Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 55 x^{16} + 288 x^{15} + 1222 x^{14} - 6888 x^{13} - 13745 x^{12} + 88434 x^{11} + \cdots - 115488 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.44612\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(5\) | −3.44612 | −1.54115 | −0.770576 | − | 0.637348i | \(-0.780031\pi\) | ||||
−0.770576 | + | 0.637348i | \(0.780031\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.67774 | 1.76802 | 0.884009 | − | 0.467470i | \(-0.154834\pi\) | ||||
0.884009 | + | 0.467470i | \(0.154834\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.77983 | −1.13966 | −0.569831 | − | 0.821762i | \(-0.692991\pi\) | ||||
−0.569831 | + | 0.821762i | \(0.692991\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51025 | −0.973568 | −0.486784 | − | 0.873522i | \(-0.661830\pi\) | ||||
−0.486784 | + | 0.873522i | \(0.661830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.44612 | −0.889785 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.12984 | −1.97178 | −0.985888 | − | 0.167407i | \(-0.946461\pi\) | ||||
−0.985888 | + | 0.167407i | \(0.946461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.33577 | 1.22411 | 0.612055 | − | 0.790815i | \(-0.290343\pi\) | ||||
0.612055 | + | 0.790815i | \(0.290343\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.67774 | 1.02077 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.87575 | 1.37515 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.72230 | −1.74618 | −0.873088 | − | 0.487562i | \(-0.837886\pi\) | ||||
−0.873088 | + | 0.487562i | \(0.837886\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.77983 | −0.657984 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.1200 | −2.72479 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.45986 | 1.22639 | 0.613197 | − | 0.789930i | \(-0.289883\pi\) | ||||
0.613197 | + | 0.789930i | \(0.289883\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.51025 | −0.562090 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.95562 | 0.617764 | 0.308882 | − | 0.951100i | \(-0.400045\pi\) | ||||
0.308882 | + | 0.951100i | \(0.400045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.47386 | −0.377259 | −0.188630 | − | 0.982048i | \(-0.560405\pi\) | ||||
−0.188630 | + | 0.982048i | \(0.560405\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.44612 | −0.513717 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.53158 | −0.515134 | −0.257567 | − | 0.966260i | \(-0.582921\pi\) | ||||
−0.257567 | + | 0.966260i | \(0.582921\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.8812 | 2.12589 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.12984 | −1.13841 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.38979 | 1.28979 | 0.644893 | − | 0.764272i | \(-0.276902\pi\) | ||||
0.644893 | + | 0.764272i | \(0.276902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.0258 | 1.75639 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.33577 | 0.706740 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.971003 | 0.126414 | 0.0632069 | − | 0.998000i | \(-0.479867\pi\) | ||||
0.0632069 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.8969 | −1.65128 | −0.825638 | − | 0.564201i | \(-0.809184\pi\) | ||||
−0.825638 | + | 0.564201i | \(0.809184\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.67774 | 0.589339 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0967 | 1.50042 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4797 | 1.76898 | 0.884491 | − | 0.466557i | \(-0.154506\pi\) | ||||
0.884491 | + | 0.466557i | \(0.154506\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.25213 | 1.09803 | 0.549013 | − | 0.835814i | \(-0.315004\pi\) | ||||
0.549013 | + | 0.835814i | \(0.315004\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1166 | 1.18406 | 0.592030 | − | 0.805916i | \(-0.298327\pi\) | ||||
0.592030 | + | 0.805916i | \(0.298327\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.87575 | 0.793944 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.6811 | −2.01494 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.1749 | 1.59480 | 0.797399 | − | 0.603453i | \(-0.206209\pi\) | ||||
0.797399 | + | 0.603453i | \(0.206209\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.7640 | 1.18151 | 0.590753 | − | 0.806852i | \(-0.298831\pi\) | ||||
0.590753 | + | 0.806852i | \(0.298831\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.0164 | 3.03881 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.4033 | −1.63275 | −0.816373 | − | 0.577525i | \(-0.804019\pi\) | ||||
−0.816373 | + | 0.577525i | \(0.804019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.4200 | −1.72129 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.72230 | −1.00816 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.3877 | −1.88654 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.6078 | −1.48319 | −0.741597 | − | 0.670846i | \(-0.765931\pi\) | ||||
−0.741597 | + | 0.670846i | \(0.765931\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.77983 | −0.379887 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.45378 | 0.144657 | 0.0723284 | − | 0.997381i | \(-0.476957\pi\) | ||||
0.0723284 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.66441 | 0.755197 | 0.377598 | − | 0.925970i | \(-0.376750\pi\) | ||||
0.377598 | + | 0.925970i | \(0.376750\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16.1200 | −1.57316 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.2562 | 1.95824 | 0.979122 | − | 0.203274i | \(-0.0651583\pi\) | ||||
0.979122 | + | 0.203274i | \(0.0651583\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.12731 | −0.586890 | −0.293445 | − | 0.955976i | \(-0.594802\pi\) | ||||
−0.293445 | + | 0.955976i | \(0.594802\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.45986 | 0.708059 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.43980 | 0.417661 | 0.208831 | − | 0.977952i | \(-0.433034\pi\) | ||||
