Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, 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("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.9301.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.68863\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.148523 | −0.0561363 | −0.0280681 | − | 0.999606i | \(-0.508936\pi\) | ||||
−0.0280681 | + | 0.999606i | \(0.508936\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.688632 | −0.207630 | −0.103815 | − | 0.994597i | \(-0.533105\pi\) | ||||
−0.103815 | + | 0.994597i | \(0.533105\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0605682 | 0.0167986 | 0.00839930 | − | 0.999965i | \(-0.497326\pi\) | ||||
0.00839930 | + | 0.999965i | \(0.497326\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.628064 | 0.152328 | 0.0761639 | − | 0.997095i | \(-0.475733\pi\) | ||||
0.0761639 | + | 0.997095i | \(0.475733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.223414 | −0.0512546 | −0.0256273 | − | 0.999672i | \(-0.508158\pi\) | ||||
−0.0256273 | + | 0.999672i | \(0.508158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.148523 | 0.0324103 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.29705 | 0.270453 | 0.135226 | − | 0.990815i | \(-0.456824\pi\) | ||||
0.135226 | + | 0.990815i | \(0.456824\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.675569 | 0.125450 | 0.0627250 | − | 0.998031i | \(-0.480021\pi\) | ||||
0.0627250 | + | 0.998031i | \(0.480021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.47954 | −0.804549 | −0.402275 | − | 0.915519i | \(-0.631780\pi\) | ||||
−0.402275 | + | 0.915519i | \(0.631780\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.688632 | 0.119875 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.148523 | 0.0251049 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.824091 | −0.135480 | −0.0677399 | − | 0.997703i | \(-0.521579\pi\) | ||||
−0.0677399 | + | 0.997703i | \(0.521579\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0605682 | −0.00969867 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.75046 | −0.429550 | −0.214775 | − | 0.976664i | \(-0.568902\pi\) | ||||
−0.214775 | + | 0.976664i | \(0.568902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.23648 | 0.493558 | 0.246779 | − | 0.969072i | \(-0.420628\pi\) | ||||
0.246779 | + | 0.969072i | \(0.420628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.96488 | 1.01593 | 0.507966 | − | 0.861377i | \(-0.330398\pi\) | ||||
0.507966 | + | 0.861377i | \(0.330398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.97794 | −0.996849 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.628064 | −0.0879465 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.23407 | −0.856315 | −0.428158 | − | 0.903704i | \(-0.640837\pi\) | ||||
−0.428158 | + | 0.903704i | \(0.640837\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.688632 | 0.0928551 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.223414 | 0.0295919 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7742 | 1.53287 | 0.766434 | − | 0.642323i | \(-0.222029\pi\) | ||||
0.766434 | + | 0.642323i | \(0.222029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.58521 | 0.971186 | 0.485593 | − | 0.874185i | \(-0.338604\pi\) | ||||
0.485593 | + | 0.874185i | \(0.338604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.148523 | −0.0187121 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0605682 | −0.00751256 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000 | 0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.29705 | −0.156146 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.7669 | 1.27780 | 0.638899 | − | 0.769291i | \(-0.279390\pi\) | ||||
0.638899 | + | 0.769291i | \(0.279390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.2869 | −1.43807 | −0.719036 | − | 0.694972i | \(-0.755417\pi\) | ||||
−0.719036 | + | 0.694972i | \(0.755417\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.102277 | 0.0116556 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.34214 | −1.05107 | −0.525537 | − | 0.850771i | \(-0.676135\pi\) | ||||
−0.525537 | + | 0.850771i | \(0.676135\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.63580 | 0.179552 | 0.0897762 | − | 0.995962i | \(-0.471385\pi\) | ||||
0.0897762 | + | 0.995962i | \(0.471385\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.628064 | −0.0681231 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.675569 | −0.0724286 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.9174 | −1.26324 | −0.631619 | − | 0.775279i | \(-0.717609\pi\) | ||||
−0.631619 | + | 0.775279i | \(0.717609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.00899575 | −0.000943010 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.47954 | 0.464507 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.223414 | 0.0229218 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.01432 | −0.407593 | −0.203796 | − | 0.979013i | \(-0.565328\pi\) | ||||
−0.203796 | + | 0.979013i | \(0.565328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.688632 | −0.0692101 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.1057 | −1.70208 | −0.851039 | − | 0.525103i | \(-0.824027\pi\) | ||||
−0.851039 | + | 0.525103i | \(0.824027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.23648 | −0.318900 | −0.159450 | − | 0.987206i | \(-0.550972\pi\) | ||||
−0.159450 | + | 0.987206i | \(0.550972\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.148523 | −0.0144943 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.7313 | −1.71415 | −0.857076 | − | 0.515191i | \(-0.827721\pi\) | ||||
−0.857076 | + | 0.515191i | \(0.827721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.37485 | 0.802166 | 0.401083 | − | 0.916042i | \(-0.368634\pi\) | ||||
0.401083 | + | 0.916042i | \(0.368634\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.824091 | 0.0782193 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.2935 | 1.72091 | 0.860453 | − | 0.509529i | \(-0.170180\pi\) | ||||
