Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6480,2,Mod(1,6480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6480, 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("6480.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6480.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: | \(51.7430605098\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1620) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6480.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.73205 | 1.03262 | 0.516309 | − | 0.856402i | \(-0.327306\pi\) | ||||
0.516309 | + | 0.856402i | \(0.327306\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73205 | −0.522233 | −0.261116 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261116 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.46410 | 1.51547 | 0.757735 | − | 0.652563i | \(-0.226306\pi\) | ||||
0.757735 | + | 0.652563i | \(0.226306\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.73205 | −1.14769 | −0.573845 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46410 | 1.02414 | 0.512068 | − | 0.858945i | \(-0.328880\pi\) | ||||
0.512068 | + | 0.858945i | \(0.328880\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.73205 | −1.43581 | −0.717903 | − | 0.696143i | \(-0.754898\pi\) | ||||
−0.717903 | + | 0.696143i | \(0.754898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92820 | −1.06474 | −0.532368 | − | 0.846513i | \(-0.678698\pi\) | ||||
−0.532368 | + | 0.846513i | \(0.678698\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.73205 | −0.461801 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.19615 | −1.01864 | −0.509321 | − | 0.860577i | \(-0.670103\pi\) | ||||
−0.509321 | + | 0.860577i | \(0.670103\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1962 | −1.74855 | −0.874273 | − | 0.485435i | \(-0.838661\pi\) | ||||
−0.874273 | + | 0.485435i | \(0.838661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.26795 | −0.498358 | −0.249179 | − | 0.968458i | \(-0.580161\pi\) | ||||
−0.249179 | + | 0.968458i | \(0.580161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.26795 | 0.184949 | 0.0924747 | − | 0.995715i | \(-0.470522\pi\) | ||||
0.0924747 | + | 0.995715i | \(0.470522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.26795 | −0.998330 | −0.499165 | − | 0.866507i | \(-0.666360\pi\) | ||||
−0.499165 | + | 0.866507i | \(0.666360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.73205 | 0.233550 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.73205 | 1.00663 | 0.503314 | − | 0.864104i | \(-0.332114\pi\) | ||||
0.503314 | + | 0.864104i | \(0.332114\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | −0.512148 | −0.256074 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.46410 | −0.677738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.39230 | −0.780944 | −0.390472 | − | 0.920615i | \(-0.627688\pi\) | ||||
−0.390472 | + | 0.920615i | \(0.627688\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1962 | 1.32874 | 0.664369 | − | 0.747404i | \(-0.268700\pi\) | ||||
0.664369 | + | 0.747404i | \(0.268700\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.196152 | −0.0229579 | −0.0114790 | − | 0.999934i | \(-0.503654\pi\) | ||||
−0.0114790 | + | 0.999934i | \(0.503654\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.73205 | −0.539267 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.3923 | 1.61926 | 0.809630 | − | 0.586940i | \(-0.199668\pi\) | ||||
0.809630 | + | 0.586940i | \(0.199668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.1244 | 1.66011 | 0.830057 | − | 0.557679i | \(-0.188308\pi\) | ||||
0.830057 | + | 0.557679i | \(0.188308\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.73205 | 0.513263 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.19615 | 0.550791 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.9282 | 1.56490 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.46410 | −0.458007 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.732051 | 0.0743285 | 0.0371642 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371642 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.12436 | 0.609396 | 0.304698 | − | 0.952449i | \(-0.401444\pi\) | ||||
0.304698 | + | 0.952449i | \(0.401444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.3923 | −1.81225 | −0.906124 | − | 0.423013i | \(-0.860973\pi\) | ||||
−0.906124 | + | 0.423013i | \(0.860973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.46410 | −0.334887 | −0.167444 | − | 0.985882i | \(-0.553551\pi\) | ||||
−0.167444 | + | 0.985882i | \(0.553551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.92820 | −0.759384 | −0.379692 | − | 0.925113i | \(-0.623970\pi\) | ||||
−0.379692 | + | 0.925113i | \(0.623970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.339746 | −0.0319606 | −0.0159803 | − | 0.999872i | \(-0.505087\pi\) | ||||
