Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.13304 | −1.80886 | −0.904432 | − | 0.426618i | \(-0.859705\pi\) | ||||
−0.904432 | + | 0.426618i | \(0.859705\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −3.13304 | −1.27906 | ||||||||
\(7\) | −3.32735 | −1.25762 | −0.628810 | − | 0.777559i | \(-0.716458\pi\) | ||||
−0.628810 | + | 0.777559i | \(0.716458\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.81597 | 2.27199 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.28351 | −0.688504 | −0.344252 | − | 0.938877i | \(-0.611867\pi\) | ||||
−0.344252 | + | 0.938877i | \(0.611867\pi\) | |||||||
\(12\) | −3.13304 | −0.904432 | ||||||||
\(13\) | −5.71900 | −1.58617 | −0.793083 | − | 0.609114i | \(-0.791525\pi\) | ||||
−0.793083 | + | 0.609114i | \(0.791525\pi\) | |||||||
\(14\) | −3.32735 | −0.889272 | ||||||||
\(15\) | 3.13304 | 0.808949 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.86619 | −0.695154 | −0.347577 | − | 0.937651i | \(-0.612996\pi\) | ||||
−0.347577 | + | 0.937651i | \(0.612996\pi\) | |||||||
\(18\) | 6.81597 | 1.60654 | ||||||||
\(19\) | 7.01791 | 1.61002 | 0.805010 | − | 0.593262i | \(-0.202160\pi\) | ||||
0.805010 | + | 0.593262i | \(0.202160\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 10.4247 | 2.27486 | ||||||||
\(22\) | −2.28351 | −0.486846 | ||||||||
\(23\) | 5.35441 | 1.11647 | 0.558236 | − | 0.829682i | \(-0.311478\pi\) | ||||
0.558236 | + | 0.829682i | \(0.311478\pi\) | |||||||
\(24\) | −3.13304 | −0.639530 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.71900 | −1.12159 | ||||||||
\(27\) | −11.9556 | −2.30085 | ||||||||
\(28\) | −3.32735 | −0.628810 | ||||||||
\(29\) | 7.71402 | 1.43246 | 0.716229 | − | 0.697866i | \(-0.245867\pi\) | ||||
0.716229 | + | 0.697866i | \(0.245867\pi\) | |||||||
\(30\) | 3.13304 | 0.572013 | ||||||||
\(31\) | 5.44874 | 0.978622 | 0.489311 | − | 0.872109i | \(-0.337248\pi\) | ||||
0.489311 | + | 0.872109i | \(0.337248\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 7.15433 | 1.24541 | ||||||||
\(34\) | −2.86619 | −0.491548 | ||||||||
\(35\) | 3.32735 | 0.562425 | ||||||||
\(36\) | 6.81597 | 1.13599 | ||||||||
\(37\) | 2.29615 | 0.377484 | 0.188742 | − | 0.982027i | \(-0.439559\pi\) | ||||
0.188742 | + | 0.982027i | \(0.439559\pi\) | |||||||
\(38\) | 7.01791 | 1.13846 | ||||||||
\(39\) | 17.9179 | 2.86916 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −5.44074 | −0.849700 | −0.424850 | − | 0.905264i | \(-0.639673\pi\) | ||||
−0.424850 | + | 0.905264i | \(0.639673\pi\) | |||||||
\(42\) | 10.4247 | 1.60857 | ||||||||
\(43\) | −5.84523 | −0.891389 | −0.445694 | − | 0.895185i | \(-0.647043\pi\) | ||||
−0.445694 | + | 0.895185i | \(0.647043\pi\) | |||||||
\(44\) | −2.28351 | −0.344252 | ||||||||
\(45\) | −6.81597 | −1.01606 | ||||||||
\(46\) | 5.35441 | 0.789465 | ||||||||
\(47\) | −6.79959 | −0.991823 | −0.495911 | − | 0.868373i | \(-0.665166\pi\) | ||||
−0.495911 | + | 0.868373i | \(0.665166\pi\) | |||||||
\(48\) | −3.13304 | −0.452216 | ||||||||
\(49\) | 4.07127 | 0.581610 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 8.97991 | 1.25744 | ||||||||
\(52\) | −5.71900 | −0.793083 | ||||||||
\(53\) | 4.78179 | 0.656829 | 0.328414 | − | 0.944534i | \(-0.393486\pi\) | ||||
0.328414 | + | 0.944534i | \(0.393486\pi\) | |||||||
\(54\) | −11.9556 | −1.62695 | ||||||||
\(55\) | 2.28351 | 0.307908 | ||||||||
\(56\) | −3.32735 | −0.444636 | ||||||||
\(57\) | −21.9874 | −2.91231 | ||||||||
\(58\) | 7.71402 | 1.01290 | ||||||||
\(59\) | 12.6266 | 1.64385 | 0.821925 | − | 0.569596i | \(-0.192900\pi\) | ||||
0.821925 | + | 0.569596i | \(0.192900\pi\) | |||||||
\(60\) | 3.13304 | 0.404474 | ||||||||
\(61\) | 4.57895 | 0.586275 | 0.293137 | − | 0.956070i | \(-0.405301\pi\) | ||||
0.293137 | + | 0.956070i | \(0.405301\pi\) | |||||||
\(62\) | 5.44874 | 0.691990 | ||||||||
\(63\) | −22.6791 | −2.85730 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.71900 | 0.709355 | ||||||||
\(66\) | 7.15433 | 0.880638 | ||||||||
\(67\) | −1.95789 | −0.239194 | −0.119597 | − | 0.992822i | \(-0.538160\pi\) | ||||
−0.119597 | + | 0.992822i | \(0.538160\pi\) | |||||||
\(68\) | −2.86619 | −0.347577 | ||||||||
\(69\) | −16.7756 | −2.01955 | ||||||||
\(70\) | 3.32735 | 0.397695 | ||||||||
\(71\) | 4.10993 | 0.487759 | 0.243879 | − | 0.969806i | \(-0.421580\pi\) | ||||
0.243879 | + | 0.969806i | \(0.421580\pi\) | |||||||
\(72\) | 6.81597 | 0.803269 | ||||||||
\(73\) | −5.81595 | −0.680705 | −0.340353 | − | 0.940298i | \(-0.610546\pi\) | ||||
−0.340353 | + | 0.940298i | \(0.610546\pi\) | |||||||
\(74\) | 2.29615 | 0.266922 | ||||||||
\(75\) | −3.13304 | −0.361773 | ||||||||
\(76\) | 7.01791 | 0.805010 | ||||||||
\(77\) | 7.59804 | 0.865877 | ||||||||
\(78\) | 17.9179 | 2.02880 | ||||||||
\(79\) | 6.18394 | 0.695747 | 0.347874 | − | 0.937541i | \(-0.386904\pi\) | ||||
0.347874 | + | 0.937541i | \(0.386904\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 17.0095 | 1.88994 | ||||||||
\(82\) | −5.44074 | −0.600829 | ||||||||
\(83\) | 4.12859 | 0.453172 | 0.226586 | − | 0.973991i | \(-0.427244\pi\) | ||||
0.226586 | + | 0.973991i | \(0.427244\pi\) | |||||||
\(84\) | 10.4247 | 1.13743 | ||||||||
\(85\) | 2.86619 | 0.310882 | ||||||||
\(86\) | −5.84523 | −0.630307 | ||||||||
\(87\) | −24.1684 | −2.59112 | ||||||||
\(88\) | −2.28351 | −0.243423 | ||||||||
\(89\) | −16.4434 | −1.74300 | −0.871500 | − | 0.490395i | \(-0.836853\pi\) | ||||
−0.871500 | + | 0.490395i | \(0.836853\pi\) | |||||||
\(90\) | −6.81597 | −0.718466 | ||||||||
\(91\) | 19.0291 | 1.99479 | ||||||||
\(92\) | 5.35441 | 0.558236 | ||||||||
\(93\) | −17.0711 | −1.77019 | ||||||||
\(94\) | −6.79959 | −0.701325 | ||||||||
\(95\) | −7.01791 | −0.720022 | ||||||||
\(96\) | −3.13304 | −0.319765 | ||||||||
\(97\) | −5.84681 | −0.593653 | −0.296827 | − | 0.954931i | \(-0.595928\pi\) | ||||
−0.296827 | + | 0.954931i | \(0.595928\pi\) | |||||||
\(98\) | 4.07127 | 0.411260 | ||||||||
\(99\) | −15.5643 | −1.56427 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.4032 | −1.23417 | −0.617083 | − | 0.786898i | \(-0.711686\pi\) | ||||
−0.617083 | + | 0.786898i | \(0.711686\pi\) | |||||||
\(102\) | 8.97991 | 0.889144 | ||||||||
\(103\) | 11.1019 | 1.09390 | 0.546950 | − | 0.837165i | \(-0.315789\pi\) | ||||
0.546950 | + | 0.837165i | \(0.315789\pi\) | |||||||
\(104\) | −5.71900 | −0.560794 | ||||||||
\(105\) | −10.4247 | −1.01735 | ||||||||
\(106\) | 4.78179 | 0.464448 | ||||||||
\(107\) | 5.54492 | 0.536048 | 0.268024 | − | 0.963412i | \(-0.413629\pi\) | ||||
0.268024 | + | 0.963412i | \(0.413629\pi\) | |||||||
\(108\) | −11.9556 | −1.15043 | ||||||||
\(109\) | −3.08254 | −0.295254 | −0.147627 | − | 0.989043i | \(-0.547163\pi\) | ||||
−0.147627 | + | 0.989043i | \(0.547163\pi\) | |||||||
\(110\) | 2.28351 | 0.217724 | ||||||||
\(111\) | −7.19393 | −0.682818 | ||||||||
\(112\) | −3.32735 | −0.314405 | ||||||||
\(113\) | 14.1167 | 1.32799 | 0.663995 | − | 0.747737i | \(-0.268860\pi\) | ||||
0.663995 | + | 0.747737i | \(0.268860\pi\) | |||||||
\(114\) | −21.9874 | −2.05931 | ||||||||
