Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6020,2,Mod(1,6020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6020, 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("6020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6020 = 2^{2} \cdot 5 \cdot 7 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6020.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: | \(48.0699420168\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 27 x^{11} - 2 x^{10} + 268 x^{9} + 37 x^{8} - 1201 x^{7} - 189 x^{6} + 2384 x^{5} + 231 x^{4} - 1729 x^{3} + 20 x^{2} + 105 x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.30831\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6020.1 |
$q$-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 | ||||||||
\(3\) | −1.30831 | −0.755356 | −0.377678 | − | 0.925937i | \(-0.623277\pi\) | ||||
−0.377678 | + | 0.925937i | \(0.623277\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.28831 | −0.429438 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.23892 | 0.373548 | 0.186774 | − | 0.982403i | \(-0.440197\pi\) | ||||
0.186774 | + | 0.982403i | \(0.440197\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.90271 | 0.805067 | 0.402534 | − | 0.915405i | \(-0.368130\pi\) | ||||
0.402534 | + | 0.915405i | \(0.368130\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.30831 | −0.337805 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.12861 | −1.48641 | −0.743203 | − | 0.669065i | \(-0.766695\pi\) | ||||
−0.743203 | + | 0.669065i | \(0.766695\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.73312 | −1.31527 | −0.657634 | − | 0.753337i | \(-0.728443\pi\) | ||||
−0.657634 | + | 0.753337i | \(0.728443\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30831 | 0.285498 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.92684 | 0.401774 | 0.200887 | − | 0.979614i | \(-0.435618\pi\) | ||||
0.200887 | + | 0.979614i | \(0.435618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.61046 | 1.07973 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.54393 | 1.40087 | 0.700436 | − | 0.713715i | \(-0.252989\pi\) | ||||
0.700436 | + | 0.713715i | \(0.252989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.21855 | −1.65570 | −0.827850 | − | 0.560949i | \(-0.810436\pi\) | ||||
−0.827850 | + | 0.560949i | \(0.810436\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.62090 | −0.282162 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.93752 | −1.30492 | −0.652460 | − | 0.757823i | \(-0.726263\pi\) | ||||
−0.652460 | + | 0.757823i | \(0.726263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.79766 | −0.608112 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.47495 | 0.230349 | 0.115174 | − | 0.993345i | \(-0.463257\pi\) | ||||
0.115174 | + | 0.993345i | \(0.463257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.28831 | −0.192050 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.53769 | 0.807755 | 0.403878 | − | 0.914813i | \(-0.367662\pi\) | ||||
0.403878 | + | 0.914813i | \(0.367662\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.01815 | 1.12277 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4850 | 1.57758 | 0.788790 | − | 0.614662i | \(-0.210708\pi\) | ||||
0.788790 | + | 0.614662i | \(0.210708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.23892 | 0.167056 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.50073 | 0.993496 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.80965 | −0.626163 | −0.313081 | − | 0.949726i | \(-0.601361\pi\) | ||||
−0.313081 | + | 0.949726i | \(0.601361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.61188 | 0.206381 | 0.103190 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103190 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.28831 | 0.162312 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.90271 | 0.360037 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.62612 | −0.565171 | −0.282585 | − | 0.959242i | \(-0.591192\pi\) | ||||
−0.282585 | + | 0.959242i | \(0.591192\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.52091 | −0.303482 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5579 | 1.72771 | 0.863853 | − | 0.503745i | \(-0.168045\pi\) | ||||
0.863853 | + | 0.503745i | \(0.168045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.30509 | −0.386832 | −0.193416 | − | 0.981117i | \(-0.561957\pi\) | ||||
−0.193416 | + | 0.981117i | \(0.561957\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.30831 | −0.151071 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.23892 | −0.141188 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.77804 | 0.312554 | 0.156277 | − | 0.987713i | \(-0.450051\pi\) | ||||
0.156277 | + | 0.987713i | \(0.450051\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.47531 | −0.386145 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.41048 | −0.923170 | −0.461585 | − | 0.887096i | \(-0.652719\pi\) | ||||
−0.461585 | + | 0.887096i | \(0.652719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.12861 | −0.664741 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.86983 | −1.05816 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.1801 | 1.71509 | 0.857544 | − | 0.514410i | \(-0.171989\pi\) | ||||
0.857544 | + | 0.514410i | \(0.171989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.90271 | −0.304287 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.0608 | 1.25064 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.73312 | −0.588206 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.64353 | 0.166875 | 0.0834376 | − | 0.996513i | \(-0.473410\pi\) | ||||
0.0834376 | + | 0.996513i | \(0.473410\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.59612 | −0.160416 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.1247 | −1.30596 | −0.652980 | − | 0.757375i | \(-0.726482\pi\) | ||||
−0.652980 | + | 0.757375i | \(0.726482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.157689 | 0.0155375 | 0.00776876 | − | 0.999970i | \(-0.497527\pi\) | ||||
0.00776876 | + | 0.999970i | \(0.497527\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30831 | 0.127678 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.9459 | −1.73489 | −0.867447 | − | 0.497529i | \(-0.834241\pi\) | ||||
−0.867447 | + | 0.497529i | \(0.834241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.86657 | 0.370350 | 0.185175 | − | 0.982706i | \(-0.440715\pi\) | ||||
