Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, 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("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | 2.68133 | 1.54807 | 0.774033 | − | 0.633145i | \(-0.218236\pi\) | ||||
0.774033 | + | 0.633145i | \(0.218236\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.18953 | 1.20553 | 0.602765 | − | 0.797919i | \(-0.294066\pi\) | ||||
0.602765 | + | 0.797919i | \(0.294066\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.18953 | 1.39651 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.681331 | 0.188967 | 0.0944836 | − | 0.995526i | \(-0.469880\pi\) | ||||
0.0944836 | + | 0.995526i | \(0.469880\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.18953 | 0.288504 | 0.144252 | − | 0.989541i | \(-0.453922\pi\) | ||||
0.144252 | + | 0.989541i | \(0.453922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.55220 | 1.86624 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.17313 | 0.453128 | 0.226564 | − | 0.973996i | \(-0.427251\pi\) | ||||
0.226564 | + | 0.973996i | \(0.427251\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.18953 | 0.613826 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.81047 | 0.521890 | 0.260945 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260945 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.37907 | 1.14571 | 0.572857 | − | 0.819655i | \(-0.305835\pi\) | ||||
0.572857 | + | 0.819655i | \(0.305835\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.87086 | −1.29396 | −0.646981 | − | 0.762506i | \(-0.723969\pi\) | ||||
−0.646981 | + | 0.762506i | \(0.723969\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.82687 | 0.292534 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.983593 | 0.153611 | 0.0768057 | − | 0.997046i | \(-0.475528\pi\) | ||||
0.0768057 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.36266 | −0.207804 | −0.103902 | − | 0.994588i | \(-0.533133\pi\) | ||||
−0.103902 | + | 0.994588i | \(0.533133\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.7417 | −1.71271 | −0.856354 | − | 0.516390i | \(-0.827276\pi\) | ||||
−0.856354 | + | 0.516390i | \(0.827276\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.17313 | 0.453304 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.18953 | 0.446624 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.69774 | 0.233202 | 0.116601 | − | 0.993179i | \(-0.462800\pi\) | ||||
0.116601 | + | 0.993179i | \(0.462800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.68133 | 0.355151 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.5358 | 1.50183 | 0.750916 | − | 0.660398i | \(-0.229612\pi\) | ||||
0.750916 | + | 0.660398i | \(0.229612\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.36266 | 0.942692 | 0.471346 | − | 0.881948i | \(-0.343768\pi\) | ||||
0.471346 | + | 0.881948i | \(0.343768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.3627 | 1.68354 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.02759 | −0.858556 | −0.429278 | − | 0.903172i | \(-0.641232\pi\) | ||||
−0.429278 | + | 0.903172i | \(0.641232\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.82687 | 0.701473 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7581 | −1.51411 | −0.757056 | − | 0.653350i | \(-0.773363\pi\) | ||||
−0.757056 | + | 0.653350i | \(0.773363\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.53579 | 0.647915 | 0.323958 | − | 0.946072i | \(-0.394987\pi\) | ||||
0.323958 | + | 0.946072i | \(0.394987\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.36266 | 0.603347 | 0.301673 | − | 0.953411i | \(-0.402455\pi\) | ||||
0.301673 | + | 0.953411i | \(0.402455\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.01641 | −0.446267 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.37907 | −0.261137 | −0.130568 | − | 0.991439i | \(-0.541680\pi\) | ||||
−0.130568 | + | 0.991439i | \(0.541680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.53579 | 0.807921 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.01641 | 0.319738 | 0.159869 | − | 0.987138i | \(-0.448893\pi\) | ||||
0.159869 | + | 0.987138i | \(0.448893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.17313 | 0.227806 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17.1044 | 1.77364 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.88727 | −0.496227 | −0.248114 | − | 0.968731i | \(-0.579811\pi\) | ||||
−0.248114 | + | 0.968731i | \(0.579811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1208 | 1.20606 | 0.603032 | − | 0.797717i | \(-0.293959\pi\) | ||||
0.603032 | + | 0.797717i | \(0.293959\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8709 | 1.76087 | 0.880434 | − | 0.474168i | \(-0.157251\pi\) | ||||
0.880434 | + | 0.474168i | \(0.157251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.4231 | −1.39433 | −0.697165 | − | 0.716911i | \(-0.745555\pi\) | ||||
−0.697165 | + | 0.716911i | \(0.745555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.2059 | 0.977552 | 0.488776 | − | 0.872409i | \(-0.337444\pi\) | ||||
0.488776 | + | 0.872409i | \(0.337444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.1044 | −2.00314 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.49180 | 0.140336 | 0.0701682 | − | 0.997535i | \(-0.477646\pi\) | ||||
