Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3856,2,Mod(1,3856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3856 = 2^{4} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3856.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: | \(30.7903150194\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.31056073.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.27758\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3856.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.494846 | 0.285699 | 0.142850 | − | 0.989744i | \(-0.454373\pi\) | ||||
0.142850 | + | 0.989744i | \(0.454373\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.23324 | −0.551523 | −0.275761 | − | 0.961226i | \(-0.588930\pi\) | ||||
−0.275761 | + | 0.961226i | \(0.588930\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.36627 | −0.516400 | −0.258200 | − | 0.966092i | \(-0.583129\pi\) | ||||
−0.258200 | + | 0.966092i | \(0.583129\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.75513 | −0.918376 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.69806 | 1.41652 | 0.708259 | − | 0.705952i | \(-0.249481\pi\) | ||||
0.708259 | + | 0.705952i | \(0.249481\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0431968 | −0.0119806 | −0.00599032 | − | 0.999982i | \(-0.501907\pi\) | ||||
−0.00599032 | + | 0.999982i | \(0.501907\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.610264 | −0.157570 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.31430 | −1.77398 | −0.886989 | − | 0.461790i | \(-0.847207\pi\) | ||||
−0.886989 | + | 0.461790i | \(0.847207\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.697489 | 0.160015 | 0.0800075 | − | 0.996794i | \(-0.474506\pi\) | ||||
0.0800075 | + | 0.996794i | \(0.474506\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.676090 | −0.147535 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.41195 | −0.294412 | −0.147206 | − | 0.989106i | \(-0.547028\pi\) | ||||
−0.147206 | + | 0.989106i | \(0.547028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47911 | −0.695823 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.84790 | −0.548078 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.30334 | 1.54189 | 0.770946 | − | 0.636901i | \(-0.219784\pi\) | ||||
0.770946 | + | 0.636901i | \(0.219784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.39655 | −0.610038 | −0.305019 | − | 0.952346i | \(-0.598663\pi\) | ||||
−0.305019 | + | 0.952346i | \(0.598663\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.32481 | 0.404698 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.68494 | 0.284806 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.15948 | 1.17701 | 0.588506 | − | 0.808493i | \(-0.299716\pi\) | ||||
0.588506 | + | 0.808493i | \(0.299716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0213757 | −0.00342286 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.45541 | 0.851992 | 0.425996 | − | 0.904725i | \(-0.359924\pi\) | ||||
0.425996 | + | 0.904725i | \(0.359924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7568 | 1.79290 | 0.896448 | − | 0.443149i | \(-0.146139\pi\) | ||||
0.896448 | + | 0.443149i | \(0.146139\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.39774 | 0.506505 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.24836 | 0.765551 | 0.382776 | − | 0.923841i | \(-0.374968\pi\) | ||||
0.382776 | + | 0.923841i | \(0.374968\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.13332 | −0.733331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.61945 | −0.506824 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.57769 | −1.17824 | −0.589118 | − | 0.808047i | \(-0.700525\pi\) | ||||
−0.589118 | + | 0.808047i | \(0.700525\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.79385 | −0.781242 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.345149 | 0.0457162 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.9925 | 1.69148 | 0.845738 | − | 0.533598i | \(-0.179160\pi\) | ||||
0.845738 | + | 0.533598i | \(0.179160\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1636 | 1.30132 | 0.650658 | − | 0.759371i | \(-0.274493\pi\) | ||||
0.650658 | + | 0.759371i | \(0.274493\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.76423 | 0.474249 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0532721 | 0.00660759 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1259 | −1.23707 | −0.618536 | − | 0.785757i | \(-0.712274\pi\) | ||||
−0.618536 | + | 0.785757i | \(0.712274\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.698697 | −0.0841132 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.86703 | −0.221576 | −0.110788 | − | 0.993844i | \(-0.535337\pi\) | ||||
−0.110788 | + | 0.993844i | \(0.535337\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.47826 | 0.758223 | 0.379111 | − | 0.925351i | \(-0.376230\pi\) | ||||
0.379111 | + | 0.925351i | \(0.376230\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.72162 | −0.198796 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.41880 | −0.731490 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.9436 | 1.45627 | 0.728136 | − | 0.685432i | \(-0.240387\pi\) | ||||
0.728136 | + | 0.685432i | \(0.240387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.85611 | 0.761790 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.32915 | 0.255657 | 0.127829 | − | 0.991796i | \(-0.459199\pi\) | ||||
0.127829 | + | 0.991796i | \(0.459199\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.02030 | 0.978389 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.10887 | 0.440517 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5180 | −1.53890 | −0.769450 | − | 0.638707i | \(-0.779470\pi\) | ||||
−0.769450 | + | 0.638707i | \(0.779470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0590183 | 0.00618680 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.68077 | −0.174287 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.860173 | −0.0882519 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.23725 | −0.227158 | −0.113579 | − | 0.993529i | \(-0.536231\pi\) | ||||
−0.113579 | + | 0.993529i | \(0.536231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.9438 | −1.30090 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.01607 | −0.399614 | −0.199807 | − | 0.979835i | \(-0.564031\pi\) | ||||
−0.199807 | + | 0.979835i | \(0.564031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.25187 | 0.517482 | 0.258741 | − | 0.965947i | \(-0.416692\pi\) | ||||