0.185175 | + | 0.982706i | \(0.440715\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.3848 | 0.985679 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.45169 | 0.136563 | 0.0682815 | − | 0.997666i | \(-0.478248\pi\) | ||||
0.0682815 | + | 0.997666i | \(0.478248\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.92684 | 0.179679 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.73960 | −0.345726 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.12861 | 0.561809 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.46508 | −0.860462 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.92970 | −0.173995 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7997 | 1.13579 | 0.567896 | − | 0.823101i | \(-0.307758\pi\) | ||||
0.567896 | + | 0.823101i | \(0.307758\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.30831 | −0.115191 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4073 | 1.60825 | 0.804126 | − | 0.594458i | \(-0.202633\pi\) | ||||
0.804126 | + | 0.594458i | \(0.202633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.73312 | 0.497125 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.61046 | 0.482872 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9856 | 1.10943 | 0.554716 | − | 0.832040i | \(-0.312827\pi\) | ||||
0.554716 | + | 0.832040i | \(0.312827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.05439 | −0.683164 | −0.341582 | − | 0.939852i | \(-0.610963\pi\) | ||||
−0.341582 | + | 0.939852i | \(0.610963\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.24504 | −0.610142 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.59623 | 0.300732 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.54393 | 0.626489 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.30831 | −0.107908 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.80585 | −0.311787 | −0.155894 | − | 0.987774i | \(-0.549826\pi\) | ||||
−0.155894 | + | 0.987774i | \(0.549826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.28473 | −0.348686 | −0.174343 | − | 0.984685i | \(-0.555780\pi\) | ||||
−0.174343 | + | 0.984685i | \(0.555780\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.89558 | 0.638319 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.21855 | −0.740452 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4427 | 1.31227 | 0.656135 | − | 0.754643i | \(-0.272190\pi\) | ||||
0.656135 | + | 0.754643i | \(0.272190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.0259 | −1.19163 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.92684 | −0.151856 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4106 | 1.05040 | 0.525198 | − | 0.850980i | \(-0.323991\pi\) | ||||
0.525198 | + | 0.850980i | \(0.323991\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.62090 | −0.126187 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.57973 | 0.509155 | 0.254577 | − | 0.967052i | \(-0.418064\pi\) | ||||
0.254577 | + | 0.967052i | \(0.418064\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.57426 | −0.351867 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.38606 | 0.564826 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3221 | 1.62109 | 0.810546 | − | 0.585675i | \(-0.199170\pi\) | ||||
0.810546 | + | 0.585675i | \(0.199170\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.29253 | 0.472975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.54369 | −0.489098 | −0.244549 | − | 0.969637i | \(-0.578640\pi\) | ||||
−0.244549 | + | 0.969637i | \(0.578640\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.70779 | −0.126939 | −0.0634694 | − | 0.997984i | \(-0.520217\pi\) | ||||
−0.0634694 | + | 0.997984i | \(0.520217\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.10885 | −0.155891 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.93752 | −0.583578 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.59286 | −0.555245 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.61046 | −0.408101 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0481 | −1.45063 | −0.725315 | − | 0.688417i | \(-0.758306\pi\) | ||||
−0.725315 | + | 0.688417i | \(0.758306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.5384 | 1.62235 | 0.811174 | − | 0.584806i | \(-0.198829\pi\) | ||||
0.811174 | + | 0.584806i | \(0.198829\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.79766 | −0.271956 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1729 | 1.00978 | 0.504889 | − | 0.863184i | \(-0.331533\pi\) | ||||
0.504889 | + | 0.863184i | \(0.331533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.48412 | 0.317871 | 0.158935 | − | 0.987289i | \(-0.449194\pi\) | ||||
0.158935 | + | 0.987289i | \(0.449194\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.05242 | 0.426905 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.54393 | −0.529480 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.47495 | 0.103015 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.48237 | −0.172537 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.10288 | −0.491317 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.29006 | −0.433026 | −0.216513 | − | 0.976280i | \(-0.569468\pi\) | ||||
−0.216513 | + | 0.976280i | \(0.569468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −19.0463 | −1.30503 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.21855 | 0.625796 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.32410 | 0.292196 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.7896 | −1.19666 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6695 | 1.58503 | 0.792515 | − | 0.609852i | \(-0.208771\pi\) | ||||
0.792515 | + | 0.609852i | \(0.208771\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.28831 | −0.0858876 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.3568 | −1.48387 | −0.741936 | − | 0.670471i | \(-0.766092\pi\) | ||||
−0.741936 | + | 0.670471i | \(0.766092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.64565 | −0.439157 | −0.219579 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219579 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.62090 | 0.106647 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.71170 | 0.243162 | 0.121581 | − | 0.992582i | \(-0.461204\pi\) | ||||
