26352 | −0.0728280 | ||||||||
\(302\) | 29.0351 | 1.67078 | ||||||||
\(303\) | −5.95811 | −0.342285 | ||||||||
\(304\) | 3.47060 | 0.199053 | ||||||||
\(305\) | −1.14022 | −0.0652885 | ||||||||
\(306\) | 7.53983 | 0.431023 | ||||||||
\(307\) | −15.8821 | −0.906438 | −0.453219 | − | 0.891399i | \(-0.649724\pi\) | ||||
−0.453219 | + | 0.891399i | \(0.649724\pi\) | |||||||
\(308\) | −1.58853 | −0.0905147 | ||||||||
\(309\) | −2.75877 | −0.156941 | ||||||||
\(310\) | 1.59627 | 0.0906619 | ||||||||
\(311\) | −10.1976 | −0.578252 | −0.289126 | − | 0.957291i | \(-0.593365\pi\) | ||||
−0.289126 | + | 0.957291i | \(0.593365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.6578 | −1.05460 | −0.527299 | − | 0.849680i | \(-0.676795\pi\) | ||||
−0.527299 | + | 0.849680i | \(0.676795\pi\) | |||||||
\(314\) | −28.6236 | −1.61532 | ||||||||
\(315\) | −0.120615 | −0.00679587 | ||||||||
\(316\) | −2.84255 | −0.159906 | ||||||||
\(317\) | −15.3746 | −0.863526 | −0.431763 | − | 0.901987i | \(-0.642108\pi\) | ||||
−0.431763 | + | 0.901987i | \(0.642108\pi\) | |||||||
\(318\) | 14.5517 | 0.816018 | ||||||||
\(319\) | 48.7606 | 2.73007 | ||||||||
\(320\) | 0.744223 | 0.0416033 | ||||||||
\(321\) | −3.86484 | −0.215714 | ||||||||
\(322\) | 8.38919 | 0.467511 | ||||||||
\(323\) | −3.73412 | −0.207772 | ||||||||
\(324\) | 0.347296 | 0.0192942 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 30.6955 | 1.70007 | ||||||||
\(327\) | −12.0496 | −0.666346 | ||||||||
\(328\) | −27.6168 | −1.52488 | ||||||||
\(329\) | −5.94356 | −0.327679 | ||||||||
\(330\) | 0.845237 | 0.0465288 | ||||||||
\(331\) | −6.95636 | −0.382356 | −0.191178 | − | 0.981555i | \(-0.561231\pi\) | ||||
−0.191178 | + | 0.981555i | \(0.561231\pi\) | |||||||
\(332\) | 4.25402 | 0.233470 | ||||||||
\(333\) | −4.70233 | −0.257686 | ||||||||
\(334\) | −3.09421 | −0.169307 | ||||||||
\(335\) | 1.57161 | 0.0858664 | ||||||||
\(336\) | 4.57398 | 0.249531 | ||||||||
\(337\) | −12.1111 | −0.659735 | −0.329867 | − | 0.944027i | \(-0.607004\pi\) | ||||
−0.329867 | + | 0.944027i | \(0.607004\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.57398 | 0.411362 | ||||||||
\(340\) | 0.206148 | 0.0111799 | ||||||||
\(341\) | 39.5107 | 2.13963 | ||||||||
\(342\) | −1.16250 | −0.0628610 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.19934 | −0.172497 | ||||||||
\(345\) | −0.660444 | −0.0355571 | ||||||||
\(346\) | 3.36959 | 0.181150 | ||||||||
\(347\) | −24.9172 | −1.33762 | −0.668811 | − | 0.743432i | \(-0.733197\pi\) | ||||
−0.668811 | + | 0.743432i | \(0.733197\pi\) | |||||||
\(348\) | 3.70233 | 0.198466 | ||||||||
\(349\) | −4.09421 | −0.219158 | −0.109579 | − | 0.993978i | \(-0.534950\pi\) | ||||
−0.109579 | + | 0.993978i | \(0.534950\pi\) | |||||||
\(350\) | 7.63816 | 0.408277 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.88981 | −0.473829 | ||||||||
\(353\) | −6.79561 | −0.361694 | −0.180847 | − | 0.983511i | \(-0.557884\pi\) | ||||
−0.180847 | + | 0.983511i | \(0.557884\pi\) | |||||||
\(354\) | −13.7784 | −0.732312 | ||||||||
\(355\) | 0.298600 | 0.0158481 | ||||||||
\(356\) | −2.34730 | −0.124406 | ||||||||
\(357\) | −4.92127 | −0.260461 | ||||||||
\(358\) | −13.1402 | −0.694482 | ||||||||
\(359\) | −9.77425 | −0.515865 | −0.257933 | − | 0.966163i | \(-0.583041\pi\) | ||||
−0.257933 | + | 0.966163i | \(0.583041\pi\) | |||||||
\(360\) | −0.305407 | −0.0160964 | ||||||||
\(361\) | −18.4243 | −0.969698 | ||||||||
\(362\) | 18.2080 | 0.956992 | ||||||||
\(363\) | 9.92127 | 0.520732 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.710895 | 0.0372100 | ||||||||
\(366\) | −14.4834 | −0.757059 | ||||||||
\(367\) | −5.40198 | −0.281981 | −0.140990 | − | 0.990011i | \(-0.545029\pi\) | ||||
−0.140990 | + | 0.990011i | \(0.545029\pi\) | |||||||
\(368\) | 25.0455 | 1.30559 | ||||||||
\(369\) | 10.9067 | 0.567781 | ||||||||
\(370\) | −0.868956 | −0.0451749 | ||||||||
\(371\) | −9.49794 | −0.493109 | ||||||||
\(372\) | 3.00000 | 0.155543 | ||||||||
\(373\) | −35.5594 | −1.84120 | −0.920599 | − | 0.390510i | \(-0.872299\pi\) | ||||
−0.920599 | + | 0.390510i | \(0.872299\pi\) | |||||||
\(374\) | 34.4870 | 1.78328 | ||||||||
\(375\) | −1.20439 | −0.0621946 | ||||||||
\(376\) | −15.0496 | −0.776125 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.53209 | −0.0788021 | ||||||||
\(379\) | 12.3250 | 0.633093 | 0.316547 | − | 0.948577i | \(-0.397477\pi\) | ||||
0.316547 | + | 0.948577i | \(0.397477\pi\) | |||||||
\(380\) | −0.0317842 | −0.00163049 | ||||||||
\(381\) | −9.87939 | −0.506136 | ||||||||
\(382\) | −21.1438 | −1.08181 | ||||||||
\(383\) | −6.38507 | −0.326262 | −0.163131 | − | 0.986604i | \(-0.552159\pi\) | ||||
−0.163131 | + | 0.986604i | \(0.552159\pi\) | |||||||
\(384\) | 13.3405 | 0.680779 | ||||||||
\(385\) | −0.551689 | −0.0281167 | ||||||||
\(386\) | 27.9067 | 1.42041 | ||||||||
\(387\) | 1.26352 | 0.0642282 | ||||||||