0.258741 | + | 0.965947i | \(0.416692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.833783 | 0.0813689 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.60385 | −0.541745 | −0.270873 | − | 0.962615i | \(-0.587312\pi\) | ||||
−0.270873 | + | 0.962615i | \(0.587312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.77557 | −0.457416 | −0.228708 | − | 0.973495i | \(-0.573450\pi\) | ||||
−0.228708 | + | 0.973495i | \(0.573450\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.54284 | 0.336271 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.6186 | −1.18706 | −0.593531 | − | 0.804811i | \(-0.702267\pi\) | ||||
−0.593531 | + | 0.804811i | \(0.702267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.74127 | 0.162375 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.119013 | 0.0110027 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.99327 | 0.916082 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.0718 | 1.00653 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.69959 | 0.243413 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.4568 | 0.935285 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.427651 | −0.0379479 | −0.0189740 | − | 0.999820i | \(-0.506040\pi\) | ||||
−0.0189740 | + | 0.999820i | \(0.506040\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.81780 | 0.512229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3633 | 1.16756 | 0.583780 | − | 0.811912i | \(-0.301573\pi\) | ||||
0.583780 | + | 0.811912i | \(0.301573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.952955 | −0.0826317 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.51215 | 0.302278 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.2702 | 0.962874 | 0.481437 | − | 0.876481i | \(-0.340115\pi\) | ||||
0.481437 | + | 0.876481i | \(0.340115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.927184 | 0.0786427 | 0.0393214 | − | 0.999227i | \(-0.487480\pi\) | ||||
0.0393214 | + | 0.999227i | \(0.487480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.59713 | 0.218717 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.202941 | −0.0169708 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2400 | −0.850388 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.54020 | −0.209512 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.8757 | 1.05481 | 0.527407 | − | 0.849612i | \(-0.323164\pi\) | ||||
0.527407 | + | 0.849612i | \(0.323164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.2436 | 1.72878 | 0.864390 | − | 0.502823i | \(-0.167705\pi\) | ||||
0.864390 | + | 0.502823i | \(0.167705\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.1518 | 1.62918 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.18876 | 0.336450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.1798 | 1.37110 | 0.685550 | − | 0.728026i | \(-0.259562\pi\) | ||||
0.685550 | + | 0.728026i | \(0.259562\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.24463 | −0.336621 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.92910 | 0.152034 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1081 | −0.870055 | −0.435028 | − | 0.900417i | \(-0.643261\pi\) | ||||
−0.435028 | + | 0.900417i | \(0.643261\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.86706 | −0.223200 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.3791 | 1.73174 | 0.865872 | − | 0.500266i | \(-0.166764\pi\) | ||||
0.865872 | + | 0.500266i | \(0.166764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9981 | −0.999856 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.92167 | −0.146954 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.16100 | 0.316355 | 0.158178 | − | 0.987411i | \(-0.449438\pi\) | ||||
0.158178 | + | 0.987411i | \(0.449438\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.75339 | 0.359323 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.42927 | 0.483254 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.79009 | 0.432772 | 0.216386 | − | 0.976308i | \(-0.430573\pi\) | ||||
0.216386 | + | 0.976308i | \(0.430573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.4917 | 1.30015 | 0.650076 | − | 0.759869i | \(-0.274737\pi\) | ||||
0.650076 | + | 0.759869i | \(0.274737\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.02941 | 0.371785 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.82937 | −0.649148 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.3630 | −2.51287 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.89099 | 0.283028 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6074 | 1.56346 | 0.781728 | − | 0.623620i | \(-0.214339\pi\) | ||||
0.781728 | + | 0.623620i | \(0.214339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.30886 | 0.166195 | 0.0830977 | − | 0.996541i | \(-0.473519\pi\) | ||||
0.0830977 | + | 0.996541i | \(0.473519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0263615 | 0.00188778 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.91876 | 0.136706 | 0.0683531 | − | 0.997661i | \(-0.478226\pi\) | ||||
0.0683531 | + | 0.997661i | \(0.478226\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.2430 | −1.50588 | −0.752938 | − | 0.658091i | \(-0.771364\pi\) | ||||
−0.752938 | + | 0.658091i | \(0.771364\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.01074 | −0.353430 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.3446 | −0.796232 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.72784 | −0.469893 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.89010 | 0.270381 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.27685 | 0.226664 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0961 | 1.31463 | 0.657314 | − | 0.753616i | \(-0.271692\pi\) | ||||
0.657314 | + | 0.753616i | \(0.271692\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.923892 | −0.0633040 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.4990 | −0.988823 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.64058 | 0.315023 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.20574 | 0.216624 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.315954 | 0.0212534 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.41781 | −0.563698 | −0.281849 | − | 0.959459i | \(-0.590948\pi\) | ||||
−0.281849 | + | 0.959459i | \(0.590948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.58540 | 0.639027 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.82854 | −0.121364 | −0.0606821 | − | 0.998157i | \(-0.519328\pi\) | ||||
