Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73205 | −1.93185 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.46410 | 2.73205 | ||||||||
\(5\) | −3.73205 | −1.66902 | −0.834512 | − | 0.550990i | \(-0.814250\pi\) | ||||
−0.834512 | + | 0.550990i | \(0.814250\pi\) | |||||||
\(6\) | 2.73205 | 1.11536 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.46410 | −3.34607 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 10.1962 | 3.22431 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −5.46410 | −1.57735 | ||||||||
\(13\) | 0.732051 | 0.203034 | 0.101517 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101517 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(14\) | −2.73205 | −0.730171 | ||||||||
\(15\) | 3.73205 | 0.963611 | ||||||||
\(16\) | 14.9282 | 3.73205 | ||||||||
\(17\) | 0.267949 | 0.0649872 | 0.0324936 | − | 0.999472i | \(-0.489655\pi\) | ||||
0.0324936 | + | 0.999472i | \(0.489655\pi\) | |||||||
\(18\) | −2.73205 | −0.643951 | ||||||||
\(19\) | −8.19615 | −1.88033 | −0.940163 | − | 0.340725i | \(-0.889328\pi\) | ||||
−0.940163 | + | 0.340725i | \(0.889328\pi\) | |||||||
\(20\) | −20.3923 | −4.55986 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.73205 | 1.40373 | 0.701865 | − | 0.712310i | \(-0.252351\pi\) | ||||
0.701865 | + | 0.712310i | \(0.252351\pi\) | |||||||
\(24\) | 9.46410 | 1.93185 | ||||||||
\(25\) | 8.92820 | 1.78564 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.46410 | 1.03262 | ||||||||
\(29\) | −4.73205 | −0.878720 | −0.439360 | − | 0.898311i | \(-0.644795\pi\) | ||||
−0.439360 | + | 0.898311i | \(0.644795\pi\) | |||||||
\(30\) | −10.1962 | −1.86155 | ||||||||
\(31\) | 0.535898 | 0.0962502 | 0.0481251 | − | 0.998841i | \(-0.484675\pi\) | ||||
0.0481251 | + | 0.998841i | \(0.484675\pi\) | |||||||
\(32\) | −21.8564 | −3.86370 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.732051 | −0.125546 | ||||||||
\(35\) | −3.73205 | −0.630832 | ||||||||
\(36\) | 5.46410 | 0.910684 | ||||||||
\(37\) | −2.53590 | −0.416899 | −0.208450 | − | 0.978033i | \(-0.566842\pi\) | ||||
−0.208450 | + | 0.978033i | \(0.566842\pi\) | |||||||
\(38\) | 22.3923 | 3.63251 | ||||||||
\(39\) | −0.732051 | −0.117222 | ||||||||
\(40\) | 35.3205 | 5.58466 | ||||||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 2.73205 | 0.421565 | ||||||||
\(43\) | 6.46410 | 0.985766 | 0.492883 | − | 0.870096i | \(-0.335943\pi\) | ||||
0.492883 | + | 0.870096i | \(0.335943\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.73205 | −0.556341 | ||||||||
\(46\) | −18.3923 | −2.71180 | ||||||||
\(47\) | 1.19615 | 0.174477 | 0.0872384 | − | 0.996187i | \(-0.472196\pi\) | ||||
0.0872384 | + | 0.996187i | \(0.472196\pi\) | |||||||
\(48\) | −14.9282 | −2.15470 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −24.3923 | −3.44959 | ||||||||
\(51\) | −0.267949 | −0.0375204 | ||||||||
\(52\) | 4.00000 | 0.554700 | ||||||||
\(53\) | 9.46410 | 1.29999 | 0.649997 | − | 0.759937i | \(-0.274770\pi\) | ||||
0.649997 | + | 0.759937i | \(0.274770\pi\) | |||||||
\(54\) | 2.73205 | 0.371785 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −9.46410 | −1.26469 | ||||||||
\(57\) | 8.19615 | 1.08561 | ||||||||
\(58\) | 12.9282 | 1.69756 | ||||||||
\(59\) | 14.1244 | 1.83883 | 0.919417 | − | 0.393284i | \(-0.128661\pi\) | ||||
0.919417 | + | 0.393284i | \(0.128661\pi\) | |||||||
\(60\) | 20.3923 | 2.63264 | ||||||||
\(61\) | 2.19615 | 0.281189 | 0.140594 | − | 0.990067i | \(-0.455099\pi\) | ||||
0.140594 | + | 0.990067i | \(0.455099\pi\) | |||||||
\(62\) | −1.46410 | −0.185941 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 29.8564 | 3.73205 | ||||||||
\(65\) | −2.73205 | −0.338869 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | −0.855186 | −0.427593 | − | 0.903971i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(68\) | 1.46410 | 0.177548 | ||||||||
\(69\) | −6.73205 | −0.810444 | ||||||||
\(70\) | 10.1962 | 1.21867 | ||||||||
\(71\) | −15.1244 | −1.79493 | −0.897465 | − | 0.441085i | \(-0.854594\pi\) | ||||
−0.897465 | + | 0.441085i | \(0.854594\pi\) | |||||||
\(72\) | −9.46410 | −1.11536 | ||||||||
\(73\) | 3.26795 | 0.382485 | 0.191242 | − | 0.981543i | \(-0.438748\pi\) | ||||
0.191242 | + | 0.981543i | \(0.438748\pi\) | |||||||
\(74\) | 6.92820 | 0.805387 | ||||||||
\(75\) | −8.92820 | −1.03094 | ||||||||
\(76\) | −44.7846 | −5.13715 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | 7.46410 | 0.839777 | 0.419889 | − | 0.907576i | \(-0.362069\pi\) | ||||
0.419889 | + | 0.907576i | \(0.362069\pi\) | |||||||
\(80\) | −55.7128 | −6.22888 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.9282 | 1.20682 | ||||||||
\(83\) | −7.73205 | −0.848703 | −0.424351 | − | 0.905498i | \(-0.639498\pi\) | ||||
−0.424351 | + | 0.905498i | \(0.639498\pi\) | |||||||
\(84\) | −5.46410 | −0.596182 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | −17.6603 | −1.90435 | ||||||||
\(87\) | 4.73205 | 0.507329 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.66025 | 0.281986 | 0.140993 | − | 0.990011i | \(-0.454970\pi\) | ||||
0.140993 | + | 0.990011i | \(0.454970\pi\) | |||||||
\(90\) | 10.1962 | 1.07477 | ||||||||
\(91\) | 0.732051 | 0.0767398 | ||||||||
\(92\) | 36.7846 | 3.83506 | ||||||||
\(93\) | −0.535898 | −0.0555701 | ||||||||
\(94\) | −3.26795 | −0.337063 | ||||||||
\(95\) | 30.5885 | 3.13831 | ||||||||
\(96\) | 21.8564 | 2.23071 | ||||||||
\(97\) | 6.73205 | 0.683536 | 0.341768 | − | 0.939784i | \(-0.388974\pi\) | ||||
0.341768 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(98\) | −2.73205 | −0.275979 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 48.7846 | 4.87846 | ||||||||
\(101\) | −6.26795 | −0.623684 | −0.311842 | − | 0.950134i | \(-0.600946\pi\) | ||||
−0.311842 | + | 0.950134i | \(0.600946\pi\) | |||||||
\(102\) | 0.732051 | 0.0724838 | ||||||||
\(103\) | −6.19615 | −0.610525 | −0.305263 | − | 0.952268i | \(-0.598744\pi\) | ||||
−0.305263 | + | 0.952268i | \(0.598744\pi\) | |||||||
\(104\) | −6.92820 | −0.679366 | ||||||||
\(105\) | 3.73205 | 0.364211 | ||||||||
\(106\) | −25.8564 | −2.51140 | ||||||||
\(107\) | 12.5885 | 1.21697 | 0.608486 | − | 0.793565i | \(-0.291777\pi\) | ||||
0.608486 | + | 0.793565i | \(0.291777\pi\) | |||||||
\(108\) | −5.46410 | −0.525783 | ||||||||
\(109\) | 3.39230 | 0.324924 | 0.162462 | − | 0.986715i | \(-0.448057\pi\) | ||||
0.162462 | + | 0.986715i | \(0.448057\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.53590 | 0.240697 | ||||||||
\(112\) | 14.9282 | 1.41058 | ||||||||
\(113\) | 15.4641 | 1.45474 | 0.727370 | − | 0.686245i | \(-0.240742\pi\) | ||||
0.727370 | + | 0.686245i | \(0.240742\pi\) | |||||||
\(114\) | −22.3923 | −2.09723 | ||||||||
\(115\) | −25.1244 | −2.34286 | ||||||||
\(116\) | −25.8564 | −2.40071 | ||||||||
\(117\) | 0.732051 | 0.0676781 | ||||||||
\(118\) | −38.5885 | −3.55236 | ||||||||
\(119\) | 0.267949 | 0.0245629 | ||||||||
