Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1480,2,Mod(1,1480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1480.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1480 = 2^{3} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1480.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: | \(11.8178594991\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.693982032.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 16x^{4} + 12x^{3} + 60x^{2} - 18x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.07986\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1480.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.07986 | 0.623459 | 0.311730 | − | 0.950171i | \(-0.399092\pi\) | ||||
0.311730 | + | 0.950171i | \(0.399092\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.77160 | 1.42553 | 0.712765 | − | 0.701403i | \(-0.247443\pi\) | ||||
0.712765 | + | 0.701403i | \(0.247443\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.83390 | −0.611299 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.592024 | 0.178502 | 0.0892509 | − | 0.996009i | \(-0.471553\pi\) | ||||
0.0892509 | + | 0.996009i | \(0.471553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.63293 | −1.00759 | −0.503796 | − | 0.863823i | \(-0.668064\pi\) | ||||
−0.503796 | + | 0.863823i | \(0.668064\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.07986 | 0.278819 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24187 | 1.02881 | 0.514403 | − | 0.857549i | \(-0.328014\pi\) | ||||
0.514403 | + | 0.857549i | \(0.328014\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.63998 | 0.605653 | 0.302827 | − | 0.953046i | \(-0.402070\pi\) | ||||
0.302827 | + | 0.953046i | \(0.402070\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.07281 | 0.888760 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.35915 | 0.908945 | 0.454473 | − | 0.890761i | \(-0.349828\pi\) | ||||
0.454473 | + | 0.890761i | \(0.349828\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.21995 | −1.00458 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.768672 | 0.142739 | 0.0713694 | − | 0.997450i | \(-0.477263\pi\) | ||||
0.0713694 | + | 0.997450i | \(0.477263\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.69522 | 1.20250 | 0.601249 | − | 0.799062i | \(-0.294670\pi\) | ||||
0.601249 | + | 0.799062i | \(0.294670\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.639305 | 0.111289 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.77160 | 0.637516 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.92306 | −0.628193 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.71226 | 1.20445 | 0.602226 | − | 0.798325i | \(-0.294281\pi\) | ||||
0.602226 | + | 0.798325i | \(0.294281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.33160 | 0.355566 | 0.177783 | − | 0.984070i | \(-0.443107\pi\) | ||||
0.177783 | + | 0.984070i | \(0.443107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.83390 | −0.273381 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.64640 | −1.11534 | −0.557671 | − | 0.830062i | \(-0.688305\pi\) | ||||
−0.557671 | + | 0.830062i | \(0.688305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.22495 | 1.03214 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.58064 | 0.641418 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.432298 | 0.0593806 | 0.0296903 | − | 0.999559i | \(-0.490548\pi\) | ||||
0.0296903 | + | 0.999559i | \(0.490548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.592024 | 0.0798285 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.85082 | 0.377600 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.2065 | −1.71934 | −0.859671 | − | 0.510848i | \(-0.829331\pi\) | ||||
−0.859671 | + | 0.510848i | \(0.829331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.39105 | −0.178106 | −0.0890531 | − | 0.996027i | \(-0.528384\pi\) | ||||
−0.0890531 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.91672 | −0.871424 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.63293 | −0.450609 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.83940 | 0.591227 | 0.295614 | − | 0.955308i | \(-0.404476\pi\) | ||||
0.295614 | + | 0.955308i | \(0.404476\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.70728 | 0.566690 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.639305 | 0.0758715 | 0.0379358 | − | 0.999280i | \(-0.487922\pi\) | ||||
0.0379358 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.23872 | −0.964269 | −0.482134 | − | 0.876097i | \(-0.660138\pi\) | ||||
−0.482134 | + | 0.876097i | \(0.660138\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.07986 | 0.124692 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.23288 | 0.254460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.94066 | −0.668377 | −0.334188 | − | 0.942506i | \(-0.608462\pi\) | ||||
−0.334188 | + | 0.942506i | \(0.608462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.135139 | −0.0150155 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.80252 | −0.527145 | −0.263573 | − | 0.964640i | \(-0.584901\pi\) | ||||
−0.263573 | + | 0.964640i | \(0.584901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24187 | 0.460096 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.830060 | 0.0889918 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.4653 | 1.85132 | 0.925658 | − | 0.378362i | \(-0.123513\pi\) | ||||
0.925658 | + | 0.378362i | \(0.123513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.7019 | −1.43635 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.22993 | 0.749708 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.63998 | 0.270856 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.77889 | 0.789826 | 0.394913 | − | 0.918718i | \(-0.370775\pi\) | ||||
0.394913 | + | 0.918718i | \(0.370775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.08571 | −0.109118 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4320 | 1.03802 | 0.519009 | − | 0.854769i | \(-0.326301\pi\) | ||||
0.519009 | + | 0.854769i | \(0.326301\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.30428 | −0.621179 | −0.310590 | − | 0.950544i | \(-0.600527\pi\) | ||||
−0.310590 | + | 0.950544i | \(0.600527\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.07281 | 0.397465 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1260 | 0.978915 | 0.489457 | − | 0.872027i | \(-0.337195\pi\) | ||||
