Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-2.53438\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | 2.53438 | 1.46322 | 0.731611 | − | 0.681722i | \(-0.238769\pi\) | ||||
0.731611 | + | 0.681722i | \(0.238769\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.27936 | −1.01936 | −0.509680 | − | 0.860364i | \(-0.670236\pi\) | ||||
−0.509680 | + | 0.860364i | \(0.670236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.27718 | 0.482728 | 0.241364 | − | 0.970435i | \(-0.422405\pi\) | ||||
0.241364 | + | 0.970435i | \(0.422405\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.42306 | 1.14102 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.683995 | 0.206232 | 0.103116 | − | 0.994669i | \(-0.467119\pi\) | ||||
0.103116 | + | 0.994669i | \(0.467119\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.05395 | −1.12436 | −0.562181 | − | 0.827014i | \(-0.690038\pi\) | ||||
−0.562181 | + | 0.827014i | \(0.690038\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.77675 | −1.49155 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.471295 | 0.114306 | 0.0571529 | − | 0.998365i | \(-0.481798\pi\) | ||||
0.0571529 | + | 0.998365i | \(0.481798\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.23685 | 0.706338 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.28297 | −0.893061 | −0.446531 | − | 0.894768i | \(-0.647341\pi\) | ||||
−0.446531 | + | 0.894768i | \(0.647341\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.195468 | 0.0390937 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.07220 | 0.206344 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.77368 | −1.81493 | −0.907464 | − | 0.420131i | \(-0.861984\pi\) | ||||
−0.907464 | + | 0.420131i | \(0.861984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.37733 | −1.68422 | −0.842109 | − | 0.539308i | \(-0.818686\pi\) | ||||
−0.842109 | + | 0.539308i | \(0.818686\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.73350 | 0.301764 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.91114 | −0.492073 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.27596 | 0.374166 | 0.187083 | − | 0.982344i | \(-0.440097\pi\) | ||||
0.187083 | + | 0.982344i | \(0.440097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.2742 | −1.64519 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.23060 | 0.192187 | 0.0960937 | − | 0.995372i | \(-0.469365\pi\) | ||||
0.0960937 | + | 0.995372i | \(0.469365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.166983 | −0.0254646 | −0.0127323 | − | 0.999919i | \(-0.504053\pi\) | ||||
−0.0127323 | + | 0.999919i | \(0.504053\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.80238 | −1.16311 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.60808 | 0.818023 | 0.409011 | − | 0.912529i | \(-0.365874\pi\) | ||||
0.409011 | + | 0.912529i | \(0.365874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.36882 | −0.766974 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.19444 | 0.167255 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.55907 | −0.210225 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.53438 | −0.335686 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.90151 | −1.02869 | −0.514345 | − | 0.857584i | \(-0.671965\pi\) | ||||
−0.514345 | + | 0.857584i | \(0.671965\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.280568 | 0.0359230 | 0.0179615 | − | 0.999839i | \(-0.494282\pi\) | ||||
0.0179615 | + | 0.999839i | \(0.494282\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.37185 | 0.550802 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.24039 | 1.14613 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.83519 | 0.346374 | 0.173187 | − | 0.984889i | \(-0.444594\pi\) | ||||
0.173187 | + | 0.984889i | \(0.444594\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.8547 | −1.30675 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.88384 | 1.17300 | 0.586498 | − | 0.809951i | \(-0.300506\pi\) | ||||
0.586498 | + | 0.809951i | \(0.300506\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.2089 | 1.42894 | 0.714471 | − | 0.699665i | \(-0.246667\pi\) | ||||
0.714471 | + | 0.699665i | \(0.246667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.495391 | 0.0572028 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.873582 | 0.0995539 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.28523 | −1.04467 | −0.522335 | − | 0.852740i | \(-0.674939\pi\) | ||||
−0.522335 | + | 0.852740i | \(0.674939\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.55184 | −0.839093 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.4165 | 1.36289 | 0.681444 | − | 0.731870i | \(-0.261352\pi\) | ||||
0.681444 | + | 0.731870i | \(0.261352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.07425 | −0.116519 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.7702 | −2.65564 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.1886 | −1.39799 | −0.698995 | − | 0.715126i | \(-0.746369\pi\) | ||||
−0.698995 | + | 0.715126i | \(0.746369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.17761 | −0.542761 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.7657 | −2.46438 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.27936 | 0.233857 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0580025 | −0.00588926 | −0.00294463 | − | 0.999996i | \(-0.500937\pi\) | ||||
−0.00294463 | + | 0.999996i | \(0.500937\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.34136 | 0.235315 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.6990 | −1.46260 | −0.731302 | − | 0.682054i | \(-0.761087\pi\) | ||||
−0.731302 | + | 0.682054i | \(0.761087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.8976 | 1.46790 | 0.733952 | − | 0.679201i | \(-0.237674\pi\) | ||||
0.733952 | + | 0.679201i | \(0.237674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.37793 | −0.720012 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.2259 | 1.76196 | 0.880981 | − | 0.473152i | \(-0.156884\pi\) | ||||
0.880981 | + | 0.473152i | \(0.156884\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.25332 | −0.790524 | −0.395262 | − | 0.918568i | \(-0.629346\pi\) | ||||
−0.395262 | + | 0.918568i | \(0.629346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.76815 | 0.547488 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7052 | 1.10113 | 0.550564 | − | 0.834793i | \(-0.314413\pi\) | ||||