−0.0159803 | + | 0.999872i | \(0.505087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.46410 | 0.323029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.9282 | −1.18513 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.19615 | −0.372348 | −0.186174 | − | 0.982517i | \(-0.559609\pi\) | ||||
−0.186174 | + | 0.982517i | \(0.559609\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2679 | −0.897115 | −0.448557 | − | 0.893754i | \(-0.648062\pi\) | ||||
−0.448557 | + | 0.893754i | \(0.648062\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1962 | 1.05754 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.39230 | 0.375260 | 0.187630 | − | 0.982240i | \(-0.439919\pi\) | ||||
0.187630 | + | 0.982240i | \(0.439919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3923 | −1.30556 | −0.652779 | − | 0.757548i | \(-0.726397\pi\) | ||||
−0.652779 | + | 0.757548i | \(0.726397\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.46410 | −0.791428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.73205 | 0.642112 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3923 | 1.41537 | 0.707683 | − | 0.706530i | \(-0.249741\pi\) | ||||
0.707683 | + | 0.706530i | \(0.249741\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.92820 | 0.476165 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.26795 | 0.260811 | 0.130405 | − | 0.991461i | \(-0.458372\pi\) | ||||
0.130405 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.46410 | −0.745876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.7321 | −1.46721 | −0.733604 | − | 0.679577i | \(-0.762163\pi\) | ||||
−0.733604 | + | 0.679577i | \(0.762163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.1244 | 1.63465 | 0.817326 | − | 0.576176i | \(-0.195456\pi\) | ||||
0.817326 | + | 0.576176i | \(0.195456\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.2487 | −1.84360 | −0.921798 | − | 0.387671i | \(-0.873280\pi\) | ||||
−0.921798 | + | 0.387671i | \(0.873280\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.73205 | 0.206524 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1244 | 0.906217 | 0.453108 | − | 0.891455i | \(-0.350315\pi\) | ||||
0.453108 | + | 0.891455i | \(0.350315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4641 | −1.22377 | −0.611884 | − | 0.790948i | \(-0.709588\pi\) | ||||
−0.611884 | + | 0.790948i | \(0.709588\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.19615 | 0.455550 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.19615 | 0.599362 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.0526 | −1.37859 | −0.689297 | − | 0.724479i | \(-0.742081\pi\) | ||||
−0.689297 | + | 0.724479i | \(0.742081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5885 | −0.762174 | −0.381087 | − | 0.924539i | \(-0.624450\pi\) | ||||
−0.381087 | + | 0.924539i | \(0.624450\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.8564 | −0.987228 | −0.493614 | − | 0.869681i | \(-0.664324\pi\) | ||||
−0.493614 | + | 0.869681i | \(0.664324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.8564 | −1.12403 | −0.562015 | − | 0.827127i | \(-0.689974\pi\) | ||||
−0.562015 | + | 0.827127i | \(0.689974\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.1244 | −1.48264 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1962 | 0.781973 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.73205 | −0.534837 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9282 | 1.37191 | 0.685957 | − | 0.727642i | \(-0.259384\pi\) | ||||
0.685957 | + | 0.727642i | \(0.259384\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.26795 | 0.222872 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.1962 | −1.09947 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.8564 | −1.73929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.85641 | 0.392174 | 0.196087 | − | 0.980587i | \(-0.437177\pi\) | ||||
0.196087 | + | 0.980587i | \(0.437177\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.1962 | −1.73870 | −0.869350 | − | 0.494197i | \(-0.835462\pi\) | ||||
−0.869350 | + | 0.494197i | \(0.835462\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.8564 | −1.17998 | −0.589992 | − | 0.807409i | \(-0.700869\pi\) | ||||
−0.589992 | + | 0.807409i | \(0.700869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.5885 | 1.61084 | 0.805422 | − | 0.592702i | \(-0.201939\pi\) | ||||
0.805422 | + | 0.592702i | \(0.201939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.26795 | −0.0827119 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.53590 | −0.552141 | −0.276071 | − | 0.961137i | \(-0.589032\pi\) | ||||
−0.276071 | + | 0.961137i | \(0.589032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3205 | 0.664802 | 0.332401 | − | 0.943138i | \(-0.392141\pi\) | ||||