0.208831 | + | 0.977952i | \(0.433034\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.44612 | 0.321352 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.51025 | −0.324523 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −38.0292 | −3.48614 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.28712 | 0.298829 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.95562 | 0.356666 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.46407 | −0.578164 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.12568 | 0.366095 | 0.183047 | − | 0.983104i | \(-0.441404\pi\) | ||||
0.183047 | + | 0.983104i | \(0.441404\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.47386 | −0.217811 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1176 | 0.971352 | 0.485676 | − | 0.874139i | \(-0.338573\pi\) | ||||
0.485676 | + | 0.874139i | \(0.338573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.9593 | 2.16425 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.44612 | −0.296595 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.5291 | −1.58305 | −0.791524 | − | 0.611137i | \(-0.790712\pi\) | ||||
−0.791524 | + | 0.611137i | \(0.790712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.48110 | 0.380082 | 0.190041 | − | 0.981776i | \(-0.439138\pi\) | ||||
0.190041 | + | 0.981776i | \(0.439138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.53158 | −0.297413 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.2681 | 1.10954 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.44612 | −0.286185 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.8812 | 1.22738 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.33782 | 0.519214 | 0.259607 | − | 0.965714i | \(-0.416407\pi\) | ||||
0.259607 | + | 0.965714i | \(0.416407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.55727 | 0.452244 | 0.226122 | − | 0.974099i | \(-0.427395\pi\) | ||||
0.226122 | + | 0.974099i | \(0.427395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.12984 | −0.657259 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.5042 | 2.69112 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.14436 | −0.171138 | −0.0855692 | − | 0.996332i | \(-0.527271\pi\) | ||||
−0.0855692 | + | 0.996332i | \(0.527271\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.38979 | 0.744659 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.67774 | −0.368657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.26347 | −0.647245 | −0.323623 | − | 0.946186i | \(-0.604901\pi\) | ||||
−0.323623 | + | 0.946186i | \(0.604901\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.0258 | 1.01405 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.48777 | 0.734186 | 0.367093 | − | 0.930184i | \(-0.380353\pi\) | ||||
0.367093 | + | 0.930184i | \(0.380353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.678155 | −0.0521658 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.33577 | 0.408037 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.73038 | −0.131558 | −0.0657790 | − | 0.997834i | \(-0.520953\pi\) | ||||
−0.0657790 | + | 0.997834i | \(0.520953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32.1630 | 2.43129 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.971003 | 0.0729850 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.0890 | 1.05306 | 0.526531 | − | 0.850156i | \(-0.323493\pi\) | ||||
0.526531 | + | 0.850156i | \(0.323493\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.89981 | 0.661517 | 0.330759 | − | 0.943715i | \(-0.392695\pi\) | ||||
0.330759 | + | 0.943715i | \(0.392695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.8969 | −0.953364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.7076 | −1.89006 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.7294 | 2.24716 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.67774 | 0.340255 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.4148 | −1.62188 | −0.810940 | − | 0.585129i | \(-0.801044\pi\) | ||||
−0.810940 | + | 0.585129i | \(0.801044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.4446 | 1.61559 | 0.807797 | − | 0.589461i | \(-0.200660\pi\) | ||||
0.807797 | + | 0.589461i | \(0.200660\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.0967 | 0.866266 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.86856 | 0.204377 | 0.102188 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102188 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8844 | 0.842459 | 0.421230 | − | 0.906954i | \(-0.361599\pi\) | ||||
0.421230 | + | 0.906954i | \(0.361599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.4797 | 1.02132 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.67774 | 0.328313 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.6315 | −0.952068 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.1683 | −1.39507 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.40524 | −0.440955 | −0.220477 | − | 0.975392i | \(-0.570762\pi\) | ||||
−0.220477 | + | 0.975392i | \(0.570762\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.25213 | 0.633945 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.52521 | 0.581414 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −45.4784 | −3.08727 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.1166 | 0.683618 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.5378 | 1.91966 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.73456 | 0.183120 | 0.0915600 | − | 0.995800i | \(-0.470815\pi\) | ||||
0.0915600 | + | 0.995800i | \(0.470815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.87575 | 0.458384 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.5888 | 1.83113 | 0.915566 | − | 0.402168i | \(-0.131743\pi\) | ||||
0.915566 | + | 0.402168i | \(0.131743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.8421 | −1.37728 | −0.688641 | − | 0.725102i | \(-0.741793\pi\) | ||||
−0.688641 | + | 0.725102i | \(0.741793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.6811 | −1.16333 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1311 | −0.663712 | −0.331856 | − | 0.943330i | \(-0.607675\pi\) | ||||
−0.331856 | + | 0.943330i | \(0.607675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1703 | 0.793900 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.1749 | 0.920757 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7910 | 0.698015 | 0.349007 | − | 0.937120i | \(-0.386519\pi\) | ||||
0.349007 | + | 0.937120i | \(0.386519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.64672 | 0.556984 | 0.278492 | − | 0.960438i | \(-0.410165\pi\) | ||||