0.121581 | + | 0.992582i | \(0.461204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.53769 | 0.361239 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.63455 | −0.236089 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 30.3199 | 1.96123 | 0.980615 | − | 0.195945i | \(-0.0627773\pi\) | ||||
0.980615 | + | 0.195945i | \(0.0627773\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.743833 | 0.0479145 | 0.0239572 | − | 0.999713i | \(-0.492373\pi\) | ||||
0.0239572 | + | 0.999713i | \(0.492373\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.2846 | −0.788057 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.6416 | −1.05888 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.0035 | 0.697322 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.41950 | −0.0895980 | −0.0447990 | − | 0.998996i | \(-0.514265\pi\) | ||||
−0.0447990 | + | 0.998996i | \(0.514265\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.38720 | 0.150082 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.01815 | 0.502116 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.6806 | −0.978126 | −0.489063 | − | 0.872248i | \(-0.662661\pi\) | ||||
−0.489063 | + | 0.872248i | \(0.662661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.93752 | 0.493214 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.71895 | −0.601588 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.81953 | 0.420510 | 0.210255 | − | 0.977647i | \(-0.432571\pi\) | ||||
0.210255 | + | 0.977647i | \(0.432571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4850 | 0.705516 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.1687 | −1.29550 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1168 | 0.799747 | 0.399874 | − | 0.916570i | \(-0.369054\pi\) | ||||
0.399874 | + | 0.916570i | \(0.369054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.88076 | −0.296485 | −0.148242 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148242 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.79766 | 0.229845 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.23892 | 0.0747097 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6270 | 0.638517 | 0.319258 | − | 0.947668i | \(-0.396566\pi\) | ||||
0.319258 | + | 0.947668i | \(0.396566\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.8764 | 0.711021 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4670 | −1.04200 | −0.520998 | − | 0.853558i | \(-0.674440\pi\) | ||||
−0.520998 | + | 0.853558i | \(0.674440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.147036 | 0.00874038 | 0.00437019 | − | 0.999990i | \(-0.498609\pi\) | ||||
0.00437019 | + | 0.999990i | \(0.498609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.50073 | 0.444305 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.47495 | −0.0870636 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.5599 | 1.20941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.15025 | −0.126050 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.60003 | 0.268737 | 0.134368 | − | 0.990931i | \(-0.457099\pi\) | ||||
0.134368 | + | 0.990931i | \(0.457099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.80965 | −0.280028 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.95091 | 0.403333 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.59306 | 0.323455 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | −0.0576390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.1713 | 0.986465 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.61188 | 0.0922962 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9599 | −0.682589 | −0.341295 | − | 0.939956i | \(-0.610865\pi\) | ||||
−0.341295 | + | 0.939956i | \(0.610865\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.206306 | −0.0117364 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0828 | 1.02538 | 0.512690 | − | 0.858574i | \(-0.328649\pi\) | ||||
0.512690 | + | 0.858574i | \(0.328649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.38689 | −0.0783916 | −0.0391958 | − | 0.999232i | \(-0.512480\pi\) | ||||
−0.0391958 | + | 0.999232i | \(0.512480\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.28831 | 0.0725883 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.5960 | 1.15679 | 0.578395 | − | 0.815757i | \(-0.303679\pi\) | ||||
0.578395 | + | 0.815757i | \(0.303679\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.34633 | 0.523294 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.4789 | 1.31046 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.1361 | 1.95502 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.90271 | 0.161013 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.05869 | −0.279746 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.53769 | −0.305303 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.94575 | −0.436738 | −0.218369 | − | 0.975866i | \(-0.570074\pi\) | ||||
−0.218369 | + | 0.975866i | \(0.570074\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2260 | 0.560382 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.62612 | −0.252752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.0122 | 1.79829 | 0.899145 | − | 0.437650i | \(-0.144189\pi\) | ||||
0.899145 | + | 0.437650i | \(0.144189\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.89926 | −0.103154 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4210 | −0.618484 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.52091 | −0.135721 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.5710 | 1.31904 | 0.659521 | − | 0.751686i | \(-0.270759\pi\) | ||||
0.659521 | + | 0.751686i | \(0.270759\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2276 | 1.08276 | 0.541379 | − | 0.840778i | \(-0.317902\pi\) | ||||
0.541379 | + | 0.840778i | \(0.317902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.2856 | 0.869259 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.72446 | −0.0917839 | −0.0458919 | − | 0.998946i | \(-0.514613\pi\) | ||||
−0.0458919 | + | 0.998946i | \(0.514613\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.5579 | 0.772653 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.01815 | −0.424366 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.47147 | 0.130439 | 0.0652195 | − | 0.997871i | \(-0.479225\pi\) | ||||
