Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6840,2,Mod(1,6840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6840.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: | \(54.6176749826\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
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 | 1.1 | ||
Root | \(-0.254102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6840.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.18953 | −1.20553 | −0.602765 | − | 0.797919i | \(-0.705934\pi\) | ||||
−0.602765 | + | 0.797919i | \(0.705934\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | \(-0.530120\pi\) | ||||
−0.0944836 | + | 0.995526i | \(0.530120\pi\) | |||||||
\(14\) | 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 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.17313 | 0.453128 | 0.226564 | − | 0.973996i | \(-0.427251\pi\) | ||||
0.226564 | + | 0.973996i | \(0.427251\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.81047 | −0.521890 | −0.260945 | − | 0.965354i | \(-0.584034\pi\) | ||||
−0.260945 | + | 0.965354i | \(0.584034\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | 3.18953 | 0.539130 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.87086 | 1.29396 | 0.646981 | − | 0.762506i | \(-0.276031\pi\) | ||||
0.646981 | + | 0.762506i | \(0.276031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.983593 | −0.153611 | −0.0768057 | − | 0.997046i | \(-0.524472\pi\) | ||||
−0.0768057 | + | 0.997046i | \(0.524472\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.36266 | 0.207804 | 0.103902 | − | 0.994588i | \(-0.466867\pi\) | ||||
0.103902 | + | 0.994588i | \(0.466867\pi\) | |||||||
\(44\) | 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 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.5358 | −1.50183 | −0.750916 | − | 0.660398i | \(-0.770388\pi\) | ||||
−0.750916 | + | 0.660398i | \(0.770388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.36266 | 0.942692 | 0.471346 | − | 0.881948i | \(-0.343768\pi\) | ||||
0.471346 | + | 0.881948i | \(0.343768\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.681331 | 0.0845087 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.02759 | 0.858556 | 0.429278 | − | 0.903172i | \(-0.358768\pi\) | ||||
0.429278 | + | 0.903172i | \(0.358768\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7581 | 1.51411 | 0.757056 | − | 0.653350i | \(-0.226637\pi\) | ||||
0.757056 | + | 0.653350i | \(0.226637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.53579 | −0.647915 | −0.323958 | − | 0.946072i | \(-0.605013\pi\) | ||||
−0.323958 | + | 0.946072i | \(0.605013\pi\) | |||||||
\(74\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.37907 | −0.261137 | −0.130568 | − | 0.991439i | \(-0.541680\pi\) | ||||
−0.130568 | + | 0.991439i | \(0.541680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.18953 | −0.129023 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.01641 | −0.319738 | −0.159869 | − | 0.987138i | \(-0.551107\pi\) | ||||
−0.159869 | + | 0.987138i | \(0.551107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.17313 | 0.227806 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.88727 | 0.496227 | 0.248114 | − | 0.968731i | \(-0.420189\pi\) | ||||
0.248114 | + | 0.968731i | \(0.420189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.1208 | −1.20606 | −0.603032 | − | 0.797717i | \(-0.706041\pi\) | ||||
−0.603032 | + | 0.797717i | \(0.706041\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8709 | −1.76087 | −0.880434 | − | 0.474168i | \(-0.842749\pi\) | ||||
−0.880434 | + | 0.474168i | \(0.842749\pi\) | |||||||
\(104\) | 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 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.49180 | 0.140336 | 0.0701682 | − | 0.997535i | \(-0.477646\pi\) | ||||
0.0701682 | + | 0.997535i | \(0.477646\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.17313 | −0.202645 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.79406 | −0.347801 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.24993 | 0.732063 | 0.366032 | − | 0.930602i | \(-0.380716\pi\) | ||||
0.366032 | + | 0.930602i | \(0.380716\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.75814 | −0.765202 | −0.382601 | − | 0.923914i | \(-0.624972\pi\) | ||||
−0.382601 | + | 0.923914i | \(0.624972\pi\) | |||||||
\(132\) | 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 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.81047 | 0.233396 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.8461 | 1.54393 | 0.771967 | − | 0.635662i | \(-0.219273\pi\) | ||||