0.278492 | + | 0.960438i | \(0.410165\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −51.2825 | −3.27632 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.7299 | −1.19175 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.7640 | 0.682143 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1724 | −0.768313 | −0.384156 | − | 0.923268i | \(-0.625508\pi\) | ||||
−0.384156 | + | 0.923268i | \(0.625508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.77983 | 0.237636 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 28.0164 | 1.75446 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.6720 | −1.97564 | −0.987822 | − | 0.155591i | \(-0.950272\pi\) | ||||
−0.987822 | + | 0.155591i | \(0.950272\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34.8953 | 2.16829 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.9941 | 1.17123 | 0.585613 | − | 0.810591i | \(-0.300854\pi\) | ||||
0.585613 | + | 0.810591i | \(0.300854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.3584 | −1.98776 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.4033 | −0.942667 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.758985 | −0.0462761 | −0.0231381 | − | 0.999732i | \(-0.507366\pi\) | ||||
−0.0231381 | + | 0.999732i | \(0.507366\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8284 | −1.20449 | −0.602244 | − | 0.798312i | \(-0.705727\pi\) | ||||
−0.602244 | + | 0.798312i | \(0.705727\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.4200 | −0.993785 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −25.9892 | −1.56721 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.27693 | −0.0767232 | −0.0383616 | − | 0.999264i | \(-0.512214\pi\) | ||||
−0.0383616 | + | 0.999264i | \(0.512214\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.72230 | −0.582059 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.58038 | 0.511863 | 0.255931 | − | 0.966695i | \(-0.417618\pi\) | ||||
0.255931 | + | 0.966695i | \(0.417618\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.23788 | −0.370804 | −0.185402 | − | 0.982663i | \(-0.559359\pi\) | ||||
−0.185402 | + | 0.982663i | \(0.559359\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.3877 | −1.08919 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.5033 | 1.09222 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.0943 | 2.88790 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.6078 | −0.856322 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.5887 | 0.618596 | 0.309298 | − | 0.950965i | \(-0.399906\pi\) | ||||
0.309298 | + | 0.950965i | \(0.399906\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.34619 | −0.194823 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.77983 | −0.219328 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.51025 | 0.203003 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.5720 | −0.667002 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.45378 | 0.0835176 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 44.4442 | 2.54487 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7072 | 0.725237 | 0.362618 | − | 0.931938i | \(-0.381883\pi\) | ||||
0.362618 | + | 0.931938i | \(0.381883\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.66441 | 0.436013 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.170695 | −0.00967922 | −0.00483961 | − | 0.999988i | \(-0.501541\pi\) | ||||
−0.00483961 | + | 0.999988i | \(0.501541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.414275 | −0.0234162 | −0.0117081 | − | 0.999931i | \(-0.503727\pi\) | ||||
−0.0117081 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.1200 | −0.908262 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.3331 | −0.973526 | −0.486763 | − | 0.873534i | \(-0.661822\pi\) | ||||
−0.486763 | + | 0.873534i | \(0.661822\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.77983 | −0.211630 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.2562 | 1.13059 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.3790 | −2.41367 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.1356 | −1.33880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.12731 | −0.338841 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.5198 | −0.910766 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.522129 | −0.0286988 | −0.0143494 | − | 0.999897i | \(-0.504568\pi\) | ||||
−0.0143494 | + | 0.999897i | \(0.504568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.45986 | 0.408798 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −49.8990 | −2.72627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.0909 | −1.63916 | −0.819578 | − | 0.572968i | \(-0.805792\pi\) | ||||
−0.819578 | + | 0.572968i | \(0.805792\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.43980 | 0.241137 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.7486 | 1.99005 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 36.8662 | 1.99059 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.44612 | 0.185533 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.1601 | −0.974884 | −0.487442 | − | 0.873155i | \(-0.662070\pi\) | ||||
−0.487442 | + | 0.873155i | \(0.662070\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.88270 | 0.475480 | 0.237740 | − | 0.971329i | \(-0.423593\pi\) | ||||
0.237740 | + | 0.971329i | \(0.423593\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.51025 | −0.187363 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.0169 | 1.70409 | 0.852043 | − | 0.523472i | \(-0.175364\pi\) | ||||
0.852043 | + | 0.523472i | \(0.175364\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.8840 | −1.69222 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −38.0292 | −2.01272 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0964 | 0.585645 | 0.292823 | − | 0.956167i | \(-0.405405\pi\) | ||||
0.292823 | + | 0.956167i | \(0.405405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.47048 | 0.498446 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.28712 | 0.172529 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.8631 | −1.82482 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4290 | 0.805388 | 0.402694 | − | 0.915335i | \(-0.368074\pi\) | ||||