−0.0606821 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.52038 | 0.166551 | 0.0832756 | − | 0.996527i | \(-0.473462\pi\) | ||||
0.0832756 | + | 0.996527i | \(0.473462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.17631 | −0.208986 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.3812 | 1.07317 | 0.536585 | − | 0.843847i | \(-0.319714\pi\) | ||||
0.536585 | + | 0.843847i | \(0.319714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.47249 | −0.422219 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.40510 | 0.416056 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7430 | 0.694909 | 0.347455 | − | 0.937697i | \(-0.387046\pi\) | ||||
0.347455 | + | 0.937697i | \(0.387046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.9364 | 0.765721 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.33063 | 0.404449 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0301293 | −0.00191708 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.15257 | 0.0730411 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.8819 | −1.50741 | −0.753706 | − | 0.657212i | \(-0.771736\pi\) | ||||
−0.753706 | + | 0.657212i | \(0.771736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.63342 | −0.417040 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.46366 | 0.279525 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.25407 | 0.327740 | 0.163870 | − | 0.986482i | \(-0.447602\pi\) | ||||
0.163870 | + | 0.986482i | \(0.447602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.78175 | −0.607808 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.8768 | −1.41604 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.10964 | 0.0684235 | 0.0342118 | − | 0.999415i | \(-0.489108\pi\) | ||||
0.0342118 | + | 0.999415i | \(0.489108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5784 | 0.649824 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.18414 | −0.439662 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.84634 | −0.173544 | −0.0867722 | − | 0.996228i | \(-0.527655\pi\) | ||||
−0.0867722 | + | 0.996228i | \(0.527655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.1029 | −0.795946 | −0.397973 | − | 0.917397i | \(-0.630286\pi\) | ||||
−0.397973 | + | 0.917397i | \(0.630286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0292049 | 0.00176756 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.3451 | −0.985646 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.4634 | −1.40978 | −0.704888 | − | 0.709318i | \(-0.749003\pi\) | ||||
−0.704888 | + | 0.709318i | \(0.749003\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.35792 | 0.560244 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.91165 | 0.531625 | 0.265812 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265812 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8040 | 0.939453 | 0.469726 | − | 0.882812i | \(-0.344353\pi\) | ||||
0.469726 | + | 0.882812i | \(0.344353\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.425653 | −0.0252135 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.45354 | −0.439968 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.4990 | 2.14700 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.10709 | −0.0648988 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.9425 | 1.92452 | 0.962261 | − | 0.272127i | \(-0.0877272\pi\) | ||||
0.962261 | + | 0.272127i | \(0.0877272\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −16.0229 | −0.932888 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.3796 | −0.776363 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0609917 | 0.00352724 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0629 | −0.925851 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.98733 | −0.114169 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.5342 | −0.717705 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2343 | −1.15483 | −0.577416 | − | 0.816450i | \(-0.695939\pi\) | ||||
−0.577416 | + | 0.816450i | \(0.695939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.59886 | 0.147844 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.27289 | −0.128884 | −0.0644420 | − | 0.997921i | \(-0.520527\pi\) | ||||
−0.0644420 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.1142 | 0.741257 | 0.370629 | − | 0.928781i | \(-0.379142\pi\) | ||||
0.370629 | + | 0.928781i | \(0.379142\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.64221 | −0.261559 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.86525 | −0.441757 | −0.220878 | − | 0.975301i | \(-0.570892\pi\) | ||||
−0.220878 | + | 0.975301i | \(0.570892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.0096 | 2.18412 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.77304 | −0.154776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.10164 | −0.283863 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.150287 | 0.00833640 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.36317 | −0.130683 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.17065 | −0.395331 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3752 | 1.06496 | 0.532480 | − | 0.846443i | \(-0.321260\pi\) | ||||
0.532480 | + | 0.846443i | \(0.321260\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.7253 | −1.08094 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4876 | 0.682273 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.2459 | −1.42970 | −0.714852 | − | 0.699276i | \(-0.753506\pi\) | ||||
−0.714852 | + | 0.699276i | \(0.753506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.24428 | −0.339143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.9572 | −0.864130 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.5773 | 0.895092 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.861662 | 0.0463903 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.65189 | 0.196044 | 0.0980219 | − | 0.995184i | \(-0.468748\pi\) | ||||
0.0980219 | + | 0.995184i | \(0.468748\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.818652 | −0.0438214 | −0.0219107 | − | 0.999760i | \(-0.506975\pi\) | ||||
−0.0219107 | + | 0.999760i | \(0.506975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.123020 | 0.00656633 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.5367 | −1.51886 | −0.759428 | − | 0.650591i | \(-0.774521\pi\) | ||||
−0.759428 | + | 0.650591i | \(0.774521\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.30250 | 0.122204 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.94513 | 0.261724 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.8623 | 0.837180 | 0.418590 | − | 0.908175i | \(-0.362524\pi\) | ||||