0.332401 | + | 0.943138i | \(0.392141\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.464102 | −0.0296504 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.3923 | 1.55205 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5359 | −1.29621 | −0.648107 | − | 0.761549i | \(-0.724439\pi\) | ||||
−0.648107 | + | 0.761549i | \(0.724439\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.4641 | 0.964624 | 0.482312 | − | 0.875999i | \(-0.339797\pi\) | ||||
0.482312 | + | 0.875999i | \(0.339797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.9282 | −1.05187 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.2487 | 1.49524 | 0.747620 | − | 0.664127i | \(-0.231197\pi\) | ||||
0.747620 | + | 0.664127i | \(0.231197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.26795 | 0.446467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.2679 | −0.991874 | −0.495937 | − | 0.868358i | \(-0.665175\pi\) | ||||
−0.495937 | + | 0.868358i | \(0.665175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.7846 | −1.01959 | −0.509796 | − | 0.860295i | \(-0.670279\pi\) | ||||
−0.509796 | + | 0.860295i | \(0.670279\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.73205 | −0.104447 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.12436 | 0.307893 | 0.153946 | − | 0.988079i | \(-0.450802\pi\) | ||||
0.153946 | + | 0.988079i | \(0.450802\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3205 | 1.74911 | 0.874557 | − | 0.484922i | \(-0.161152\pi\) | ||||
0.874557 | + | 0.484922i | \(0.161152\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5359 | −0.982957 | −0.491479 | − | 0.870890i | \(-0.663543\pi\) | ||||
−0.491479 | + | 0.870890i | \(0.663543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.5885 | −1.80558 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.39230 | 0.317194 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.5885 | 1.43647 | 0.718237 | − | 0.695799i | \(-0.244950\pi\) | ||||
0.718237 | + | 0.695799i | \(0.244950\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.73205 | −0.450177 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.9282 | −1.09465 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.92820 | −0.514613 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.00000 | 0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.80385 | 0.102951 | 0.0514755 | − | 0.998674i | \(-0.483608\pi\) | ||||
0.0514755 | + | 0.998674i | \(0.483608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5167 | 0.936574 | 0.468287 | − | 0.883576i | \(-0.344871\pi\) | ||||
0.468287 | + | 0.883576i | \(0.344871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.9282 | 0.843792 | 0.421896 | − | 0.906644i | \(-0.361365\pi\) | ||||
0.421896 | + | 0.906644i | \(0.361365\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.12436 | 0.175481 | 0.0877406 | − | 0.996143i | \(-0.472035\pi\) | ||||
0.0877406 | + | 0.996143i | \(0.472035\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3923 | 0.749825 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.1244 | −1.17539 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.46410 | 0.303094 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.46410 | 0.190982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.3923 | 1.61555 | 0.807774 | − | 0.589493i | \(-0.200672\pi\) | ||||
0.807774 | + | 0.589493i | \(0.200672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.39230 | 0.349249 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.2487 | −1.86565 | −0.932823 | − | 0.360335i | \(-0.882662\pi\) | ||||
−0.932823 | + | 0.360335i | \(0.882662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2679 | 0.556041 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8564 | −0.964155 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.8038 | −1.17049 | −0.585246 | − | 0.810856i | \(-0.699002\pi\) | ||||
−0.585246 | + | 0.810856i | \(0.699002\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.0000 | −1.33822 | −0.669110 | − | 0.743164i | \(-0.733324\pi\) | ||||
−0.669110 | + | 0.743164i | \(0.733324\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.9808 | −1.54249 | −0.771245 | − | 0.636538i | \(-0.780366\pi\) | ||||
−0.771245 | + | 0.636538i | \(0.780366\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.1962 | −0.594230 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.33975 | −0.492933 | −0.246466 | − | 0.969151i | \(-0.579270\pi\) | ||||
−0.246466 | + | 0.969151i | \(0.579270\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.928203 | 0.0488528 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.196152 | 0.0102671 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.3923 | 1.37767 | 0.688834 | − | 0.724920i | \(-0.258123\pi\) | ||||
0.688834 | + | 0.724920i | \(0.258123\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.8564 | −1.03089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0526 | −0.727614 | −0.363807 | − | 0.931474i | \(-0.618523\pi\) | ||||