0.0701682 | + | 0.997535i | \(0.477646\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.85446 | 0.263895 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.79406 | 0.347801 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.63734 | 0.237801 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.24993 | −0.732063 | −0.366032 | − | 0.930602i | \(-0.619284\pi\) | ||||
−0.366032 | + | 0.930602i | \(0.619284\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.65375 | −0.321694 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.75814 | 0.765202 | 0.382601 | − | 0.923914i | \(-0.375028\pi\) | ||||
0.382601 | + | 0.923914i | \(0.375028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.18953 | 0.276568 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.9149 | 1.01795 | 0.508977 | − | 0.860780i | \(-0.330024\pi\) | ||||
0.508977 | + | 0.860780i | \(0.330024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.4835 | −1.99184 | −0.995920 | − | 0.0902352i | \(-0.971238\pi\) | ||||
−0.995920 | + | 0.0902352i | \(0.971238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.4835 | −2.65139 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.50820 | 0.701745 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.8461 | −1.54393 | −0.771967 | − | 0.635662i | \(-0.780727\pi\) | ||||
−0.771967 | + | 0.635662i | \(0.780727\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0880 | −1.30922 | −0.654611 | − | 0.755966i | \(-0.727167\pi\) | ||||
−0.654611 | + | 0.755966i | \(0.727167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.98359 | 0.402900 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7417 | 1.09671 | 0.548355 | − | 0.836246i | \(-0.315254\pi\) | ||||
0.548355 | + | 0.836246i | \(0.315254\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.55220 | 0.361013 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.93126 | 0.546260 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.6373 | 1.14648 | 0.573242 | − | 0.819386i | \(-0.305685\pi\) | ||||
0.573242 | + | 0.819386i | \(0.305685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.9588 | −1.38970 | −0.694849 | − | 0.719156i | \(-0.744529\pi\) | ||||
−0.694849 | + | 0.719156i | \(0.744529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5358 | −0.964291 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.18953 | 0.320382 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.85446 | −0.521135 | −0.260567 | − | 0.965456i | \(-0.583910\pi\) | ||||
−0.260567 | + | 0.965456i | \(0.583910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.9313 | 2.32494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.01641 | 0.374944 | 0.187472 | − | 0.982270i | \(-0.439971\pi\) | ||||
0.187472 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7253 | 1.24318 | 0.621592 | − | 0.783341i | \(-0.286486\pi\) | ||||
0.621592 | + | 0.783341i | \(0.286486\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.7417 | 1.45935 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.1731 | 0.739986 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.2775 | −0.816013 | −0.408006 | − | 0.912979i | \(-0.633776\pi\) | ||||
−0.408006 | + | 0.912979i | \(0.633776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.5798 | −0.977494 | −0.488747 | − | 0.872426i | \(-0.662546\pi\) | ||||
−0.488747 | + | 0.872426i | \(0.662546\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.6566 | 1.81875 | 0.909374 | − | 0.415980i | \(-0.136562\pi\) | ||||
0.909374 | + | 0.415980i | \(0.136562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.8433 | −1.32910 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.96408 | 0.629155 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.10439 | 0.632799 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2939 | 1.12172 | 0.560860 | − | 0.827911i | \(-0.310471\pi\) | ||||
0.560860 | + | 0.827911i | \(0.310471\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −34.2088 | −2.34395 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3463 | 1.38119 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.8433 | 1.00302 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.810466 | 0.0545178 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.2499 | 1.62390 | 0.811948 | − | 0.583730i | \(-0.198407\pi\) | ||||
0.811948 | + | 0.583730i | \(0.198407\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.31867 | −0.353012 | −0.176506 | − | 0.984300i | \(-0.556480\pi\) | ||||
−0.176506 | + | 0.984300i | \(0.556480\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.7089 | 0.773747 | 0.386873 | − | 0.922133i | \(-0.373555\pi\) | ||||
0.386873 | + | 0.922133i | \(0.373555\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.5163 | −1.80265 | −0.901325 | − | 0.433142i | \(-0.857405\pi\) | ||||
−0.901325 | + | 0.433142i | \(0.857405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.3791 | 0.934021 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.9313 | 0.965823 | 0.482912 | − | 0.875669i | \(-0.339579\pi\) | ||||
0.482912 | + | 0.875669i | \(0.339579\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.32985 | −0.600988 | −0.300494 | − | 0.953784i | \(-0.597152\pi\) | ||||