0.550564 | + | 0.834793i | \(0.314413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.76242 | 0.910350 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.8769 | −1.28292 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.601927 | 0.0551786 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5322 | −0.957468 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.11880 | 0.281213 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.9512 | 0.979509 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.48112 | −0.663842 | −0.331921 | − | 0.943307i | \(-0.607697\pi\) | ||||
−0.331921 | + | 0.943307i | \(0.607697\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.423197 | −0.0372604 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.12916 | −0.186026 | −0.0930130 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930130 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.27718 | −0.110745 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.44392 | −0.210339 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.92478 | −0.164445 | −0.0822224 | − | 0.996614i | \(-0.526202\pi\) | ||||
−0.0822224 | + | 0.996614i | \(0.526202\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2021 | −1.11979 | −0.559894 | − | 0.828564i | \(-0.689158\pi\) | ||||
−0.559894 | + | 0.828564i | \(0.689158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.2130 | 1.19695 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.77288 | −0.231880 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.2777 | 1.85006 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.6066 | −1.12225 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.44056 | 0.199938 | 0.0999692 | − | 0.994991i | \(-0.468126\pi\) | ||||
0.0999692 | + | 0.994991i | \(0.468126\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.96295 | −0.648016 | −0.324008 | − | 0.946054i | \(-0.605030\pi\) | ||||
−0.324008 | + | 0.946054i | \(0.605030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.61327 | 0.130425 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.3743 | 1.71682 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.20936 | 0.256134 | 0.128067 | − | 0.991765i | \(-0.459123\pi\) | ||||
0.128067 | + | 0.991765i | \(0.459123\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.53438 | 0.200989 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.47011 | −0.431105 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.18403 | −0.562697 | −0.281348 | − | 0.959606i | \(-0.590782\pi\) | ||||
−0.281348 | + | 0.959606i | \(0.590782\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.95126 | −0.307606 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.29950 | −0.487470 | −0.243735 | − | 0.969842i | \(-0.578373\pi\) | ||||
−0.243735 | + | 0.969842i | \(0.578373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.43448 | 0.264191 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.42306 | −0.261768 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.62900 | −0.427965 | −0.213983 | − | 0.976837i | \(-0.568644\pi\) | ||||
−0.213983 | + | 0.976837i | \(0.568644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.249648 | 0.0188716 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.0254 | −1.50520 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.95898 | −0.445395 | −0.222698 | − | 0.974888i | \(-0.571486\pi\) | ||||
−0.222698 | + | 0.974888i | \(0.571486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.4109 | −0.922497 | −0.461248 | − | 0.887271i | \(-0.652598\pi\) | ||||
−0.461248 | + | 0.887271i | \(0.652598\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.711065 | 0.0525634 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.18773 | −0.381410 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.322363 | 0.0235735 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.36938 | 0.0996079 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.3275 | −1.03670 | −0.518351 | − | 0.855168i | \(-0.673454\pi\) | ||||
−0.518351 | + | 0.855168i | \(0.673454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.27032 | −0.451347 | −0.225674 | − | 0.974203i | \(-0.572458\pi\) | ||||
−0.225674 | + | 0.974203i | \(0.572458\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.4186 | 1.67704 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3079 | −1.23314 | −0.616570 | − | 0.787300i | \(-0.711478\pi\) | ||||
−0.616570 | + | 0.787300i | \(0.711478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6715 | 0.969146 | 0.484573 | − | 0.874751i | \(-0.338975\pi\) | ||||
0.484573 | + | 0.874751i | \(0.338975\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.18544 | 0.506822 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.4827 | −0.876115 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.80498 | −0.195908 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.6609 | −1.01900 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.683995 | −0.0473129 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0437 | 1.24218 | 0.621091 | − | 0.783739i | \(-0.286690\pi\) | ||||
0.621091 | + | 0.783739i | \(0.286690\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.0494 | 1.71635 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.380614 | 0.0259576 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.9765 | −0.813018 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.9419 | 2.09086 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.91061 | −0.128521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.67427 | 0.379977 | 0.189989 | − | 0.981786i | \(-0.439155\pi\) | ||||
0.189989 | + | 0.981786i | \(0.439155\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.669101 | 0.0446067 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.4395 | 1.88760 | 0.943799 | − | 0.330521i | \(-0.107224\pi\) | ||||
0.943799 | + | 0.330521i | \(0.107224\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.0630 | −1.52405 | −0.762024 | − | 0.647548i | \(-0.775794\pi\) | ||||
−0.762024 | + | 0.647548i | \(0.775794\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.21399 | 0.145670 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.42250 | −0.289727 | −0.144864 | − | 0.989452i | \(-0.546274\pi\) | ||||