\(115\) | −5.35441 | −0.499301 | ||||||||
\(116\) | 7.71402 | 0.716229 | ||||||||
\(117\) | −38.9805 | −3.60375 | ||||||||
\(118\) | 12.6266 | 1.16238 | ||||||||
\(119\) | 9.53684 | 0.874240 | ||||||||
\(120\) | 3.13304 | 0.286006 | ||||||||
\(121\) | −5.78559 | −0.525963 | ||||||||
\(122\) | 4.57895 | 0.414559 | ||||||||
\(123\) | 17.0461 | 1.53699 | ||||||||
\(124\) | 5.44874 | 0.489311 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −22.6791 | −2.02042 | ||||||||
\(127\) | −7.80540 | −0.692617 | −0.346309 | − | 0.938121i | \(-0.612565\pi\) | ||||
−0.346309 | + | 0.938121i | \(0.612565\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 18.3134 | 1.61240 | ||||||||
\(130\) | 5.71900 | 0.501590 | ||||||||
\(131\) | −14.3412 | −1.25300 | −0.626498 | − | 0.779423i | \(-0.715512\pi\) | ||||
−0.626498 | + | 0.779423i | \(0.715512\pi\) | |||||||
\(132\) | 7.15433 | 0.622705 | ||||||||
\(133\) | −23.3511 | −2.02479 | ||||||||
\(134\) | −1.95789 | −0.169136 | ||||||||
\(135\) | 11.9556 | 1.02897 | ||||||||
\(136\) | −2.86619 | −0.245774 | ||||||||
\(137\) | 5.65409 | 0.483062 | 0.241531 | − | 0.970393i | \(-0.422351\pi\) | ||||
0.241531 | + | 0.970393i | \(0.422351\pi\) | |||||||
\(138\) | −16.7756 | −1.42803 | ||||||||
\(139\) | −14.1896 | −1.20355 | −0.601773 | − | 0.798667i | \(-0.705539\pi\) | ||||
−0.601773 | + | 0.798667i | \(0.705539\pi\) | |||||||
\(140\) | 3.32735 | 0.281213 | ||||||||
\(141\) | 21.3034 | 1.79407 | ||||||||
\(142\) | 4.10993 | 0.344897 | ||||||||
\(143\) | 13.0594 | 1.09208 | ||||||||
\(144\) | 6.81597 | 0.567997 | ||||||||
\(145\) | −7.71402 | −0.640614 | ||||||||
\(146\) | −5.81595 | −0.481331 | ||||||||
\(147\) | −12.7555 | −1.05205 | ||||||||
\(148\) | 2.29615 | 0.188742 | ||||||||
\(149\) | −14.2981 | −1.17135 | −0.585675 | − | 0.810546i | \(-0.699170\pi\) | ||||
−0.585675 | + | 0.810546i | \(0.699170\pi\) | |||||||
\(150\) | −3.13304 | −0.255812 | ||||||||
\(151\) | 2.17667 | 0.177135 | 0.0885675 | − | 0.996070i | \(-0.471771\pi\) | ||||
0.0885675 | + | 0.996070i | \(0.471771\pi\) | |||||||
\(152\) | 7.01791 | 0.569228 | ||||||||
\(153\) | −19.5359 | −1.57938 | ||||||||
\(154\) | 7.59804 | 0.612267 | ||||||||
\(155\) | −5.44874 | −0.437653 | ||||||||
\(156\) | 17.9179 | 1.43458 | ||||||||
\(157\) | 4.36210 | 0.348133 | 0.174067 | − | 0.984734i | \(-0.444309\pi\) | ||||
0.174067 | + | 0.984734i | \(0.444309\pi\) | |||||||
\(158\) | 6.18394 | 0.491968 | ||||||||
\(159\) | −14.9815 | −1.18811 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −17.8160 | −1.40410 | ||||||||
\(162\) | 17.0095 | 1.33639 | ||||||||
\(163\) | 17.5782 | 1.37683 | 0.688414 | − | 0.725318i | \(-0.258307\pi\) | ||||
0.688414 | + | 0.725318i | \(0.258307\pi\) | |||||||
\(164\) | −5.44074 | −0.424850 | ||||||||
\(165\) | −7.15433 | −0.556964 | ||||||||
\(166\) | 4.12859 | 0.320441 | ||||||||
\(167\) | 15.3337 | 1.18656 | 0.593279 | − | 0.804997i | \(-0.297833\pi\) | ||||
0.593279 | + | 0.804997i | \(0.297833\pi\) | |||||||
\(168\) | 10.4247 | 0.804286 | ||||||||
\(169\) | 19.7070 | 1.51592 | ||||||||
\(170\) | 2.86619 | 0.219827 | ||||||||
\(171\) | 47.8338 | 3.65795 | ||||||||
\(172\) | −5.84523 | −0.445694 | ||||||||
\(173\) | 1.04475 | 0.0794310 | 0.0397155 | − | 0.999211i | \(-0.487355\pi\) | ||||
0.0397155 | + | 0.999211i | \(0.487355\pi\) | |||||||
\(174\) | −24.1684 | −1.83220 | ||||||||
\(175\) | −3.32735 | −0.251524 | ||||||||
\(176\) | −2.28351 | −0.172126 | ||||||||
\(177\) | −39.5598 | −2.97350 | ||||||||
\(178\) | −16.4434 | −1.23249 | ||||||||
\(179\) | 6.91419 | 0.516791 | 0.258396 | − | 0.966039i | \(-0.416806\pi\) | ||||
0.258396 | + | 0.966039i | \(0.416806\pi\) | |||||||
\(180\) | −6.81597 | −0.508032 | ||||||||
\(181\) | 1.62026 | 0.120433 | 0.0602167 | − | 0.998185i | \(-0.480821\pi\) | ||||
0.0602167 | + | 0.998185i | \(0.480821\pi\) | |||||||
\(182\) | 19.0291 | 1.41053 | ||||||||
\(183\) | −14.3461 | −1.06049 | ||||||||
\(184\) | 5.35441 | 0.394732 | ||||||||
\(185\) | −2.29615 | −0.168816 | ||||||||
\(186\) | −17.0711 | −1.25172 | ||||||||
\(187\) | 6.54498 | 0.478616 | ||||||||
\(188\) | −6.79959 | −0.495911 | ||||||||
\(189\) | 39.7805 | 2.89360 | ||||||||
\(190\) | −7.01791 | −0.509133 | ||||||||
\(191\) | −22.0018 | −1.59199 | −0.795996 | − | 0.605302i | \(-0.793052\pi\) | ||||
−0.795996 | + | 0.605302i | \(0.793052\pi\) | |||||||
\(192\) | −3.13304 | −0.226108 | ||||||||
\(193\) | −1.66682 | −0.119981 | −0.0599903 | − | 0.998199i | \(-0.519107\pi\) | ||||
−0.0599903 | + | 0.998199i | \(0.519107\pi\) | |||||||
\(194\) | −5.84681 | −0.419776 | ||||||||
\(195\) | −17.9179 | −1.28313 | ||||||||
\(196\) | 4.07127 | 0.290805 | ||||||||
\(197\) | 14.4823 | 1.03182 | 0.515911 | − | 0.856642i | \(-0.327454\pi\) | ||||
0.515911 | + | 0.856642i | \(0.327454\pi\) | |||||||
\(198\) | −15.5643 | −1.10611 | ||||||||
\(199\) | −6.58139 | −0.466542 | −0.233271 | − | 0.972412i | \(-0.574943\pi\) | ||||
−0.233271 | + | 0.972412i | \(0.574943\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 6.13416 | 0.432670 | ||||||||
\(202\) | −12.4032 | −0.872688 | ||||||||
\(203\) | −25.6673 | −1.80149 | ||||||||
\(204\) | 8.97991 | 0.628720 | ||||||||
\(205\) | 5.44074 | 0.379997 | ||||||||
\(206\) | 11.1019 | 0.773504 | ||||||||
\(207\) | 36.4955 | 2.53661 | ||||||||
\(208\) | −5.71900 | −0.396541 | ||||||||
\(209\) | −16.0255 | −1.10850 | ||||||||
\(210\) | −10.4247 | −0.719375 | ||||||||
\(211\) | −20.5347 | −1.41366 | −0.706832 | − | 0.707381i | \(-0.749876\pi\) | ||||
−0.706832 | + | 0.707381i | \(0.749876\pi\) | |||||||
\(212\) | 4.78179 | 0.328414 | ||||||||
\(213\) | −12.8766 | −0.882289 | ||||||||
\(214\) | 5.54492 | 0.379043 | ||||||||
\(215\) | 5.84523 | 0.398641 | ||||||||
\(216\) | −11.9556 | −0.813475 | ||||||||
\(217\) | −18.1299 | −1.23074 | ||||||||
\(218\) | −3.08254 | −0.208776 | ||||||||
\(219\) | 18.2216 | 1.23130 | ||||||||
\(220\) | 2.28351 | 0.153954 | ||||||||
\(221\) | 16.3918 | 1.10263 | ||||||||
\(222\) | −7.19393 | −0.482825 | ||||||||
\(223\) | 4.44359 | 0.297565 | 0.148782 | − | 0.988870i | \(-0.452465\pi\) | ||||
0.148782 | + | 0.988870i | \(0.452465\pi\) | |||||||
\(224\) | −3.32735 | −0.222318 | ||||||||
\(225\) | 6.81597 | 0.454398 | ||||||||
\(226\) | 14.1167 | 0.939031 | ||||||||
\(227\) | −13.4043 | −0.889673 | −0.444836 | − | 0.895612i | \(-0.646738\pi\) | ||||
−0.444836 | + | 0.895612i | \(0.646738\pi\) | |||||||
\(228\) | −21.9874 | −1.45615 | ||||||||
\(229\) | −20.5573 | −1.35846 | −0.679231 | − | 0.733925i | \(-0.737687\pi\) | ||||
−0.679231 | + | 0.733925i | \(0.737687\pi\) | |||||||
\(230\) | −5.35441 | −0.353059 | ||||||||
\(231\) | −23.8050 | −1.56625 | ||||||||
\(232\) | 7.71402 | 0.506450 | ||||||||
\(233\) | −24.1978 | −1.58525 | −0.792626 | − | 0.609708i | \(-0.791287\pi\) | ||||
−0.792626 | + | 0.609708i | \(0.791287\pi\) | |||||||
\(234\) | −38.9805 | −2.54824 | ||||||||
\(235\) | 6.79959 | 0.443557 | ||||||||
\(236\) | 12.6266 | 0.821925 | ||||||||
\(237\) | −19.3745 | −1.25851 | ||||||||
\(238\) | 9.53684 | 0.618181 | ||||||||