\(388\) | −3.49794 | −0.177581 | ||||||||
\(389\) | −23.4492 | −1.18892 | −0.594462 | − | 0.804124i | \(-0.702635\pi\) | ||||
−0.594462 | + | 0.804124i | \(0.702635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.9472 | −1.36278 | ||||||||
\(392\) | −2.53209 | −0.127890 | ||||||||
\(393\) | 15.5253 | 0.783147 | ||||||||
\(394\) | 5.46791 | 0.275469 | ||||||||
\(395\) | −0.987207 | −0.0496718 | ||||||||
\(396\) | 1.58853 | 0.0798264 | ||||||||
\(397\) | 17.4260 | 0.874587 | 0.437293 | − | 0.899319i | \(-0.355937\pi\) | ||||
0.437293 | + | 0.899319i | \(0.355937\pi\) | |||||||
\(398\) | −14.9172 | −0.747729 | ||||||||
\(399\) | 0.758770 | 0.0379860 | ||||||||
\(400\) | 22.8033 | 1.14017 | ||||||||
\(401\) | −9.28136 | −0.463489 | −0.231745 | − | 0.972777i | \(-0.574443\pi\) | ||||
−0.231745 | + | 0.972777i | \(0.574443\pi\) | |||||||
\(402\) | 19.9632 | 0.995672 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.06923 | −0.102948 | ||||||||
\(405\) | 0.120615 | 0.00599340 | ||||||||
\(406\) | −16.3327 | −0.810581 | ||||||||
\(407\) | −21.5084 | −1.06613 | ||||||||
\(408\) | −12.4611 | −0.616917 | ||||||||
\(409\) | 14.4875 | 0.716361 | 0.358181 | − | 0.933652i | \(-0.383397\pi\) | ||||
0.358181 | + | 0.933652i | \(0.383397\pi\) | |||||||
\(410\) | 2.01548 | 0.0995375 | ||||||||
\(411\) | −1.56624 | −0.0772568 | ||||||||
\(412\) | −0.958111 | −0.0472027 | ||||||||
\(413\) | 8.99319 | 0.442526 | ||||||||
\(414\) | −8.38919 | −0.412306 | ||||||||
\(415\) | 1.47741 | 0.0725230 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5030 | 0.514334 | ||||||||
\(418\) | −5.31727 | −0.260076 | ||||||||
\(419\) | 5.53890 | 0.270593 | 0.135296 | − | 0.990805i | \(-0.456801\pi\) | ||||
0.135296 | + | 0.990805i | \(0.456801\pi\) | |||||||
\(420\) | −0.0418891 | −0.00204398 | ||||||||
\(421\) | 24.8949 | 1.21330 | 0.606651 | − | 0.794968i | \(-0.292513\pi\) | ||||
0.606651 | + | 0.794968i | \(0.292513\pi\) | |||||||
\(422\) | −33.7939 | −1.64506 | ||||||||
\(423\) | 5.94356 | 0.288986 | ||||||||
\(424\) | −24.0496 | −1.16795 | ||||||||
\(425\) | −24.5348 | −1.19011 | ||||||||
\(426\) | 3.79292 | 0.183768 | ||||||||
\(427\) | 9.45336 | 0.457480 | ||||||||
\(428\) | −1.34224 | −0.0648798 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.233489 | 0.0112598 | ||||||||
\(431\) | 17.1070 | 0.824015 | 0.412008 | − | 0.911180i | \(-0.364828\pi\) | ||||
0.412008 | + | 0.911180i | \(0.364828\pi\) | |||||||
\(432\) | −4.57398 | −0.220066 | ||||||||
\(433\) | −11.8966 | −0.571715 | −0.285858 | − | 0.958272i | \(-0.592278\pi\) | ||||
−0.285858 | + | 0.958272i | \(0.592278\pi\) | |||||||
\(434\) | −13.2344 | −0.635273 | ||||||||
\(435\) | 1.28581 | 0.0616497 | ||||||||
\(436\) | −4.18479 | −0.200415 | ||||||||
\(437\) | 4.15476 | 0.198749 | ||||||||
\(438\) | 9.03003 | 0.431471 | ||||||||
\(439\) | −12.4347 | −0.593476 | −0.296738 | − | 0.954959i | \(-0.595899\pi\) | ||||
−0.296738 | + | 0.954959i | \(0.595899\pi\) | |||||||
\(440\) | −1.39693 | −0.0665958 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.27631 | 0.108151 | 0.0540754 | − | 0.998537i | \(-0.482779\pi\) | ||||
0.0540754 | + | 0.998537i | \(0.482779\pi\) | |||||||
\(444\) | −1.63310 | −0.0775037 | ||||||||
\(445\) | −0.815207 | −0.0386445 | ||||||||
\(446\) | −5.29086 | −0.250529 | ||||||||
\(447\) | 0.248970 | 0.0117759 | ||||||||
\(448\) | −6.17024 | −0.291517 | ||||||||
\(449\) | 0.175297 | 0.00827278 | 0.00413639 | − | 0.999991i | \(-0.498683\pi\) | ||||
0.00413639 | + | 0.999991i | \(0.498683\pi\) | |||||||
\(450\) | −7.63816 | −0.360066 | ||||||||
\(451\) | 49.8871 | 2.34909 | ||||||||
\(452\) | 2.63041 | 0.123724 | ||||||||
\(453\) | 18.9513 | 0.890410 | ||||||||
\(454\) | −7.84524 | −0.368195 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.92127 | 0.0899719 | ||||||||
\(457\) | −11.5047 | −0.538169 | −0.269085 | − | 0.963117i | \(-0.586721\pi\) | ||||
−0.269085 | + | 0.963117i | \(0.586721\pi\) | |||||||
\(458\) | −23.5371 | −1.09982 | ||||||||
\(459\) | 4.92127 | 0.229705 | ||||||||
\(460\) | −0.229370 | −0.0106944 | ||||||||
\(461\) | 8.48070 | 0.394986 | 0.197493 | − | 0.980304i | \(-0.436720\pi\) | ||||
0.197493 | + | 0.980304i | \(0.436720\pi\) | |||||||
\(462\) | −7.00774 | −0.326030 | ||||||||
\(463\) | −11.2790 | −0.524180 | −0.262090 | − | 0.965043i | \(-0.584412\pi\) | ||||
−0.262090 | + | 0.965043i | \(0.584412\pi\) | |||||||
\(464\) | −48.7606 | −2.26366 | ||||||||
\(465\) | 1.04189 | 0.0483164 | ||||||||
\(466\) | 9.54757 | 0.442283 | ||||||||
\(467\) | 20.3063 | 0.939665 | 0.469833 | − | 0.882755i | \(-0.344314\pi\) | ||||
0.469833 | + | 0.882755i | \(0.344314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.0300 | −0.601671 | ||||||||
\(470\) | 1.09833 | 0.0506620 | ||||||||
\(471\) | −18.6827 | −0.860855 | ||||||||
\(472\) | 22.7716 | 1.04815 | ||||||||
\(473\) | 5.77930 | 0.265733 | ||||||||
