Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, 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("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3040) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.438447 | 0.165717 | 0.0828587 | − | 0.996561i | \(-0.473595\pi\) | ||||
0.0828587 | + | 0.996561i | \(0.473595\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000 | 1.20605 | 0.603023 | − | 0.797724i | \(-0.293963\pi\) | ||||
0.603023 | + | 0.797724i | \(0.293963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.56155 | 0.433097 | 0.216548 | − | 0.976272i | \(-0.430520\pi\) | ||||
0.216548 | + | 0.976272i | \(0.430520\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56155 | −0.403191 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56155 | 0.863803 | 0.431902 | − | 0.901921i | \(-0.357843\pi\) | ||||
0.431902 | + | 0.901921i | \(0.357843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.684658 | −0.149405 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.68466 | 1.39385 | 0.696924 | − | 0.717145i | \(-0.254552\pi\) | ||||
0.696924 | + | 0.717145i | \(0.254552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.56155 | 1.40415 | 0.702073 | − | 0.712105i | \(-0.252258\pi\) | ||||
0.702073 | + | 0.712105i | \(0.252258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12311 | 0.560926 | 0.280463 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280463 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.24621 | −1.08733 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.438447 | 0.0741111 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.12311 | −1.17103 | −0.585516 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585516 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.43845 | −0.390464 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.24621 | −1.28784 | −0.643921 | − | 0.765092i | \(-0.722693\pi\) | ||||
−0.643921 | + | 0.765092i | \(0.722693\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.12311 | −0.747282 | −0.373641 | − | 0.927573i | \(-0.621891\pi\) | ||||
−0.373641 | + | 0.927573i | \(0.621891\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.80776 | −0.972538 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.56155 | −0.778773 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.43845 | −0.334946 | −0.167473 | − | 0.985877i | \(-0.553561\pi\) | ||||
−0.167473 | + | 0.985877i | \(0.553561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56155 | −0.206833 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.80776 | 1.01648 | 0.508242 | − | 0.861214i | \(-0.330295\pi\) | ||||
0.508242 | + | 0.861214i | \(0.330295\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1231 | 1.68024 | 0.840121 | − | 0.542399i | \(-0.182484\pi\) | ||||
0.840121 | + | 0.542399i | \(0.182484\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.246211 | −0.0310197 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.56155 | 0.193687 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.43845 | 0.786582 | 0.393291 | − | 0.919414i | \(-0.371337\pi\) | ||||
0.393291 | + | 0.919414i | \(0.371337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.4384 | −1.25664 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.80776 | −0.679747 | −0.339874 | − | 0.940471i | \(-0.610384\pi\) | ||||
−0.339874 | + | 0.940471i | \(0.610384\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.75379 | 0.199863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.12311 | −0.351377 | −0.175688 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175688 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.0000 | 1.53670 | 0.768350 | − | 0.640030i | \(-0.221078\pi\) | ||||
0.768350 | + | 0.640030i | \(0.221078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.56155 | 0.386305 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.8078 | −1.26593 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.684658 | 0.0717717 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.87689 | −0.505710 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.12311 | 0.723242 | 0.361621 | − | 0.932325i | \(-0.382223\pi\) | ||||
0.361621 | + | 0.932325i | \(0.382223\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.24621 | −0.225753 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.12311 | −0.509768 | −0.254884 | − | 0.966972i | \(-0.582037\pi\) | ||||
−0.254884 | + | 0.966972i | \(0.582037\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.684658 | −0.0668158 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.684658 | −0.0661884 | −0.0330942 | − | 0.999452i | \(-0.510536\pi\) | ||||
−0.0330942 | + | 0.999452i | \(0.510536\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.5616 | −1.49053 | −0.745263 | − | 0.666770i | \(-0.767676\pi\) | ||||
−0.745263 | + | 0.666770i | \(0.767676\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.1231 | 1.05576 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2462 | 0.963882 | 0.481941 | − | 0.876204i | \(-0.339932\pi\) | ||||
0.481941 | + | 0.876204i | \(0.339932\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.68466 | 0.623348 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.876894 | −0.0810689 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.56155 | 0.143147 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.8769 | 1.16107 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.36932 | 0.831392 | 0.415696 | − | 0.909504i | \(-0.363538\pi\) | ||||
0.415696 | + | 0.909504i | \(0.363538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.12311 | −0.274974 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0000 | 1.39793 | 0.698963 | − | 0.715158i | \(-0.253645\pi\) | ||||
0.698963 | + | 0.715158i | \(0.253645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.438447 | 0.0380182 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.56155 | 0.478662 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.8078 | 1.52142 | 0.760710 | − | 0.649092i | \(-0.224851\pi\) | ||||