\(239\) | −14.5154 | −0.938926 | −0.469463 | − | 0.882952i | \(-0.655552\pi\) | ||||
−0.469463 | + | 0.882952i | \(0.655552\pi\) | |||||||
\(240\) | 3.13304 | 0.202237 | ||||||||
\(241\) | 18.5561 | 1.19530 | 0.597652 | − | 0.801756i | \(-0.296101\pi\) | ||||
0.597652 | + | 0.801756i | \(0.296101\pi\) | |||||||
\(242\) | −5.78559 | −0.371912 | ||||||||
\(243\) | −17.4247 | −1.11780 | ||||||||
\(244\) | 4.57895 | 0.293137 | ||||||||
\(245\) | −4.07127 | −0.260104 | ||||||||
\(246\) | 17.0461 | 1.08682 | ||||||||
\(247\) | −40.1354 | −2.55376 | ||||||||
\(248\) | 5.44874 | 0.345995 | ||||||||
\(249\) | −12.9351 | −0.819727 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 25.3790 | 1.60191 | 0.800955 | − | 0.598724i | \(-0.204325\pi\) | ||||
0.800955 | + | 0.598724i | \(0.204325\pi\) | |||||||
\(252\) | −22.6791 | −1.42865 | ||||||||
\(253\) | −12.2268 | −0.768695 | ||||||||
\(254\) | −7.80540 | −0.489754 | ||||||||
\(255\) | −8.97991 | −0.562344 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.41001 | −0.275089 | −0.137544 | − | 0.990496i | \(-0.543921\pi\) | ||||
−0.137544 | + | 0.990496i | \(0.543921\pi\) | |||||||
\(258\) | 18.3134 | 1.14014 | ||||||||
\(259\) | −7.64009 | −0.474732 | ||||||||
\(260\) | 5.71900 | 0.354677 | ||||||||
\(261\) | 52.5785 | 3.25453 | ||||||||
\(262\) | −14.3412 | −0.886002 | ||||||||
\(263\) | 5.99193 | 0.369478 | 0.184739 | − | 0.982788i | \(-0.440856\pi\) | ||||
0.184739 | + | 0.982788i | \(0.440856\pi\) | |||||||
\(264\) | 7.15433 | 0.440319 | ||||||||
\(265\) | −4.78179 | −0.293743 | ||||||||
\(266\) | −23.3511 | −1.43175 | ||||||||
\(267\) | 51.5180 | 3.15285 | ||||||||
\(268\) | −1.95789 | −0.119597 | ||||||||
\(269\) | 8.90076 | 0.542689 | 0.271345 | − | 0.962482i | \(-0.412532\pi\) | ||||
0.271345 | + | 0.962482i | \(0.412532\pi\) | |||||||
\(270\) | 11.9556 | 0.727594 | ||||||||
\(271\) | −32.0806 | −1.94876 | −0.974379 | − | 0.224914i | \(-0.927790\pi\) | ||||
−0.974379 | + | 0.224914i | \(0.927790\pi\) | |||||||
\(272\) | −2.86619 | −0.173789 | ||||||||
\(273\) | −59.6191 | −3.60831 | ||||||||
\(274\) | 5.65409 | 0.341576 | ||||||||
\(275\) | −2.28351 | −0.137701 | ||||||||
\(276\) | −16.7756 | −1.00977 | ||||||||
\(277\) | 1.74567 | 0.104887 | 0.0524436 | − | 0.998624i | \(-0.483299\pi\) | ||||
0.0524436 | + | 0.998624i | \(0.483299\pi\) | |||||||
\(278\) | −14.1896 | −0.851036 | ||||||||
\(279\) | 37.1384 | 2.22342 | ||||||||
\(280\) | 3.32735 | 0.198847 | ||||||||
\(281\) | −28.8021 | −1.71819 | −0.859093 | − | 0.511819i | \(-0.828972\pi\) | ||||
−0.859093 | + | 0.511819i | \(0.828972\pi\) | |||||||
\(282\) | 21.3034 | 1.26860 | ||||||||
\(283\) | 15.7280 | 0.934933 | 0.467467 | − | 0.884011i | \(-0.345167\pi\) | ||||
0.467467 | + | 0.884011i | \(0.345167\pi\) | |||||||
\(284\) | 4.10993 | 0.243879 | ||||||||
\(285\) | 21.9874 | 1.30242 | ||||||||
\(286\) | 13.0594 | 0.772218 | ||||||||
\(287\) | 18.1032 | 1.06860 | ||||||||
\(288\) | 6.81597 | 0.401635 | ||||||||
\(289\) | −8.78493 | −0.516761 | ||||||||
\(290\) | −7.71402 | −0.452983 | ||||||||
\(291\) | 18.3183 | 1.07384 | ||||||||
\(292\) | −5.81595 | −0.340353 | ||||||||
\(293\) | −29.8634 | −1.74464 | −0.872320 | − | 0.488936i | \(-0.837385\pi\) | ||||
−0.872320 | + | 0.488936i | \(0.837385\pi\) | |||||||
\(294\) | −12.7555 | −0.743914 | ||||||||
\(295\) | −12.6266 | −0.735152 | ||||||||
\(296\) | 2.29615 | 0.133461 | ||||||||
\(297\) | 27.3007 | 1.58415 | ||||||||
\(298\) | −14.2981 | −0.828269 | ||||||||
\(299\) | −30.6219 | −1.77091 | ||||||||
\(300\) | −3.13304 | −0.180886 | ||||||||
\(301\) | 19.4491 | 1.12103 | ||||||||
\(302\) | 2.17667 | 0.125253 | ||||||||
\(303\) | 38.8599 | 2.23244 | ||||||||
\(304\) | 7.01791 | 0.402505 | ||||||||
\(305\) | −4.57895 | −0.262190 | ||||||||
\(306\) | −19.5359 | −1.11679 | ||||||||
\(307\) | 32.5376 | 1.85702 | 0.928510 | − | 0.371307i | \(-0.121090\pi\) | ||||
0.928510 | + | 0.371307i | \(0.121090\pi\) | |||||||
\(308\) | 7.59804 | 0.432938 | ||||||||
\(309\) | −34.7826 | −1.97872 | ||||||||
\(310\) | −5.44874 | −0.309468 | ||||||||
\(311\) | 17.6527 | 1.00099 | 0.500495 | − | 0.865739i | \(-0.333151\pi\) | ||||
0.500495 | + | 0.865739i | \(0.333151\pi\) | |||||||
\(312\) | 17.9179 | 1.01440 | ||||||||
\(313\) | 13.2919 | 0.751301 | 0.375650 | − | 0.926761i | \(-0.377419\pi\) | ||||
0.375650 | + | 0.926761i | \(0.377419\pi\) | |||||||
\(314\) | 4.36210 | 0.246167 | ||||||||
\(315\) | 22.6791 | 1.27782 | ||||||||
\(316\) | 6.18394 | 0.347874 | ||||||||
\(317\) | 32.2538 | 1.81155 | 0.905777 | − | 0.423754i | \(-0.139288\pi\) | ||||
0.905777 | + | 0.423754i | \(0.139288\pi\) | |||||||
\(318\) | −14.9815 | −0.840124 | ||||||||
\(319\) | −17.6150 | −0.986252 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −17.3725 | −0.969637 | ||||||||
\(322\) | −17.8160 | −0.992847 | ||||||||
\(323\) | −20.1147 | −1.11921 | ||||||||
\(324\) | 17.0095 | 0.944972 | ||||||||
\(325\) | −5.71900 | −0.317233 | ||||||||
\(326\) | 17.5782 | 0.973564 | ||||||||
\(327\) | 9.65773 | 0.534073 | ||||||||
\(328\) | −5.44074 | −0.300414 | ||||||||
\(329\) | 22.6246 | 1.24734 | ||||||||
\(330\) | −7.15433 | −0.393833 | ||||||||
\(331\) | 13.8549 | 0.761535 | 0.380767 | − | 0.924671i | \(-0.375660\pi\) | ||||
0.380767 | + | 0.924671i | \(0.375660\pi\) | |||||||
\(332\) | 4.12859 | 0.226586 | ||||||||
\(333\) | 15.6505 | 0.857640 | ||||||||
\(334\) | 15.3337 | 0.839024 | ||||||||
\(335\) | 1.95789 | 0.106971 | ||||||||
\(336\) | 10.4247 | 0.568716 | ||||||||
\(337\) | −16.1211 | −0.878174 | −0.439087 | − | 0.898445i | \(-0.644698\pi\) | ||||
−0.439087 | + | 0.898445i | \(0.644698\pi\) | |||||||
\(338\) | 19.7070 | 1.07192 | ||||||||
\(339\) | −44.2283 | −2.40215 | ||||||||
\(340\) | 2.86619 | 0.155441 | ||||||||
\(341\) | −12.4422 | −0.673785 | ||||||||
\(342\) | 47.8338 | 2.58656 | ||||||||
\(343\) | 9.74492 | 0.526176 | ||||||||
\(344\) | −5.84523 | −0.315154 | ||||||||
\(345\) | 16.7756 | 0.903168 | ||||||||
\(346\) | 1.04475 | 0.0561662 | ||||||||
\(347\) | −19.8396 | −1.06505 | −0.532523 | − | 0.846415i | \(-0.678756\pi\) | ||||
−0.532523 | + | 0.846415i | \(0.678756\pi\) | |||||||
\(348\) | −24.1684 | −1.29556 | ||||||||
\(349\) | −6.98979 | −0.374155 | −0.187077 | − | 0.982345i | \(-0.559901\pi\) | ||||
−0.187077 | + | 0.982345i | \(0.559901\pi\) | |||||||
\(350\) | −3.32735 | −0.177854 | ||||||||
\(351\) | 68.3740 | 3.64954 | ||||||||
\(352\) | −2.28351 | −0.121711 | ||||||||
\(353\) | −35.8141 | −1.90619 | −0.953097 | − | 0.302665i | \(-0.902124\pi\) | ||||
−0.953097 | + | 0.302665i | \(0.902124\pi\) | |||||||
\(354\) | −39.5598 | −2.10258 | ||||||||
\(355\) | −4.10993 | −0.218132 | ||||||||
\(356\) | −16.4434 | −0.871500 | ||||||||
\(357\) | −29.8793 | −1.58138 | ||||||||
\(358\) | 6.91419 | 0.365427 | ||||||||
\(359\) | 8.32788 | 0.439528 | 0.219764 | − | 0.975553i | \(-0.429471\pi\) | ||||
0.219764 | + | 0.975553i | \(0.429471\pi\) | |||||||
\(360\) | −6.81597 | −0.359233 | ||||||||
\(361\) | 30.2511 | 1.59216 | ||||||||
\(362\) | 1.62026 | 0.0851592 | ||||||||
\(363\) | 18.1265 | 0.951395 | ||||||||