0.489457 | + | 0.872027i | \(0.337195\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.53997 | −0.243285 | −0.121643 | − | 0.992574i | \(-0.538816\pi\) | ||||
−0.121643 | + | 0.992574i | \(0.538816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.07986 | −0.102496 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.76075 | −0.824142 | −0.412071 | − | 0.911152i | \(-0.635194\pi\) | ||||
−0.412071 | + | 0.911152i | \(0.635194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.35915 | 0.406493 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.66241 | 0.615940 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.9986 | 1.46659 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6495 | −0.968137 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.32818 | 0.750927 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.3305 | 1.80404 | 0.902022 | − | 0.431690i | \(-0.142082\pi\) | ||||
0.902022 | + | 0.431690i | \(0.142082\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.51781 | 0.221681 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.07705 | −0.0941022 | −0.0470511 | − | 0.998892i | \(-0.514982\pi\) | ||||
−0.0470511 | + | 0.998892i | \(0.514982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.95694 | 0.863377 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.21995 | −0.449261 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.21099 | −0.274333 | −0.137167 | − | 0.990548i | \(-0.543800\pi\) | ||||
−0.137167 | + | 0.990548i | \(0.543800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6116 | −1.49379 | −0.746897 | − | 0.664940i | \(-0.768457\pi\) | ||||
−0.746897 | + | 0.664940i | \(0.768457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.25706 | −0.695370 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.15078 | −0.179857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.768672 | 0.0638347 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.80196 | 0.643495 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.9003 | 1.30261 | 0.651303 | − | 0.758818i | \(-0.274223\pi\) | ||||
0.651303 | + | 0.758818i | \(0.274223\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5458 | −1.34648 | −0.673240 | − | 0.739424i | \(-0.735098\pi\) | ||||
−0.673240 | + | 0.739424i | \(0.735098\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.77915 | −0.628907 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.69522 | 0.537773 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.09573 | −0.566301 | −0.283150 | − | 0.959076i | \(-0.591380\pi\) | ||||
−0.283150 | + | 0.959076i | \(0.591380\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.466822 | 0.0370214 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.4410 | 1.29573 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.4729 | −1.21193 | −0.605964 | − | 0.795492i | \(-0.707212\pi\) | ||||
−0.605964 | + | 0.795492i | \(0.707212\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.639305 | 0.0497698 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.35479 | −0.104837 | −0.0524183 | − | 0.998625i | \(-0.516693\pi\) | ||||
−0.0524183 | + | 0.998625i | \(0.516693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.198155 | 0.0152427 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.84145 | −0.370235 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0106237 | 0.000807708 0 | 0.000403854 | − | 1.00000i | \(-0.499871\pi\) | ||||
0.000403854 | 1.00000i | \(0.499871\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.77160 | 0.285106 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.2612 | −1.07194 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.3180 | −1.29441 | −0.647204 | − | 0.762317i | \(-0.724062\pi\) | ||||
−0.647204 | + | 0.762317i | \(0.724062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.6673 | −1.38753 | −0.693763 | − | 0.720203i | \(-0.744049\pi\) | ||||
−0.693763 | + | 0.720203i | \(0.744049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.50215 | −0.111042 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.51129 | 0.183644 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −19.6875 | −1.43206 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.02878 | −0.363870 | −0.181935 | − | 0.983311i | \(-0.558236\pi\) | ||||
−0.181935 | + | 0.983311i | \(0.558236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.84163 | −0.564453 | −0.282226 | − | 0.959348i | \(-0.591073\pi\) | ||||
−0.282226 | + | 0.959348i | \(0.591073\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.92306 | −0.280936 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.9703 | 1.42283 | 0.711413 | − | 0.702774i | \(-0.248055\pi\) | ||||
0.711413 | + | 0.702774i | \(0.248055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.52822 | 0.462773 | 0.231386 | − | 0.972862i | \(-0.425674\pi\) | ||||
0.231386 | + | 0.972862i | \(0.425674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.22589 | 0.368606 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.89912 | 0.203478 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.71226 | 0.538647 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.99422 | −0.555637 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.56293 | 0.108110 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.514103 | 0.0353923 | 0.0176962 | − | 0.999843i | \(-0.494367\pi\) | ||||
0.0176962 | + | 0.999843i | \(0.494367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.690361 | 0.0473028 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.33160 | 0.159014 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.2517 | 1.71420 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.89669 | −0.601182 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.4104 | −1.03662 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.80468 | 0.388710 | 0.194355 | − | 0.980931i | \(-0.437739\pi\) | ||||
0.194355 | + | 0.980931i | \(0.437739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.83390 | −0.122260 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.92840 | 0.194365 | 0.0971823 | − | 0.995267i | \(-0.469017\pi\) | ||||
0.0971823 | + | 0.995267i | \(0.469017\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1595 | 1.13393 | 0.566967 | − | 0.823741i | \(-0.308117\pi\) | ||||
0.566967 | + | 0.823741i | \(0.308117\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.41120 | 0.158645 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.39737 | −0.157057 | −0.0785286 | − | 0.996912i | \(-0.525022\pi\) | ||||
