Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8450,2,Mod(1,8450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8450.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: | \(67.4735897080\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 650) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.30278 | 0.752158 | 0.376079 | − | 0.926588i | \(-0.377272\pi\) | ||||
0.376079 | + | 0.926588i | \(0.377272\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.30278 | 0.531856 | ||||||||
\(7\) | 4.30278 | 1.62630 | 0.813148 | − | 0.582057i | \(-0.197752\pi\) | ||||
0.813148 | + | 0.582057i | \(0.197752\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.30278 | −0.434259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.30278 | −1.29734 | −0.648668 | − | 0.761072i | \(-0.724674\pi\) | ||||
−0.648668 | + | 0.761072i | \(0.724674\pi\) | |||||||
\(12\) | 1.30278 | 0.376079 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.30278 | 1.14997 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.90833 | −1.91805 | −0.959026 | − | 0.283320i | \(-0.908564\pi\) | ||||
−0.959026 | + | 0.283320i | \(0.908564\pi\) | |||||||
\(18\) | −1.30278 | −0.307067 | ||||||||
\(19\) | −7.60555 | −1.74483 | −0.872417 | − | 0.488763i | \(-0.837448\pi\) | ||||
−0.872417 | + | 0.488763i | \(0.837448\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.60555 | 1.22323 | ||||||||
\(22\) | −4.30278 | −0.917355 | ||||||||
\(23\) | 1.60555 | 0.334781 | 0.167390 | − | 0.985891i | \(-0.446466\pi\) | ||||
0.167390 | + | 0.985891i | \(0.446466\pi\) | |||||||
\(24\) | 1.30278 | 0.265928 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.60555 | −1.07879 | ||||||||
\(28\) | 4.30278 | 0.813148 | ||||||||
\(29\) | −0.302776 | −0.0562240 | −0.0281120 | − | 0.999605i | \(-0.508950\pi\) | ||||
−0.0281120 | + | 0.999605i | \(0.508950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.39445 | −0.250450 | −0.125225 | − | 0.992128i | \(-0.539965\pi\) | ||||
−0.125225 | + | 0.992128i | \(0.539965\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.60555 | −0.975801 | ||||||||
\(34\) | −7.90833 | −1.35627 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.30278 | −0.217129 | ||||||||
\(37\) | −7.30278 | −1.20057 | −0.600284 | − | 0.799787i | \(-0.704946\pi\) | ||||
−0.600284 | + | 0.799787i | \(0.704946\pi\) | |||||||
\(38\) | −7.60555 | −1.23378 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | 0.0780869 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780869 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(42\) | 5.60555 | 0.864955 | ||||||||
\(43\) | −9.51388 | −1.45085 | −0.725426 | − | 0.688300i | \(-0.758357\pi\) | ||||
−0.725426 | + | 0.688300i | \(0.758357\pi\) | |||||||
\(44\) | −4.30278 | −0.648668 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.60555 | 0.236726 | ||||||||
\(47\) | 6.69722 | 0.976891 | 0.488445 | − | 0.872595i | \(-0.337564\pi\) | ||||
0.488445 | + | 0.872595i | \(0.337564\pi\) | |||||||
\(48\) | 1.30278 | 0.188039 | ||||||||
\(49\) | 11.5139 | 1.64484 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.3028 | −1.44268 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.21110 | 0.303718 | 0.151859 | − | 0.988402i | \(-0.451474\pi\) | ||||
0.151859 | + | 0.988402i | \(0.451474\pi\) | |||||||
\(54\) | −5.60555 | −0.762819 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.30278 | 0.574983 | ||||||||
\(57\) | −9.90833 | −1.31239 | ||||||||
\(58\) | −0.302776 | −0.0397564 | ||||||||
\(59\) | 4.21110 | 0.548239 | 0.274119 | − | 0.961696i | \(-0.411614\pi\) | ||||
0.274119 | + | 0.961696i | \(0.411614\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2111 | −1.30740 | −0.653699 | − | 0.756755i | \(-0.726784\pi\) | ||||
−0.653699 | + | 0.756755i | \(0.726784\pi\) | |||||||
\(62\) | −1.39445 | −0.177095 | ||||||||
\(63\) | −5.60555 | −0.706233 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.60555 | −0.689996 | ||||||||
\(67\) | −1.60555 | −0.196149 | −0.0980747 | − | 0.995179i | \(-0.531268\pi\) | ||||
−0.0980747 | + | 0.995179i | \(0.531268\pi\) | |||||||
\(68\) | −7.90833 | −0.959026 | ||||||||
\(69\) | 2.09167 | 0.251808 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.39445 | −0.402847 | −0.201423 | − | 0.979504i | \(-0.564557\pi\) | ||||
−0.201423 | + | 0.979504i | \(0.564557\pi\) | |||||||
\(72\) | −1.30278 | −0.153534 | ||||||||
\(73\) | −8.00000 | −0.936329 | −0.468165 | − | 0.883641i | \(-0.655085\pi\) | ||||
−0.468165 | + | 0.883641i | \(0.655085\pi\) | |||||||
\(74\) | −7.30278 | −0.848930 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.60555 | −0.872417 | ||||||||
\(77\) | −18.5139 | −2.10985 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.69722 | 0.640988 | 0.320494 | − | 0.947251i | \(-0.396151\pi\) | ||||
0.320494 | + | 0.947251i | \(0.396151\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | −4.81665 | −0.528696 | −0.264348 | − | 0.964427i | \(-0.585157\pi\) | ||||
−0.264348 | + | 0.964427i | \(0.585157\pi\) | |||||||
\(84\) | 5.60555 | 0.611616 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.51388 | −1.02591 | ||||||||
\(87\) | −0.394449 | −0.0422893 | ||||||||
\(88\) | −4.30278 | −0.458677 | ||||||||
\(89\) | 10.9083 | 1.15628 | 0.578140 | − | 0.815937i | \(-0.303779\pi\) | ||||
0.578140 | + | 0.815937i | \(0.303779\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.60555 | 0.167390 | ||||||||
\(93\) | −1.81665 | −0.188378 | ||||||||
\(94\) | 6.69722 | 0.690766 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.30278 | 0.132964 | ||||||||
\(97\) | −15.3028 | −1.55376 | −0.776881 | − | 0.629648i | \(-0.783199\pi\) | ||||
−0.776881 | + | 0.629648i | \(0.783199\pi\) | |||||||
\(98\) | 11.5139 | 1.16308 | ||||||||
\(99\) | 5.60555 | 0.563379 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.21110 | 0.817035 | 0.408518 | − | 0.912750i | \(-0.366046\pi\) | ||||
0.408518 | + | 0.912750i | \(0.366046\pi\) | |||||||
\(102\) | −10.3028 | −1.02013 | ||||||||
\(103\) | 13.6056 | 1.34059 | 0.670297 | − | 0.742093i | \(-0.266167\pi\) | ||||
0.670297 | + | 0.742093i | \(0.266167\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.21110 | 0.214761 | ||||||||
\(107\) | −7.81665 | −0.755664 | −0.377832 | − | 0.925874i | \(-0.623330\pi\) | ||||
−0.377832 | + | 0.925874i | \(0.623330\pi\) | |||||||
\(108\) | −5.60555 | −0.539394 | ||||||||
\(109\) | 4.39445 | 0.420912 | 0.210456 | − | 0.977603i | \(-0.432505\pi\) | ||||
0.210456 | + | 0.977603i | \(0.432505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.51388 | −0.903017 | ||||||||
\(112\) | 4.30278 | 0.406574 | ||||||||
\(113\) | 7.51388 | 0.706846 | 0.353423 | − | 0.935464i | \(-0.385018\pi\) | ||||
0.353423 | + | 0.935464i | \(0.385018\pi\) | |||||||