\(364\) | 19.0291 | 0.997397 | ||||||||
\(365\) | 5.81595 | 0.304421 | ||||||||
\(366\) | −14.3461 | −0.749880 | ||||||||
\(367\) | −16.5165 | −0.862154 | −0.431077 | − | 0.902315i | \(-0.641866\pi\) | ||||
−0.431077 | + | 0.902315i | \(0.641866\pi\) | |||||||
\(368\) | 5.35441 | 0.279118 | ||||||||
\(369\) | −37.0839 | −1.93051 | ||||||||
\(370\) | −2.29615 | −0.119371 | ||||||||
\(371\) | −15.9107 | −0.826042 | ||||||||
\(372\) | −17.0711 | −0.885097 | ||||||||
\(373\) | −23.4075 | −1.21199 | −0.605997 | − | 0.795467i | \(-0.707226\pi\) | ||||
−0.605997 | + | 0.795467i | \(0.707226\pi\) | |||||||
\(374\) | 6.54498 | 0.338433 | ||||||||
\(375\) | 3.13304 | 0.161790 | ||||||||
\(376\) | −6.79959 | −0.350662 | ||||||||
\(377\) | −44.1165 | −2.27211 | ||||||||
\(378\) | 39.7805 | 2.04609 | ||||||||
\(379\) | 3.29299 | 0.169150 | 0.0845748 | − | 0.996417i | \(-0.473047\pi\) | ||||
0.0845748 | + | 0.996417i | \(0.473047\pi\) | |||||||
\(380\) | −7.01791 | −0.360011 | ||||||||
\(381\) | 24.4547 | 1.25285 | ||||||||
\(382\) | −22.0018 | −1.12571 | ||||||||
\(383\) | 27.5083 | 1.40561 | 0.702805 | − | 0.711382i | \(-0.251931\pi\) | ||||
0.702805 | + | 0.711382i | \(0.251931\pi\) | |||||||
\(384\) | −3.13304 | −0.159882 | ||||||||
\(385\) | −7.59804 | −0.387232 | ||||||||
\(386\) | −1.66682 | −0.0848390 | ||||||||
\(387\) | −39.8409 | −2.02523 | ||||||||
\(388\) | −5.84681 | −0.296827 | ||||||||
\(389\) | −4.63597 | −0.235053 | −0.117526 | − | 0.993070i | \(-0.537496\pi\) | ||||
−0.117526 | + | 0.993070i | \(0.537496\pi\) | |||||||
\(390\) | −17.9179 | −0.907307 | ||||||||
\(391\) | −15.3468 | −0.776120 | ||||||||
\(392\) | 4.07127 | 0.205630 | ||||||||
\(393\) | 44.9316 | 2.26650 | ||||||||
\(394\) | 14.4823 | 0.729608 | ||||||||
\(395\) | −6.18394 | −0.311148 | ||||||||
\(396\) | −15.5643 | −0.782136 | ||||||||
\(397\) | −30.8511 | −1.54837 | −0.774187 | − | 0.632957i | \(-0.781841\pi\) | ||||
−0.774187 | + | 0.632957i | \(0.781841\pi\) | |||||||
\(398\) | −6.58139 | −0.329895 | ||||||||
\(399\) | 73.1599 | 3.66258 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −5.81994 | −0.290634 | −0.145317 | − | 0.989385i | \(-0.546420\pi\) | ||||
−0.145317 | + | 0.989385i | \(0.546420\pi\) | |||||||
\(402\) | 6.13416 | 0.305944 | ||||||||
\(403\) | −31.1613 | −1.55226 | ||||||||
\(404\) | −12.4032 | −0.617083 | ||||||||
\(405\) | −17.0095 | −0.845209 | ||||||||
\(406\) | −25.6673 | −1.27384 | ||||||||
\(407\) | −5.24327 | −0.259899 | ||||||||
\(408\) | 8.97991 | 0.444572 | ||||||||
\(409\) | −35.4794 | −1.75435 | −0.877173 | − | 0.480175i | \(-0.840573\pi\) | ||||
−0.877173 | + | 0.480175i | \(0.840573\pi\) | |||||||
\(410\) | 5.44074 | 0.268699 | ||||||||
\(411\) | −17.7145 | −0.873793 | ||||||||
\(412\) | 11.1019 | 0.546950 | ||||||||
\(413\) | −42.0133 | −2.06734 | ||||||||
\(414\) | 36.4955 | 1.79366 | ||||||||
\(415\) | −4.12859 | −0.202665 | ||||||||
\(416\) | −5.71900 | −0.280397 | ||||||||
\(417\) | 44.4567 | 2.17705 | ||||||||
\(418\) | −16.0255 | −0.783831 | ||||||||
\(419\) | −5.20695 | −0.254376 | −0.127188 | − | 0.991879i | \(-0.540595\pi\) | ||||
−0.127188 | + | 0.991879i | \(0.540595\pi\) | |||||||
\(420\) | −10.4247 | −0.508675 | ||||||||
\(421\) | 16.9532 | 0.826250 | 0.413125 | − | 0.910674i | \(-0.364437\pi\) | ||||
0.413125 | + | 0.910674i | \(0.364437\pi\) | |||||||
\(422\) | −20.5347 | −0.999612 | ||||||||
\(423\) | −46.3458 | −2.25341 | ||||||||
\(424\) | 4.78179 | 0.232224 | ||||||||
\(425\) | −2.86619 | −0.139031 | ||||||||
\(426\) | −12.8766 | −0.623873 | ||||||||
\(427\) | −15.2358 | −0.737311 | ||||||||
\(428\) | 5.54492 | 0.268024 | ||||||||
\(429\) | −40.9156 | −1.97543 | ||||||||
\(430\) | 5.84523 | 0.281882 | ||||||||
\(431\) | −25.6428 | −1.23517 | −0.617586 | − | 0.786504i | \(-0.711889\pi\) | ||||
−0.617586 | + | 0.786504i | \(0.711889\pi\) | |||||||
\(432\) | −11.9556 | −0.575214 | ||||||||
\(433\) | −0.0124318 | −0.000597433 0 | −0.000298717 | − | 1.00000i | \(-0.500095\pi\) | ||||
−0.000298717 | 1.00000i | \(0.500095\pi\) | ||||||||
\(434\) | −18.1299 | −0.870262 | ||||||||
\(435\) | 24.1684 | 1.15878 | ||||||||
\(436\) | −3.08254 | −0.147627 | ||||||||
\(437\) | 37.5768 | 1.79754 | ||||||||
\(438\) | 18.2216 | 0.870663 | ||||||||
\(439\) | −24.1016 | −1.15031 | −0.575154 | − | 0.818045i | \(-0.695058\pi\) | ||||
−0.575154 | + | 0.818045i | \(0.695058\pi\) | |||||||
\(440\) | 2.28351 | 0.108862 | ||||||||
\(441\) | 27.7496 | 1.32141 | ||||||||
\(442\) | 16.3918 | 0.779677 | ||||||||
\(443\) | −25.9745 | −1.23409 | −0.617043 | − | 0.786929i | \(-0.711670\pi\) | ||||
−0.617043 | + | 0.786929i | \(0.711670\pi\) | |||||||
\(444\) | −7.19393 | −0.341409 | ||||||||
\(445\) | 16.4434 | 0.779494 | ||||||||
\(446\) | 4.44359 | 0.210410 | ||||||||
\(447\) | 44.7967 | 2.11881 | ||||||||
\(448\) | −3.32735 | −0.157203 | ||||||||
\(449\) | −5.64460 | −0.266385 | −0.133193 | − | 0.991090i | \(-0.542523\pi\) | ||||
−0.133193 | + | 0.991090i | \(0.542523\pi\) | |||||||
\(450\) | 6.81597 | 0.321308 | ||||||||
\(451\) | 12.4240 | 0.585022 | ||||||||
\(452\) | 14.1167 | 0.663995 | ||||||||
\(453\) | −6.81961 | −0.320413 | ||||||||
\(454\) | −13.4043 | −0.629094 | ||||||||
\(455\) | −19.0291 | −0.892099 | ||||||||
\(456\) | −21.9874 | −1.02966 | ||||||||
\(457\) | −20.2448 | −0.947010 | −0.473505 | − | 0.880791i | \(-0.657011\pi\) | ||||
−0.473505 | + | 0.880791i | \(0.657011\pi\) | |||||||
\(458\) | −20.5573 | −0.960578 | ||||||||
\(459\) | 34.2670 | 1.59945 | ||||||||
\(460\) | −5.35441 | −0.249651 | ||||||||
\(461\) | −8.98189 | −0.418328 | −0.209164 | − | 0.977881i | \(-0.567074\pi\) | ||||
−0.209164 | + | 0.977881i | \(0.567074\pi\) | |||||||
\(462\) | −23.8050 | −1.10751 | ||||||||
\(463\) | 13.7804 | 0.640428 | 0.320214 | − | 0.947345i | \(-0.396245\pi\) | ||||
0.320214 | + | 0.947345i | \(0.396245\pi\) | |||||||
\(464\) | 7.71402 | 0.358114 | ||||||||
\(465\) | 17.0711 | 0.791655 | ||||||||
\(466\) | −24.1978 | −1.12094 | ||||||||
\(467\) | 21.2600 | 0.983794 | 0.491897 | − | 0.870653i | \(-0.336304\pi\) | ||||
0.491897 | + | 0.870653i | \(0.336304\pi\) | |||||||
\(468\) | −38.9805 | −1.80187 | ||||||||
\(469\) | 6.51459 | 0.300816 | ||||||||
\(470\) | 6.79959 | 0.313642 | ||||||||
\(471\) | −13.6666 | −0.629726 | ||||||||
\(472\) | 12.6266 | 0.581189 | ||||||||
\(473\) | 13.3476 | 0.613725 | ||||||||
\(474\) | −19.3745 | −0.889902 | ||||||||
\(475\) | 7.01791 | 0.322004 | ||||||||
\(476\) | 9.53684 | 0.437120 | ||||||||
\(477\) | 32.5925 | 1.49231 | ||||||||
\(478\) | −14.5154 | −0.663921 | ||||||||
\(479\) | 0.670853 | 0.0306521 | 0.0153260 | − | 0.999883i | \(-0.495121\pi\) | ||||
0.0153260 | + | 0.999883i | \(0.495121\pi\) | |||||||
\(480\) | 3.13304 | 0.143003 | ||||||||
\(481\) | −13.1317 | −0.598753 | ||||||||
\(482\) | 18.5561 | 0.845207 | ||||||||
\(483\) | 55.8183 | 2.53982 | ||||||||
\(484\) | −5.78559 | −0.262981 | ||||||||
\(485\) | 5.84681 | 0.265490 | ||||||||
\(486\) | −17.4247 | −0.790402 | ||||||||
\(487\) | −0.120064 | −0.00544063 | −0.00272032 | − | 0.999996i | \(-0.500866\pi\) | ||||