0.418590 | + | 0.908175i | \(0.362524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5135 | −0.974395 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.47882 | 0.287563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.98926 | −0.418177 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9937 | −0.730463 | −0.365232 | − | 0.930917i | \(-0.619010\pi\) | ||||
−0.365232 | + | 0.930917i | \(0.619010\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.0304 | −0.782449 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.7194 | 0.608441 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.2336 | 0.633434 | 0.316717 | − | 0.948520i | \(-0.397419\pi\) | ||||
0.316717 | + | 0.948520i | \(0.397419\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.17450 | 0.267210 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.358678 | −0.0184728 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.284829 | −0.0146307 | −0.00731535 | − | 0.999973i | \(-0.502329\pi\) | ||||
−0.00731535 | + | 0.999973i | \(0.502329\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.211621 | −0.0108417 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.8268 | −1.52408 | −0.762038 | − | 0.647532i | \(-0.775801\pi\) | ||||
−0.762038 | + | 0.647532i | \(0.775801\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.91593 | 0.403433 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.3915 | −1.64655 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.88544 | −0.450510 | −0.225255 | − | 0.974300i | \(-0.572321\pi\) | ||||
−0.225255 | + | 0.974300i | \(0.572321\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3274 | 0.522280 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.61279 | 0.333571 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.9626 | −0.803167 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.5831 | −1.48473 | −0.742367 | − | 0.669993i | \(-0.766297\pi\) | ||||
−0.742367 | + | 0.669993i | \(0.766297\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.471566 | −0.0236078 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.30306 | 0.314760 | 0.157380 | − | 0.987538i | \(-0.449695\pi\) | ||||
0.157380 | + | 0.987538i | \(0.449695\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.146720 | 0.00730864 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.45525 | −0.420145 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.6357 | 1.66726 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.63163 | −0.377360 | −0.188680 | − | 0.982039i | \(-0.560421\pi\) | ||||
−0.188680 | + | 0.982039i | \(0.560421\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.57699 | 0.275092 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.7512 | −0.873478 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.87240 | −0.141001 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.458813 | 0.0224682 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.34760 | −0.114688 | −0.0573439 | − | 0.998354i | \(-0.518263\pi\) | ||||
−0.0573439 | + | 0.998354i | \(0.518263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.61693 | 0.419963 | 0.209982 | − | 0.977705i | \(-0.432660\pi\) | ||||
0.209982 | + | 0.977705i | \(0.432660\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.4599 | −0.703064 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.4473 | 1.23437 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8862 | −0.671999 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.100425 | −0.00484854 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.73295 | 0.131641 | 0.0658207 | − | 0.997831i | \(-0.479033\pi\) | ||||
0.0658207 | + | 0.997831i | \(0.479033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.8768 | 0.714934 | 0.357467 | − | 0.933926i | \(-0.383640\pi\) | ||||
0.357467 | + | 0.933926i | \(0.383640\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.06723 | −0.242955 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.984819 | −0.0471103 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.8115 | 0.945552 | 0.472776 | − | 0.881183i | \(-0.343252\pi\) | ||||
0.472776 | + | 0.881183i | \(0.343252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.1430 | 0.673474 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.5818 | 1.88059 | 0.940293 | − | 0.340366i | \(-0.110551\pi\) | ||||
0.940293 | + | 0.340366i | \(0.110551\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.9041 | 0.848738 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.37146 | 0.301360 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.9205 | −1.08169 | −0.540843 | − | 0.841124i | \(-0.681895\pi\) | ||||
−0.540843 | + | 0.841124i | \(0.681895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.6299 | 1.20686 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.5123 | 0.493911 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0727838 | −0.00341216 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.66494 | −0.452107 | −0.226053 | − | 0.974115i | \(-0.572582\pi\) | ||||
−0.226053 | + | 0.974115i | \(0.572582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.8304 | 0.972279 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.28046 | 0.292510 | 0.146255 | − | 0.989247i | \(-0.453278\pi\) | ||||
0.146255 | + | 0.989247i | \(0.453278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.64337 | 0.355218 | 0.177609 | − | 0.984101i | \(-0.443164\pi\) | ||||
0.177609 | + | 0.984101i | \(0.443164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.07279 | 0.0961234 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.8943 | −1.19824 | −0.599122 | − | 0.800658i | \(-0.704484\pi\) | ||||
−0.599122 | + | 0.800658i | \(0.704484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.8346 | 0.638823 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.50136 | 0.391722 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 55.2342 | 2.53967 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.42664 | −0.111342 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.6326 | 1.08206 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.6131 | −0.576309 | −0.288155 | − | 0.957584i | \(-0.593042\pi\) | ||||
