Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + x^{18} + 4x^{16} + 8x^{12} + 4x^{10} + 32x^{8} + 256x^{4} + 256x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.8 | ||
Root | \(-0.328272 - 1.37559i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.e.3025.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | − 0.512447i | − 0.229173i | −0.993413 | − | 0.114587i | \(-0.963446\pi\) | ||||
0.993413 | − | 0.114587i | \(-0.0365543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.82890i | − 0.551433i | −0.961239 | − | 0.275716i | \(-0.911085\pi\) | ||||
0.961239 | − | 0.275716i | \(-0.0889151\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.80627i | 0.500968i | 0.968121 | + | 0.250484i | \(0.0805898\pi\) | ||||
−0.968121 | + | 0.250484i | \(0.919410\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.11456 | 1.96807 | 0.984035 | − | 0.177977i | \(-0.0569552\pi\) | ||||
0.984035 | + | 0.177977i | \(0.0569552\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.43946i | − 0.789066i | −0.918882 | − | 0.394533i | \(-0.870906\pi\) | ||||
0.918882 | − | 0.394533i | \(-0.129094\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.65626 | 0.762384 | 0.381192 | − | 0.924496i | \(-0.375514\pi\) | ||||
0.381192 | + | 0.924496i | \(0.375514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.73740 | 0.947480 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.98990i | 1.48369i | 0.670573 | + | 0.741843i | \(0.266048\pi\) | ||||
−0.670573 | + | 0.741843i | \(0.733952\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56895 | 0.281792 | 0.140896 | − | 0.990024i | \(-0.455002\pi\) | ||||
0.140896 | + | 0.990024i | \(0.455002\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 0.512447i | − 0.0866193i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.44370i | − 1.38814i | −0.719909 | − | 0.694068i | \(-0.755817\pi\) | ||||
0.719909 | − | 0.694068i | \(-0.244183\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.30828 | −0.360493 | −0.180247 | − | 0.983621i | \(-0.557690\pi\) | ||||
−0.180247 | + | 0.983621i | \(0.557690\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7778i | 1.64360i | 0.569773 | + | 0.821802i | \(0.307031\pi\) | ||||
−0.569773 | + | 0.821802i | \(0.692969\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3833 | −1.66043 | −0.830216 | − | 0.557442i | \(-0.811783\pi\) | ||||
−0.830216 | + | 0.557442i | \(0.811783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.87795i | 1.21948i | 0.792601 | + | 0.609740i | \(0.208726\pi\) | ||||
−0.792601 | + | 0.609740i | \(0.791274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.937212 | −0.126374 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 2.50234i | − 0.325778i | −0.986644 | − | 0.162889i | \(-0.947919\pi\) | ||||
0.986644 | − | 0.162889i | \(-0.0520812\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.31310i | − 0.680272i | −0.940376 | − | 0.340136i | \(-0.889527\pi\) | ||||
0.940376 | − | 0.340136i | \(-0.110473\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.925616 | 0.114809 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.44648i | − 0.787562i | −0.919204 | − | 0.393781i | \(-0.871167\pi\) | ||||
0.919204 | − | 0.393781i | \(-0.128833\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.10975 | −1.08113 | −0.540564 | − | 0.841303i | \(-0.681789\pi\) | ||||
−0.540564 | + | 0.841303i | \(0.681789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.24419 | 1.08195 | 0.540975 | − | 0.841039i | \(-0.318055\pi\) | ||||
0.540975 | + | 0.841039i | \(0.318055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.82890i | − 0.208422i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.64300 | −0.409870 | −0.204935 | − | 0.978776i | \(-0.565698\pi\) | ||||
−0.204935 | + | 0.978776i | \(0.565698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 4.53105i | − 0.497348i | −0.968587 | − | 0.248674i | \(-0.920005\pi\) | ||||
0.968587 | − | 0.248674i | \(-0.0799948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 4.15828i | − 0.451029i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7359 | −1.24401 | −0.622003 | − | 0.783015i | \(-0.713681\pi\) | ||||
−0.622003 | + | 0.783015i | \(0.713681\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.80627i | 0.189348i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.76254 | −0.180833 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.2323 | 1.54661 | 0.773303 | − | 0.634037i | \(-0.218603\pi\) | ||||
0.773303 | + | 0.634037i | \(0.218603\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.13524i | 0.809487i | 0.914430 | + | 0.404744i | \(0.132639\pi\) | ||||
−0.914430 | + | 0.404744i | \(0.867361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9816 | 1.57471 | 0.787356 | − | 0.616498i | \(-0.211449\pi\) | ||||
0.787356 | + | 0.616498i | \(0.211449\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 12.1695i | − 1.17647i | −0.808690 | − | 0.588235i | \(-0.799823\pi\) | ||||
0.808690 | − | 0.588235i | \(-0.200177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8452i | 1.03878i | 0.854537 | + | 0.519391i | \(0.173841\pi\) | ||||