\(114\) | −9.90833 | −0.928000 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.302776 | −0.0281120 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.21110 | 0.387663 | ||||||||
\(119\) | −34.0278 | −3.11932 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.51388 | 0.683080 | ||||||||
\(122\) | −10.2111 | −0.924470 | ||||||||
\(123\) | 1.30278 | 0.117467 | ||||||||
\(124\) | −1.39445 | −0.125225 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.60555 | −0.499382 | ||||||||
\(127\) | −5.90833 | −0.524279 | −0.262140 | − | 0.965030i | \(-0.584428\pi\) | ||||
−0.262140 | + | 0.965030i | \(0.584428\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.3944 | −1.09127 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8167 | −1.11980 | −0.559898 | − | 0.828561i | \(-0.689160\pi\) | ||||
−0.559898 | + | 0.828561i | \(0.689160\pi\) | |||||||
\(132\) | −5.60555 | −0.487901 | ||||||||
\(133\) | −32.7250 | −2.83762 | ||||||||
\(134\) | −1.60555 | −0.138699 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.90833 | −0.678133 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 2.09167 | 0.178055 | ||||||||
\(139\) | 11.8167 | 1.00228 | 0.501138 | − | 0.865368i | \(-0.332915\pi\) | ||||
0.501138 | + | 0.865368i | \(0.332915\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.72498 | 0.734776 | ||||||||
\(142\) | −3.39445 | −0.284856 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.30278 | −0.108565 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.00000 | −0.662085 | ||||||||
\(147\) | 15.0000 | 1.23718 | ||||||||
\(148\) | −7.30278 | −0.600284 | ||||||||
\(149\) | −4.69722 | −0.384812 | −0.192406 | − | 0.981315i | \(-0.561629\pi\) | ||||
−0.192406 | + | 0.981315i | \(0.561629\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1194 | 1.06764 | 0.533822 | − | 0.845597i | \(-0.320755\pi\) | ||||
0.533822 | + | 0.845597i | \(0.320755\pi\) | |||||||
\(152\) | −7.60555 | −0.616892 | ||||||||
\(153\) | 10.3028 | 0.832930 | ||||||||
\(154\) | −18.5139 | −1.49189 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.42221 | 0.352930 | 0.176465 | − | 0.984307i | \(-0.443534\pi\) | ||||
0.176465 | + | 0.984307i | \(0.443534\pi\) | |||||||
\(158\) | 5.69722 | 0.453247 | ||||||||
\(159\) | 2.88057 | 0.228444 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.90833 | 0.544452 | ||||||||
\(162\) | −3.39445 | −0.266693 | ||||||||
\(163\) | 8.90833 | 0.697754 | 0.348877 | − | 0.937169i | \(-0.386563\pi\) | ||||
0.348877 | + | 0.937169i | \(0.386563\pi\) | |||||||
\(164\) | 1.00000 | 0.0780869 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.81665 | −0.373845 | ||||||||
\(167\) | 3.60555 | 0.279006 | 0.139503 | − | 0.990222i | \(-0.455450\pi\) | ||||
0.139503 | + | 0.990222i | \(0.455450\pi\) | |||||||
\(168\) | 5.60555 | 0.432478 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.90833 | 0.757709 | ||||||||
\(172\) | −9.51388 | −0.725426 | ||||||||
\(173\) | 24.5139 | 1.86376 | 0.931878 | − | 0.362772i | \(-0.118170\pi\) | ||||
0.931878 | + | 0.362772i | \(0.118170\pi\) | |||||||
\(174\) | −0.394449 | −0.0299031 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.30278 | −0.324334 | ||||||||
\(177\) | 5.48612 | 0.412362 | ||||||||
\(178\) | 10.9083 | 0.817614 | ||||||||
\(179\) | −7.21110 | −0.538983 | −0.269492 | − | 0.963003i | \(-0.586856\pi\) | ||||
−0.269492 | + | 0.963003i | \(0.586856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.09167 | −0.527120 | −0.263560 | − | 0.964643i | \(-0.584897\pi\) | ||||
−0.263560 | + | 0.964643i | \(0.584897\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3028 | −0.983369 | ||||||||
\(184\) | 1.60555 | 0.118363 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.81665 | −0.133204 | ||||||||
\(187\) | 34.0278 | 2.48836 | ||||||||
\(188\) | 6.69722 | 0.488445 | ||||||||
\(189\) | −24.1194 | −1.75443 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8167 | 0.782666 | 0.391333 | − | 0.920249i | \(-0.372014\pi\) | ||||
0.391333 | + | 0.920249i | \(0.372014\pi\) | |||||||
\(192\) | 1.30278 | 0.0940197 | ||||||||
\(193\) | −0.513878 | −0.0369898 | −0.0184949 | − | 0.999829i | \(-0.505887\pi\) | ||||
−0.0184949 | + | 0.999829i | \(0.505887\pi\) | |||||||
\(194\) | −15.3028 | −1.09868 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.5139 | 0.822420 | ||||||||
\(197\) | −18.6972 | −1.33212 | −0.666061 | − | 0.745897i | \(-0.732021\pi\) | ||||
−0.666061 | + | 0.745897i | \(0.732021\pi\) | |||||||
\(198\) | 5.60555 | 0.398369 | ||||||||
\(199\) | −6.90833 | −0.489718 | −0.244859 | − | 0.969559i | \(-0.578742\pi\) | ||||
−0.244859 | + | 0.969559i | \(0.578742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.09167 | −0.147535 | ||||||||
\(202\) | 8.21110 | 0.577731 | ||||||||
\(203\) | −1.30278 | −0.0914369 | ||||||||
\(204\) | −10.3028 | −0.721339 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 13.6056 | 0.947944 | ||||||||
\(207\) | −2.09167 | −0.145381 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.7250 | 2.26363 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8167 | 1.02002 | 0.510010 | − | 0.860168i | \(-0.329642\pi\) | ||||
0.510010 | + | 0.860168i | \(0.329642\pi\) | |||||||
\(212\) | 2.21110 | 0.151859 | ||||||||
\(213\) | −4.42221 | −0.303005 | ||||||||
\(214\) | −7.81665 | −0.534335 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.60555 | −0.381409 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 4.39445 | 0.297630 | ||||||||
\(219\) | −10.4222 | −0.704267 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.51388 | −0.638530 | ||||||||
\(223\) | 5.18335 | 0.347103 | 0.173551 | − | 0.984825i | \(-0.444476\pi\) | ||||
0.173551 | + | 0.984825i | \(0.444476\pi\) | |||||||
\(224\) | 4.30278 | 0.287491 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.51388 | 0.499816 | ||||||||
\(227\) | −19.0000 | −1.26107 | −0.630537 | − | 0.776159i | \(-0.717165\pi\) | ||||
−0.630537 | + | 0.776159i | \(0.717165\pi\) | |||||||
\(228\) | −9.90833 | −0.656195 | ||||||||
\(229\) | −10.5139 | −0.694777 | −0.347388 | − | 0.937721i | \(-0.612931\pi\) | ||||
−0.347388 | + | 0.937721i | \(0.612931\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.1194 | −1.58694 | ||||||||
\(232\) | −0.302776 | −0.0198782 | ||||||||
\(233\) | 21.0000 | 1.37576 | 0.687878 | − | 0.725826i | \(-0.258542\pi\) | ||||
0.687878 | + | 0.725826i | \(0.258542\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.21110 | 0.274119 | ||||||||
\(237\) | 7.42221 | 0.482124 | ||||||||
\(238\) | −34.0278 | −2.20569 | ||||||||
\(239\) | −29.4222 | −1.90316 | −0.951582 | − | 0.307395i | \(-0.900543\pi\) | ||||
−0.951582 | + | 0.307395i | \(0.900543\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | 0.322078 | 0.161039 | − | 0.986948i | \(-0.448515\pi\) | ||||