−0.0785286 | + | 0.996912i | \(0.525022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.64640 | −0.498796 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.41510 | −0.416706 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.6560 | −1.53018 | −0.765091 | − | 0.643922i | \(-0.777306\pi\) | ||||
−0.765091 | + | 0.643922i | \(0.777306\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2110 | −0.722163 | −0.361082 | − | 0.932534i | \(-0.617592\pi\) | ||||
−0.361082 | + | 0.932534i | \(0.617592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5139 | 0.995217 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.22495 | 0.461585 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.59085 | −0.610251 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.18606 | −0.328653 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.4734 | −1.29227 | −0.646133 | − | 0.763225i | \(-0.723615\pi\) | ||||
−0.646133 | + | 0.763225i | \(0.723615\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.58072 | 0.162248 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.58064 | 0.286851 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5889 | 0.660516 | 0.330258 | − | 0.943891i | \(-0.392864\pi\) | ||||
0.330258 | + | 0.943891i | \(0.392864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.77160 | −0.234356 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.40966 | −0.0872560 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3030 | −0.635310 | −0.317655 | − | 0.948206i | \(-0.602895\pi\) | ||||
−0.317655 | + | 0.948206i | \(0.602895\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.432298 | 0.0265558 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.8601 | 1.15422 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.05589 | −0.491176 | −0.245588 | − | 0.969374i | \(-0.578981\pi\) | ||||
−0.245588 | + | 0.969374i | \(0.578981\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.439883 | −0.0267210 | −0.0133605 | − | 0.999911i | \(-0.504253\pi\) | ||||
−0.0133605 | + | 0.999911i | \(0.504253\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.7962 | −0.895508 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.592024 | 0.0357004 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.3387 | −1.52245 | −0.761227 | − | 0.648486i | \(-0.775403\pi\) | ||||
−0.761227 | + | 0.648486i | \(0.775403\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.2783 | −0.735085 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.36373 | 0.558594 | 0.279297 | − | 0.960205i | \(-0.409899\pi\) | ||||
0.279297 | + | 0.960205i | \(0.409899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.99025 | −0.415527 | −0.207764 | − | 0.978179i | \(-0.566619\pi\) | ||||
−0.207764 | + | 0.978179i | \(0.566619\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.85082 | 0.168868 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 29.0875 | 1.71698 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.993477 | 0.0584398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.40013 | 0.492424 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.6724 | 0.623486 | 0.311743 | − | 0.950166i | \(-0.399087\pi\) | ||||
0.311743 | + | 0.950166i | \(0.399087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.2065 | −0.768913 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.09033 | −0.179319 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.8365 | −0.915846 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.79387 | 0.506870 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.2651 | 0.647162 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.39105 | −0.0796516 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.9040 | −1.02184 | −0.510918 | − | 0.859630i | \(-0.670694\pi\) | ||||
−0.510918 | + | 0.859630i | \(0.670694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.80776 | −0.387280 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6173 | 0.602052 | 0.301026 | − | 0.953616i | \(-0.402671\pi\) | ||||
0.301026 | + | 0.953616i | \(0.402671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.4102 | −1.04061 | −0.520303 | − | 0.853982i | \(-0.674181\pi\) | ||||
−0.520303 | + | 0.853982i | \(0.674181\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.91672 | −0.389713 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.1211 | 1.69177 | 0.845885 | − | 0.533365i | \(-0.179073\pi\) | ||||
0.845885 | + | 0.533365i | \(0.179073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.455072 | 0.0254791 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.9347 | 0.610314 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.1985 | 0.623099 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.63293 | −0.201519 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.74282 | −0.151678 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.8391 | −1.58995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.8280 | −1.58453 | −0.792265 | − | 0.610177i | \(-0.791098\pi\) | ||||
−0.792265 | + | 0.610177i | \(0.791098\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.83390 | 0.100497 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.83940 | 0.264405 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.3662 | 1.81757 | 0.908785 | − | 0.417264i | \(-0.137011\pi\) | ||||
0.908785 | + | 0.417264i | \(0.137011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.46041 | −0.513819 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.96373 | 0.214648 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.848422 | 0.0458105 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.70728 | 0.253432 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.2626 | −0.873023 | −0.436512 | − | 0.899699i | \(-0.643786\pi\) | ||||
−0.436512 | + | 0.899699i | \(0.643786\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.1613 | −0.704509 | −0.352255 | − | 0.935904i | \(-0.614585\pi\) | ||||
−0.352255 | + | 0.935904i | \(0.614585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9637 | 1.01221 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.1014 | −1.70858 | −0.854292 | − | 0.519793i | \(-0.826009\pi\) | ||||
−0.854292 | + | 0.519793i | \(0.826009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.639305 | 0.0339308 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.2763 | 0.914361 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.53580 | 0.239390 | 0.119695 | − | 0.992811i | \(-0.461808\pi\) | ||||