0.0652195 | + | 0.997871i | \(0.479225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.8687 | 0.729932 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.3833 | 0.649954 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.30509 | −0.172996 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.4696 | 1.79930 | 0.899650 | − | 0.436612i | \(-0.143822\pi\) | ||||
0.899650 | + | 0.436612i | \(0.143822\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.90020 | −0.0989205 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.4850 | −0.596270 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.2740 | 1.82642 | 0.913210 | − | 0.407490i | \(-0.133596\pi\) | ||||
0.913210 | + | 0.407490i | \(0.133596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.30831 | −0.0675611 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.8979 | 1.12780 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.02417 | −0.360807 | −0.180404 | − | 0.983593i | \(-0.557740\pi\) | ||||
−0.180404 | + | 0.983593i | \(0.557740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.7461 | −0.857926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.4855 | −1.76213 | −0.881063 | − | 0.472999i | \(-0.843172\pi\) | ||||
−0.881063 | + | 0.472999i | \(0.843172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.23892 | −0.0631412 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.28831 | −0.0654887 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.9699 | 0.759004 | 0.379502 | − | 0.925191i | \(-0.376095\pi\) | ||||
0.379502 | + | 0.925191i | \(0.376095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.8088 | −0.597199 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.0825 | −1.21480 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.77804 | 0.139778 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.5107 | 1.68186 | 0.840928 | − | 0.541147i | \(-0.182010\pi\) | ||||
0.840928 | + | 0.541147i | \(0.182010\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.50073 | −0.375506 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.4759 | 0.573079 | 0.286539 | − | 0.958068i | \(-0.407495\pi\) | ||||
0.286539 | + | 0.958068i | \(0.407495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.7588 | −1.33295 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.47531 | −0.172689 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.83395 | −0.487451 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2267 | 1.39572 | 0.697861 | − | 0.716233i | \(-0.254135\pi\) | ||||
0.697861 | + | 0.716233i | \(0.254135\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.9892 | −0.838015 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.80965 | 0.236667 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.41048 | −0.412854 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5377 | 0.516032 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.6705 | −1.59606 | −0.798029 | − | 0.602619i | \(-0.794124\pi\) | ||||
−0.798029 | + | 0.602619i | \(0.794124\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.1217 | −0.590774 | −0.295387 | − | 0.955378i | \(-0.595449\pi\) | ||||
−0.295387 | + | 0.955378i | \(0.595449\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.13428 | −0.346881 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.12861 | −0.297281 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.61188 | −0.0780046 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.70500 | −0.227159 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.95544 | −0.286864 | −0.143432 | − | 0.989660i | \(-0.545814\pi\) | ||||
−0.143432 | + | 0.989660i | \(0.545814\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9181 | 0.813031 | 0.406515 | − | 0.913644i | \(-0.366744\pi\) | ||||
0.406515 | + | 0.913644i | \(0.366744\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.86983 | −0.473222 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.0468 | −0.528440 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.35549 | −0.112421 | −0.0562107 | − | 0.998419i | \(-0.517902\pi\) | ||||
−0.0562107 | + | 0.998419i | \(0.517902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.28831 | −0.0613483 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.11901 | −0.338234 | −0.169117 | − | 0.985596i | \(-0.554092\pi\) | ||||
−0.169117 | + | 0.985596i | \(0.554092\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.1801 | 0.767011 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.97925 | 0.235510 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.9736 | −0.989805 | −0.494903 | − | 0.868949i | \(-0.664796\pi\) | ||||
−0.494903 | + | 0.868949i | \(0.664796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.82735 | 0.0860464 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.60578 | 0.263382 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.90271 | −0.136081 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.8604 | 0.882251 | 0.441126 | − | 0.897445i | \(-0.354579\pi\) | ||||
0.441126 | + | 0.897445i | \(0.354579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −34.3843 | −1.60492 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4892 | 0.628253 | 0.314127 | − | 0.949381i | \(-0.398288\pi\) | ||||
0.314127 | + | 0.949381i | \(0.398288\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.8444 | −1.01520 | −0.507598 | − | 0.861594i | \(-0.669467\pi\) | ||||
−0.507598 | + | 0.861594i | \(0.669467\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.0608 | 0.559305 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.28941 | −0.198490 | −0.0992452 | − | 0.995063i | \(-0.531643\pi\) | ||||
−0.0992452 | + | 0.995063i | \(0.531643\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.62612 | 0.213615 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.5122 | −0.991231 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.23892 | 0.0569656 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.73312 | −0.263054 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.7962 | −0.677473 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.9883 | 1.50727 | 0.753637 | − | 0.657290i | \(-0.228297\pi\) | ||||
0.753637 | + | 0.657290i | \(0.228297\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.0403 | −1.05055 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.52091 | 0.114705 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.64353 | 0.0746288 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.09704 | −0.185655 | −0.0928273 | − | 0.995682i | \(-0.529590\pi\) | ||||