0.161039 | + | 0.986948i | \(0.448515\pi\) | |||||||
\(242\) | 7.51388 | 0.483010 | ||||||||
\(243\) | 12.3944 | 0.795104 | ||||||||
\(244\) | −10.2111 | −0.653699 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.30278 | 0.0830619 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.39445 | −0.0885476 | ||||||||
\(249\) | −6.27502 | −0.397663 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.3305 | 1.40949 | 0.704745 | − | 0.709460i | \(-0.251061\pi\) | ||||
0.704745 | + | 0.709460i | \(0.251061\pi\) | |||||||
\(252\) | −5.60555 | −0.353117 | ||||||||
\(253\) | −6.90833 | −0.434323 | ||||||||
\(254\) | −5.90833 | −0.370721 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.60555 | 0.100152 | 0.0500758 | − | 0.998745i | \(-0.484054\pi\) | ||||
0.0500758 | + | 0.998745i | \(0.484054\pi\) | |||||||
\(258\) | −12.3944 | −0.771645 | ||||||||
\(259\) | −31.4222 | −1.95248 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.394449 | 0.0244158 | ||||||||
\(262\) | −12.8167 | −0.791816 | ||||||||
\(263\) | 13.7250 | 0.846319 | 0.423159 | − | 0.906055i | \(-0.360921\pi\) | ||||
0.423159 | + | 0.906055i | \(0.360921\pi\) | |||||||
\(264\) | −5.60555 | −0.344998 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −32.7250 | −2.00650 | ||||||||
\(267\) | 14.2111 | 0.869705 | ||||||||
\(268\) | −1.60555 | −0.0980747 | ||||||||
\(269\) | −7.18335 | −0.437976 | −0.218988 | − | 0.975728i | \(-0.570276\pi\) | ||||
−0.218988 | + | 0.975728i | \(0.570276\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.4222 | −1.60503 | −0.802517 | − | 0.596629i | \(-0.796506\pi\) | ||||
−0.802517 | + | 0.596629i | \(0.796506\pi\) | |||||||
\(272\) | −7.90833 | −0.479513 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.09167 | 0.125904 | ||||||||
\(277\) | 6.88057 | 0.413413 | 0.206707 | − | 0.978403i | \(-0.433725\pi\) | ||||
0.206707 | + | 0.978403i | \(0.433725\pi\) | |||||||
\(278\) | 11.8167 | 0.708716 | ||||||||
\(279\) | 1.81665 | 0.108760 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.69722 | 0.578488 | 0.289244 | − | 0.957255i | \(-0.406596\pi\) | ||||
0.289244 | + | 0.957255i | \(0.406596\pi\) | |||||||
\(282\) | 8.72498 | 0.519565 | ||||||||
\(283\) | −4.48612 | −0.266672 | −0.133336 | − | 0.991071i | \(-0.542569\pi\) | ||||
−0.133336 | + | 0.991071i | \(0.542569\pi\) | |||||||
\(284\) | −3.39445 | −0.201423 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.30278 | 0.253985 | ||||||||
\(288\) | −1.30278 | −0.0767668 | ||||||||
\(289\) | 45.5416 | 2.67892 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.9361 | −1.16867 | ||||||||
\(292\) | −8.00000 | −0.468165 | ||||||||
\(293\) | 15.5139 | 0.906330 | 0.453165 | − | 0.891427i | \(-0.350295\pi\) | ||||
0.453165 | + | 0.891427i | \(0.350295\pi\) | |||||||
\(294\) | 15.0000 | 0.874818 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.30278 | −0.424465 | ||||||||
\(297\) | 24.1194 | 1.39955 | ||||||||
\(298\) | −4.69722 | −0.272103 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.9361 | −2.35952 | ||||||||
\(302\) | 13.1194 | 0.754938 | ||||||||
\(303\) | 10.6972 | 0.614539 | ||||||||
\(304\) | −7.60555 | −0.436208 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.3028 | 0.588970 | ||||||||
\(307\) | 3.21110 | 0.183267 | 0.0916337 | − | 0.995793i | \(-0.470791\pi\) | ||||
0.0916337 | + | 0.995793i | \(0.470791\pi\) | |||||||
\(308\) | −18.5139 | −1.05493 | ||||||||
\(309\) | 17.7250 | 1.00834 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.908327 | 0.0515065 | 0.0257532 | − | 0.999668i | \(-0.491802\pi\) | ||||
0.0257532 | + | 0.999668i | \(0.491802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.09167 | 0.287798 | 0.143899 | − | 0.989592i | \(-0.454036\pi\) | ||||
0.143899 | + | 0.989592i | \(0.454036\pi\) | |||||||
\(314\) | 4.42221 | 0.249559 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.69722 | 0.320494 | ||||||||
\(317\) | −29.5139 | −1.65766 | −0.828832 | − | 0.559497i | \(-0.810994\pi\) | ||||
−0.828832 | + | 0.559497i | \(0.810994\pi\) | |||||||
\(318\) | 2.88057 | 0.161534 | ||||||||
\(319\) | 1.30278 | 0.0729414 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.1833 | −0.568379 | ||||||||
\(322\) | 6.90833 | 0.384986 | ||||||||
\(323\) | 60.1472 | 3.34668 | ||||||||
\(324\) | −3.39445 | −0.188580 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.90833 | 0.493387 | ||||||||
\(327\) | 5.72498 | 0.316592 | ||||||||
\(328\) | 1.00000 | 0.0552158 | ||||||||
\(329\) | 28.8167 | 1.58871 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0917 | −0.554689 | −0.277344 | − | 0.960771i | \(-0.589454\pi\) | ||||
−0.277344 | + | 0.960771i | \(0.589454\pi\) | |||||||
\(332\) | −4.81665 | −0.264348 | ||||||||
\(333\) | 9.51388 | 0.521357 | ||||||||
\(334\) | 3.60555 | 0.197287 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.60555 | 0.305808 | ||||||||
\(337\) | 22.0278 | 1.19993 | 0.599964 | − | 0.800027i | \(-0.295181\pi\) | ||||
0.599964 | + | 0.800027i | \(0.295181\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.78890 | 0.531660 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 9.90833 | 0.535781 | ||||||||
\(343\) | 19.4222 | 1.04870 | ||||||||
\(344\) | −9.51388 | −0.512954 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.5139 | 1.31787 | ||||||||
\(347\) | −12.2111 | −0.655526 | −0.327763 | − | 0.944760i | \(-0.606295\pi\) | ||||
−0.327763 | + | 0.944760i | \(0.606295\pi\) | |||||||
\(348\) | −0.394449 | −0.0211447 | ||||||||
\(349\) | −1.27502 | −0.0682502 | −0.0341251 | − | 0.999418i | \(-0.510864\pi\) | ||||
−0.0341251 | + | 0.999418i | \(0.510864\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.30278 | −0.229339 | ||||||||
\(353\) | −2.48612 | −0.132323 | −0.0661615 | − | 0.997809i | \(-0.521075\pi\) | ||||
−0.0661615 | + | 0.997809i | \(0.521075\pi\) | |||||||
\(354\) | 5.48612 | 0.291584 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.9083 | 0.578140 | ||||||||
\(357\) | −44.3305 | −2.34622 | ||||||||
\(358\) | −7.21110 | −0.381119 | ||||||||
\(359\) | 23.9361 | 1.26330 | 0.631649 | − | 0.775254i | \(-0.282378\pi\) | ||||
0.631649 | + | 0.775254i | \(0.282378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.8444 | 2.04444 | ||||||||
\(362\) | −7.09167 | −0.372730 | ||||||||
\(363\) | 9.78890 | 0.513784 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.3028 | −0.695347 | ||||||||
\(367\) | 4.18335 | 0.218369 | 0.109184 | − | 0.994022i | \(-0.465176\pi\) | ||||
0.109184 | + | 0.994022i | \(0.465176\pi\) | |||||||
\(368\) | 1.60555 | 0.0836951 | ||||||||
\(369\) | −1.30278 | −0.0678198 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.51388 | 0.493936 | ||||||||