−0.854537 | + | 0.519391i | \(0.826159\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.07563 | 0.289331 | 0.144665 | − | 0.989481i | \(-0.453789\pi\) | ||||
0.144665 | + | 0.989481i | \(0.453789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1.87364i | − 0.174718i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.11456 | 0.743860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.65514 | 0.695922 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 4.98990i | − 0.446310i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.67524 | −0.592332 | −0.296166 | − | 0.955137i | \(-0.595708\pi\) | ||||
−0.296166 | + | 0.955137i | \(0.595708\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1.26995i | − 0.110956i | −0.998460 | − | 0.0554778i | \(-0.982332\pi\) | ||||
0.998460 | − | 0.0554778i | \(-0.0176682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3.43946i | − 0.298239i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.8507 | 1.69596 | 0.847980 | − | 0.530029i | \(-0.177819\pi\) | ||||
0.847980 | + | 0.530029i | \(0.177819\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9758i | 1.18541i | 0.805419 | + | 0.592706i | \(0.201941\pi\) | ||||
−0.805419 | + | 0.592706i | \(0.798059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.30348 | 0.276251 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.09440 | 0.340021 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 11.8561i | − 0.971286i | −0.874157 | − | 0.485643i | \(-0.838585\pi\) | ||||
0.874157 | − | 0.485643i | \(-0.161415\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.4949 | 1.09820 | 0.549100 | − | 0.835757i | \(-0.314971\pi\) | ||||
0.549100 | + | 0.835757i | \(0.314971\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 0.804003i | − 0.0645791i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 9.88593i | − 0.788983i | −0.918900 | − | 0.394492i | \(-0.870921\pi\) | ||||
0.918900 | − | 0.394492i | \(-0.129079\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.65626 | 0.288154 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.43706i | 0.347537i | 0.984786 | + | 0.173769i | \(0.0555945\pi\) | ||||
−0.984786 | + | 0.173769i | \(0.944405\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.38391 | 0.416619 | 0.208310 | − | 0.978063i | \(-0.433204\pi\) | ||||
0.208310 | + | 0.978063i | \(0.433204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.73740 | 0.749031 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.9611i | 1.36556i | 0.730624 | + | 0.682780i | \(0.239229\pi\) | ||||
−0.730624 | + | 0.682780i | \(0.760771\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.73740 | 0.358114 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 16.0482i | − 1.19950i | −0.800188 | − | 0.599749i | \(-0.795267\pi\) | ||||
0.800188 | − | 0.599749i | \(-0.204733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 5.91861i | − 0.439927i | −0.975508 | − | 0.219964i | \(-0.929406\pi\) | ||||
0.975508 | − | 0.219964i | \(-0.0705938\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.32695 | −0.318123 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 14.8407i | − 1.08526i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0697837 | −0.00504937 | −0.00252469 | − | 0.999997i | \(-0.500804\pi\) | ||||
−0.00252469 | + | 0.999997i | \(0.500804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.24356 | −0.593384 | −0.296692 | − | 0.954973i | \(-0.595884\pi\) | ||||
−0.296692 | + | 0.954973i | \(0.595884\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.91295i | − 0.136292i | −0.997675 | − | 0.0681459i | \(-0.978292\pi\) | ||||
0.997675 | − | 0.0681459i | \(-0.0217083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.70579 | 0.262696 | 0.131348 | − | 0.991336i | \(-0.458069\pi\) | ||||
0.131348 | + | 0.991336i | \(0.458069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.98990i | 0.560781i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.18287i | 0.0826153i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.29041 | −0.435117 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 25.6006i | − 1.76242i | −0.472724 | − | 0.881210i | \(-0.656729\pi\) | ||||
0.472724 | − | 0.881210i | \(-0.343271\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.52307 | 0.376670 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.56895 | 0.106507 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6571i | 0.985941i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.2639 | 0.955182 | 0.477591 | − | 0.878582i | \(-0.341510\pi\) | ||||
0.477591 | + | 0.878582i | \(0.341510\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.58553i | 0.171608i | 0.996312 | + | 0.0858039i | \(0.0273458\pi\) | ||||
−0.996312 | + | 0.0858039i | \(0.972654\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.5800i | 1.82254i | 0.411813 | + | 0.911268i | \(0.364896\pi\) | ||||
−0.411813 | + | 0.911268i | \(0.635104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.61196 | 0.367652 | 0.183826 | − | 0.982959i | \(-0.441152\pi\) | ||||