−0.144864 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.7828 | −0.833859 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.5323 | −1.52858 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.23936 | 0.0801675 | 0.0400837 | − | 0.999196i | \(-0.487238\pi\) | ||||
0.0400837 | + | 0.999196i | \(0.487238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3316 | −0.665518 | −0.332759 | − | 0.943012i | \(-0.607980\pi\) | ||||
−0.332759 | + | 0.943012i | \(0.607980\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3558 | −1.43412 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2375 | 0.781822 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.05395 | 0.257946 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 31.4681 | 1.99421 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.88927 | −0.245489 | −0.122744 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122744 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.92953 | −0.184178 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.72255 | −0.170493 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.70877 | 0.480860 | 0.240430 | − | 0.970667i | \(-0.422712\pi\) | ||||
0.240430 | + | 0.970667i | \(0.422712\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.90681 | 0.180620 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33.4559 | −2.07087 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.7299 | 0.723298 | 0.361649 | − | 0.932314i | \(-0.382214\pi\) | ||||
0.361649 | + | 0.932314i | \(0.382214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.27936 | −0.140020 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −33.4249 | −2.04557 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.2401 | −1.29503 | −0.647516 | − | 0.762052i | \(-0.724192\pi\) | ||||
−0.647516 | + | 0.762052i | \(0.724192\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.4709 | −0.636065 | −0.318032 | − | 0.948080i | \(-0.603022\pi\) | ||||
−0.318032 | + | 0.948080i | \(0.603022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.1220 | −0.794180 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.133699 | 0.00806238 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.1470 | −1.09035 | −0.545173 | − | 0.838323i | \(-0.683536\pi\) | ||||
−0.545173 | + | 0.838323i | \(0.683536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −32.0992 | −1.92173 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.75924 | −0.343568 | −0.171784 | − | 0.985135i | \(-0.554953\pi\) | ||||
−0.171784 | + | 0.985135i | \(0.554953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.4253 | −0.798053 | −0.399027 | − | 0.916939i | \(-0.630652\pi\) | ||||
−0.399027 | + | 0.916939i | \(0.630652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.77675 | 0.342185 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.57169 | 0.0927742 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7779 | −0.986934 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.147000 | −0.00861730 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.18029 | 0.127374 | 0.0636868 | − | 0.997970i | \(-0.479714\pi\) | ||||
0.0636868 | + | 0.997970i | \(0.479714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.0104 | 1.04860 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.733376 | 0.0425548 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.3629 | 1.00412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.213267 | −0.0122925 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −37.2527 | −2.14011 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.639514 | −0.0366185 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.4042 | 0.879165 | 0.439583 | − | 0.898202i | \(-0.355126\pi\) | ||||
0.439583 | + | 0.898202i | \(0.355126\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 37.7561 | 2.14787 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9536 | 0.677826 | 0.338913 | − | 0.940818i | \(-0.389941\pi\) | ||||
0.338913 | + | 0.940818i | \(0.389941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.866842 | 0.0489968 | 0.0244984 | − | 0.999700i | \(-0.492201\pi\) | ||||
0.0244984 | + | 0.999700i | \(0.492201\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.96502 | −0.561465 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.9663 | 1.17758 | 0.588792 | − | 0.808284i | \(-0.299604\pi\) | ||||
0.588792 | + | 0.808284i | \(0.299604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.68515 | −0.374296 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 46.1912 | 2.57814 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.471295 | −0.0262236 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.792419 | −0.0439555 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.9170 | −1.15671 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.16251 | 0.394882 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.0956 | 1.48931 | 0.744654 | − | 0.667451i | \(-0.232615\pi\) | ||||
0.744654 | + | 0.667451i | \(0.232615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.79076 | 0.426931 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.46242 | −0.353080 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.9085 | 1.84711 | 0.923556 | − | 0.383464i | \(-0.125269\pi\) | ||||
0.923556 | + | 0.383464i | \(0.125269\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.6653 | 1.61120 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.41404 | −0.347340 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.7972 | −0.852967 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.7416 | 1.33205 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.1422 | −1.56444 | −0.782219 | − | 0.623004i | \(-0.785912\pi\) | ||||
−0.782219 | + | 0.623004i | \(0.785912\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2954 | −0.604629 | −0.302315 | − | 0.953208i | \(-0.597759\pi\) | ||||
−0.302315 | + | 0.953208i | \(0.597759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.34662 | −0.232005 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.3141 | 1.18766 | 0.593830 | − | 0.804591i | \(-0.297615\pi\) | ||||
0.593830 | + | 0.804591i | \(0.297615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.5288 | −1.19570 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.52551 | 0.0807385 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.3908 | 1.70952 | 0.854761 | − | 0.519021i | \(-0.173704\pi\) | ||||