−0.300494 | + | 0.953784i | \(0.597152\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.3379 | −1.30468 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.681331 | 0.0433520 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.37907 | −0.404257 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.27468 | 0.0804569 | 0.0402285 | − | 0.999191i | \(-0.487191\pi\) | ||||
0.0402285 | + | 0.999191i | \(0.487191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −31.2887 | −1.95174 | −0.975868 | − | 0.218363i | \(-0.929928\pi\) | ||||
−0.975868 | + | 0.218363i | \(0.929928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.1044 | −1.55991 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.7745 | 0.728826 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.5163 | −1.57340 | −0.786700 | − | 0.617335i | \(-0.788212\pi\) | ||||
−0.786700 | + | 0.617335i | \(0.788212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.08798 | 0.494977 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.7581 | 1.63147 | 0.815736 | − | 0.578424i | \(-0.196332\pi\) | ||||
0.815736 | + | 0.578424i | \(0.196332\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.1731 | 0.860956 | 0.430478 | − | 0.902601i | \(-0.358345\pi\) | ||||
0.430478 | + | 0.902601i | \(0.358345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.82687 | 0.352658 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.08798 | −0.365791 | −0.182896 | − | 0.983132i | \(-0.558547\pi\) | ||||
−0.182896 | + | 0.983132i | \(0.558547\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.7253 | 1.60000 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.7089 | −0.937115 | −0.468558 | − | 0.883433i | \(-0.655226\pi\) | ||||
−0.468558 | + | 0.883433i | \(0.655226\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.346255 | −0.0205827 | −0.0102913 | − | 0.999947i | \(-0.503276\pi\) | ||||
−0.0102913 | + | 0.999947i | \(0.503276\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.13720 | 0.185183 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5850 | −0.916765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1044 | −0.768193 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.71414 | −0.392244 | −0.196122 | − | 0.980579i | \(-0.562835\pi\) | ||||
−0.196122 | + | 0.980579i | \(0.562835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.48062 | 0.0856264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.34625 | −0.250514 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.4999 | 1.86707 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.6126 | 1.00520 | 0.502602 | − | 0.864518i | \(-0.332376\pi\) | ||||
0.502602 | + | 0.864518i | \(0.332376\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 47.9177 | 2.72594 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.58501 | −0.373402 | −0.186701 | − | 0.982417i | \(-0.559779\pi\) | ||||
−0.186701 | + | 0.982417i | \(0.559779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.6178 | 1.05234 | 0.526171 | − | 0.850379i | \(-0.323627\pi\) | ||||
0.526171 | + | 0.850379i | \(0.323627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.7857 | 0.998946 | 0.499473 | − | 0.866330i | \(-0.333527\pi\) | ||||
0.499473 | + | 0.866330i | \(0.333527\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −38.6730 | −2.15852 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.18953 | 0.0661874 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 27.3655 | 1.51332 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.4506 | −2.06472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.53579 | −0.194345 | −0.0971723 | − | 0.995268i | \(-0.530980\pi\) | ||||
−0.0971723 | + | 0.995268i | \(0.530980\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −32.9753 | −1.80703 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.87086 | 0.428753 | 0.214377 | − | 0.976751i | \(-0.431228\pi\) | ||||
0.214377 | + | 0.976751i | \(0.431228\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.2059 | −0.659059 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.6537 | −0.840337 | −0.420169 | − | 0.907446i | \(-0.638029\pi\) | ||||
−0.420169 | + | 0.907446i | \(0.638029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.4178 | −1.14647 | −0.573235 | − | 0.819391i | \(-0.694312\pi\) | ||||
−0.573235 | + | 0.819391i | \(0.694312\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.17313 | 0.115993 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.15672 | −0.168015 | −0.0840076 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840076 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.1731 | 0.538419 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.8269 | 0.940866 | 0.470433 | − | 0.882436i | \(-0.344098\pi\) | ||||
0.470433 | + | 0.882436i | \(0.344098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −29.4946 | −1.54807 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2252 | −1.00355 | −0.501773 | − | 0.864999i | \(-0.667319\pi\) | ||||