\(474\) | −12.5398 | −0.575973 | ||||||||
\(475\) | 3.78281 | 0.173567 | ||||||||
\(476\) | −1.70914 | −0.0783383 | ||||||||
\(477\) | 9.49794 | 0.434881 | ||||||||
\(478\) | −6.82295 | −0.312074 | ||||||||
\(479\) | −23.0027 | −1.05102 | −0.525510 | − | 0.850788i | \(-0.676125\pi\) | ||||
−0.525510 | + | 0.850788i | \(0.676125\pi\) | |||||||
\(480\) | −0.234422 | −0.0106999 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −13.8607 | −0.631338 | ||||||||
\(483\) | 5.47565 | 0.249151 | ||||||||
\(484\) | 3.44562 | 0.156619 | ||||||||
\(485\) | −1.21482 | −0.0551622 | ||||||||
\(486\) | 1.53209 | 0.0694970 | ||||||||
\(487\) | 17.1976 | 0.779297 | 0.389648 | − | 0.920964i | \(-0.372597\pi\) | ||||
0.389648 | + | 0.920964i | \(0.372597\pi\) | |||||||
\(488\) | 23.9368 | 1.08357 | ||||||||
\(489\) | 20.0351 | 0.906018 | ||||||||
\(490\) | 0.184793 | 0.00834808 | ||||||||
\(491\) | 40.5577 | 1.83034 | 0.915171 | − | 0.403066i | \(-0.132055\pi\) | ||||
0.915171 | + | 0.403066i | \(0.132055\pi\) | |||||||
\(492\) | 3.78787 | 0.170770 | ||||||||
\(493\) | 52.4630 | 2.36281 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.551689 | 0.0247966 | ||||||||
\(496\) | −39.5107 | −1.77408 | ||||||||
\(497\) | −2.47565 | −0.111048 | ||||||||
\(498\) | 18.7665 | 0.840947 | ||||||||
\(499\) | −5.54757 | −0.248343 | −0.124172 | − | 0.992261i | \(-0.539627\pi\) | ||||
−0.124172 | + | 0.992261i | \(0.539627\pi\) | |||||||
\(500\) | −0.418281 | −0.0187061 | ||||||||
\(501\) | −2.01960 | −0.0902291 | ||||||||
\(502\) | −2.97771 | −0.132902 | ||||||||
\(503\) | −22.7588 | −1.01476 | −0.507382 | − | 0.861721i | \(-0.669387\pi\) | ||||
−0.507382 | + | 0.861721i | \(0.669387\pi\) | |||||||
\(504\) | 2.53209 | 0.112788 | ||||||||
\(505\) | −0.718636 | −0.0319789 | ||||||||
\(506\) | −38.3719 | −1.70584 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.43107 | −0.152229 | ||||||||
\(509\) | −25.0196 | −1.10897 | −0.554487 | − | 0.832192i | \(-0.687086\pi\) | ||||
−0.554487 | + | 0.832192i | \(0.687086\pi\) | |||||||
\(510\) | 0.909415 | 0.0402696 | ||||||||
\(511\) | −5.89393 | −0.260732 | ||||||||
\(512\) | −14.2736 | −0.630811 | ||||||||
\(513\) | −0.758770 | −0.0335005 | ||||||||
\(514\) | −31.4989 | −1.38936 | ||||||||
\(515\) | −0.332748 | −0.0146626 | ||||||||
\(516\) | 0.438815 | 0.0193178 | ||||||||
\(517\) | 27.1857 | 1.19563 | ||||||||
\(518\) | 7.20439 | 0.316543 | ||||||||
\(519\) | 2.19934 | 0.0965403 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.0051 | 0.438329 | 0.219165 | − | 0.975688i | \(-0.429667\pi\) | ||||
0.219165 | + | 0.975688i | \(0.429667\pi\) | |||||||
\(522\) | 16.3327 | 0.714865 | ||||||||
\(523\) | −43.6049 | −1.90671 | −0.953355 | − | 0.301850i | \(-0.902396\pi\) | ||||
−0.953355 | + | 0.301850i | \(0.902396\pi\) | |||||||
\(524\) | 5.39187 | 0.235545 | ||||||||
\(525\) | 4.98545 | 0.217583 | ||||||||
\(526\) | 24.6759 | 1.07592 | ||||||||
\(527\) | 42.5107 | 1.85180 | ||||||||
\(528\) | −20.9213 | −0.910482 | ||||||||
\(529\) | 6.98276 | 0.303598 | ||||||||
\(530\) | 1.75515 | 0.0762388 | ||||||||
\(531\) | −8.99319 | −0.390271 | ||||||||
\(532\) | 0.263518 | 0.0114250 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −10.3550 | −0.448106 | ||||||||
\(535\) | −0.466156 | −0.0201537 | ||||||||
\(536\) | −32.9932 | −1.42509 | ||||||||
\(537\) | −8.57667 | −0.370110 | ||||||||
\(538\) | −6.58441 | −0.283874 | ||||||||
\(539\) | 4.57398 | 0.197015 | ||||||||
\(540\) | 0.0418891 | 0.00180262 | ||||||||
\(541\) | 31.1002 | 1.33710 | 0.668551 | − | 0.743666i | \(-0.266915\pi\) | ||||
0.668551 | + | 0.743666i | \(0.266915\pi\) | |||||||
\(542\) | 18.2344 | 0.783236 | ||||||||
\(543\) | 11.8844 | 0.510010 | ||||||||
\(544\) | −9.56481 | −0.410088 | ||||||||
\(545\) | −1.45336 | −0.0622552 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.5827 | 1.64968 | 0.824838 | − | 0.565370i | \(-0.191267\pi\) | ||||
0.824838 | + | 0.565370i | \(0.191267\pi\) | |||||||
\(548\) | −0.543948 | −0.0232363 | ||||||||
\(549\) | −9.45336 | −0.403460 | ||||||||
\(550\) | −34.9368 | −1.48971 | ||||||||
\(551\) | −8.08883 | −0.344596 | ||||||||
\(552\) | 13.8648 | 0.590127 | ||||||||
\(553\) | 8.18479 | 0.348053 | ||||||||
\(554\) | 16.5817 | 0.704490 | ||||||||
\(555\) | −0.567171 | −0.0240751 | ||||||||
\(556\) | 3.64765 | 0.154695 | ||||||||
\(557\) | 41.1840 | 1.74502 | 0.872510 | − | 0.488595i | \(-0.162491\pi\) | ||||
0.872510 | + | 0.488595i | \(0.162491\pi\) | |||||||
\(558\) | 13.2344 | 0.560258 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0.551689 | 0.0233131 | ||||||||
\(561\) | 22.5098 | 0.950365 | ||||||||
\(562\) | 10.4715 | 0.441715 | ||||||||
\(563\) | −22.7638 | −0.959381 | −0.479690 | − | 0.877438i | \(-0.659251\pi\) | ||||
−0.479690 | + | 0.877438i | \(0.659251\pi\) | |||||||
\(564\) | 2.06418 | 0.0869176 | ||||||||
\(565\) | 0.913534 | 0.0384326 | ||||||||