−0.00272032 | + | 0.999996i | \(0.500866\pi\) | |||||||
\(488\) | 4.57895 | 0.207279 | ||||||||
\(489\) | −55.0732 | −2.49049 | ||||||||
\(490\) | −4.07127 | −0.183921 | ||||||||
\(491\) | −15.2734 | −0.689280 | −0.344640 | − | 0.938735i | \(-0.611999\pi\) | ||||
−0.344640 | + | 0.938735i | \(0.611999\pi\) | |||||||
\(492\) | 17.0461 | 0.768496 | ||||||||
\(493\) | −22.1099 | −0.995779 | ||||||||
\(494\) | −40.1354 | −1.80578 | ||||||||
\(495\) | 15.5643 | 0.699564 | ||||||||
\(496\) | 5.44874 | 0.244656 | ||||||||
\(497\) | −13.6752 | −0.613415 | ||||||||
\(498\) | −12.9351 | −0.579634 | ||||||||
\(499\) | −43.2431 | −1.93583 | −0.967914 | − | 0.251280i | \(-0.919149\pi\) | ||||
−0.967914 | + | 0.251280i | \(0.919149\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −48.0412 | −2.14632 | ||||||||
\(502\) | 25.3790 | 1.13272 | ||||||||
\(503\) | −41.3190 | −1.84232 | −0.921161 | − | 0.389181i | \(-0.872758\pi\) | ||||
−0.921161 | + | 0.389181i | \(0.872758\pi\) | |||||||
\(504\) | −22.6791 | −1.01021 | ||||||||
\(505\) | 12.4032 | 0.551936 | ||||||||
\(506\) | −12.2268 | −0.543550 | ||||||||
\(507\) | −61.7428 | −2.74209 | ||||||||
\(508\) | −7.80540 | −0.346309 | ||||||||
\(509\) | 24.0420 | 1.06564 | 0.532822 | − | 0.846227i | \(-0.321132\pi\) | ||||
0.532822 | + | 0.846227i | \(0.321132\pi\) | |||||||
\(510\) | −8.97991 | −0.397637 | ||||||||
\(511\) | 19.3517 | 0.856069 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −83.9033 | −3.70442 | ||||||||
\(514\) | −4.41001 | −0.194517 | ||||||||
\(515\) | −11.1019 | −0.489207 | ||||||||
\(516\) | 18.3134 | 0.806200 | ||||||||
\(517\) | 15.5269 | 0.682874 | ||||||||
\(518\) | −7.64009 | −0.335686 | ||||||||
\(519\) | −3.27325 | −0.143680 | ||||||||
\(520\) | 5.71900 | 0.250795 | ||||||||
\(521\) | −2.59240 | −0.113575 | −0.0567876 | − | 0.998386i | \(-0.518086\pi\) | ||||
−0.0567876 | + | 0.998386i | \(0.518086\pi\) | |||||||
\(522\) | 52.5785 | 2.30130 | ||||||||
\(523\) | −26.7581 | −1.17005 | −0.585025 | − | 0.811015i | \(-0.698915\pi\) | ||||
−0.585025 | + | 0.811015i | \(0.698915\pi\) | |||||||
\(524\) | −14.3412 | −0.626498 | ||||||||
\(525\) | 10.4247 | 0.454973 | ||||||||
\(526\) | 5.99193 | 0.261260 | ||||||||
\(527\) | −15.6171 | −0.680293 | ||||||||
\(528\) | 7.15433 | 0.311352 | ||||||||
\(529\) | 5.66972 | 0.246510 | ||||||||
\(530\) | −4.78179 | −0.207708 | ||||||||
\(531\) | 86.0628 | 3.73481 | ||||||||
\(532\) | −23.3511 | −1.01240 | ||||||||
\(533\) | 31.1156 | 1.34777 | ||||||||
\(534\) | 51.5180 | 2.22940 | ||||||||
\(535\) | −5.54492 | −0.239728 | ||||||||
\(536\) | −1.95789 | −0.0845680 | ||||||||
\(537\) | −21.6625 | −0.934805 | ||||||||
\(538\) | 8.90076 | 0.383739 | ||||||||
\(539\) | −9.29678 | −0.400441 | ||||||||
\(540\) | 11.9556 | 0.514487 | ||||||||
\(541\) | −5.82473 | −0.250425 | −0.125212 | − | 0.992130i | \(-0.539961\pi\) | ||||
−0.125212 | + | 0.992130i | \(0.539961\pi\) | |||||||
\(542\) | −32.0806 | −1.37798 | ||||||||
\(543\) | −5.07636 | −0.217847 | ||||||||
\(544\) | −2.86619 | −0.122887 | ||||||||
\(545\) | 3.08254 | 0.132041 | ||||||||
\(546\) | −59.6191 | −2.55146 | ||||||||
\(547\) | 26.4717 | 1.13185 | 0.565925 | − | 0.824457i | \(-0.308519\pi\) | ||||
0.565925 | + | 0.824457i | \(0.308519\pi\) | |||||||
\(548\) | 5.65409 | 0.241531 | ||||||||
\(549\) | 31.2100 | 1.33201 | ||||||||
\(550\) | −2.28351 | −0.0973691 | ||||||||
\(551\) | 54.1363 | 2.30628 | ||||||||
\(552\) | −16.7756 | −0.714017 | ||||||||
\(553\) | −20.5761 | −0.874986 | ||||||||
\(554\) | 1.74567 | 0.0741665 | ||||||||
\(555\) | 7.19393 | 0.305366 | ||||||||
\(556\) | −14.1896 | −0.601773 | ||||||||
\(557\) | 15.1208 | 0.640690 | 0.320345 | − | 0.947301i | \(-0.396201\pi\) | ||||
0.320345 | + | 0.947301i | \(0.396201\pi\) | |||||||
\(558\) | 37.1384 | 1.57219 | ||||||||
\(559\) | 33.4289 | 1.41389 | ||||||||
\(560\) | 3.32735 | 0.140606 | ||||||||
\(561\) | −20.5057 | −0.865752 | ||||||||
\(562\) | −28.8021 | −1.21494 | ||||||||
\(563\) | −13.6335 | −0.574582 | −0.287291 | − | 0.957843i | \(-0.592755\pi\) | ||||
−0.287291 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(564\) | 21.3034 | 0.897036 | ||||||||
\(565\) | −14.1167 | −0.593895 | ||||||||
\(566\) | 15.7280 | 0.661098 | ||||||||
\(567\) | −56.5966 | −2.37683 | ||||||||
\(568\) | 4.10993 | 0.172449 | ||||||||
\(569\) | −0.398579 | −0.0167093 | −0.00835465 | − | 0.999965i | \(-0.502659\pi\) | ||||
−0.00835465 | + | 0.999965i | \(0.502659\pi\) | |||||||
\(570\) | 21.9874 | 0.920952 | ||||||||
\(571\) | −17.2304 | −0.721069 | −0.360535 | − | 0.932746i | \(-0.617406\pi\) | ||||
−0.360535 | + | 0.932746i | \(0.617406\pi\) | |||||||
\(572\) | 13.0594 | 0.546040 | ||||||||
\(573\) | 68.9325 | 2.87970 | ||||||||
\(574\) | 18.1032 | 0.755615 | ||||||||
\(575\) | 5.35441 | 0.223294 | ||||||||
\(576\) | 6.81597 | 0.283999 | ||||||||
\(577\) | 27.8512 | 1.15946 | 0.579729 | − | 0.814809i | \(-0.303158\pi\) | ||||
0.579729 | + | 0.814809i | \(0.303158\pi\) | |||||||
\(578\) | −8.78493 | −0.365405 | ||||||||
\(579\) | 5.22223 | 0.217028 | ||||||||
\(580\) | −7.71402 | −0.320307 | ||||||||
\(581\) | −13.7373 | −0.569919 | ||||||||
\(582\) | 18.3183 | 0.759318 | ||||||||
\(583\) | −10.9193 | −0.452229 | ||||||||
\(584\) | −5.81595 | −0.240666 | ||||||||
\(585\) | 38.9805 | 1.61165 | ||||||||
\(586\) | −29.8634 | −1.23365 | ||||||||
\(587\) | 32.5195 | 1.34222 | 0.671112 | − | 0.741356i | \(-0.265817\pi\) | ||||
0.671112 | + | 0.741356i | \(0.265817\pi\) | |||||||
\(588\) | −12.7555 | −0.526027 | ||||||||
\(589\) | 38.2388 | 1.57560 | ||||||||
\(590\) | −12.6266 | −0.519831 | ||||||||
\(591\) | −45.3737 | −1.86643 | ||||||||
\(592\) | 2.29615 | 0.0943711 | ||||||||
\(593\) | −40.6760 | −1.67037 | −0.835183 | − | 0.549973i | \(-0.814638\pi\) | ||||
−0.835183 | + | 0.549973i | \(0.814638\pi\) | |||||||
\(594\) | 27.3007 | 1.12016 | ||||||||
\(595\) | −9.53684 | −0.390972 | ||||||||
\(596\) | −14.2981 | −0.585675 | ||||||||
\(597\) | 20.6198 | 0.843911 | ||||||||
\(598\) | −30.6219 | −1.25222 | ||||||||
\(599\) | 25.9105 | 1.05868 | 0.529338 | − | 0.848411i | \(-0.322440\pi\) | ||||
0.529338 | + | 0.848411i | \(0.322440\pi\) | |||||||
\(600\) | −3.13304 | −0.127906 | ||||||||
\(601\) | 1.00000 | 0.0407909 | ||||||||
\(602\) | 19.4491 | 0.792687 | ||||||||
\(603\) | −13.3449 | −0.543447 | ||||||||
\(604\) | 2.17667 | 0.0885675 | ||||||||
\(605\) | 5.78559 | 0.235218 | ||||||||
\(606\) | 38.8599 | 1.57857 | ||||||||
\(607\) | 11.0759 | 0.449558 | 0.224779 | − | 0.974410i | \(-0.427834\pi\) | ||||
0.224779 | + | 0.974410i | \(0.427834\pi\) | |||||||
\(608\) | 7.01791 | 0.284614 | ||||||||
\(609\) | 80.4166 | 3.25865 | ||||||||
\(610\) | −4.57895 | −0.185396 | ||||||||
\(611\) | 38.8869 | 1.57319 | ||||||||
\(612\) | −19.5359 | −0.789691 | ||||||||
\(613\) | −42.3475 | −1.71040 | −0.855200 | − | 0.518298i | \(-0.826566\pi\) | ||||
−0.855200 | + | 0.518298i | \(0.826566\pi\) | |||||||
\(614\) | 32.5376 | 1.31311 | ||||||||
\(615\) | −17.0461 | −0.687364 | ||||||||
\(616\) | 7.59804 | 0.306134 | ||||||||