0.119695 | + | 0.992811i | \(0.461808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0305 | −0.633184 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.5000 | −0.603594 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.23872 | −0.431234 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2661 | 0.535887 | 0.267944 | − | 0.963435i | \(-0.413656\pi\) | ||||
0.267944 | + | 0.963435i | \(0.413656\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.1435 | −0.736280 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.63045 | 0.0846489 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.3891 | 1.05571 | 0.527854 | − | 0.849335i | \(-0.322997\pi\) | ||||
0.527854 | + | 0.849335i | \(0.322997\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.07986 | 0.0557639 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.79253 | −0.143822 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.8176 | −1.63436 | −0.817180 | − | 0.576383i | \(-0.804464\pi\) | ||||
−0.817180 | + | 0.576383i | \(0.804464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.9542 | 1.12475 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.3238 | 1.08960 | 0.544798 | − | 0.838567i | \(-0.316606\pi\) | ||||
0.544798 | + | 0.838567i | \(0.316606\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.23288 | 0.113798 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.27592 | −0.217357 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.0717 | 1.47399 | 0.736996 | − | 0.675897i | \(-0.236243\pi\) | ||||
0.736996 | + | 0.675897i | \(0.236243\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.4909 | 0.935127 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.16307 | −0.0586689 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.94066 | −0.298907 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.703118 | −0.0352885 | −0.0176442 | − | 0.999844i | \(-0.505617\pi\) | ||||
−0.0176442 | + | 0.999844i | \(0.505617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.7521 | 0.538280 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.9306 | −1.44472 | −0.722361 | − | 0.691516i | \(-0.756943\pi\) | ||||
−0.722361 | + | 0.691516i | \(0.756943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.3233 | −1.21163 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.135139 | −0.00671512 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.592024 | −0.0293455 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.42859 | 0.317873 | 0.158937 | − | 0.987289i | \(-0.449193\pi\) | ||||
0.158937 | + | 0.987289i | \(0.449193\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.46743 | −0.171036 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −49.8097 | −2.45097 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.80252 | −0.235746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.0181 | −0.931319 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.02413 | 0.0988850 | 0.0494425 | − | 0.998777i | \(-0.484256\pi\) | ||||
0.0494425 | + | 0.998777i | \(0.484256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.5472 | −1.68373 | −0.841863 | − | 0.539691i | \(-0.818541\pi\) | ||||
−0.841863 | + | 0.539691i | \(0.818541\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.0227 | 0.681807 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.24187 | 0.205761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.24650 | −0.253896 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.32255 | −0.112134 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.7081 | −0.756631 | −0.378316 | − | 0.925677i | \(-0.623497\pi\) | ||||
−0.378316 | + | 0.925677i | \(0.623497\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.5812 | −1.32547 | −0.662734 | − | 0.748855i | \(-0.730604\pi\) | ||||
−0.662734 | + | 0.748855i | \(0.730604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.830060 | 0.0397983 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.5081 | 0.550505 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9495 | 0.904411 | 0.452205 | − | 0.891914i | \(-0.350637\pi\) | ||||
0.452205 | + | 0.891914i | \(0.350637\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.2498 | −0.630943 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3423 | 0.681424 | 0.340712 | − | 0.940168i | \(-0.389332\pi\) | ||||
0.340712 | + | 0.940168i | \(0.389332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.4653 | 0.827933 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.1702 | 0.812121 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.2535 | −1.52214 | −0.761069 | − | 0.648671i | \(-0.775325\pi\) | ||||
−0.761069 | + | 0.648671i | \(0.775325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.56584 | 0.214997 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.8672 | −0.839475 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.7019 | −0.642357 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.1417 | 0.801856 | 0.400928 | − | 0.916110i | \(-0.368688\pi\) | ||||
0.400928 | + | 0.916110i | \(0.368688\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.1423 | −1.03352 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.53862 | 0.118235 | 0.0591177 | − | 0.998251i | \(-0.481171\pi\) | ||||
0.0591177 | + | 0.998251i | \(0.481171\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.8147 | 1.33913 | 0.669566 | − | 0.742753i | \(-0.266480\pi\) | ||||
0.669566 | + | 0.742753i | \(0.266480\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.22993 | 0.335280 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.5498 | −0.997206 | −0.498603 | − | 0.866831i | \(-0.666153\pi\) | ||||
−0.498603 | + | 0.866831i | \(0.666153\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.2523 | 0.842812 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.66241 | −0.353065 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.38036 | 0.0634692 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.63998 | 0.121131 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.792789 | −0.0362993 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.2747 | −0.697920 | −0.348960 | − | 0.937138i | \(-0.613465\pi\) | ||||