−0.363807 | + | 0.931474i | \(0.618523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.2487 | −2.17592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.53590 | −0.232993 | −0.116497 | − | 0.993191i | \(-0.537166\pi\) | ||||
−0.116497 | + | 0.993191i | \(0.537166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.2487 | −0.932466 | −0.466233 | − | 0.884662i | \(-0.654389\pi\) | ||||
−0.466233 | + | 0.884662i | \(0.654389\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.73205 | 0.241168 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.4641 | 1.39249 | 0.696243 | − | 0.717807i | \(-0.254854\pi\) | ||||
0.696243 | + | 0.717807i | \(0.254854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.3923 | 0.828994 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.3923 | −0.724155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.3205 | 1.87306 | 0.936531 | − | 0.350584i | \(-0.114017\pi\) | ||||
0.936531 | + | 0.350584i | \(0.114017\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7846 | −0.738308 | −0.369154 | − | 0.929368i | \(-0.620353\pi\) | ||||
−0.369154 | + | 0.929368i | \(0.620353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.3923 | −1.61358 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7321 | 0.531968 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8564 | −0.882942 | −0.441471 | − | 0.897275i | \(-0.645543\pi\) | ||||
−0.441471 | + | 0.897275i | \(0.645543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.1244 | 1.03946 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.1244 | −0.742425 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.4641 | −1.04859 | −0.524295 | − | 0.851537i | \(-0.675671\pi\) | ||||
−0.524295 | + | 0.851537i | \(0.675671\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7846 | 0.671821 | 0.335910 | − | 0.941894i | \(-0.390956\pi\) | ||||
0.335910 | + | 0.941894i | \(0.390956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.73205 | −0.229538 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.9282 | −0.528853 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.5885 | 1.61790 | 0.808950 | − | 0.587878i | \(-0.200037\pi\) | ||||
0.808950 | + | 0.587878i | \(0.200037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4641 | 0.550930 | 0.275465 | − | 0.961311i | \(-0.411168\pi\) | ||||
0.275465 | + | 0.961311i | \(0.411168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.4641 | −0.739748 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.60770 | −0.315368 | −0.157684 | − | 0.987490i | \(-0.550403\pi\) | ||||
−0.157684 | + | 0.987490i | \(0.550403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.2679 | −1.77065 | −0.885327 | − | 0.464969i | \(-0.846065\pi\) | ||||
−0.885327 | + | 0.464969i | \(0.846065\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.19615 | −0.246321 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.1244 | 1.13850 | 0.569249 | − | 0.822165i | \(-0.307234\pi\) | ||||
0.569249 | + | 0.822165i | \(0.307234\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.3923 | 0.913148 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.9282 | −0.699845 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1962 | 1.03829 | 0.519146 | − | 0.854686i | \(-0.326250\pi\) | ||||
0.519146 | + | 0.854686i | \(0.326250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.58846 | 0.446579 | 0.223289 | − | 0.974752i | \(-0.428320\pi\) | ||||
0.223289 | + | 0.974752i | \(0.428320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.39230 | 0.111180 | 0.0555899 | − | 0.998454i | \(-0.482296\pi\) | ||||
0.0555899 | + | 0.998454i | \(0.482296\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.1962 | −1.21221 | −0.606107 | − | 0.795383i | \(-0.707270\pi\) | ||||
−0.606107 | + | 0.795383i | \(0.707270\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.4641 | −0.806417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.66025 | 0.260259 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.46410 | 0.204827 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.33975 | 0.152597 | 0.0762984 | − | 0.997085i | \(-0.475690\pi\) | ||||
0.0762984 | + | 0.997085i | \(0.475690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.8564 | −1.54372 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.732051 | −0.0332407 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.5359 | 1.38371 | 0.691857 | − | 0.722035i | \(-0.256793\pi\) | ||||
0.691857 | + | 0.722035i | \(0.256793\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.26795 | 0.192610 | 0.0963049 | − | 0.995352i | \(-0.469298\pi\) | ||||