0.760710 | + | 0.649092i | \(0.224851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2462 | 1.20835 | 0.604174 | − | 0.796852i | \(-0.293503\pi\) | ||||
0.604174 | + | 0.796852i | \(0.293503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.24621 | 0.522334 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.56155 | 0.627953 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.6307 | 0.876804 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.12311 | 0.419701 | 0.209851 | − | 0.977733i | \(-0.432702\pi\) | ||||
0.209851 | + | 0.977733i | \(0.432702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.87689 | 0.396876 | 0.198438 | − | 0.980113i | \(-0.436413\pi\) | ||||
0.198438 | + | 0.980113i | \(0.436413\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.12311 | 0.250854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00000 | −0.478852 | −0.239426 | − | 0.970915i | \(-0.576959\pi\) | ||||
−0.239426 | + | 0.970915i | \(0.576959\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.80776 | 0.301975 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.93087 | 0.230985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.2462 | −1.58581 | −0.792903 | − | 0.609348i | \(-0.791431\pi\) | ||||
−0.792903 | + | 0.609348i | \(0.791431\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.24621 | −0.486267 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.36932 | 0.415490 | 0.207745 | − | 0.978183i | \(-0.433388\pi\) | ||||
0.207745 | + | 0.978183i | \(0.433388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5616 | −0.812427 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.561553 | −0.0429430 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.1231 | −0.845674 | −0.422837 | − | 0.906206i | \(-0.638966\pi\) | ||||
−0.422837 | + | 0.906206i | \(0.638966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.438447 | 0.0331435 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.1922 | −0.916425 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.24621 | 0.167890 | 0.0839449 | − | 0.996470i | \(-0.473248\pi\) | ||||
0.0839449 | + | 0.996470i | \(0.473248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.2462 | −1.80221 | −0.901103 | − | 0.433604i | \(-0.857242\pi\) | ||||
−0.901103 | + | 0.433604i | \(0.857242\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.4924 | −1.51484 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.12311 | −0.523701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2462 | 1.04179 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.43845 | 0.177371 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.6847 | 1.20726 | 0.603630 | − | 0.797265i | \(-0.293721\pi\) | ||||
0.603630 | + | 0.797265i | \(0.293721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.876894 | 0.0631202 | 0.0315601 | − | 0.999502i | \(-0.489952\pi\) | ||||
0.0315601 | + | 0.999502i | \(0.489952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.43845 | −0.174621 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.75379 | 0.552435 | 0.276217 | − | 0.961095i | \(-0.410919\pi\) | ||||
0.276217 | + | 0.961095i | \(0.410919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.56155 | −0.677801 | −0.338900 | − | 0.940822i | \(-0.610055\pi\) | ||||
−0.338900 | + | 0.940822i | \(0.610055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0540 | −0.709153 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.31534 | 0.232691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.24621 | −0.575940 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.75379 | −0.260906 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0540 | 0.967516 | 0.483758 | − | 0.875202i | \(-0.339272\pi\) | ||||
0.483758 | + | 0.875202i | \(0.339272\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.4924 | 0.855967 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.36932 | 0.0929553 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.06913 | 0.612835 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.56155 | 0.374111 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.36932 | −0.627416 | −0.313708 | − | 0.949520i | \(-0.601571\pi\) | ||||
−0.313708 | + | 0.949520i | \(0.601571\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.561553 | −0.0374369 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.6847 | 1.10740 | 0.553700 | − | 0.832716i | \(-0.313216\pi\) | ||||
0.553700 | + | 0.832716i | \(0.313216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7386 | −1.37045 | −0.685224 | − | 0.728333i | \(-0.740296\pi\) | ||||
−0.685224 | + | 0.728333i | \(0.740296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.73863 | −0.180189 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.49242 | 0.425333 | 0.212666 | − | 0.977125i | \(-0.431785\pi\) | ||||
0.212666 | + | 0.977125i | \(0.431785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.12311 | −0.334195 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.87689 | 0.316788 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.8078 | −1.54000 | −0.769998 | − | 0.638046i | \(-0.779743\pi\) | ||||
−0.769998 | + | 0.638046i | \(0.779743\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.8617 | 1.79473 | 0.897366 | − | 0.441287i | \(-0.145478\pi\) | ||||
0.897366 | + | 0.441287i | \(0.145478\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.80776 | −0.434932 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.56155 | 0.0993592 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.8617 | −1.38543 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.2462 | −1.40417 | −0.702084 | − | 0.712094i | \(-0.747747\pi\) | ||||
−0.702084 | + | 0.712094i | \(0.747747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.7386 | 1.68104 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.56155 | −0.348278 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.63068 | −0.413611 | −0.206805 | − | 0.978382i | \(-0.566307\pi\) | ||||