\(372\) | −1.81665 | −0.0941891 | ||||||||
\(373\) | 0.788897 | 0.0408476 | 0.0204238 | − | 0.999791i | \(-0.493498\pi\) | ||||
0.0204238 | + | 0.999791i | \(0.493498\pi\) | |||||||
\(374\) | 34.0278 | 1.75953 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.69722 | 0.345383 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −24.1194 | −1.24057 | ||||||||
\(379\) | −13.1833 | −0.677183 | −0.338592 | − | 0.940933i | \(-0.609950\pi\) | ||||
−0.338592 | + | 0.940933i | \(0.609950\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.69722 | −0.394341 | ||||||||
\(382\) | 10.8167 | 0.553428 | ||||||||
\(383\) | −4.39445 | −0.224546 | −0.112273 | − | 0.993677i | \(-0.535813\pi\) | ||||
−0.112273 | + | 0.993677i | \(0.535813\pi\) | |||||||
\(384\) | 1.30278 | 0.0664820 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.513878 | −0.0261557 | ||||||||
\(387\) | 12.3944 | 0.630045 | ||||||||
\(388\) | −15.3028 | −0.776881 | ||||||||
\(389\) | 5.21110 | 0.264213 | 0.132107 | − | 0.991236i | \(-0.457826\pi\) | ||||
0.132107 | + | 0.991236i | \(0.457826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.6972 | −0.642126 | ||||||||
\(392\) | 11.5139 | 0.581539 | ||||||||
\(393\) | −16.6972 | −0.842264 | ||||||||
\(394\) | −18.6972 | −0.941953 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.60555 | 0.281690 | ||||||||
\(397\) | −29.3305 | −1.47206 | −0.736029 | − | 0.676950i | \(-0.763301\pi\) | ||||
−0.736029 | + | 0.676950i | \(0.763301\pi\) | |||||||
\(398\) | −6.90833 | −0.346283 | ||||||||
\(399\) | −42.6333 | −2.13433 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.7250 | −0.885143 | −0.442572 | − | 0.896733i | \(-0.645934\pi\) | ||||
−0.442572 | + | 0.896733i | \(0.645934\pi\) | |||||||
\(402\) | −2.09167 | −0.104323 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 8.21110 | 0.408518 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.30278 | −0.0646557 | ||||||||
\(407\) | 31.4222 | 1.55754 | ||||||||
\(408\) | −10.3028 | −0.510063 | ||||||||
\(409\) | −19.7889 | −0.978498 | −0.489249 | − | 0.872144i | \(-0.662729\pi\) | ||||
−0.489249 | + | 0.872144i | \(0.662729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.6056 | 0.670297 | ||||||||
\(413\) | 18.1194 | 0.891599 | ||||||||
\(414\) | −2.09167 | −0.102800 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.3944 | 0.753869 | ||||||||
\(418\) | 32.7250 | 1.60063 | ||||||||
\(419\) | 13.6972 | 0.669153 | 0.334577 | − | 0.942369i | \(-0.391407\pi\) | ||||
0.334577 | + | 0.942369i | \(0.391407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0917 | −0.930471 | −0.465236 | − | 0.885187i | \(-0.654030\pi\) | ||||
−0.465236 | + | 0.885187i | \(0.654030\pi\) | |||||||
\(422\) | 14.8167 | 0.721263 | ||||||||
\(423\) | −8.72498 | −0.424223 | ||||||||
\(424\) | 2.21110 | 0.107381 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.42221 | −0.214257 | ||||||||
\(427\) | −43.9361 | −2.12622 | ||||||||
\(428\) | −7.81665 | −0.377832 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.90833 | −0.477267 | −0.238634 | − | 0.971110i | \(-0.576700\pi\) | ||||
−0.238634 | + | 0.971110i | \(0.576700\pi\) | |||||||
\(432\) | −5.60555 | −0.269697 | ||||||||
\(433\) | −15.1833 | −0.729665 | −0.364833 | − | 0.931073i | \(-0.618874\pi\) | ||||
−0.364833 | + | 0.931073i | \(0.618874\pi\) | |||||||
\(434\) | −6.00000 | −0.288009 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.39445 | 0.210456 | ||||||||
\(437\) | −12.2111 | −0.584136 | ||||||||
\(438\) | −10.4222 | −0.497992 | ||||||||
\(439\) | −25.0278 | −1.19451 | −0.597255 | − | 0.802052i | \(-0.703742\pi\) | ||||
−0.597255 | + | 0.802052i | \(0.703742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.1194 | −1.57355 | −0.786776 | − | 0.617239i | \(-0.788251\pi\) | ||||
−0.786776 | + | 0.617239i | \(0.788251\pi\) | |||||||
\(444\) | −9.51388 | −0.451509 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.18335 | 0.245439 | ||||||||
\(447\) | −6.11943 | −0.289439 | ||||||||
\(448\) | 4.30278 | 0.203287 | ||||||||
\(449\) | 26.0917 | 1.23134 | 0.615671 | − | 0.788003i | \(-0.288885\pi\) | ||||
0.615671 | + | 0.788003i | \(0.288885\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.30278 | −0.202610 | ||||||||
\(452\) | 7.51388 | 0.353423 | ||||||||
\(453\) | 17.0917 | 0.803037 | ||||||||
\(454\) | −19.0000 | −0.891714 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.90833 | −0.464000 | ||||||||
\(457\) | 7.51388 | 0.351484 | 0.175742 | − | 0.984436i | \(-0.443767\pi\) | ||||
0.175742 | + | 0.984436i | \(0.443767\pi\) | |||||||
\(458\) | −10.5139 | −0.491281 | ||||||||
\(459\) | 44.3305 | 2.06917 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.5139 | 1.23487 | 0.617437 | − | 0.786620i | \(-0.288171\pi\) | ||||
0.617437 | + | 0.786620i | \(0.288171\pi\) | |||||||
\(462\) | −24.1194 | −1.12214 | ||||||||
\(463\) | −28.5139 | −1.32515 | −0.662576 | − | 0.748995i | \(-0.730537\pi\) | ||||
−0.662576 | + | 0.748995i | \(0.730537\pi\) | |||||||
\(464\) | −0.302776 | −0.0140560 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.0000 | 0.972806 | ||||||||
\(467\) | −34.5139 | −1.59711 | −0.798556 | − | 0.601921i | \(-0.794402\pi\) | ||||
−0.798556 | + | 0.601921i | \(0.794402\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.90833 | −0.318997 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.76114 | 0.265459 | ||||||||
\(472\) | 4.21110 | 0.193832 | ||||||||
\(473\) | 40.9361 | 1.88224 | ||||||||
\(474\) | 7.42221 | 0.340913 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −34.0278 | −1.55966 | ||||||||
\(477\) | −2.88057 | −0.131892 | ||||||||
\(478\) | −29.4222 | −1.34574 | ||||||||
\(479\) | −0.724981 | −0.0331252 | −0.0165626 | − | 0.999863i | \(-0.505272\pi\) | ||||
−0.0165626 | + | 0.999863i | \(0.505272\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.00000 | 0.227744 | ||||||||
\(483\) | 9.00000 | 0.409514 | ||||||||
\(484\) | 7.51388 | 0.341540 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 12.3944 | 0.562224 | ||||||||
\(487\) | −3.30278 | −0.149663 | −0.0748315 | − | 0.997196i | \(-0.523842\pi\) | ||||
−0.0748315 | + | 0.997196i | \(0.523842\pi\) | |||||||
\(488\) | −10.2111 | −0.462235 | ||||||||
\(489\) | 11.6056 | 0.524821 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.57779 | −0.387110 | −0.193555 | − | 0.981089i | \(-0.562002\pi\) | ||||
−0.193555 | + | 0.981089i | \(0.562002\pi\) | |||||||
\(492\) | 1.30278 | 0.0587337 | ||||||||
\(493\) | 2.39445 | 0.107841 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.39445 | −0.0626126 | ||||||||
\(497\) | −14.6056 | −0.655149 | ||||||||
\(498\) | −6.27502 | −0.281190 | ||||||||
\(499\) | 14.6333 | 0.655077 | 0.327538 | − | 0.944838i | \(-0.393781\pi\) | ||||