0.771967 | + | 0.635662i | \(0.219273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0880 | −1.30922 | −0.654611 | − | 0.755966i | \(-0.727167\pi\) | ||||
−0.654611 | + | 0.755966i | \(0.727167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.37907 | −0.512379 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.7417 | −1.09671 | −0.548355 | − | 0.836246i | \(-0.684746\pi\) | ||||
−0.548355 | + | 0.836246i | \(0.684746\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.93126 | −0.546260 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.6373 | −1.14648 | −0.573242 | − | 0.819386i | \(-0.694315\pi\) | ||||
−0.573242 | + | 0.819386i | \(0.694315\pi\) | |||||||
\(164\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.85446 | −0.521135 | −0.260567 | − | 0.965456i | \(-0.583910\pi\) | ||||
−0.260567 | + | 0.965456i | \(0.583910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.18953 | −0.241106 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.01641 | −0.374944 | −0.187472 | − | 0.982270i | \(-0.560029\pi\) | ||||
−0.187472 | + | 0.982270i | \(0.560029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7253 | 1.24318 | 0.621592 | − | 0.783341i | \(-0.286486\pi\) | ||||
0.621592 | + | 0.783341i | \(0.286486\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.87086 | −0.578677 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2775 | 0.816013 | 0.408006 | − | 0.912979i | \(-0.366224\pi\) | ||||
0.408006 | + | 0.912979i | \(0.366224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.5798 | 0.977494 | 0.488747 | − | 0.872426i | \(-0.337454\pi\) | ||||
0.488747 | + | 0.872426i | \(0.337454\pi\) | |||||||
\(194\) | 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 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.96408 | 0.629155 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.983593 | 0.0686971 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.36266 | −0.0929327 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.3463 | −1.38119 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.810466 | −0.0545178 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.2499 | −1.62390 | −0.811948 | − | 0.583730i | \(-0.801593\pi\) | ||||
−0.811948 | + | 0.583730i | \(0.801593\pi\) | |||||||
\(224\) | 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 | ||||||||
\(235\) | 11.7417 | 0.765946 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.9313 | −0.965823 | −0.482912 | − | 0.875669i | \(-0.660421\pi\) | ||||
−0.482912 | + | 0.875669i | \(0.660421\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.32985 | −0.600988 | −0.300494 | − | 0.953784i | \(-0.597152\pi\) | ||||
−0.300494 | + | 0.953784i | \(0.597152\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.17313 | −0.202724 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.681331 | −0.0433520 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.27468 | −0.0804569 | −0.0402285 | − | 0.999191i | \(-0.512809\pi\) | ||||
−0.0402285 | + | 0.999191i | \(0.512809\pi\) | |||||||
\(252\) | 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 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.5163 | −1.57340 | −0.786700 | − | 0.617335i | \(-0.788212\pi\) | ||||
−0.786700 | + | 0.617335i | \(0.788212\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.69774 | −0.104291 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.7581 | −1.63147 | −0.815736 | − | 0.578424i | \(-0.803668\pi\) | ||||
−0.815736 | + | 0.578424i | \(0.803668\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.1731 | 0.860956 | 0.430478 | − | 0.902601i | \(-0.358345\pi\) | ||||
0.430478 | + | 0.902601i | \(0.358345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.08798 | 0.365791 | 0.182896 | − | 0.983132i | \(-0.441453\pi\) | ||||
0.182896 | + | 0.983132i | \(0.441453\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.7089 | 0.937115 | 0.468558 | − | 0.883433i | \(-0.344774\pi\) | ||||
0.468558 | + | 0.883433i | \(0.344774\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.346255 | 0.0205827 | 0.0102913 | − | 0.999947i | \(-0.496724\pi\) | ||||
0.0102913 | + | 0.999947i | \(0.496724\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.13720 | 0.185183 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5850 | −0.916765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.71414 | −0.392244 | −0.196122 | − | 0.980579i | \(-0.562835\pi\) | ||||