0.860453 | + | 0.509529i | \(0.170180\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.29705 | −0.120950 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0605682 | 0.00559953 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.0932816 | −0.00855111 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5258 | −0.956890 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.75046 | 0.248001 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.88660 | −0.167409 | −0.0837043 | − | 0.996491i | \(-0.526675\pi\) | ||||
−0.0837043 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.23648 | −0.284956 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.7051 | −1.45953 | −0.729765 | − | 0.683698i | \(-0.760370\pi\) | ||||
−0.729765 | + | 0.683698i | \(0.760370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0331820 | 0.00287724 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.5881 | 1.92983 | 0.964917 | − | 0.262556i | \(-0.0845654\pi\) | ||||
0.964917 | + | 0.262556i | \(0.0845654\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.70170 | −0.483611 | −0.241806 | − | 0.970325i | \(-0.577740\pi\) | ||||
−0.241806 | + | 0.970325i | \(0.577740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.96488 | −0.586549 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0417092 | −0.00348790 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.675569 | −0.0561029 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.97794 | 0.575531 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.62680 | −0.297119 | −0.148560 | − | 0.988903i | \(-0.547464\pi\) | ||||
−0.148560 | + | 0.988903i | \(0.547464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.7267 | −1.76809 | −0.884046 | − | 0.467400i | \(-0.845191\pi\) | ||||
−0.884046 | + | 0.467400i | \(0.845191\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.628064 | 0.0507759 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.47954 | 0.359805 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.12240 | −0.408812 | −0.204406 | − | 0.978886i | \(-0.565526\pi\) | ||||
−0.204406 | + | 0.978886i | \(0.565526\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.23407 | 0.494394 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.192641 | −0.0151822 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.77292 | 0.687148 | 0.343574 | − | 0.939126i | \(-0.388362\pi\) | ||||
0.343574 | + | 0.939126i | \(0.388362\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.688632 | −0.0536099 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.01771 | −0.620429 | −0.310215 | − | 0.950667i | \(-0.600401\pi\) | ||||
−0.310215 | + | 0.950667i | \(0.600401\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9963 | −0.999718 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.223414 | −0.0170849 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.40930 | 0.563318 | 0.281659 | − | 0.959515i | \(-0.409115\pi\) | ||||
0.281659 | + | 0.959515i | \(0.409115\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.148523 | −0.0112273 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.7742 | −0.885001 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.7676 | 0.804807 | 0.402404 | − | 0.915462i | \(-0.368175\pi\) | ||||
0.402404 | + | 0.915462i | \(0.368175\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.7403 | −1.76460 | −0.882302 | − | 0.470684i | \(-0.844007\pi\) | ||||
−0.882302 | + | 0.470684i | \(0.844007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.58521 | −0.560715 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.824091 | 0.0605884 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.432505 | −0.0316279 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.148523 | 0.0108034 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00465 | −0.651553 | −0.325777 | − | 0.945447i | \(-0.605626\pi\) | ||||
−0.325777 | + | 0.945447i | \(0.605626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.24180 | −0.377313 | −0.188657 | − | 0.982043i | \(-0.560413\pi\) | ||||
−0.188657 | + | 0.982043i | \(0.560413\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0605682 | 0.00433738 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.74020 | −0.408973 | −0.204486 | − | 0.978869i | \(-0.565552\pi\) | ||||
−0.204486 | + | 0.978869i | \(0.565552\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.09695 | −0.361313 | −0.180657 | − | 0.983546i | \(-0.557822\pi\) | ||||
−0.180657 | + | 0.983546i | \(0.557822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.100337 | −0.00704229 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.75046 | 0.192100 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.29705 | 0.0901509 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.153850 | 0.0106420 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.60486 | 0.661226 | 0.330613 | − | 0.943766i | \(-0.392745\pi\) | ||||
0.330613 | + | 0.943766i | \(0.392745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.7669 | −0.737737 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.23648 | −0.220726 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.665313 | 0.0451644 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.2869 | 0.830272 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0380407 | 0.00255889 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.314287 | 0.0210462 | 0.0105231 | − | 0.999945i | \(-0.496650\pi\) | ||||
0.0105231 | + | 0.999945i | \(0.496650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.298305 | 0.0197992 | 0.00989960 | − | 0.999951i | \(-0.496849\pi\) | ||||
0.00989960 | + | 0.999951i | \(0.496849\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.150931 | −0.00997382 | −0.00498691 | − | 0.999988i | \(-0.501587\pi\) | ||||
−0.00498691 | + | 0.999988i | \(0.501587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.102277 | −0.00672936 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.1762 | −1.71486 | −0.857430 | − | 0.514600i | \(-0.827940\pi\) | ||||
−0.857430 | + | 0.514600i | \(0.827940\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.96488 | −0.454339 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.34214 | 0.606837 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.2727 | −0.987908 | −0.493954 | − | 0.869488i | \(-0.664449\pi\) | ||||
−0.493954 | + | 0.869488i | \(0.664449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.37388 | −0.410577 | −0.205289 | − | 0.978701i | \(-0.565813\pi\) | ||||