−0.348960 | + | 0.937138i | \(0.613465\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.63293 | 0.165647 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17.7540 | 0.807834 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.77889 | 0.353221 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0338 | 0.454677 | 0.227338 | − | 0.973816i | \(-0.426998\pi\) | ||||
0.227338 | + | 0.973816i | \(0.426998\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.7086 | −0.755588 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0308 | 1.35527 | 0.677636 | − | 0.735397i | \(-0.263004\pi\) | ||||
0.677636 | + | 0.735397i | \(0.263004\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.26061 | 0.146850 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.08571 | −0.0487990 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.41120 | 0.108157 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.2377 | −0.726901 | −0.363451 | − | 0.931614i | \(-0.618401\pi\) | ||||
−0.363451 | + | 0.931614i | \(0.618401\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.46298 | −0.0653613 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.4896 | 1.09194 | 0.545969 | − | 0.837806i | \(-0.316162\pi\) | ||||
0.545969 | + | 0.837806i | \(0.316162\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4320 | 0.464216 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.213981 | 0.00950321 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.7544 | −0.521004 | −0.260502 | − | 0.965473i | \(-0.583888\pi\) | ||||
−0.260502 | + | 0.965473i | \(0.583888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.0731 | −1.37459 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.7806 | −0.608426 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.30428 | −0.277800 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.52685 | −0.199091 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.0114722 | 0.000503573 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.2637 | 1.41350 | 0.706748 | − | 0.707465i | \(-0.250161\pi\) | ||||
0.706748 | + | 0.707465i | \(0.250161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.6565 | −1.29679 | −0.648394 | − | 0.761305i | \(-0.724559\pi\) | ||||
−0.648394 | + | 0.761305i | \(0.724559\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.07281 | 0.177752 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.4003 | 1.23714 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.99783 | −0.173819 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.2194 | 1.05103 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.0181 | −1.21360 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.1260 | 0.437784 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.7011 | −0.807010 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.27734 | 0.184238 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.79143 | −0.291986 | −0.145993 | − | 0.989286i | \(-0.546638\pi\) | ||||
−0.145993 | + | 0.989286i | \(0.546638\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.1581 | −0.865066 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.53997 | −0.108800 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.5412 | −0.835523 | −0.417762 | − | 0.908557i | \(-0.637185\pi\) | ||||
−0.417762 | + | 0.908557i | \(0.637185\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.55105 | 0.108876 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.02928 | 0.0864501 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.4058 | −0.952791 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.07986 | −0.0458376 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.2741 | −1.15564 | −0.577820 | − | 0.816164i | \(-0.696096\pi\) | ||||
−0.577820 | + | 0.816164i | \(0.696096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.47054 | −0.358266 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.71185 | 0.114494 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0787 | 0.509055 | 0.254528 | − | 0.967066i | \(-0.418080\pi\) | ||||
0.254528 | + | 0.967066i | \(0.418080\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.76075 | −0.368567 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.509691 | −0.0214050 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.9855 | −0.921680 | −0.460840 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460840 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.4836 | 1.56864 | 0.784321 | − | 0.620356i | \(-0.213012\pi\) | ||||
0.784321 | + | 0.620356i | \(0.213012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.43040 | −0.226858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.35915 | 0.181789 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1575 | 0.464493 | 0.232247 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232247 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.46788 | −0.351913 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.1132 | −0.751461 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.255931 | 0.0105996 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.66241 | 0.275457 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.9471 | −0.947127 | −0.473564 | − | 0.880760i | \(-0.657033\pi\) | ||||
−0.473564 | + | 0.880760i | \(0.657033\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.6753 | 0.728296 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.5652 | 0.887074 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.7268 | 0.481563 | 0.240781 | − | 0.970579i | \(-0.422596\pi\) | ||||
0.240781 | + | 0.970579i | \(0.422596\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.9986 | 0.655880 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.04958 | 0.288520 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.9905 | 1.34795 | 0.673977 | − | 0.738752i | \(-0.264585\pi\) | ||||
0.673977 | + | 0.738752i | \(0.264585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.5572 | 1.00171 | 0.500855 | − | 0.865531i | \(-0.333019\pi\) | ||||
0.500855 | + | 0.865531i | \(0.333019\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.87496 | −0.361416 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.6495 | −0.432964 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.91430 | 0.118288 | 0.0591439 | − | 0.998249i | \(-0.481163\pi\) | ||||
0.0591439 | + | 0.998249i | \(0.481163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.13065 | 0.126860 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.7788 | 1.12381 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.36977 | −0.257273 | −0.128636 | − | 0.991692i | \(-0.541060\pi\) | ||||