\(566\) | −34.8462 | −1.46469 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −6.26857 | −0.263023 | ||||||||
\(569\) | −26.2986 | −1.10249 | −0.551247 | − | 0.834342i | \(-0.685848\pi\) | ||||
−0.551247 | + | 0.834342i | \(0.685848\pi\) | |||||||
\(570\) | −0.140215 | −0.00587297 | ||||||||
\(571\) | 13.8435 | 0.579332 | 0.289666 | − | 0.957128i | \(-0.406456\pi\) | ||||
0.289666 | + | 0.957128i | \(0.406456\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8007 | −0.576531 | ||||||||
\(574\) | −16.7101 | −0.697465 | ||||||||
\(575\) | 27.2986 | 1.13843 | ||||||||
\(576\) | 6.17024 | 0.257094 | ||||||||
\(577\) | 13.9290 | 0.579872 | 0.289936 | − | 0.957046i | \(-0.406366\pi\) | ||||
0.289936 | + | 0.957046i | \(0.406366\pi\) | |||||||
\(578\) | 11.0601 | 0.460038 | ||||||||
\(579\) | 18.2148 | 0.756982 | ||||||||
\(580\) | 0.446556 | 0.0185422 | ||||||||
\(581\) | −12.2490 | −0.508173 | ||||||||
\(582\) | −15.4311 | −0.639639 | ||||||||
\(583\) | 43.4434 | 1.79924 | ||||||||
\(584\) | −14.9240 | −0.617558 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.1712 | 1.32898 | ||||||||
\(587\) | −43.3928 | −1.79101 | −0.895506 | − | 0.445049i | \(-0.853186\pi\) | ||||
−0.895506 | + | 0.445049i | \(0.853186\pi\) | |||||||
\(588\) | 0.347296 | 0.0143223 | ||||||||
\(589\) | −6.55438 | −0.270068 | ||||||||
\(590\) | −1.66187 | −0.0684183 | ||||||||
\(591\) | 3.56893 | 0.146806 | ||||||||
\(592\) | 21.5084 | 0.883989 | ||||||||
\(593\) | −2.20708 | −0.0906340 | −0.0453170 | − | 0.998973i | \(-0.514430\pi\) | ||||
−0.0453170 | + | 0.998973i | \(0.514430\pi\) | |||||||
\(594\) | 7.00774 | 0.287531 | ||||||||
\(595\) | −0.593578 | −0.0243343 | ||||||||
\(596\) | 0.0864665 | 0.00354180 | ||||||||
\(597\) | −9.73648 | −0.398488 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.1729 | 1.35541 | 0.677705 | − | 0.735334i | \(-0.262975\pi\) | ||||
0.677705 | + | 0.735334i | \(0.262975\pi\) | |||||||
\(600\) | 12.6236 | 0.515357 | ||||||||
\(601\) | 18.7124 | 0.763296 | 0.381648 | − | 0.924308i | \(-0.375357\pi\) | ||||
0.381648 | + | 0.924308i | \(0.375357\pi\) | |||||||
\(602\) | −1.93582 | −0.0788982 | ||||||||
\(603\) | 13.0300 | 0.530624 | ||||||||
\(604\) | 6.58172 | 0.267806 | ||||||||
\(605\) | 1.19665 | 0.0486508 | ||||||||
\(606\) | −9.12836 | −0.370814 | ||||||||
\(607\) | −1.14889 | −0.0466320 | −0.0233160 | − | 0.999728i | \(-0.507422\pi\) | ||||
−0.0233160 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(608\) | 1.47472 | 0.0598077 | ||||||||
\(609\) | −10.6604 | −0.431983 | ||||||||
\(610\) | −1.74691 | −0.0707304 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.70914 | 0.0690879 | ||||||||
\(613\) | −12.7760 | −0.516018 | −0.258009 | − | 0.966143i | \(-0.583066\pi\) | ||||
−0.258009 | + | 0.966143i | \(0.583066\pi\) | |||||||
\(614\) | −24.3327 | −0.981990 | ||||||||
\(615\) | 1.31551 | 0.0530466 | ||||||||
\(616\) | 11.5817 | 0.466641 | ||||||||
\(617\) | 7.25847 | 0.292215 | 0.146107 | − | 0.989269i | \(-0.453325\pi\) | ||||
0.146107 | + | 0.989269i | \(0.453325\pi\) | |||||||
\(618\) | −4.22668 | −0.170022 | ||||||||
\(619\) | 10.8966 | 0.437972 | 0.218986 | − | 0.975728i | \(-0.429725\pi\) | ||||
0.218986 | + | 0.975728i | \(0.429725\pi\) | |||||||
\(620\) | 0.361844 | 0.0145320 | ||||||||
\(621\) | −5.47565 | −0.219730 | ||||||||
\(622\) | −15.6236 | −0.626450 | ||||||||
\(623\) | 6.75877 | 0.270784 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7820 | 0.991280 | ||||||||
\(626\) | −28.5853 | −1.14250 | ||||||||
\(627\) | −3.47060 | −0.138602 | ||||||||
\(628\) | −6.48845 | −0.258917 | ||||||||
\(629\) | −23.1415 | −0.922711 | ||||||||
\(630\) | −0.184793 | −0.00736231 | ||||||||
\(631\) | −26.3705 | −1.04979 | −0.524897 | − | 0.851166i | \(-0.675896\pi\) | ||||
−0.524897 | + | 0.851166i | \(0.675896\pi\) | |||||||
\(632\) | 20.7246 | 0.824381 | ||||||||
\(633\) | −22.0574 | −0.876702 | ||||||||
\(634\) | −23.5553 | −0.935501 | ||||||||
\(635\) | −1.19160 | −0.0472872 | ||||||||
\(636\) | 3.29860 | 0.130798 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 74.7056 | 2.95762 | ||||||||
\(639\) | 2.47565 | 0.0979353 | ||||||||
\(640\) | 1.60906 | 0.0636037 | ||||||||
\(641\) | 9.56481 | 0.377787 | 0.188894 | − | 0.981998i | \(-0.439510\pi\) | ||||
0.188894 | + | 0.981998i | \(0.439510\pi\) | |||||||
\(642\) | −5.92127 | −0.233694 | ||||||||
\(643\) | −48.7606 | −1.92293 | −0.961466 | − | 0.274924i | \(-0.911347\pi\) | ||||
−0.961466 | + | 0.274924i | \(0.911347\pi\) | |||||||
\(644\) | 1.90167 | 0.0749365 | ||||||||
\(645\) | 0.152399 | 0.00600070 | ||||||||
\(646\) | −5.72100 | −0.225090 | ||||||||
\(647\) | −18.3455 | −0.721238 | −0.360619 | − | 0.932713i | \(-0.617434\pi\) | ||||
−0.360619 | + | 0.932713i | \(0.617434\pi\) | |||||||
\(648\) | −2.53209 | −0.0994698 | ||||||||
\(649\) | −41.1347 | −1.61468 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.63816 | −0.338556 | ||||||||