0.327538 | + | 0.944838i | \(0.393781\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.69722 | 0.209857 | ||||||||
\(502\) | 22.3305 | 0.996660 | ||||||||
\(503\) | 17.3944 | 0.775580 | 0.387790 | − | 0.921748i | \(-0.373239\pi\) | ||||
0.387790 | + | 0.921748i | \(0.373239\pi\) | |||||||
\(504\) | −5.60555 | −0.249691 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.90833 | −0.307113 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.90833 | −0.262140 | ||||||||
\(509\) | −25.8167 | −1.14430 | −0.572152 | − | 0.820148i | \(-0.693891\pi\) | ||||
−0.572152 | + | 0.820148i | \(0.693891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.4222 | −1.52275 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 42.6333 | 1.88231 | ||||||||
\(514\) | 1.60555 | 0.0708178 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.3944 | −0.545635 | ||||||||
\(517\) | −28.8167 | −1.26735 | ||||||||
\(518\) | −31.4222 | −1.38061 | ||||||||
\(519\) | 31.9361 | 1.40184 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.8444 | 1.52656 | 0.763281 | − | 0.646067i | \(-0.223587\pi\) | ||||
0.763281 | + | 0.646067i | \(0.223587\pi\) | |||||||
\(522\) | 0.394449 | 0.0172646 | ||||||||
\(523\) | −8.78890 | −0.384312 | −0.192156 | − | 0.981364i | \(-0.561548\pi\) | ||||
−0.192156 | + | 0.981364i | \(0.561548\pi\) | |||||||
\(524\) | −12.8167 | −0.559898 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.7250 | 0.598438 | ||||||||
\(527\) | 11.0278 | 0.480377 | ||||||||
\(528\) | −5.60555 | −0.243950 | ||||||||
\(529\) | −20.4222 | −0.887922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.48612 | −0.238077 | ||||||||
\(532\) | −32.7250 | −1.41881 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.2111 | 0.614975 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.60555 | −0.0693493 | ||||||||
\(537\) | −9.39445 | −0.405400 | ||||||||
\(538\) | −7.18335 | −0.309696 | ||||||||
\(539\) | −49.5416 | −2.13391 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.81665 | −0.164091 | −0.0820454 | − | 0.996629i | \(-0.526145\pi\) | ||||
−0.0820454 | + | 0.996629i | \(0.526145\pi\) | |||||||
\(542\) | −26.4222 | −1.13493 | ||||||||
\(543\) | −9.23886 | −0.396477 | ||||||||
\(544\) | −7.90833 | −0.339067 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.3944 | 0.615462 | 0.307731 | − | 0.951473i | \(-0.400430\pi\) | ||||
0.307731 | + | 0.951473i | \(0.400430\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.3028 | 0.567749 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.30278 | 0.0981015 | ||||||||
\(552\) | 2.09167 | 0.0890275 | ||||||||
\(553\) | 24.5139 | 1.04244 | ||||||||
\(554\) | 6.88057 | 0.292327 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.8167 | 0.501138 | ||||||||
\(557\) | −11.8167 | −0.500688 | −0.250344 | − | 0.968157i | \(-0.580544\pi\) | ||||
−0.250344 | + | 0.968157i | \(0.580544\pi\) | |||||||
\(558\) | 1.81665 | 0.0769051 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.3305 | 1.87164 | ||||||||
\(562\) | 9.69722 | 0.409053 | ||||||||
\(563\) | 11.7250 | 0.494149 | 0.247075 | − | 0.968996i | \(-0.420531\pi\) | ||||
0.247075 | + | 0.968996i | \(0.420531\pi\) | |||||||
\(564\) | 8.72498 | 0.367388 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.48612 | −0.188566 | ||||||||
\(567\) | −14.6056 | −0.613375 | ||||||||
\(568\) | −3.39445 | −0.142428 | ||||||||
\(569\) | −33.1472 | −1.38960 | −0.694801 | − | 0.719202i | \(-0.744508\pi\) | ||||
−0.694801 | + | 0.719202i | \(0.744508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.51388 | −0.188900 | −0.0944500 | − | 0.995530i | \(-0.530109\pi\) | ||||
−0.0944500 | + | 0.995530i | \(0.530109\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0917 | 0.588688 | ||||||||
\(574\) | 4.30278 | 0.179594 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.30278 | −0.0542823 | ||||||||
\(577\) | −16.3944 | −0.682510 | −0.341255 | − | 0.939971i | \(-0.610852\pi\) | ||||
−0.341255 | + | 0.939971i | \(0.610852\pi\) | |||||||
\(578\) | 45.5416 | 1.89428 | ||||||||
\(579\) | −0.669468 | −0.0278221 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.7250 | −0.859817 | ||||||||
\(582\) | −19.9361 | −0.826377 | ||||||||
\(583\) | −9.51388 | −0.394025 | ||||||||
\(584\) | −8.00000 | −0.331042 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.5139 | 0.640872 | ||||||||
\(587\) | −32.5139 | −1.34199 | −0.670996 | − | 0.741461i | \(-0.734133\pi\) | ||||
−0.670996 | + | 0.741461i | \(0.734133\pi\) | |||||||
\(588\) | 15.0000 | 0.618590 | ||||||||
\(589\) | 10.6056 | 0.436994 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3583 | −1.00197 | ||||||||
\(592\) | −7.30278 | −0.300142 | ||||||||
\(593\) | 36.6611 | 1.50549 | 0.752745 | − | 0.658313i | \(-0.228729\pi\) | ||||
0.752745 | + | 0.658313i | \(0.228729\pi\) | |||||||
\(594\) | 24.1194 | 0.989632 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.69722 | −0.192406 | ||||||||
\(597\) | −9.00000 | −0.368345 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.6611 | −1.70222 | −0.851112 | − | 0.524983i | \(-0.824072\pi\) | ||||
−0.851112 | + | 0.524983i | \(0.824072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.6056 | −0.636564 | −0.318282 | − | 0.947996i | \(-0.603106\pi\) | ||||
−0.318282 | + | 0.947996i | \(0.603106\pi\) | |||||||
\(602\) | −40.9361 | −1.66843 | ||||||||
\(603\) | 2.09167 | 0.0851795 | ||||||||
\(604\) | 13.1194 | 0.533822 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.6972 | 0.434545 | ||||||||
\(607\) | −41.0555 | −1.66639 | −0.833196 | − | 0.552978i | \(-0.813491\pi\) | ||||
−0.833196 | + | 0.552978i | \(0.813491\pi\) | |||||||
\(608\) | −7.60555 | −0.308446 | ||||||||
\(609\) | −1.69722 | −0.0687750 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.3028 | 0.416465 | ||||||||
\(613\) | 43.4500 | 1.75493 | 0.877464 | − | 0.479643i | \(-0.159234\pi\) | ||||
0.877464 | + | 0.479643i | \(0.159234\pi\) | |||||||
\(614\) | 3.21110 | 0.129590 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.5139 | −0.745945 | ||||||||
\(617\) | 49.0555 | 1.97490 | 0.987450 | − | 0.157930i | \(-0.0504821\pi\) | ||||
0.987450 | + | 0.157930i | \(0.0504821\pi\) | |||||||
\(618\) | 17.7250 | 0.713003 | ||||||||
\(619\) | −32.3305 | −1.29947 | −0.649737 | − | 0.760159i | \(-0.725121\pi\) | ||||
−0.649737 | + | 0.760159i | \(0.725121\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.00000 | −0.361158 | ||||||||
\(622\) | 0.908327 | 0.0364206 | ||||||||
\(623\) | 46.9361 | 1.88045 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.09167 | 0.203504 | ||||||||
\(627\) | 42.6333 | 1.70261 | ||||||||
\(628\) | 4.42221 | 0.176465 | ||||||||