−0.288155 | + | 0.957584i | \(0.593042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.309267 | −0.0141013 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.954605 | 0.0434360 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.75907 | 0.125283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.7807 | −1.44012 | −0.720061 | − | 0.693910i | \(-0.755886\pi\) | ||||
−0.720061 | + | 0.693910i | \(0.755886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.49680 | −0.248574 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.2151 | 0.461001 | 0.230500 | − | 0.973072i | \(-0.425964\pi\) | ||||
0.230500 | + | 0.973072i | \(0.425964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.7331 | −2.73528 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.9628 | 0.717474 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.55086 | 0.114422 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.35390 | 0.418738 | 0.209369 | − | 0.977837i | \(-0.432859\pi\) | ||||
0.209369 | + | 0.977837i | \(0.432859\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.0742 | 0.494758 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.7659 | 0.613792 | 0.306896 | − | 0.951743i | \(-0.400710\pi\) | ||||
0.306896 | + | 0.951743i | \(0.400710\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.95278 | 0.220396 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.43207 | −0.285658 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.6367 | 1.00335 | 0.501677 | − | 0.865055i | \(-0.332717\pi\) | ||||
0.501677 | + | 0.865055i | \(0.332717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.85102 | −0.391546 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.98638 | −0.0877008 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.47682 | −0.285403 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.6571 | 1.08442 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.05905 | 0.0903824 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.8738 | −0.476389 | −0.238194 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238194 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.43232 | 0.150085 | 0.0750424 | − | 0.997180i | \(-0.476091\pi\) | ||||
0.0750424 | + | 0.997180i | \(0.476091\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.35219 | 0.102658 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.8434 | 1.08219 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0064 | −0.913322 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.7959 | −1.55341 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.235656 | −0.0102074 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.91091 | 0.298785 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.86520 | 0.123643 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.1167 | −1.03878 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00758 | −0.0433193 | −0.0216597 | − | 0.999765i | \(-0.506895\pi\) | ||||
−0.0216597 | + | 0.999765i | \(0.506895\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.65571 | 0.371452 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.88943 | 0.252275 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6391 | −0.454894 | −0.227447 | − | 0.973791i | \(-0.573038\pi\) | ||||
−0.227447 | + | 0.973791i | \(0.573038\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.0020 | −1.19510 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.79149 | 0.246726 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.6844 | −0.752019 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.36917 | −0.185461 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.9092 | 0.801207 | 0.400603 | − | 0.916252i | \(-0.368801\pi\) | ||||
0.400603 | + | 0.916252i | \(0.368801\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.507856 | −0.0214800 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0044 | −0.717926 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.1768 | −1.18751 | −0.593756 | − | 0.804645i | \(-0.702356\pi\) | ||||
−0.593756 | + | 0.804645i | \(0.702356\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.5618 | 0.654692 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.36727 | −0.393388 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.499818 | −0.0209534 | −0.0104767 | − | 0.999945i | \(-0.503335\pi\) | ||||
−0.0104767 | + | 0.999945i | \(0.503335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.2303 | 1.18140 | 0.590702 | − | 0.806890i | \(-0.298851\pi\) | ||||
0.590702 | + | 0.806890i | \(0.298851\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.6923 | 0.446678 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.91233 | 0.204858 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3728 | −1.51422 | −0.757111 | − | 0.653287i | \(-0.773390\pi\) | ||||
−0.757111 | + | 0.653287i | \(0.773390\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.14253 | 0.0474819 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.18224 | −0.132021 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.2985 | −1.66899 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.146771 | −0.00606825 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.1223 | −0.665437 | −0.332718 | − | 0.943026i | \(-0.607966\pi\) | ||||
−0.332718 | + | 0.943026i | \(0.607966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.36905 | −0.0976152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.949491 | 0.0390569 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.8487 | 1.02041 | 0.510207 | − | 0.860052i | \(-0.329569\pi\) | ||||
0.510207 | + | 0.860052i | \(0.329569\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.3241 | −0.505240 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.5120 | −0.430228 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.50155 | 0.0613517 | 0.0306759 | − | 0.999529i | \(-0.490234\pi\) | ||||
0.0306759 | + | 0.999529i | \(0.490234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0828 | −0.982356 | −0.491178 | − | 0.871059i | \(-0.663434\pi\) | ||||
−0.491178 | + | 0.871059i | \(0.663434\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.8981 | 1.13610 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.6542 | −0.555121 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0760 | −0.652506 | −0.326253 | − | 0.945283i | \(-0.605786\pi\) | ||||
−0.326253 | + | 0.945283i | \(0.605786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.61381 | −0.227483 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.226712 | −0.00917179 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.5233 | 1.75789 | 0.878945 | − | 0.476923i | \(-0.158248\pi\) | ||||