0.854761 | + | 0.519021i | \(0.173704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.6924 | −1.40099 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.8284 | −1.45661 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.8121 | 1.13858 | 0.569292 | − | 0.822135i | \(-0.307217\pi\) | ||||
0.569292 | + | 0.822135i | \(0.307217\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.21242 | 0.219290 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.27718 | 0.0663077 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.02171 | 0.467127 | 0.233563 | − | 0.972342i | \(-0.424961\pi\) | ||||
0.233563 | + | 0.972342i | \(0.424961\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.7546 | 1.43324 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.6220 | 2.04064 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0094 | 0.616881 | 0.308440 | − | 0.951244i | \(-0.400193\pi\) | ||||
0.308440 | + | 0.951244i | \(0.400193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.9600 | −0.971349 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.44318 | −0.0737430 | −0.0368715 | − | 0.999320i | \(-0.511739\pi\) | ||||
−0.0368715 | + | 0.999320i | \(0.511739\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.99121 | −0.101481 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.571592 | −0.0290557 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.6304 | 1.65443 | 0.827213 | − | 0.561889i | \(-0.189925\pi\) | ||||
0.827213 | + | 0.561889i | \(0.189925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.01854 | −0.102082 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.39610 | −0.272197 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.1644 | 1.06489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5675 | −0.982065 | −0.491032 | − | 0.871141i | \(-0.663380\pi\) | ||||
−0.491032 | + | 0.871141i | \(0.663380\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.23685 | −0.162045 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.11783 | −0.105759 | −0.0528797 | − | 0.998601i | \(-0.516840\pi\) | ||||
−0.0528797 | + | 0.998601i | \(0.516840\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0152 | 1.89367 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.2133 | 0.855337 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.55675 | 0.0771651 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6225 | 0.574694 | 0.287347 | − | 0.957827i | \(-0.407227\pi\) | ||||
0.287347 | + | 0.957827i | \(0.407227\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.87811 | −0.240619 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.0916 | −0.496577 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.3017 | −1.38927 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.4591 | −1.63850 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.4119 | −0.508657 | −0.254328 | − | 0.967118i | \(-0.581854\pi\) | ||||
−0.254328 | + | 0.967118i | \(0.581854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.67091 | 0.422594 | 0.211297 | − | 0.977422i | \(-0.432231\pi\) | ||||
0.211297 | + | 0.977422i | \(0.432231\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.1968 | 0.933380 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.0921233 | 0.00446864 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.358335 | 0.0173410 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.02752 | −0.339292 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.404087 | −0.0194642 | −0.00973210 | − | 0.999953i | \(-0.503098\pi\) | ||||
−0.00973210 | + | 0.999953i | \(0.503098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.3610 | 1.36294 | 0.681472 | − | 0.731844i | \(-0.261340\pi\) | ||||
0.681472 | + | 0.731844i | \(0.261340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 56.4601 | 2.70705 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.28297 | 0.204882 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.2499 | 1.73011 | 0.865056 | − | 0.501676i | \(-0.167283\pi\) | ||||
0.865056 | + | 0.501676i | \(0.167283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.3778 | −0.875133 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.10105 | −0.289870 | −0.144935 | − | 0.989441i | \(-0.546297\pi\) | ||||
−0.144935 | + | 0.989441i | \(0.546297\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.0616 | 1.42505 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.18530 | 0.292554 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.12113 | 0.383260 | 0.191630 | − | 0.981467i | \(-0.438623\pi\) | ||||
0.191630 | + | 0.981467i | \(0.438623\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.841724 | 0.0396352 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.1811 | −0.948191 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.8016 | 0.553268 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.5365 | −0.960657 | −0.480329 | − | 0.877089i | \(-0.659483\pi\) | ||||
−0.480329 | + | 0.877089i | \(0.659483\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.505320 | 0.0235863 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.96682 | 0.138178 | 0.0690892 | − | 0.997610i | \(-0.477991\pi\) | ||||
0.0690892 | + | 0.997610i | \(0.477991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.4093 | −1.08792 | −0.543962 | − | 0.839110i | \(-0.683076\pi\) | ||||
−0.543962 | + | 0.839110i | \(0.683076\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 54.1704 | 2.51209 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.8918 | 1.29068 | 0.645339 | − | 0.763896i | \(-0.276716\pi\) | ||||
0.645339 | + | 0.763896i | \(0.276716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.62104 | 0.167204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.13371 | 0.374782 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.114215 | −0.00525163 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.195468 | −0.00896871 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.42306 | 0.156731 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.2425 | 0.467993 | 0.233996 | − | 0.972237i | \(-0.424820\pi\) | ||||
0.233996 | + | 0.972237i | \(0.424820\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.22663 | −0.420698 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.8633 | −0.630803 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.132208 | 0.00600328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.09948 | 0.276394 | 0.138197 | − | 0.990405i | \(-0.455869\pi\) | ||||