\(629\) | 57.7527 | 2.30275 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.9083 | −0.633300 | −0.316650 | − | 0.948542i | \(-0.602558\pi\) | ||||
−0.316650 | + | 0.948542i | \(0.602558\pi\) | |||||||
\(632\) | 5.69722 | 0.226623 | ||||||||
\(633\) | 19.3028 | 0.767216 | ||||||||
\(634\) | −29.5139 | −1.17215 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.88057 | 0.114222 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.30278 | 0.0515774 | ||||||||
\(639\) | 4.42221 | 0.174940 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −50.1749 | −1.98179 | −0.990896 | − | 0.134633i | \(-0.957014\pi\) | ||||
−0.990896 | + | 0.134633i | \(0.957014\pi\) | |||||||
\(642\) | −10.1833 | −0.401905 | ||||||||
\(643\) | −6.57779 | −0.259403 | −0.129701 | − | 0.991553i | \(-0.541402\pi\) | ||||
−0.129701 | + | 0.991553i | \(0.541402\pi\) | |||||||
\(644\) | 6.90833 | 0.272226 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 60.1472 | 2.36646 | ||||||||
\(647\) | 12.6972 | 0.499179 | 0.249590 | − | 0.968352i | \(-0.419704\pi\) | ||||
0.249590 | + | 0.968352i | \(0.419704\pi\) | |||||||
\(648\) | −3.39445 | −0.133347 | ||||||||
\(649\) | −18.1194 | −0.711250 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.81665 | −0.306359 | ||||||||
\(652\) | 8.90833 | 0.348877 | ||||||||
\(653\) | 6.21110 | 0.243059 | 0.121530 | − | 0.992588i | \(-0.461220\pi\) | ||||
0.121530 | + | 0.992588i | \(0.461220\pi\) | |||||||
\(654\) | 5.72498 | 0.223864 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.00000 | 0.0390434 | ||||||||
\(657\) | 10.4222 | 0.406609 | ||||||||
\(658\) | 28.8167 | 1.12339 | ||||||||
\(659\) | 5.21110 | 0.202996 | 0.101498 | − | 0.994836i | \(-0.467636\pi\) | ||||
0.101498 | + | 0.994836i | \(0.467636\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.6972 | −0.960611 | −0.480305 | − | 0.877101i | \(-0.659474\pi\) | ||||
−0.480305 | + | 0.877101i | \(0.659474\pi\) | |||||||
\(662\) | −10.0917 | −0.392224 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.81665 | −0.186922 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.51388 | 0.368655 | ||||||||
\(667\) | −0.486122 | −0.0188227 | ||||||||
\(668\) | 3.60555 | 0.139503 | ||||||||
\(669\) | 6.75274 | 0.261076 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.9361 | 1.69613 | ||||||||
\(672\) | 5.60555 | 0.216239 | ||||||||
\(673\) | −21.0278 | −0.810560 | −0.405280 | − | 0.914193i | \(-0.632826\pi\) | ||||
−0.405280 | + | 0.914193i | \(0.632826\pi\) | |||||||
\(674\) | 22.0278 | 0.848477 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.4222 | −0.823322 | −0.411661 | − | 0.911337i | \(-0.635051\pi\) | ||||
−0.411661 | + | 0.911337i | \(0.635051\pi\) | |||||||
\(678\) | 9.78890 | 0.375940 | ||||||||
\(679\) | −65.8444 | −2.52688 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.7527 | −0.948527 | ||||||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | −26.6333 | −1.01910 | −0.509548 | − | 0.860442i | \(-0.670187\pi\) | ||||
−0.509548 | + | 0.860442i | \(0.670187\pi\) | |||||||
\(684\) | 9.90833 | 0.378854 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.4222 | 0.741543 | ||||||||
\(687\) | −13.6972 | −0.522582 | ||||||||
\(688\) | −9.51388 | −0.362713 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.6056 | −1.16429 | −0.582145 | − | 0.813085i | \(-0.697786\pi\) | ||||
−0.582145 | + | 0.813085i | \(0.697786\pi\) | |||||||
\(692\) | 24.5139 | 0.931878 | ||||||||
\(693\) | 24.1194 | 0.916221 | ||||||||
\(694\) | −12.2111 | −0.463527 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.394449 | −0.0149515 | ||||||||
\(697\) | −7.90833 | −0.299549 | ||||||||
\(698\) | −1.27502 | −0.0482602 | ||||||||
\(699\) | 27.3583 | 1.03479 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.9083 | −0.525310 | −0.262655 | − | 0.964890i | \(-0.584598\pi\) | ||||
−0.262655 | + | 0.964890i | \(0.584598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.5416 | 2.09479 | ||||||||
\(704\) | −4.30278 | −0.162167 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.48612 | −0.0935664 | ||||||||
\(707\) | 35.3305 | 1.32874 | ||||||||
\(708\) | 5.48612 | 0.206181 | ||||||||
\(709\) | −47.5416 | −1.78546 | −0.892732 | − | 0.450588i | \(-0.851214\pi\) | ||||
−0.892732 | + | 0.450588i | \(0.851214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.42221 | −0.278354 | ||||||||
\(712\) | 10.9083 | 0.408807 | ||||||||
\(713\) | −2.23886 | −0.0838459 | ||||||||
\(714\) | −44.3305 | −1.65903 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.21110 | −0.269492 | ||||||||
\(717\) | −38.3305 | −1.43148 | ||||||||
\(718\) | 23.9361 | 0.893287 | ||||||||
\(719\) | 38.9361 | 1.45207 | 0.726035 | − | 0.687657i | \(-0.241361\pi\) | ||||
0.726035 | + | 0.687657i | \(0.241361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 58.5416 | 2.18020 | ||||||||
\(722\) | 38.8444 | 1.44564 | ||||||||
\(723\) | 6.51388 | 0.242254 | ||||||||
\(724\) | −7.09167 | −0.263560 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.78890 | 0.363300 | ||||||||
\(727\) | −30.0555 | −1.11470 | −0.557349 | − | 0.830279i | \(-0.688181\pi\) | ||||
−0.557349 | + | 0.830279i | \(0.688181\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.3305 | 0.975205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 75.2389 | 2.78281 | ||||||||
\(732\) | −13.3028 | −0.491685 | ||||||||
\(733\) | 12.5416 | 0.463236 | 0.231618 | − | 0.972807i | \(-0.425598\pi\) | ||||
0.231618 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(734\) | 4.18335 | 0.154410 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.60555 | 0.0591814 | ||||||||
\(737\) | 6.90833 | 0.254471 | ||||||||
\(738\) | −1.30278 | −0.0479558 | ||||||||
\(739\) | 17.7250 | 0.652024 | 0.326012 | − | 0.945366i | \(-0.394295\pi\) | ||||
0.326012 | + | 0.945366i | \(0.394295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.51388 | 0.349265 | ||||||||
\(743\) | −20.7889 | −0.762671 | −0.381335 | − | 0.924437i | \(-0.624536\pi\) | ||||
−0.381335 | + | 0.924437i | \(0.624536\pi\) | |||||||
\(744\) | −1.81665 | −0.0666018 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.788897 | 0.0288836 | ||||||||
\(747\) | 6.27502 | 0.229591 | ||||||||
\(748\) | 34.0278 | 1.24418 | ||||||||
\(749\) | −33.6333 | −1.22893 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.6333 | −0.388015 | −0.194007 | − | 0.981000i | \(-0.562149\pi\) | ||||
−0.194007 | + | 0.981000i | \(0.562149\pi\) | |||||||
\(752\) | 6.69722 | 0.244223 | ||||||||
\(753\) | 29.0917 | 1.06016 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −24.1194 | −0.877215 | ||||||||
\(757\) | 24.2111 | 0.879967 | 0.439984 | − | 0.898006i | \(-0.354984\pi\) | ||||
0.439984 | + | 0.898006i | \(0.354984\pi\) | |||||||
\(758\) | −13.1833 | −0.478841 | ||||||||