−0.128636 | + | 0.991692i | \(0.541060\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.32818 | 0.335825 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0123562 | 0.000497441 0 | 0.000248721 | − | 1.00000i | \(-0.499921\pi\) | ||||
0.000248721 | 1.00000i | \(0.499921\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.07442 | −0.364732 | −0.182366 | − | 0.983231i | \(-0.558376\pi\) | ||||
−0.182366 | + | 0.983231i | \(0.558376\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.7545 | −0.913107 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 65.8720 | 2.63911 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.68775 | 0.0674023 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.24187 | −0.169135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.1582 | 1.00153 | 0.500767 | − | 0.865582i | \(-0.333051\pi\) | ||||
0.500767 | + | 0.865582i | \(0.333051\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.555161 | 0.0220657 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.3305 | 0.806793 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.2477 | −1.03997 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.17242 | −0.0463801 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.3446 | 1.51452 | 0.757260 | − | 0.653113i | \(-0.226538\pi\) | ||||
0.757260 | + | 0.653113i | \(0.226538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.3835 | 1.31652 | 0.658259 | − | 0.752791i | \(-0.271293\pi\) | ||||
0.658259 | + | 0.752791i | \(0.271293\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.51781 | 0.0991387 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.7815 | 1.44603 | 0.723015 | − | 0.690832i | \(-0.242756\pi\) | ||||
0.723015 | + | 0.690832i | \(0.242756\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.81857 | −0.306906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.2684 | 1.06873 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.9336 | 0.427867 | 0.213933 | − | 0.976848i | \(-0.431372\pi\) | ||||
0.213933 | + | 0.976848i | \(0.431372\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.07705 | −0.0420838 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.1089 | 0.589456 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.74959 | 0.379790 | 0.189895 | − | 0.981804i | \(-0.439185\pi\) | ||||
0.189895 | + | 0.981804i | \(0.439185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.93560 | −0.347555 | −0.173777 | − | 0.984785i | \(-0.555597\pi\) | ||||
−0.173777 | + | 0.984785i | \(0.555597\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.6411 | −0.646288 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.95694 | 0.386114 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.35075 | 0.129742 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.26826 | 0.242345 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.823537 | −0.0317923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.5283 | 1.60080 | 0.800399 | − | 0.599468i | \(-0.204621\pi\) | ||||
0.800399 | + | 0.599468i | \(0.204621\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.21995 | −0.200916 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.9150 | −1.45719 | −0.728595 | − | 0.684945i | \(-0.759826\pi\) | ||||
−0.728595 | + | 0.684945i | \(0.759826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.3388 | 1.12592 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.16227 | 0.121178 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.5541 | 1.28391 | 0.641955 | − | 0.766742i | \(-0.278123\pi\) | ||||
0.641955 | + | 0.766742i | \(0.278123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.21099 | −0.122686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.5299 | 0.706961 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.57051 | −0.0598315 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.03668 | 0.0394370 | 0.0197185 | − | 0.999806i | \(-0.493723\pi\) | ||||
0.0197185 | + | 0.999806i | \(0.493723\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.09486 | −0.155551 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.6116 | −0.668045 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.7144 | 1.23915 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.58883 | −0.0979187 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.8334 | 0.749096 | 0.374548 | − | 0.927208i | \(-0.377798\pi\) | ||||
0.374548 | + | 0.927208i | \(0.377798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.63998 | −0.0995687 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.25706 | −0.310979 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.3451 | 1.47973 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.7110 | −1.45382 | −0.726911 | − | 0.686731i | \(-0.759045\pi\) | ||||
−0.726911 | + | 0.686731i | \(0.759045\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.8946 | 0.408578 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.1855 | 1.09300 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.15078 | −0.0804346 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.5453 | −0.954006 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.7655 | −0.811715 | −0.405857 | − | 0.913936i | \(-0.633027\pi\) | ||||
−0.405857 | + | 0.913936i | \(0.633027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.7772 | −0.885510 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.1063 | −0.450239 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.768672 | 0.0285477 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.2072 | −0.823618 | −0.411809 | − | 0.911270i | \(-0.635103\pi\) | ||||
−0.411809 | + | 0.911270i | \(0.635103\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.1583 | 0.635493 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.89036 | 0.365808 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.71719 | −0.0634260 | −0.0317130 | − | 0.999497i | \(-0.510096\pi\) | ||||
−0.0317130 | + | 0.999497i | \(0.510096\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.80196 | 0.287780 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.86504 | 0.105535 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.6254 | −0.832289 | −0.416145 | − | 0.909298i | \(-0.636619\pi\) | ||||
−0.416145 | + | 0.909298i | \(0.636619\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.3568 | −0.380467 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.1746 | 0.593388 | 0.296694 | − | 0.954973i | \(-0.404116\pi\) | ||||