−0.205289 | + | 0.978701i | \(0.565813\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.97794 | 0.445804 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0135318 | −0.000861006 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.63580 | −0.103665 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.9065 | 1.44585 | 0.722924 | − | 0.690927i | \(-0.242798\pi\) | ||||
0.722924 | + | 0.690927i | \(0.242798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.893187 | −0.0561542 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.628064 | 0.0393309 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.6334 | −1.09994 | −0.549970 | − | 0.835184i | \(-0.685361\pi\) | ||||
−0.549970 | + | 0.835184i | \(0.685361\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.122396 | 0.00760533 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.675569 | 0.0418166 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.12840 | −0.0695804 | −0.0347902 | − | 0.999395i | \(-0.511076\pi\) | ||||
−0.0347902 | + | 0.999395i | \(0.511076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.23407 | 0.382956 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.9174 | 0.729331 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.450895 | 0.0274916 | 0.0137458 | − | 0.999906i | \(-0.495624\pi\) | ||||
0.0137458 | + | 0.999906i | \(0.495624\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.0615 | −1.64387 | −0.821936 | − | 0.569580i | \(-0.807106\pi\) | ||||
−0.821936 | + | 0.569580i | \(0.807106\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.00899575 | 0.000544447 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.688632 | −0.0415261 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.45295 | −0.147383 | −0.0736916 | − | 0.997281i | \(-0.523478\pi\) | ||||
−0.0736916 | + | 0.997281i | \(0.523478\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.47954 | −0.268183 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.1442 | −1.85791 | −0.928953 | − | 0.370198i | \(-0.879290\pi\) | ||||
−0.928953 | + | 0.370198i | \(0.879290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9775 | 0.711987 | 0.355993 | − | 0.934488i | \(-0.384143\pi\) | ||||
0.355993 | + | 0.934488i | \(0.384143\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.223414 | −0.0132339 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.408505 | 0.0241133 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6055 | −0.976796 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.01432 | 0.235324 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.02951 | 0.410669 | 0.205334 | − | 0.978692i | \(-0.434172\pi\) | ||||
0.205334 | + | 0.978692i | \(0.434172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7742 | −0.685519 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.688632 | 0.0399585 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0785597 | 0.00454322 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.480690 | −0.0277065 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.1057 | 0.982695 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.58521 | −0.434328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.5548 | −1.34435 | −0.672173 | − | 0.740394i | \(-0.734639\pi\) | ||||
−0.672173 | + | 0.740394i | \(0.734639\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.23648 | 0.184117 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.5721 | 1.27995 | 0.639974 | − | 0.768396i | \(-0.278945\pi\) | ||||
0.639974 | + | 0.768396i | \(0.278945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.70702 | 0.492150 | 0.246075 | − | 0.969251i | \(-0.420859\pi\) | ||||
0.246075 | + | 0.969251i | \(0.420859\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.148523 | 0.00836830 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.0278 | −0.675548 | −0.337774 | − | 0.941227i | \(-0.609674\pi\) | ||||
−0.337774 | + | 0.941227i | \(0.609674\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.465218 | −0.0260472 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.7313 | 0.989666 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.140318 | −0.00780751 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0605682 | 0.00335972 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.37485 | −0.463131 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.03444 | −0.0570306 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.08022 | −0.334199 | −0.167100 | − | 0.985940i | \(-0.553440\pi\) | ||||
−0.167100 | + | 0.985940i | \(0.553440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.824091 | −0.0451599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5651 | −0.793411 | −0.396705 | − | 0.917946i | \(-0.629847\pi\) | ||||
−0.396705 | + | 0.917946i | \(0.629847\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.2935 | −0.993566 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.08475 | 0.167049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.07604 | 0.112096 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.29705 | 0.0698306 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.5925 | 0.998096 | 0.499048 | − | 0.866574i | \(-0.333683\pi\) | ||||
0.499048 | + | 0.866574i | \(0.333683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1294 | −1.23809 | −0.619044 | − | 0.785357i | \(-0.712480\pi\) | ||||
−0.619044 | + | 0.785357i | \(0.712480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0605682 | −0.00323289 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.5152 | −1.57093 | −0.785467 | − | 0.618903i | \(-0.787577\pi\) | ||||
−0.785467 | + | 0.618903i | \(0.787577\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.7669 | −0.571448 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0932816 | 0.00493699 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.03919 | 0.318736 | 0.159368 | − | 0.987219i | \(-0.449054\pi\) | ||||
0.159368 | + | 0.987219i | \(0.449054\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9501 | −0.997373 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.5258 | 0.552461 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.2869 | 0.643126 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0076 | 1.14879 | 0.574393 | − | 0.818580i | \(-0.305238\pi\) | ||||