0.183826 | + | 0.982959i | \(0.441152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.83336i | 0.380526i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.69275 | −0.109495 | −0.0547476 | − | 0.998500i | \(-0.517435\pi\) | ||||
−0.0547476 | + | 0.998500i | \(0.517435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.6246 | −1.45738 | −0.728689 | − | 0.684845i | \(-0.759870\pi\) | ||||
−0.728689 | + | 0.684845i | \(0.759870\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 0.512447i | − 0.0327390i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.21258 | 0.395297 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.1391i | 1.14493i | 0.819930 | + | 0.572464i | \(0.194012\pi\) | ||||
−0.819930 | + | 0.572464i | \(0.805988\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.68693i | − 0.420403i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.62562 | −0.538051 | −0.269026 | − | 0.963133i | \(-0.586702\pi\) | ||||
−0.269026 | + | 0.963133i | \(0.586702\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 8.44370i | − 0.524666i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.79262 | −0.172201 | −0.0861003 | − | 0.996286i | \(-0.527441\pi\) | ||||
−0.0861003 | + | 0.996286i | \(0.527441\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.54948 | 0.279472 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 17.8391i | − 1.08767i | −0.839192 | − | 0.543836i | \(-0.816971\pi\) | ||||
0.839192 | − | 0.543836i | \(-0.183029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.5304 | 1.36863 | 0.684313 | − | 0.729188i | \(-0.260102\pi\) | ||||
0.684313 | + | 0.729188i | \(0.260102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 8.66421i | − 0.522472i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.18249i | − 0.131133i | −0.997848 | − | 0.0655666i | \(-0.979115\pi\) | ||||
0.997848 | − | 0.0655666i | \(-0.0208855\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.54152 | 0.449890 | 0.224945 | − | 0.974372i | \(-0.427780\pi\) | ||||
0.224945 | + | 0.974372i | \(0.427780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.5743i | − 0.688021i | −0.938966 | − | 0.344011i | \(-0.888214\pi\) | ||||
0.938966 | − | 0.344011i | \(-0.111786\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.30828 | −0.136254 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 48.8460 | 2.87330 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.12045i | − 0.474402i | −0.971461 | − | 0.237201i | \(-0.923770\pi\) | ||||
0.971461 | − | 0.237201i | \(-0.0762300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.28232 | −0.0746595 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.60419i | 0.381930i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.7778i | 0.621224i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.72268 | −0.155900 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.73852i | − 0.156295i | −0.996942 | − | 0.0781477i | \(-0.975099\pi\) | ||||
0.996942 | − | 0.0781477i | \(-0.0249006\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.9488 | −1.01778 | −0.508891 | − | 0.860831i | \(-0.669945\pi\) | ||||
−0.508891 | + | 0.860831i | \(0.669945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.95819 | 0.336777 | 0.168388 | − | 0.985721i | \(-0.446144\pi\) | ||||
0.168388 | + | 0.985721i | \(0.446144\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.6033i | 1.21336i | 0.794945 | + | 0.606682i | \(0.207500\pi\) | ||||
−0.794945 | + | 0.606682i | \(0.792500\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.6127 | 0.818154 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 27.9097i | − 1.55294i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.55701i | 0.474657i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3833 | −0.627584 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 12.6066i | − 0.692920i | −0.938065 | − | 0.346460i | \(-0.887384\pi\) | ||||
0.938065 | − | 0.346460i | \(-0.112616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.30348 | −0.180488 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.9818 | −1.57874 | −0.789370 | − | 0.613917i | \(-0.789593\pi\) | ||||
−0.789370 | + | 0.613917i | \(0.789593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 2.86945i | − 0.155389i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 12.2675i | − 0.658553i | −0.944234 | − | 0.329277i | \(-0.893195\pi\) | ||||
0.944234 | − | 0.329277i | \(-0.106805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 28.3289i | − 1.51641i | −0.652016 | − | 0.758205i | \(-0.726077\pi\) | ||||
0.652016 | − | 0.758205i | \(-0.273923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.40996 | −0.0750444 | −0.0375222 | − | 0.999296i | \(-0.511946\pi\) | ||||
−0.0375222 | + | 0.999296i | \(0.511946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.66826i | 0.247766i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.0581 | −0.900290 | −0.450145 | − | 0.892955i | \(-0.648628\pi\) | ||||