−0.206805 | + | 0.978382i | \(0.566307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.12311 | −0.194060 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24621 | −0.262834 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.3693 | 0.947713 | 0.473856 | − | 0.880602i | \(-0.342862\pi\) | ||||
0.473856 | + | 0.880602i | \(0.342862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.43845 | −0.149793 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.6155 | 0.955655 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.75379 | 0.472757 | 0.236378 | − | 0.971661i | \(-0.424040\pi\) | ||||
0.236378 | + | 0.971661i | \(0.424040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1771 | 1.52940 | 0.764699 | − | 0.644387i | \(-0.222887\pi\) | ||||
0.764699 | + | 0.644387i | \(0.222887\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.06913 | −0.0647067 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | 0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.6155 | −1.29875 | −0.649376 | − | 0.760468i | \(-0.724970\pi\) | ||||
−0.649376 | + | 0.760468i | \(0.724970\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.75379 | −0.104997 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.75379 | 0.462552 | 0.231276 | − | 0.972888i | \(-0.425710\pi\) | ||||
0.231276 | + | 0.972888i | \(0.425710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.00000 | 0.356663 | 0.178331 | − | 0.983970i | \(-0.442930\pi\) | ||||
0.178331 | + | 0.983970i | \(0.442930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.56155 | −0.0924984 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.61553 | −0.213418 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.31534 | −0.253844 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.1231 | −0.652048 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.9309 | 1.33964 | 0.669818 | − | 0.742525i | \(-0.266372\pi\) | ||||
0.669818 | + | 0.742525i | \(0.266372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.80776 | 0.454586 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 22.2462 | 1.29086 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.4384 | 0.603671 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.876894 | 0.0505434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.00000 | 0.459588 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1231 | 0.751427 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.2462 | 1.26966 | 0.634829 | − | 0.772653i | \(-0.281070\pi\) | ||||
0.634829 | + | 0.772653i | \(0.281070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24.9848 | 1.42134 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.56155 | −0.542186 | −0.271093 | − | 0.962553i | \(-0.587385\pi\) | ||||
−0.271093 | + | 0.962553i | \(0.587385\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1771 | 0.857859 | 0.428930 | − | 0.903338i | \(-0.358891\pi\) | ||||
0.428930 | + | 0.903338i | \(0.358891\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.246211 | −0.0138724 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.56155 | −0.537030 | −0.268515 | − | 0.963275i | \(-0.586533\pi\) | ||||
−0.268515 | + | 0.963275i | \(0.586533\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.2462 | 1.69346 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.06913 | 0.0596730 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.56155 | 0.198170 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.56155 | 0.0866194 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.3002 | 1.34380 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.24621 | −0.123838 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.80776 | −0.429154 | −0.214577 | − | 0.976707i | \(-0.568837\pi\) | ||||
−0.214577 | + | 0.976707i | \(0.568837\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.43845 | 0.351770 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.1231 | 1.25960 | 0.629798 | − | 0.776759i | \(-0.283138\pi\) | ||||
0.629798 | + | 0.776759i | \(0.283138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.0000 | −0.869001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.4924 | 0.676503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.05398 | −0.326884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.4384 | −0.561987 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0000 | 0.966291 | 0.483145 | − | 0.875540i | \(-0.339494\pi\) | ||||
0.483145 | + | 0.875540i | \(0.339494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.68466 | 0.463553 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.4233 | 1.35315 | 0.676573 | − | 0.736376i | \(-0.263464\pi\) | ||||
0.676573 | + | 0.736376i | \(0.263464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.00000 | −0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.43845 | −0.129056 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.9309 | −1.21025 | −0.605123 | − | 0.796132i | \(-0.706876\pi\) | ||||
−0.605123 | + | 0.796132i | \(0.706876\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.80776 | −0.409801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.80776 | −0.303992 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.8769 | 1.40296 | 0.701481 | − | 0.712688i | \(-0.252522\pi\) | ||||
0.701481 | + | 0.712688i | \(0.252522\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.63068 | 0.241064 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.06913 | −0.0555065 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.19224 | 0.217066 | 0.108533 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108533 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.56155 | −0.0806382 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.8078 | 0.608131 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.6847 | −1.06250 | −0.531250 | − | 0.847215i | \(-0.678277\pi\) | ||||
−0.531250 | + | 0.847215i | \(0.678277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.6307 | −0.749553 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.7386 | −1.16189 | −0.580945 | − | 0.813943i | \(-0.697317\pi\) | ||||