\(652\) | 6.95811 | 0.272501 | ||||||||
\(653\) | 3.53714 | 0.138419 | 0.0692095 | − | 0.997602i | \(-0.477952\pi\) | ||||
0.0692095 | + | 0.997602i | \(0.477952\pi\) | |||||||
\(654\) | −18.4611 | −0.721886 | ||||||||
\(655\) | 1.87258 | 0.0731677 | ||||||||
\(656\) | −49.8871 | −1.94777 | ||||||||
\(657\) | 5.89393 | 0.229944 | ||||||||
\(658\) | −9.10607 | −0.354991 | ||||||||
\(659\) | 20.7510 | 0.808345 | 0.404173 | − | 0.914683i | \(-0.367559\pi\) | ||||
0.404173 | + | 0.914683i | \(0.367559\pi\) | |||||||
\(660\) | 0.191600 | 0.00745801 | ||||||||
\(661\) | −22.4516 | −0.873266 | −0.436633 | − | 0.899640i | \(-0.643829\pi\) | ||||
−0.436633 | + | 0.899640i | \(0.643829\pi\) | |||||||
\(662\) | −10.6578 | −0.414225 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.0155 | −1.20363 | ||||||||
\(665\) | 0.0915189 | 0.00354895 | ||||||||
\(666\) | −7.20439 | −0.279165 | ||||||||
\(667\) | −58.3729 | −2.26021 | ||||||||
\(668\) | −0.701400 | −0.0271380 | ||||||||
\(669\) | −3.45336 | −0.133515 | ||||||||
\(670\) | 2.40785 | 0.0930234 | ||||||||
\(671\) | −43.2395 | −1.66924 | ||||||||
\(672\) | 1.94356 | 0.0749746 | ||||||||
\(673\) | 24.0438 | 0.926819 | 0.463409 | − | 0.886144i | \(-0.346626\pi\) | ||||
0.463409 | + | 0.886144i | \(0.346626\pi\) | |||||||
\(674\) | −18.5553 | −0.714724 | ||||||||
\(675\) | −4.98545 | −0.191890 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.5321 | −1.48091 | −0.740454 | − | 0.672107i | \(-0.765390\pi\) | ||||
−0.740454 | + | 0.672107i | \(0.765390\pi\) | |||||||
\(678\) | 11.6040 | 0.445649 | ||||||||
\(679\) | 10.0719 | 0.386525 | ||||||||
\(680\) | −1.50299 | −0.0576372 | ||||||||
\(681\) | −5.12061 | −0.196222 | ||||||||
\(682\) | 60.5340 | 2.31796 | ||||||||
\(683\) | −25.6195 | −0.980303 | −0.490151 | − | 0.871637i | \(-0.663058\pi\) | ||||
−0.490151 | + | 0.871637i | \(0.663058\pi\) | |||||||
\(684\) | −0.263518 | −0.0100759 | ||||||||
\(685\) | −0.188911 | −0.00721793 | ||||||||
\(686\) | −1.53209 | −0.0584954 | ||||||||
\(687\) | −15.3628 | −0.586127 | ||||||||
\(688\) | −5.77930 | −0.220334 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.01186 | −0.0385208 | ||||||||
\(691\) | 34.3087 | 1.30516 | 0.652582 | − | 0.757718i | \(-0.273686\pi\) | ||||
0.652582 | + | 0.757718i | \(0.273686\pi\) | |||||||
\(692\) | 0.763823 | 0.0290362 | ||||||||
\(693\) | −4.57398 | −0.173751 | ||||||||
\(694\) | −38.1753 | −1.44911 | ||||||||
\(695\) | 1.26682 | 0.0480531 | ||||||||
\(696\) | −26.9932 | −1.02317 | ||||||||
\(697\) | 53.6750 | 2.03309 | ||||||||
\(698\) | −6.27269 | −0.237425 | ||||||||
\(699\) | 6.23173 | 0.235706 | ||||||||
\(700\) | 1.73143 | 0.0654419 | ||||||||
\(701\) | −2.03415 | −0.0768287 | −0.0384144 | − | 0.999262i | \(-0.512231\pi\) | ||||
−0.0384144 | + | 0.999262i | \(0.512231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.56799 | 0.134569 | ||||||||
\(704\) | 28.2226 | 1.06368 | ||||||||
\(705\) | 0.716881 | 0.0269993 | ||||||||
\(706\) | −10.4115 | −0.391841 | ||||||||
\(707\) | 5.95811 | 0.224078 | ||||||||
\(708\) | −3.12330 | −0.117381 | ||||||||
\(709\) | −14.3027 | −0.537150 | −0.268575 | − | 0.963259i | \(-0.586553\pi\) | ||||
−0.268575 | + | 0.963259i | \(0.586553\pi\) | |||||||
\(710\) | 0.457482 | 0.0171690 | ||||||||
\(711\) | −8.18479 | −0.306954 | ||||||||
\(712\) | 17.1138 | 0.641367 | ||||||||
\(713\) | −47.2995 | −1.77138 | ||||||||
\(714\) | −7.53983 | −0.282171 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.97864 | −0.111317 | ||||||||
\(717\) | −4.45336 | −0.166314 | ||||||||
\(718\) | −14.9750 | −0.558863 | ||||||||
\(719\) | 0.205327 | 0.00765739 | 0.00382869 | − | 0.999993i | \(-0.498781\pi\) | ||||
0.00382869 | + | 0.999993i | \(0.498781\pi\) | |||||||
\(720\) | −0.551689 | −0.0205602 | ||||||||
\(721\) | 2.75877 | 0.102742 | ||||||||
\(722\) | −28.2276 | −1.05052 | ||||||||
\(723\) | −9.04694 | −0.336459 | ||||||||
\(724\) | 4.12742 | 0.153394 | ||||||||
\(725\) | −53.1471 | −1.97384 | ||||||||
\(726\) | 15.2003 | 0.564135 | ||||||||
\(727\) | 18.0395 | 0.669049 | 0.334524 | − | 0.942387i | \(-0.391424\pi\) | ||||
0.334524 | + | 0.942387i | \(0.391424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.08915 | 0.0403114 | ||||||||
\(731\) | 6.21812 | 0.229985 | ||||||||
\(732\) | −3.28312 | −0.121348 | ||||||||
\(733\) | −20.9760 | −0.774765 | −0.387382 | − | 0.921919i | \(-0.626621\pi\) | ||||
−0.387382 | + | 0.921919i | \(0.626621\pi\) | |||||||
\(734\) | −8.27631 | −0.305484 | ||||||||
\(735\) | 0.120615 | 0.00444894 | ||||||||
\(736\) | 10.6423 | 0.392279 | ||||||||
\(737\) | 59.5991 | 2.19536 | ||||||||
\(738\) | 16.7101 | 0.615106 | ||||||||
\(739\) | 22.1019 | 0.813033 | 0.406517 | − | 0.913643i | \(-0.366743\pi\) | ||||
0.406517 | + | 0.913643i | \(0.366743\pi\) | |||||||