−0.501773 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.12080 | 0.214520 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.41499 | 0.281132 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.95601 | −0.515503 | −0.257751 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257751 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.91486 | 0.0986201 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.6238 | −1.00801 | −0.504003 | − | 0.863702i | \(-0.668140\pi\) | ||||
−0.504003 | + | 0.863702i | \(0.668140\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.1208 | −1.13328 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9037 | −0.608250 | −0.304125 | − | 0.952632i | \(-0.598364\pi\) | ||||
−0.304125 | + | 0.952632i | \(0.598364\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.70892 | −0.290201 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.3463 | 0.524576 | 0.262288 | − | 0.964990i | \(-0.415523\pi\) | ||||
0.262288 | + | 0.964990i | \(0.415523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58501 | 0.130730 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.4835 | 1.18458 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.1536 | −1.31261 | −0.656306 | − | 0.754495i | \(-0.727882\pi\) | ||||
−0.656306 | + | 0.754495i | \(0.727882\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.55220 | 0.428145 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.7253 | −1.63422 | −0.817112 | − | 0.576479i | \(-0.804426\pi\) | ||||
−0.817112 | + | 0.576479i | \(0.804426\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.34625 | 0.216502 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.03281 | 0.199410 | 0.0997049 | − | 0.995017i | \(-0.468210\pi\) | ||||
0.0997049 | + | 0.995017i | \(0.468210\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.9477 | 1.57586 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.7938 | 1.81050 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −62.9669 | −3.08350 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8297 | −0.773332 | −0.386666 | − | 0.922220i | \(-0.626373\pi\) | ||||
−0.386666 | + | 0.922220i | \(0.626373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.05233 | 0.294973 | 0.147486 | − | 0.989064i | \(-0.452882\pi\) | ||||
0.147486 | + | 0.989064i | \(0.452882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −49.1924 | −2.39182 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.4835 | 1.13644 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7089 | 1.23835 | 0.619177 | − | 0.785251i | \(-0.287466\pi\) | ||||
0.619177 | + | 0.785251i | \(0.287466\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.57383 | −0.123690 | −0.0618452 | − | 0.998086i | \(-0.519699\pi\) | ||||
−0.0618452 | + | 0.998086i | \(0.519699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.17313 | 0.103955 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.8133 | 1.27973 | 0.639865 | − | 0.768488i | \(-0.278990\pi\) | ||||
0.639865 | + | 0.768488i | \(0.278990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.2939 | 0.633044 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.7909 | −0.512693 | −0.256347 | − | 0.966585i | \(-0.582519\pi\) | ||||
−0.256347 | + | 0.966585i | \(0.582519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −50.5327 | −2.39011 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.4835 | −1.39141 | −0.695705 | − | 0.718327i | \(-0.744908\pi\) | ||||
−0.695705 | + | 0.718327i | \(0.744908\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −43.1372 | −2.02676 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.8269 | 0.553238 | 0.276619 | − | 0.960980i | \(-0.410786\pi\) | ||||
0.276619 | + | 0.960980i | \(0.410786\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.79406 | 0.177092 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.45065 | −0.347011 | −0.173506 | − | 0.984833i | \(-0.555509\pi\) | ||||
−0.173506 | + | 0.984833i | \(0.555509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.4506 | 1.74048 | 0.870240 | − | 0.492629i | \(-0.163964\pi\) | ||||
0.870240 | + | 0.492629i | \(0.163964\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.4835 | 1.27178 | 0.635891 | − | 0.771779i | \(-0.280633\pi\) | ||||
0.635891 | + | 0.771779i | \(0.280633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.4147 | −1.03502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.8461 | 1.69778 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.11273 | 0.325669 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.6597 | 0.487054 | 0.243527 | − | 0.969894i | \(-0.421696\pi\) | ||||
0.243527 | + | 0.969894i | \(0.421696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.36266 | −0.244516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.5850 | 0.845647 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.92604 | −0.359163 | −0.179581 | − | 0.983743i | \(-0.557474\pi\) | ||||
−0.179581 | + | 0.983743i | \(0.557474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 39.2475 | 1.77484 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.68656 | −0.0761133 | −0.0380567 | − | 0.999276i | \(-0.512117\pi\) | ||||
−0.0380567 | + | 0.999276i | \(0.512117\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.34314 | 0.150568 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.6925 | −1.82531 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3463 | −0.910823 | −0.455412 | − | 0.890281i | \(-0.650508\pi\) | ||||