0.878945 | + | 0.476923i | \(0.158248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.32924 | −0.134248 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.82544 | −0.154006 | −0.0770032 | − | 0.997031i | \(-0.524535\pi\) | ||||
−0.0770032 | + | 0.997031i | \(0.524535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.69881 | −0.349635 | −0.174817 | − | 0.984601i | \(-0.555934\pi\) | ||||
−0.174817 | + | 0.984601i | \(0.555934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.02109 | 0.161361 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.8354 | 0.794687 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.49981 | 0.179992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.62153 | 0.0647578 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.3666 | −2.08799 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0264 | 1.11571 | 0.557856 | − | 0.829938i | \(-0.311624\pi\) | ||||
0.557856 | + | 0.829938i | \(0.311624\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.44961 | 0.375588 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.527398 | 0.0209291 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.221743 | 0.00878578 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.14391 | 0.203490 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.7621 | 0.899048 | 0.449524 | − | 0.893268i | \(-0.351594\pi\) | ||||
0.449524 | + | 0.893268i | \(0.351594\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.9559 | −1.41796 | −0.708981 | − | 0.705228i | \(-0.750845\pi\) | ||||
−0.708981 | + | 0.705228i | \(0.750845\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.17476 | −0.282506 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.94619 | 0.0765127 | 0.0382564 | − | 0.999268i | \(-0.487820\pi\) | ||||
0.0382564 | + | 0.999268i | \(0.487820\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.0395 | 2.39601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.29637 | 0.0900019 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.3392 | 0.952467 | 0.476233 | − | 0.879319i | \(-0.342002\pi\) | ||||
0.476233 | + | 0.879319i | \(0.342002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.4802 | −0.643936 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.8484 | −0.696334 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.16907 | 0.240313 | 0.120156 | − | 0.992755i | \(-0.461660\pi\) | ||||
0.120156 | + | 0.992755i | \(0.461660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.1704 | −1.87361 | −0.936807 | − | 0.349848i | \(-0.886233\pi\) | ||||
−0.936807 | + | 0.349848i | \(0.886233\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.156349 | 0.00607208 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.17522 | 0.0455732 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.7239 | −0.453951 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.16551 | −0.161048 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.7492 | 1.84334 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.2071 | −0.740381 | −0.370190 | − | 0.928956i | \(-0.620708\pi\) | ||||
−0.370190 | + | 0.928956i | \(0.620708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.90817 | 0.381366 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.9094 | −0.573014 | −0.286507 | − | 0.958078i | \(-0.592494\pi\) | ||||
−0.286507 | + | 0.958078i | \(0.592494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.05667 | 0.117304 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.904843 | −0.0346737 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.8682 | 0.875029 | 0.437515 | − | 0.899211i | \(-0.355859\pi\) | ||||
0.437515 | + | 0.899211i | \(0.355859\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8988 | −0.531047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.24720 | 0.0475835 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.370529 | 0.0141160 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.5210 | 1.35128 | 0.675641 | − | 0.737231i | \(-0.263867\pi\) | ||||
0.675641 | + | 0.737231i | \(0.263867\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.6846 | 0.671783 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.14344 | −0.0433732 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.9025 | −1.51142 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.10617 | 0.306604 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.22303 | 0.348349 | 0.174175 | − | 0.984715i | \(-0.444274\pi\) | ||||
0.174175 | + | 0.984715i | \(0.444274\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.99366 | 0.188339 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.20288 | −0.120628 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.48701 | 0.206360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7763 | 1.08072 | 0.540358 | − | 0.841435i | \(-0.318289\pi\) | ||||
0.540358 | + | 0.841435i | \(0.318289\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.6614 | −1.33741 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.79575 | 0.179602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.250276 | 0.00935978 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.31614 | 0.198535 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.1878 | 0.902055 | 0.451027 | − | 0.892510i | \(-0.351058\pi\) | ||||
0.451027 | + | 0.892510i | \(0.351058\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.17544 | −0.267227 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.494846 | −0.0184035 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.8883 | −1.07288 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.73994 | −0.361235 | −0.180617 | − | 0.983553i | \(-0.557810\pi\) | ||||
−0.180617 | + | 0.983553i | \(0.557810\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.6617 | −0.543024 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −85.9928 | −3.18056 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.38060 | −0.161801 | −0.0809006 | − | 0.996722i | \(-0.525780\pi\) | ||||
−0.0809006 | + | 0.996722i | \(0.525780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.13268 | 0.115551 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −47.5719 | −1.75234 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.21520 | 0.228630 | 0.114315 | − | 0.993445i | \(-0.463533\pi\) | ||||
0.114315 | + | 0.993445i | \(0.463533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0149094 | −0.000547709 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7097 | −0.979885 | −0.489942 | − | 0.871755i | \(-0.662982\pi\) | ||||