\(120\) | −35.3205 | −3.22431 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −6.00000 | −0.543214 | ||||||||
\(123\) | 4.00000 | 0.360668 | ||||||||
\(124\) | 2.92820 | 0.262960 | ||||||||
\(125\) | −14.6603 | −1.31125 | ||||||||
\(126\) | −2.73205 | −0.243390 | ||||||||
\(127\) | 10.4641 | 0.928539 | 0.464269 | − | 0.885694i | \(-0.346317\pi\) | ||||
0.464269 | + | 0.885694i | \(0.346317\pi\) | |||||||
\(128\) | −37.8564 | −3.34607 | ||||||||
\(129\) | −6.46410 | −0.569132 | ||||||||
\(130\) | 7.46410 | 0.654645 | ||||||||
\(131\) | 5.19615 | 0.453990 | 0.226995 | − | 0.973896i | \(-0.427110\pi\) | ||||
0.226995 | + | 0.973896i | \(0.427110\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.19615 | −0.710697 | ||||||||
\(134\) | 19.1244 | 1.65209 | ||||||||
\(135\) | 3.73205 | 0.321204 | ||||||||
\(136\) | −2.53590 | −0.217451 | ||||||||
\(137\) | −3.66025 | −0.312717 | −0.156358 | − | 0.987700i | \(-0.549975\pi\) | ||||
−0.156358 | + | 0.987700i | \(0.549975\pi\) | |||||||
\(138\) | 18.3923 | 1.56566 | ||||||||
\(139\) | −18.1962 | −1.54338 | −0.771689 | − | 0.636000i | \(-0.780588\pi\) | ||||
−0.771689 | + | 0.636000i | \(0.780588\pi\) | |||||||
\(140\) | −20.3923 | −1.72346 | ||||||||
\(141\) | −1.19615 | −0.100734 | ||||||||
\(142\) | 41.3205 | 3.46754 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 14.9282 | 1.24402 | ||||||||
\(145\) | 17.6603 | 1.46660 | ||||||||
\(146\) | −8.92820 | −0.738903 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −13.8564 | −1.13899 | ||||||||
\(149\) | −0.732051 | −0.0599719 | −0.0299860 | − | 0.999550i | \(-0.509546\pi\) | ||||
−0.0299860 | + | 0.999550i | \(0.509546\pi\) | |||||||
\(150\) | 24.3923 | 1.99162 | ||||||||
\(151\) | 11.3923 | 0.927093 | 0.463546 | − | 0.886073i | \(-0.346577\pi\) | ||||
0.463546 | + | 0.886073i | \(0.346577\pi\) | |||||||
\(152\) | 77.5692 | 6.29169 | ||||||||
\(153\) | 0.267949 | 0.0216624 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | −13.4641 | −1.07455 | −0.537276 | − | 0.843406i | \(-0.680547\pi\) | ||||
−0.537276 | + | 0.843406i | \(0.680547\pi\) | |||||||
\(158\) | −20.3923 | −1.62232 | ||||||||
\(159\) | −9.46410 | −0.750552 | ||||||||
\(160\) | 81.5692 | 6.44861 | ||||||||
\(161\) | 6.73205 | 0.530560 | ||||||||
\(162\) | −2.73205 | −0.214650 | ||||||||
\(163\) | 0.535898 | 0.0419748 | 0.0209874 | − | 0.999780i | \(-0.493319\pi\) | ||||
0.0209874 | + | 0.999780i | \(0.493319\pi\) | |||||||
\(164\) | −21.8564 | −1.70670 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.1244 | 1.63957 | ||||||||
\(167\) | 13.0526 | 1.01004 | 0.505019 | − | 0.863108i | \(-0.331486\pi\) | ||||
0.505019 | + | 0.863108i | \(0.331486\pi\) | |||||||
\(168\) | 9.46410 | 0.730171 | ||||||||
\(169\) | −12.4641 | −0.958777 | ||||||||
\(170\) | 2.73205 | 0.209539 | ||||||||
\(171\) | −8.19615 | −0.626775 | ||||||||
\(172\) | 35.3205 | 2.69316 | ||||||||
\(173\) | 5.19615 | 0.395056 | 0.197528 | − | 0.980297i | \(-0.436709\pi\) | ||||
0.197528 | + | 0.980297i | \(0.436709\pi\) | |||||||
\(174\) | −12.9282 | −0.980085 | ||||||||
\(175\) | 8.92820 | 0.674909 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.1244 | −1.06165 | ||||||||
\(178\) | −7.26795 | −0.544756 | ||||||||
\(179\) | 16.3923 | 1.22522 | 0.612609 | − | 0.790386i | \(-0.290120\pi\) | ||||
0.612609 | + | 0.790386i | \(0.290120\pi\) | |||||||
\(180\) | −20.3923 | −1.51995 | ||||||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | −2.19615 | −0.162344 | ||||||||
\(184\) | −63.7128 | −4.69697 | ||||||||
\(185\) | 9.46410 | 0.695815 | ||||||||
\(186\) | 1.46410 | 0.107353 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.53590 | 0.476679 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −83.5692 | −6.06275 | ||||||||
\(191\) | 5.80385 | 0.419952 | 0.209976 | − | 0.977707i | \(-0.432661\pi\) | ||||
0.209976 | + | 0.977707i | \(0.432661\pi\) | |||||||
\(192\) | −29.8564 | −2.15470 | ||||||||
\(193\) | 5.00000 | 0.359908 | 0.179954 | − | 0.983675i | \(-0.442405\pi\) | ||||
0.179954 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(194\) | −18.3923 | −1.32049 | ||||||||
\(195\) | 2.73205 | 0.195646 | ||||||||
\(196\) | 5.46410 | 0.390293 | ||||||||
\(197\) | −19.4641 | −1.38676 | −0.693380 | − | 0.720572i | \(-0.743879\pi\) | ||||
−0.693380 | + | 0.720572i | \(0.743879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.80385 | −0.694976 | −0.347488 | − | 0.937684i | \(-0.612965\pi\) | ||||
−0.347488 | + | 0.937684i | \(0.612965\pi\) | |||||||
\(200\) | −84.4974 | −5.97487 | ||||||||
\(201\) | 7.00000 | 0.493742 | ||||||||
\(202\) | 17.1244 | 1.20487 | ||||||||
\(203\) | −4.73205 | −0.332125 | ||||||||
\(204\) | −1.46410 | −0.102508 | ||||||||
\(205\) | 14.9282 | 1.04263 | ||||||||
\(206\) | 16.9282 | 1.17944 | ||||||||
\(207\) | 6.73205 | 0.467910 | ||||||||
\(208\) | 10.9282 | 0.757735 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −10.1962 | −0.703601 | ||||||||
\(211\) | −23.7846 | −1.63740 | −0.818700 | − | 0.574221i | \(-0.805305\pi\) | ||||
−0.818700 | + | 0.574221i | \(0.805305\pi\) | |||||||
\(212\) | 51.7128 | 3.55165 | ||||||||
\(213\) | 15.1244 | 1.03630 | ||||||||
\(214\) | −34.3923 | −2.35101 | ||||||||
\(215\) | −24.1244 | −1.64527 | ||||||||
\(216\) | 9.46410 | 0.643951 | ||||||||
\(217\) | 0.535898 | 0.0363792 | ||||||||
\(218\) | −9.26795 | −0.627705 | ||||||||
\(219\) | −3.26795 | −0.220828 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.196152 | 0.0131946 | ||||||||
\(222\) | −6.92820 | −0.464991 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | −21.8564 | −1.46034 | ||||||||
\(225\) | 8.92820 | 0.595214 | ||||||||
\(226\) | −42.2487 | −2.81034 | ||||||||
\(227\) | 2.66025 | 0.176567 | 0.0882836 | − | 0.996095i | \(-0.471862\pi\) | ||||
0.0882836 | + | 0.996095i | \(0.471862\pi\) | |||||||
\(228\) | 44.7846 | 2.96593 | ||||||||
\(229\) | −6.92820 | −0.457829 | −0.228914 | − | 0.973447i | \(-0.573518\pi\) | ||||
−0.228914 | + | 0.973447i | \(0.573518\pi\) | |||||||
\(230\) | 68.6410 | 4.52605 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 44.7846 | 2.94025 | ||||||||
\(233\) | −9.80385 | −0.642271 | −0.321136 | − | 0.947033i | \(-0.604065\pi\) | ||||
−0.321136 | + | 0.947033i | \(0.604065\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −4.46410 | −0.291206 | ||||||||
\(236\) | 77.1769 | 5.02379 | ||||||||
\(237\) | −7.46410 | −0.484846 | ||||||||
\(238\) | −0.732051 | −0.0474518 | ||||||||
\(239\) | −11.0718 | −0.716175 | −0.358087 | − | 0.933688i | \(-0.616571\pi\) | ||||
−0.358087 | + | 0.933688i | \(0.616571\pi\) | |||||||
\(240\) | 55.7128 | 3.59625 | ||||||||
\(241\) | 1.66025 | 0.106946 | 0.0534732 | − | 0.998569i | \(-0.482971\pi\) | ||||
0.0534732 | + | 0.998569i | \(0.482971\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.0000 | 0.768221 | ||||||||
\(245\) | −3.73205 | −0.238432 | ||||||||