−0.455412 | + | 0.890281i | \(0.650508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −48.1536 | −2.15134 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.06874 | −0.0476526 | −0.0238263 | − | 0.999716i | \(-0.507585\pi\) | ||||
−0.0238263 | + | 0.999716i | \(0.507585\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.6126 | −1.49279 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0164 | −0.842887 | −0.421444 | − | 0.906855i | \(-0.638476\pi\) | ||||
−0.421444 | + | 0.906855i | \(0.638476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.6566 | 0.781081 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.18953 | 0.140821 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.3791 | −0.806752 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.07158 | 0.397433 | 0.198717 | − | 0.980057i | \(-0.436323\pi\) | ||||
0.198717 | + | 0.980057i | \(0.436323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.4946 | 0.590079 | 0.295040 | − | 0.955485i | \(-0.404667\pi\) | ||||
0.295040 | + | 0.955485i | \(0.404667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.58812 | 0.330544 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2775 | −0.794675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.3296 | 2.09733 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.670152 | 0.0290275 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.4506 | 0.580438 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.63734 | 0.199375 | 0.0996874 | − | 0.995019i | \(-0.468216\pi\) | ||||
0.0996874 | + | 0.995019i | \(0.468216\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 44.8461 | 1.92453 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1291 | 0.775146 | 0.387573 | − | 0.921839i | \(-0.373314\pi\) | ||||
0.387573 | + | 0.921839i | \(0.373314\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.8461 | 1.31648 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.81047 | 0.119730 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1044 | 0.727353 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.2968 | −1.36846 | −0.684229 | − | 0.729267i | \(-0.739861\pi\) | ||||
−0.684229 | + | 0.729267i | \(0.739861\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.928423 | −0.0392681 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.3871 | 1.32281 | 0.661405 | − | 0.750029i | \(-0.269960\pi\) | ||||
0.661405 | + | 0.750029i | \(0.269960\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.8105 | −0.537989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.7969 | −1.33300 | −0.666498 | − | 0.745507i | \(-0.732207\pi\) | ||||
−0.666498 | + | 0.745507i | \(0.732207\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3134 | 0.766394 | 0.383197 | − | 0.923667i | \(-0.374823\pi\) | ||||
0.383197 | + | 0.923667i | \(0.374823\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.2388 | −1.26324 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.7282 | −1.11271 | −0.556354 | − | 0.830945i | \(-0.687800\pi\) | ||||
−0.556354 | + | 0.830945i | \(0.687800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.4119 | −1.51323 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.58812 | −0.314808 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24.3463 | −1.00488 | −0.502439 | − | 0.864613i | \(-0.667564\pi\) | ||||
−0.502439 | + | 0.864613i | \(0.667564\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.37907 | 0.262845 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.36266 | 0.220590 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.7253 | −0.522566 | −0.261283 | − | 0.965262i | \(-0.584146\pi\) | ||||
−0.261283 | + | 0.965262i | \(0.584146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 68.7938 | 2.81554 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.6373 | 0.434630 | 0.217315 | − | 0.976102i | \(-0.430270\pi\) | ||||
0.217315 | + | 0.976102i | \(0.430270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5329 | 0.470439 | 0.235219 | − | 0.971942i | \(-0.424419\pi\) | ||||
0.235219 | + | 0.971942i | \(0.424419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.4423 | −1.19898 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.2827 | 0.742074 | 0.371037 | − | 0.928618i | \(-0.379002\pi\) | ||||
0.371037 | + | 0.928618i | \(0.379002\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.0357 | 0.973974 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.84612 | 0.276512 | 0.138256 | − | 0.990397i | \(-0.455850\pi\) | ||||
0.138256 | + | 0.990397i | \(0.455850\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0820 | −0.607180 | −0.303590 | − | 0.952803i | \(-0.598185\pi\) | ||||
−0.303590 | + | 0.952803i | \(0.598185\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.7253 | −1.71728 | −0.858638 | − | 0.512583i | \(-0.828689\pi\) | ||||
−0.858638 | + | 0.512583i | \(0.828689\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.93126 | 0.278142 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.62093 | 0.385454 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.36266 | −0.373314 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.7909 | 1.06653 | 0.533265 | − | 0.845948i | \(-0.320965\pi\) | ||||