−0.489942 | + | 0.871755i | \(0.662982\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.8788 | −0.581754 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.41710 | −0.234790 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.65635 | 0.279757 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.9924 | −1.71478 | −0.857388 | − | 0.514670i | \(-0.827915\pi\) | ||||
−0.857388 | + | 0.514670i | \(0.827915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.8178 | −0.430666 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.1985 | −0.953461 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.2425 | −1.28091 | −0.640456 | − | 0.767995i | \(-0.721255\pi\) | ||||
−0.640456 | + | 0.767995i | \(0.721255\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.28252 | −0.119148 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.1109 | −1.70777 | −0.853885 | − | 0.520461i | \(-0.825760\pi\) | ||||
−0.853885 | + | 0.520461i | \(0.825760\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.52469 | 0.236210 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −24.8521 | −0.898529 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.561234 | −0.0202650 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.8827 | −1.94306 | −0.971530 | − | 0.236915i | \(-0.923864\pi\) | ||||
−0.971530 | + | 0.236915i | \(0.923864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.59995 | 0.0936350 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.33241 | −0.263728 | −0.131864 | − | 0.991268i | \(-0.542096\pi\) | ||||
−0.131864 | + | 0.991268i | \(0.542096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.8170 | 0.424478 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.84045 | −0.173650 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.80509 | 0.136332 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.77143 | −0.313866 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.6471 | −0.845078 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.1869 | −0.756193 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.274880 | 0.00979841 | 0.00489921 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489921 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.549102 | 0.0195485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.2404 | 0.612998 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.439035 | −0.0155906 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.23466 | 0.185654 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.42858 | −0.263134 | −0.131567 | − | 0.991307i | \(-0.542001\pi\) | ||||
−0.131567 | + | 0.991307i | \(0.542001\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.3881 | −1.35807 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.9988 | 1.41329 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.4353 | 1.07404 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.37904 | −0.0838502 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.40850 | −0.0495815 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.6491 | 1.49946 | 0.749730 | − | 0.661743i | \(-0.230183\pi\) | ||||
0.749730 | + | 0.661743i | \(0.230183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.6139 | −0.899425 | −0.449713 | − | 0.893173i | \(-0.648474\pi\) | ||||
−0.449713 | + | 0.893173i | \(0.648474\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.48392 | −0.227401 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.6990 | 0.479855 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.20024 | 0.286890 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.162603 | −0.00568181 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.8573 | 0.762826 | 0.381413 | − | 0.924405i | \(-0.375438\pi\) | ||||
0.381413 | + | 0.924405i | \(0.375438\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.58270 | −0.0551693 | −0.0275847 | − | 0.999619i | \(-0.508782\pi\) | ||||
−0.0275847 | + | 0.999619i | \(0.508782\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.08830 | −0.281598 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.2198 | −1.25949 | −0.629743 | − | 0.776803i | \(-0.716840\pi\) | ||||
−0.629743 | + | 0.776803i | \(0.716840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.5957 | 1.06263 | 0.531316 | − | 0.847174i | \(-0.321698\pi\) | ||||
0.531316 | + | 0.847174i | \(0.321698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.6107 | −0.402772 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.5466 | 1.30091 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.5988 | −0.955096 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.67303 | 0.334349 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.85906 | 0.340373 | 0.170186 | − | 0.985412i | \(-0.445563\pi\) | ||||
0.170186 | + | 0.985412i | \(0.445563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.9455 | 1.37743 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.40989 | 0.151885 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.0298 | 0.551443 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.1270 | −0.519769 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.82056 | 0.268401 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.1088 | −0.346526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.6701 | 0.707730 | 0.353865 | − | 0.935296i | \(-0.384867\pi\) | ||||
0.353865 | + | 0.935296i | \(0.384867\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.36989 | 0.0810484 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.0858 | 1.23267 | 0.616334 | − | 0.787485i | \(-0.288617\pi\) | ||||
0.616334 | + | 0.787485i | \(0.288617\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.7566 | −1.39060 | −0.695299 | − | 0.718720i | \(-0.744728\pi\) | ||||
−0.695299 | + | 0.718720i | \(0.744728\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.68835 | −0.125699 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.5125 | −0.732295 | −0.366148 | − | 0.930557i | \(-0.619323\pi\) | ||||
−0.366148 | + | 0.930557i | \(0.619323\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.13152 | −0.174477 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.0614 | 0.613396 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.8100 | 2.06284 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.437405 | 0.0148209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.16390 | 0.208616 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.2868 | −0.482981 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −47.8912 | −1.61717 | −0.808586 | − | 0.588378i | \(-0.799767\pi\) | ||||