\(246\) | −10.9282 | −0.696757 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | −5.07180 | −0.322059 | ||||||||
\(249\) | 7.73205 | 0.489999 | ||||||||
\(250\) | 40.0526 | 2.53315 | ||||||||
\(251\) | −14.9282 | −0.942260 | −0.471130 | − | 0.882064i | \(-0.656154\pi\) | ||||
−0.471130 | + | 0.882064i | \(0.656154\pi\) | |||||||
\(252\) | 5.46410 | 0.344206 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −28.5885 | −1.79380 | ||||||||
\(255\) | 1.00000 | 0.0626224 | ||||||||
\(256\) | 43.7128 | 2.73205 | ||||||||
\(257\) | −20.1244 | −1.25532 | −0.627661 | − | 0.778486i | \(-0.715988\pi\) | ||||
−0.627661 | + | 0.778486i | \(0.715988\pi\) | |||||||
\(258\) | 17.6603 | 1.09948 | ||||||||
\(259\) | −2.53590 | −0.157573 | ||||||||
\(260\) | −14.9282 | −0.925808 | ||||||||
\(261\) | −4.73205 | −0.292907 | ||||||||
\(262\) | −14.1962 | −0.877041 | ||||||||
\(263\) | −16.1962 | −0.998698 | −0.499349 | − | 0.866401i | \(-0.666427\pi\) | ||||
−0.499349 | + | 0.866401i | \(0.666427\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.3205 | −2.16972 | ||||||||
\(266\) | 22.3923 | 1.37296 | ||||||||
\(267\) | −2.66025 | −0.162805 | ||||||||
\(268\) | −38.2487 | −2.33641 | ||||||||
\(269\) | −3.85641 | −0.235129 | −0.117565 | − | 0.993065i | \(-0.537509\pi\) | ||||
−0.117565 | + | 0.993065i | \(0.537509\pi\) | |||||||
\(270\) | −10.1962 | −0.620518 | ||||||||
\(271\) | −24.3923 | −1.48173 | −0.740863 | − | 0.671656i | \(-0.765583\pi\) | ||||
−0.740863 | + | 0.671656i | \(0.765583\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | −0.732051 | −0.0443057 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −36.7846 | −2.21417 | ||||||||
\(277\) | −15.7846 | −0.948405 | −0.474203 | − | 0.880416i | \(-0.657264\pi\) | ||||
−0.474203 | + | 0.880416i | \(0.657264\pi\) | |||||||
\(278\) | 49.7128 | 2.98158 | ||||||||
\(279\) | 0.535898 | 0.0320834 | ||||||||
\(280\) | 35.3205 | 2.11080 | ||||||||
\(281\) | −27.7128 | −1.65321 | −0.826604 | − | 0.562784i | \(-0.809730\pi\) | ||||
−0.826604 | + | 0.562784i | \(0.809730\pi\) | |||||||
\(282\) | 3.26795 | 0.194604 | ||||||||
\(283\) | −22.2487 | −1.32255 | −0.661274 | − | 0.750144i | \(-0.729984\pi\) | ||||
−0.661274 | + | 0.750144i | \(0.729984\pi\) | |||||||
\(284\) | −82.6410 | −4.90384 | ||||||||
\(285\) | −30.5885 | −1.81190 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | −21.8564 | −1.28790 | ||||||||
\(289\) | −16.9282 | −0.995777 | ||||||||
\(290\) | −48.2487 | −2.83326 | ||||||||
\(291\) | −6.73205 | −0.394640 | ||||||||
\(292\) | 17.8564 | 1.04497 | ||||||||
\(293\) | 19.7321 | 1.15276 | 0.576379 | − | 0.817182i | \(-0.304465\pi\) | ||||
0.576379 | + | 0.817182i | \(0.304465\pi\) | |||||||
\(294\) | 2.73205 | 0.159336 | ||||||||
\(295\) | −52.7128 | −3.06906 | ||||||||
\(296\) | 24.0000 | 1.39497 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.00000 | 0.115857 | ||||||||
\(299\) | 4.92820 | 0.285005 | ||||||||
\(300\) | −48.7846 | −2.81658 | ||||||||
\(301\) | 6.46410 | 0.372585 | ||||||||
\(302\) | −31.1244 | −1.79101 | ||||||||
\(303\) | 6.26795 | 0.360084 | ||||||||
\(304\) | −122.354 | −7.01747 | ||||||||
\(305\) | −8.19615 | −0.469310 | ||||||||
\(306\) | −0.732051 | −0.0418486 | ||||||||
\(307\) | 4.58846 | 0.261877 | 0.130939 | − | 0.991390i | \(-0.458201\pi\) | ||||
0.130939 | + | 0.991390i | \(0.458201\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.19615 | 0.352487 | ||||||||
\(310\) | 5.46410 | 0.310340 | ||||||||
\(311\) | −19.0526 | −1.08037 | −0.540186 | − | 0.841546i | \(-0.681646\pi\) | ||||
−0.540186 | + | 0.841546i | \(0.681646\pi\) | |||||||
\(312\) | 6.92820 | 0.392232 | ||||||||
\(313\) | −20.3923 | −1.15264 | −0.576321 | − | 0.817224i | \(-0.695512\pi\) | ||||
−0.576321 | + | 0.817224i | \(0.695512\pi\) | |||||||
\(314\) | 36.7846 | 2.07588 | ||||||||
\(315\) | −3.73205 | −0.210277 | ||||||||
\(316\) | 40.7846 | 2.29431 | ||||||||
\(317\) | −15.5167 | −0.871502 | −0.435751 | − | 0.900067i | \(-0.643517\pi\) | ||||
−0.435751 | + | 0.900067i | \(0.643517\pi\) | |||||||
\(318\) | 25.8564 | 1.44996 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −111.426 | −6.22888 | ||||||||
\(321\) | −12.5885 | −0.702619 | ||||||||
\(322\) | −18.3923 | −1.02496 | ||||||||
\(323\) | −2.19615 | −0.122197 | ||||||||
\(324\) | 5.46410 | 0.303561 | ||||||||
\(325\) | 6.53590 | 0.362546 | ||||||||
\(326\) | −1.46410 | −0.0810891 | ||||||||
\(327\) | −3.39230 | −0.187595 | ||||||||
\(328\) | 37.8564 | 2.09027 | ||||||||
\(329\) | 1.19615 | 0.0659460 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −36.1769 | −1.98846 | −0.994232 | − | 0.107255i | \(-0.965794\pi\) | ||||
−0.994232 | + | 0.107255i | \(0.965794\pi\) | |||||||
\(332\) | −42.2487 | −2.31870 | ||||||||
\(333\) | −2.53590 | −0.138966 | ||||||||
\(334\) | −35.6603 | −1.95124 | ||||||||
\(335\) | 26.1244 | 1.42733 | ||||||||
\(336\) | −14.9282 | −0.814400 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 34.0526 | 1.85222 | ||||||||
\(339\) | −15.4641 | −0.839895 | ||||||||
\(340\) | −5.46410 | −0.296333 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 22.3923 | 1.21084 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −61.1769 | −3.29844 | ||||||||
\(345\) | 25.1244 | 1.35265 | ||||||||
\(346\) | −14.1962 | −0.763190 | ||||||||
\(347\) | 12.0526 | 0.647015 | 0.323508 | − | 0.946226i | \(-0.395138\pi\) | ||||
0.323508 | + | 0.946226i | \(0.395138\pi\) | |||||||
\(348\) | 25.8564 | 1.38605 | ||||||||
\(349\) | −22.3923 | −1.19863 | −0.599316 | − | 0.800512i | \(-0.704561\pi\) | ||||
−0.599316 | + | 0.800512i | \(0.704561\pi\) | |||||||
\(350\) | −24.3923 | −1.30382 | ||||||||
\(351\) | −0.732051 | −0.0390740 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.9282 | −1.32679 | −0.663397 | − | 0.748267i | \(-0.730886\pi\) | ||||
−0.663397 | + | 0.748267i | \(0.730886\pi\) | |||||||
\(354\) | 38.5885 | 2.05095 | ||||||||
\(355\) | 56.4449 | 2.99578 | ||||||||
\(356\) | 14.5359 | 0.770401 | ||||||||
\(357\) | −0.267949 | −0.0141814 | ||||||||
\(358\) | −44.7846 | −2.36694 | ||||||||
\(359\) | −0.875644 | −0.0462147 | −0.0231074 | − | 0.999733i | \(-0.507356\pi\) | ||||
−0.0231074 | + | 0.999733i | \(0.507356\pi\) | |||||||
\(360\) | 35.3205 | 1.86155 | ||||||||
\(361\) | 48.1769 | 2.53563 | ||||||||
\(362\) | 21.8564 | 1.14875 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −12.1962 | −0.638376 | ||||||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | −9.26795 | −0.483783 | −0.241892 | − | 0.970303i | \(-0.577768\pi\) | ||||
−0.241892 | + | 0.970303i | \(0.577768\pi\) | |||||||
\(368\) | 100.497 | 5.23879 | ||||||||
\(369\) | −4.00000 | −0.208232 | ||||||||
\(370\) | −25.8564 | −1.34421 | ||||||||
\(371\) | 9.46410 | 0.491352 | ||||||||
\(372\) | −2.92820 | −0.151820 | ||||||||
\(373\) | 10.0718 | 0.521498 | 0.260749 | − | 0.965407i | \(-0.416031\pi\) | ||||