0.574393 | + | 0.818580i | \(0.305238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.75046 | −0.143183 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.925900 | 0.0480703 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5561 | 0.546574 | 0.273287 | − | 0.961933i | \(-0.411889\pi\) | ||||
0.273287 | + | 0.961933i | \(0.411889\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0409180 | 0.00210738 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2199 | 1.08999 | 0.544995 | − | 0.838439i | \(-0.316531\pi\) | ||||
0.544995 | + | 0.838439i | \(0.316531\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.88660 | 0.0966534 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.0427 | 1.38182 | 0.690908 | − | 0.722942i | \(-0.257211\pi\) | ||||
0.690908 | + | 0.722942i | \(0.257211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.102277 | −0.00521254 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.23648 | 0.164519 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.9113 | 1.71937 | 0.859685 | − | 0.510824i | \(-0.170660\pi\) | ||||
0.859685 | + | 0.510824i | \(0.170660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.814627 | 0.0411975 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.7051 | 0.842660 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.34214 | 0.470054 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.8921 | −1.60062 | −0.800310 | − | 0.599587i | \(-0.795332\pi\) | ||||
−0.800310 | + | 0.599587i | \(0.795332\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0331820 | −0.00166118 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.54670 | −0.177114 | −0.0885568 | − | 0.996071i | \(-0.528225\pi\) | ||||
−0.0885568 | + | 0.996071i | \(0.528225\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.271318 | −0.0135153 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.567495 | 0.0281297 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.71109 | 0.430736 | 0.215368 | − | 0.976533i | \(-0.430905\pi\) | ||||
0.215368 | + | 0.976533i | \(0.430905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.5881 | −1.11419 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.74873 | −0.0860494 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.63580 | −0.0802982 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.70170 | 0.279213 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6612 | 0.618542 | 0.309271 | − | 0.950974i | \(-0.399915\pi\) | ||||
0.309271 | + | 0.950974i | \(0.399915\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3943 | −1.14017 | −0.570084 | − | 0.821586i | \(-0.693089\pi\) | ||||
−0.570084 | + | 0.821586i | \(0.693089\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.96488 | 0.338644 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.628064 | 0.0304656 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.12657 | −0.0545188 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0417092 | 0.00201374 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.4009 | −1.31985 | −0.659927 | − | 0.751330i | \(-0.729413\pi\) | ||||
−0.659927 | + | 0.751330i | \(0.729413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6696 | 1.61806 | 0.809029 | − | 0.587769i | \(-0.199994\pi\) | ||||
0.809029 | + | 0.587769i | \(0.199994\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.675569 | 0.0323910 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.289778 | −0.0138620 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.64462 | 0.460313 | 0.230156 | − | 0.973154i | \(-0.426076\pi\) | ||||
0.230156 | + | 0.973154i | \(0.426076\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.97794 | −0.332283 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.04333 | 0.144593 | 0.0722964 | − | 0.997383i | \(-0.476967\pi\) | ||||
0.0722964 | + | 0.997383i | \(0.476967\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.9174 | 0.564938 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.62680 | 0.171542 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.10343 | 0.429617 | 0.214809 | − | 0.976656i | \(-0.431087\pi\) | ||||
0.214809 | + | 0.976656i | \(0.431087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.89405 | 0.0891875 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.7267 | 1.02081 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.00899575 | 0.000421727 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.1659 | 0.662652 | 0.331326 | − | 0.943516i | \(-0.392504\pi\) | ||||
0.331326 | + | 0.943516i | \(0.392504\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.628064 | −0.0293155 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.6945 | −1.89533 | −0.947665 | − | 0.319266i | \(-0.896564\pi\) | ||||
−0.947665 | + | 0.319266i | \(0.896564\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.9445 | −1.53106 | −0.765530 | − | 0.643400i | \(-0.777523\pi\) | ||||
−0.765530 | + | 0.643400i | \(0.777523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.47954 | −0.207734 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.5203 | 0.949566 | 0.474783 | − | 0.880103i | \(-0.342527\pi\) | ||||
0.474783 | + | 0.880103i | \(0.342527\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.148523 | −0.00685814 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.12240 | 0.236028 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.22874 | −0.102478 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.223414 | −0.0102509 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.23407 | −0.285438 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5904 | −0.620962 | −0.310481 | − | 0.950580i | \(-0.600490\pi\) | ||||
−0.310481 | + | 0.950580i | \(0.600490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.0499137 | −0.00227587 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.192641 | 0.00876545 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.01432 | 0.182281 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.93284 | −0.404786 | −0.202393 | − | 0.979304i | \(-0.564872\pi\) | ||||
−0.202393 | + | 0.979304i | \(0.564872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.77292 | −0.396725 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0961 | −0.455630 | −0.227815 | − | 0.973704i | \(-0.573158\pi\) | ||||