0.0963049 | + | 0.995352i | \(0.469298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.5885 | 1.64786 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.5885 | 1.37208 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.3923 | −1.22625 | −0.613124 | − | 0.789987i | \(-0.710087\pi\) | ||||
−0.613124 | + | 0.789987i | \(0.710087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.3205 | 1.57486 | 0.787432 | − | 0.616402i | \(-0.211410\pi\) | ||||
0.787432 | + | 0.616402i | \(0.211410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.12436 | −0.272530 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.7846 | −1.18721 | −0.593603 | − | 0.804758i | \(-0.702295\pi\) | ||||
−0.593603 | + | 0.804758i | \(0.702295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.535898 | −0.0237067 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.3923 | 0.810462 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.19615 | −0.0965867 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3923 | −0.455295 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.60770 | −0.157753 | −0.0788767 | − | 0.996884i | \(-0.525133\pi\) | ||||
−0.0788767 | + | 0.996884i | \(0.525133\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.0526 | 1.22199 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −61.1769 | −2.64987 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.46410 | 0.149766 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.803848 | −0.0346242 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.46410 | 0.105940 | 0.0529700 | − | 0.998596i | \(-0.483131\pi\) | ||||
0.0529700 | + | 0.998596i | \(0.483131\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.92820 | 0.339607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.78461 | −0.204575 | −0.102288 | − | 0.994755i | \(-0.532616\pi\) | ||||
−0.102288 | + | 0.994755i | \(0.532616\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.5167 | −1.47046 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.3205 | 1.67208 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.39230 | −0.186108 | −0.0930540 | − | 0.995661i | \(-0.529663\pi\) | ||||
−0.0930540 | + | 0.995661i | \(0.529663\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.8564 | −0.755246 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.7321 | −0.958042 | −0.479021 | − | 0.877804i | \(-0.659008\pi\) | ||||
−0.479021 | + | 0.877804i | \(0.659008\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.339746 | 0.0142932 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −43.0526 | −1.80486 | −0.902429 | − | 0.430839i | \(-0.858218\pi\) | ||||
−0.902429 | + | 0.430839i | \(0.858218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.856406 | −0.0358395 | −0.0179197 | − | 0.999839i | \(-0.505704\pi\) | ||||
−0.0179197 | + | 0.999839i | \(0.505704\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.46410 | −0.144463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.8038 | 0.491401 | 0.245700 | − | 0.969346i | \(-0.420982\pi\) | ||||
0.245700 | + | 0.969346i | \(0.420982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.3205 | 1.71426 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.5885 | 0.521361 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.80385 | −0.157002 | −0.0785008 | − | 0.996914i | \(-0.525013\pi\) | ||||
−0.0785008 | + | 0.996914i | \(0.525013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.4641 | −1.09043 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.0718 | −0.947445 | −0.473723 | − | 0.880674i | \(-0.657090\pi\) | ||||
−0.473723 | + | 0.880674i | \(0.657090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.9282 | 0.530005 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.4115 | 0.588840 | 0.294420 | − | 0.955676i | \(-0.404874\pi\) | ||||
0.294420 | + | 0.955676i | \(0.404874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3205 | −0.992054 | −0.496027 | − | 0.868307i | \(-0.665208\pi\) | ||||
−0.496027 | + | 0.868307i | \(0.665208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.00000 | 0.325246 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.58846 | −0.105062 | −0.0525311 | − | 0.998619i | \(-0.516729\pi\) | ||||
−0.0525311 | + | 0.998619i | \(0.516729\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.92820 | 0.280285 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3923 | 0.985196 | 0.492598 | − | 0.870257i | \(-0.336047\pi\) | ||||
0.492598 | + | 0.870257i | \(0.336047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14.1962 | 0.568757 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.3205 | 1.16909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0717968 | 0.00285818 | 0.00142909 | − | 0.999999i | \(-0.499545\pi\) | ||||
0.00142909 | + | 0.999999i | \(0.499545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.19615 | 0.166519 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.53590 | 0.100476 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.8038 | −0.505722 | −0.252861 | − | 0.967503i | \(-0.581371\pi\) | ||||