0.260749 | + | 0.965407i | \(0.416031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.6603 | 0.757052 | ||||||||
\(376\) | −11.3205 | −0.583811 | ||||||||
\(377\) | −3.46410 | −0.178410 | ||||||||
\(378\) | 2.73205 | 0.140522 | ||||||||
\(379\) | 10.4641 | 0.537505 | 0.268752 | − | 0.963209i | \(-0.413389\pi\) | ||||
0.268752 | + | 0.963209i | \(0.413389\pi\) | |||||||
\(380\) | 167.138 | 8.57402 | ||||||||
\(381\) | −10.4641 | −0.536092 | ||||||||
\(382\) | −15.8564 | −0.811284 | ||||||||
\(383\) | −9.87564 | −0.504622 | −0.252311 | − | 0.967646i | \(-0.581191\pi\) | ||||
−0.252311 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(384\) | 37.8564 | 1.93185 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.6603 | −0.695289 | ||||||||
\(387\) | 6.46410 | 0.328589 | ||||||||
\(388\) | 36.7846 | 1.86746 | ||||||||
\(389\) | −4.39230 | −0.222699 | −0.111349 | − | 0.993781i | \(-0.535517\pi\) | ||||
−0.111349 | + | 0.993781i | \(0.535517\pi\) | |||||||
\(390\) | −7.46410 | −0.377959 | ||||||||
\(391\) | 1.80385 | 0.0912245 | ||||||||
\(392\) | −9.46410 | −0.478009 | ||||||||
\(393\) | −5.19615 | −0.262111 | ||||||||
\(394\) | 53.1769 | 2.67901 | ||||||||
\(395\) | −27.8564 | −1.40161 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.3205 | 1.07005 | 0.535023 | − | 0.844838i | \(-0.320303\pi\) | ||||
0.535023 | + | 0.844838i | \(0.320303\pi\) | |||||||
\(398\) | 26.7846 | 1.34259 | ||||||||
\(399\) | 8.19615 | 0.410321 | ||||||||
\(400\) | 133.282 | 6.66410 | ||||||||
\(401\) | −16.0000 | −0.799002 | −0.399501 | − | 0.916733i | \(-0.630817\pi\) | ||||
−0.399501 | + | 0.916733i | \(0.630817\pi\) | |||||||
\(402\) | −19.1244 | −0.953836 | ||||||||
\(403\) | 0.392305 | 0.0195421 | ||||||||
\(404\) | −34.2487 | −1.70394 | ||||||||
\(405\) | −3.73205 | −0.185447 | ||||||||
\(406\) | 12.9282 | 0.641616 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.53590 | 0.125546 | ||||||||
\(409\) | 6.33975 | 0.313480 | 0.156740 | − | 0.987640i | \(-0.449901\pi\) | ||||
0.156740 | + | 0.987640i | \(0.449901\pi\) | |||||||
\(410\) | −40.7846 | −2.01421 | ||||||||
\(411\) | 3.66025 | 0.180547 | ||||||||
\(412\) | −33.8564 | −1.66799 | ||||||||
\(413\) | 14.1244 | 0.695014 | ||||||||
\(414\) | −18.3923 | −0.903932 | ||||||||
\(415\) | 28.8564 | 1.41651 | ||||||||
\(416\) | −16.0000 | −0.784465 | ||||||||
\(417\) | 18.1962 | 0.891069 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.26795 | 0.306209 | 0.153105 | − | 0.988210i | \(-0.451073\pi\) | ||||
0.153105 | + | 0.988210i | \(0.451073\pi\) | |||||||
\(420\) | 20.3923 | 0.995043 | ||||||||
\(421\) | 11.1436 | 0.543106 | 0.271553 | − | 0.962424i | \(-0.412463\pi\) | ||||
0.271553 | + | 0.962424i | \(0.412463\pi\) | |||||||
\(422\) | 64.9808 | 3.16321 | ||||||||
\(423\) | 1.19615 | 0.0581589 | ||||||||
\(424\) | −89.5692 | −4.34987 | ||||||||
\(425\) | 2.39230 | 0.116044 | ||||||||
\(426\) | −41.3205 | −2.00199 | ||||||||
\(427\) | 2.19615 | 0.106279 | ||||||||
\(428\) | 68.7846 | 3.32483 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 65.9090 | 3.17841 | ||||||||
\(431\) | 11.3205 | 0.545290 | 0.272645 | − | 0.962115i | \(-0.412102\pi\) | ||||
0.272645 | + | 0.962115i | \(0.412102\pi\) | |||||||
\(432\) | −14.9282 | −0.718234 | ||||||||
\(433\) | −31.9090 | −1.53345 | −0.766724 | − | 0.641977i | \(-0.778114\pi\) | ||||
−0.766724 | + | 0.641977i | \(0.778114\pi\) | |||||||
\(434\) | −1.46410 | −0.0702791 | ||||||||
\(435\) | −17.6603 | −0.846744 | ||||||||
\(436\) | 18.5359 | 0.887709 | ||||||||
\(437\) | −55.1769 | −2.63947 | ||||||||
\(438\) | 8.92820 | 0.426606 | ||||||||
\(439\) | 27.8564 | 1.32951 | 0.664757 | − | 0.747060i | \(-0.268535\pi\) | ||||
0.664757 | + | 0.747060i | \(0.268535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −0.535898 | −0.0254901 | ||||||||
\(443\) | −16.1962 | −0.769502 | −0.384751 | − | 0.923020i | \(-0.625713\pi\) | ||||
−0.384751 | + | 0.923020i | \(0.625713\pi\) | |||||||
\(444\) | 13.8564 | 0.657596 | ||||||||
\(445\) | −9.92820 | −0.470642 | ||||||||
\(446\) | −43.7128 | −2.06986 | ||||||||
\(447\) | 0.732051 | 0.0346248 | ||||||||
\(448\) | 29.8564 | 1.41058 | ||||||||
\(449\) | 32.2487 | 1.52191 | 0.760955 | − | 0.648804i | \(-0.224731\pi\) | ||||
0.760955 | + | 0.648804i | \(0.224731\pi\) | |||||||
\(450\) | −24.3923 | −1.14986 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 84.4974 | 3.97442 | ||||||||
\(453\) | −11.3923 | −0.535257 | ||||||||
\(454\) | −7.26795 | −0.341102 | ||||||||
\(455\) | −2.73205 | −0.128081 | ||||||||
\(456\) | −77.5692 | −3.63251 | ||||||||
\(457\) | 20.0718 | 0.938919 | 0.469460 | − | 0.882954i | \(-0.344449\pi\) | ||||
0.469460 | + | 0.882954i | \(0.344449\pi\) | |||||||
\(458\) | 18.9282 | 0.884457 | ||||||||
\(459\) | −0.267949 | −0.0125068 | ||||||||
\(460\) | −137.282 | −6.40081 | ||||||||
\(461\) | −3.58846 | −0.167131 | −0.0835656 | − | 0.996502i | \(-0.526631\pi\) | ||||
−0.0835656 | + | 0.996502i | \(0.526631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.5359 | 1.14028 | 0.570140 | − | 0.821548i | \(-0.306889\pi\) | ||||
0.570140 | + | 0.821548i | \(0.306889\pi\) | |||||||
\(464\) | −70.6410 | −3.27943 | ||||||||
\(465\) | 2.00000 | 0.0927478 | ||||||||
\(466\) | 26.7846 | 1.24077 | ||||||||
\(467\) | −13.6077 | −0.629689 | −0.314845 | − | 0.949143i | \(-0.601952\pi\) | ||||
−0.314845 | + | 0.949143i | \(0.601952\pi\) | |||||||
\(468\) | 4.00000 | 0.184900 | ||||||||
\(469\) | −7.00000 | −0.323230 | ||||||||
\(470\) | 12.1962 | 0.562567 | ||||||||
\(471\) | 13.4641 | 0.620393 | ||||||||
\(472\) | −133.674 | −6.15286 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 20.3923 | 0.936650 | ||||||||
\(475\) | −73.1769 | −3.35759 | ||||||||
\(476\) | 1.46410 | 0.0671070 | ||||||||
\(477\) | 9.46410 | 0.433331 | ||||||||
\(478\) | 30.2487 | 1.38354 | ||||||||
\(479\) | 40.3731 | 1.84469 | 0.922346 | − | 0.386364i | \(-0.126269\pi\) | ||||
0.922346 | + | 0.386364i | \(0.126269\pi\) | |||||||
\(480\) | −81.5692 | −3.72311 | ||||||||
\(481\) | −1.85641 | −0.0846448 | ||||||||
\(482\) | −4.53590 | −0.206605 | ||||||||
\(483\) | −6.73205 | −0.306319 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.1244 | −1.14084 | ||||||||
\(486\) | 2.73205 | 0.123928 | ||||||||
\(487\) | −20.1769 | −0.914303 | −0.457152 | − | 0.889389i | \(-0.651130\pi\) | ||||
−0.457152 | + | 0.889389i | \(0.651130\pi\) | |||||||
\(488\) | −20.7846 | −0.940875 | ||||||||
\(489\) | −0.535898 | −0.0242342 | ||||||||
\(490\) | 10.1962 | 0.460615 | ||||||||
\(491\) | −38.0526 | −1.71729 | −0.858644 | − | 0.512572i | \(-0.828693\pi\) | ||||
−0.858644 | + | 0.512572i | \(0.828693\pi\) | |||||||
\(492\) | 21.8564 | 0.985363 | ||||||||
\(493\) | −1.26795 | −0.0571056 | ||||||||
\(494\) | 16.3923 | 0.737525 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −15.1244 | −0.678420 | ||||||||