\(617\) | −15.0284 | −0.605020 | −0.302510 | − | 0.953146i | \(-0.597824\pi\) | ||||
−0.302510 | + | 0.953146i | \(0.597824\pi\) | |||||||
\(618\) | −34.7826 | −1.39916 | ||||||||
\(619\) | 32.7880 | 1.31786 | 0.658931 | − | 0.752203i | \(-0.271009\pi\) | ||||
0.658931 | + | 0.752203i | \(0.271009\pi\) | |||||||
\(620\) | −5.44874 | −0.218827 | ||||||||
\(621\) | −64.0151 | −2.56884 | ||||||||
\(622\) | 17.6527 | 0.707807 | ||||||||
\(623\) | 54.7131 | 2.19203 | ||||||||
\(624\) | 17.9179 | 0.717289 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 13.2919 | 0.531250 | ||||||||
\(627\) | 50.2085 | 2.00513 | ||||||||
\(628\) | 4.36210 | 0.174067 | ||||||||
\(629\) | −6.58121 | −0.262410 | ||||||||
\(630\) | 22.6791 | 0.903558 | ||||||||
\(631\) | 22.0176 | 0.876507 | 0.438253 | − | 0.898851i | \(-0.355597\pi\) | ||||
0.438253 | + | 0.898851i | \(0.355597\pi\) | |||||||
\(632\) | 6.18394 | 0.245984 | ||||||||
\(633\) | 64.3360 | 2.55713 | ||||||||
\(634\) | 32.2538 | 1.28096 | ||||||||
\(635\) | 7.80540 | 0.309748 | ||||||||
\(636\) | −14.9815 | −0.594057 | ||||||||
\(637\) | −23.2836 | −0.922530 | ||||||||
\(638\) | −17.6150 | −0.697386 | ||||||||
\(639\) | 28.0131 | 1.10818 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 4.43149 | 0.175033 | 0.0875167 | − | 0.996163i | \(-0.472107\pi\) | ||||
0.0875167 | + | 0.996163i | \(0.472107\pi\) | |||||||
\(642\) | −17.3725 | −0.685637 | ||||||||
\(643\) | 22.6179 | 0.891961 | 0.445981 | − | 0.895043i | \(-0.352855\pi\) | ||||
0.445981 | + | 0.895043i | \(0.352855\pi\) | |||||||
\(644\) | −17.8160 | −0.702049 | ||||||||
\(645\) | −18.3134 | −0.721088 | ||||||||
\(646\) | −20.1147 | −0.791402 | ||||||||
\(647\) | 22.5137 | 0.885105 | 0.442552 | − | 0.896743i | \(-0.354073\pi\) | ||||
0.442552 | + | 0.896743i | \(0.354073\pi\) | |||||||
\(648\) | 17.0095 | 0.668196 | ||||||||
\(649\) | −28.8331 | −1.13180 | ||||||||
\(650\) | −5.71900 | −0.224318 | ||||||||
\(651\) | 56.8017 | 2.22623 | ||||||||
\(652\) | 17.5782 | 0.688414 | ||||||||
\(653\) | 22.1426 | 0.866508 | 0.433254 | − | 0.901272i | \(-0.357365\pi\) | ||||
0.433254 | + | 0.901272i | \(0.357365\pi\) | |||||||
\(654\) | 9.65773 | 0.377647 | ||||||||
\(655\) | 14.3412 | 0.560357 | ||||||||
\(656\) | −5.44074 | −0.212425 | ||||||||
\(657\) | −39.6413 | −1.54655 | ||||||||
\(658\) | 22.6246 | 0.882000 | ||||||||
\(659\) | 39.1211 | 1.52394 | 0.761972 | − | 0.647610i | \(-0.224231\pi\) | ||||
0.761972 | + | 0.647610i | \(0.224231\pi\) | |||||||
\(660\) | −7.15433 | −0.278482 | ||||||||
\(661\) | 15.4960 | 0.602726 | 0.301363 | − | 0.953510i | \(-0.402558\pi\) | ||||
0.301363 | + | 0.953510i | \(0.402558\pi\) | |||||||
\(662\) | 13.8549 | 0.538486 | ||||||||
\(663\) | −51.3561 | −1.99451 | ||||||||
\(664\) | 4.12859 | 0.160221 | ||||||||
\(665\) | 23.3511 | 0.905515 | ||||||||
\(666\) | 15.6505 | 0.606443 | ||||||||
\(667\) | 41.3040 | 1.59930 | ||||||||
\(668\) | 15.3337 | 0.593279 | ||||||||
\(669\) | −13.9220 | −0.538254 | ||||||||
\(670\) | 1.95789 | 0.0756399 | ||||||||
\(671\) | −10.4561 | −0.403652 | ||||||||
\(672\) | 10.4247 | 0.402143 | ||||||||
\(673\) | 42.3649 | 1.63305 | 0.816523 | − | 0.577313i | \(-0.195899\pi\) | ||||
0.816523 | + | 0.577313i | \(0.195899\pi\) | |||||||
\(674\) | −16.1211 | −0.620963 | ||||||||
\(675\) | −11.9556 | −0.460171 | ||||||||
\(676\) | 19.7070 | 0.757960 | ||||||||
\(677\) | 17.2004 | 0.661064 | 0.330532 | − | 0.943795i | \(-0.392772\pi\) | ||||
0.330532 | + | 0.943795i | \(0.392772\pi\) | |||||||
\(678\) | −44.2283 | −1.69858 | ||||||||
\(679\) | 19.4544 | 0.746591 | ||||||||
\(680\) | 2.86619 | 0.109914 | ||||||||
\(681\) | 41.9962 | 1.60930 | ||||||||
\(682\) | −12.4422 | −0.476438 | ||||||||
\(683\) | 19.2386 | 0.736145 | 0.368073 | − | 0.929797i | \(-0.380018\pi\) | ||||
0.368073 | + | 0.929797i | \(0.380018\pi\) | |||||||
\(684\) | 47.8338 | 1.82897 | ||||||||
\(685\) | −5.65409 | −0.216032 | ||||||||
\(686\) | 9.74492 | 0.372063 | ||||||||
\(687\) | 64.4068 | 2.45727 | ||||||||
\(688\) | −5.84523 | −0.222847 | ||||||||
\(689\) | −27.3470 | −1.04184 | ||||||||
\(690\) | 16.7756 | 0.638636 | ||||||||
\(691\) | −8.28888 | −0.315324 | −0.157662 | − | 0.987493i | \(-0.550396\pi\) | ||||
−0.157662 | + | 0.987493i | \(0.550396\pi\) | |||||||
\(692\) | 1.04475 | 0.0397155 | ||||||||
\(693\) | 51.7880 | 1.96726 | ||||||||
\(694\) | −19.8396 | −0.753102 | ||||||||
\(695\) | 14.1896 | 0.538243 | ||||||||
\(696\) | −24.1684 | −0.916099 | ||||||||
\(697\) | 15.5942 | 0.590673 | ||||||||
\(698\) | −6.98979 | −0.264567 | ||||||||
\(699\) | 75.8128 | 2.86750 | ||||||||
\(700\) | −3.32735 | −0.125762 | ||||||||
\(701\) | −9.28449 | −0.350670 | −0.175335 | − | 0.984509i | \(-0.556101\pi\) | ||||
−0.175335 | + | 0.984509i | \(0.556101\pi\) | |||||||
\(702\) | 68.3740 | 2.58061 | ||||||||
\(703\) | 16.1142 | 0.607757 | ||||||||
\(704\) | −2.28351 | −0.0860630 | ||||||||
\(705\) | −21.3034 | −0.802334 | ||||||||
\(706\) | −35.8141 | −1.34788 | ||||||||
\(707\) | 41.2699 | 1.55211 | ||||||||
\(708\) | −39.5598 | −1.48675 | ||||||||
\(709\) | 51.4294 | 1.93147 | 0.965736 | − | 0.259528i | \(-0.0835670\pi\) | ||||
0.965736 | + | 0.259528i | \(0.0835670\pi\) | |||||||
\(710\) | −4.10993 | −0.154243 | ||||||||
\(711\) | 42.1495 | 1.58073 | ||||||||
\(712\) | −16.4434 | −0.616244 | ||||||||
\(713\) | 29.1748 | 1.09260 | ||||||||
\(714\) | −29.8793 | −1.11821 | ||||||||
\(715\) | −13.0594 | −0.488393 | ||||||||
\(716\) | 6.91419 | 0.258396 | ||||||||
\(717\) | 45.4775 | 1.69839 | ||||||||
\(718\) | 8.32788 | 0.310794 | ||||||||
\(719\) | −0.355781 | −0.0132684 | −0.00663420 | − | 0.999978i | \(-0.502112\pi\) | ||||
−0.00663420 | + | 0.999978i | \(0.502112\pi\) | |||||||
\(720\) | −6.81597 | −0.254016 | ||||||||
\(721\) | −36.9398 | −1.37571 | ||||||||
\(722\) | 30.2511 | 1.12583 | ||||||||
\(723\) | −58.1371 | −2.16214 | ||||||||
\(724\) | 1.62026 | 0.0602167 | ||||||||
\(725\) | 7.71402 | 0.286491 | ||||||||
\(726\) | 18.1265 | 0.672738 | ||||||||
\(727\) | −28.8880 | −1.07140 | −0.535698 | − | 0.844410i | \(-0.679951\pi\) | ||||
−0.535698 | + | 0.844410i | \(0.679951\pi\) | |||||||
\(728\) | 19.0291 | 0.705266 | ||||||||
\(729\) | 3.56396 | 0.131998 | ||||||||
\(730\) | 5.81595 | 0.215258 | ||||||||
\(731\) | 16.7536 | 0.619653 | ||||||||
\(732\) | −14.3461 | −0.530246 | ||||||||
\(733\) | 24.5263 | 0.905901 | 0.452951 | − | 0.891536i | \(-0.350371\pi\) | ||||
0.452951 | + | 0.891536i | \(0.350371\pi\) | |||||||
\(734\) | −16.5165 | −0.609635 | ||||||||
\(735\) | 12.7555 | 0.470493 | ||||||||
\(736\) | 5.35441 | 0.197366 | ||||||||
\(737\) | 4.47086 | 0.164686 | ||||||||
\(738\) | −37.0839 | −1.36508 | ||||||||
\(739\) | 24.4832 | 0.900627 | 0.450314 | − | 0.892870i | \(-0.351312\pi\) | ||||
0.450314 | + | 0.892870i | \(0.351312\pi\) | |||||||
\(740\) | −2.29615 | −0.0844081 | ||||||||
\(741\) | 125.746 | 4.61940 | ||||||||
\(742\) | −15.9107 | −0.584100 | ||||||||
\(743\) | 28.9324 | 1.06143 | 0.530713 | − | 0.847552i | \(-0.321924\pi\) | ||||
0.530713 | + | 0.847552i | \(0.321924\pi\) | |||||||