0.402694 | + | 0.915335i | \(0.368074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.95562 | 0.205921 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 43.9230 | 2.28037 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.8381 | −0.612955 | −0.306478 | − | 0.951878i | \(-0.599150\pi\) | ||||
−0.306478 | + | 0.951878i | \(0.599150\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.46407 | −0.333803 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.51025 | −0.180787 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.6109 | 1.00734 | 0.503672 | − | 0.863895i | \(-0.331982\pi\) | ||||
0.503672 | + | 0.863895i | \(0.331982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.12568 | 0.211365 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.2295 | 0.522703 | 0.261352 | − | 0.965244i | \(-0.415832\pi\) | ||||
0.261352 | + | 0.965244i | \(0.415832\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 60.9310 | 3.10533 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.47386 | −0.125753 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.7177 | 1.20253 | 0.601267 | − | 0.799048i | \(-0.294663\pi\) | ||||
0.601267 | + | 0.799048i | \(0.294663\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.12984 | 0.411144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.1176 | 0.560811 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −48.8483 | −2.45783 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.6869 | −1.43975 | −0.719877 | − | 0.694102i | \(-0.755802\pi\) | ||||
−0.719877 | + | 0.694102i | \(0.755802\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.9593 | 1.24953 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.38220 | 0.218837 | 0.109418 | − | 0.993996i | \(-0.465101\pi\) | ||||
0.109418 | + | 0.993996i | \(0.465101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.1277 | 1.70002 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.44612 | −0.171239 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.1970 | −1.39767 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.8465 | −0.684664 | −0.342332 | − | 0.939579i | \(-0.611217\pi\) | ||||
−0.342332 | + | 0.939579i | \(0.611217\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.5291 | −0.913974 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.54209 | 0.223502 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.0942 | −1.82088 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.48110 | 0.219440 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.9630 | −1.51264 | −0.756320 | − | 0.654202i | \(-0.773005\pi\) | ||||
−0.756320 | + | 0.654202i | \(0.773005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7315 | 1.49776 | 0.748880 | − | 0.662706i | \(-0.230592\pi\) | ||||
0.748880 | + | 0.662706i | \(0.230592\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.53158 | −0.171711 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −55.8988 | −2.71149 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −60.3282 | −2.91948 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.2681 | 0.640592 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.9916 | 1.25197 | 0.625985 | − | 0.779835i | \(-0.284697\pi\) | ||||
0.625985 | + | 0.779835i | \(0.284697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.170347 | −0.00818634 | −0.00409317 | − | 0.999992i | \(-0.501303\pi\) | ||||
−0.00409317 | + | 0.999992i | \(0.501303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.44612 | −0.165229 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.33577 | −0.255245 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.83101 | 0.373754 | 0.186877 | − | 0.982383i | \(-0.440163\pi\) | ||||
0.186877 | + | 0.982383i | \(0.440163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.8812 | 0.708629 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0164 | 1.33110 | 0.665550 | − | 0.746354i | \(-0.268197\pi\) | ||||
0.665550 | + | 0.746354i | \(0.268197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 53.0816 | 2.51631 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.33782 | 0.299769 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.3399 | 1.10148 | 0.550738 | − | 0.834678i | \(-0.314346\pi\) | ||||
0.550738 | + | 0.834678i | \(0.314346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.9516 | −0.704042 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.55727 | 0.261103 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 56.5854 | 2.65276 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.1467 | 1.41021 | 0.705103 | − | 0.709105i | \(-0.250901\pi\) | ||||
0.705103 | + | 0.709105i | \(0.250901\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.12984 | −0.379468 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.02110 | −0.327005 | −0.163503 | − | 0.986543i | \(-0.552279\pi\) | ||||
−0.163503 | + | 0.986543i | \(0.552279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.05569 | 0.0955358 | 0.0477679 | − | 0.998858i | \(-0.484789\pi\) | ||||
0.0477679 | + | 0.998858i | \(0.484789\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 33.5042 | 1.55372 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.46555 | 0.299190 | 0.149595 | − | 0.988747i | \(-0.452203\pi\) | ||||
0.149595 | + | 0.988747i | \(0.452203\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 67.7324 | 3.12759 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.14436 | −0.0988068 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.35076 | 0.429948 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 36.6875 | 1.68334 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.38979 | 0.429929 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.1412 | −1.74272 | −0.871358 | − | 0.490648i | \(-0.836760\pi\) | ||||
−0.871358 | + | 0.490648i | \(0.836760\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1860 | −1.19398 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.67774 | −0.212844 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 50.3401 | 2.28583 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.3846 | −0.651827 | −0.325914 | − | 0.945400i | \(-0.605672\pi\) | ||||