\(740\) | −0.196976 | −0.00724099 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.5517 | −0.534209 | ||||||||
\(743\) | 6.12330 | 0.224642 | 0.112321 | − | 0.993672i | \(-0.464171\pi\) | ||||
0.112321 | + | 0.993672i | \(0.464171\pi\) | |||||||
\(744\) | −21.8726 | −0.801888 | ||||||||
\(745\) | 0.0300295 | 0.00110020 | ||||||||
\(746\) | −54.4802 | −1.99466 | ||||||||
\(747\) | 12.2490 | 0.448166 | ||||||||
\(748\) | 7.81757 | 0.285839 | ||||||||
\(749\) | 3.86484 | 0.141218 | ||||||||
\(750\) | −1.84524 | −0.0673785 | ||||||||
\(751\) | 14.2517 | 0.520050 | 0.260025 | − | 0.965602i | \(-0.416269\pi\) | ||||
0.260025 | + | 0.965602i | \(0.416269\pi\) | |||||||
\(752\) | −27.1857 | −0.991361 | ||||||||
\(753\) | −1.94356 | −0.0708274 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.28581 | 0.0831890 | ||||||||
\(756\) | −0.347296 | −0.0126310 | ||||||||
\(757\) | −10.9094 | −0.396509 | −0.198255 | − | 0.980151i | \(-0.563527\pi\) | ||||
−0.198255 | + | 0.980151i | \(0.563527\pi\) | |||||||
\(758\) | 18.8830 | 0.685862 | ||||||||
\(759\) | −25.0455 | −0.909094 | ||||||||
\(760\) | 0.231734 | 0.00840588 | ||||||||
\(761\) | 51.3346 | 1.86088 | 0.930439 | − | 0.366446i | \(-0.119426\pi\) | ||||
0.930439 | + | 0.366446i | \(0.119426\pi\) | |||||||
\(762\) | −15.1361 | −0.548323 | ||||||||
\(763\) | 12.0496 | 0.436226 | ||||||||
\(764\) | −4.79292 | −0.173402 | ||||||||
\(765\) | 0.593578 | 0.0214609 | ||||||||
\(766\) | −9.78249 | −0.353456 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 8.09833 | 0.292223 | ||||||||
\(769\) | 8.92221 | 0.321743 | 0.160872 | − | 0.986975i | \(-0.448570\pi\) | ||||
0.160872 | + | 0.986975i | \(0.448570\pi\) | |||||||
\(770\) | −0.845237 | −0.0304602 | ||||||||
\(771\) | −20.5594 | −0.740430 | ||||||||
\(772\) | 6.32594 | 0.227676 | ||||||||
\(773\) | −51.9172 | −1.86733 | −0.933665 | − | 0.358147i | \(-0.883409\pi\) | ||||
−0.933665 | + | 0.358147i | \(0.883409\pi\) | |||||||
\(774\) | 1.93582 | 0.0695817 | ||||||||
\(775\) | −43.0651 | −1.54694 | ||||||||
\(776\) | 25.5030 | 0.915504 | ||||||||
\(777\) | 4.70233 | 0.168695 | ||||||||
\(778\) | −35.9263 | −1.28802 | ||||||||
\(779\) | −8.27570 | −0.296508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3236 | 0.405189 | ||||||||
\(782\) | −41.2855 | −1.47637 | ||||||||
\(783\) | 10.6604 | 0.380973 | ||||||||
\(784\) | −4.57398 | −0.163356 | ||||||||
\(785\) | −2.25341 | −0.0804278 | ||||||||
\(786\) | 23.7861 | 0.848423 | ||||||||
\(787\) | 1.28136 | 0.0456757 | 0.0228378 | − | 0.999739i | \(-0.492730\pi\) | ||||
0.0228378 | + | 0.999739i | \(0.492730\pi\) | |||||||
\(788\) | 1.23947 | 0.0441545 | ||||||||
\(789\) | 16.1061 | 0.573391 | ||||||||
\(790\) | −1.51249 | −0.0538119 | ||||||||
\(791\) | −7.57398 | −0.269300 | ||||||||
\(792\) | −11.5817 | −0.411538 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 26.6982 | 0.947484 | ||||||||
\(795\) | 1.14559 | 0.0406300 | ||||||||
\(796\) | −3.38144 | −0.119852 | ||||||||
\(797\) | −48.4466 | −1.71607 | −0.858033 | − | 0.513595i | \(-0.828313\pi\) | ||||
−0.858033 | + | 0.513595i | \(0.828313\pi\) | |||||||
\(798\) | 1.16250 | 0.0411522 | ||||||||
\(799\) | 29.2499 | 1.03479 | ||||||||
\(800\) | 9.68954 | 0.342577 | ||||||||
\(801\) | −6.75877 | −0.238809 | ||||||||
\(802\) | −14.2199 | −0.502121 | ||||||||
\(803\) | 26.9587 | 0.951353 | ||||||||
\(804\) | 4.52528 | 0.159594 | ||||||||
\(805\) | 0.660444 | 0.0232776 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.29767 | −0.151285 | ||||||||
\(808\) | 15.0865 | 0.530740 | ||||||||
\(809\) | 10.2849 | 0.361597 | 0.180798 | − | 0.983520i | \(-0.442132\pi\) | ||||
0.180798 | + | 0.983520i | \(0.442132\pi\) | |||||||
\(810\) | 0.184793 | 0.00649295 | ||||||||
\(811\) | −3.60813 | −0.126698 | −0.0633492 | − | 0.997991i | \(-0.520178\pi\) | ||||
−0.0633492 | + | 0.997991i | \(0.520178\pi\) | |||||||
\(812\) | −3.70233 | −0.129926 | ||||||||
\(813\) | 11.9017 | 0.417410 | ||||||||
\(814\) | −32.9527 | −1.15499 | ||||||||
\(815\) | 2.41653 | 0.0846472 | ||||||||
\(816\) | −22.5098 | −0.788001 | ||||||||
\(817\) | −0.958720 | −0.0335414 | ||||||||
\(818\) | 22.1962 | 0.776070 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.456873 | 0.0159547 | ||||||||
\(821\) | −51.7398 | −1.80573 | −0.902865 | − | 0.429923i | \(-0.858541\pi\) | ||||
−0.902865 | + | 0.429923i | \(0.858541\pi\) | |||||||
\(822\) | −2.39961 | −0.0836962 | ||||||||
\(823\) | 37.6519 | 1.31246 | 0.656231 | − | 0.754560i | \(-0.272150\pi\) | ||||
0.656231 | + | 0.754560i | \(0.272150\pi\) | |||||||
\(824\) | 6.98545 | 0.243350 | ||||||||
\(825\) | −22.8033 | −0.793911 | ||||||||
\(826\) | 13.7784 | 0.479411 | ||||||||
\(827\) | 31.3509 | 1.09018 | 0.545089 | − | 0.838378i | \(-0.316496\pi\) | ||||
0.545089 | + | 0.838378i | \(0.316496\pi\) | |||||||
\(828\) | −1.90167 | −0.0660877 | ||||||||
\(829\) | 38.4635 | 1.33589 | 0.667946 | − | 0.744210i | \(-0.267174\pi\) | ||||