−0.0928273 | + | 0.995682i | \(0.529590\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.5452 | −0.793423 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.6073 | 1.60694 | 0.803468 | − | 0.595348i | \(-0.202986\pi\) | ||||
0.803468 | + | 0.595348i | \(0.202986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −46.2338 | −2.08227 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.59612 | −0.0717402 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.5579 | −0.653011 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.9895 | −0.626257 | −0.313128 | − | 0.949711i | \(-0.601377\pi\) | ||||
−0.313128 | + | 0.949711i | \(0.601377\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.60835 | −0.384593 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.4420 | 0.777701 | 0.388850 | − | 0.921301i | \(-0.372872\pi\) | ||||
0.388850 | + | 0.921301i | \(0.372872\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.1247 | −0.584043 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.98458 | 0.265784 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.2919 | 1.16537 | 0.582683 | − | 0.812699i | \(-0.302003\pi\) | ||||
0.582683 | + | 0.812699i | \(0.302003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.30509 | 0.146209 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −32.1655 | −1.42014 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.157689 | 0.00694859 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.86076 | 0.301736 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.8961 | −1.22450 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.7842 | −1.65536 | −0.827679 | − | 0.561202i | \(-0.810339\pi\) | ||||
−0.827679 | + | 0.561202i | \(0.810339\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.9099 | 1.22041 | 0.610207 | − | 0.792242i | \(-0.291086\pi\) | ||||
0.610207 | + | 0.792242i | \(0.291086\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.30831 | 0.0570995 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.4969 | 2.46105 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2873 | −0.838578 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.19633 | 0.268898 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.28136 | 0.185446 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.9459 | −0.775869 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.56120 | 0.369443 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.23892 | 0.0533641 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7760 | 0.678263 | 0.339132 | − | 0.940739i | \(-0.389867\pi\) | ||||
0.339132 | + | 0.940739i | \(0.389867\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.23432 | 0.0958840 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.86657 | 0.165626 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0312 | −0.856472 | −0.428236 | − | 0.903667i | \(-0.640865\pi\) | ||||
−0.428236 | + | 0.903667i | \(0.640865\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.07661 | −0.0886277 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −43.2503 | −1.84252 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.77804 | −0.118134 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.3848 | 0.440809 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.4546 | 1.12092 | 0.560459 | − | 0.828182i | \(-0.310625\pi\) | ||||
0.560459 | + | 0.828182i | \(0.310625\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.90271 | 0.122772 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.93385 | 0.419407 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.8319 | −1.84729 | −0.923647 | − | 0.383245i | \(-0.874806\pi\) | ||||
−0.923647 | + | 0.383245i | \(0.874806\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.45169 | 0.0610729 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.47531 | 0.145949 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0973 | −0.632912 | −0.316456 | − | 0.948607i | \(-0.602493\pi\) | ||||
−0.316456 | + | 0.948607i | \(0.602493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0890 | −0.924395 | −0.462197 | − | 0.886777i | \(-0.652939\pi\) | ||||
−0.462197 | + | 0.886777i | \(0.652939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.2292 | 1.09574 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.92684 | 0.0803547 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.6953 | −1.15297 | −0.576485 | − | 0.817107i | \(-0.695576\pi\) | ||||
−0.576485 | + | 0.817107i | \(0.695576\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.4873 | −1.22545 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.41048 | 0.348925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.2289 | 0.589303 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.73960 | −0.154614 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.1716 | 1.69933 | 0.849667 | − | 0.527320i | \(-0.176803\pi\) | ||||
0.849667 | + | 0.527320i | \(0.176803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 52.8511 | 2.17769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.5426 | −0.762742 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.00108 | −0.246435 | −0.123217 | − | 0.992380i | \(-0.539321\pi\) | ||||
−0.123217 | + | 0.992380i | \(0.539321\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.12861 | 0.251249 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.86664 | −0.240106 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.1384 | 1.68087 | 0.840436 | − | 0.541911i | \(-0.182299\pi\) | ||||
0.840436 | + | 0.541911i | \(0.182299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.18862 | 0.334021 | 0.167010 | − | 0.985955i | \(-0.446589\pi\) | ||||
0.167010 | + | 0.985955i | \(0.446589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.95990 | 0.242706 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.46508 | −0.384810 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.93184 | 0.119000 | 0.0594998 | − | 0.998228i | \(-0.481049\pi\) | ||||
0.0594998 | + | 0.998228i | \(0.481049\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.86983 | 0.399946 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0743 | 0.650297 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.90975 | 0.279082 | 0.139541 | − | 0.990216i | \(-0.455437\pi\) | ||||