−0.325914 | + | 0.945400i | \(0.605672\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.26347 | −0.373687 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.7557 | 1.29773 | 0.648863 | − | 0.760905i | \(-0.275245\pi\) | ||||
0.648863 | + | 0.760905i | \(0.275245\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.12984 | −0.366150 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.0258 | 0.585464 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.2790 | 1.94133 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.6705 | 0.925339 | 0.462669 | − | 0.886531i | \(-0.346892\pi\) | ||||
0.462669 | + | 0.886531i | \(0.346892\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.48777 | 0.423882 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.0955 | 1.38648 | 0.693240 | − | 0.720706i | \(-0.256182\pi\) | ||||
0.693240 | + | 0.720706i | \(0.256182\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.00991 | −0.222938 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.678155 | −0.0301179 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5883 | −0.557966 | −0.278983 | − | 0.960296i | \(-0.589997\pi\) | ||||
−0.278983 | + | 0.960296i | \(0.589997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.3229 | 2.09344 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.33577 | 0.235580 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.4125 | −1.16387 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3488 | 0.587079 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.73038 | −0.0759551 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.1795 | −0.577405 | −0.288702 | − | 0.957419i | \(-0.593224\pi\) | ||||
−0.288702 | + | 0.957419i | \(0.593224\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.75682 | −0.426636 | −0.213318 | − | 0.976983i | \(-0.568427\pi\) | ||||
−0.213318 | + | 0.976983i | \(0.568427\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.1630 | 1.40371 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 79.0407 | 3.44307 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.971003 | 0.0421379 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.8852 | −0.601435 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −69.8054 | −3.01795 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.0890 | 0.607985 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −56.2485 | −2.42279 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.48118 | 0.192661 | 0.0963304 | − | 0.995349i | \(-0.469289\pi\) | ||||
0.0963304 | + | 0.995349i | \(0.469289\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.89981 | 0.381927 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.1155 | 0.904487 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.8881 | 0.893109 | 0.446554 | − | 0.894757i | \(-0.352651\pi\) | ||||
0.446554 | + | 0.894757i | \(0.352651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.8969 | −0.550425 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.33577 | 0.227312 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 66.3063 | 2.81963 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.7076 | −1.09123 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 40.4571 | 1.71422 | 0.857112 | − | 0.515130i | \(-0.172257\pi\) | ||||
0.857112 | + | 0.515130i | \(0.172257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.68385 | 0.367288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.7294 | 1.29740 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.3385 | 1.02575 | 0.512873 | − | 0.858464i | \(-0.328581\pi\) | ||||
0.512873 | + | 0.858464i | \(0.328581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.3001 | −0.643679 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.67774 | 0.196446 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.7044 | −0.867974 | −0.433987 | − | 0.900919i | \(-0.642894\pi\) | ||||
−0.433987 | + | 0.900919i | \(0.642894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.9870 | 1.00383 | 0.501913 | − | 0.864918i | \(-0.332630\pi\) | ||||
0.501913 | + | 0.864918i | \(0.332630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.4148 | −0.936393 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.87575 | −0.286739 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.22207 | −0.342289 | −0.171145 | − | 0.985246i | \(-0.554747\pi\) | ||||
−0.171145 | + | 0.985246i | \(0.554747\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.4446 | 0.932764 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.3513 | 2.08893 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.4918 | −1.46992 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0967 | 0.500139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.75665 | −0.320151 | −0.160076 | − | 0.987105i | \(-0.551174\pi\) | ||||
−0.160076 | + | 0.987105i | \(0.551174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.8760 | −2.13751 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.86856 | 0.117997 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.4988 | 1.00605 | 0.503023 | − | 0.864273i | \(-0.332221\pi\) | ||||
0.503023 | + | 0.864273i | \(0.332221\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 131.053 | 5.37267 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.8844 | 0.486394 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.81077 | −0.155704 | −0.0778519 | − | 0.996965i | \(-0.524806\pi\) | ||||
−0.0778519 | + | 0.996965i | \(0.524806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.3072 | −1.23626 | −0.618128 | − | 0.786077i | \(-0.712109\pi\) | ||||
−0.618128 | + | 0.786077i | \(0.712109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4797 | 0.589661 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.3278 | −0.460541 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.05353 | −0.367471 | −0.183736 | − | 0.982976i | \(-0.558819\pi\) | ||||
−0.183736 | + | 0.982976i | \(0.558819\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.67774 | 0.189551 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.3967 | 0.501518 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.2807 | −0.657573 | −0.328786 | − | 0.944404i | \(-0.606640\pi\) | ||||
−0.328786 | + | 0.944404i | \(0.606640\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.6315 | −0.549677 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6136 | −0.467546 | −0.233773 | − | 0.972291i | \(-0.575107\pi\) | ||||