−0.450145 | + | 0.892955i | \(0.648628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.17014 | 0.377376 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 4.73715i | − 0.247954i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.4558 | 1.32878 | 0.664390 | − | 0.747386i | \(-0.268692\pi\) | ||||
0.664390 | + | 0.747386i | \(0.268692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.87795i | 0.460920i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.3176i | − 1.05201i | −0.850483 | − | 0.526003i | \(-0.823690\pi\) | ||||
0.850483 | − | 0.526003i | \(-0.176310\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.4319 | −0.743280 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8832i | 0.610397i | 0.952289 | + | 0.305198i | \(0.0987228\pi\) | ||||
−0.952289 | + | 0.305198i | \(0.901277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.6261 | 0.951749 | 0.475874 | − | 0.879513i | \(-0.342132\pi\) | ||||
0.475874 | + | 0.879513i | \(0.342132\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.937212 | −0.0477647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.7636i | 1.05276i | 0.850251 | + | 0.526378i | \(0.176450\pi\) | ||||
−0.850251 | + | 0.526378i | \(0.823550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.6690 | 1.50042 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.86684i | 0.0939311i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 20.9726i | − 1.05259i | −0.850303 | − | 0.526293i | \(-0.823582\pi\) | ||||
0.850303 | − | 0.526293i | \(-0.176418\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.476166 | −0.0237786 | −0.0118893 | − | 0.999929i | \(-0.503785\pi\) | ||||
−0.0118893 | + | 0.999929i | \(0.503785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.83394i | 0.141169i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.4427 | −0.765464 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.08700 | −0.103196 | −0.0515978 | − | 0.998668i | \(-0.516431\pi\) | ||||
−0.0515978 | + | 0.998668i | \(0.516431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 2.50234i | − 0.123132i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.32192 | −0.113979 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8104i | 0.772388i | 0.922418 | + | 0.386194i | \(0.126210\pi\) | ||||
−0.922418 | + | 0.386194i | \(0.873790\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8824i | 1.06648i | 0.845963 | + | 0.533241i | \(0.179026\pi\) | ||||
−0.845963 | + | 0.533241i | \(0.820974\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.4419 | 1.86471 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 5.31310i | − 0.257119i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.3231 | −1.21977 | −0.609885 | − | 0.792490i | \(-0.708784\pi\) | ||||
−0.609885 | + | 0.792490i | \(0.708784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.9197 | 1.48590 | 0.742952 | − | 0.669344i | \(-0.233425\pi\) | ||||
0.742952 | + | 0.669344i | \(0.233425\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 12.5756i | − 0.601571i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.75669 | 0.417934 | 0.208967 | − | 0.977923i | \(-0.432990\pi\) | ||||
0.208967 | + | 0.977923i | \(0.432990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.6190i | 1.31222i | 0.754666 | + | 0.656109i | \(0.227799\pi\) | ||||
−0.754666 | + | 0.656109i | \(0.772201\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.01404i | 0.285093i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.6994 | 0.646516 | 0.323258 | − | 0.946311i | \(-0.395222\pi\) | ||||
0.323258 | + | 0.946311i | \(0.395222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.22161i | 0.198788i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.925616 | 0.0433935 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.85452 | 0.273863 | 0.136931 | − | 0.990581i | \(-0.456276\pi\) | ||||
0.136931 | + | 0.990581i | \(0.456276\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.42544i | 0.112964i | 0.998404 | + | 0.0564821i | \(0.0179884\pi\) | ||||
−0.998404 | + | 0.0564821i | \(0.982012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.26366 | 0.0587273 | 0.0293636 | − | 0.999569i | \(-0.490652\pi\) | ||||
0.0293636 | + | 0.999569i | \(0.490652\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 27.2456i | − 1.26078i | −0.776280 | − | 0.630388i | \(-0.782896\pi\) | ||||
0.776280 | − | 0.630388i | \(-0.217104\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 6.44648i | − 0.297671i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.7115 | 0.906338 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 16.2941i | − 0.747624i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.4035 | 1.25210 | 0.626050 | − | 0.779783i | \(-0.284671\pi\) | ||||
0.626050 | + | 0.779783i | \(0.284671\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2516 | 0.695412 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 7.80574i | − 0.354440i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.0530 | −1.22589 | −0.612944 | − | 0.790126i | \(-0.710015\pi\) | ||||