−0.196122 | + | 0.980579i | \(0.562835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5358 | 0.671640 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.48062 | −0.0856264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.34625 | −0.250514 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.36266 | −0.421585 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.6126 | −1.00520 | −0.502602 | − | 0.864518i | \(-0.667624\pi\) | ||||
−0.502602 | + | 0.864518i | \(0.667624\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.58501 | 0.373402 | 0.186701 | − | 0.982417i | \(-0.440221\pi\) | ||||
0.186701 | + | 0.982417i | \(0.440221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.6178 | −1.05234 | −0.526171 | − | 0.850379i | \(-0.676373\pi\) | ||||
−0.526171 | + | 0.850379i | \(0.676373\pi\) | |||||||
\(314\) | 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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.18953 | 0.0661874 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.681331 | −0.0377934 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.02759 | −0.383958 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.87086 | −0.428753 | −0.214377 | − | 0.976751i | \(-0.568772\pi\) | ||||
−0.214377 | + | 0.976751i | \(0.568772\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.15672 | −0.168015 | −0.0840076 | − | 0.996465i | \(-0.526772\pi\) | ||||
−0.0840076 | + | 0.996465i | \(0.526772\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7581 | −0.677132 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.8269 | −0.940866 | −0.470433 | − | 0.882436i | \(-0.655902\pi\) | ||||
−0.470433 | + | 0.882436i | \(0.655902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.53579 | 0.289756 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.2252 | 1.00355 | 0.501773 | − | 0.864999i | \(-0.332681\pi\) | ||||
0.501773 | + | 0.864999i | \(0.332681\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.41499 | −0.281132 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.95601 | 0.515503 | 0.257751 | − | 0.966211i | \(-0.417018\pi\) | ||||
0.257751 | + | 0.966211i | \(0.417018\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.3463 | −0.524576 | −0.262288 | − | 0.964990i | \(-0.584477\pi\) | ||||
−0.262288 | + | 0.964990i | \(0.584477\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58501 | 0.130730 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.36266 | −0.269825 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.1536 | 1.31261 | 0.656306 | − | 0.754495i | \(-0.272118\pi\) | ||||
0.656306 | + | 0.754495i | \(0.272118\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.7253 | 1.63422 | 0.817112 | − | 0.576479i | \(-0.195574\pi\) | ||||
0.817112 | + | 0.576479i | \(0.195574\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.7938 | 1.81050 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.37907 | 0.116784 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8297 | 0.773332 | 0.386666 | − | 0.922220i | \(-0.373627\pi\) | ||||
0.386666 | + | 0.922220i | \(0.373627\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.05233 | 0.294973 | 0.147486 | − | 0.989064i | \(-0.452882\pi\) | ||||
0.147486 | + | 0.989064i | \(0.452882\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.18953 | 0.0577009 | ||||||||
\(426\) | 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 | \(-0.712534\pi\) | ||||
−0.619177 | + | 0.785251i | \(0.712534\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.57383 | 0.123690 | 0.0618452 | − | 0.998086i | \(-0.480301\pi\) | ||||
0.0618452 | + | 0.998086i | \(0.480301\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.7909 | −0.512693 | −0.256347 | − | 0.966585i | \(-0.582519\pi\) | ||||
−0.256347 | + | 0.966585i | \(0.582519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.01641 | 0.142991 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.4835 | 1.39141 | 0.695705 | − | 0.718327i | \(-0.255092\pi\) | ||||
0.695705 | + | 0.718327i | \(0.255092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.17313 | −0.101878 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.8269 | −0.553238 | −0.276619 | − | 0.960980i | \(-0.589214\pi\) | ||||
−0.276619 | + | 0.960980i | \(0.589214\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.45065 | 0.347011 | 0.173506 | − | 0.984833i | \(-0.444491\pi\) | ||||
0.173506 | + | 0.984833i | \(0.444491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.4506 | −1.74048 | −0.870240 | − | 0.492629i | \(-0.836036\pi\) | ||||
−0.870240 | + | 0.492629i | \(0.836036\pi\) | |||||||
\(464\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.6597 | −0.487054 | −0.243527 | − | 0.969894i | \(-0.578304\pi\) | ||||