0.138197 | + | 0.990405i | \(0.455869\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.2070 | −0.823350 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.8845 | 1.07789 | 0.538946 | − | 0.842340i | \(-0.318823\pi\) | ||||
0.538946 | + | 0.842340i | \(0.318823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.60629 | −0.207457 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.33679 | −0.239871 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.6234 | 0.566237 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.4851 | −1.58853 | −0.794265 | − | 0.607572i | \(-0.792144\pi\) | ||||
−0.794265 | + | 0.607572i | \(0.792144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.9653 | −0.713277 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.8640 | 0.974867 | 0.487433 | − | 0.873160i | \(-0.337933\pi\) | ||||
0.487433 | + | 0.873160i | \(0.337933\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.5042 | 1.49092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.70427 | 0.386570 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.8469 | −1.27862 | −0.639309 | − | 0.768950i | \(-0.720779\pi\) | ||||
−0.639309 | + | 0.768950i | \(0.720779\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.5929 | 0.689790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.07220 | −0.0473386 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −33.9569 | −1.49632 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.83590 | 0.168703 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.2660 | −0.626208 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.8171 | 1.74442 | 0.872209 | − | 0.489134i | \(-0.162687\pi\) | ||||
0.872209 | + | 0.489134i | \(0.162687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.3763 | −0.847265 | −0.423633 | − | 0.905834i | \(-0.639245\pi\) | ||||
−0.423633 | + | 0.905834i | \(0.639245\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.632701 | 0.0276134 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.41949 | −0.192516 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.65616 | −0.202442 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.0474 | −1.17376 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.98879 | −0.216088 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.5433 | −1.79607 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.1023 | −0.651712 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.67224 | −0.158175 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.7548 | 0.763341 | 0.381670 | − | 0.924299i | \(-0.375349\pi\) | ||||
0.381670 | + | 0.924299i | \(0.375349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31.4539 | −1.34982 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.8123 | 0.805828 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.5212 | −1.09121 | −0.545604 | − | 0.838043i | \(-0.683700\pi\) | ||||
−0.545604 | + | 0.838043i | \(0.683700\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.960401 | 0.0409889 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.77368 | 0.416373 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.8589 | −0.504291 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.1477 | −0.558087 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2435 | 1.15435 | 0.577173 | − | 0.816622i | \(-0.304156\pi\) | ||||
0.577173 | + | 0.816622i | \(0.304156\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.676940 | 0.0286315 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.816990 | 0.0344933 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7988 | 0.750130 | 0.375065 | − | 0.926999i | \(-0.377620\pi\) | ||||
0.375065 | + | 0.926999i | \(0.377620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.6802 | −1.12245 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.64503 | −0.405053 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.8181 | 1.62734 | 0.813671 | − | 0.581326i | \(-0.197466\pi\) | ||||
0.813671 | + | 0.581326i | \(0.197466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.7885 | 0.618880 | 0.309440 | − | 0.950919i | \(-0.399858\pi\) | ||||
0.309440 | + | 0.950919i | \(0.399858\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.3113 | −1.51693 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.837186 | −0.0349131 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.1701 | −1.25600 | −0.627999 | − | 0.778214i | \(-0.716126\pi\) | ||||
−0.627999 | + | 0.778214i | \(0.716126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.8913 | −0.660422 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.8581 | 0.657904 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.683995 | 0.0283282 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.6304 | 1.30776 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.2448 | −0.753044 | −0.376522 | − | 0.926408i | \(-0.622880\pi\) | ||||
−0.376522 | + | 0.926408i | \(0.622880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.37733 | 0.386386 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −43.8648 | −1.80436 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.0618 | −1.07023 | −0.535115 | − | 0.844779i | \(-0.679732\pi\) | ||||
−0.535115 | + | 0.844779i | \(0.679732\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37201 | −0.0562468 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.6487 | 1.41808 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.7331 | 1.17400 | 0.587002 | − | 0.809585i | \(-0.300308\pi\) | ||||
0.587002 | + | 0.809585i | \(0.300308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.4158 | −1.15910 | −0.579552 | − | 0.814935i | \(-0.696772\pi\) | ||||
−0.579552 | + | 0.814935i | \(0.696772\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.70504 | 0.395220 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.0065 | 0.976004 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.7862 | −1.24957 | −0.624786 | − | 0.780796i | \(-0.714814\pi\) | ||||
−0.624786 | + | 0.780796i | \(0.714814\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.6359 | −1.28195 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.7349 | −0.919754 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.5989 | 1.03393 | 0.516964 | − | 0.856007i | \(-0.327062\pi\) | ||||