\(759\) | −9.00000 | −0.326679 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.3944 | −0.449298 | −0.224649 | − | 0.974440i | \(-0.572124\pi\) | ||||
−0.224649 | + | 0.974440i | \(0.572124\pi\) | |||||||
\(762\) | −7.69722 | −0.278841 | ||||||||
\(763\) | 18.9083 | 0.684527 | ||||||||
\(764\) | 10.8167 | 0.391333 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.39445 | −0.158778 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.30278 | 0.0470099 | ||||||||
\(769\) | −43.4500 | −1.56685 | −0.783423 | − | 0.621489i | \(-0.786528\pi\) | ||||
−0.783423 | + | 0.621489i | \(0.786528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.09167 | 0.0753298 | ||||||||
\(772\) | −0.513878 | −0.0184949 | ||||||||
\(773\) | −16.8444 | −0.605851 | −0.302926 | − | 0.953014i | \(-0.597963\pi\) | ||||
−0.302926 | + | 0.953014i | \(0.597963\pi\) | |||||||
\(774\) | 12.3944 | 0.445509 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −15.3028 | −0.549338 | ||||||||
\(777\) | −40.9361 | −1.46857 | ||||||||
\(778\) | 5.21110 | 0.186827 | ||||||||
\(779\) | −7.60555 | −0.272497 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6056 | 0.522628 | ||||||||
\(782\) | −12.6972 | −0.454052 | ||||||||
\(783\) | 1.69722 | 0.0606539 | ||||||||
\(784\) | 11.5139 | 0.411210 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.6972 | −0.595570 | ||||||||
\(787\) | −14.6972 | −0.523899 | −0.261950 | − | 0.965082i | \(-0.584365\pi\) | ||||
−0.261950 | + | 0.965082i | \(0.584365\pi\) | |||||||
\(788\) | −18.6972 | −0.666061 | ||||||||
\(789\) | 17.8806 | 0.636565 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.3305 | 1.14954 | ||||||||
\(792\) | 5.60555 | 0.199185 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −29.3305 | −1.04090 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.90833 | −0.244859 | ||||||||
\(797\) | −1.00000 | −0.0354218 | −0.0177109 | − | 0.999843i | \(-0.505638\pi\) | ||||
−0.0177109 | + | 0.999843i | \(0.505638\pi\) | |||||||
\(798\) | −42.6333 | −1.50920 | ||||||||
\(799\) | −52.9638 | −1.87373 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.2111 | −0.502125 | ||||||||
\(802\) | −17.7250 | −0.625891 | ||||||||
\(803\) | 34.4222 | 1.21473 | ||||||||
\(804\) | −2.09167 | −0.0737676 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.35829 | −0.329427 | ||||||||
\(808\) | 8.21110 | 0.288866 | ||||||||
\(809\) | 29.6333 | 1.04185 | 0.520926 | − | 0.853602i | \(-0.325587\pi\) | ||||
0.520926 | + | 0.853602i | \(0.325587\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.3028 | −0.888501 | −0.444250 | − | 0.895903i | \(-0.646530\pi\) | ||||
−0.444250 | + | 0.895903i | \(0.646530\pi\) | |||||||
\(812\) | −1.30278 | −0.0457185 | ||||||||
\(813\) | −34.4222 | −1.20724 | ||||||||
\(814\) | 31.4222 | 1.10135 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.3028 | −0.360669 | ||||||||
\(817\) | 72.3583 | 2.53150 | ||||||||
\(818\) | −19.7889 | −0.691903 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5778 | 0.369168 | 0.184584 | − | 0.982817i | \(-0.440906\pi\) | ||||
0.184584 | + | 0.982817i | \(0.440906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.8167 | 1.17877 | 0.589387 | − | 0.807851i | \(-0.299369\pi\) | ||||
0.589387 | + | 0.807851i | \(0.299369\pi\) | |||||||
\(824\) | 13.6056 | 0.473972 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.1194 | 0.630456 | ||||||||
\(827\) | 14.4500 | 0.502474 | 0.251237 | − | 0.967926i | \(-0.419163\pi\) | ||||
0.251237 | + | 0.967926i | \(0.419163\pi\) | |||||||
\(828\) | −2.09167 | −0.0726907 | ||||||||
\(829\) | 28.0917 | 0.975664 | 0.487832 | − | 0.872937i | \(-0.337788\pi\) | ||||
0.487832 | + | 0.872937i | \(0.337788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.96384 | 0.310952 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −91.0555 | −3.15489 | ||||||||
\(834\) | 15.3944 | 0.533066 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.7250 | 1.13182 | ||||||||
\(837\) | 7.81665 | 0.270183 | ||||||||
\(838\) | 13.6972 | 0.473163 | ||||||||
\(839\) | −33.9361 | −1.17160 | −0.585802 | − | 0.810454i | \(-0.699220\pi\) | ||||
−0.585802 | + | 0.810454i | \(0.699220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9083 | −0.996839 | ||||||||
\(842\) | −19.0917 | −0.657943 | ||||||||
\(843\) | 12.6333 | 0.435114 | ||||||||
\(844\) | 14.8167 | 0.510010 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.72498 | −0.299971 | ||||||||
\(847\) | 32.3305 | 1.11089 | ||||||||
\(848\) | 2.21110 | 0.0759296 | ||||||||
\(849\) | −5.84441 | −0.200580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.7250 | −0.401927 | ||||||||
\(852\) | −4.42221 | −0.151502 | ||||||||
\(853\) | −40.7250 | −1.39440 | −0.697198 | − | 0.716878i | \(-0.745570\pi\) | ||||
−0.697198 | + | 0.716878i | \(0.745570\pi\) | |||||||
\(854\) | −43.9361 | −1.50346 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.81665 | −0.267168 | ||||||||
\(857\) | 49.4222 | 1.68823 | 0.844115 | − | 0.536162i | \(-0.180126\pi\) | ||||
0.844115 | + | 0.536162i | \(0.180126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1194 | −0.345270 | −0.172635 | − | 0.984986i | \(-0.555228\pi\) | ||||
−0.172635 | + | 0.984986i | \(0.555228\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.60555 | 0.191037 | ||||||||
\(862\) | −9.90833 | −0.337479 | ||||||||
\(863\) | 32.0278 | 1.09024 | 0.545119 | − | 0.838359i | \(-0.316485\pi\) | ||||
0.545119 | + | 0.838359i | \(0.316485\pi\) | |||||||
\(864\) | −5.60555 | −0.190705 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.1833 | −0.515951 | ||||||||
\(867\) | 59.3305 | 2.01497 | ||||||||
\(868\) | −6.00000 | −0.203653 | ||||||||
\(869\) | −24.5139 | −0.831576 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.39445 | 0.148815 | ||||||||
\(873\) | 19.9361 | 0.674734 | ||||||||
\(874\) | −12.2111 | −0.413047 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.4222 | −0.352134 | ||||||||
\(877\) | 53.4777 | 1.80581 | 0.902907 | − | 0.429836i | \(-0.141429\pi\) | ||||
0.902907 | + | 0.429836i | \(0.141429\pi\) | |||||||
\(878\) | −25.0278 | −0.844646 | ||||||||
\(879\) | 20.2111 | 0.681704 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −57.5694 | −1.93956 | −0.969781 | − | 0.243977i | \(-0.921548\pi\) | ||||
−0.969781 | + | 0.243977i | \(0.921548\pi\) | |||||||
\(882\) | −15.0000 | −0.505076 | ||||||||
\(883\) | −23.1194 | −0.778031 | −0.389015 | − | 0.921231i | \(-0.627185\pi\) | ||||
−0.389015 | + | 0.921231i | \(0.627185\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.1194 | −1.11267 | ||||||||
\(887\) | 9.57779 | 0.321591 | 0.160795 | − | 0.986988i | \(-0.448594\pi\) | ||||
0.160795 | + | 0.986988i | \(0.448594\pi\) | |||||||