−0.612944 | + | 0.790126i | \(0.710015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.2739i | 1.32111i | 0.750776 | + | 0.660556i | \(0.229680\pi\) | ||||
−0.750776 | + | 0.660556i | \(0.770320\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 64.8345i | 2.92000i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.10975 | −0.408628 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.8348i | 1.78325i | 0.452775 | + | 0.891625i | \(0.350434\pi\) | ||||
−0.452775 | + | 0.891625i | \(0.649566\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.3079 | 1.61889 | 0.809444 | − | 0.587197i | \(-0.199769\pi\) | ||||
0.809444 | + | 0.587197i | \(0.199769\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.16888 | 0.185513 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 22.2853i | − 0.987778i | −0.869525 | − | 0.493889i | \(-0.835575\pi\) | ||||
0.869525 | − | 0.493889i | \(-0.164425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.24419 | 0.408939 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 8.18971i | − 0.360882i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.8190i | 0.915617i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.8909 | −1.26573 | −0.632866 | − | 0.774261i | \(-0.718122\pi\) | ||||
−0.632866 | + | 0.774261i | \(0.718122\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22.7284i | − 0.993842i | −0.867796 | − | 0.496921i | \(-0.834464\pi\) | ||||
0.867796 | − | 0.496921i | \(-0.165536\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.7313 | 0.554585 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.63174 | −0.418771 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.16938i | − 0.180596i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.23622 | −0.269615 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.82890i | − 0.0787761i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 12.7291i | − 0.547268i | −0.961834 | − | 0.273634i | \(-0.911774\pi\) | ||||
0.961834 | − | 0.273634i | \(-0.0882257\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.55759 | 0.238061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.7154i | 1.22778i | 0.789391 | + | 0.613890i | \(0.210396\pi\) | ||||
−0.789391 | + | 0.613890i | \(0.789604\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.4809 | 1.17073 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.64300 | −0.154916 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7.36295i | − 0.311978i | −0.987759 | − | 0.155989i | \(-0.950143\pi\) | ||||
0.987759 | − | 0.155989i | \(-0.0498565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.4676 | −0.823394 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 15.9713i | − 0.673110i | −0.941664 | − | 0.336555i | \(-0.890738\pi\) | ||||
0.941664 | − | 0.336555i | \(-0.109262\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.57610i | − 0.0663068i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.9769 | −1.13093 | −0.565465 | − | 0.824772i | \(-0.691303\pi\) | ||||
−0.565465 | + | 0.824772i | \(0.691303\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 35.5632i | − 1.48827i | −0.668027 | − | 0.744137i | \(-0.732861\pi\) | ||||
0.668027 | − | 0.744137i | \(-0.267139\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.3212 | 0.722343 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4330 | −0.975528 | −0.487764 | − | 0.872976i | \(-0.662187\pi\) | ||||
−0.487764 | + | 0.872976i | \(0.662187\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.53105i | − 0.187980i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.2369 | 0.672462 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.1113i | 1.53175i | 0.642991 | + | 0.765874i | \(0.277693\pi\) | ||||
−0.642991 | + | 0.765874i | \(0.722307\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 5.39633i | − 0.222352i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.8317 | 0.978650 | 0.489325 | − | 0.872102i | \(-0.337243\pi\) | ||||
0.489325 | + | 0.872102i | \(0.337243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.15828i | − 0.170473i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0955 | −0.494210 | −0.247105 | − | 0.968989i | \(-0.579479\pi\) | ||||
−0.247105 | + | 0.968989i | \(0.579479\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.4752 | 0.835202 | 0.417601 | − | 0.908631i | \(-0.362871\pi\) | ||||
0.417601 | + | 0.908631i | \(0.362871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.92285i | − 0.159487i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0329 | 0.975466 | 0.487733 | − | 0.872993i | \(-0.337824\pi\) | ||||
0.487733 | + | 0.872993i | \(0.337824\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 20.5614i | − 0.831824i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 45.2862i | − 1.82909i | −0.404480 | − | 0.914547i | \(-0.632548\pi\) | ||||
0.404480 | − | 0.914547i | \(-0.367452\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.4393 | −0.822855 | −0.411428 | − | 0.911442i | \(-0.634970\pi\) | ||||
−0.411428 | + | 0.911442i | \(0.634970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 15.3328i | − 0.616277i | −0.951342 | − | 0.308138i | \(-0.900294\pi\) | ||||