−0.252861 | + | 0.967503i | \(0.581371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5885 | −0.575313 | −0.287656 | − | 0.957734i | \(-0.592876\pi\) | ||||
−0.287656 | + | 0.957734i | \(0.592876\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.248711 | −0.00977785 | −0.00488893 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488893 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.3923 | −0.525694 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.53590 | −0.0992374 | −0.0496187 | − | 0.998768i | \(-0.515801\pi\) | ||||
−0.0496187 | + | 0.998768i | \(0.515801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.2679 | 0.401202 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.53590 | 0.0987846 | 0.0493923 | − | 0.998779i | \(-0.484272\pi\) | ||||
0.0493923 | + | 0.998779i | \(0.484272\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3923 | 0.598691 | 0.299346 | − | 0.954145i | \(-0.403232\pi\) | ||||
0.299346 | + | 0.954145i | \(0.403232\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.1962 | −0.472947 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.7846 | 1.03710 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.92820 | 0.267460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.3923 | −1.47991 | −0.739957 | − | 0.672654i | \(-0.765154\pi\) | ||||
−0.739957 | + | 0.672654i | \(0.765154\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.6410 | 1.56196 | 0.780981 | − | 0.624555i | \(-0.214720\pi\) | ||||
0.780981 | + | 0.624555i | \(0.214720\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.00000 | 0.0767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.4641 | −0.821301 | −0.410651 | − | 0.911793i | \(-0.634698\pi\) | ||||
−0.410651 | + | 0.911793i | \(0.634698\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.39230 | −0.167821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.7128 | −1.51294 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | 0.380418 | 0.190209 | − | 0.981744i | \(-0.439083\pi\) | ||||
0.190209 | + | 0.981744i | \(0.439083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.3923 | 0.583863 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.9808 | 2.00679 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.8756 | −0.675154 | −0.337577 | − | 0.941298i | \(-0.609607\pi\) | ||||
−0.337577 | + | 0.941298i | \(0.609607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.6603 | −1.04323 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.7321 | 0.629274 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.5359 | 0.395684 | 0.197842 | − | 0.980234i | \(-0.436607\pi\) | ||||
0.197842 | + | 0.980234i | \(0.436607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.5359 | 0.769075 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.46410 | 0.353937 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.1962 | 0.641308 | 0.320654 | − | 0.947196i | \(-0.396097\pi\) | ||||
0.320654 | + | 0.947196i | \(0.396097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.2487 | −1.87136 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.73205 | −0.287161 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.1769 | 1.08211 | 0.541056 | − | 0.840987i | \(-0.318025\pi\) | ||||
0.541056 | + | 0.840987i | \(0.318025\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4641 | 0.571960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.5692 | 1.60927 | 0.804633 | − | 0.593773i | \(-0.202362\pi\) | ||||
0.804633 | + | 0.593773i | \(0.202362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.0718 | 0.407835 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.1769 | 0.962933 | 0.481467 | − | 0.876464i | \(-0.340104\pi\) | ||||
0.481467 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.41154 | 0.198530 | 0.0992651 | − | 0.995061i | \(-0.468351\pi\) | ||||
0.0992651 | + | 0.995061i | \(0.468351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.46410 | −0.345811 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.7846 | −1.48825 | −0.744126 | − | 0.668040i | \(-0.767134\pi\) | ||||
−0.744126 | + | 0.668040i | \(0.767134\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.3923 | −0.632971 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.3923 | −0.741171 | −0.370585 | − | 0.928798i | \(-0.620843\pi\) | ||||
−0.370585 | + | 0.928798i | \(0.620843\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.1244 | −1.09201 | −0.546004 | − | 0.837783i | \(-0.683851\pi\) | ||||
−0.546004 | + | 0.837783i | \(0.683851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.6603 | −0.784154 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 42.2487 | 1.52551 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.2487 | 1.27110 | 0.635551 | − | 0.772059i | \(-0.280773\pi\) | ||||