\(744\) | −17.0711 | −0.625858 | ||||||||
\(745\) | 14.2981 | 0.523843 | ||||||||
\(746\) | −23.4075 | −0.857009 | ||||||||
\(747\) | 28.1404 | 1.02960 | ||||||||
\(748\) | 6.54498 | 0.239308 | ||||||||
\(749\) | −18.4499 | −0.674145 | ||||||||
\(750\) | 3.13304 | 0.114403 | ||||||||
\(751\) | −22.9311 | −0.836769 | −0.418384 | − | 0.908270i | \(-0.637403\pi\) | ||||
−0.418384 | + | 0.908270i | \(0.637403\pi\) | |||||||
\(752\) | −6.79959 | −0.247956 | ||||||||
\(753\) | −79.5137 | −2.89764 | ||||||||
\(754\) | −44.1165 | −1.60663 | ||||||||
\(755\) | −2.17667 | −0.0792172 | ||||||||
\(756\) | 39.7805 | 1.44680 | ||||||||
\(757\) | −7.74385 | −0.281455 | −0.140728 | − | 0.990048i | \(-0.544944\pi\) | ||||
−0.140728 | + | 0.990048i | \(0.544944\pi\) | |||||||
\(758\) | 3.29299 | 0.119607 | ||||||||
\(759\) | 38.3072 | 1.39046 | ||||||||
\(760\) | −7.01791 | −0.254566 | ||||||||
\(761\) | −7.60887 | −0.275821 | −0.137911 | − | 0.990445i | \(-0.544039\pi\) | ||||
−0.137911 | + | 0.990445i | \(0.544039\pi\) | |||||||
\(762\) | 24.4547 | 0.885899 | ||||||||
\(763\) | 10.2567 | 0.371317 | ||||||||
\(764\) | −22.0018 | −0.795996 | ||||||||
\(765\) | 19.5359 | 0.706321 | ||||||||
\(766\) | 27.5083 | 0.993917 | ||||||||
\(767\) | −72.2118 | −2.60742 | ||||||||
\(768\) | −3.13304 | −0.113054 | ||||||||
\(769\) | −54.7236 | −1.97338 | −0.986692 | − | 0.162600i | \(-0.948012\pi\) | ||||
−0.986692 | + | 0.162600i | \(0.948012\pi\) | |||||||
\(770\) | −7.59804 | −0.273814 | ||||||||
\(771\) | 13.8168 | 0.497599 | ||||||||
\(772\) | −1.66682 | −0.0599903 | ||||||||
\(773\) | −4.96234 | −0.178483 | −0.0892414 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892414 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(774\) | −39.8409 | −1.43205 | ||||||||
\(775\) | 5.44874 | 0.195724 | ||||||||
\(776\) | −5.84681 | −0.209888 | ||||||||
\(777\) | 23.9368 | 0.858726 | ||||||||
\(778\) | −4.63597 | −0.166208 | ||||||||
\(779\) | −38.1826 | −1.36803 | ||||||||
\(780\) | −17.9179 | −0.641563 | ||||||||
\(781\) | −9.38506 | −0.335824 | ||||||||
\(782\) | −15.3468 | −0.548800 | ||||||||
\(783\) | −92.2256 | −3.29588 | ||||||||
\(784\) | 4.07127 | 0.145402 | ||||||||
\(785\) | −4.36210 | −0.155690 | ||||||||
\(786\) | 44.9316 | 1.60266 | ||||||||
\(787\) | 11.2463 | 0.400887 | 0.200444 | − | 0.979705i | \(-0.435762\pi\) | ||||
0.200444 | + | 0.979705i | \(0.435762\pi\) | |||||||
\(788\) | 14.4823 | 0.515911 | ||||||||
\(789\) | −18.7730 | −0.668336 | ||||||||
\(790\) | −6.18394 | −0.220015 | ||||||||
\(791\) | −46.9713 | −1.67011 | ||||||||
\(792\) | −15.5643 | −0.553054 | ||||||||
\(793\) | −26.1870 | −0.929929 | ||||||||
\(794\) | −30.8511 | −1.09487 | ||||||||
\(795\) | 14.9815 | 0.531341 | ||||||||
\(796\) | −6.58139 | −0.233271 | ||||||||
\(797\) | −2.65747 | −0.0941324 | −0.0470662 | − | 0.998892i | \(-0.514987\pi\) | ||||
−0.0470662 | + | 0.998892i | \(0.514987\pi\) | |||||||
\(798\) | 73.1599 | 2.58983 | ||||||||
\(799\) | 19.4890 | 0.689470 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −112.078 | −3.96008 | ||||||||
\(802\) | −5.81994 | −0.205509 | ||||||||
\(803\) | 13.2808 | 0.468668 | ||||||||
\(804\) | 6.13416 | 0.216335 | ||||||||
\(805\) | 17.8160 | 0.627932 | ||||||||
\(806\) | −31.1613 | −1.09761 | ||||||||
\(807\) | −27.8865 | −0.981651 | ||||||||
\(808\) | −12.4032 | −0.436344 | ||||||||
\(809\) | 40.8239 | 1.43529 | 0.717645 | − | 0.696409i | \(-0.245220\pi\) | ||||
0.717645 | + | 0.696409i | \(0.245220\pi\) | |||||||
\(810\) | −17.0095 | −0.597653 | ||||||||
\(811\) | 2.40839 | 0.0845701 | 0.0422850 | − | 0.999106i | \(-0.486536\pi\) | ||||
0.0422850 | + | 0.999106i | \(0.486536\pi\) | |||||||
\(812\) | −25.6673 | −0.900744 | ||||||||
\(813\) | 100.510 | 3.52504 | ||||||||
\(814\) | −5.24327 | −0.183777 | ||||||||
\(815\) | −17.5782 | −0.615736 | ||||||||
\(816\) | 8.97991 | 0.314360 | ||||||||
\(817\) | −41.0213 | −1.43515 | ||||||||
\(818\) | −35.4794 | −1.24051 | ||||||||
\(819\) | 129.702 | 4.53215 | ||||||||
\(820\) | 5.44074 | 0.189999 | ||||||||
\(821\) | −41.9781 | −1.46505 | −0.732523 | − | 0.680742i | \(-0.761657\pi\) | ||||
−0.732523 | + | 0.680742i | \(0.761657\pi\) | |||||||
\(822\) | −17.7145 | −0.617865 | ||||||||
\(823\) | −48.3360 | −1.68489 | −0.842443 | − | 0.538785i | \(-0.818884\pi\) | ||||
−0.842443 | + | 0.538785i | \(0.818884\pi\) | |||||||
\(824\) | 11.1019 | 0.386752 | ||||||||
\(825\) | 7.15433 | 0.249082 | ||||||||
\(826\) | −42.0133 | −1.46183 | ||||||||
\(827\) | −12.2376 | −0.425545 | −0.212772 | − | 0.977102i | \(-0.568249\pi\) | ||||
−0.212772 | + | 0.977102i | \(0.568249\pi\) | |||||||
\(828\) | 36.4955 | 1.26831 | ||||||||
\(829\) | 43.1833 | 1.49982 | 0.749909 | − | 0.661541i | \(-0.230097\pi\) | ||||
0.749909 | + | 0.661541i | \(0.230097\pi\) | |||||||
\(830\) | −4.12859 | −0.143306 | ||||||||
\(831\) | −5.46927 | −0.189727 | ||||||||
\(832\) | −5.71900 | −0.198271 | ||||||||
\(833\) | −11.6690 | −0.404309 | ||||||||
\(834\) | 44.4567 | 1.53941 | ||||||||
\(835\) | −15.3337 | −0.530645 | ||||||||
\(836\) | −16.0255 | −0.554252 | ||||||||
\(837\) | −65.1429 | −2.25167 | ||||||||
\(838\) | −5.20695 | −0.179871 | ||||||||
\(839\) | −17.7217 | −0.611821 | −0.305911 | − | 0.952060i | \(-0.598961\pi\) | ||||
−0.305911 | + | 0.952060i | \(0.598961\pi\) | |||||||
\(840\) | −10.4247 | −0.359688 | ||||||||
\(841\) | 30.5061 | 1.05193 | ||||||||
\(842\) | 16.9532 | 0.584247 | ||||||||
\(843\) | 90.2381 | 3.10797 | ||||||||
\(844\) | −20.5347 | −0.706832 | ||||||||
\(845\) | −19.7070 | −0.677940 | ||||||||
\(846\) | −46.3458 | −1.59340 | ||||||||
\(847\) | 19.2507 | 0.661461 | ||||||||
\(848\) | 4.78179 | 0.164207 | ||||||||
\(849\) | −49.2766 | −1.69117 | ||||||||
\(850\) | −2.86619 | −0.0983097 | ||||||||
\(851\) | 12.2945 | 0.421451 | ||||||||
\(852\) | −12.8766 | −0.441145 | ||||||||
\(853\) | −22.9308 | −0.785134 | −0.392567 | − | 0.919723i | \(-0.628413\pi\) | ||||
−0.392567 | + | 0.919723i | \(0.628413\pi\) | |||||||
\(854\) | −15.2358 | −0.521358 | ||||||||
\(855\) | −47.8338 | −1.63588 | ||||||||
\(856\) | 5.54492 | 0.189521 | ||||||||
\(857\) | −10.3690 | −0.354197 | −0.177099 | − | 0.984193i | \(-0.556671\pi\) | ||||
−0.177099 | + | 0.984193i | \(0.556671\pi\) | |||||||
\(858\) | −40.9156 | −1.39684 | ||||||||
\(859\) | 4.79487 | 0.163599 | 0.0817994 | − | 0.996649i | \(-0.473933\pi\) | ||||
0.0817994 | + | 0.996649i | \(0.473933\pi\) | |||||||
\(860\) | 5.84523 | 0.199321 | ||||||||
\(861\) | −56.7183 | −1.93295 | ||||||||
\(862\) | −25.6428 | −0.873398 | ||||||||
\(863\) | −41.3420 | −1.40730 | −0.703649 | − | 0.710547i | \(-0.748447\pi\) | ||||
−0.703649 | + | 0.710547i | \(0.748447\pi\) | |||||||
\(864\) | −11.9556 | −0.406737 | ||||||||
\(865\) | −1.04475 | −0.0355226 | ||||||||
\(866\) | −0.0124318 | −0.000422449 0 | ||||||||
\(867\) | 27.5236 | 0.934750 | ||||||||
\(868\) | −18.1299 | −0.615368 | ||||||||
\(869\) | −14.1211 | −0.479025 | ||||||||
\(870\) | 24.1684 | 0.819384 | ||||||||
\(871\) | 11.1972 | 0.379402 | ||||||||
\(872\) | −3.08254 | −0.104388 | ||||||||