−0.580945 | + | 0.813943i | \(0.697317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.75379 | 0.0893814 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.12311 | −0.0570907 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.12311 | 0.0569437 | 0.0284719 | − | 0.999595i | \(-0.490936\pi\) | ||||
0.0284719 | + | 0.999595i | \(0.490936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.8078 | 1.20401 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.9848 | −1.26032 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.12311 | −0.157140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.8617 | 1.59909 | 0.799547 | − | 0.600603i | \(-0.205073\pi\) | ||||
0.799547 | + | 0.600603i | \(0.205073\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.684658 | −0.0342758 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.7386 | 1.43514 | 0.717569 | − | 0.696487i | \(-0.245255\pi\) | ||||
0.717569 | + | 0.696487i | \(0.245255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.87689 | 0.242935 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.4924 | −1.41232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.7386 | −1.22325 | −0.611623 | − | 0.791149i | \(-0.709483\pi\) | ||||
−0.611623 | + | 0.791149i | \(0.709483\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.8078 | −1.37166 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.42329 | 0.168449 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.0000 | 0.687233 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.2462 | −1.08940 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1231 | 1.52046 | 0.760232 | − | 0.649652i | \(-0.225085\pi\) | ||||
0.760232 | + | 0.649652i | \(0.225085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.3002 | 1.67169 | 0.835844 | − | 0.548966i | \(-0.184979\pi\) | ||||
0.835844 | + | 0.548966i | \(0.184979\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.87689 | 0.139879 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.56155 | 0.172761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.75379 | 0.278445 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.75379 | −0.470917 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.4924 | −0.601739 | −0.300869 | − | 0.953665i | \(-0.597277\pi\) | ||||
−0.300869 | + | 0.953665i | \(0.597277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.8078 | −0.566139 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.68466 | 0.319771 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.63068 | 0.316465 | 0.158233 | − | 0.987402i | \(-0.449420\pi\) | ||||
0.158233 | + | 0.987402i | \(0.449420\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.82292 | 0.182044 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.6155 | 1.40708 | 0.703538 | − | 0.710658i | \(-0.251602\pi\) | ||||
0.703538 | + | 0.710658i | \(0.251602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | −0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.00000 | −0.378387 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.7386 | −1.54503 | −0.772516 | − | 0.634996i | \(-0.781002\pi\) | ||||
−0.772516 | + | 0.634996i | \(0.781002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.9848 | −1.55320 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.61553 | −0.357809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.684658 | 0.0320973 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.4384 | 0.581846 | 0.290923 | − | 0.956746i | \(-0.406038\pi\) | ||||
0.290923 | + | 0.956746i | \(0.406038\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.8078 | 0.924547 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.75379 | −0.361130 | −0.180565 | − | 0.983563i | \(-0.557793\pi\) | ||||
−0.180565 | + | 0.983563i | \(0.557793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.8617 | 1.66664 | 0.833318 | − | 0.552794i | \(-0.186438\pi\) | ||||
0.833318 | + | 0.552794i | \(0.186438\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.87689 | −0.226161 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.8617 | −1.28929 | −0.644644 | − | 0.764483i | \(-0.722994\pi\) | ||||
−0.644644 | + | 0.764483i | \(0.722994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.82292 | 0.130350 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.36932 | 0.431715 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000 | 0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.36932 | 0.0626967 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.1231 | −0.507170 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.57671 | −0.208247 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.12311 | 0.323444 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.63068 | 0.119208 | 0.0596038 | − | 0.998222i | \(-0.481016\pi\) | ||||
0.0596038 | + | 0.998222i | \(0.481016\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31.6155 | 1.42970 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.1231 | 0.501979 | 0.250989 | − | 0.967990i | \(-0.419244\pi\) | ||||
0.250989 | + | 0.967990i | \(0.419244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.9309 | 1.21291 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.24621 | −0.100960 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.50758 | −0.157336 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.8769 | −0.934578 | −0.467289 | − | 0.884105i | \(-0.654769\pi\) | ||||
−0.467289 | + | 0.884105i | \(0.654769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.38447 | −0.374591 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4233 | 1.13357 | 0.566784 | − | 0.823866i | \(-0.308187\pi\) | ||||