0.635551 | + | 0.772059i | \(0.280773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.6603 | 0.635195 | 0.317598 | − | 0.948226i | \(-0.397124\pi\) | ||||
0.317598 | + | 0.948226i | \(0.397124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.92820 | −0.212947 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −49.9808 | −1.79075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.3923 | −0.693911 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.26795 | −0.116638 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.1962 | 1.29025 | 0.645127 | − | 0.764076i | \(-0.276805\pi\) | ||||
0.645127 | + | 0.764076i | \(0.276805\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.928203 | −0.0330031 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.8564 | −0.776144 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3205 | 0.826055 | 0.413027 | − | 0.910719i | \(-0.364471\pi\) | ||||
0.413027 | + | 0.910719i | \(0.364471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | −0.212265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.339746 | 0.0119894 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.46410 | 0.333566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.41154 | −0.295734 | −0.147867 | − | 0.989007i | \(-0.547241\pi\) | ||||
−0.147867 | + | 0.989007i | \(0.547241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.2487 | 0.886602 | 0.443301 | − | 0.896373i | \(-0.353807\pi\) | ||||
0.443301 | + | 0.896373i | \(0.353807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.7321 | 0.656155 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5885 | −0.510386 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.33975 | 0.116558 | 0.0582790 | − | 0.998300i | \(-0.481439\pi\) | ||||
0.0582790 | + | 0.998300i | \(0.481439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9282 | 0.590080 | 0.295040 | − | 0.955485i | \(-0.404667\pi\) | ||||
0.295040 | + | 0.955485i | \(0.404667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.4641 | 1.58094 | 0.790471 | − | 0.612500i | \(-0.209836\pi\) | ||||
0.790471 | + | 0.612500i | \(0.209836\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.7846 | −1.79855 | −0.899277 | − | 0.437380i | \(-0.855907\pi\) | ||||
−0.899277 | + | 0.437380i | \(0.855907\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.19615 | −0.0760922 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.1244 | −0.731038 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.41154 | 0.290399 | 0.145199 | − | 0.989402i | \(-0.453618\pi\) | ||||
0.145199 | + | 0.989402i | \(0.453618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.7846 | 1.06154 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.8564 | −0.579878 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.8564 | −0.750995 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.4641 | 0.735780 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.196152 | −0.00671613 | −0.00335807 | − | 0.999994i | \(-0.501069\pi\) | ||||
−0.00335807 | + | 0.999994i | \(0.501069\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.0718 | −0.993074 | −0.496537 | − | 0.868016i | \(-0.665395\pi\) | ||||
−0.496537 | + | 0.868016i | \(0.665395\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.78461 | −0.265607 | −0.132804 | − | 0.991142i | \(-0.542398\pi\) | ||||
−0.132804 | + | 0.991142i | \(0.542398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.5167 | 1.68557 | 0.842783 | − | 0.538253i | \(-0.180915\pi\) | ||||
0.842783 | + | 0.538253i | \(0.180915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.2487 | 0.824481 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.9282 | −0.845631 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.9282 | −1.18350 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.73205 | −0.0923602 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2487 | 0.481145 | 0.240572 | − | 0.970631i | \(-0.422665\pi\) | ||||
0.240572 | + | 0.970631i | \(0.422665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.80385 | 0.229227 | 0.114614 | − | 0.993410i | \(-0.463437\pi\) | ||||
0.114614 | + | 0.993410i | \(0.463437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.8372 | 1.57620 | 0.788098 | − | 0.615550i | \(-0.211066\pi\) | ||||
0.788098 | + | 0.615550i | \(0.211066\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.2679 | −0.445494 | −0.222747 | − | 0.974876i | \(-0.571502\pi\) | ||||
−0.222747 | + | 0.974876i | \(0.571502\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.4641 | −0.384494 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.66025 | 0.189413 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1244 | −0.405273 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.8372 | 1.52876 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.3923 | 1.14577 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.4641 | 0.547285 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.21539 | 0.0403564 | 0.0201782 | − | 0.999796i | \(-0.493577\pi\) | ||||