−0.227815 | + | 0.973704i | \(0.573158\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.424300 | 0.0191095 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.688632 | 0.0309517 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.59913 | −0.0717308 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.5242 | −1.32168 | −0.660842 | − | 0.750525i | \(-0.729801\pi\) | ||||
−0.660842 | + | 0.750525i | \(0.729801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.01771 | 0.358205 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.2721 | 1.17142 | 0.585708 | − | 0.810522i | \(-0.300817\pi\) | ||||
0.585708 | + | 0.810522i | \(0.300817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.1057 | 0.761192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9963 | 0.577187 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.10714 | −0.270694 | −0.135347 | − | 0.990798i | \(-0.543215\pi\) | ||||
−0.135347 | + | 0.990798i | \(0.543215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.82488 | 0.0807280 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.223414 | 0.00986396 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.23648 | 0.142616 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.79624 | −0.210938 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.40930 | −0.325232 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.30625 | −0.144850 | −0.0724248 | − | 0.997374i | \(-0.523074\pi\) | ||||
−0.0724248 | + | 0.997374i | \(0.523074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.90218 | 0.126904 | 0.0634518 | − | 0.997985i | \(-0.479789\pi\) | ||||
0.0634518 | + | 0.997985i | \(0.479789\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.148523 | 0.00648206 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.81344 | −0.122555 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3177 | −0.926855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.7742 | 0.510956 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.166590 | −0.00721583 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.7313 | 0.766592 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.7676 | −0.464656 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.80523 | 0.206976 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.2659 | 1.77416 | 0.887080 | − | 0.461615i | \(-0.152730\pi\) | ||||
0.887080 | + | 0.461615i | \(0.152730\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.7403 | 1.01879 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.37485 | −0.358739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.06819 | 0.0884296 | 0.0442148 | − | 0.999022i | \(-0.485921\pi\) | ||||
0.0442148 | + | 0.999022i | \(0.485921\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.58521 | 0.323729 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.150931 | −0.00642989 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.38752 | 0.0590033 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.824091 | −0.0349807 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.9281 | 1.01387 | 0.506934 | − | 0.861985i | \(-0.330779\pi\) | ||||
0.506934 | + | 0.861985i | \(0.330779\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.196028 | 0.00829108 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.432505 | 0.0182604 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2267 | 0.768163 | 0.384082 | − | 0.923299i | \(-0.374518\pi\) | ||||
0.384082 | + | 0.923299i | \(0.374518\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.2935 | −0.769613 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.148523 | −0.00623736 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.8499 | 1.16753 | 0.583765 | − | 0.811923i | \(-0.301579\pi\) | ||||
0.583765 | + | 0.811923i | \(0.301579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7090 | 0.657400 | 0.328700 | − | 0.944434i | \(-0.393390\pi\) | ||||
0.328700 | + | 0.944434i | \(0.393390\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.00465 | 0.376175 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.29705 | 0.0540905 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.3066 | 0.803742 | 0.401871 | − | 0.915696i | \(-0.368360\pi\) | ||||
0.401871 | + | 0.915696i | \(0.368360\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.24180 | 0.217842 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.242953 | −0.0100794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.29298 | 0.177797 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0605682 | −0.00250419 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.56750 | 0.105972 | 0.0529859 | − | 0.998595i | \(-0.483126\pi\) | ||||
0.0529859 | + | 0.998595i | \(0.483126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.00079 | 0.0412369 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.74020 | 0.236120 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.5394 | 1.33623 | 0.668116 | − | 0.744057i | \(-0.267101\pi\) | ||||
0.668116 | + | 0.744057i | \(0.267101\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0932816 | 0.00382417 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.09695 | 0.208604 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.3119 | 1.44280 | 0.721402 | − | 0.692516i | \(-0.243498\pi\) | ||||
0.721402 | + | 0.692516i | \(0.243498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.4173 | −1.77103 | −0.885515 | − | 0.464611i | \(-0.846194\pi\) | ||||
−0.885515 | + | 0.464611i | \(0.846194\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000 | 0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.5258 | 0.427934 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5844 | −0.835496 | −0.417748 | − | 0.908563i | \(-0.637180\pi\) | ||||
−0.417748 | + | 0.908563i | \(0.637180\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.100337 | 0.00406587 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.421850 | 0.0170662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.9712 | −1.29130 | −0.645652 | − | 0.763632i | \(-0.723414\pi\) | ||||
−0.645652 | + | 0.763632i | \(0.723414\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.75046 | −0.110909 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.16479 | 0.0871510 | 0.0435755 | − | 0.999050i | \(-0.486125\pi\) | ||||