0.139541 | + | 0.990216i | \(0.455437\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.92970 | −0.0778130 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.0412 | 0.686055 | 0.343027 | − | 0.939325i | \(-0.388548\pi\) | ||||
0.343027 | + | 0.939325i | \(0.388548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1903 | 0.771323 | 0.385661 | − | 0.922640i | \(-0.373973\pi\) | ||||
0.385661 | + | 0.922640i | \(0.373973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8105 | 0.433809 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.1801 | −0.648243 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.29280 | 0.371119 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.6460 | 1.93964 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.3435 | −1.48662 | −0.743311 | − | 0.668946i | \(-0.766746\pi\) | ||||
−0.743311 | + | 0.668946i | \(0.766746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.22938 | 0.327088 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.7997 | 0.507941 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.90271 | 0.115010 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18.7551 | −0.741942 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.7505 | −0.780099 | −0.390050 | − | 0.920794i | \(-0.627542\pi\) | ||||
−0.390050 | + | 0.920794i | \(0.627542\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.2547 | 1.50862 | 0.754309 | − | 0.656519i | \(-0.227972\pi\) | ||||
0.754309 | + | 0.656519i | \(0.227972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.30831 | −0.0515148 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.4389 | −0.685595 | −0.342797 | − | 0.939409i | \(-0.611374\pi\) | ||||
−0.342797 | + | 0.939409i | \(0.611374\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.95877 | −0.233902 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0608 | −0.472699 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.3538 | 1.14870 | 0.574352 | − | 0.818609i | \(-0.305254\pi\) | ||||
0.574352 | + | 0.818609i | \(0.305254\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.4073 | 0.719233 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.25800 | 0.166120 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.6571 | 0.843640 | 0.421820 | − | 0.906680i | \(-0.361391\pi\) | ||||
0.421820 | + | 0.906680i | \(0.361391\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.8839 | 1.39572 | 0.697861 | − | 0.716233i | \(-0.254135\pi\) | ||||
0.697861 | + | 0.716233i | \(0.254135\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2744 | 0.903902 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.73312 | 0.222321 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.5359 | 0.562834 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.9672 | −1.19726 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.99700 | 0.0770932 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.5338 | 1.83229 | 0.916147 | − | 0.400844i | \(-0.131283\pi\) | ||||
0.916147 | + | 0.400844i | \(0.131283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.61046 | 0.215947 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.05477 | −0.232704 | −0.116352 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116352 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.64353 | −0.0630729 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.2497 | 1.12085 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.80842 | −0.337045 | −0.168522 | − | 0.985698i | \(-0.553900\pi\) | ||||
−0.168522 | + | 0.985698i | \(0.553900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.9856 | 0.496153 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.69460 | 0.331720 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.3375 | 1.27006 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.1107 | −1.37372 | −0.686858 | − | 0.726791i | \(-0.741011\pi\) | ||||
−0.686858 | + | 0.726791i | \(0.741011\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.59612 | 0.0606315 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.05439 | −0.305520 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.03941 | −0.342392 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.85608 | −0.183674 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.7831 | −1.57813 | −0.789063 | − | 0.614312i | \(-0.789434\pi\) | ||||
−0.789063 | + | 0.614312i | \(0.789434\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 45.5068 | 1.71632 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.24504 | −0.272864 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.1247 | 0.493607 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.71335 | 0.177014 | 0.0885068 | − | 0.996076i | \(-0.471790\pi\) | ||||
0.0885068 | + | 0.996076i | \(0.471790\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.57898 | −0.134222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.7627 | −0.665217 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.59623 | 0.134491 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.6679 | −1.48143 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.63400 | −0.247407 | −0.123703 | − | 0.992319i | \(-0.539477\pi\) | ||||
−0.123703 | + | 0.992319i | \(0.539477\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.157689 | −0.00587263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.973167 | −0.0361925 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.54393 | 0.280175 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.1827 | −1.49029 | −0.745147 | − | 0.666900i | \(-0.767621\pi\) | ||||
−0.745147 | + | 0.666900i | \(0.767621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4980 | 0.981408 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.12861 | −0.226675 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.5151 | −0.388382 | −0.194191 | − | 0.980964i | \(-0.562208\pi\) | ||||
−0.194191 | + | 0.980964i | \(0.562208\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.30831 | −0.0482579 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.73140 | −0.211119 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.0044 | 1.28766 | 0.643829 | − | 0.765169i | \(-0.277345\pi\) | ||||
0.643829 | + | 0.765169i | \(0.277345\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.7724 | 0.799831 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4515 | −0.713606 | −0.356803 | − | 0.934180i | \(-0.616133\pi\) | ||||