0.533265 | + | 0.845948i | \(0.320965\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 43.6894 | 1.73650 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.16195 | 0.0856595 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −53.4506 | −2.11447 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1208 | 1.11070 | 0.555352 | − | 0.831615i | \(-0.312583\pi\) | ||||
0.555352 | + | 0.831615i | \(0.312583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.1372 | −0.596953 | −0.298477 | − | 0.954417i | \(-0.596478\pi\) | ||||
−0.298477 | + | 0.954417i | \(0.596478\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.06874 | −0.0420164 | −0.0210082 | − | 0.999779i | \(-0.506688\pi\) | ||||
−0.0210082 | + | 0.999779i | \(0.506688\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 54.5550 | 2.13818 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.3298 | 0.834701 | 0.417351 | − | 0.908745i | \(-0.362959\pi\) | ||||
0.417351 | + | 0.908745i | \(0.362959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.1924 | 0.904821 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.4639 | 1.77102 | 0.885512 | − | 0.464617i | \(-0.153808\pi\) | ||||
0.885512 | + | 0.464617i | \(0.153808\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.6074 | 1.11270 | 0.556349 | − | 0.830949i | \(-0.312202\pi\) | ||||
0.556349 | + | 0.830949i | \(0.312202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.17313 | 0.0843973 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.10750 | 0.236483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 65.0221 | 2.51390 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −47.1840 | −1.81881 | −0.909405 | − | 0.415911i | \(-0.863463\pi\) | ||||
−0.909405 | + | 0.415911i | \(0.863463\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.8573 | −0.801611 | −0.400806 | − | 0.916163i | \(-0.631270\pi\) | ||||
−0.400806 | + | 0.916163i | \(0.631270\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.5881 | −0.598217 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.2611 | −0.546487 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.2887 | 0.661534 | 0.330767 | − | 0.943713i | \(-0.392693\pi\) | ||||
0.330767 | + | 0.943713i | \(0.392693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 31.3955 | 1.19781 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.15672 | 0.0440675 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.8297 | −1.36303 | −0.681513 | − | 0.731806i | \(-0.738678\pi\) | ||||
−0.681513 | + | 0.731806i | \(0.738678\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.17002 | 0.0443176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −73.7802 | −2.79062 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.0880 | −1.43856 | −0.719282 | − | 0.694719i | \(-0.755529\pi\) | ||||
−0.719282 | + | 0.694719i | \(0.755529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.87086 | −0.296855 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.6597 | 1.45395 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.2747 | −0.573653 | −0.286826 | − | 0.957983i | \(-0.592600\pi\) | ||||
−0.286826 | + | 0.957983i | \(0.592600\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.4671 | 0.842580 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8625 | 0.519156 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.0357 | 1.49516 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.8597 | −1.03899 | −0.519495 | − | 0.854473i | \(-0.673880\pi\) | ||||
−0.519495 | + | 0.854473i | \(0.673880\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.9997 | 2.12278 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.0164 | −0.930370 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.4311 | 1.46242 | 0.731210 | − | 0.682153i | \(-0.238956\pi\) | ||||
0.731210 | + | 0.682153i | \(0.238956\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.4835 | −1.57346 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.62093 | −0.0599523 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.1372 | −1.22395 | −0.611975 | − | 0.790877i | \(-0.709625\pi\) | ||||
−0.611975 | + | 0.790877i | \(0.709625\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.8625 | −0.951368 | −0.475684 | − | 0.879616i | \(-0.657799\pi\) | ||||
−0.475684 | + | 0.879616i | \(0.657799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.82687 | 0.0671118 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.6842 | 1.05232 | 0.526160 | − | 0.850386i | \(-0.323631\pi\) | ||||
0.526160 | + | 0.850386i | \(0.323631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.96719 | −0.364680 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.0028 | −1.68091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.2968 | −1.25151 | −0.625753 | − | 0.780021i | \(-0.715208\pi\) | ||||
−0.625753 | + | 0.780021i | \(0.715208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.41783 | 0.124553 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6597 | −0.750889 | −0.375445 | − | 0.926845i | \(-0.622510\pi\) | ||||