0.516964 | + | 0.856007i | \(0.327062\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.10887 | −0.286657 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.7094 | −1.59864 | −0.799319 | − | 0.600907i | \(-0.794806\pi\) | ||||
−0.799319 | + | 0.600907i | \(0.794806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.0046 | −1.72850 | −0.864251 | − | 0.503060i | \(-0.832207\pi\) | ||||
−0.864251 | + | 0.503060i | \(0.832207\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.59218 | −0.184278 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.8442 | −0.674848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.9391 | −1.03757 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.73350 | −0.0692293 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.07265 | 0.0427694 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.0678 | −1.55526 | −0.777631 | − | 0.628720i | \(-0.783579\pi\) | ||||
−0.777631 | + | 0.628720i | \(0.783579\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.7296 | 1.81759 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.0522 | 0.676694 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.7649 | 0.862357 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.8330 | 1.33841 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.3811 | 1.43697 | 0.718484 | − | 0.695543i | \(-0.244836\pi\) | ||||
0.718484 | + | 0.695543i | \(0.244836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.4795 | −1.24143 | −0.620715 | − | 0.784037i | \(-0.713157\pi\) | ||||
−0.620715 | + | 0.784037i | \(0.713157\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.964618 | 0.0379818 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.2170 | 1.62041 | 0.810203 | − | 0.586149i | \(-0.199357\pi\) | ||||
0.810203 | + | 0.586149i | \(0.199357\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.40459 | −0.212149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.3530 | −1.18963 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.0470 | −0.823631 | −0.411816 | − | 0.911267i | \(-0.635105\pi\) | ||||
−0.411816 | + | 0.911267i | \(0.635105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.85312 | 0.189627 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.7918 | 1.63045 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.7553 | −1.86028 | −0.930141 | − | 0.367203i | \(-0.880315\pi\) | ||||
−0.930141 | + | 0.367203i | \(0.880315\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5466 | −0.954752 | −0.477376 | − | 0.878699i | \(-0.658412\pi\) | ||||
−0.477376 | + | 0.878699i | \(0.658412\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.84219 | −0.188055 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.91114 | 0.112889 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.8604 | 1.62084 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.3807 | 0.555991 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.191907 | 0.00740849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.1448 | −0.737979 | −0.368989 | − | 0.929434i | \(-0.620296\pi\) | ||||
−0.368989 | + | 0.929434i | \(0.620296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.209580 | 0.00806675 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.2507 | −0.509264 | −0.254632 | − | 0.967038i | \(-0.581954\pi\) | ||||
−0.254632 | + | 0.967038i | \(0.581954\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0740795 | −0.00284291 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 72.0764 | 2.76198 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.8509 | −1.67791 | −0.838954 | − | 0.544203i | \(-0.816832\pi\) | ||||
−0.838954 | + | 0.544203i | \(0.816832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.38725 | 0.167628 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −58.4504 | −2.23002 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.05395 | −0.154443 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.5843 | 1.50586 | 0.752929 | − | 0.658102i | \(-0.228641\pi\) | ||||
0.752929 | + | 0.658102i | \(0.228641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.99033 | 0.113593 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30.0923 | 1.14147 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.579976 | 0.0219682 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.2083 | −0.423936 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.8680 | −1.65687 | −0.828435 | − | 0.560085i | \(-0.810769\pi\) | ||||
−0.828435 | + | 0.560085i | \(0.810769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.27596 | −0.0858396 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.3965 | −1.22012 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.7732 | −0.706039 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −43.1969 | −1.62229 | −0.811147 | − | 0.584843i | \(-0.801156\pi\) | ||||
−0.811147 | + | 0.584843i | \(0.801156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −31.7839 | −1.19199 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.1628 | 1.50411 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.32038 | 0.236369 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.14100 | 0.117303 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.62546 | 0.209794 | 0.104897 | − | 0.994483i | \(-0.466549\pi\) | ||||
0.104897 | + | 0.994483i | \(0.466549\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.0269 | 0.708598 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.1842 | −0.973800 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.91045 | −0.0709522 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.63839 | −0.172028 | −0.0860141 | − | 0.996294i | \(-0.527413\pi\) | ||||
−0.0860141 | + | 0.996294i | \(0.527413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.0024 | −1.25935 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.0786982 | −0.00291076 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.6696 | −0.874257 | −0.437128 | − | 0.899399i | \(-0.644004\pi\) | ||||
−0.437128 | + | 0.899399i | \(0.644004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.0143 | 1.14398 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.93926 | 0.0714334 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.8493 | −0.877311 | −0.438656 | − | 0.898655i | \(-0.644545\pi\) | ||||
−0.438656 | + | 0.898655i | \(0.644545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.2742 | 0.377433 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.10688 | −0.150667 | −0.0753334 | − | 0.997158i | \(-0.524002\pi\) | ||||