0.667946 | + | 0.744210i | \(0.267174\pi\) | |||||||
\(830\) | 2.26352 | 0.0785679 | ||||||||
\(831\) | 10.8229 | 0.375444 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.92127 | 0.170512 | ||||||||
\(834\) | 16.0915 | 0.557204 | ||||||||
\(835\) | −0.243594 | −0.00842990 | ||||||||
\(836\) | −1.20533 | −0.0416871 | ||||||||
\(837\) | 8.63816 | 0.298578 | ||||||||
\(838\) | 8.48608 | 0.293147 | ||||||||
\(839\) | 17.6099 | 0.607961 | 0.303980 | − | 0.952678i | \(-0.401684\pi\) | ||||
0.303980 | + | 0.952678i | \(0.401684\pi\) | |||||||
\(840\) | 0.305407 | 0.0105376 | ||||||||
\(841\) | 84.6451 | 2.91880 | ||||||||
\(842\) | 38.1411 | 1.31443 | ||||||||
\(843\) | 6.83481 | 0.235403 | ||||||||
\(844\) | −7.66044 | −0.263683 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.10607 | 0.313073 | ||||||||
\(847\) | −9.92127 | −0.340899 | ||||||||
\(848\) | −43.4434 | −1.49185 | ||||||||
\(849\) | −22.7442 | −0.780580 | ||||||||
\(850\) | −37.5895 | −1.28931 | ||||||||
\(851\) | 25.7483 | 0.882642 | ||||||||
\(852\) | 0.859785 | 0.0294557 | ||||||||
\(853\) | −47.8120 | −1.63705 | −0.818526 | − | 0.574469i | \(-0.805209\pi\) | ||||
−0.818526 | + | 0.574469i | \(0.805209\pi\) | |||||||
\(854\) | 14.4834 | 0.495611 | ||||||||
\(855\) | −0.0915189 | −0.00312988 | ||||||||
\(856\) | 9.78611 | 0.334482 | ||||||||
\(857\) | −17.7537 | −0.606455 | −0.303228 | − | 0.952918i | \(-0.598064\pi\) | ||||
−0.303228 | + | 0.952918i | \(0.598064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.9103 | 0.986408 | 0.493204 | − | 0.869914i | \(-0.335826\pi\) | ||||
0.493204 | + | 0.869914i | \(0.335826\pi\) | |||||||
\(860\) | 0.0529276 | 0.00180482 | ||||||||
\(861\) | −10.9067 | −0.371700 | ||||||||
\(862\) | 26.2094 | 0.892697 | ||||||||
\(863\) | −12.2594 | −0.417315 | −0.208657 | − | 0.977989i | \(-0.566909\pi\) | ||||
−0.208657 | + | 0.977989i | \(0.566909\pi\) | |||||||
\(864\) | −1.94356 | −0.0661214 | ||||||||
\(865\) | 0.265273 | 0.00901955 | ||||||||
\(866\) | −18.2267 | −0.619368 | ||||||||
\(867\) | 7.21894 | 0.245168 | ||||||||
\(868\) | −3.00000 | −0.101827 | ||||||||
\(869\) | −37.4371 | −1.26997 | ||||||||
\(870\) | 1.96997 | 0.0667883 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 30.5107 | 1.03322 | ||||||||
\(873\) | −10.0719 | −0.340883 | ||||||||
\(874\) | 6.36547 | 0.215315 | ||||||||
\(875\) | 1.20439 | 0.0407159 | ||||||||
\(876\) | 2.04694 | 0.0691597 | ||||||||
\(877\) | −5.71925 | −0.193125 | −0.0965626 | − | 0.995327i | \(-0.530785\pi\) | ||||
−0.0965626 | + | 0.995327i | \(0.530785\pi\) | |||||||
\(878\) | −19.0511 | −0.642942 | ||||||||
\(879\) | 20.9982 | 0.708253 | ||||||||
\(880\) | −2.52341 | −0.0850643 | ||||||||
\(881\) | −8.74422 | −0.294600 | −0.147300 | − | 0.989092i | \(-0.547058\pi\) | ||||
−0.147300 | + | 0.989092i | \(0.547058\pi\) | |||||||
\(882\) | 1.53209 | 0.0515881 | ||||||||
\(883\) | 20.9923 | 0.706446 | 0.353223 | − | 0.935539i | \(-0.385086\pi\) | ||||
0.353223 | + | 0.935539i | \(0.385086\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.08471 | −0.0364622 | ||||||||
\(886\) | 3.48751 | 0.117165 | ||||||||
\(887\) | 13.7743 | 0.462494 | 0.231247 | − | 0.972895i | \(-0.425719\pi\) | ||||
0.231247 | + | 0.972895i | \(0.425719\pi\) | |||||||
\(888\) | 11.9067 | 0.399564 | ||||||||
\(889\) | 9.87939 | 0.331344 | ||||||||
\(890\) | −1.24897 | −0.0418656 | ||||||||
\(891\) | 4.57398 | 0.153234 | ||||||||
\(892\) | −1.19934 | −0.0401569 | ||||||||
\(893\) | −4.50980 | −0.150915 | ||||||||
\(894\) | 0.381445 | 0.0127574 | ||||||||
\(895\) | −1.03447 | −0.0345786 | ||||||||
\(896\) | −13.3405 | −0.445674 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.268571 | 0.00896232 | ||||||||
\(899\) | 92.0866 | 3.07126 | ||||||||
\(900\) | −1.73143 | −0.0577143 | ||||||||
\(901\) | 46.7420 | 1.55720 | ||||||||
\(902\) | 76.4315 | 2.54489 | ||||||||
\(903\) | −1.26352 | −0.0420473 | ||||||||
\(904\) | −19.1780 | −0.637850 | ||||||||
\(905\) | 1.43344 | 0.0476491 | ||||||||
\(906\) | 29.0351 | 0.964626 | ||||||||
\(907\) | 25.4908 | 0.846408 | 0.423204 | − | 0.906034i | \(-0.360905\pi\) | ||||
0.423204 | + | 0.906034i | \(0.360905\pi\) | |||||||
\(908\) | −1.77837 | −0.0590173 | ||||||||
\(909\) | −5.95811 | −0.197618 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.8485 | −0.525085 | −0.262543 | − | 0.964920i | \(-0.584561\pi\) | ||||
−0.262543 | + | 0.964920i | \(0.584561\pi\) | |||||||
\(912\) | 3.47060 | 0.114923 | ||||||||
\(913\) | 56.0265 | 1.85421 | ||||||||
\(914\) | −17.6263 | −0.583026 | ||||||||
\(915\) | −1.14022 | −0.0376943 | ||||||||
\(916\) | −5.33544 | −0.176288 | ||||||||
\(917\) | −15.5253 | −0.512690 | ||||||||
\(918\) | 7.53983 | 0.248851 | ||||||||
\(919\) | 44.7921 | 1.47755 | 0.738777 | − | 0.673949i | \(-0.235403\pi\) | ||||
0.738777 | + | 0.673949i | \(0.235403\pi\) | |||||||
\(920\) | 1.67230 | 0.0551342 | ||||||||