−0.356803 | + | 0.934180i | \(0.616133\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.80585 | −0.139435 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.8353 | 0.396444 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.9459 | 0.655729 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −54.2810 | −1.98074 | −0.990372 | − | 0.138435i | \(-0.955793\pi\) | ||||
−0.990372 | + | 0.138435i | \(0.955793\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.85715 | 0.0676784 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.28473 | −0.155937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.9821 | 1.16241 | 0.581205 | − | 0.813757i | \(-0.302582\pi\) | ||||
0.581205 | + | 0.813757i | \(0.302582\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.12321 | −0.113365 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.47608 | −0.0897577 | −0.0448789 | − | 0.998992i | \(-0.514290\pi\) | ||||
−0.0448789 | + | 0.998992i | \(0.514290\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.86657 | −0.139979 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.89558 | 0.285465 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.9610 | −0.504103 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.599916 | −0.0216335 | −0.0108168 | − | 0.999941i | \(-0.503443\pi\) | ||||
−0.0108168 | + | 0.999941i | \(0.503443\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.5151 | 0.738833 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.234610 | 0.00843834 | 0.00421917 | − | 0.999991i | \(-0.498657\pi\) | ||||
0.00421917 | + | 0.999991i | \(0.498657\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.21855 | −0.331140 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.3848 | −0.372552 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.45608 | −0.302970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0361 | 0.645381 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.3249 | 1.51257 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.4427 | 0.586865 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.59722 | −0.342104 | −0.171052 | − | 0.985262i | \(-0.554717\pi\) | ||||
−0.171052 | + | 0.985262i | \(0.554717\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.92209 | −0.317635 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.45169 | −0.0516160 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.67884 | 0.166150 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.0259 | −0.532915 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.9670 | −0.884377 | −0.442188 | − | 0.896922i | \(-0.645798\pi\) | ||||
−0.442188 | + | 0.896922i | \(0.645798\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.9384 | −1.20065 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.8451 | −0.736524 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.09474 | −0.144500 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.92684 | −0.0679121 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.1609 | −0.604094 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.1099 | −0.531237 | −0.265618 | − | 0.964078i | \(-0.585576\pi\) | ||||
−0.265618 | + | 0.964078i | \(0.585576\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.2016 | −0.533799 | −0.266899 | − | 0.963724i | \(-0.585999\pi\) | ||||
−0.266899 | + | 0.963724i | \(0.585999\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.38556 | 0.223952 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.4106 | 0.469751 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.73312 | −0.200577 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.73960 | 0.130672 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.9370 | 1.53341 | 0.766706 | − | 0.641999i | \(-0.221895\pi\) | ||||
0.766706 | + | 0.641999i | \(0.221895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.5188 | 0.645523 | 0.322762 | − | 0.946480i | \(-0.395389\pi\) | ||||
0.322762 | + | 0.946480i | \(0.395389\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.62090 | −0.0564324 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0560 | 0.906056 | 0.453028 | − | 0.891496i | \(-0.350344\pi\) | ||||
0.453028 | + | 0.891496i | \(0.350344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.02890 | 0.174661 | 0.0873304 | − | 0.996179i | \(-0.472166\pi\) | ||||
0.0873304 | + | 0.996179i | \(0.472166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.9035 | −0.482307 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.12861 | −0.212344 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.57973 | 0.227701 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −51.7203 | −1.78772 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.62865 | 0.0907512 | 0.0453756 | − | 0.998970i | \(-0.485552\pi\) | ||||
0.0453756 | + | 0.998970i | \(0.485552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.9109 | 0.962444 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.8524 | 0.787078 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.57426 | −0.157359 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.46508 | 0.325224 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.192369 | −0.00660210 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.2943 | −0.524282 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.2934 | −1.10570 | −0.552852 | − | 0.833280i | \(-0.686460\pi\) | ||||
−0.552852 | + | 0.833280i | \(0.686460\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.38606 | 0.252598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.8305 | −1.05315 | −0.526575 | − | 0.850129i | \(-0.676524\pi\) | ||||
−0.526575 | + | 0.850129i | \(0.676524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27.1500 | −0.926346 | −0.463173 | − | 0.886268i | \(-0.653289\pi\) | ||||
−0.463173 | + | 0.886268i | \(0.653289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.92970 | 0.0657640 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.8854 | 1.93640 | 0.968201 | − | 0.250172i | \(-0.0804873\pi\) | ||||
0.968201 | + | 0.250172i | \(0.0804873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.3221 | 0.724975 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.8988 | −0.913531 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.44177 | 0.116754 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.4283 | −0.455001 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.11738 | −0.0716625 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.8602 | 0.771934 | 0.385967 | − | 0.922513i | \(-0.373868\pi\) | ||||