\(873\) | −39.8516 | −1.34877 | ||||||||
\(874\) | 37.5768 | 1.27105 | ||||||||
\(875\) | 3.32735 | 0.112485 | ||||||||
\(876\) | 18.2216 | 0.615651 | ||||||||
\(877\) | −33.1687 | −1.12003 | −0.560013 | − | 0.828484i | \(-0.689204\pi\) | ||||
−0.560013 | + | 0.828484i | \(0.689204\pi\) | |||||||
\(878\) | −24.1016 | −0.813391 | ||||||||
\(879\) | 93.5634 | 3.15581 | ||||||||
\(880\) | 2.28351 | 0.0769771 | ||||||||
\(881\) | 55.3045 | 1.86326 | 0.931628 | − | 0.363414i | \(-0.118389\pi\) | ||||
0.931628 | + | 0.363414i | \(0.118389\pi\) | |||||||
\(882\) | 27.7496 | 0.934379 | ||||||||
\(883\) | 37.0462 | 1.24671 | 0.623353 | − | 0.781941i | \(-0.285770\pi\) | ||||
0.623353 | + | 0.781941i | \(0.285770\pi\) | |||||||
\(884\) | 16.3918 | 0.551315 | ||||||||
\(885\) | 39.5598 | 1.32979 | ||||||||
\(886\) | −25.9745 | −0.872631 | ||||||||
\(887\) | 15.4659 | 0.519293 | 0.259647 | − | 0.965704i | \(-0.416394\pi\) | ||||
0.259647 | + | 0.965704i | \(0.416394\pi\) | |||||||
\(888\) | −7.19393 | −0.241413 | ||||||||
\(889\) | 25.9713 | 0.871050 | ||||||||
\(890\) | 16.4434 | 0.551185 | ||||||||
\(891\) | −38.8413 | −1.30123 | ||||||||
\(892\) | 4.44359 | 0.148782 | ||||||||
\(893\) | −47.7189 | −1.59685 | ||||||||
\(894\) | 44.7967 | 1.49823 | ||||||||
\(895\) | −6.91419 | −0.231116 | ||||||||
\(896\) | −3.32735 | −0.111159 | ||||||||
\(897\) | 95.9397 | 3.20333 | ||||||||
\(898\) | −5.64460 | −0.188363 | ||||||||
\(899\) | 42.0317 | 1.40183 | ||||||||
\(900\) | 6.81597 | 0.227199 | ||||||||
\(901\) | −13.7055 | −0.456597 | ||||||||
\(902\) | 12.4240 | 0.413673 | ||||||||
\(903\) | −60.9350 | −2.02779 | ||||||||
\(904\) | 14.1167 | 0.469515 | ||||||||
\(905\) | −1.62026 | −0.0538594 | ||||||||
\(906\) | −6.81961 | −0.226566 | ||||||||
\(907\) | 41.4891 | 1.37762 | 0.688811 | − | 0.724941i | \(-0.258133\pi\) | ||||
0.688811 | + | 0.724941i | \(0.258133\pi\) | |||||||
\(908\) | −13.4043 | −0.444836 | ||||||||
\(909\) | −84.5400 | −2.80401 | ||||||||
\(910\) | −19.0291 | −0.630809 | ||||||||
\(911\) | −44.6851 | −1.48048 | −0.740241 | − | 0.672341i | \(-0.765289\pi\) | ||||
−0.740241 | + | 0.672341i | \(0.765289\pi\) | |||||||
\(912\) | −21.9874 | −0.728076 | ||||||||
\(913\) | −9.42768 | −0.312011 | ||||||||
\(914\) | −20.2448 | −0.669637 | ||||||||
\(915\) | 14.3461 | 0.474266 | ||||||||
\(916\) | −20.5573 | −0.679231 | ||||||||
\(917\) | 47.7182 | 1.57579 | ||||||||
\(918\) | 34.2670 | 1.13098 | ||||||||
\(919\) | −22.0227 | −0.726462 | −0.363231 | − | 0.931699i | \(-0.618326\pi\) | ||||
−0.363231 | + | 0.931699i | \(0.618326\pi\) | |||||||
\(920\) | −5.35441 | −0.176530 | ||||||||
\(921\) | −101.942 | −3.35910 | ||||||||
\(922\) | −8.98189 | −0.295803 | ||||||||
\(923\) | −23.5047 | −0.773666 | ||||||||
\(924\) | −23.8050 | −0.783126 | ||||||||
\(925\) | 2.29615 | 0.0754969 | ||||||||
\(926\) | 13.7804 | 0.452851 | ||||||||
\(927\) | 75.6700 | 2.48533 | ||||||||
\(928\) | 7.71402 | 0.253225 | ||||||||
\(929\) | 38.0273 | 1.24763 | 0.623817 | − | 0.781570i | \(-0.285581\pi\) | ||||
0.623817 | + | 0.781570i | \(0.285581\pi\) | |||||||
\(930\) | 17.0711 | 0.559785 | ||||||||
\(931\) | 28.5718 | 0.936403 | ||||||||
\(932\) | −24.1978 | −0.792626 | ||||||||
\(933\) | −55.3066 | −1.81066 | ||||||||
\(934\) | 21.2600 | 0.695647 | ||||||||
\(935\) | −6.54498 | −0.214044 | ||||||||
\(936\) | −38.9805 | −1.27412 | ||||||||
\(937\) | −30.6324 | −1.00072 | −0.500358 | − | 0.865818i | \(-0.666798\pi\) | ||||
−0.500358 | + | 0.865818i | \(0.666798\pi\) | |||||||
\(938\) | 6.51459 | 0.212709 | ||||||||
\(939\) | −41.6440 | −1.35900 | ||||||||
\(940\) | 6.79959 | 0.221778 | ||||||||
\(941\) | −14.6502 | −0.477584 | −0.238792 | − | 0.971071i | \(-0.576751\pi\) | ||||
−0.238792 | + | 0.971071i | \(0.576751\pi\) | |||||||
\(942\) | −13.6666 | −0.445283 | ||||||||
\(943\) | −29.1319 | −0.948666 | ||||||||
\(944\) | 12.6266 | 0.410962 | ||||||||
\(945\) | −39.7805 | −1.29406 | ||||||||
\(946\) | 13.3476 | 0.433969 | ||||||||
\(947\) | −6.59175 | −0.214203 | −0.107102 | − | 0.994248i | \(-0.534157\pi\) | ||||
−0.107102 | + | 0.994248i | \(0.534157\pi\) | |||||||
\(948\) | −19.3745 | −0.629256 | ||||||||
\(949\) | 33.2614 | 1.07971 | ||||||||
\(950\) | 7.01791 | 0.227691 | ||||||||
\(951\) | −101.053 | −3.27686 | ||||||||
\(952\) | 9.53684 | 0.309091 | ||||||||
\(953\) | 49.1037 | 1.59062 | 0.795312 | − | 0.606201i | \(-0.207307\pi\) | ||||
0.795312 | + | 0.606201i | \(0.207307\pi\) | |||||||
\(954\) | 32.5925 | 1.05522 | ||||||||
\(955\) | 22.0018 | 0.711961 | ||||||||
\(956\) | −14.5154 | −0.469463 | ||||||||
\(957\) | 55.1887 | 1.78400 | ||||||||
\(958\) | 0.670853 | 0.0216743 | ||||||||
\(959\) | −18.8131 | −0.607508 | ||||||||
\(960\) | 3.13304 | 0.101119 | ||||||||
\(961\) | −1.31125 | −0.0422984 | ||||||||
\(962\) | −13.1317 | −0.423382 | ||||||||
\(963\) | 37.7940 | 1.21789 | ||||||||
\(964\) | 18.5561 | 0.597652 | ||||||||
\(965\) | 1.66682 | 0.0536569 | ||||||||
\(966\) | 55.8183 | 1.79593 | ||||||||
\(967\) | 25.2387 | 0.811622 | 0.405811 | − | 0.913957i | \(-0.366989\pi\) | ||||
0.405811 | + | 0.913957i | \(0.366989\pi\) | |||||||
\(968\) | −5.78559 | −0.185956 | ||||||||
\(969\) | 63.0202 | 2.02450 | ||||||||
\(970\) | 5.84681 | 0.187730 | ||||||||
\(971\) | 50.5542 | 1.62236 | 0.811181 | − | 0.584795i | \(-0.198825\pi\) | ||||
0.811181 | + | 0.584795i | \(0.198825\pi\) | |||||||
\(972\) | −17.4247 | −0.558898 | ||||||||
\(973\) | 47.2138 | 1.51361 | ||||||||
\(974\) | −0.120064 | −0.00384711 | ||||||||
\(975\) | 17.9179 | 0.573831 | ||||||||
\(976\) | 4.57895 | 0.146569 | ||||||||
\(977\) | −13.9373 | −0.445895 | −0.222947 | − | 0.974830i | \(-0.571568\pi\) | ||||
−0.222947 | + | 0.974830i | \(0.571568\pi\) | |||||||
\(978\) | −55.0732 | −1.76105 | ||||||||
\(979\) | 37.5487 | 1.20006 | ||||||||
\(980\) | −4.07127 | −0.130052 | ||||||||
\(981\) | −21.0105 | −0.670813 | ||||||||
\(982\) | −15.2734 | −0.487395 | ||||||||
\(983\) | −7.96064 | −0.253905 | −0.126952 | − | 0.991909i | \(-0.540520\pi\) | ||||
−0.126952 | + | 0.991909i | \(0.540520\pi\) | |||||||
\(984\) | 17.0461 | 0.543409 | ||||||||
\(985\) | −14.4823 | −0.461445 | ||||||||
\(986\) | −22.1099 | −0.704122 | ||||||||
\(987\) | −70.8840 | −2.25626 | ||||||||
\(988\) | −40.1354 | −1.27688 | ||||||||
\(989\) | −31.2977 | −0.995211 | ||||||||
\(990\) | 15.5643 | 0.494666 | ||||||||
\(991\) | 46.1623 | 1.46639 | 0.733196 | − | 0.680017i | \(-0.238028\pi\) | ||||
0.733196 | + | 0.680017i | \(0.238028\pi\) | |||||||
\(992\) | 5.44874 | 0.172998 | ||||||||
\(993\) | −43.4081 | −1.37751 | ||||||||
\(994\) | −13.6752 | −0.433750 | ||||||||
\(995\) | 6.58139 | 0.208644 | ||||||||
\(996\) | −12.9351 | −0.409863 | ||||||||
\(997\) | 29.6707 | 0.939681 | 0.469840 | − | 0.882751i | \(-0.344311\pi\) | ||||
0.469840 | + | 0.882751i | \(0.344311\pi\) | |||||||
\(998\) | −43.2431 | −1.36884 | ||||||||
\(999\) | −27.4518 | −0.868537 |
(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 | 6010.2.a.f.1.2 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.f.1.2 | ✓ | 22 | 1.1 | even | 1 | trivial |