0.566784 | + | 0.823866i | \(0.308187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.12311 | −0.227975 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.4924 | 0.732454 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.00000 | 0.0886484 | 0.0443242 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443242 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.54640 | −0.112646 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56155 | 0.245549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.0000 | −0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4924 | −0.901256 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.3693 | 0.762428 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.12311 | −0.0492042 | −0.0246021 | − | 0.999697i | \(-0.507832\pi\) | ||||
−0.0246021 | + | 0.999697i | \(0.507832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.9309 | −0.652881 | −0.326441 | − | 0.945218i | \(-0.605849\pi\) | ||||
−0.326441 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.684658 | −0.0298809 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.1231 | 0.484530 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.6847 | 0.942811 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.38447 | −0.190270 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.8769 | −0.557760 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.684658 | −0.0296004 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.50758 | −0.151363 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.2311 | −1.17292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.1231 | 1.08013 | 0.540063 | − | 0.841624i | \(-0.318400\pi\) | ||||
0.540063 | + | 0.841624i | \(0.318400\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 37.8617 | 1.62480 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.5616 | −0.666584 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.2462 | 1.63529 | 0.817645 | − | 0.575723i | \(-0.195279\pi\) | ||||
0.817645 | + | 0.575723i | \(0.195279\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.36932 | −0.314515 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.56155 | 0.322133 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.36932 | −0.0582293 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.1231 | 0.472150 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.63068 | −0.196208 | −0.0981042 | − | 0.995176i | \(-0.531278\pi\) | ||||
−0.0981042 | + | 0.995176i | \(0.531278\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.12311 | 0.132093 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.2462 | −0.939236 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.7386 | 0.789739 | 0.394870 | − | 0.918737i | \(-0.370790\pi\) | ||||
0.394870 | + | 0.918737i | \(0.370790\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2462 | 0.431061 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.06913 | −0.128891 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.12311 | −0.382460 | −0.191230 | − | 0.981545i | \(-0.561248\pi\) | ||||
−0.191230 | + | 0.981545i | \(0.561248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.63068 | −0.110091 | −0.0550453 | − | 0.998484i | \(-0.517530\pi\) | ||||
−0.0550453 | + | 0.998484i | \(0.517530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.0540 | −1.08842 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.68466 | 0.278770 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.4233 | −1.39143 | −0.695715 | − | 0.718318i | \(-0.744912\pi\) | ||||
−0.695715 | + | 0.718318i | \(0.744912\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.36932 | −0.0569069 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.13826 | 0.254658 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.75379 | −0.403961 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.876894 | −0.0362551 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.2462 | 1.33094 | 0.665472 | − | 0.746423i | \(-0.268230\pi\) | ||||
0.665472 | + | 0.746423i | \(0.268230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.12311 | 0.128685 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.1080 | −0.498055 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.24621 | 0.338631 | 0.169316 | − | 0.985562i | \(-0.445844\pi\) | ||||
0.169316 | + | 0.985562i | \(0.445844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.56155 | 0.0640174 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.9309 | 0.611080 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.6155 | −1.29178 | −0.645888 | − | 0.763432i | \(-0.723513\pi\) | ||||
−0.645888 | + | 0.763432i | \(0.723513\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.738634 | 0.0301295 | 0.0150647 | − | 0.999887i | \(-0.495205\pi\) | ||||
0.0150647 | + | 0.999887i | \(0.495205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.61553 | −0.147236 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.876894 | −0.0355920 | −0.0177960 | − | 0.999842i | \(-0.505665\pi\) | ||||
−0.0177960 | + | 0.999842i | \(0.505665\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.17708 | −0.209786 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6307 | 0.671707 | 0.335853 | − | 0.941914i | \(-0.390975\pi\) | ||||
0.335853 | + | 0.941914i | \(0.390975\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.8769 | 0.519246 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.9848 | −1.73050 | −0.865252 | − | 0.501337i | \(-0.832842\pi\) | ||||
−0.865252 | + | 0.501337i | \(0.832842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.2462 | −0.572604 | −0.286302 | − | 0.958139i | \(-0.592426\pi\) | ||||
−0.286302 | + | 0.958139i | \(0.592426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.1771 | 1.49186 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.38447 | −0.175660 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.24621 | −0.249450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.3693 | −1.01154 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7386 | 0.905211 | 0.452605 | − | 0.891711i | \(-0.350495\pi\) | ||||