0.951342 | − | 0.308138i | \(-0.0997060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.7359 | −0.470190 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.1299 | 0.845197 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 68.5169i | − 2.73195i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4869 | −0.815572 | −0.407786 | − | 0.913078i | \(-0.633699\pi\) | ||||
−0.407786 | + | 0.913078i | \(0.633699\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.42070i | 0.135747i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.80627i | 0.0715669i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.6868 | −1.68603 | −0.843013 | − | 0.537893i | \(-0.819220\pi\) | ||||
−0.843013 | + | 0.537893i | \(0.819220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 29.7804i | − 1.17442i | −0.809434 | − | 0.587211i | \(-0.800226\pi\) | ||||
0.809434 | − | 0.587211i | \(-0.199774\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.63482 | −0.260842 | −0.130421 | − | 0.991459i | \(-0.541633\pi\) | ||||
−0.130421 | + | 0.991459i | \(0.541633\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.57653 | −0.179644 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 4.48147i | − 0.175373i | −0.996148 | − | 0.0876867i | \(-0.972053\pi\) | ||||
0.996148 | − | 0.0876867i | \(-0.0279474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.650779 | −0.0254281 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 49.4245i | 1.92530i | 0.270741 | + | 0.962652i | \(0.412731\pi\) | ||||
−0.270741 | + | 0.962652i | \(0.587269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 12.5279i | − 0.487278i | −0.969866 | − | 0.243639i | \(-0.921659\pi\) | ||||
0.969866 | − | 0.243639i | \(-0.0783413\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.76254 | −0.0683483 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.2132i | 1.13114i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.71710 | −0.375125 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.3343 | −1.01511 | −0.507556 | − | 0.861619i | \(-0.669451\pi\) | ||||
−0.507556 | + | 0.861619i | \(0.669451\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.4868i | 0.556774i | 0.960469 | + | 0.278387i | \(0.0897998\pi\) | ||||
−0.960469 | + | 0.278387i | \(0.910200\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.2323 | 0.584562 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.0232069i | 0 0.000887989i | 1.00000 | 0.000443994i | \(0.000141328\pi\) | |||||
−1.00000 | 0.000443994i | \(0.999859\pi\) | ||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 10.1724i | − 0.388668i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.0360 | −0.610921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.2719i | 0.657054i | 0.944495 | + | 0.328527i | \(0.106552\pi\) | ||||
−0.944495 | + | 0.328527i | \(0.893448\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.16186 | 0.271665 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.7307 | −0.709476 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 23.9519i | − 0.904651i | −0.891853 | − | 0.452326i | \(-0.850595\pi\) | ||||
0.891853 | − | 0.452326i | \(-0.149405\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.0417 | −1.09533 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.13524i | 0.305957i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 32.1099i | − 1.20591i | −0.797774 | − | 0.602956i | \(-0.793989\pi\) | ||||
0.797774 | − | 0.602956i | \(-0.206011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.73649 | 0.214833 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 1.69286i | − 0.0633092i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.4708 | −0.726139 | −0.363070 | − | 0.931762i | \(-0.618271\pi\) | ||||
−0.363070 | + | 0.931762i | \(0.618271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9816 | 0.595185 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 37.8513i | 1.40576i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.3066 | −0.678954 | −0.339477 | − | 0.940614i | \(-0.610250\pi\) | ||||
−0.339477 | + | 0.940614i | \(0.610250\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 87.4573i | 3.23473i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 36.3167i | − 1.34139i | −0.741735 | − | 0.670693i | \(-0.765997\pi\) | ||||
0.741735 | − | 0.670693i | \(-0.234003\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.7899 | −0.434288 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.6764i | 0.576665i | 0.957530 | + | 0.288332i | \(0.0931008\pi\) | ||||
−0.957530 | + | 0.288332i | \(0.906899\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.3578 | 1.81076 | 0.905381 | − | 0.424599i | \(-0.139585\pi\) | ||||
0.905381 | + | 0.424599i | \(0.139585\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.07560 | −0.222593 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 12.1695i | − 0.444664i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7930 | −1.08716 | −0.543582 | − | 0.839356i | \(-0.682932\pi\) | ||||