−0.0753334 | + | 0.997158i | \(0.524002\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.56291 | −0.203809 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.5025 | 1.55508 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.2777 | 0.850548 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.5478 | 1.44312 | 0.721560 | − | 0.692352i | \(-0.243425\pi\) | ||||
0.721560 | + | 0.692352i | \(0.243425\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.85688 | −0.359205 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.1504 | 0.660561 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.7611 | 1.04534 | 0.522670 | − | 0.852535i | \(-0.324936\pi\) | ||||
0.522670 | + | 0.852535i | \(0.324936\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.42453 | −0.269493 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3747 | −0.666083 | −0.333042 | − | 0.942912i | \(-0.608075\pi\) | ||||
−0.333042 | + | 0.942912i | \(0.608075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.5409 | −0.381608 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.67722 | −0.132950 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.0323 | 1.15662 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.6592 | 0.853174 | 0.426587 | − | 0.904447i | \(-0.359716\pi\) | ||||
0.426587 | + | 0.904447i | \(0.359716\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5369 | 0.703605 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.11589 | −0.255941 | −0.127970 | − | 0.991778i | \(-0.540846\pi\) | ||||
−0.127970 | + | 0.991778i | \(0.540846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.83297 | −0.0658423 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.36694 | 0.264288 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.23060 | −0.0440908 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.76049 | 0.241909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.4793 | −0.374499 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.31527 | −0.261093 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.0116 | −0.642045 | −0.321023 | − | 0.947072i | \(-0.604027\pi\) | ||||
−0.321023 | + | 0.947072i | \(0.604027\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.7280 | 1.05835 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.9496 | 0.531545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.13741 | −0.0403905 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.77675 | −0.204880 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.2309 | 0.893725 | 0.446863 | − | 0.894603i | \(-0.352541\pi\) | ||||
0.446863 | + | 0.894603i | \(0.352541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.64306 | 0.0935048 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −45.1454 | −1.59514 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.35082 | 0.294694 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.4683 | 0.439451 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −53.8304 | −1.89492 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.88600 | 0.136624 | 0.0683122 | − | 0.997664i | \(-0.478239\pi\) | ||||
0.0683122 | + | 0.997664i | \(0.478239\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.8142 | −1.39807 | −0.699033 | − | 0.715090i | \(-0.746386\pi\) | ||||
−0.699033 | + | 0.715090i | \(0.746386\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.5373 | −0.930704 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.3750 | 0.573590 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.166983 | 0.00584199 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.7233 | −0.619301 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.6695 | 0.581769 | 0.290885 | − | 0.956758i | \(-0.406050\pi\) | ||||
0.290885 | + | 0.956758i | \(0.406050\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.4097 | −0.606863 | −0.303432 | − | 0.952853i | \(-0.598132\pi\) | ||||
−0.303432 | + | 0.952853i | \(0.598132\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.338845 | 0.0117971 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.1975 | 1.43258 | 0.716288 | − | 0.697805i | \(-0.245840\pi\) | ||||
0.716288 | + | 0.697805i | \(0.245840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2073 | 0.701830 | 0.350915 | − | 0.936407i | \(-0.385871\pi\) | ||||
0.350915 | + | 0.936407i | \(0.385871\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.9913 | −1.59542 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.53030 | −0.0876696 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.3588 | 0.496907 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.0543 | −0.347528 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.8630 | −0.927412 | −0.463706 | − | 0.885989i | \(-0.653481\pi\) | ||||
−0.463706 | + | 0.885989i | \(0.653481\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.5249 | 2.29396 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.5961 | −0.502716 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.82841 | −0.269306 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.4514 | −0.462196 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.0248 | −1.16773 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.74788 | −0.334153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.3972 | −0.390234 | −0.195117 | − | 0.980780i | \(-0.562509\pi\) | ||||
−0.195117 | + | 0.980780i | \(0.562509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.80238 | 0.266836 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.1562 | 1.23507 | 0.617537 | − | 0.786542i | \(-0.288131\pi\) | ||||
0.617537 | + | 0.786542i | \(0.288131\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.5140 | 1.27996 | 0.639981 | − | 0.768391i | \(-0.278942\pi\) | ||||
0.639981 | + | 0.768391i | \(0.278942\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.98326 | 0.135749 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.4883 | −1.10591 | −0.552957 | − | 0.833209i | \(-0.686501\pi\) | ||||
−0.552957 | + | 0.833209i | \(0.686501\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.8305 | 0.436250 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −42.5215 | −1.44410 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.35105 | −0.215445 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.4937 | −0.389450 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.198546 | −0.00671977 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.9867 | 0.472836 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9563 | 0.640109 | 0.320055 | − | 0.947399i | \(-0.396299\pi\) | ||||