0.0435755 | + | 0.999050i | \(0.486125\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.12097 | −0.326409 | −0.163205 | − | 0.986592i | \(-0.552183\pi\) | ||||
−0.163205 | + | 0.986592i | \(0.552183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.29705 | −0.0520486 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.77000 | 0.0709135 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.153850 | −0.00614417 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.517582 | −0.0206373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.80224 | −0.230984 | −0.115492 | − | 0.993308i | \(-0.536844\pi\) | ||||
−0.115492 | + | 0.993308i | \(0.536844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.60486 | −0.381759 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.88660 | 0.0748674 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.422641 | −0.0167457 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.7669 | 0.425932 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.2254 | −0.443375 | −0.221687 | − | 0.975118i | \(-0.571156\pi\) | ||||
−0.221687 | + | 0.975118i | \(0.571156\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.0337 | 1.26329 | 0.631643 | − | 0.775260i | \(-0.282381\pi\) | ||||
0.631643 | + | 0.775260i | \(0.282381\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.23648 | 0.127436 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.6385 | −1.40110 | −0.700548 | − | 0.713605i | \(-0.747061\pi\) | ||||
−0.700548 | + | 0.713605i | \(0.747061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.10807 | −0.318270 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.665313 | −0.0260757 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.38637 | −0.0542529 | −0.0271264 | − | 0.999632i | \(-0.508636\pi\) | ||||
−0.0271264 | + | 0.999632i | \(0.508636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.7051 | 0.652722 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.2869 | −0.479358 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.4088 | 0.795015 | 0.397508 | − | 0.917599i | \(-0.369875\pi\) | ||||
0.397508 | + | 0.917599i | \(0.369875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6649 | 0.609295 | 0.304647 | − | 0.952465i | \(-0.401461\pi\) | ||||
0.304647 | + | 0.952465i | \(0.401461\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0380407 | −0.00147738 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0331820 | −0.00128674 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.876243 | 0.0339283 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.314287 | −0.0121510 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.22341 | −0.201648 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.4735 | 1.09757 | 0.548787 | − | 0.835962i | \(-0.315090\pi\) | ||||
0.548787 | + | 0.835962i | \(0.315090\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.2279 | −1.04646 | −0.523228 | − | 0.852193i | \(-0.675272\pi\) | ||||
−0.523228 | + | 0.852193i | \(0.675272\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.596218 | 0.0228807 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.298305 | −0.0114311 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.2680 | 0.775535 | 0.387768 | − | 0.921757i | \(-0.373246\pi\) | ||||
0.387768 | + | 0.921757i | \(0.373246\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.5881 | −0.863048 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.150931 | 0.00575839 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.377586 | −0.0143849 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5356 | 0.400795 | 0.200397 | − | 0.979715i | \(-0.435777\pi\) | ||||
0.200397 | + | 0.979715i | \(0.435777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.102277 | 0.00388520 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.70170 | 0.216278 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.72746 | −0.0654324 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.1762 | 0.990075 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.91942 | −0.223574 | −0.111787 | − | 0.993732i | \(-0.535657\pi\) | ||||
−0.111787 | + | 0.993732i | \(0.535657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.184113 | 0.00694397 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.96488 | 0.262312 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.54058 | 0.0955483 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.12819 | −0.267705 | −0.133852 | − | 0.991001i | \(-0.542735\pi\) | ||||
−0.133852 | + | 0.991001i | \(0.542735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.34214 | −0.350358 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.81017 | −0.217592 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0417092 | 0.00155984 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2727 | 0.570369 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.3704 | 1.43097 | 0.715487 | − | 0.698626i | \(-0.246205\pi\) | ||||
0.715487 | + | 0.698626i | \(0.246205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.480690 | 0.0179018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.37388 | 0.237047 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.675569 | 0.0250900 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.7895 | −0.993567 | −0.496783 | − | 0.867875i | \(-0.665486\pi\) | ||||
−0.496783 | + | 0.867875i | \(0.665486\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.03271 | 0.0751826 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.6819 | −0.616159 | −0.308080 | − | 0.951361i | \(-0.599686\pi\) | ||||
−0.308080 | + | 0.951361i | \(0.599686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.97794 | −0.257385 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.688632 | −0.0253661 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.0022 | 1.36115 | 0.680573 | − | 0.732680i | \(-0.261731\pi\) | ||||
0.680573 | + | 0.732680i | \(0.261731\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0135318 | 0.000497102 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.7180 | 0.429890 | 0.214945 | − | 0.976626i | \(-0.431043\pi\) | ||||
0.214945 | + | 0.976626i | \(0.431043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.62680 | 0.132876 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.63580 | 0.0598508 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.63350 | 0.0962261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.95638 | −0.180861 | −0.0904304 | − | 0.995903i | \(-0.528824\pi\) | ||||