−0.543582 | + | 0.839356i | \(0.682932\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 6.91542i | − 0.251678i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.6736i | 0.496974i | 0.968635 | + | 0.248487i | \(0.0799333\pi\) | ||||
−0.968635 | + | 0.248487i | \(0.920067\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.34618 | 0.121299 | 0.0606494 | − | 0.998159i | \(-0.480683\pi\) | ||||
0.0606494 | + | 0.998159i | \(0.480683\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8452i | 0.392623i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.51990 | 0.163204 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.2544 | 0.369783 | 0.184891 | − | 0.982759i | \(-0.440807\pi\) | ||||
0.184891 | + | 0.982759i | \(0.440807\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 27.9261i | − 1.00443i | −0.864742 | − | 0.502217i | \(-0.832518\pi\) | ||||
0.864742 | − | 0.502217i | \(-0.167482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.43274 | 0.266992 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.93924i | 0.284453i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.6608i | 0.596170i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.06601 | −0.180814 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.9536i | 0.711268i | 0.934625 | + | 0.355634i | \(0.115735\pi\) | ||||
−0.934625 | + | 0.355634i | \(0.884265\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.07563 | 0.109357 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.59687 | 0.340795 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.3652i | 0.792217i | 0.918204 | + | 0.396108i | \(0.129640\pi\) | ||||
−0.918204 | + | 0.396108i | \(0.870360\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −92.3708 | −3.26785 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 16.9067i | − 0.596623i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.87364i | − 0.0660371i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.28121 | 0.291152 | 0.145576 | − | 0.989347i | \(-0.453496\pi\) | ||||
0.145576 | + | 0.989347i | \(0.453496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5177i | 0.720474i | 0.932861 | + | 0.360237i | \(0.117304\pi\) | ||||
−0.932861 | + | 0.360237i | \(0.882696\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.27376 | 0.0796462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.0699 | 1.29691 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.88906i | 0.240430i | 0.992748 | + | 0.120215i | \(0.0383584\pi\) | ||||
−0.992748 | + | 0.120215i | \(0.961642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.14442 | 0.214181 | 0.107091 | − | 0.994249i | \(-0.465847\pi\) | ||||
0.107091 | + | 0.994249i | \(0.465847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.6562i | 1.03125i | 0.856815 | + | 0.515623i | \(0.172440\pi\) | ||||
−0.856815 | + | 0.515623i | \(0.827560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 7.16328i | − 0.248791i | −0.992233 | − | 0.124396i | \(-0.960301\pi\) | ||||
0.992233 | − | 0.124396i | \(-0.0396992\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.11456 | 0.281153 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.75897i | − 0.0954780i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.6136 | 0.539041 | 0.269520 | − | 0.962995i | \(-0.413135\pi\) | ||||
0.269520 | + | 0.962995i | \(0.413135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.8385 | −1.20133 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 4.98990i | − 0.171658i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.65514 | 0.263034 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 30.8724i | − 1.05829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.960301i | 0.0328801i | 0.999865 | + | 0.0164400i | \(0.00523327\pi\) | ||||
−0.999865 | + | 0.0164400i | \(0.994767\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.3062 | 0.591168 | 0.295584 | − | 0.955317i | \(-0.404486\pi\) | ||||
0.295584 | + | 0.955317i | \(0.404486\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5416i | 0.530273i | 0.964211 | + | 0.265137i | \(0.0854171\pi\) | ||||
−0.964211 | + | 0.265137i | \(0.914583\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30.9082 | −1.05213 | −0.526063 | − | 0.850445i | \(-0.676333\pi\) | ||||
−0.526063 | + | 0.850445i | \(0.676333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.20413 | 0.312950 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.66267i | 0.226016i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6441 | 0.394544 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 4.98990i | − 0.168689i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.0443i | 1.01452i | 0.861792 | + | 0.507262i | \(0.169342\pi\) | ||||
−0.861792 | + | 0.507262i | \(0.830658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.7362 | −1.47351 | −0.736754 | − | 0.676160i | \(-0.763643\pi\) | ||||
−0.736754 | + | 0.676160i | \(0.763643\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.9694i | 0.402804i | 0.979509 | + | 0.201402i | \(0.0645497\pi\) | ||||