−0.375445 | + | 0.926845i | \(0.622510\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1236 | 1.38198 | 0.690990 | − | 0.722864i | \(-0.257175\pi\) | ||||
0.690990 | + | 0.722864i | \(0.257175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.5522 | 1.17847 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.85969 | 0.283797 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3267 | 0.733001 | 0.366500 | − | 0.930418i | \(-0.380556\pi\) | ||||
0.366500 | + | 0.930418i | \(0.380556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −83.8953 | −3.02142 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.4559 | −0.951552 | −0.475776 | − | 0.879567i | \(-0.657833\pi\) | ||||
−0.475776 | + | 0.879567i | \(0.657833\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −67.3132 | −2.41485 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.983593 | 0.0352409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.96408 | 0.320350 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.3738 | 0.975772 | 0.487886 | − | 0.872907i | \(-0.337768\pi\) | ||||
0.487886 | + | 0.872907i | \(0.337768\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −68.4176 | −2.43573 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.75814 | 0.169180 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.01641 | 0.178138 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.4454 | −1.29096 | −0.645481 | − | 0.763776i | \(-0.723343\pi\) | ||||
−0.645481 | + | 0.763776i | \(0.723343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.9672 | −0.494124 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.6373 | 0.446518 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 71.7474 | 2.52563 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.2444 | 1.83682 | 0.918408 | − | 0.395634i | \(-0.129475\pi\) | ||||
0.918408 | + | 0.395634i | \(0.129475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.8984 | 1.15522 | 0.577610 | − | 0.816313i | \(-0.303985\pi\) | ||||
0.577610 | + | 0.816313i | \(0.303985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.0028 | 1.33282 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.36266 | −0.0476735 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.10439 | 0.318133 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.44470 | −0.155121 | −0.0775605 | − | 0.996988i | \(-0.524713\pi\) | ||||
−0.0775605 | + | 0.996988i | \(0.524713\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.7774 | 0.968259 | 0.484129 | − | 0.874996i | \(-0.339136\pi\) | ||||
0.484129 | + | 0.874996i | \(0.339136\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.5110 | −1.61735 | −0.808674 | − | 0.588257i | \(-0.799814\pi\) | ||||
−0.808674 | + | 0.588257i | \(0.799814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.2388 | 0.980772 | 0.490386 | − | 0.871505i | \(-0.336856\pi\) | ||||
0.490386 | + | 0.871505i | \(0.336856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.3239 | −0.566270 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.77454 | 0.130780 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.3463 | 0.703269 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.01641 | 0.311281 | 0.155640 | − | 0.987814i | \(-0.450256\pi\) | ||||
0.155640 | + | 0.987814i | \(0.450256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1013 | −0.727630 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −42.1208 | −1.45072 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0849 | −1.20553 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.928423 | −0.0318634 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.1044 | −0.586331 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.30749 | −0.181725 | −0.0908625 | − | 0.995863i | \(-0.528962\pi\) | ||||
−0.0908625 | + | 0.995863i | \(0.528962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.9258 | 1.32968 | 0.664839 | − | 0.746986i | \(-0.268500\pi\) | ||||
0.664839 | + | 0.746986i | \(0.268500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.1760 | 0.688395 | 0.344198 | − | 0.938897i | \(-0.388151\pi\) | ||||
0.344198 | + | 0.938897i | \(0.388151\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.41188 | 0.286676 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.3051 | 1.03160 | 0.515799 | − | 0.856710i | \(-0.327495\pi\) | ||||
0.515799 | + | 0.856710i | \(0.327495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41.7886 | −1.41921 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.78811 | −0.162239 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.4754 | −0.692987 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.43947 | −0.318748 | −0.159374 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159374 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.0028 | −0.607221 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4671 | −0.824316 | −0.412158 | − | 0.911112i | \(-0.635225\pi\) | ||||
−0.412158 | + | 0.911112i | \(0.635225\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.12080 | −0.205981 | −0.102991 | − | 0.994682i | \(-0.532841\pi\) | ||||
−0.102991 | + | 0.994682i | \(0.532841\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.4200 | −1.52505 | −0.762526 | − | 0.646957i | \(-0.776041\pi\) | ||||