0.452605 | + | 0.891711i | \(0.350495\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.9460 | −0.872276 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.36932 | 0.371810 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.6307 | −0.421203 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.49242 | 0.177717 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12311 | 0.0443600 | 0.0221800 | − | 0.999754i | \(-0.492939\pi\) | ||||
0.0221800 | + | 0.999754i | \(0.492939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.4924 | 0.729270 | 0.364635 | − | 0.931151i | \(-0.381194\pi\) | ||||
0.364635 | + | 0.931151i | \(0.381194\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.12311 | −0.122972 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.31534 | −0.208968 | −0.104484 | − | 0.994527i | \(-0.533319\pi\) | ||||
−0.104484 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.2311 | 1.22593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.13826 | −0.0838050 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.6307 | −0.807341 | −0.403671 | − | 0.914904i | \(-0.632266\pi\) | ||||
−0.403671 | + | 0.914904i | \(0.632266\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.0000 | 0.625172 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.26137 | 0.127238 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.8078 | −1.86233 | −0.931163 | − | 0.364603i | \(-0.881205\pi\) | ||||
−0.931163 | + | 0.364603i | \(0.881205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.93087 | 0.347371 | 0.173685 | − | 0.984801i | \(-0.444432\pi\) | ||||
0.173685 | + | 0.984801i | \(0.444432\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.68466 | −0.337284 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.438447 | 0.0170023 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.5464 | 1.95716 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.6307 | 0.565655 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 52.4924 | 2.02645 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.50758 | −0.135207 | −0.0676036 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676036 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.56155 | 0.214064 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.8078 | −1.37620 | −0.688102 | − | 0.725614i | \(-0.741556\pi\) | ||||
−0.688102 | + | 0.725614i | \(0.741556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.12311 | 0.119854 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.0540 | −0.998391 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.7538 | −0.679330 | −0.339665 | − | 0.940547i | \(-0.610314\pi\) | ||||
−0.339665 | + | 0.940547i | \(0.610314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.8078 | 0.680400 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.3845 | 1.23554 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.80776 | −0.145064 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.1080 | −1.52578 | −0.762889 | − | 0.646529i | \(-0.776220\pi\) | ||||
−0.762889 | + | 0.646529i | \(0.776220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.984845 | −0.0374112 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.2462 | 0.540390 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.3693 | −1.11244 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.1383 | −0.383464 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.87689 | −0.108659 | −0.0543294 | − | 0.998523i | \(-0.517302\pi\) | ||||
−0.0543294 | + | 0.998523i | \(0.517302\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.12311 | −0.268653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.24621 | −0.0844775 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.0000 | 0.976450 | 0.488225 | − | 0.872718i | \(-0.337644\pi\) | ||||
0.488225 | + | 0.872718i | \(0.337644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.75379 | 0.0657722 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.8769 | 0.781846 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.24621 | 0.233595 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 37.1771 | 1.38840 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.4233 | 1.02272 | 0.511358 | − | 0.859368i | \(-0.329143\pi\) | ||||
0.511358 | + | 0.859368i | \(0.329143\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.01515 | −0.261258 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −43.5076 | −1.61806 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.56155 | 0.280829 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.31534 | −0.0487833 | −0.0243917 | − | 0.999702i | \(-0.507765\pi\) | ||||
−0.0243917 | + | 0.999702i | \(0.507765\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.12311 | 0.263458 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.6155 | 1.68485 | 0.842424 | − | 0.538815i | \(-0.181128\pi\) | ||||
0.842424 | + | 0.538815i | \(0.181128\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.6307 | 0.392119 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7538 | 0.948653 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.87689 | −0.326542 | −0.163271 | − | 0.986581i | \(-0.552204\pi\) | ||||
−0.163271 | + | 0.986581i | \(0.552204\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.43845 | −0.0895786 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6307 | −0.390002 | −0.195001 | − | 0.980803i | \(-0.562471\pi\) | ||||
−0.195001 | + | 0.980803i | \(0.562471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.12311 | 0.187696 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.86174 | −0.287646 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.300187 | −0.0109686 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.63068 | 0.241957 | 0.120979 | − | 0.992655i | \(-0.461397\pi\) | ||||
0.120979 | + | 0.992655i | \(0.461397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.7386 | 1.26595 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.87689 | 0.177488 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.7386 | −1.33529 | −0.667644 | − | 0.744481i | \(-0.732697\pi\) | ||||