\(498\) | −21.1244 | −0.946605 | ||||||||
\(499\) | 5.67949 | 0.254249 | 0.127124 | − | 0.991887i | \(-0.459425\pi\) | ||||
0.127124 | + | 0.991887i | \(0.459425\pi\) | |||||||
\(500\) | −80.1051 | −3.58241 | ||||||||
\(501\) | −13.0526 | −0.583145 | ||||||||
\(502\) | 40.7846 | 1.82031 | ||||||||
\(503\) | −26.5167 | −1.18232 | −0.591160 | − | 0.806555i | \(-0.701330\pi\) | ||||
−0.591160 | + | 0.806555i | \(0.701330\pi\) | |||||||
\(504\) | −9.46410 | −0.421565 | ||||||||
\(505\) | 23.3923 | 1.04094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.4641 | 0.553550 | ||||||||
\(508\) | 57.1769 | 2.53682 | ||||||||
\(509\) | −6.80385 | −0.301575 | −0.150788 | − | 0.988566i | \(-0.548181\pi\) | ||||
−0.150788 | + | 0.988566i | \(0.548181\pi\) | |||||||
\(510\) | −2.73205 | −0.120977 | ||||||||
\(511\) | 3.26795 | 0.144566 | ||||||||
\(512\) | −43.7128 | −1.93185 | ||||||||
\(513\) | 8.19615 | 0.361869 | ||||||||
\(514\) | 54.9808 | 2.42510 | ||||||||
\(515\) | 23.1244 | 1.01898 | ||||||||
\(516\) | −35.3205 | −1.55490 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.92820 | 0.304408 | ||||||||
\(519\) | −5.19615 | −0.228086 | ||||||||
\(520\) | 25.8564 | 1.13388 | ||||||||
\(521\) | 31.9808 | 1.40110 | 0.700551 | − | 0.713602i | \(-0.252937\pi\) | ||||
0.700551 | + | 0.713602i | \(0.252937\pi\) | |||||||
\(522\) | 12.9282 | 0.565852 | ||||||||
\(523\) | 4.58846 | 0.200639 | 0.100320 | − | 0.994955i | \(-0.468013\pi\) | ||||
0.100320 | + | 0.994955i | \(0.468013\pi\) | |||||||
\(524\) | 28.3923 | 1.24032 | ||||||||
\(525\) | −8.92820 | −0.389659 | ||||||||
\(526\) | 44.2487 | 1.92934 | ||||||||
\(527\) | 0.143594 | 0.00625503 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3205 | 0.970457 | ||||||||
\(530\) | 96.4974 | 4.19158 | ||||||||
\(531\) | 14.1244 | 0.612945 | ||||||||
\(532\) | −44.7846 | −1.94166 | ||||||||
\(533\) | −2.92820 | −0.126835 | ||||||||
\(534\) | 7.26795 | 0.314515 | ||||||||
\(535\) | −46.9808 | −2.03116 | ||||||||
\(536\) | 66.2487 | 2.86151 | ||||||||
\(537\) | −16.3923 | −0.707380 | ||||||||
\(538\) | 10.5359 | 0.454235 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 20.3923 | 0.877545 | ||||||||
\(541\) | −20.6077 | −0.885994 | −0.442997 | − | 0.896523i | \(-0.646085\pi\) | ||||
−0.442997 | + | 0.896523i | \(0.646085\pi\) | |||||||
\(542\) | 66.6410 | 2.86248 | ||||||||
\(543\) | 8.00000 | 0.343313 | ||||||||
\(544\) | −5.85641 | −0.251091 | ||||||||
\(545\) | −12.6603 | −0.542306 | ||||||||
\(546\) | 2.00000 | 0.0855921 | ||||||||
\(547\) | −2.00000 | −0.0855138 | −0.0427569 | − | 0.999086i | \(-0.513614\pi\) | ||||
−0.0427569 | + | 0.999086i | \(0.513614\pi\) | |||||||
\(548\) | −20.0000 | −0.854358 | ||||||||
\(549\) | 2.19615 | 0.0937295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.7846 | 1.65228 | ||||||||
\(552\) | 63.7128 | 2.71180 | ||||||||
\(553\) | 7.46410 | 0.317406 | ||||||||
\(554\) | 43.1244 | 1.83218 | ||||||||
\(555\) | −9.46410 | −0.401729 | ||||||||
\(556\) | −99.4256 | −4.21659 | ||||||||
\(557\) | −3.07180 | −0.130156 | −0.0650781 | − | 0.997880i | \(-0.520730\pi\) | ||||
−0.0650781 | + | 0.997880i | \(0.520730\pi\) | |||||||
\(558\) | −1.46410 | −0.0619804 | ||||||||
\(559\) | 4.73205 | 0.200144 | ||||||||
\(560\) | −55.7128 | −2.35430 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 75.7128 | 3.19375 | ||||||||
\(563\) | 6.26795 | 0.264163 | 0.132081 | − | 0.991239i | \(-0.457834\pi\) | ||||
0.132081 | + | 0.991239i | \(0.457834\pi\) | |||||||
\(564\) | −6.53590 | −0.275211 | ||||||||
\(565\) | −57.7128 | −2.42800 | ||||||||
\(566\) | 60.7846 | 2.55497 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 143.138 | 6.00596 | ||||||||
\(569\) | −28.7321 | −1.20451 | −0.602255 | − | 0.798304i | \(-0.705731\pi\) | ||||
−0.602255 | + | 0.798304i | \(0.705731\pi\) | |||||||
\(570\) | 83.5692 | 3.50033 | ||||||||
\(571\) | −14.9282 | −0.624726 | −0.312363 | − | 0.949963i | \(-0.601120\pi\) | ||||
−0.312363 | + | 0.949963i | \(0.601120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.80385 | −0.242459 | ||||||||
\(574\) | 10.9282 | 0.456134 | ||||||||
\(575\) | 60.1051 | 2.50656 | ||||||||
\(576\) | 29.8564 | 1.24402 | ||||||||
\(577\) | 44.4449 | 1.85026 | 0.925132 | − | 0.379646i | \(-0.123954\pi\) | ||||
0.925132 | + | 0.379646i | \(0.123954\pi\) | |||||||
\(578\) | 46.2487 | 1.92369 | ||||||||
\(579\) | −5.00000 | −0.207793 | ||||||||
\(580\) | 96.4974 | 4.00684 | ||||||||
\(581\) | −7.73205 | −0.320780 | ||||||||
\(582\) | 18.3923 | 0.762386 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −30.9282 | −1.27982 | ||||||||
\(585\) | −2.73205 | −0.112956 | ||||||||
\(586\) | −53.9090 | −2.22696 | ||||||||
\(587\) | 16.1244 | 0.665523 | 0.332762 | − | 0.943011i | \(-0.392020\pi\) | ||||
0.332762 | + | 0.943011i | \(0.392020\pi\) | |||||||
\(588\) | −5.46410 | −0.225336 | ||||||||
\(589\) | −4.39230 | −0.180982 | ||||||||
\(590\) | 144.014 | 5.92897 | ||||||||
\(591\) | 19.4641 | 0.800646 | ||||||||
\(592\) | −37.8564 | −1.55589 | ||||||||
\(593\) | −4.41154 | −0.181160 | −0.0905802 | − | 0.995889i | \(-0.528872\pi\) | ||||
−0.0905802 | + | 0.995889i | \(0.528872\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.00000 | −0.0409960 | ||||||||
\(596\) | −4.00000 | −0.163846 | ||||||||
\(597\) | 9.80385 | 0.401245 | ||||||||
\(598\) | −13.4641 | −0.550588 | ||||||||
\(599\) | −39.1769 | −1.60073 | −0.800363 | − | 0.599516i | \(-0.795360\pi\) | ||||
−0.800363 | + | 0.599516i | \(0.795360\pi\) | |||||||
\(600\) | 84.4974 | 3.44959 | ||||||||
\(601\) | 33.9090 | 1.38318 | 0.691588 | − | 0.722292i | \(-0.256912\pi\) | ||||
0.691588 | + | 0.722292i | \(0.256912\pi\) | |||||||
\(602\) | −17.6603 | −0.719778 | ||||||||
\(603\) | −7.00000 | −0.285062 | ||||||||
\(604\) | 62.2487 | 2.53286 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.1244 | −0.695629 | ||||||||
\(607\) | −26.5885 | −1.07919 | −0.539596 | − | 0.841924i | \(-0.681423\pi\) | ||||
−0.539596 | + | 0.841924i | \(0.681423\pi\) | |||||||
\(608\) | 179.138 | 7.26502 | ||||||||
\(609\) | 4.73205 | 0.191752 | ||||||||
\(610\) | 22.3923 | 0.906638 | ||||||||
\(611\) | 0.875644 | 0.0354248 | ||||||||
\(612\) | 1.46410 | 0.0591828 | ||||||||
\(613\) | 35.3923 | 1.42948 | 0.714741 | − | 0.699389i | \(-0.246545\pi\) | ||||
0.714741 | + | 0.699389i | \(0.246545\pi\) | |||||||
\(614\) | −12.5359 | −0.505908 | ||||||||
\(615\) | −14.9282 | −0.601963 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.5359 | −1.30985 | −0.654923 | − | 0.755696i | \(-0.727299\pi\) | ||||
−0.654923 | + | 0.755696i | \(0.727299\pi\) | |||||||
\(618\) | −16.9282 | −0.680952 | ||||||||
\(619\) | 2.00000 | 0.0803868 | 0.0401934 | − | 0.999192i | \(-0.487203\pi\) | ||||
0.0401934 | + | 0.999192i | \(0.487203\pi\) | |||||||
\(620\) | −10.9282 | −0.438887 | ||||||||
\(621\) | −6.73205 | −0.270148 | ||||||||
\(622\) | 52.0526 | 2.08712 | ||||||||