−0.243527 | + | 0.969894i | \(0.578304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.36266 | −0.244516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.88727 | −0.221920 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.92604 | 0.359163 | 0.179581 | − | 0.983743i | \(-0.442526\pi\) | ||||
0.179581 | + | 0.983743i | \(0.442526\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.68656 | 0.0761133 | 0.0380567 | − | 0.999276i | \(-0.487883\pi\) | ||||
0.0380567 | + | 0.999276i | \(0.487883\pi\) | |||||||
\(492\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.06874 | −0.0476526 | −0.0238263 | − | 0.999716i | \(-0.507585\pi\) | ||||
−0.0238263 | + | 0.999716i | \(0.507585\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1208 | 0.539368 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.0164 | 0.842887 | 0.421444 | − | 0.906855i | \(-0.361524\pi\) | ||||
0.421444 | + | 0.906855i | \(0.361524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.6566 | 0.781081 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.8709 | 0.787484 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.07158 | −0.397433 | −0.198717 | − | 0.980057i | \(-0.563677\pi\) | ||||
−0.198717 | + | 0.980057i | \(0.563677\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.4946 | −0.590079 | −0.295040 | − | 0.955485i | \(-0.595333\pi\) | ||||
−0.295040 | + | 0.955485i | \(0.595333\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.58812 | 0.330544 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.2775 | −0.794675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.670152 | 0.0290275 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.4231 | 0.623563 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.2059 | −0.437174 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.1291 | −0.775146 | −0.387573 | − | 0.921839i | \(-0.626686\pi\) | ||||
−0.387573 | + | 0.921839i | \(0.626686\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | ||||||||
\(565\) | −1.49180 | −0.0627604 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.7969 | 1.33300 | 0.666498 | − | 0.745507i | \(-0.267793\pi\) | ||||
0.666498 | + | 0.745507i | \(0.267793\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3134 | 0.766394 | 0.383197 | − | 0.923667i | \(-0.374823\pi\) | ||||
0.383197 | + | 0.923667i | \(0.374823\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.17313 | 0.0906257 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.7282 | 1.11271 | 0.556354 | − | 0.830945i | \(-0.312200\pi\) | ||||
0.556354 | + | 0.830945i | \(0.312200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.7253 | −0.522566 | −0.261283 | − | 0.965262i | \(-0.584146\pi\) | ||||
−0.261283 | + | 0.965262i | \(0.584146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.79406 | 0.155541 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.6373 | −0.434630 | −0.217315 | − | 0.976102i | \(-0.569730\pi\) | ||||
−0.217315 | + | 0.976102i | \(0.569730\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5329 | 0.470439 | 0.235219 | − | 0.971942i | \(-0.424419\pi\) | ||||
0.235219 | + | 0.971942i | \(0.424419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.2827 | −0.742074 | −0.371037 | − | 0.928618i | \(-0.620998\pi\) | ||||
−0.371037 | + | 0.928618i | \(0.620998\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.84612 | −0.276512 | −0.138256 | − | 0.990397i | \(-0.544150\pi\) | ||||
−0.138256 | + | 0.990397i | \(0.544150\pi\) | |||||||
\(614\) | 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 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.62093 | 0.385454 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.24993 | −0.327389 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.16195 | −0.0856595 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.1208 | −1.11070 | −0.555352 | − | 0.831615i | \(-0.687417\pi\) | ||||
−0.555352 | + | 0.831615i | \(0.687417\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.1372 | 0.596953 | 0.298477 | − | 0.954417i | \(-0.403522\pi\) | ||||
0.298477 | + | 0.954417i | \(0.403522\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.3298 | 0.834701 | 0.417351 | − | 0.908745i | \(-0.362959\pi\) | ||||
0.417351 | + | 0.908745i | \(0.362959\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.75814 | 0.342209 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.4639 | −1.77102 | −0.885512 | − | 0.464617i | \(-0.846192\pi\) | ||||
−0.885512 | + | 0.464617i | \(0.846192\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.6074 | 1.11270 | 0.556349 | − | 0.830949i | \(-0.312202\pi\) | ||||
0.556349 | + | 0.830949i | \(0.312202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.18953 | 0.123685 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.10750 | −0.236483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.1840 | 1.81881 | 0.909405 | − | 0.415911i | \(-0.136537\pi\) | ||||
0.909405 | + | 0.415911i | \(0.136537\pi\) | |||||||
\(674\) | 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 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.2887 | 0.661534 | 0.330767 | − | 0.943713i | \(-0.392693\pi\) | ||||
0.330767 | + | 0.943713i | \(0.392693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.9149 | −0.455243 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(695\) | 23.4835 | 0.890778 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.17002 | −0.0443176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.0880 | 1.43856 | 0.719282 | − | 0.694719i | \(-0.244471\pi\) | ||||
0.719282 | + | 0.694719i | \(0.244471\pi\) | |||||||
\(702\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.8625 | 0.519156 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.8597 | 1.03899 | 0.519495 | − | 0.854473i | \(-0.326120\pi\) | ||||
0.519495 | + | 0.854473i | \(0.326120\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 56.9997 | 2.12278 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.81047 | −0.104378 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.4311 | −1.46242 | −0.731210 | − | 0.682153i | \(-0.761044\pi\) | ||||
−0.731210 | + | 0.682153i | \(0.761044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.62093 | 0.0599523 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.1372 | 1.22395 | 0.611975 | − | 0.790877i | \(-0.290375\pi\) | ||||
0.611975 | + | 0.790877i | \(0.290375\pi\) | |||||||
\(734\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.6842 | 1.05232 | 0.526160 | − | 0.850386i | \(-0.323631\pi\) | ||||
0.526160 | + | 0.850386i | \(0.323631\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.8461 | −0.690468 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.0880 | 0.585502 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.6597 | 0.750889 | 0.375445 | − | 0.926845i | \(-0.377490\pi\) | ||||
0.375445 | + | 0.926845i | \(0.377490\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.1236 | −1.38198 | −0.690990 | − | 0.722864i | \(-0.742825\pi\) | ||||
−0.690990 | + | 0.722864i | \(0.742825\pi\) | |||||||
\(762\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.4559 | −0.951552 | −0.475776 | − | 0.879567i | \(-0.657833\pi\) | ||||
−0.475776 | + | 0.879567i | \(0.657833\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.37907 | 0.229143 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.983593 | −0.0352409 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7417 | 0.490463 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.3738 | −0.975772 | −0.487886 | − | 0.872907i | \(-0.662232\pi\) | ||||
−0.487886 | + | 0.872907i | \(0.662232\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.93126 | 0.244295 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −52.2444 | −1.83682 | −0.918408 | − | 0.395634i | \(-0.870525\pi\) | ||||
−0.918408 | + | 0.395634i | \(0.870525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.8984 | 1.15522 | 0.577610 | − | 0.816313i | \(-0.303985\pi\) | ||||
0.577610 | + | 0.816313i | \(0.303985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.6373 | 0.512724 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.36266 | 0.0476735 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.44470 | 0.155121 | 0.0775605 | − | 0.996988i | \(-0.475287\pi\) | ||||
0.0775605 | + | 0.996988i | \(0.475287\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.7774 | −0.968259 | −0.484129 | − | 0.874996i | \(-0.660864\pi\) | ||||
−0.484129 | + | 0.874996i | \(0.660864\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.77454 | 0.130780 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.9588 | 0.621492 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.01641 | −0.311281 | −0.155640 | − | 0.987814i | \(-0.549744\pi\) | ||||
−0.155640 | + | 0.987814i | \(0.549744\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1013 | −0.727630 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.5358 | 0.431244 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.0849 | 1.20553 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.1044 | 0.586331 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.30749 | 0.181725 | 0.0908625 | − | 0.995863i | \(-0.471038\pi\) | ||||