\(921\) | −15.8821 | −0.523332 | ||||||||
\(922\) | 12.9932 | 0.427908 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.58853 | −0.0522587 | ||||||||
\(925\) | 23.4433 | 0.770810 | ||||||||
\(926\) | −17.2804 | −0.567870 | ||||||||
\(927\) | −2.75877 | −0.0906099 | ||||||||
\(928\) | −20.7192 | −0.680143 | ||||||||
\(929\) | 18.6587 | 0.612172 | 0.306086 | − | 0.952004i | \(-0.400981\pi\) | ||||
0.306086 | + | 0.952004i | \(0.400981\pi\) | |||||||
\(930\) | 1.59627 | 0.0523436 | ||||||||
\(931\) | −0.758770 | −0.0248677 | ||||||||
\(932\) | 2.16426 | 0.0708926 | ||||||||
\(933\) | −10.1976 | −0.333854 | ||||||||
\(934\) | 31.1111 | 1.01799 | ||||||||
\(935\) | 2.71501 | 0.0887905 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.1653 | 1.86751 | 0.933755 | − | 0.357914i | \(-0.116512\pi\) | ||||
0.933755 | + | 0.357914i | \(0.116512\pi\) | |||||||
\(938\) | −19.9632 | −0.651820 | ||||||||
\(939\) | −18.6578 | −0.608873 | ||||||||
\(940\) | 0.248970 | 0.00812052 | ||||||||
\(941\) | 11.7665 | 0.383577 | 0.191789 | − | 0.981436i | \(-0.438571\pi\) | ||||
0.191789 | + | 0.981436i | \(0.438571\pi\) | |||||||
\(942\) | −28.6236 | −0.932608 | ||||||||
\(943\) | −59.7214 | −1.94480 | ||||||||
\(944\) | 41.1347 | 1.33882 | ||||||||
\(945\) | −0.120615 | −0.00392360 | ||||||||
\(946\) | 8.85441 | 0.287882 | ||||||||
\(947\) | 6.79561 | 0.220828 | 0.110414 | − | 0.993886i | \(-0.464782\pi\) | ||||
0.110414 | + | 0.993886i | \(0.464782\pi\) | |||||||
\(948\) | −2.84255 | −0.0923217 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5.79561 | 0.188034 | ||||||||
\(951\) | −15.3746 | −0.498557 | ||||||||
\(952\) | 12.4611 | 0.403867 | ||||||||
\(953\) | 22.7847 | 0.738068 | 0.369034 | − | 0.929416i | \(-0.379689\pi\) | ||||
0.369034 | + | 0.929416i | \(0.379689\pi\) | |||||||
\(954\) | 14.5517 | 0.471128 | ||||||||
\(955\) | −1.66456 | −0.0538640 | ||||||||
\(956\) | −1.54664 | −0.0500218 | ||||||||
\(957\) | 48.7606 | 1.57621 | ||||||||
\(958\) | −35.2422 | −1.13862 | ||||||||
\(959\) | 1.56624 | 0.0505764 | ||||||||
\(960\) | 0.744223 | 0.0240197 | ||||||||
\(961\) | 43.6177 | 1.40702 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.86484 | −0.124543 | ||||||||
\(964\) | −3.14197 | −0.101196 | ||||||||
\(965\) | 2.19698 | 0.0707232 | ||||||||
\(966\) | 8.38919 | 0.269918 | ||||||||
\(967\) | −38.8033 | −1.24783 | −0.623916 | − | 0.781492i | \(-0.714459\pi\) | ||||
−0.623916 | + | 0.781492i | \(0.714459\pi\) | |||||||
\(968\) | −25.1215 | −0.807437 | ||||||||
\(969\) | −3.73412 | −0.119957 | ||||||||
\(970\) | −1.86122 | −0.0597600 | ||||||||
\(971\) | −21.7885 | −0.699225 | −0.349613 | − | 0.936894i | \(-0.613687\pi\) | ||||
−0.349613 | + | 0.936894i | \(0.613687\pi\) | |||||||
\(972\) | 0.347296 | 0.0111395 | ||||||||
\(973\) | −10.5030 | −0.336710 | ||||||||
\(974\) | 26.3482 | 0.844252 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 43.2395 | 1.38406 | ||||||||
\(977\) | −35.8007 | −1.14536 | −0.572682 | − | 0.819777i | \(-0.694097\pi\) | ||||
−0.572682 | + | 0.819777i | \(0.694097\pi\) | |||||||
\(978\) | 30.6955 | 0.981535 | ||||||||
\(979\) | −30.9145 | −0.988031 | ||||||||
\(980\) | 0.0418891 | 0.00133810 | ||||||||
\(981\) | −12.0496 | −0.384715 | ||||||||
\(982\) | 62.1380 | 1.98290 | ||||||||
\(983\) | 16.7060 | 0.532837 | 0.266419 | − | 0.963857i | \(-0.414160\pi\) | ||||
0.266419 | + | 0.963857i | \(0.414160\pi\) | |||||||
\(984\) | −27.6168 | −0.880391 | ||||||||
\(985\) | 0.430465 | 0.0137158 | ||||||||
\(986\) | 80.3779 | 2.55975 | ||||||||
\(987\) | −5.94356 | −0.189186 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.91859 | −0.219998 | ||||||||
\(990\) | 0.845237 | 0.0268634 | ||||||||
\(991\) | 14.1834 | 0.450549 | 0.225275 | − | 0.974295i | \(-0.427672\pi\) | ||||
0.225275 | + | 0.974295i | \(0.427672\pi\) | |||||||
\(992\) | −16.7888 | −0.533045 | ||||||||
\(993\) | −6.95636 | −0.220753 | ||||||||
\(994\) | −3.79292 | −0.120304 | ||||||||
\(995\) | −1.17436 | −0.0372298 | ||||||||
\(996\) | 4.25402 | 0.134794 | ||||||||
\(997\) | −5.55674 | −0.175984 | −0.0879919 | − | 0.996121i | \(-0.528045\pi\) | ||||
−0.0879919 | + | 0.996121i | \(0.528045\pi\) | |||||||
\(998\) | −8.49937 | −0.269043 | ||||||||
\(999\) | −4.70233 | −0.148775 |
(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 | 3549.2.a.o.1.3 | 3 | ||
13.3 | even | 3 | 273.2.k.a.22.1 | ✓ | 6 | ||
13.9 | even | 3 | 273.2.k.a.211.1 | yes | 6 | ||
13.12 | even | 2 | 3549.2.a.n.1.1 | 3 | |||
39.29 | odd | 6 | 819.2.o.g.568.3 | 6 | |||
39.35 | odd | 6 | 819.2.o.g.757.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.k.a.22.1 | ✓ | 6 | 13.3 | even | 3 | ||
273.2.k.a.211.1 | yes | 6 | 13.9 | even | 3 | ||
819.2.o.g.568.3 | 6 | 39.29 | odd | 6 | |||
819.2.o.g.757.3 | 6 | 39.35 | odd | 6 | |||
3549.2.a.n.1.1 | 3 | 13.12 | even | 2 | |||
3549.2.a.o.1.3 | 3 | 1.1 | even | 1 | trivial |