\(623\) | 2.66025 | 0.106581 | ||||||||
\(624\) | −10.9282 | −0.437478 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 55.7128 | 2.22673 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −73.5692 | −2.93573 | ||||||||
\(629\) | −0.679492 | −0.0270931 | ||||||||
\(630\) | 10.1962 | 0.406224 | ||||||||
\(631\) | 26.8564 | 1.06914 | 0.534568 | − | 0.845125i | \(-0.320474\pi\) | ||||
0.534568 | + | 0.845125i | \(0.320474\pi\) | |||||||
\(632\) | −70.6410 | −2.80995 | ||||||||
\(633\) | 23.7846 | 0.945353 | ||||||||
\(634\) | 42.3923 | 1.68361 | ||||||||
\(635\) | −39.0526 | −1.54975 | ||||||||
\(636\) | −51.7128 | −2.05055 | ||||||||
\(637\) | 0.732051 | 0.0290049 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.1244 | −0.598310 | ||||||||
\(640\) | 141.282 | 5.58466 | ||||||||
\(641\) | −29.9090 | −1.18133 | −0.590667 | − | 0.806916i | \(-0.701135\pi\) | ||||
−0.590667 | + | 0.806916i | \(0.701135\pi\) | |||||||
\(642\) | 34.3923 | 1.35736 | ||||||||
\(643\) | −14.1436 | −0.557769 | −0.278884 | − | 0.960325i | \(-0.589965\pi\) | ||||
−0.278884 | + | 0.960325i | \(0.589965\pi\) | |||||||
\(644\) | 36.7846 | 1.44952 | ||||||||
\(645\) | 24.1244 | 0.949896 | ||||||||
\(646\) | 6.00000 | 0.236067 | ||||||||
\(647\) | −16.8038 | −0.660627 | −0.330314 | − | 0.943871i | \(-0.607155\pi\) | ||||
−0.330314 | + | 0.943871i | \(0.607155\pi\) | |||||||
\(648\) | −9.46410 | −0.371785 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −17.8564 | −0.700386 | ||||||||
\(651\) | −0.535898 | −0.0210035 | ||||||||
\(652\) | 2.92820 | 0.114677 | ||||||||
\(653\) | −30.9808 | −1.21237 | −0.606185 | − | 0.795323i | \(-0.707301\pi\) | ||||
−0.606185 | + | 0.795323i | \(0.707301\pi\) | |||||||
\(654\) | 9.26795 | 0.362405 | ||||||||
\(655\) | −19.3923 | −0.757720 | ||||||||
\(656\) | −59.7128 | −2.33139 | ||||||||
\(657\) | 3.26795 | 0.127495 | ||||||||
\(658\) | −3.26795 | −0.127398 | ||||||||
\(659\) | −41.5167 | −1.61726 | −0.808630 | − | 0.588318i | \(-0.799790\pi\) | ||||
−0.808630 | + | 0.588318i | \(0.799790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.1436 | −0.705704 | −0.352852 | − | 0.935679i | \(-0.614788\pi\) | ||||
−0.352852 | + | 0.935679i | \(0.614788\pi\) | |||||||
\(662\) | 98.8372 | 3.84142 | ||||||||
\(663\) | −0.196152 | −0.00761793 | ||||||||
\(664\) | 73.1769 | 2.83982 | ||||||||
\(665\) | 30.5885 | 1.18617 | ||||||||
\(666\) | 6.92820 | 0.268462 | ||||||||
\(667\) | −31.8564 | −1.23348 | ||||||||
\(668\) | 71.3205 | 2.75947 | ||||||||
\(669\) | −16.0000 | −0.618596 | ||||||||
\(670\) | −71.3731 | −2.75738 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 21.8564 | 0.843129 | ||||||||
\(673\) | 29.3923 | 1.13299 | 0.566495 | − | 0.824065i | \(-0.308299\pi\) | ||||
0.566495 | + | 0.824065i | \(0.308299\pi\) | |||||||
\(674\) | −76.4974 | −2.94657 | ||||||||
\(675\) | −8.92820 | −0.343647 | ||||||||
\(676\) | −68.1051 | −2.61943 | ||||||||
\(677\) | 3.58846 | 0.137916 | 0.0689578 | − | 0.997620i | \(-0.478033\pi\) | ||||
0.0689578 | + | 0.997620i | \(0.478033\pi\) | |||||||
\(678\) | 42.2487 | 1.62255 | ||||||||
\(679\) | 6.73205 | 0.258352 | ||||||||
\(680\) | 9.46410 | 0.362932 | ||||||||
\(681\) | −2.66025 | −0.101941 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.2487 | 0.774795 | 0.387398 | − | 0.921913i | \(-0.373374\pi\) | ||||
0.387398 | + | 0.921913i | \(0.373374\pi\) | |||||||
\(684\) | −44.7846 | −1.71238 | ||||||||
\(685\) | 13.6603 | 0.521931 | ||||||||
\(686\) | −2.73205 | −0.104310 | ||||||||
\(687\) | 6.92820 | 0.264327 | ||||||||
\(688\) | 96.4974 | 3.67893 | ||||||||
\(689\) | 6.92820 | 0.263944 | ||||||||
\(690\) | −68.6410 | −2.61312 | ||||||||
\(691\) | 12.3923 | 0.471425 | 0.235713 | − | 0.971823i | \(-0.424258\pi\) | ||||
0.235713 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(692\) | 28.3923 | 1.07931 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.9282 | −1.24994 | ||||||||
\(695\) | 67.9090 | 2.57593 | ||||||||
\(696\) | −44.7846 | −1.69756 | ||||||||
\(697\) | −1.07180 | −0.0405972 | ||||||||
\(698\) | 61.1769 | 2.31558 | ||||||||
\(699\) | 9.80385 | 0.370816 | ||||||||
\(700\) | 48.7846 | 1.84388 | ||||||||
\(701\) | 3.66025 | 0.138246 | 0.0691229 | − | 0.997608i | \(-0.477980\pi\) | ||||
0.0691229 | + | 0.997608i | \(0.477980\pi\) | |||||||
\(702\) | 2.00000 | 0.0754851 | ||||||||
\(703\) | 20.7846 | 0.783906 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.46410 | 0.168128 | ||||||||
\(706\) | 68.1051 | 2.56317 | ||||||||
\(707\) | −6.26795 | −0.235730 | ||||||||
\(708\) | −77.1769 | −2.90049 | ||||||||
\(709\) | −29.3923 | −1.10385 | −0.551926 | − | 0.833893i | \(-0.686107\pi\) | ||||
−0.551926 | + | 0.833893i | \(0.686107\pi\) | |||||||
\(710\) | −154.210 | −5.78741 | ||||||||
\(711\) | 7.46410 | 0.279926 | ||||||||
\(712\) | −25.1769 | −0.943545 | ||||||||
\(713\) | 3.60770 | 0.135109 | ||||||||
\(714\) | 0.732051 | 0.0273963 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 89.5692 | 3.34736 | ||||||||
\(717\) | 11.0718 | 0.413484 | ||||||||
\(718\) | 2.39230 | 0.0892800 | ||||||||
\(719\) | 32.1051 | 1.19732 | 0.598659 | − | 0.801004i | \(-0.295700\pi\) | ||||
0.598659 | + | 0.801004i | \(0.295700\pi\) | |||||||
\(720\) | −55.7128 | −2.07629 | ||||||||
\(721\) | −6.19615 | −0.230757 | ||||||||
\(722\) | −131.622 | −4.89846 | ||||||||
\(723\) | −1.66025 | −0.0617455 | ||||||||
\(724\) | −43.7128 | −1.62457 | ||||||||
\(725\) | −42.2487 | −1.56908 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.51666 | −0.278778 | −0.139389 | − | 0.990238i | \(-0.544514\pi\) | ||||
−0.139389 | + | 0.990238i | \(0.544514\pi\) | |||||||
\(728\) | −6.92820 | −0.256776 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 33.3205 | 1.23325 | ||||||||
\(731\) | 1.73205 | 0.0640622 | ||||||||
\(732\) | −12.0000 | −0.443533 | ||||||||
\(733\) | −44.4449 | −1.64161 | −0.820804 | − | 0.571210i | \(-0.806474\pi\) | ||||
−0.820804 | + | 0.571210i | \(0.806474\pi\) | |||||||
\(734\) | 25.3205 | 0.934597 | ||||||||
\(735\) | 3.73205 | 0.137659 | ||||||||
\(736\) | −147.138 | −5.42359 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.9282 | 0.402273 | ||||||||
\(739\) | 33.3205 | 1.22571 | 0.612857 | − | 0.790194i | \(-0.290020\pi\) | ||||
0.612857 | + | 0.790194i | \(0.290020\pi\) | |||||||
\(740\) | 51.7128 | 1.90100 | ||||||||
\(741\) | 6.00000 | 0.220416 | ||||||||
\(742\) | −25.8564 | −0.949219 | ||||||||
\(743\) | −7.12436 | −0.261367 | −0.130684 | − | 0.991424i | \(-0.541717\pi\) | ||||
−0.130684 | + | 0.991424i | \(0.541717\pi\) | |||||||
\(744\) | 5.07180 | 0.185941 | ||||||||
\(745\) | 2.73205 | 0.100095 | ||||||||
\(746\) | −27.5167 | −1.00746 | ||||||||
\(747\) | −7.73205 | −0.282901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.5885 | 0.459972 | ||||||||
\(750\) | −40.0526 | −1.46251 | ||||||||