0.296694 | + | 0.954973i | \(0.404116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.9003 | 0.582543 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.80732 | 0.322243 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.1911 | 1.39547 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.30012 | −0.229895 | −0.114947 | − | 0.993372i | \(-0.536670\pi\) | ||||
−0.114947 | + | 0.993372i | \(0.536670\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.1084 | −0.805675 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.5458 | −0.602164 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.40584 | −0.0510963 | −0.0255481 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255481 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.78682 | 0.101155 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.57362 | −0.202044 | −0.101022 | − | 0.994884i | \(-0.532211\pi\) | ||||
−0.101022 | + | 0.994884i | \(0.532211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.57975 | −0.346810 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.77915 | −0.281256 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 47.9783 | 1.73240 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.14124 | −0.293581 | −0.146790 | − | 0.989168i | \(-0.546894\pi\) | ||||
−0.146790 | + | 0.989168i | \(0.546894\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.4345 | 0.411805 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.2184 | 1.48252 | 0.741261 | − | 0.671217i | \(-0.234228\pi\) | ||||
0.741261 | + | 0.671217i | \(0.234228\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.69522 | 0.240500 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.07281 | −0.146111 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.3602 | 0.729480 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.378484 | 0.0135432 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.01242 | −0.143392 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.09573 | −0.253257 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.8596 | −1.70601 | −0.853006 | − | 0.521901i | \(-0.825223\pi\) | ||||
−0.853006 | + | 0.521901i | \(0.825223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.1258 | −0.396090 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.0420 | −1.17484 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.05360 | 0.179459 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.466822 | 0.0165565 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.0039 | 1.34617 | 0.673084 | − | 0.739566i | \(-0.264969\pi\) | ||||
0.673084 | + | 0.739566i | \(0.264969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.4350 | −1.14747 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.0295 | −1.13171 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.87752 | −0.172124 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.4410 | 0.579467 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.69926 | −0.306228 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.46341 | −0.156925 | −0.0784626 | − | 0.996917i | \(-0.525001\pi\) | ||||
−0.0784626 | + | 0.996917i | \(0.525001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.1300 | −0.987780 | −0.493890 | − | 0.869525i | \(-0.664425\pi\) | ||||
−0.493890 | + | 0.869525i | \(0.664425\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.475013 | −0.0166594 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.4729 | −0.541991 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.15539 | 0.215350 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.1279 | 0.878041 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.265657 | −0.00927150 | −0.00463575 | − | 0.999989i | \(-0.501476\pi\) | ||||
−0.00463575 | + | 0.999989i | \(0.501476\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.7932 | 0.829378 | 0.414689 | − | 0.909963i | \(-0.363890\pi\) | ||||
0.414689 | + | 0.909963i | \(0.363890\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.639305 | 0.0222577 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.9323 | 0.971301 | 0.485651 | − | 0.874153i | \(-0.338583\pi\) | ||||
0.485651 | + | 0.874153i | \(0.338583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.8474 | 1.41869 | 0.709345 | − | 0.704861i | \(-0.248991\pi\) | ||||
0.709345 | + | 0.704861i | \(0.248991\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.3623 | −0.949187 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.6473 | 1.06187 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.35479 | −0.0468843 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.9487 | −1.20800 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.6220 | −0.539331 | −0.269666 | − | 0.962954i | \(-0.586913\pi\) | ||||
−0.269666 | + | 0.962954i | \(0.586913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4091 | −0.979626 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.1116 | 0.348260 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.198155 | 0.00681675 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40.1657 | −1.38011 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.54852 | −0.259064 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.35915 | −0.149430 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.2878 | 1.92726 | 0.963629 | − | 0.267243i | \(-0.0861128\pi\) | ||||
0.963629 | + | 0.267243i | \(0.0861128\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.84145 | −0.165574 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.8188 | 0.813635 | 0.406817 | − | 0.913509i | \(-0.366639\pi\) | ||||
0.406817 | + | 0.913509i | \(0.366639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9856 | 0.443063 | 0.221532 | − | 0.975153i | \(-0.428894\pi\) | ||||
0.221532 | + | 0.975153i | \(0.428894\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.4106 | 1.07047 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.4615 | −1.00288 | −0.501440 | − | 0.865192i | \(-0.667196\pi\) | ||||
−0.501440 | + | 0.865192i | \(0.667196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.0106237 | 0.000361218 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.07282 | 0.0364349 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.51701 | −0.119306 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.5812 | −0.595716 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.2657 | −0.482820 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.77160 | 0.127503 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.2127 | −0.344860 | −0.172430 | − | 0.985022i | \(-0.555162\pi\) | ||||