−0.0904304 | + | 0.995903i | \(0.528824\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.9065 | −0.834761 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.7267 | 0.790715 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0672 | 1.52896 | 0.764479 | − | 0.644649i | \(-0.222996\pi\) | ||||
0.764479 | + | 0.644649i | \(0.222996\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.893187 | 0.0324206 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.54000 | −0.309575 | −0.154787 | − | 0.987948i | \(-0.549469\pi\) | ||||
−0.154787 | + | 0.987948i | \(0.549469\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.24386 | −0.0450306 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.628064 | −0.0227077 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.713141 | 0.0257500 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.5867 | 0.922678 | 0.461339 | − | 0.887224i | \(-0.347369\pi\) | ||||
0.461339 | + | 0.887224i | \(0.347369\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6334 | 0.635051 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.4563 | −0.951568 | −0.475784 | − | 0.879562i | \(-0.657836\pi\) | ||||
−0.475784 | + | 0.879562i | \(0.657836\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.47954 | −0.160910 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.122396 | −0.00439094 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.614491 | 0.0220164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.41444 | −0.265309 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.675569 | −0.0241429 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.12240 | 0.182826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.6851 | −0.915574 | −0.457787 | − | 0.889062i | \(-0.651358\pi\) | ||||
−0.457787 | + | 0.889062i | \(0.651358\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.12840 | 0.0401722 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.71700 | −0.0966053 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.459422 | 0.0163146 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.23407 | −0.221100 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.6939 | −0.768436 | −0.384218 | − | 0.923242i | \(-0.625529\pi\) | ||||
−0.384218 | + | 0.923242i | \(0.625529\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.37439 | 0.154755 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.9174 | −0.421080 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.46115 | 0.298588 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.192641 | 0.00678969 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.450895 | −0.0158723 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.59100 | −0.266885 | −0.133443 | − | 0.991057i | \(-0.542603\pi\) | ||||
−0.133443 | + | 0.991057i | \(0.542603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.11978 | 0.144665 | 0.0723324 | − | 0.997381i | \(-0.476956\pi\) | ||||
0.0723324 | + | 0.997381i | \(0.476956\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.0615 | 0.949090 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.77292 | −0.307302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.723074 | −0.0252971 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.00899575 | −0.000314337 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.4111 | 1.06135 | 0.530677 | − | 0.847574i | \(-0.321938\pi\) | ||||
0.530677 | + | 0.847574i | \(0.321938\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.9671 | 1.28859 | 0.644296 | − | 0.764776i | \(-0.277150\pi\) | ||||
0.644296 | + | 0.764776i | \(0.277150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.688632 | 0.0239751 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.6727 | 0.475445 | 0.237722 | − | 0.971333i | \(-0.423599\pi\) | ||||
0.237722 | + | 0.971333i | \(0.423599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.2070 | −1.46591 | −0.732955 | − | 0.680278i | \(-0.761859\pi\) | ||||
−0.732955 | + | 0.680278i | \(0.761859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.45295 | 0.0850918 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.38259 | −0.151848 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.01771 | 0.277464 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.47954 | 0.154836 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.28185 | 0.182350 | 0.0911749 | − | 0.995835i | \(-0.470938\pi\) | ||||
0.0911749 | + | 0.995835i | \(0.470938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5436 | −0.984262 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.1442 | 1.07266 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.9963 | 0.447087 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.56332 | 0.0537162 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.9775 | −0.411066 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.06888 | −0.0366409 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.6140 | 1.04820 | 0.524102 | − | 0.851655i | \(-0.324401\pi\) | ||||
0.524102 | + | 0.851655i | \(0.324401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.223414 | 0.00764059 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.9493 | −0.442339 | −0.221170 | − | 0.975235i | \(-0.570987\pi\) | ||||
−0.221170 | + | 0.975235i | \(0.570987\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.7777 | −1.35720 | −0.678598 | − | 0.734510i | \(-0.737412\pi\) | ||||
−0.678598 | + | 0.734510i | \(0.737412\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.408505 | −0.0139218 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.7486 | 1.08073 | 0.540367 | − | 0.841430i | \(-0.318285\pi\) | ||||
0.540367 | + | 0.841430i | \(0.318285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.40930 | −0.251924 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6055 | 0.563954 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.43330 | 0.218235 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0605682 | 0.00205228 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.01432 | −0.135864 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.148523 | 0.00502098 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.9908 | 1.75561 | 0.877803 | − | 0.479022i | \(-0.159009\pi\) | ||||