\(751\) | −9.39230 | −0.342730 | −0.171365 | − | 0.985208i | \(-0.554818\pi\) | ||||
−0.171365 | + | 0.985208i | \(0.554818\pi\) | |||||||
\(752\) | 17.8564 | 0.651156 | ||||||||
\(753\) | 14.9282 | 0.544014 | ||||||||
\(754\) | 9.46410 | 0.344662 | ||||||||
\(755\) | −42.5167 | −1.54734 | ||||||||
\(756\) | −5.46410 | −0.198727 | ||||||||
\(757\) | 5.92820 | 0.215464 | 0.107732 | − | 0.994180i | \(-0.465641\pi\) | ||||
0.107732 | + | 0.994180i | \(0.465641\pi\) | |||||||
\(758\) | −28.5885 | −1.03838 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −289.492 | −10.5010 | ||||||||
\(761\) | 44.9090 | 1.62795 | 0.813974 | − | 0.580901i | \(-0.197300\pi\) | ||||
0.813974 | + | 0.580901i | \(0.197300\pi\) | |||||||
\(762\) | 28.5885 | 1.03565 | ||||||||
\(763\) | 3.39230 | 0.122810 | ||||||||
\(764\) | 31.7128 | 1.14733 | ||||||||
\(765\) | −1.00000 | −0.0361551 | ||||||||
\(766\) | 26.9808 | 0.974855 | ||||||||
\(767\) | 10.3397 | 0.373347 | ||||||||
\(768\) | −43.7128 | −1.57735 | ||||||||
\(769\) | −30.6410 | −1.10494 | −0.552472 | − | 0.833532i | \(-0.686315\pi\) | ||||
−0.552472 | + | 0.833532i | \(0.686315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.1244 | 0.724761 | ||||||||
\(772\) | 27.3205 | 0.983287 | ||||||||
\(773\) | 1.73205 | 0.0622975 | 0.0311488 | − | 0.999515i | \(-0.490083\pi\) | ||||
0.0311488 | + | 0.999515i | \(0.490083\pi\) | |||||||
\(774\) | −17.6603 | −0.634785 | ||||||||
\(775\) | 4.78461 | 0.171868 | ||||||||
\(776\) | −63.7128 | −2.28716 | ||||||||
\(777\) | 2.53590 | 0.0909748 | ||||||||
\(778\) | 12.0000 | 0.430221 | ||||||||
\(779\) | 32.7846 | 1.17463 | ||||||||
\(780\) | 14.9282 | 0.534515 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.92820 | −0.176232 | ||||||||
\(783\) | 4.73205 | 0.169110 | ||||||||
\(784\) | 14.9282 | 0.533150 | ||||||||
\(785\) | 50.2487 | 1.79345 | ||||||||
\(786\) | 14.1962 | 0.506360 | ||||||||
\(787\) | −47.1769 | −1.68168 | −0.840838 | − | 0.541287i | \(-0.817937\pi\) | ||||
−0.840838 | + | 0.541287i | \(0.817937\pi\) | |||||||
\(788\) | −106.354 | −3.78870 | ||||||||
\(789\) | 16.1962 | 0.576598 | ||||||||
\(790\) | 76.1051 | 2.70770 | ||||||||
\(791\) | 15.4641 | 0.549840 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.60770 | 0.0570909 | ||||||||
\(794\) | −58.2487 | −2.06717 | ||||||||
\(795\) | 35.3205 | 1.25269 | ||||||||
\(796\) | −53.5692 | −1.89871 | ||||||||
\(797\) | 46.9090 | 1.66160 | 0.830800 | − | 0.556570i | \(-0.187883\pi\) | ||||
0.830800 | + | 0.556570i | \(0.187883\pi\) | |||||||
\(798\) | −22.3923 | −0.792679 | ||||||||
\(799\) | 0.320508 | 0.0113388 | ||||||||
\(800\) | −195.138 | −6.89919 | ||||||||
\(801\) | 2.66025 | 0.0939955 | ||||||||
\(802\) | 43.7128 | 1.54355 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 38.2487 | 1.34893 | ||||||||
\(805\) | −25.1244 | −0.885517 | ||||||||
\(806\) | −1.07180 | −0.0377524 | ||||||||
\(807\) | 3.85641 | 0.135752 | ||||||||
\(808\) | 59.3205 | 2.08689 | ||||||||
\(809\) | 38.4449 | 1.35165 | 0.675825 | − | 0.737062i | \(-0.263788\pi\) | ||||
0.675825 | + | 0.737062i | \(0.263788\pi\) | |||||||
\(810\) | 10.1962 | 0.358256 | ||||||||
\(811\) | 19.9090 | 0.699098 | 0.349549 | − | 0.936918i | \(-0.386335\pi\) | ||||
0.349549 | + | 0.936918i | \(0.386335\pi\) | |||||||
\(812\) | −25.8564 | −0.907382 | ||||||||
\(813\) | 24.3923 | 0.855475 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | −52.9808 | −1.85356 | ||||||||
\(818\) | −17.3205 | −0.605597 | ||||||||
\(819\) | 0.732051 | 0.0255799 | ||||||||
\(820\) | 81.5692 | 2.84852 | ||||||||
\(821\) | 3.85641 | 0.134590 | 0.0672948 | − | 0.997733i | \(-0.478563\pi\) | ||||
0.0672948 | + | 0.997733i | \(0.478563\pi\) | |||||||
\(822\) | −10.0000 | −0.348790 | ||||||||
\(823\) | 5.32051 | 0.185461 | 0.0927306 | − | 0.995691i | \(-0.470440\pi\) | ||||
0.0927306 | + | 0.995691i | \(0.470440\pi\) | |||||||
\(824\) | 58.6410 | 2.04286 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.5885 | −1.34266 | ||||||||
\(827\) | −15.5167 | −0.539567 | −0.269784 | − | 0.962921i | \(-0.586952\pi\) | ||||
−0.269784 | + | 0.962921i | \(0.586952\pi\) | |||||||
\(828\) | 36.7846 | 1.27835 | ||||||||
\(829\) | 42.1962 | 1.46553 | 0.732766 | − | 0.680480i | \(-0.238229\pi\) | ||||
0.732766 | + | 0.680480i | \(0.238229\pi\) | |||||||
\(830\) | −78.8372 | −2.73648 | ||||||||
\(831\) | 15.7846 | 0.547562 | ||||||||
\(832\) | 21.8564 | 0.757735 | ||||||||
\(833\) | 0.267949 | 0.00928389 | ||||||||
\(834\) | −49.7128 | −1.72141 | ||||||||
\(835\) | −48.7128 | −1.68578 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.535898 | −0.0185234 | ||||||||
\(838\) | −17.1244 | −0.591551 | ||||||||
\(839\) | −52.2295 | −1.80316 | −0.901581 | − | 0.432611i | \(-0.857592\pi\) | ||||
−0.901581 | + | 0.432611i | \(0.857592\pi\) | |||||||
\(840\) | −35.3205 | −1.21867 | ||||||||
\(841\) | −6.60770 | −0.227852 | ||||||||
\(842\) | −30.4449 | −1.04920 | ||||||||
\(843\) | 27.7128 | 0.954480 | ||||||||
\(844\) | −129.962 | −4.47346 | ||||||||
\(845\) | 46.5167 | 1.60022 | ||||||||
\(846\) | −3.26795 | −0.112354 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 141.282 | 4.85164 | ||||||||
\(849\) | 22.2487 | 0.763574 | ||||||||
\(850\) | −6.53590 | −0.224179 | ||||||||
\(851\) | −17.0718 | −0.585214 | ||||||||
\(852\) | 82.6410 | 2.83123 | ||||||||
\(853\) | 4.00000 | 0.136957 | 0.0684787 | − | 0.997653i | \(-0.478185\pi\) | ||||
0.0684787 | + | 0.997653i | \(0.478185\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 30.5885 | 1.04610 | ||||||||
\(856\) | −119.138 | −4.07207 | ||||||||
\(857\) | −1.87564 | −0.0640708 | −0.0320354 | − | 0.999487i | \(-0.510199\pi\) | ||||
−0.0320354 | + | 0.999487i | \(0.510199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.0000 | −1.02359 | −0.511793 | − | 0.859109i | \(-0.671019\pi\) | ||||
−0.511793 | + | 0.859109i | \(0.671019\pi\) | |||||||
\(860\) | −131.818 | −4.49495 | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | −30.9282 | −1.05342 | ||||||||
\(863\) | 12.9282 | 0.440081 | 0.220041 | − | 0.975491i | \(-0.429381\pi\) | ||||
0.220041 | + | 0.975491i | \(0.429381\pi\) | |||||||
\(864\) | 21.8564 | 0.743570 | ||||||||
\(865\) | −19.3923 | −0.659358 | ||||||||
\(866\) | 87.1769 | 2.96239 | ||||||||
\(867\) | 16.9282 | 0.574912 | ||||||||
\(868\) | 2.92820 | 0.0993897 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 48.2487 | 1.63578 | ||||||||
\(871\) | −5.12436 | −0.173632 | ||||||||
\(872\) | −32.1051 | −1.08722 | ||||||||
\(873\) | 6.73205 | 0.227845 | ||||||||
\(874\) | 150.746 | 5.09906 | ||||||||
\(875\) | −14.6603 | −0.495607 | ||||||||
\(876\) | −17.8564 | −0.603312 | ||||||||
\(877\) | 37.1769 | 1.25538 | 0.627688 | − | 0.778465i | \(-0.284002\pi\) | ||||
0.627688 | + | 0.778465i | \(0.284002\pi\) | |||||||
\(878\) | −76.1051 | −2.56842 | ||||||||