0.0201782 | + | 0.999796i | \(0.493577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.80385 | 0.225422 | 0.112711 | − | 0.993628i | \(-0.464047\pi\) | ||||
0.112711 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.1962 | −0.866966 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.0526 | −0.926377 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.3923 | −1.69528 | −0.847638 | − | 0.530575i | \(-0.821976\pi\) | ||||
−0.847638 | + | 0.530575i | \(0.821976\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.1769 | 2.01366 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.19615 | −0.203728 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.48334 | 0.0486668 | 0.0243334 | − | 0.999704i | \(-0.492254\pi\) | ||||
0.0243334 | + | 0.999704i | \(0.492254\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.07180 | 0.0679004 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.19615 | −0.268043 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0718 | 0.623048 | 0.311524 | − | 0.950238i | \(-0.399160\pi\) | ||||
0.311524 | + | 0.950238i | \(0.399160\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.53590 | −0.278262 | −0.139131 | − | 0.990274i | \(-0.544431\pi\) | ||||
−0.139131 | + | 0.990274i | \(0.544431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.7846 | 1.26300 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.6410 | 1.71060 | 0.855302 | − | 0.518130i | \(-0.173372\pi\) | ||||
0.855302 | + | 0.518130i | \(0.173372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.07180 | −0.0347920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.53590 | −0.0821458 | −0.0410729 | − | 0.999156i | \(-0.513078\pi\) | ||||
−0.0410729 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.0526 | 0.616526 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.14359 | 0.133664 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.5885 | 0.340854 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.41154 | −0.238339 | −0.119170 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119170 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.2679 | −0.714612 | −0.357306 | − | 0.933987i | \(-0.616305\pi\) | ||||
−0.357306 | + | 0.933987i | \(0.616305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.0526 | −1.34814 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.39230 | 0.140522 | 0.0702611 | − | 0.997529i | \(-0.477617\pi\) | ||||
0.0702611 | + | 0.997529i | \(0.477617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.00000 | −0.287641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.7321 | 1.68189 | 0.840946 | − | 0.541120i | \(-0.181999\pi\) | ||||
0.840946 | + | 0.541120i | \(0.181999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.8564 | 0.441502 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3205 | 0.359971 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.7846 | −1.77206 | −0.886028 | − | 0.463631i | \(-0.846546\pi\) | ||||
−0.886028 | + | 0.463631i | \(0.846546\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.8564 | 0.502682 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.1962 | 1.65307 | 0.826534 | − | 0.562886i | \(-0.190309\pi\) | ||||
0.826534 | + | 0.562886i | \(0.190309\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6480.2.a.bh.1.2 | 2 | ||
3.2 | odd | 2 | 6480.2.a.bp.1.2 | 2 | |||
4.3 | odd | 2 | 1620.2.a.g.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 1620.2.a.h.1.1 | yes | 2 | ||
20.3 | even | 4 | 8100.2.d.m.649.4 | 4 | |||
20.7 | even | 4 | 8100.2.d.m.649.1 | 4 | |||
20.19 | odd | 2 | 8100.2.a.t.1.2 | 2 | |||
36.7 | odd | 6 | 1620.2.i.n.1081.2 | 4 | |||
36.11 | even | 6 | 1620.2.i.m.1081.2 | 4 | |||
36.23 | even | 6 | 1620.2.i.m.541.2 | 4 | |||
36.31 | odd | 6 | 1620.2.i.n.541.2 | 4 | |||
60.23 | odd | 4 | 8100.2.d.l.649.4 | 4 | |||
60.47 | odd | 4 | 8100.2.d.l.649.1 | 4 | |||
60.59 | even | 2 | 8100.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.2.a.g.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
1620.2.a.h.1.1 | yes | 2 | 12.11 | even | 2 | ||
1620.2.i.m.541.2 | 4 | 36.23 | even | 6 | |||
1620.2.i.m.1081.2 | 4 | 36.11 | even | 6 | |||
1620.2.i.n.541.2 | 4 | 36.31 | odd | 6 | |||
1620.2.i.n.1081.2 | 4 | 36.7 | odd | 6 | |||
6480.2.a.bh.1.2 | 2 | 1.1 | even | 1 | trivial | ||
6480.2.a.bp.1.2 | 2 | 3.2 | odd | 2 | |||
8100.2.a.s.1.2 | 2 | 60.59 | even | 2 | |||
8100.2.a.t.1.2 | 2 | 20.19 | odd | 2 | |||
8100.2.d.l.649.1 | 4 | 60.47 | odd | 4 | |||
8100.2.d.l.649.4 | 4 | 60.23 | odd | 4 | |||
8100.2.d.m.649.1 | 4 | 20.7 | even | 4 | |||
8100.2.d.m.649.4 | 4 | 20.3 | even | 4 |