\(888\) | −9.51388 | −0.319265 | ||||||||
\(889\) | −25.4222 | −0.852633 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.6056 | 0.489304 | ||||||||
\(892\) | 5.18335 | 0.173551 | ||||||||
\(893\) | −50.9361 | −1.70451 | ||||||||
\(894\) | −6.11943 | −0.204664 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.30278 | 0.143746 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.0917 | 0.870690 | ||||||||
\(899\) | 0.422205 | 0.0140813 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.4861 | −0.582547 | ||||||||
\(902\) | −4.30278 | −0.143267 | ||||||||
\(903\) | −53.3305 | −1.77473 | ||||||||
\(904\) | 7.51388 | 0.249908 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17.0917 | 0.567833 | ||||||||
\(907\) | 33.6611 | 1.11770 | 0.558849 | − | 0.829270i | \(-0.311243\pi\) | ||||
0.558849 | + | 0.829270i | \(0.311243\pi\) | |||||||
\(908\) | −19.0000 | −0.630537 | ||||||||
\(909\) | −10.6972 | −0.354805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.4222 | 1.23985 | 0.619926 | − | 0.784660i | \(-0.287162\pi\) | ||||
0.619926 | + | 0.784660i | \(0.287162\pi\) | |||||||
\(912\) | −9.90833 | −0.328097 | ||||||||
\(913\) | 20.7250 | 0.685897 | ||||||||
\(914\) | 7.51388 | 0.248537 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.5139 | −0.347388 | ||||||||
\(917\) | −55.1472 | −1.82112 | ||||||||
\(918\) | 44.3305 | 1.46313 | ||||||||
\(919\) | −22.2389 | −0.733592 | −0.366796 | − | 0.930301i | \(-0.619545\pi\) | ||||
−0.366796 | + | 0.930301i | \(0.619545\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.18335 | 0.137846 | ||||||||
\(922\) | 26.5139 | 0.873188 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −24.1194 | −0.793471 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −28.5139 | −0.937024 | ||||||||
\(927\) | −17.7250 | −0.582165 | ||||||||
\(928\) | −0.302776 | −0.00993910 | ||||||||
\(929\) | 38.6611 | 1.26843 | 0.634214 | − | 0.773157i | \(-0.281324\pi\) | ||||
0.634214 | + | 0.773157i | \(0.281324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −87.5694 | −2.86997 | ||||||||
\(932\) | 21.0000 | 0.687878 | ||||||||
\(933\) | 1.18335 | 0.0387410 | ||||||||
\(934\) | −34.5139 | −1.12933 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.33053 | 0.0434666 | 0.0217333 | − | 0.999764i | \(-0.493082\pi\) | ||||
0.0217333 | + | 0.999764i | \(0.493082\pi\) | |||||||
\(938\) | −6.90833 | −0.225565 | ||||||||
\(939\) | 6.63331 | 0.216470 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.5694 | 1.55072 | 0.775359 | − | 0.631521i | \(-0.217569\pi\) | ||||
0.775359 | + | 0.631521i | \(0.217569\pi\) | |||||||
\(942\) | 5.76114 | 0.187708 | ||||||||
\(943\) | 1.60555 | 0.0522839 | ||||||||
\(944\) | 4.21110 | 0.137060 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.9361 | 1.33095 | ||||||||
\(947\) | 11.6695 | 0.379207 | 0.189603 | − | 0.981861i | \(-0.439280\pi\) | ||||
0.189603 | + | 0.981861i | \(0.439280\pi\) | |||||||
\(948\) | 7.42221 | 0.241062 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.4500 | −1.24683 | ||||||||
\(952\) | −34.0278 | −1.10285 | ||||||||
\(953\) | −43.4777 | −1.40838 | −0.704191 | − | 0.710011i | \(-0.748690\pi\) | ||||
−0.704191 | + | 0.710011i | \(0.748690\pi\) | |||||||
\(954\) | −2.88057 | −0.0932619 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29.4222 | −0.951582 | ||||||||
\(957\) | 1.69722 | 0.0548635 | ||||||||
\(958\) | −0.724981 | −0.0234231 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0555 | −0.937275 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.1833 | 0.328154 | ||||||||
\(964\) | 5.00000 | 0.161039 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.00000 | 0.289570 | ||||||||
\(967\) | 4.97224 | 0.159897 | 0.0799483 | − | 0.996799i | \(-0.474524\pi\) | ||||
0.0799483 | + | 0.996799i | \(0.474524\pi\) | |||||||
\(968\) | 7.51388 | 0.241505 | ||||||||
\(969\) | 78.3583 | 2.51723 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.4500 | 1.49065 | 0.745325 | − | 0.666701i | \(-0.232294\pi\) | ||||
0.745325 | + | 0.666701i | \(0.232294\pi\) | |||||||
\(972\) | 12.3944 | 0.397552 | ||||||||
\(973\) | 50.8444 | 1.63000 | ||||||||
\(974\) | −3.30278 | −0.105828 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.2111 | −0.326849 | ||||||||
\(977\) | −4.81665 | −0.154098 | −0.0770492 | − | 0.997027i | \(-0.524550\pi\) | ||||
−0.0770492 | + | 0.997027i | \(0.524550\pi\) | |||||||
\(978\) | 11.6056 | 0.371105 | ||||||||
\(979\) | −46.9361 | −1.50008 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.72498 | −0.182785 | ||||||||
\(982\) | −8.57779 | −0.273728 | ||||||||
\(983\) | −53.9638 | −1.72118 | −0.860590 | − | 0.509299i | \(-0.829905\pi\) | ||||
−0.860590 | + | 0.509299i | \(0.829905\pi\) | |||||||
\(984\) | 1.30278 | 0.0415310 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.39445 | 0.0762548 | ||||||||
\(987\) | 37.5416 | 1.19496 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.2750 | −0.485717 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.8444 | −1.74219 | −0.871095 | − | 0.491114i | \(-0.836590\pi\) | ||||
−0.871095 | + | 0.491114i | \(0.836590\pi\) | |||||||
\(992\) | −1.39445 | −0.0442738 | ||||||||
\(993\) | −13.1472 | −0.417213 | ||||||||
\(994\) | −14.6056 | −0.463260 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.27502 | −0.198832 | ||||||||
\(997\) | −11.9083 | −0.377140 | −0.188570 | − | 0.982060i | \(-0.560385\pi\) | ||||
−0.188570 | + | 0.982060i | \(0.560385\pi\) | |||||||
\(998\) | 14.6333 | 0.463209 | ||||||||
\(999\) | 40.9361 | 1.29516 |
(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 | 8450.2.a.bi.1.2 | 2 | ||
5.4 | even | 2 | 8450.2.a.bd.1.1 | 2 | |||
13.3 | even | 3 | 650.2.e.e.451.1 | ✓ | 4 | ||
13.9 | even | 3 | 650.2.e.e.601.1 | yes | 4 | ||
13.12 | even | 2 | 8450.2.a.ba.1.2 | 2 | |||
65.3 | odd | 12 | 650.2.o.h.399.3 | 8 | |||
65.9 | even | 6 | 650.2.e.g.601.2 | yes | 4 | ||
65.22 | odd | 12 | 650.2.o.h.549.3 | 8 | |||
65.29 | even | 6 | 650.2.e.g.451.2 | yes | 4 | ||
65.42 | odd | 12 | 650.2.o.h.399.2 | 8 | |||
65.48 | odd | 12 | 650.2.o.h.549.2 | 8 | |||
65.64 | even | 2 | 8450.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
650.2.e.e.451.1 | ✓ | 4 | 13.3 | even | 3 | ||
650.2.e.e.601.1 | yes | 4 | 13.9 | even | 3 | ||
650.2.e.g.451.2 | yes | 4 | 65.29 | even | 6 | ||
650.2.e.g.601.2 | yes | 4 | 65.9 | even | 6 | ||
650.2.o.h.399.2 | 8 | 65.42 | odd | 12 | |||
650.2.o.h.399.3 | 8 | 65.3 | odd | 12 | |||
650.2.o.h.549.2 | 8 | 65.48 | odd | 12 | |||
650.2.o.h.549.3 | 8 | 65.22 | odd | 12 | |||
8450.2.a.ba.1.2 | 2 | 13.12 | even | 2 | |||
8450.2.a.bd.1.1 | 2 | 5.4 | even | 2 | |||
8450.2.a.bi.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8450.2.a.bl.1.1 | 2 | 65.64 | even | 2 |