\(879\) | −19.7321 | −0.665546 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.1436 | 0.409128 | 0.204564 | − | 0.978853i | \(-0.434422\pi\) | ||||
0.204564 | + | 0.978853i | \(0.434422\pi\) | |||||||
\(882\) | −2.73205 | −0.0919929 | ||||||||
\(883\) | −13.7846 | −0.463889 | −0.231945 | − | 0.972729i | \(-0.574509\pi\) | ||||
−0.231945 | + | 0.972729i | \(0.574509\pi\) | |||||||
\(884\) | 1.07180 | 0.0360484 | ||||||||
\(885\) | 52.7128 | 1.77192 | ||||||||
\(886\) | 44.2487 | 1.48656 | ||||||||
\(887\) | −14.1244 | −0.474249 | −0.237125 | − | 0.971479i | \(-0.576205\pi\) | ||||
−0.237125 | + | 0.971479i | \(0.576205\pi\) | |||||||
\(888\) | −24.0000 | −0.805387 | ||||||||
\(889\) | 10.4641 | 0.350955 | ||||||||
\(890\) | 27.1244 | 0.909210 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 87.4256 | 2.92723 | ||||||||
\(893\) | −9.80385 | −0.328073 | ||||||||
\(894\) | −2.00000 | −0.0668900 | ||||||||
\(895\) | −61.1769 | −2.04492 | ||||||||
\(896\) | −37.8564 | −1.26469 | ||||||||
\(897\) | −4.92820 | −0.164548 | ||||||||
\(898\) | −88.1051 | −2.94011 | ||||||||
\(899\) | −2.53590 | −0.0845769 | ||||||||
\(900\) | 48.7846 | 1.62615 | ||||||||
\(901\) | 2.53590 | 0.0844830 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.46410 | −0.215112 | ||||||||
\(904\) | −146.354 | −4.86766 | ||||||||
\(905\) | 29.8564 | 0.992461 | ||||||||
\(906\) | 31.1244 | 1.03404 | ||||||||
\(907\) | −38.7846 | −1.28782 | −0.643911 | − | 0.765100i | \(-0.722689\pi\) | ||||
−0.643911 | + | 0.765100i | \(0.722689\pi\) | |||||||
\(908\) | 14.5359 | 0.482391 | ||||||||
\(909\) | −6.26795 | −0.207895 | ||||||||
\(910\) | 7.46410 | 0.247433 | ||||||||
\(911\) | −14.7846 | −0.489836 | −0.244918 | − | 0.969544i | \(-0.578761\pi\) | ||||
−0.244918 | + | 0.969544i | \(0.578761\pi\) | |||||||
\(912\) | 122.354 | 4.05154 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −54.8372 | −1.81385 | ||||||||
\(915\) | 8.19615 | 0.270956 | ||||||||
\(916\) | −37.8564 | −1.25081 | ||||||||
\(917\) | 5.19615 | 0.171592 | ||||||||
\(918\) | 0.732051 | 0.0241613 | ||||||||
\(919\) | −14.3923 | −0.474758 | −0.237379 | − | 0.971417i | \(-0.576288\pi\) | ||||
−0.237379 | + | 0.971417i | \(0.576288\pi\) | |||||||
\(920\) | 237.779 | 7.83936 | ||||||||
\(921\) | −4.58846 | −0.151195 | ||||||||
\(922\) | 9.80385 | 0.322873 | ||||||||
\(923\) | −11.0718 | −0.364433 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.6410 | −0.744432 | ||||||||
\(926\) | −67.0333 | −2.20285 | ||||||||
\(927\) | −6.19615 | −0.203508 | ||||||||
\(928\) | 103.426 | 3.39511 | ||||||||
\(929\) | −2.66025 | −0.0872801 | −0.0436401 | − | 0.999047i | \(-0.513895\pi\) | ||||
−0.0436401 | + | 0.999047i | \(0.513895\pi\) | |||||||
\(930\) | −5.46410 | −0.179175 | ||||||||
\(931\) | −8.19615 | −0.268618 | ||||||||
\(932\) | −53.5692 | −1.75472 | ||||||||
\(933\) | 19.0526 | 0.623753 | ||||||||
\(934\) | 37.1769 | 1.21647 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.92820 | −0.226455 | ||||||||
\(937\) | −10.4449 | −0.341219 | −0.170609 | − | 0.985339i | \(-0.554574\pi\) | ||||
−0.170609 | + | 0.985339i | \(0.554574\pi\) | |||||||
\(938\) | 19.1244 | 0.624432 | ||||||||
\(939\) | 20.3923 | 0.665478 | ||||||||
\(940\) | −24.3923 | −0.795589 | ||||||||
\(941\) | 34.3923 | 1.12116 | 0.560579 | − | 0.828101i | \(-0.310579\pi\) | ||||
0.560579 | + | 0.828101i | \(0.310579\pi\) | |||||||
\(942\) | −36.7846 | −1.19851 | ||||||||
\(943\) | −26.9282 | −0.876903 | ||||||||
\(944\) | 210.851 | 6.86262 | ||||||||
\(945\) | 3.73205 | 0.121404 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.0718 | 1.13968 | 0.569840 | − | 0.821756i | \(-0.307005\pi\) | ||||
0.569840 | + | 0.821756i | \(0.307005\pi\) | |||||||
\(948\) | −40.7846 | −1.32462 | ||||||||
\(949\) | 2.39230 | 0.0776575 | ||||||||
\(950\) | 199.923 | 6.48636 | ||||||||
\(951\) | 15.5167 | 0.503162 | ||||||||
\(952\) | −2.53590 | −0.0821889 | ||||||||
\(953\) | 14.6795 | 0.475515 | 0.237758 | − | 0.971324i | \(-0.423588\pi\) | ||||
0.237758 | + | 0.971324i | \(0.423588\pi\) | |||||||
\(954\) | −25.8564 | −0.837132 | ||||||||
\(955\) | −21.6603 | −0.700909 | ||||||||
\(956\) | −60.4974 | −1.95663 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −110.301 | −3.56367 | ||||||||
\(959\) | −3.66025 | −0.118196 | ||||||||
\(960\) | 111.426 | 3.59625 | ||||||||
\(961\) | −30.7128 | −0.990736 | ||||||||
\(962\) | 5.07180 | 0.163521 | ||||||||
\(963\) | 12.5885 | 0.405657 | ||||||||
\(964\) | 9.07180 | 0.292183 | ||||||||
\(965\) | −18.6603 | −0.600695 | ||||||||
\(966\) | 18.3923 | 0.591763 | ||||||||
\(967\) | −8.60770 | −0.276805 | −0.138402 | − | 0.990376i | \(-0.544197\pi\) | ||||
−0.138402 | + | 0.990376i | \(0.544197\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.19615 | 0.0705506 | ||||||||
\(970\) | 68.6410 | 2.20393 | ||||||||
\(971\) | −46.1244 | −1.48020 | −0.740101 | − | 0.672496i | \(-0.765222\pi\) | ||||
−0.740101 | + | 0.672496i | \(0.765222\pi\) | |||||||
\(972\) | −5.46410 | −0.175261 | ||||||||
\(973\) | −18.1962 | −0.583342 | ||||||||
\(974\) | 55.1244 | 1.76630 | ||||||||
\(975\) | −6.53590 | −0.209316 | ||||||||
\(976\) | 32.7846 | 1.04941 | ||||||||
\(977\) | 39.8038 | 1.27344 | 0.636719 | − | 0.771096i | \(-0.280291\pi\) | ||||
0.636719 | + | 0.771096i | \(0.280291\pi\) | |||||||
\(978\) | 1.46410 | 0.0468168 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −20.3923 | −0.651408 | ||||||||
\(981\) | 3.39230 | 0.108308 | ||||||||
\(982\) | 103.962 | 3.31755 | ||||||||
\(983\) | −32.7846 | −1.04567 | −0.522833 | − | 0.852435i | \(-0.675125\pi\) | ||||
−0.522833 | + | 0.852435i | \(0.675125\pi\) | |||||||
\(984\) | −37.8564 | −1.20682 | ||||||||
\(985\) | 72.6410 | 2.31454 | ||||||||
\(986\) | 3.46410 | 0.110319 | ||||||||
\(987\) | −1.19615 | −0.0380740 | ||||||||
\(988\) | −32.7846 | −1.04302 | ||||||||
\(989\) | 43.5167 | 1.38375 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.3923 | 1.21957 | 0.609786 | − | 0.792566i | \(-0.291255\pi\) | ||||
0.609786 | + | 0.792566i | \(0.291255\pi\) | |||||||
\(992\) | −11.7128 | −0.371882 | ||||||||
\(993\) | 36.1769 | 1.14804 | ||||||||
\(994\) | 41.3205 | 1.31061 | ||||||||
\(995\) | 36.5885 | 1.15993 | ||||||||
\(996\) | 42.2487 | 1.33870 | ||||||||
\(997\) | −29.0333 | −0.919495 | −0.459747 | − | 0.888050i | \(-0.652060\pi\) | ||||
−0.459747 | + | 0.888050i | \(0.652060\pi\) | |||||||
\(998\) | −15.5167 | −0.491171 | ||||||||
\(999\) | 2.53590 | 0.0802323 |
(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 | 2541.2.a.o.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 7623.2.a.bv.1.2 | 2 | |||
11.10 | odd | 2 | 2541.2.a.be.1.2 | yes | 2 | ||
33.32 | even | 2 | 7623.2.a.x.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.o.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2541.2.a.be.1.2 | yes | 2 | 11.10 | odd | 2 | ||
7623.2.a.x.1.1 | 2 | 33.32 | even | 2 | |||
7623.2.a.bv.1.2 | 2 | 3.2 | odd | 2 |