−0.808586 | + | 0.588378i | \(0.799767\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.3015 | 0.549835 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.2689 | −0.615496 | −0.307748 | − | 0.951468i | \(-0.599575\pi\) | ||||
−0.307748 | + | 0.951468i | \(0.599575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.0354 | 1.24634 | 0.623170 | − | 0.782087i | \(-0.285845\pi\) | ||||
0.623170 | + | 0.782087i | \(0.285845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.92885 | −0.266525 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.7619 | 0.462080 | 0.231040 | − | 0.972944i | \(-0.425787\pi\) | ||||
0.231040 | + | 0.972944i | \(0.425787\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.584285 | 0.0195963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.2104 | 1.07909 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.66067 | 0.122500 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.14059 | −0.238684 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0301815 | 0.00100773 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.2027 | −0.940613 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.7398 | 2.09017 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.94866 | −0.264515 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.5716 | −0.717063 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.1842 | 0.902637 | 0.451319 | − | 0.892363i | \(-0.350954\pi\) | ||||
0.451319 | + | 0.892363i | \(0.350954\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.0648 | 0.366996 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.4894 | −0.977027 | −0.488513 | − | 0.872556i | \(-0.662461\pi\) | ||||
−0.488513 | + | 0.872556i | \(0.662461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9425 | 0.362143 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.20248 | −0.205048 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.2579 | −0.602928 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.2354 | 1.45919 | 0.729596 | − | 0.683878i | \(-0.239708\pi\) | ||||
0.729596 | + | 0.683878i | \(0.239708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0128 | −0.329935 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0806498 | 0.00265462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.9086 | −0.818991 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.4696 | −0.475243 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.7425 | 0.582112 | 0.291056 | − | 0.956706i | \(-0.405993\pi\) | ||||
0.291056 | + | 0.956706i | \(0.405993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.58043 | −0.117344 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.12473 | −0.0368220 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.3779 | 1.38591 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1680 | 1.50824 | 0.754121 | − | 0.656735i | \(-0.228063\pi\) | ||||
0.754121 | + | 0.656735i | \(0.228063\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.48949 | 0.211777 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.0383 | −0.718428 | −0.359214 | − | 0.933255i | \(-0.616955\pi\) | ||||
−0.359214 | + | 0.933255i | \(0.616955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.70276 | −0.250836 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.79853 | −0.156096 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.5940 | 1.12416 | 0.562078 | − | 0.827085i | \(-0.310002\pi\) | ||||
0.562078 | + | 0.827085i | \(0.310002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.279840 | −0.00908399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.89209 | −0.126210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.9799 | −0.679607 | −0.339803 | − | 0.940496i | \(-0.610361\pi\) | ||||
−0.339803 | + | 0.940496i | \(0.610361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.6471 | −0.862281 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.3037 | 0.624001 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.3980 | −0.497228 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.4635 | −0.627854 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.4393 | 0.497526 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.84738 | −0.0916605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.0716187 | 0.00230310 | 0.00115155 | − | 0.999999i | \(-0.499633\pi\) | ||||
0.00115155 | + | 0.999999i | \(0.499633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.52453 | −0.0810995 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.18205 | 0.262575 | 0.131287 | − | 0.991344i | \(-0.458089\pi\) | ||||
0.131287 | + | 0.991344i | \(0.458089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.26678 | −0.0406111 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0743687 | 0.00238170 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.6886 | 0.725872 | 0.362936 | − | 0.931814i | \(-0.381774\pi\) | ||||
0.362936 | + | 0.931814i | \(0.381774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −68.2062 | −2.17988 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.1573 | 0.420080 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.8463 | 0.601103 | 0.300551 | − | 0.953766i | \(-0.402829\pi\) | ||||
0.300551 | + | 0.953766i | \(0.402829\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.36630 | −0.0753966 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.54836 | −0.112946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.6000 | −0.527850 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8310 | 0.534655 | 0.267328 | − | 0.963606i | \(-0.413859\pi\) | ||||
0.267328 | + | 0.963606i | \(0.413859\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.58775 | 0.304258 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26.1978 | 0.830525 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60.1343 | 1.90447 | 0.952236 | − | 0.305363i | \(-0.0987779\pi\) | ||||
0.952236 | + | 0.305363i | \(0.0987779\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.3895 | −0.645095 |
(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 | 3856.2.a.j.1.4 | 7 | ||
4.3 | odd | 2 | 241.2.a.a.1.5 | ✓ | 7 | ||
12.11 | even | 2 | 2169.2.a.e.1.3 | 7 | |||
20.19 | odd | 2 | 6025.2.a.f.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.a.1.5 | ✓ | 7 | 4.3 | odd | 2 | ||
2169.2.a.e.1.3 | 7 | 12.11 | even | 2 | |||
3856.2.a.j.1.4 | 7 | 1.1 | even | 1 | trivial | ||
6025.2.a.f.1.3 | 7 | 20.19 | odd | 2 |