0.320055 | + | 0.947399i | \(0.396299\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.52567 | 0.186376 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.9684 | 0.504299 | 0.252149 | − | 0.967688i | \(-0.418863\pi\) | ||||
0.252149 | + | 0.967688i | \(0.418863\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.9519 | 1.44545 | 0.722724 | − | 0.691137i | \(-0.242890\pi\) | ||||
0.722724 | + | 0.691137i | \(0.242890\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 45.6450 | 1.53434 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.7975 | −1.13481 | −0.567404 | − | 0.823440i | \(-0.692052\pi\) | ||||
−0.567404 | + | 0.823440i | \(0.692052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.55472 | −0.320455 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.16542 | −0.173048 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.60808 | −0.187667 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.5826 | 0.454018 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.0042 | 1.46926 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 91.6510 | 3.05673 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.471295 | 0.0157011 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.540498 | −0.0179866 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.2889 | 0.940356 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.9182 | −1.75712 | −0.878560 | − | 0.477632i | \(-0.841495\pi\) | ||||
−0.878560 | + | 0.477632i | \(0.841495\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −50.3155 | −1.66886 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.46241 | 0.313503 | 0.156752 | − | 0.987638i | \(-0.449898\pi\) | ||||
0.156752 | + | 0.987638i | \(0.449898\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.49283 | 0.281071 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.62077 | −0.0535810 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.71932 | −0.0897998 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.5335 | −1.46902 | −0.734512 | − | 0.678596i | \(-0.762589\pi\) | ||||
−0.734512 | + | 0.678596i | \(0.762589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.0401 | 1.28641 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.0685 | −1.31887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.444879 | 0.0146275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 50.9954 | 1.67491 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 58.7018 | 1.92594 | 0.962971 | − | 0.269604i | \(-0.0868927\pi\) | ||||
0.962971 | + | 0.269604i | \(0.0868927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.36882 | 0.175956 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.2949 | 0.991811 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.734781 | −0.0240299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.1190 | −1.60465 | −0.802323 | − | 0.596890i | \(-0.796403\pi\) | ||||
−0.802323 | + | 0.596890i | \(0.796403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.19690 | 0.0716932 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.186194 | 0.00606975 | 0.00303487 | − | 0.999995i | \(-0.499034\pi\) | ||||
0.00303487 | + | 0.999995i | \(0.499034\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.27062 | −0.171635 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.12131 | −0.101536 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.5194 | −0.861764 | −0.430882 | − | 0.902408i | \(-0.641797\pi\) | ||||
−0.430882 | + | 0.902408i | \(0.641797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.4942 | −1.60665 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 53.1365 | 1.72307 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.310683 | −0.0100640 | −0.00503200 | − | 0.999987i | \(-0.501602\pi\) | ||||
−0.00503200 | + | 0.999987i | \(0.501602\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.6575 | 1.05677 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.9427 | −0.547679 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.45828 | −0.0793820 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.9342 | 1.83659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 62.3883 | 2.01043 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.2923 | 0.460085 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.4435 | −0.721734 | −0.360867 | − | 0.932617i | \(-0.617519\pi\) | ||||
−0.360867 | + | 0.932617i | \(0.617519\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.19444 | −0.0383709 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.77769 | 0.121232 | 0.0606159 | − | 0.998161i | \(-0.480694\pi\) | ||||
0.0606159 | + | 0.998161i | \(0.480694\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.8614 | −0.540553 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.00829 | −0.0643167 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0410 | −0.577184 | −0.288592 | − | 0.957452i | \(-0.593187\pi\) | ||||
−0.288592 | + | 0.957452i | \(0.593187\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.02094 | −0.288311 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.2516 | −0.902004 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.3170 | 1.54107 | 0.770537 | − | 0.637395i | \(-0.219988\pi\) | ||||
0.770537 | + | 0.637395i | \(0.219988\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.4510 | 1.25701 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.1525 | 0.577800 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.715183 | 0.0227415 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.2630 | −0.738974 | −0.369487 | − | 0.929236i | \(-0.620467\pi\) | ||||
−0.369487 | + | 0.929236i | \(0.620467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 68.6704 | 2.17919 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.1622 | −0.987908 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.2301 | 0.482343 | 0.241172 | − | 0.970482i | \(-0.422468\pi\) | ||||
0.241172 | + | 0.970482i | \(0.422468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.44028 | 0.0772069 |
(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 | 4028.2.a.d.1.17 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.17 | ✓ | 19 | 1.1 | even | 1 | trivial |