−0.233773 | + | 0.972291i | \(0.575107\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.3699 | 1.42164 | 0.710818 | − | 0.703376i | \(-0.248325\pi\) | ||||
0.710818 | + | 0.703376i | \(0.248325\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −72.0526 | −2.88673 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.1028 | −0.484111 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.1683 | −0.805445 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −60.6475 | −2.41817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.2301 | −0.447063 | −0.223532 | − | 0.974697i | \(-0.571759\pi\) | ||||
−0.223532 | + | 0.974697i | \(0.571759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.40524 | −0.254585 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.2176 | −0.564208 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −52.2368 | −2.06970 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.25213 | 0.366008 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.2220 | 0.917215 | 0.458608 | − | 0.888639i | \(-0.348348\pi\) | ||||
0.458608 | + | 0.888639i | \(0.348348\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.1524 | 1.46515 | 0.732573 | − | 0.680688i | \(-0.238319\pi\) | ||||
0.732573 | + | 0.680688i | \(0.238319\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.52521 | 0.335680 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.30473 | −0.129922 | −0.0649611 | − | 0.997888i | \(-0.520692\pi\) | ||||
−0.0649611 | + | 0.997888i | \(0.520692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.67023 | −0.144069 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.4784 | −1.78244 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.4065 | −0.759436 | −0.379718 | − | 0.925102i | \(-0.623979\pi\) | ||||
−0.379718 | + | 0.925102i | \(0.623979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.3127 | −1.49700 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.1166 | 0.394687 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.7540 | 0.925323 | 0.462662 | − | 0.886535i | \(-0.346894\pi\) | ||||
0.462662 | + | 0.886535i | \(0.346894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.2657 | −1.60505 | −0.802525 | − | 0.596618i | \(-0.796511\pi\) | ||||
−0.802525 | + | 0.596618i | \(0.796511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.5378 | 1.10831 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −86.0129 | −3.33544 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.73456 | 0.105724 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.7480 | 1.88190 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0875 | −0.889959 | −0.444980 | − | 0.895541i | \(-0.646789\pi\) | ||||
−0.444980 | + | 0.895541i | \(0.646789\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.87575 | 0.264648 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.46122 | 0.209892 | 0.104946 | − | 0.994478i | \(-0.466533\pi\) | ||||
0.104946 | + | 0.994478i | \(0.466533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −68.3312 | −2.62231 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.5888 | 1.05720 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.06714 | 0.155625 | 0.0778124 | − | 0.996968i | \(-0.475206\pi\) | ||||
0.0778124 | + | 0.996968i | \(0.475206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 63.8536 | 2.43972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.8421 | −0.795175 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.9605 | −1.25570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.1398 | 0.918322 | 0.459161 | − | 0.888353i | \(-0.348150\pi\) | ||||
0.459161 | + | 0.888353i | \(0.348150\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.6811 | −0.671648 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.4424 | −0.585764 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.1585 | −1.21809 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.1311 | −0.383194 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0106 | −0.453632 | −0.226816 | − | 0.973938i | \(-0.572832\pi\) | ||||
−0.226816 | + | 0.973938i | \(0.572832\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.8041 | 1.50124 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.1703 | 0.458358 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.80041 | 0.255756 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50719 | −0.0941594 | −0.0470797 | − | 0.998891i | \(-0.514991\pi\) | ||||
−0.0470797 | + | 0.998891i | \(0.514991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.1749 | 0.531599 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.72230 | 0.364103 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45.7236 | −1.70997 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.7910 | 0.402999 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.2810 | 0.569886 | 0.284943 | − | 0.958544i | \(-0.408025\pi\) | ||||
0.284943 | + | 0.958544i | \(0.408025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.8521 | 1.33520 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.64672 | 0.321575 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.87575 | 0.255359 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.3691 | 1.20050 | 0.600251 | − | 0.799812i | \(-0.295067\pi\) | ||||
0.600251 | + | 0.799812i | \(0.295067\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.1121 | 0.743871 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.3689 | −1.23251 | −0.616254 | − | 0.787548i | \(-0.711350\pi\) | ||||
−0.616254 | + | 0.787548i | \(0.711350\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −51.2825 | −1.89158 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54.7310 | −2.01604 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.4338 | −0.457385 | −0.228693 | − | 0.973499i | \(-0.573445\pi\) | ||||
−0.228693 | + | 0.973499i | \(0.573445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.7299 | −0.688060 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.90265 | −0.106488 | −0.0532439 | − | 0.998582i | \(-0.516956\pi\) | ||||