−0.667644 | + | 0.744481i | \(0.732697\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −41.7538 | −1.51557 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.6847 | 1.11232 | 0.556159 | − | 0.831076i | \(-0.312275\pi\) | ||||
0.556159 | + | 0.831076i | \(0.312275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.82292 | −0.247006 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | −0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.1922 | 0.440236 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.17708 | −0.258812 | −0.129406 | − | 0.991592i | \(-0.541307\pi\) | ||||
−0.129406 | + | 0.991592i | \(0.541307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3542 | 0.372896 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.1771 | 0.905557 | 0.452778 | − | 0.891623i | \(-0.350433\pi\) | ||||
0.452778 | + | 0.891623i | \(0.350433\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.12311 | 0.112185 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.87689 | 0.174958 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.24621 | −0.295451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.0540 | 1.50289 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.00000 | −0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.05398 | −0.0732163 | −0.0366082 | − | 0.999330i | \(-0.511655\pi\) | ||||
−0.0366082 | + | 0.999330i | \(0.511655\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24.0000 | −0.854423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.49242 | 0.159732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.4924 | 0.727707 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.80776 | 0.135047 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.19224 | −0.148497 | −0.0742483 | − | 0.997240i | \(-0.523656\pi\) | ||||
−0.0742483 | + | 0.997240i | \(0.523656\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.2462 | −0.645505 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.61553 | 0.198415 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.2311 | −0.819806 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.93087 | 0.103300 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.1080 | −0.426220 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0691 | 0.389170 | 0.194585 | − | 0.980886i | \(-0.437664\pi\) | ||||
0.194585 | + | 0.980886i | \(0.437664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.0388 | −1.93267 | −0.966337 | − | 0.257279i | \(-0.917174\pi\) | ||||
−0.966337 | + | 0.257279i | \(0.917174\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.3153 | −1.37885 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.2462 | −0.709194 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | 0.0699711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.384472 | −0.0134345 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.1231 | −0.458000 | −0.229000 | − | 0.973426i | \(-0.573546\pi\) | ||||
−0.229000 | + | 0.973426i | \(0.573546\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.4233 | −1.44393 | −0.721963 | − | 0.691932i | \(-0.756760\pi\) | ||||
−0.721963 | + | 0.691932i | \(0.756760\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.24621 | −0.217465 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.94602 | 0.0676699 | 0.0338350 | − | 0.999427i | \(-0.489228\pi\) | ||||
0.0338350 | + | 0.999427i | \(0.489228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47.5616 | −1.65188 | −0.825941 | − | 0.563757i | \(-0.809355\pi\) | ||||
−0.825941 | + | 0.563757i | \(0.809355\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.7538 | 1.17091 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.2462 | −0.840081 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.36932 | 0.185813 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.3693 | 0.600371 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.2311 | −1.63060 | −0.815299 | − | 0.579041i | \(-0.803427\pi\) | ||||
−0.815299 | + | 0.579041i | \(0.803427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1771 | 0.971623 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12.1080 | −0.417020 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.5616 | −0.363328 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.19224 | 0.0753261 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.36932 | −0.321554 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.6155 | −1.63224 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.73863 | −0.162248 | −0.0811239 | − | 0.996704i | \(-0.525851\pi\) | ||||
−0.0811239 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.561553 | −0.0192047 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.9848 | 1.40002 | 0.700008 | − | 0.714135i | \(-0.253180\pi\) | ||||
0.700008 | + | 0.714135i | \(0.253180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.7386 | 1.86766 | 0.933829 | − | 0.357720i | \(-0.116446\pi\) | ||||
0.933829 | + | 0.357720i | \(0.116446\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.64584 | 0.192410 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.4773 | −1.68423 | −0.842113 | − | 0.539301i | \(-0.818688\pi\) | ||||
−0.842113 | + | 0.539301i | \(0.818688\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1231 | −0.378197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.73863 | 0.228856 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.4924 | −0.423776 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0540 | 0.340666 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | −0.135379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.438447 | 0.0148222 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.19224 | 0.141562 | 0.0707809 | − | 0.997492i | \(-0.477451\pi\) | ||||
0.0707809 | + | 0.997492i | \(0.477451\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −35.8078 | −1.20777 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.49242 | 0.218735 | 0.109368 | − | 0.994001i | \(-0.465117\pi\) | ||||
0.109368 | + | 0.994001i | \(0.465117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.2462 | −1.21978 | −0.609891 | − | 0.792485i | \(-0.708787\pi\) | ||||