−0.762526 | + | 0.646957i | \(0.776041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.3134 | −0.882524 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.7417 | −0.392922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.97003 | 0.132555 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9282 | 0.597937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.01952 | 0.0672798 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.6537 | −0.387812 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.2694 | 0.340991 | 0.170496 | − | 0.985358i | \(-0.445463\pi\) | ||||
0.170496 | + | 0.985358i | \(0.445463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50.7805 | 1.68428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.9180 | −0.361728 | −0.180864 | − | 0.983508i | \(-0.557889\pi\) | ||||
−0.180864 | + | 0.983508i | \(0.557889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.9344 | 0.922474 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.9313 | −1.28422 | −0.642112 | − | 0.766611i | \(-0.721942\pi\) | ||||
−0.642112 | + | 0.766611i | \(0.721942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 47.2252 | 1.55612 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.69251 | −0.286117 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 74.8706 | 2.45907 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.9700 | 0.720813 | 0.360407 | − | 0.932795i | \(-0.382638\pi\) | ||||
0.360407 | + | 0.932795i | \(0.382638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.17313 | 0.103995 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.6566 | −0.578051 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.6402 | −0.347600 | −0.173800 | − | 0.984781i | \(-0.555605\pi\) | ||||
−0.173800 | + | 0.984781i | \(0.555605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.9205 | 1.62910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.8656 | −0.680200 | −0.340100 | − | 0.940389i | \(-0.610461\pi\) | ||||
−0.340100 | + | 0.940389i | \(0.610461\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.13747 | 0.0696057 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.6925 | −0.412451 | −0.206226 | − | 0.978504i | \(-0.566118\pi\) | ||||
−0.206226 | + | 0.978504i | \(0.566118\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.77170 | 0.122435 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.6894 | 1.54643 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.7337 | −0.542056 | −0.271028 | − | 0.962571i | \(-0.587364\pi\) | ||||
−0.271028 | + | 0.962571i | \(0.587364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 38.0028 | 1.22718 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.69251 | 0.312662 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −60.4259 | −1.94720 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.62688 | −0.148790 | −0.0743952 | − | 0.997229i | \(-0.523703\pi\) | ||||
−0.0743952 | + | 0.997229i | \(0.523703\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.18953 | 0.102463 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4506 | −1.58695 | −0.793473 | − | 0.608605i | \(-0.791729\pi\) | ||||
−0.793473 | + | 0.608605i | \(0.791729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −74.9013 | −2.40123 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22.5962 | −0.722916 | −0.361458 | − | 0.932388i | \(-0.617721\pi\) | ||||
−0.361458 | + | 0.932388i | \(0.617721\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42.7581 | 1.36516 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.9424 | −1.05070 | −0.525350 | − | 0.850886i | \(-0.676066\pi\) | ||||
−0.525350 | + | 0.850886i | \(0.676066\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −100.418 | −3.19633 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.96124 | −0.0941618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.7802 | −1.58132 | −0.790660 | − | 0.612255i | \(-0.790263\pi\) | ||||
−0.790660 | + | 0.612255i | \(0.790263\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.48062 | −0.300858 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.4014 | 1.15284 | 0.576422 | − | 0.817152i | \(-0.304448\pi\) | ||||
0.576422 | + | 0.817152i | \(0.304448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.1044 | −0.794268 |
(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 | 3800.2.a.x.1.3 | 3 | ||
4.3 | odd | 2 | 7600.2.a.bq.1.1 | 3 | |||
5.2 | odd | 4 | 3800.2.d.l.3649.1 | 6 | |||
5.3 | odd | 4 | 3800.2.d.l.3649.6 | 6 | |||
5.4 | even | 2 | 760.2.a.j.1.1 | ✓ | 3 | ||
15.14 | odd | 2 | 6840.2.a.bg.1.1 | 3 | |||
20.19 | odd | 2 | 1520.2.a.s.1.3 | 3 | |||
40.19 | odd | 2 | 6080.2.a.bq.1.1 | 3 | |||
40.29 | even | 2 | 6080.2.a.bv.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.j.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
1520.2.a.s.1.3 | 3 | 20.19 | odd | 2 | |||
3800.2.a.x.1.3 | 3 | 1.1 | even | 1 | trivial | ||
3800.2.d.l.3649.1 | 6 | 5.2 | odd | 4 | |||
3800.2.d.l.3649.6 | 6 | 5.3 | odd | 4 | |||
6080.2.a.bq.1.1 | 3 | 40.19 | odd | 2 | |||
6080.2.a.bv.1.3 | 3 | 40.29 | even | 2 | |||
6840.2.a.bg.1.1 | 3 | 15.14 | odd | 2 | |||
7600.2.a.bq.1.1 | 3 | 4.3 | odd | 2 |