−0.0532439 | + | 0.998582i | \(0.516956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.8409 | −0.800189 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.7640 | 0.393836 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 94.7533 | 3.46221 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.1303 | −1.06298 | −0.531491 | − | 0.847064i | \(-0.678368\pi\) | ||||
−0.531491 | + | 0.847064i | \(0.678368\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.1724 | −0.443586 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.1510 | −0.696978 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.171557 | 0.00623535 | 0.00311767 | − | 0.999995i | \(-0.499008\pi\) | ||||
0.00311767 | + | 0.999995i | \(0.499008\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.77983 | 0.137199 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.7066 | −0.714365 | −0.357182 | − | 0.934035i | \(-0.616263\pi\) | ||||
−0.357182 | + | 0.934035i | \(0.616263\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.6619 | −1.03763 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 28.0164 | 1.01294 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.40846 | −0.123072 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.9009 | 0.753705 | 0.376853 | − | 0.926273i | \(-0.377006\pi\) | ||||
0.376853 | + | 0.926273i | \(0.377006\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.6720 | −1.14064 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.23704 | 0.0804609 | 0.0402304 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402304 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −66.8481 | −2.40126 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.8953 | 1.25186 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.1063 | 0.756211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.9715 | −1.25138 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.38972 | 0.263750 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.75870 | −0.169629 | −0.0848146 | − | 0.996397i | \(-0.527030\pi\) | ||||
−0.0848146 | + | 0.996397i | \(0.527030\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.9941 | 0.676207 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7682 | 0.738432 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 45.2712 | 1.60763 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.3584 | −1.14763 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32.0330 | 1.13467 | 0.567334 | − | 0.823488i | \(-0.307975\pi\) | ||||
0.567334 | + | 0.823488i | \(0.307975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.7112 | 1.01573 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4033 | −0.544249 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38.2391 | −1.34943 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.1200 | 0.568157 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.758985 | −0.0267175 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.4503 | −0.472887 | −0.236444 | − | 0.971645i | \(-0.575982\pi\) | ||||
−0.236444 | + | 0.971645i | \(0.575982\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.3121 | −0.678139 | −0.339069 | − | 0.940761i | \(-0.610112\pi\) | ||||
−0.339069 | + | 0.940761i | \(0.610112\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.8284 | −0.695411 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.4769 | 0.997503 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.1999 | −0.461807 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.4200 | −0.573762 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.6697 | 0.477074 | 0.238537 | − | 0.971133i | \(-0.423332\pi\) | ||||
0.238537 | + | 0.971133i | \(0.423332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.2534 | −1.54258 | −0.771289 | − | 0.636485i | \(-0.780388\pi\) | ||||
−0.771289 | + | 0.636485i | \(0.780388\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.9892 | −0.904827 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.49234 | −0.121441 | −0.0607203 | − | 0.998155i | \(-0.519340\pi\) | ||||
−0.0607203 | + | 0.998155i | \(0.519340\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0956 | 1.56623 | 0.783117 | − | 0.621875i | \(-0.213629\pi\) | ||||
0.783117 | + | 0.621875i | \(0.213629\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.27693 | −0.0442962 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −120.982 | −4.19177 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.6960 | −1.13149 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.72230 | −0.336052 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.1486 | −0.384893 | −0.192446 | − | 0.981307i | \(-0.561642\pi\) | ||||
−0.192446 | + | 0.981307i | \(0.561642\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.58038 | 0.295524 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.33701 | 0.0803954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.3763 | 0.528335 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.23788 | −0.214084 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.45986 | −0.255721 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.2489 | −0.453632 | −0.226816 | − | 0.973938i | \(-0.572832\pi\) | ||||
−0.226816 | + | 0.973938i | \(0.572832\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.3877 | −0.628847 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.7504 | −1.93856 | −0.969278 | − | 0.245966i | \(-0.920895\pi\) | ||||
−0.969278 | + | 0.245966i | \(0.920895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.4878 | 0.494318 | 0.247159 | − | 0.968975i | \(-0.420503\pi\) | ||||
0.247159 | + | 0.968975i | \(0.420503\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.5033 | 0.630592 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.5463 | 0.971729 | 0.485864 | − | 0.874034i | \(-0.338505\pi\) | ||||
0.485864 | + | 0.874034i | \(0.338505\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.96309 | 0.202751 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 49.0943 | 1.66733 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.5786 | −1.81753 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50.8275 | −1.72222 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.6078 | −0.494398 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.2372 | −1.02220 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.39579 | 0.283506 | 0.141753 | − | 0.989902i | \(-0.454726\pi\) | ||||