−0.979509 | + | 0.201402i | \(0.935450\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −50.6980 | −1.70227 | −0.851136 | − | 0.524945i | \(-0.824086\pi\) | ||||
−0.851136 | + | 0.524945i | \(0.824086\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.67524 | −0.223880 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.1525i | 1.31019i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.22384 | −0.274893 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5357i | 0.418090i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 72.0406i | 2.40002i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.03297 | −0.100819 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.94868i | 0.197523i | 0.995111 | + | 0.0987614i | \(0.0314881\pi\) | ||||
−0.995111 | + | 0.0987614i | \(0.968512\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.6827 | 1.64606 | 0.823031 | − | 0.567996i | \(-0.192281\pi\) | ||||
0.823031 | + | 0.567996i | \(0.192281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.28683 | −0.274254 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.26995i | − 0.0419373i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.5497 | −0.545923 | −0.272961 | − | 0.962025i | \(-0.588003\pi\) | ||||
−0.272961 | + | 0.962025i | \(0.588003\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 16.4546i | − 0.541611i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 40.0012i | − 1.31523i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.8292 | −0.519339 | −0.259669 | − | 0.965698i | \(-0.583614\pi\) | ||||
−0.259669 | + | 0.965698i | \(0.583614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3.43946i | − 0.112724i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.60506 | −0.248712 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.1814 | −0.463286 | −0.231643 | − | 0.972801i | \(-0.574410\pi\) | ||||
−0.231643 | + | 0.972801i | \(0.574410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 59.4006i | − 1.93641i | −0.250166 | − | 0.968203i | \(-0.580485\pi\) | ||||
0.250166 | − | 0.968203i | \(-0.419515\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.43969 | −0.274834 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.81038i | 0.221308i | 0.993859 | + | 0.110654i | \(0.0352945\pi\) | ||||
−0.993859 | + | 0.110654i | \(0.964706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.6975i | 0.542023i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.4827 | −0.825466 | −0.412733 | − | 0.910852i | \(-0.635426\pi\) | ||||
−0.412733 | + | 0.910852i | \(0.635426\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0357604i | 0.00115718i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.8507 | 0.641012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5384 | −0.920593 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.22439i | 0.135988i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.8473 | −1.44219 | −0.721096 | − | 0.692835i | \(-0.756361\pi\) | ||||
−0.721096 | + | 0.692835i | \(0.756361\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 23.4868i | − 0.753728i | −0.926269 | − | 0.376864i | \(-0.877002\pi\) | ||||
0.926269 | − | 0.376864i | \(-0.122998\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.9758i | 0.448044i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.0970 | 1.73072 | 0.865359 | − | 0.501153i | \(-0.167091\pi\) | ||||
0.865359 | + | 0.501153i | \(0.167091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.4638i | 0.685986i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.0476 | −0.479943 | −0.239972 | − | 0.970780i | \(-0.577138\pi\) | ||||
−0.239972 | + | 0.970780i | \(0.577138\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.980283 | −0.0312344 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.4066i | 1.25306i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0651 | −0.764455 | −0.382227 | − | 0.924068i | \(-0.624843\pi\) | ||||
−0.382227 | + | 0.924068i | \(0.624843\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1.89902i | − 0.0602030i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 46.1183i | − 1.46058i | −0.683136 | − | 0.730291i | \(-0.739384\pi\) | ||||
0.683136 | − | 0.730291i | \(-0.260616\pi\) | |||||||
\(998\) | 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 | 6048.2.c.e.3025.8 | 20 | ||
3.2 | odd | 2 | inner | 6048.2.c.e.3025.14 | 20 | ||
4.3 | odd | 2 | 1512.2.c.e.757.11 | yes | 20 | ||
8.3 | odd | 2 | 1512.2.c.e.757.12 | yes | 20 | ||
8.5 | even | 2 | inner | 6048.2.c.e.3025.13 | 20 | ||
12.11 | even | 2 | 1512.2.c.e.757.10 | yes | 20 | ||
24.5 | odd | 2 | inner | 6048.2.c.e.3025.7 | 20 | ||
24.11 | even | 2 | 1512.2.c.e.757.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.e.757.9 | ✓ | 20 | 24.11 | even | 2 | ||
1512.2.c.e.757.10 | yes | 20 | 12.11 | even | 2 | ||
1512.2.c.e.757.11 | yes | 20 | 4.3 | odd | 2 | ||
1512.2.c.e.757.12 | yes | 20 | 8.3 | odd | 2 | ||
6048.2.c.e.3025.7 | 20 | 24.5 | odd | 2 | inner | ||
6048.2.c.e.3025.8 | 20 | 1.1 | even | 1 | trivial | ||
6048.2.c.e.3025.13 | 20 | 8.5 | even | 2 | inner | ||
6048.2.c.e.3025.14 | 20 | 3.2 | odd | 2 | inner |