−0.609891 | + | 0.792485i | \(0.708787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.1922 | −0.409838 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.0000 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.10795 | 0.137776 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.0000 | −0.938035 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.12311 | −0.171438 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.24621 | 0.0750826 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.3002 | −0.544247 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.6155 | 0.787622 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.68466 | −0.289328 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.36932 | −0.0455680 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.2462 | −0.805971 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.4233 | −0.644940 | −0.322470 | − | 0.946580i | \(-0.604513\pi\) | ||||
−0.322470 | + | 0.946580i | \(0.604513\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.87689 | 0.0954206 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.7386 | 0.885890 | 0.442945 | − | 0.896549i | \(-0.353934\pi\) | ||||
0.442945 | + | 0.896549i | \(0.353934\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.0000 | 1.85333 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.4924 | −0.677459 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.01515 | 0.231661 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.192236 | −0.00634128 | −0.00317064 | − | 0.999995i | \(-0.501009\pi\) | ||||
−0.00317064 | + | 0.999995i | \(0.501009\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.7386 | −1.14468 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.4924 | −0.411193 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.12311 | −0.234206 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.98485 | 0.295101 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.0540 | 1.05166 | 0.525828 | − | 0.850591i | \(-0.323755\pi\) | ||||
0.525828 | + | 0.850591i | \(0.323755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.80776 | −0.223115 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.9309 | 0.488815 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.2462 | 0.465901 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.0540 | −0.655135 | −0.327567 | − | 0.944828i | \(-0.606229\pi\) | ||||
−0.327567 | + | 0.944828i | \(0.606229\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.6998 | −0.773414 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6847 | −0.869895 | −0.434948 | − | 0.900456i | \(-0.643233\pi\) | ||||
−0.434948 | + | 0.900456i | \(0.643233\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55.1231 | −1.79506 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.43845 | 0.0793227 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.63068 | 0.280460 | 0.140230 | − | 0.990119i | \(-0.455216\pi\) | ||||
0.140230 | + | 0.990119i | \(0.455216\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.06913 | −0.294396 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.9309 | 0.484167 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.2311 | −1.01167 | −0.505837 | − | 0.862629i | \(-0.668816\pi\) | ||||
−0.505837 | + | 0.862629i | \(0.668816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.6847 | 0.539903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.2311 | −1.52676 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.80776 | 0.252126 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2462 | −0.685362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.384472 | 0.0123894 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.876894 | 0.0282282 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.8769 | 0.992934 | 0.496467 | − | 0.868056i | \(-0.334630\pi\) | ||||
0.496467 | + | 0.868056i | \(0.334630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.56155 | −0.178663 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.9848 | 1.70036 | 0.850182 | − | 0.526488i | \(-0.176492\pi\) | ||||
0.850182 | + | 0.526488i | \(0.176492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.24621 | 0.200244 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.43845 | −0.0780928 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.12311 | −0.0999170 | −0.0499585 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499585 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.0000 | −1.27841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.73863 | 0.279003 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.6155 | −0.370478 | −0.185239 | − | 0.982694i | \(-0.559306\pi\) | ||||
−0.185239 | + | 0.982694i | \(0.559306\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.75379 | 0.247056 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.50758 | 0.111647 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.3693 | 0.425120 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.8769 | 0.409048 | 0.204524 | − | 0.978862i | \(-0.434435\pi\) | ||||
0.204524 | + | 0.978862i | \(0.434435\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.1922 | 0.386909 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.56155 | −0.303122 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.24621 | 0.261160 | 0.130580 | − | 0.991438i | \(-0.458316\pi\) | ||||
0.130580 | + | 0.991438i | \(0.458316\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −39.6155 | −1.25338 |
(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 | 6080.2.a.bi.1.1 | 2 | ||
4.3 | odd | 2 | 6080.2.a.bc.1.2 | 2 | |||
8.3 | odd | 2 | 3040.2.a.h.1.1 | yes | 2 | ||
8.5 | even | 2 | 3040.2.a.e.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3040.2.a.e.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
3040.2.a.h.1.1 | yes | 2 | 8.3 | odd | 2 | ||
6080.2.a.bc.1.2 | 2 | 4.3 | odd | 2 | |||
6080.2.a.bi.1.1 | 2 | 1.1 | even | 1 | trivial |