0.141753 | + | 0.989902i | \(0.454726\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.5887 | 0.357147 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.79317 | 0.228868 | 0.114434 | − | 0.993431i | \(-0.463495\pi\) | ||||
0.114434 | + | 0.993431i | \(0.463495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.86314 | −0.0626997 | −0.0313498 | − | 0.999508i | \(-0.509981\pi\) | ||||
−0.0313498 | + | 0.999508i | \(0.509981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.34619 | −0.112481 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.9765 | 0.570015 | 0.285007 | − | 0.958525i | \(-0.408004\pi\) | ||||
0.285007 | + | 0.958525i | \(0.408004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.2988 | 0.647262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.77983 | −0.126629 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.8437 | −0.630581 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −48.5524 | −1.62293 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.51025 | 0.117204 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.72230 | −0.324257 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −76.3375 | −2.54317 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.5720 | −0.385094 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.6698 | −1.01950 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.12320 | −0.136909 | −0.0684544 | − | 0.997654i | \(-0.521807\pi\) | ||||
−0.0684544 | + | 0.997654i | \(0.521807\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.45378 | 0.0482189 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7395 | −0.653998 | −0.326999 | − | 0.945025i | \(-0.606037\pi\) | ||||
−0.326999 | + | 0.945025i | \(0.606037\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.6862 | −1.34652 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 44.4442 | 1.46928 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.0054 | 1.71737 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.8701 | 0.523505 | 0.261752 | − | 0.965135i | \(-0.415700\pi\) | ||||
0.261752 | + | 0.965135i | \(0.415700\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.7072 | 0.418716 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.4773 | −1.06900 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 51.2922 | 1.68648 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.66441 | 0.251732 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.1494 | 0.661080 | 0.330540 | − | 0.943792i | \(-0.392769\pi\) | ||||
0.330540 | + | 0.943792i | \(0.392769\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 79.4028 | 2.60232 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.170695 | −0.00558830 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −105.897 | −3.46321 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.2269 | 1.15081 | 0.575406 | − | 0.817868i | \(-0.304844\pi\) | ||||
0.575406 | + | 0.817868i | \(0.304844\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.414275 | −0.0135194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.20126 | −0.0717591 | −0.0358795 | − | 0.999356i | \(-0.511423\pi\) | ||||
−0.0358795 | + | 0.999356i | \(0.511423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.95562 | −0.128813 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.1200 | −0.524385 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.304367 | −0.00989059 | −0.00494530 | − | 0.999988i | \(-0.501574\pi\) | ||||
−0.00494530 | + | 0.999988i | \(0.501574\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.5118 | −1.15276 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.3331 | −0.562065 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.99275 | 0.258911 | 0.129455 | − | 0.991585i | \(-0.458677\pi\) | ||||
0.129455 | + | 0.991585i | \(0.458677\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 77.2442 | 2.49957 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.77983 | −0.122185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −86.6743 | −2.79886 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63.5231 | 2.04913 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.2562 | 0.652748 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −77.3467 | −2.48988 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.7469 | −0.538544 | −0.269272 | − | 0.963064i | \(-0.586783\pi\) | ||||
−0.269272 | + | 0.963064i | \(0.586783\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43.3790 | −1.39353 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.9854 | 0.416721 | 0.208361 | − | 0.978052i | \(-0.433187\pi\) | ||||
0.208361 | + | 0.978052i | \(0.433187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9614 | 0.671992 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −24.1356 | −0.772958 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.88074 | 0.316113 | 0.158056 | − | 0.987430i | \(-0.449477\pi\) | ||||
0.158056 | + | 0.987430i | \(0.449477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.2219 | 1.86078 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.12731 | −0.195630 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0024 | 0.510399 | 0.255199 | − | 0.966888i | \(-0.417859\pi\) | ||||
0.255199 | + | 0.966888i | \(0.417859\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.88541 | −0.314975 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.5198 | −0.525831 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.47386 | 0.0786640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.97246 | 0.253253 | 0.126627 | − | 0.991950i | \(-0.459585\pi\) | ||||
0.126627 | + | 0.991950i | \(0.459585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.522129 | −0.0165693 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.9549 | −1.29836 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.2848 | 0.389062 | 0.194531 | − | 0.980896i | \(-0.437681\pi\) | ||||
0.194531 | + | 0.980896i | \(0.437681\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.45986 | 0.236020 |
(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 | 8004.2.a.k.1.2 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.k.1.2 | ✓ | 18 | 1.1 | even | 1 | trivial |