0.385967 | + | 0.922513i | \(0.373868\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.01828 | −0.202992 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.08133 | 0.137504 | 0.0687518 | − | 0.997634i | \(-0.478098\pi\) | ||||
0.0687518 | + | 0.997634i | \(0.478098\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.5304 | −0.388030 | −0.194015 | − | 0.980999i | \(-0.562151\pi\) | ||||
−0.194015 | + | 0.980999i | \(0.562151\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.29253 | 0.211521 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.25829 | −0.0758261 | −0.0379131 | − | 0.999281i | \(-0.512071\pi\) | ||||
−0.0379131 | + | 0.999281i | \(0.512071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.7997 | −0.429289 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.30563 | −0.144244 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.7483 | −1.06242 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.54369 | −0.218731 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.31747 | −0.244323 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −69.5441 | −2.31943 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.3869 | −2.34493 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.30831 | 0.0435380 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.70779 | −0.0567688 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.8040 | −1.38808 | −0.694040 | − | 0.719937i | \(-0.744171\pi\) | ||||
−0.694040 | + | 0.719937i | \(0.744171\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.9088 | 0.560829 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.3597 | 1.07212 | 0.536062 | − | 0.844179i | \(-0.319911\pi\) | ||||
0.536062 | + | 0.844179i | \(0.319911\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.4199 | −0.344849 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.10885 | −0.0697165 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.4073 | −0.607862 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.7266 | 0.617733 | 0.308867 | − | 0.951105i | \(-0.400050\pi\) | ||||
0.308867 | + | 0.951105i | \(0.400050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.6473 | 0.515598 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 42.2574 | 1.39092 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.93752 | −0.260984 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.203152 | −0.00667240 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.2370 | −1.32013 | −0.660067 | − | 0.751206i | \(-0.729472\pi\) | ||||
−0.660067 | + | 0.751206i | \(0.729472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.73312 | −0.187896 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.6580 | −0.774527 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.59286 | −0.248313 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.7895 | −0.483152 | −0.241576 | − | 0.970382i | \(-0.577664\pi\) | ||||
−0.241576 | + | 0.970382i | \(0.577664\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.81449 | 0.0592136 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.4761 | −1.05869 | −0.529346 | − | 0.848406i | \(-0.677563\pi\) | ||||
−0.529346 | + | 0.848406i | \(0.677563\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.84199 | 0.0925480 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.61046 | −0.182508 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.3125 | −0.822546 | −0.411273 | − | 0.911512i | \(-0.634916\pi\) | ||||
−0.411273 | + | 0.911512i | \(0.634916\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.59373 | −0.311426 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.9461 | −0.873787 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.3834 | 0.725068 | 0.362534 | − | 0.931970i | \(-0.381912\pi\) | ||||
0.362534 | + | 0.931970i | \(0.381912\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.0481 | −0.648742 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.2279 | −0.395273 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.9856 | −0.419326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.9817 | 1.74135 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.1199 | 0.745030 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.5384 | 0.725536 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.68590 | −0.279320 | −0.139660 | − | 0.990200i | \(-0.544601\pi\) | ||||
−0.139660 | + | 0.990200i | \(0.544601\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −45.9691 | −1.47674 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.4274 | 0.944371 | 0.472185 | − | 0.881499i | \(-0.343465\pi\) | ||||
0.472185 | + | 0.881499i | \(0.343465\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.05439 | 0.258212 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.79766 | −0.121622 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.3083 | −1.00164 | −0.500820 | − | 0.865551i | \(-0.666968\pi\) | ||||
−0.500820 | + | 0.865551i | \(0.666968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0459 | 0.640669 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.98136 | −0.159043 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.2231 | −1.05965 | −0.529827 | − | 0.848106i | \(-0.677743\pi\) | ||||
−0.529827 | + | 0.848106i | \(0.677743\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.1729 | 0.451587 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.24504 | 0.230612 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.92684 | 0.0612699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.8580 | −0.408448 | −0.204224 | − | 0.978924i | \(-0.565467\pi\) | ||||
−0.204224 | + | 0.978924i | \(0.565467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3955 | 0.329892 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.48412 | 0.142156 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.9955 | −1.29834 | −0.649170 | − | 0.760643i | \(-0.724884\pi\) | ||||
−0.649170 | + | 0.760643i | \(0.724884\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −44.5332 | −1.40897 |
(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 | 6020.2.a.k.1.5 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6020.2.a.k.1.5 | ✓ | 13 | 1.1 | even | 1 | trivial |