−0.172430 | + | 0.985022i | \(0.555162\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.5247 | 0.388718 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.1715 | 0.949123 | 0.474561 | − | 0.880222i | \(-0.342607\pi\) | ||||
0.474561 | + | 0.880222i | \(0.342607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.8877 | −1.03945 | −0.519727 | − | 0.854332i | \(-0.673966\pi\) | ||||
−0.519727 | + | 0.854332i | \(0.673966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.2612 | −0.479386 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.9698 | 1.57709 | 0.788546 | − | 0.614975i | \(-0.210834\pi\) | ||||
0.788546 | + | 0.614975i | \(0.210834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 76.6786 | 2.57172 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0800056 | −0.00268029 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.1863 | −0.675510 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.3180 | −0.578876 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.1012 | −0.570993 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.14643 | 0.171643 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.83375 | 0.0610911 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.49617 | 0.316013 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.6673 | −0.620521 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.8914 | −1.15855 | −0.579276 | − | 0.815132i | \(-0.696665\pi\) | ||||
−0.579276 | + | 0.815132i | \(0.696665\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.1311 | −0.634539 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.21530 | −0.0402647 | −0.0201323 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201323 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.84321 | −0.0940964 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.50215 | −0.0496595 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.06220 | −0.134146 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.6507 | −0.483282 | −0.241641 | − | 0.970366i | \(-0.577686\pi\) | ||||
−0.241641 | + | 0.970366i | \(0.577686\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.3339 | −0.637073 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.32255 | −0.0764476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.5614 | 0.379726 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.5478 | 1.29752 | 0.648760 | − | 0.760993i | \(-0.275288\pi\) | ||||
0.648760 | + | 0.760993i | \(0.275288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.0737 | 0.625116 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.4652 | 0.375355 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.51129 | 0.0821279 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.6343 | 1.52348 | 0.761739 | − | 0.647884i | \(-0.224346\pi\) | ||||
0.761739 | + | 0.647884i | \(0.224346\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.8805 | −0.648776 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.0119 | −0.717568 | −0.358784 | − | 0.933421i | \(-0.616809\pi\) | ||||
−0.358784 | + | 0.933421i | \(0.616809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.6189 | 1.09478 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19.6875 | −0.640436 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.46400 | 0.242547 | 0.121274 | − | 0.992619i | \(-0.461302\pi\) | ||||
0.121274 | + | 0.992619i | \(0.461302\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.9307 | 0.971590 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.5267 | 1.05475 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.15089 | −0.0372811 | −0.0186405 | − | 0.999826i | \(-0.505934\pi\) | ||||
−0.0186405 | + | 0.999826i | \(0.505934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.02878 | −0.162728 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.491415 | 0.0158852 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.1106 | −0.391070 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8260 | 0.446001 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.5700 | −0.598409 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.84163 | −0.252431 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.8018 | 1.76231 | 0.881153 | − | 0.472832i | \(-0.156768\pi\) | ||||
0.881153 | + | 0.472832i | \(0.156768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.0928 | 0.388477 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.9615 | 0.929418 | 0.464709 | − | 0.885463i | \(-0.346159\pi\) | ||||
0.464709 | + | 0.885463i | \(0.346159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −66.4237 | −2.12945 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.92306 | −0.125639 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.5806 | 1.55423 | 0.777116 | − | 0.629357i | \(-0.216682\pi\) | ||||
0.777116 | + | 0.629357i | \(0.216682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3399 | 0.330463 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.65804 | 0.148720 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.9133 | 0.411871 | 0.205935 | − | 0.978566i | \(-0.433976\pi\) | ||||
0.205935 | + | 0.978566i | \(0.433976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.9703 | 0.636307 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.1423 | −0.991271 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.1638 | 0.323190 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.97819 | 0.285202 | 0.142601 | − | 0.989780i | \(-0.454453\pi\) | ||||
0.142601 | + | 0.989780i | \(0.454453\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.1303 | −0.987890 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.52822 | 0.206958 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.7518 | 0.403853 | 0.201926 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201926 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.21995 | 0.165152 |
(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 | 1480.2.a.k.1.4 | ✓ | 6 | |
4.3 | odd | 2 | 2960.2.a.bc.1.3 | 6 | |||
5.4 | even | 2 | 7400.2.a.s.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.k.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
2960.2.a.bc.1.3 | 6 | 4.3 | odd | 2 | |||
7400.2.a.s.1.3 | 6 | 5.4 | even | 2 |