0.877803 | + | 0.479022i | \(0.159009\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.02951 | −0.237100 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.79447 | −0.195221 | −0.0976103 | − | 0.995225i | \(-0.531120\pi\) | ||||
−0.0976103 | + | 0.995225i | \(0.531120\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.2763 | 1.79289 | 0.896444 | − | 0.443156i | \(-0.146141\pi\) | ||||
0.896444 | + | 0.443156i | \(0.146141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.7742 | 0.395785 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.6087 | 0.691973 | 0.345986 | − | 0.938240i | \(-0.387544\pi\) | ||||
0.345986 | + | 0.938240i | \(0.387544\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.280203 | 0.00939770 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.688632 | −0.0230700 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.55605 | −0.0520712 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.7676 | −0.359921 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0785597 | −0.00262303 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.02624 | −0.100931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.91539 | −0.130441 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.480690 | 0.0159964 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.7403 | 0.789155 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.8440 | −0.592502 | −0.296251 | − | 0.955110i | \(-0.595736\pi\) | ||||
−0.296251 | + | 0.955110i | \(0.595736\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.1057 | −0.567359 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.0058 | 0.828480 | 0.414240 | − | 0.910168i | \(-0.364047\pi\) | ||||
0.414240 | + | 0.910168i | \(0.364047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.12646 | −0.0372805 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.58521 | 0.250759 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.48108 | 0.0819326 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.2586 | −1.72385 | −0.861925 | − | 0.507035i | \(-0.830741\pi\) | ||||
−0.861925 | + | 0.507035i | \(0.830741\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.5548 | 0.776158 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.652132 | 0.0214652 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.824091 | −0.0270960 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.23648 | −0.106300 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.2212 | −1.25400 | −0.626999 | − | 0.779020i | \(-0.715717\pi\) | ||||
−0.626999 | + | 0.779020i | \(0.715717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.55897 | 0.0510931 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.5721 | −0.738979 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.432505 | 0.0141444 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.9315 | −0.814477 | −0.407239 | − | 0.913322i | \(-0.633508\pi\) | ||||
−0.407239 | + | 0.913322i | \(0.633508\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.70702 | −0.284143 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.2412 | −0.627244 | −0.313622 | − | 0.949548i | \(-0.601542\pi\) | ||||
−0.313622 | + | 0.949548i | \(0.601542\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.56747 | −0.116173 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.148523 | −0.00483144 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.3169 | 1.18014 | 0.590070 | − | 0.807352i | \(-0.299100\pi\) | ||||
0.590070 | + | 0.807352i | \(0.299100\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.744195 | −0.0241576 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.0278 | 0.390028 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.8461 | 0.966810 | 0.483405 | − | 0.875397i | \(-0.339400\pi\) | ||||
0.483405 | + | 0.875397i | \(0.339400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.00465 | 0.291384 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.465218 | 0.0150384 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.35485 | −0.108334 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.9337 | −0.352700 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.7313 | −0.571384 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.24180 | 0.168740 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.7932 | −0.636508 | −0.318254 | − | 0.948005i | \(-0.603096\pi\) | ||||
−0.318254 | + | 0.948005i | \(0.603096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.140318 | 0.00450767 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2682 | −0.425798 | −0.212899 | − | 0.977074i | \(-0.568290\pi\) | ||||
−0.212899 | + | 0.977074i | \(0.568290\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.846831 | 0.0271481 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0605682 | −0.00193973 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.5787 | 0.786343 | 0.393172 | − | 0.919465i | \(-0.371378\pi\) | ||||
0.393172 | + | 0.919465i | \(0.371378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.20668 | 0.262287 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.37485 | 0.267389 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.8773 | −0.889148 | −0.444574 | − | 0.895742i | \(-0.646645\pi\) | ||||
−0.444574 | + | 0.895742i | \(0.646645\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.74020 | 0.182898 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.03444 | 0.0329266 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.19786 | 0.133484 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.2253 | −1.50016 | −0.750080 | − | 0.661347i | \(-0.769985\pi\) | ||||
−0.750080 | + | 0.661347i | \(0.769985\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.08022 | 0.192950 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.09695 | 0.161584 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.5349 | 0.808698 | 0.404349 | − | 0.914605i | \(-0.367498\pi\) | ||||
0.404349 | + | 0.914605i | \(0.367498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.824091 | 0.0260731 |
(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 | 4020.2.a.b.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.b.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial |