Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6075,2,Mod(1,6075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6075 = 3^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6075.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.5091192279\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 243) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.347296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34730 | 0.952682 | 0.476341 | − | 0.879261i | \(-0.341963\pi\) | ||||
0.476341 | + | 0.879261i | \(0.341963\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.184793 | −0.0923963 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.41147 | −0.911452 | −0.455726 | − | 0.890120i | \(-0.650620\pi\) | ||||
−0.455726 | + | 0.890120i | \(0.650620\pi\) | |||||||
\(8\) | −2.94356 | −1.04071 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.94356 | −1.79205 | −0.896026 | − | 0.444002i | \(-0.853558\pi\) | ||||
−0.896026 | + | 0.444002i | \(0.853558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.22668 | 0.894920 | 0.447460 | − | 0.894304i | \(-0.352329\pi\) | ||||
0.447460 | + | 0.894304i | \(0.352329\pi\) | |||||||
\(14\) | −3.24897 | −0.868324 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.59627 | −0.899067 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.63816 | −1.52290 | −0.761449 | − | 0.648225i | \(-0.775512\pi\) | ||||
−0.761449 | + | 0.648225i | \(0.775512\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.00774 | −1.70726 | ||||||||
\(23\) | −2.94356 | −0.613775 | −0.306888 | − | 0.951746i | \(-0.599288\pi\) | ||||
−0.306888 | + | 0.951746i | \(0.599288\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.34730 | 0.852575 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.445622 | 0.0842147 | ||||||||
\(29\) | 1.29086 | 0.239707 | 0.119853 | − | 0.992792i | \(-0.461758\pi\) | ||||
0.119853 | + | 0.992792i | \(0.461758\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.588526 | −0.105702 | −0.0528512 | − | 0.998602i | \(-0.516831\pi\) | ||||
−0.0528512 | + | 0.998602i | \(0.516831\pi\) | |||||||
\(32\) | 1.04189 | 0.184182 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.04189 | 0.693178 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0418891 | −0.00688652 | −0.00344326 | − | 0.999994i | \(-0.501096\pi\) | ||||
−0.00344326 | + | 0.999994i | \(0.501096\pi\) | |||||||
\(38\) | −8.94356 | −1.45084 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.90167 | 0.765513 | 0.382756 | − | 0.923849i | \(-0.374975\pi\) | ||||
0.382756 | + | 0.923849i | \(0.374975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.18479 | 0.790673 | 0.395337 | − | 0.918536i | \(-0.370628\pi\) | ||||
0.395337 | + | 0.918536i | \(0.370628\pi\) | |||||||
\(44\) | 1.09833 | 0.165579 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.96585 | −0.584733 | ||||||||
\(47\) | −3.73648 | −0.545022 | −0.272511 | − | 0.962153i | \(-0.587854\pi\) | ||||
−0.272511 | + | 0.962153i | \(0.587854\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.18479 | −0.169256 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.596267 | −0.0826873 | ||||||||
\(53\) | 11.6382 | 1.59862 | 0.799312 | − | 0.600916i | \(-0.205198\pi\) | ||||
0.799312 | + | 0.600916i | \(0.205198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.09833 | 0.948554 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.73917 | 0.228364 | ||||||||
\(59\) | 7.34730 | 0.956537 | 0.478268 | − | 0.878214i | \(-0.341265\pi\) | ||||
0.478268 | + | 0.878214i | \(0.341265\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.0496 | 1.41476 | 0.707380 | − | 0.706833i | \(-0.249877\pi\) | ||||
0.707380 | + | 0.706833i | \(0.249877\pi\) | |||||||
\(62\) | −0.792919 | −0.100701 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.59627 | 1.07453 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.85710 | −0.226880 | −0.113440 | − | 0.993545i | \(-0.536187\pi\) | ||||
−0.113440 | + | 0.993545i | \(0.536187\pi\) | |||||||
\(68\) | −0.554378 | −0.0672282 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.51249 | 0.654212 | 0.327106 | − | 0.944988i | \(-0.393927\pi\) | ||||
0.327106 | + | 0.944988i | \(0.393927\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.55438 | −0.650091 | −0.325045 | − | 0.945698i | \(-0.605380\pi\) | ||||
−0.325045 | + | 0.945698i | \(0.605380\pi\) | |||||||
\(74\) | −0.0564370 | −0.00656067 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.22668 | 0.140710 | ||||||||
\(77\) | 14.3327 | 1.63337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.78106 | −0.425402 | −0.212701 | − | 0.977117i | \(-0.568226\pi\) | ||||
−0.212701 | + | 0.977117i | \(0.568226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.60401 | 0.729291 | ||||||||
\(83\) | 3.98545 | 0.437460 | 0.218730 | − | 0.975785i | \(-0.429809\pi\) | ||||
0.218730 | + | 0.975785i | \(0.429809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.98545 | 0.753261 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 17.4953 | 1.86500 | ||||||||
\(89\) | −8.15064 | −0.863967 | −0.431983 | − | 0.901882i | \(-0.642186\pi\) | ||||
−0.431983 | + | 0.901882i | \(0.642186\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.78106 | −0.815677 | ||||||||
\(92\) | 0.543948 | 0.0567105 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.03415 | −0.519233 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.260830 | −0.0264833 | −0.0132416 | − | 0.999912i | \(-0.504215\pi\) | ||||
−0.0132416 | + | 0.999912i | \(0.504215\pi\) | |||||||
\(98\) | −1.59627 | −0.161247 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0273 | −1.09726 | −0.548631 | − | 0.836065i | \(-0.684851\pi\) | ||||
−0.548631 | + | 0.836065i | \(0.684851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.90673 | 0.384941 | 0.192471 | − | 0.981303i | \(-0.438350\pi\) | ||||
0.192471 | + | 0.981303i | \(0.438350\pi\) | |||||||
\(104\) | −9.49794 | −0.931350 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.6800 | 1.52298 | ||||||||
\(107\) | −2.63816 | −0.255040 | −0.127520 | − | 0.991836i | \(-0.540702\pi\) | ||||
−0.127520 | + | 0.991836i | \(0.540702\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.95811 | −0.858031 | −0.429016 | − | 0.903297i | \(-0.641140\pi\) | ||||
−0.429016 | + | 0.903297i | \(0.641140\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.67230 | 0.819456 | ||||||||
\(113\) | 15.9290 | 1.49848 | 0.749238 | − | 0.662301i | \(-0.230420\pi\) | ||||
0.749238 | + | 0.662301i | \(0.230420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.238541 | −0.0221480 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.89899 | 0.911275 | ||||||||
\(119\) | −7.23442 | −0.663178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.3259 | 2.21145 | ||||||||
\(122\) | 14.8871 | 1.34782 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.108755 | 0.00976650 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.59627 | −0.319117 | −0.159559 | − | 0.987188i | \(-0.551007\pi\) | ||||
−0.159559 | + | 0.987188i | \(0.551007\pi\) | |||||||
\(128\) | 9.49794 | 0.839507 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7074 | 1.54710 | 0.773551 | − | 0.633734i | \(-0.218479\pi\) | ||||
0.773551 | + | 0.633734i | \(0.218479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.0077 | 1.38805 | ||||||||
\(134\) | −2.50206 | −0.216145 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.83069 | −0.757225 | ||||||||
\(137\) | −3.92902 | −0.335678 | −0.167839 | − | 0.985814i | \(-0.553679\pi\) | ||||
−0.167839 | + | 0.985814i | \(0.553679\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.9659 | 1.01493 | 0.507465 | − | 0.861672i | \(-0.330583\pi\) | ||||
0.507465 | + | 0.861672i | \(0.330583\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.42696 | 0.623256 | ||||||||
\(143\) | −19.1780 | −1.60374 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −7.48339 | −0.619330 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.00774079 | 0.000636289 0 | ||||||||
\(149\) | −20.5253 | −1.68150 | −0.840748 | − | 0.541426i | \(-0.817885\pi\) | ||||
−0.840748 | + | 0.541426i | \(0.817885\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0077 | 1.30269 | 0.651346 | − | 0.758781i | \(-0.274205\pi\) | ||||
0.651346 | + | 0.758781i | \(0.274205\pi\) | |||||||
\(152\) | 19.5398 | 1.58489 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.3105 | 1.55608 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.9736 | 1.75368 | 0.876842 | − | 0.480779i | \(-0.159646\pi\) | ||||
0.876842 | + | 0.480779i | \(0.159646\pi\) | |||||||
\(158\) | −5.09421 | −0.405273 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.09833 | 0.559426 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.5107 | −1.60652 | −0.803262 | − | 0.595625i | \(-0.796904\pi\) | ||||
−0.803262 | + | 0.595625i | \(0.796904\pi\) | |||||||
\(164\) | −0.905793 | −0.0707305 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.36959 | 0.416761 | ||||||||
\(167\) | 4.29086 | 0.332037 | 0.166018 | − | 0.986123i | \(-0.446909\pi\) | ||||
0.166018 | + | 0.986123i | \(0.446909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.58853 | −0.199117 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.958111 | −0.0730553 | ||||||||
\(173\) | 3.79292 | 0.288370 | 0.144185 | − | 0.989551i | \(-0.453944\pi\) | ||||
0.144185 | + | 0.989551i | \(0.453944\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21.3746 | 1.61117 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.9813 | −0.823086 | ||||||||
\(179\) | −8.27631 | −0.618601 | −0.309300 | − | 0.950964i | \(-0.600095\pi\) | ||||
−0.309300 | + | 0.950964i | \(0.600095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.72193 | 0.499637 | 0.249819 | − | 0.968293i | \(-0.419629\pi\) | ||||
0.249819 | + | 0.968293i | \(0.419629\pi\) | |||||||
\(182\) | −10.4834 | −0.777081 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.66456 | 0.638760 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.8307 | −1.30391 | ||||||||
\(188\) | 0.690474 | 0.0503580 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.01455 | 0.362840 | 0.181420 | − | 0.983406i | \(-0.441931\pi\) | ||||
0.181420 | + | 0.983406i | \(0.441931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8648 | 1.28594 | 0.642970 | − | 0.765892i | \(-0.277702\pi\) | ||||
0.642970 | + | 0.765892i | \(0.277702\pi\) | |||||||
\(194\) | −0.351415 | −0.0252301 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.218941 | 0.0156386 | ||||||||
\(197\) | 0.723689 | 0.0515607 | 0.0257803 | − | 0.999668i | \(-0.491793\pi\) | ||||
0.0257803 | + | 0.999668i | \(0.491793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.1925 | −0.722530 | −0.361265 | − | 0.932463i | \(-0.617655\pi\) | ||||
−0.361265 | + | 0.932463i | \(0.617655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.8571 | −1.04534 | ||||||||
\(203\) | −3.11287 | −0.218481 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.26352 | 0.366727 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.6040 | −0.804593 | ||||||||
\(209\) | 39.4543 | 2.72911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8648 | −1.02334 | −0.511669 | − | 0.859183i | \(-0.670973\pi\) | ||||
−0.511669 | + | 0.859183i | \(0.670973\pi\) | |||||||
\(212\) | −2.15064 | −0.147707 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.55438 | −0.242972 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41921 | 0.0963426 | ||||||||
\(218\) | −12.0692 | −0.817431 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.68004 | 0.651150 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9486 | 0.733174 | 0.366587 | − | 0.930384i | \(-0.380526\pi\) | ||||
0.366587 | + | 0.930384i | \(0.380526\pi\) | |||||||
\(224\) | −2.51249 | −0.167873 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.4611 | 1.42757 | ||||||||
\(227\) | −17.3327 | −1.15041 | −0.575207 | − | 0.818008i | \(-0.695079\pi\) | ||||
−0.575207 | + | 0.818008i | \(0.695079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.56212 | 0.103228 | 0.0516138 | − | 0.998667i | \(-0.483563\pi\) | ||||
0.0516138 | + | 0.998667i | \(0.483563\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.79973 | −0.249464 | ||||||||
\(233\) | 16.7888 | 1.09987 | 0.549935 | − | 0.835207i | \(-0.314652\pi\) | ||||
0.549935 | + | 0.835207i | \(0.314652\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.35773 | −0.0883804 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.74691 | −0.631798 | ||||||||
\(239\) | 4.02910 | 0.260621 | 0.130310 | − | 0.991473i | \(-0.458403\pi\) | ||||
0.130310 | + | 0.991473i | \(0.458403\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.35235 | −0.215944 | −0.107972 | − | 0.994154i | \(-0.534436\pi\) | ||||
−0.107972 | + | 0.994154i | \(0.534436\pi\) | |||||||
\(242\) | 32.7743 | 2.10681 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.04189 | −0.130719 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.4192 | −1.36287 | ||||||||
\(248\) | 1.73236 | 0.110005 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.1506 | 1.46126 | 0.730628 | − | 0.682776i | \(-0.239227\pi\) | ||||
0.730628 | + | 0.682776i | \(0.239227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.4953 | 1.09992 | ||||||||
\(254\) | −4.84524 | −0.304017 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.39599 | −0.274750 | ||||||||
\(257\) | 12.0128 | 0.749337 | 0.374669 | − | 0.927159i | \(-0.377756\pi\) | ||||
0.374669 | + | 0.927159i | \(0.377756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.101014 | 0.00627673 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 23.8571 | 1.47390 | ||||||||
\(263\) | 16.9017 | 1.04220 | 0.521101 | − | 0.853495i | \(-0.325522\pi\) | ||||
0.521101 | + | 0.853495i | \(0.325522\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.5672 | 1.32237 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.343178 | 0.0209629 | ||||||||
\(269\) | 7.91447 | 0.482554 | 0.241277 | − | 0.970456i | \(-0.422434\pi\) | ||||
0.241277 | + | 0.970456i | \(0.422434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.2344 | −1.04692 | −0.523458 | − | 0.852051i | \(-0.675358\pi\) | ||||
−0.523458 | + | 0.852051i | \(0.675358\pi\) | |||||||
\(272\) | −10.7888 | −0.654167 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.29355 | −0.319795 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.4347 | −1.58831 | −0.794153 | − | 0.607717i | \(-0.792085\pi\) | ||||
−0.794153 | + | 0.607717i | \(0.792085\pi\) | |||||||
\(278\) | 16.1215 | 0.966906 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9959 | 1.13320 | 0.566600 | − | 0.823993i | \(-0.308259\pi\) | ||||
0.566600 | + | 0.823993i | \(0.308259\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.5868 | 0.985981 | 0.492991 | − | 0.870035i | \(-0.335904\pi\) | ||||
0.492991 | + | 0.870035i | \(0.335904\pi\) | |||||||
\(284\) | −1.01867 | −0.0604467 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −25.8384 | −1.52786 | ||||||||
\(287\) | −11.8203 | −0.697728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.02641 | 0.0600660 | ||||||||
\(293\) | 19.3577 | 1.13089 | 0.565445 | − | 0.824786i | \(-0.308704\pi\) | ||||
0.565445 | + | 0.824786i | \(0.308704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.123303 | 0.00716685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −27.6536 | −1.60193 | ||||||||
\(299\) | −9.49794 | −0.549280 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5030 | −0.720661 | ||||||||
\(302\) | 21.5672 | 1.24105 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23.8726 | 1.36919 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.8057 | −1.18744 | −0.593722 | − | 0.804670i | \(-0.702342\pi\) | ||||
−0.593722 | + | 0.804670i | \(0.702342\pi\) | |||||||
\(308\) | −2.64858 | −0.150917 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.6655 | 0.604785 | 0.302392 | − | 0.953184i | \(-0.402215\pi\) | ||||
0.302392 | + | 0.953184i | \(0.402215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.81521 | −0.215648 | −0.107824 | − | 0.994170i | \(-0.534388\pi\) | ||||
−0.107824 | + | 0.994170i | \(0.534388\pi\) | |||||||
\(314\) | 29.6049 | 1.67070 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.698711 | 0.0393056 | ||||||||
\(317\) | 26.3892 | 1.48216 | 0.741082 | − | 0.671414i | \(-0.234313\pi\) | ||||
0.741082 | + | 0.671414i | \(0.234313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.67230 | −0.429567 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.56355 | 0.532956 | ||||||||
\(323\) | −19.9145 | −1.10807 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27.6340 | −1.53051 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.4284 | −0.796674 | ||||||||
\(329\) | 9.01043 | 0.496761 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.57161 | −0.0863837 | −0.0431919 | − | 0.999067i | \(-0.513753\pi\) | ||||
−0.0431919 | + | 0.999067i | \(0.513753\pi\) | |||||||
\(332\) | −0.736482 | −0.0404197 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.78106 | 0.316325 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.01548 | 0.436631 | 0.218316 | − | 0.975878i | \(-0.429944\pi\) | ||||
0.218316 | + | 0.975878i | \(0.429944\pi\) | |||||||
\(338\) | −3.48751 | −0.189696 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.49794 | 0.189424 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7374 | 1.06572 | ||||||||
\(344\) | −15.2618 | −0.822859 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.11019 | 0.274725 | ||||||||
\(347\) | 19.8452 | 1.06535 | 0.532674 | − | 0.846320i | \(-0.321187\pi\) | ||||
0.532674 | + | 0.846320i | \(0.321187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0933 | 0.593809 | 0.296905 | − | 0.954907i | \(-0.404046\pi\) | ||||
0.296905 | + | 0.954907i | \(0.404046\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.19253 | −0.330063 | ||||||||
\(353\) | −2.86390 | −0.152430 | −0.0762151 | − | 0.997091i | \(-0.524284\pi\) | ||||
−0.0762151 | + | 0.997091i | \(0.524284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.50618 | 0.0798273 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.1506 | −0.589330 | ||||||||
\(359\) | −28.7888 | −1.51941 | −0.759707 | − | 0.650265i | \(-0.774658\pi\) | ||||
−0.759707 | + | 0.650265i | \(0.774658\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.0651 | 1.31922 | ||||||||
\(362\) | 9.05644 | 0.475996 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.43788 | 0.0753655 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9923 | 0.573791 | 0.286896 | − | 0.957962i | \(-0.407377\pi\) | ||||
0.286896 | + | 0.957962i | \(0.407377\pi\) | |||||||
\(368\) | 10.5858 | 0.551825 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −28.0651 | −1.45707 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.4097 | −1.72989 | −0.864945 | − | 0.501867i | \(-0.832647\pi\) | ||||
−0.864945 | + | 0.501867i | \(0.832647\pi\) | |||||||
\(374\) | −24.0232 | −1.24221 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.9986 | 0.567208 | ||||||||
\(377\) | 4.16519 | 0.214518 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9394 | 1.07559 | 0.537794 | − | 0.843077i | \(-0.319258\pi\) | ||||
0.537794 | + | 0.843077i | \(0.319258\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.75608 | 0.345671 | ||||||||
\(383\) | −4.11112 | −0.210068 | −0.105034 | − | 0.994469i | \(-0.533495\pi\) | ||||
−0.105034 | + | 0.994469i | \(0.533495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.0692 | 1.22509 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0481994 | 0.00244695 | ||||||||
\(389\) | −17.0942 | −0.866711 | −0.433355 | − | 0.901223i | \(-0.642670\pi\) | ||||
−0.433355 | + | 0.901223i | \(0.642670\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.83069 | −0.446587 | ||||||||
\(392\) | 3.48751 | 0.176146 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.975023 | 0.0491209 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.4020 | −1.12432 | −0.562162 | − | 0.827027i | \(-0.690030\pi\) | ||||
−0.562162 | + | 0.827027i | \(0.690030\pi\) | |||||||
\(398\) | −13.7324 | −0.688341 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5817 | 0.728176 | 0.364088 | − | 0.931364i | \(-0.381381\pi\) | ||||
0.364088 | + | 0.931364i | \(0.381381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.89899 | −0.0945952 | ||||||||
\(404\) | 2.03777 | 0.101383 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.19396 | −0.208143 | ||||||||
\(407\) | 0.248970 | 0.0123410 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.5030 | −0.865467 | −0.432734 | − | 0.901522i | \(-0.642451\pi\) | ||||
−0.432734 | + | 0.901522i | \(0.642451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.721934 | −0.0355671 | ||||||||
\(413\) | −17.7178 | −0.871837 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.36184 | 0.164828 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 53.1566 | 2.59998 | ||||||||
\(419\) | −18.8621 | −0.921476 | −0.460738 | − | 0.887536i | \(-0.652415\pi\) | ||||
−0.460738 | + | 0.887536i | \(0.652415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.3337 | −1.57585 | −0.787924 | − | 0.615773i | \(-0.788844\pi\) | ||||
−0.787924 | + | 0.615773i | \(0.788844\pi\) | |||||||
\(422\) | −20.0273 | −0.974916 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −34.2576 | −1.66370 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.6459 | −1.28949 | ||||||||
\(428\) | 0.487511 | 0.0235648 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.3164 | −1.65297 | −0.826483 | − | 0.562962i | \(-0.809662\pi\) | ||||
−0.826483 | + | 0.562962i | \(0.809662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.0669 | 1.20464 | 0.602318 | − | 0.798256i | \(-0.294244\pi\) | ||||
0.602318 | + | 0.798256i | \(0.294244\pi\) | |||||||
\(434\) | 1.91210 | 0.0917839 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.65539 | 0.0792789 | ||||||||
\(437\) | 19.5398 | 0.934717 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.2080 | −1.10766 | −0.553829 | − | 0.832630i | \(-0.686834\pi\) | ||||
−0.553829 | + | 0.832630i | \(0.686834\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.0419 | 0.620339 | ||||||||
\(443\) | −4.12155 | −0.195821 | −0.0979103 | − | 0.995195i | \(-0.531216\pi\) | ||||
−0.0979103 | + | 0.995195i | \(0.531216\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.7510 | 0.698482 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.7297 | −0.979385 | ||||||||
\(449\) | −18.3414 | −0.865585 | −0.432793 | − | 0.901494i | \(-0.642472\pi\) | ||||
−0.432793 | + | 0.901494i | \(0.642472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.1334 | −1.37184 | ||||||||
\(452\) | −2.94356 | −0.138454 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −23.3523 | −1.09598 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4611 | 0.910352 | 0.455176 | − | 0.890401i | \(-0.349576\pi\) | ||||
0.455176 | + | 0.890401i | \(0.349576\pi\) | |||||||
\(458\) | 2.10464 | 0.0983432 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.7493 | −1.29241 | −0.646206 | − | 0.763163i | \(-0.723645\pi\) | ||||
−0.646206 | + | 0.763163i | \(0.723645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.6860 | −1.79789 | −0.898946 | − | 0.438059i | \(-0.855666\pi\) | ||||
−0.898946 | + | 0.438059i | \(0.855666\pi\) | |||||||
\(464\) | −4.64227 | −0.215512 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.6195 | 1.04783 | ||||||||
\(467\) | 29.7638 | 1.37731 | 0.688653 | − | 0.725091i | \(-0.258202\pi\) | ||||
0.688653 | + | 0.725091i | \(0.258202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.47834 | 0.206791 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −21.6272 | −0.995474 | ||||||||
\(473\) | −30.8161 | −1.41693 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.33687 | 0.0612752 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.42839 | 0.248289 | ||||||||
\(479\) | 37.6759 | 1.72146 | 0.860728 | − | 0.509064i | \(-0.170008\pi\) | ||||
0.860728 | + | 0.509064i | \(0.170008\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.135163 | −0.00616289 | ||||||||
\(482\) | −4.51661 | −0.205726 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.49525 | −0.204330 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.763823 | 0.0346121 | 0.0173061 | − | 0.999850i | \(-0.494491\pi\) | ||||
0.0173061 | + | 0.999850i | \(0.494491\pi\) | |||||||
\(488\) | −32.5253 | −1.47235 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.497941 | 0.0224717 | 0.0112359 | − | 0.999937i | \(-0.496423\pi\) | ||||
0.0112359 | + | 0.999937i | \(0.496423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.87258 | 0.174412 | ||||||||
\(494\) | −28.8580 | −1.29838 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.11650 | 0.0950335 | ||||||||
\(497\) | −13.2932 | −0.596283 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.96585 | 0.401367 | 0.200683 | − | 0.979656i | \(-0.435684\pi\) | ||||
0.200683 | + | 0.979656i | \(0.435684\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 31.1908 | 1.39211 | ||||||||
\(503\) | 18.3618 | 0.818714 | 0.409357 | − | 0.912374i | \(-0.365753\pi\) | ||||
0.409357 | + | 0.912374i | \(0.365753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 23.5713 | 1.04787 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.664563 | 0.0294852 | ||||||||
\(509\) | 28.3705 | 1.25750 | 0.628751 | − | 0.777607i | \(-0.283567\pi\) | ||||
0.628751 | + | 0.777607i | \(0.283567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.3942 | 0.592526 | ||||||||
\(512\) | −24.9186 | −1.10126 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.1848 | 0.713881 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.2080 | 0.976707 | ||||||||
\(518\) | 0.136096 | 0.00597973 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.6382 | 1.42990 | 0.714952 | − | 0.699174i | \(-0.246449\pi\) | ||||
0.714952 | + | 0.699174i | \(0.246449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.0232 | 0.963008 | 0.481504 | − | 0.876444i | \(-0.340091\pi\) | ||||
0.481504 | + | 0.876444i | \(0.340091\pi\) | |||||||
\(524\) | −3.27219 | −0.142946 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.7716 | 0.992887 | ||||||||
\(527\) | −1.76558 | −0.0769098 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.3354 | −0.623280 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.95811 | −0.128250 | ||||||||
\(533\) | 15.8161 | 0.685073 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.46648 | 0.236116 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.6631 | 0.459720 | ||||||||
\(539\) | 7.04189 | 0.303316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.7870 | −0.678738 | −0.339369 | − | 0.940653i | \(-0.610214\pi\) | ||||
−0.339369 | + | 0.940653i | \(0.610214\pi\) | |||||||
\(542\) | −23.2199 | −0.997379 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.12567 | 0.134012 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.4192 | 1.17236 | 0.586180 | − | 0.810180i | \(-0.300631\pi\) | ||||
0.586180 | + | 0.810180i | \(0.300631\pi\) | |||||||
\(548\) | 0.726053 | 0.0310154 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.56893 | −0.365048 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.11793 | 0.387734 | ||||||||
\(554\) | −35.6154 | −1.51315 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.21120 | −0.0937758 | ||||||||
\(557\) | 29.4020 | 1.24580 | 0.622901 | − | 0.782301i | \(-0.285954\pi\) | ||||
0.622901 | + | 0.782301i | \(0.285954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.7297 | 0.707590 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.5931 | 1.07958 | ||||||||
\(563\) | −10.3705 | −0.437065 | −0.218533 | − | 0.975830i | \(-0.570127\pi\) | ||||
−0.218533 | + | 0.975830i | \(0.570127\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.3473 | 0.939327 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.2264 | −0.680843 | ||||||||
\(569\) | 32.9691 | 1.38214 | 0.691069 | − | 0.722788i | \(-0.257140\pi\) | ||||
0.691069 | + | 0.722788i | \(0.257140\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.737415 | −0.0308599 | −0.0154299 | − | 0.999881i | \(-0.504912\pi\) | ||||
−0.0154299 | + | 0.999881i | \(0.504912\pi\) | |||||||
\(572\) | 3.54395 | 0.148180 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.9254 | −0.664713 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.3432 | −0.805267 | −0.402634 | − | 0.915361i | \(-0.631905\pi\) | ||||
−0.402634 | + | 0.915361i | \(0.631905\pi\) | |||||||
\(578\) | −10.7784 | −0.448321 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.61081 | −0.398724 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −69.1721 | −2.86482 | ||||||||
\(584\) | 16.3497 | 0.676554 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.0806 | 1.07738 | ||||||||
\(587\) | −31.9121 | −1.31715 | −0.658577 | − | 0.752514i | \(-0.728841\pi\) | ||||
−0.658577 | + | 0.752514i | \(0.728841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.90673 | 0.160974 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.150644 | 0.00619144 | ||||||||
\(593\) | 31.6783 | 1.30087 | 0.650436 | − | 0.759561i | \(-0.274586\pi\) | ||||
0.650436 | + | 0.759561i | \(0.274586\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.79292 | 0.155364 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.7965 | −0.523289 | ||||||||
\(599\) | 12.6236 | 0.515787 | 0.257893 | − | 0.966173i | \(-0.416972\pi\) | ||||
0.257893 | + | 0.966173i | \(0.416972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.90848 | −0.363385 | −0.181692 | − | 0.983355i | \(-0.558157\pi\) | ||||
−0.181692 | + | 0.983355i | \(0.558157\pi\) | |||||||
\(602\) | −16.8452 | −0.686561 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.95811 | −0.120364 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.1242 | 1.34447 | 0.672236 | − | 0.740337i | \(-0.265334\pi\) | ||||
0.672236 | + | 0.740337i | \(0.265334\pi\) | |||||||
\(608\) | −6.91622 | −0.280490 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0564 | −0.487751 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6800 | −0.714090 | −0.357045 | − | 0.934087i | \(-0.616216\pi\) | ||||
−0.357045 | + | 0.934087i | \(0.616216\pi\) | |||||||
\(614\) | −28.0315 | −1.13126 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −42.1893 | −1.69986 | ||||||||
\(617\) | −25.7324 | −1.03595 | −0.517973 | − | 0.855397i | \(-0.673313\pi\) | ||||
−0.517973 | + | 0.855397i | \(0.673313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.7948 | 1.11717 | 0.558583 | − | 0.829448i | \(-0.311345\pi\) | ||||
0.558583 | + | 0.829448i | \(0.311345\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.3696 | 0.576168 | ||||||||
\(623\) | 19.6551 | 0.787464 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.14022 | −0.205444 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.06056 | −0.162034 | ||||||||
\(629\) | −0.125667 | −0.00501068 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8138 | 1.06744 | 0.533720 | − | 0.845661i | \(-0.320794\pi\) | ||||
0.533720 | + | 0.845661i | \(0.320794\pi\) | |||||||
\(632\) | 11.1298 | 0.442719 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 35.5541 | 1.41203 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.82295 | −0.151471 | ||||||||
\(638\) | −10.3369 | −0.409240 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6905 | −0.501244 | −0.250622 | − | 0.968085i | \(-0.580635\pi\) | ||||
−0.250622 | + | 0.968085i | \(0.580635\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.4766 | −0.610337 | −0.305168 | − | 0.952298i | \(-0.598713\pi\) | ||||
−0.305168 | + | 0.952298i | \(0.598713\pi\) | |||||||
\(644\) | −1.31172 | −0.0516889 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.8307 | −1.05564 | ||||||||
\(647\) | 11.1506 | 0.438377 | 0.219189 | − | 0.975683i | \(-0.429659\pi\) | ||||
0.219189 | + | 0.975683i | \(0.429659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.6691 | −1.71416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.79023 | 0.148437 | ||||||||
\(653\) | 44.5921 | 1.74503 | 0.872513 | − | 0.488591i | \(-0.162489\pi\) | ||||
0.872513 | + | 0.488591i | \(0.162489\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −17.6277 | −0.688247 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.1397 | 0.473255 | ||||||||
\(659\) | 14.0966 | 0.549124 | 0.274562 | − | 0.961569i | \(-0.411467\pi\) | ||||
0.274562 | + | 0.961569i | \(0.411467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.1147 | 1.40470 | 0.702350 | − | 0.711831i | \(-0.252134\pi\) | ||||
0.702350 | + | 0.711831i | \(0.252134\pi\) | |||||||
\(662\) | −2.11743 | −0.0822962 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.7314 | −0.455268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.79973 | −0.147126 | ||||||||
\(668\) | −0.792919 | −0.0306789 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.6742 | −2.53532 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.24216 | −0.0864290 | −0.0432145 | − | 0.999066i | \(-0.513760\pi\) | ||||
−0.0432145 | + | 0.999066i | \(0.513760\pi\) | |||||||
\(674\) | 10.7992 | 0.415971 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.478340 | 0.0183977 | ||||||||
\(677\) | 35.1762 | 1.35193 | 0.675966 | − | 0.736933i | \(-0.263727\pi\) | ||||
0.675966 | + | 0.736933i | \(0.263727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.628984 | 0.0241382 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.71276 | 0.180461 | ||||||||
\(683\) | −17.7638 | −0.679714 | −0.339857 | − | 0.940477i | \(-0.610379\pi\) | ||||
−0.339857 | + | 0.940477i | \(0.610379\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.5921 | 1.01529 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.6459 | −0.710868 | ||||||||
\(689\) | 37.5526 | 1.43064 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.0306 | −1.67500 | −0.837502 | − | 0.546434i | \(-0.815985\pi\) | ||||
−0.837502 | + | 0.546434i | \(0.815985\pi\) | |||||||
\(692\) | −0.700903 | −0.0266443 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.7374 | 1.01494 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7050 | 0.556992 | ||||||||
\(698\) | 14.9459 | 0.565712 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.1052 | 1.13706 | 0.568530 | − | 0.822663i | \(-0.307512\pi\) | ||||
0.568530 | + | 0.822663i | \(0.307512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.278066 | 0.0104875 | ||||||||
\(704\) | −51.0925 | −1.92562 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.85853 | −0.145218 | ||||||||
\(707\) | 26.5921 | 1.00010 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.7374 | −0.929033 | −0.464517 | − | 0.885564i | \(-0.653772\pi\) | ||||
−0.464517 | + | 0.885564i | \(0.653772\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.9919 | 0.899136 | ||||||||
\(713\) | 1.73236 | 0.0648775 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.52940 | 0.0571564 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −38.7870 | −1.44752 | ||||||||
\(719\) | 43.5526 | 1.62424 | 0.812119 | − | 0.583491i | \(-0.198314\pi\) | ||||
0.812119 | + | 0.583491i | \(0.198314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.42097 | −0.350855 | ||||||||
\(722\) | 33.7701 | 1.25679 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.24216 | −0.0461646 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5371 | −0.761680 | −0.380840 | − | 0.924641i | \(-0.624365\pi\) | ||||
−0.380840 | + | 0.924641i | \(0.624365\pi\) | |||||||
\(728\) | 22.9040 | 0.848880 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.5544 | 0.575299 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0060 | −0.517323 | −0.258661 | − | 0.965968i | \(-0.583281\pi\) | ||||
−0.258661 | + | 0.965968i | \(0.583281\pi\) | |||||||
\(734\) | 14.8098 | 0.546641 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.06687 | −0.113046 | ||||||||
\(737\) | 11.0378 | 0.406581 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.9813 | −1.54431 | −0.772154 | − | 0.635435i | \(-0.780821\pi\) | ||||
−0.772154 | + | 0.635435i | \(0.780821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37.8120 | −1.38812 | ||||||||
\(743\) | 27.8621 | 1.02216 | 0.511082 | − | 0.859532i | \(-0.329245\pi\) | ||||
0.511082 | + | 0.859532i | \(0.329245\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −45.0128 | −1.64804 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.29498 | 0.120476 | ||||||||
\(749\) | 6.36184 | 0.232457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.9050 | −1.93053 | −0.965265 | − | 0.261273i | \(-0.915858\pi\) | ||||
−0.965265 | + | 0.261273i | \(0.915858\pi\) | |||||||
\(752\) | 13.4374 | 0.490011 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.61175 | 0.204368 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.4858 | 1.50783 | 0.753913 | − | 0.656975i | \(-0.228164\pi\) | ||||
0.753913 | + | 0.656975i | \(0.228164\pi\) | |||||||
\(758\) | 28.2116 | 1.02469 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.3874 | 1.64529 | 0.822647 | − | 0.568553i | \(-0.192497\pi\) | ||||
0.822647 | + | 0.568553i | \(0.192497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.6023 | 0.782054 | ||||||||
\(764\) | −0.926651 | −0.0335251 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.53890 | −0.200128 | ||||||||
\(767\) | 23.7074 | 0.856024 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.11650 | 0.184506 | 0.0922528 | − | 0.995736i | \(-0.470593\pi\) | ||||
0.0922528 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.30129 | −0.118816 | ||||||||
\(773\) | −52.6427 | −1.89343 | −0.946713 | − | 0.322077i | \(-0.895619\pi\) | ||||
−0.946713 | + | 0.322077i | \(0.895619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.767769 | 0.0275613 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.0310 | −0.825700 | ||||||||
\(779\) | −32.5381 | −1.16580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.7638 | −1.17238 | ||||||||
\(782\) | −11.8976 | −0.425456 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.26083 | 0.152172 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.7624 | 0.740099 | 0.370050 | − | 0.929012i | \(-0.379341\pi\) | ||||
0.370050 | + | 0.929012i | \(0.379341\pi\) | |||||||
\(788\) | −0.133732 | −0.00476401 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.4124 | −1.36579 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.6536 | 1.26610 | ||||||||
\(794\) | −30.1821 | −1.07112 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.88350 | 0.0667590 | ||||||||
\(797\) | −45.5800 | −1.61453 | −0.807263 | − | 0.590192i | \(-0.799052\pi\) | ||||
−0.807263 | + | 0.590192i | \(0.799052\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.2094 | −0.396562 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.6459 | 0.693721 | ||||||||
\(803\) | 33.0128 | 1.16500 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.55850 | −0.0901192 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 32.4597 | 1.14193 | ||||||||
\(809\) | 4.21120 | 0.148058 | 0.0740290 | − | 0.997256i | \(-0.476414\pi\) | ||||
0.0740290 | + | 0.997256i | \(0.476414\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.3618 | 0.398968 | 0.199484 | − | 0.979901i | \(-0.436073\pi\) | ||||
0.199484 | + | 0.979901i | \(0.436073\pi\) | |||||||
\(812\) | 0.575236 | 0.0201868 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.335437 | 0.0117571 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.4175 | −1.20411 | ||||||||
\(818\) | −23.5817 | −0.824515 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.64227 | −0.0573158 | −0.0286579 | − | 0.999589i | \(-0.509123\pi\) | ||||
−0.0286579 | + | 0.999589i | \(0.509123\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2189 | −0.391068 | −0.195534 | − | 0.980697i | \(-0.562644\pi\) | ||||
−0.195534 | + | 0.980697i | \(0.562644\pi\) | |||||||
\(824\) | −11.4997 | −0.400611 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −23.8711 | −0.830583 | ||||||||
\(827\) | −9.61318 | −0.334283 | −0.167141 | − | 0.985933i | \(-0.553454\pi\) | ||||
−0.167141 | + | 0.985933i | \(0.553454\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.4938 | 1.16329 | 0.581644 | − | 0.813443i | \(-0.302410\pi\) | ||||
0.581644 | + | 0.813443i | \(0.302410\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 27.7374 | 0.961622 | ||||||||
\(833\) | −3.55438 | −0.123152 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.29086 | −0.252160 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.4129 | −0.877874 | ||||||||
\(839\) | 31.9941 | 1.10456 | 0.552280 | − | 0.833659i | \(-0.313758\pi\) | ||||
0.552280 | + | 0.833659i | \(0.313758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3337 | −0.942541 | ||||||||
\(842\) | −43.5631 | −1.50128 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.74691 | 0.0945526 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −58.6614 | −2.01563 | ||||||||
\(848\) | −41.8539 | −1.43727 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.123303 | 0.00422678 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.2422 | −1.20667 | −0.603334 | − | 0.797488i | \(-0.706162\pi\) | ||||
−0.603334 | + | 0.797488i | \(0.706162\pi\) | |||||||
\(854\) | −35.8999 | −1.22847 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.76558 | 0.265422 | ||||||||
\(857\) | −21.2490 | −0.725851 | −0.362925 | − | 0.931818i | \(-0.618222\pi\) | ||||
−0.362925 | + | 0.931818i | \(0.618222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.8384 | 1.76870 | 0.884352 | − | 0.466820i | \(-0.154601\pi\) | ||||
0.884352 | + | 0.466820i | \(0.154601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −46.2344 | −1.57475 | ||||||||
\(863\) | −22.6783 | −0.771978 | −0.385989 | − | 0.922503i | \(-0.626140\pi\) | ||||
−0.385989 | + | 0.922503i | \(0.626140\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 33.7725 | 1.14764 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.262260 | −0.00890170 | ||||||||
\(869\) | 22.4730 | 0.762343 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.99226 | −0.203040 | ||||||||
\(872\) | 26.3688 | 0.892959 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26.3259 | 0.890488 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.13341 | −0.0382725 | −0.0191362 | − | 0.999817i | \(-0.506092\pi\) | ||||
−0.0191362 | + | 0.999817i | \(0.506092\pi\) | |||||||
\(878\) | −31.2681 | −1.05525 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.8289 | 1.03865 | 0.519327 | − | 0.854576i | \(-0.326183\pi\) | ||||
0.519327 | + | 0.854576i | \(0.326183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.33511 | 0.314152 | 0.157076 | − | 0.987587i | \(-0.449793\pi\) | ||||
0.157076 | + | 0.987587i | \(0.449793\pi\) | |||||||
\(884\) | −1.78880 | −0.0601639 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.55295 | −0.186555 | ||||||||
\(887\) | −14.0942 | −0.473237 | −0.236619 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236619 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.67230 | 0.290860 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.02322 | −0.0677425 | ||||||||
\(893\) | 24.8033 | 0.830012 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −22.9040 | −0.765170 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.7113 | −0.824628 | ||||||||
\(899\) | −0.759704 | −0.0253376 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9145 | 1.16317 | ||||||||
\(902\) | −39.2513 | −1.30693 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −46.8881 | −1.55947 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.73917 | 0.290179 | 0.145090 | − | 0.989419i | \(-0.453653\pi\) | ||||
0.145090 | + | 0.989419i | \(0.453653\pi\) | |||||||
\(908\) | 3.20296 | 0.106294 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.6509 | 0.684196 | 0.342098 | − | 0.939664i | \(-0.388862\pi\) | ||||
0.342098 | + | 0.939664i | \(0.388862\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.6878 | −0.783951 | ||||||||
\(914\) | 26.2199 | 0.867276 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.288668 | −0.00953785 | ||||||||
\(917\) | −42.7009 | −1.41011 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.36009 | −0.0778522 | −0.0389261 | − | 0.999242i | \(-0.512394\pi\) | ||||
−0.0389261 | + | 0.999242i | \(0.512394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37.3865 | −1.23126 | ||||||||
\(923\) | 17.7870 | 0.585468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −52.1215 | −1.71282 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.34493 | 0.0441496 | ||||||||
\(929\) | 26.8203 | 0.879944 | 0.439972 | − | 0.898011i | \(-0.354988\pi\) | ||||
0.439972 | + | 0.898011i | \(0.354988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.86484 | 0.257760 | ||||||||
\(932\) | −3.10244 | −0.101624 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.1007 | 1.31213 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.93313 | −0.0631527 | −0.0315764 | − | 0.999501i | \(-0.510053\pi\) | ||||
−0.0315764 | + | 0.999501i | \(0.510053\pi\) | |||||||
\(938\) | 6.03365 | 0.197006 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.9103 | −0.388266 | −0.194133 | − | 0.980975i | \(-0.562189\pi\) | ||||
−0.194133 | + | 0.980975i | \(0.562189\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.4284 | −0.469853 | ||||||||
\(944\) | −26.4228 | −0.859990 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.5185 | −1.34988 | ||||||||
\(947\) | −0.315836 | −0.0102633 | −0.00513165 | − | 0.999987i | \(-0.501633\pi\) | ||||
−0.00513165 | + | 0.999987i | \(0.501633\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9222 | −0.581779 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.2950 | 0.690174 | ||||||||
\(953\) | 3.25133 | 0.105321 | 0.0526605 | − | 0.998612i | \(-0.483230\pi\) | ||||
0.0526605 | + | 0.998612i | \(0.483230\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.744547 | −0.0240804 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 50.7606 | 1.64000 | ||||||||
\(959\) | 9.47472 | 0.305955 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6536 | −0.988827 | ||||||||
\(962\) | −0.182104 | −0.00587127 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.619489 | 0.0199524 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.9676 | −0.352694 | −0.176347 | − | 0.984328i | \(-0.556428\pi\) | ||||
−0.176347 | + | 0.984328i | \(0.556428\pi\) | |||||||
\(968\) | −71.6049 | −2.30147 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.3868 | −0.750519 | −0.375259 | − | 0.926920i | \(-0.622446\pi\) | ||||
−0.375259 | + | 0.926920i | \(0.622446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.8553 | −0.925060 | ||||||||
\(974\) | 1.02910 | 0.0329744 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −39.7374 | −1.27196 | ||||||||
\(977\) | −50.1762 | −1.60528 | −0.802640 | − | 0.596464i | \(-0.796572\pi\) | ||||
−0.802640 | + | 0.596464i | \(0.796572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.4439 | 1.54827 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.670874 | 0.0214084 | ||||||||
\(983\) | −14.6946 | −0.468685 | −0.234342 | − | 0.972154i | \(-0.575294\pi\) | ||||
−0.234342 | + | 0.972154i | \(0.575294\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.21751 | 0.166159 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.95811 | 0.125924 | ||||||||
\(989\) | −15.2618 | −0.485296 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | −0.613179 | −0.0194684 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17.9099 | −0.568068 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.8863 | 1.45323 | 0.726617 | − | 0.687043i | \(-0.241092\pi\) | ||||
0.726617 | + | 0.687043i | \(0.241092\pi\) | |||||||
\(998\) | 12.0797 | 0.382375 | ||||||||
\(999\) | 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 | 6075.2.a.bv.1.2 | 3 | ||
3.2 | odd | 2 | 6075.2.a.bq.1.2 | 3 | |||
5.4 | even | 2 | 243.2.a.e.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 243.2.a.f.1.2 | yes | 3 | ||
20.19 | odd | 2 | 3888.2.a.bd.1.2 | 3 | |||
45.4 | even | 6 | 243.2.c.f.163.2 | 6 | |||
45.14 | odd | 6 | 243.2.c.e.163.2 | 6 | |||
45.29 | odd | 6 | 243.2.c.e.82.2 | 6 | |||
45.34 | even | 6 | 243.2.c.f.82.2 | 6 | |||
60.59 | even | 2 | 3888.2.a.bk.1.2 | 3 | |||
135.4 | even | 18 | 729.2.e.h.406.1 | 6 | |||
135.14 | odd | 18 | 729.2.e.b.163.1 | 6 | |||
135.29 | odd | 18 | 729.2.e.b.568.1 | 6 | |||
135.34 | even | 18 | 729.2.e.h.325.1 | 6 | |||
135.49 | even | 18 | 729.2.e.a.649.1 | 6 | |||
135.59 | odd | 18 | 729.2.e.i.649.1 | 6 | |||
135.74 | odd | 18 | 729.2.e.c.325.1 | 6 | |||
135.79 | even | 18 | 729.2.e.g.568.1 | 6 | |||
135.94 | even | 18 | 729.2.e.g.163.1 | 6 | |||
135.104 | odd | 18 | 729.2.e.c.406.1 | 6 | |||
135.119 | odd | 18 | 729.2.e.i.82.1 | 6 | |||
135.124 | even | 18 | 729.2.e.a.82.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
243.2.a.e.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
243.2.a.f.1.2 | yes | 3 | 15.14 | odd | 2 | ||
243.2.c.e.82.2 | 6 | 45.29 | odd | 6 | |||
243.2.c.e.163.2 | 6 | 45.14 | odd | 6 | |||
243.2.c.f.82.2 | 6 | 45.34 | even | 6 | |||
243.2.c.f.163.2 | 6 | 45.4 | even | 6 | |||
729.2.e.a.82.1 | 6 | 135.124 | even | 18 | |||
729.2.e.a.649.1 | 6 | 135.49 | even | 18 | |||
729.2.e.b.163.1 | 6 | 135.14 | odd | 18 | |||
729.2.e.b.568.1 | 6 | 135.29 | odd | 18 | |||
729.2.e.c.325.1 | 6 | 135.74 | odd | 18 | |||
729.2.e.c.406.1 | 6 | 135.104 | odd | 18 | |||
729.2.e.g.163.1 | 6 | 135.94 | even | 18 | |||
729.2.e.g.568.1 | 6 | 135.79 | even | 18 | |||
729.2.e.h.325.1 | 6 | 135.34 | even | 18 | |||
729.2.e.h.406.1 | 6 | 135.4 | even | 18 | |||
729.2.e.i.82.1 | 6 | 135.119 | odd | 18 | |||
729.2.e.i.649.1 | 6 | 135.59 | odd | 18 | |||
3888.2.a.bd.1.2 | 3 | 20.19 | odd | 2 | |||
3888.2.a.bk.1.2 | 3 | 60.59 | even | 2 | |||
6075.2.a.bq.1.2 | 3 | 3.2 | odd | 2 | |||
6075.2.a.bv.1.2 | 3 | 1.1 | even | 1 | trivial |