0.0908625 | + | 0.995863i | \(0.471038\pi\) | |||||||
\(854\) | 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 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.3051 | 1.03160 | 0.515799 | − | 0.856710i | \(-0.327495\pi\) | ||||
0.515799 | + | 0.856710i | \(0.327495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.85446 | 0.233059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.78811 | −0.162239 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.18953 | 0.107826 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.43947 | 0.318748 | 0.159374 | − | 0.987218i | \(-0.449052\pi\) | ||||
0.159374 | + | 0.987218i | \(0.449052\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.4671 | 0.824316 | 0.412158 | − | 0.911112i | \(-0.364775\pi\) | ||||
0.412158 | + | 0.911112i | \(0.364775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.12080 | 0.205981 | 0.102991 | − | 0.994682i | \(-0.467159\pi\) | ||||
0.102991 | + | 0.994682i | \(0.467159\pi\) | |||||||
\(884\) | 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 | ||||||||
\(895\) | 5.01641 | 0.167680 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.9282 | −0.597937 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.01952 | 0.0672798 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.7253 | −0.555969 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.2694 | −0.340991 | −0.170496 | − | 0.985358i | \(-0.554537\pi\) | ||||
−0.170496 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.9180 | 0.361728 | 0.180864 | − | 0.983508i | \(-0.442111\pi\) | ||||
0.180864 | + | 0.983508i | \(0.442111\pi\) | |||||||
\(912\) | 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 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.69251 | −0.286117 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.87086 | 0.258792 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.9700 | −0.720813 | −0.360407 | − | 0.932795i | \(-0.617362\pi\) | ||||
−0.360407 | + | 0.932795i | \(0.617362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.17313 | 0.103995 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6402 | 0.347600 | 0.173800 | − | 0.984781i | \(-0.444395\pi\) | ||||
0.173800 | + | 0.984781i | \(0.444395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.8656 | 0.680200 | 0.340100 | − | 0.940389i | \(-0.389539\pi\) | ||||
0.340100 | + | 0.940389i | \(0.389539\pi\) | |||||||
\(942\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.7337 | −0.542056 | −0.271028 | − | 0.962571i | \(-0.587364\pi\) | ||||
−0.271028 | + | 0.962571i | \(0.587364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.2775 | −0.364932 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.0028 | −1.22718 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.69251 | 0.312662 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.5798 | −0.437149 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.62688 | 0.148790 | 0.0743952 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743952 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.4506 | 1.58695 | 0.793473 | − | 0.608605i | \(-0.208271\pi\) | ||||
0.793473 | + | 0.608605i | \(0.208271\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.9424 | −1.05070 | −0.525350 | − | 0.850886i | \(-0.676066\pi\) | ||||
−0.525350 | + | 0.850886i | \(0.676066\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00000 | −0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.6566 | −0.813368 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.4014 | −1.15284 | −0.576422 | − | 0.817152i | \(-0.695552\pi\) | ||||
−0.576422 | + | 0.817152i | \(0.695552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 6840.2.a.bg.1.1 | 3 | ||
3.2 | odd | 2 | 760.2.a.j.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 1520.2.a.s.1.3 | 3 | |||
15.2 | even | 4 | 3800.2.d.l.3649.6 | 6 | |||
15.8 | even | 4 | 3800.2.d.l.3649.1 | 6 | |||
15.14 | odd | 2 | 3800.2.a.x.1.3 | 3 | |||
24.5 | odd | 2 | 6080.2.a.bv.1.3 | 3 | |||
24.11 | even | 2 | 6080.2.a.bq.1.1 | 3 | |||
60.59 | even | 2 | 7600.2.a.bq.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.j.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
1520.2.a.s.1.3 | 3 | 12.11 | even | 2 | |||
3800.2.a.x.1.3 | 3 | 15.14 | odd | 2 | |||
3800.2.d.l.3649.1 | 6 | 15.8 | even | 4 | |||
3800.2.d.l.3649.6 | 6 | 15.2 | even | 4 | |||
6080.2.a.bq.1.1 | 3 | 24.11 | even | 2 | |||
6080.2.a.bv.1.3 | 3 | 24.5 | odd | 2 | |||
6840.2.a.bg.1.1 | 3 | 1.1 | even | 1 | trivial | ||
7600.2.a.bq.1.1 | 3 | 60.59 | even | 2 |