Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6480,2,Mod(1,6480)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6480, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6480.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6480 = 2^{4} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6480.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: | \(51.7430605098\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 360) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6480.1 |
$q$-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 | ||||||||
\(7\) | −3.44949 | −1.30378 | −0.651892 | − | 0.758312i | \(-0.726025\pi\) | ||||
−0.651892 | + | 0.758312i | \(0.726025\pi\) | |||||||
\(8\) | 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 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.89898 | 1.58273 | 0.791367 | − | 0.611341i | \(-0.209370\pi\) | ||||
0.791367 | + | 0.611341i | \(0.209370\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.44949 | 1.55333 | 0.776663 | − | 0.629916i | \(-0.216911\pi\) | ||||
0.776663 | + | 0.629916i | \(0.216911\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.89898 | −0.352632 | −0.176316 | − | 0.984334i | \(-0.556418\pi\) | ||||
−0.176316 | + | 0.984334i | \(0.556418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.10102 | −0.197749 | −0.0988746 | − | 0.995100i | \(-0.531524\pi\) | ||||
−0.0988746 | + | 0.995100i | \(0.531524\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.44949 | 0.583070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.89898 | −1.54596 | −0.772980 | − | 0.634430i | \(-0.781235\pi\) | ||||
−0.772980 | + | 0.634430i | \(0.781235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7980 | −1.79917 | −0.899586 | − | 0.436744i | \(-0.856132\pi\) | ||||
−0.899586 | + | 0.436744i | \(0.856132\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.44949 | 1.37835 | 0.689175 | − | 0.724595i | \(-0.257973\pi\) | ||||
0.689175 | + | 0.724595i | \(0.257973\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89898 | 0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.79796 | 1.07113 | 0.535566 | − | 0.844493i | \(-0.320098\pi\) | ||||
0.535566 | + | 0.844493i | \(0.320098\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.10102 | 0.143341 | 0.0716703 | − | 0.997428i | \(-0.477167\pi\) | ||||
0.0716703 | + | 0.997428i | \(0.477167\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | −0.384111 | −0.192055 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.2474 | 1.61843 | 0.809217 | − | 0.587510i | \(-0.199892\pi\) | ||||
0.809217 | + | 0.587510i | \(0.199892\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.79796 | −1.16280 | −0.581402 | − | 0.813617i | \(-0.697496\pi\) | ||||
−0.581402 | + | 0.813617i | \(0.697496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.7980 | 1.61493 | 0.807464 | − | 0.589916i | \(-0.200839\pi\) | ||||
0.807464 | + | 0.589916i | \(0.200839\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.89898 | 0.776196 | 0.388098 | − | 0.921618i | \(-0.373132\pi\) | ||||
0.388098 | + | 0.921618i | \(0.373132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.44949 | 0.598159 | 0.299080 | − | 0.954228i | \(-0.403320\pi\) | ||||
0.299080 | + | 0.954228i | \(0.403320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.79796 | 0.296583 | 0.148292 | − | 0.988944i | \(-0.452623\pi\) | ||||
0.148292 | + | 0.988944i | \(0.452623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.89898 | −0.707820 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0000 | −0.985329 | −0.492665 | − | 0.870219i | \(-0.663977\pi\) | ||||
−0.492665 | + | 0.870219i | \(0.663977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.3485 | 1.19377 | 0.596886 | − | 0.802326i | \(-0.296405\pi\) | ||||
0.596886 | + | 0.802326i | \(0.296405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.7980 | −1.03426 | −0.517128 | − | 0.855908i | \(-0.672999\pi\) | ||||
−0.517128 | + | 0.855908i | \(0.672999\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.79796 | −0.921714 | −0.460857 | − | 0.887474i | \(-0.652458\pi\) | ||||
−0.460857 | + | 0.887474i | \(0.652458\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.44949 | −0.694669 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.89898 | 0.632428 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.348469 | −0.0309216 | −0.0154608 | − | 0.999880i | \(-0.504922\pi\) | ||||
−0.0154608 | + | 0.999880i | \(0.504922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.89898 | −0.253285 | −0.126643 | − | 0.991948i | \(-0.540420\pi\) | ||||
−0.126643 | + | 0.991948i | \(0.540420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.7980 | −2.06354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5959 | 1.67419 | 0.837096 | − | 0.547056i | \(-0.184251\pi\) | ||||
0.837096 | + | 0.547056i | \(0.184251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.5959 | −1.66210 | −0.831052 | − | 0.556195i | \(-0.812261\pi\) | ||||
−0.831052 | + | 0.556195i | \(0.812261\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.89898 | 0.157702 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.0000 | −1.72039 | −0.860194 | − | 0.509968i | \(-0.829657\pi\) | ||||
−0.860194 | + | 0.509968i | \(0.829657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.10102 | 0.0884361 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.7980 | −1.89928 | −0.949642 | − | 0.313337i | \(-0.898553\pi\) | ||||
−0.949642 | + | 0.313337i | \(0.898553\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.6969 | −2.02520 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.79796 | 0.610783 | 0.305392 | − | 0.952227i | \(-0.401213\pi\) | ||||
0.305392 | + | 0.952227i | \(0.401213\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.34847 | −0.646024 | −0.323012 | − | 0.946395i | \(-0.604695\pi\) | ||||
−0.323012 | + | 0.946395i | \(0.604695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.0000 | −0.912343 | −0.456172 | − | 0.889892i | \(-0.650780\pi\) | ||||
−0.456172 | + | 0.889892i | \(0.650780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.44949 | −0.260757 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7980 | 1.03131 | 0.515654 | − | 0.856797i | \(-0.327549\pi\) | ||||
0.515654 | + | 0.856797i | \(0.327549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.69694 | −0.720768 | −0.360384 | − | 0.932804i | \(-0.617354\pi\) | ||||
−0.360384 | + | 0.932804i | \(0.617354\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8990 | 1.07805 | 0.539026 | − | 0.842289i | \(-0.318792\pi\) | ||||
0.539026 | + | 0.842289i | \(0.318792\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.20204 | −0.158506 | −0.0792532 | − | 0.996855i | \(-0.525254\pi\) | ||||
−0.0792532 | + | 0.996855i | \(0.525254\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5959 | −1.11116 | −0.555582 | − | 0.831462i | \(-0.687504\pi\) | ||||
−0.555582 | + | 0.831462i | \(0.687504\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.8990 | −1.62327 | −0.811633 | − | 0.584168i | \(-0.801421\pi\) | ||||
−0.811633 | + | 0.584168i | \(0.801421\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.55051 | 0.459756 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.89898 | 0.691375 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.7980 | 0.804614 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.79796 | 0.257822 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.44949 | −0.364925 | −0.182462 | − | 0.983213i | \(-0.558407\pi\) | ||||
−0.182462 | + | 0.983213i | \(0.558407\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.20204 | 0.544389 | 0.272194 | − | 0.962242i | \(-0.412251\pi\) | ||||
0.272194 | + | 0.962242i | \(0.412251\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.10102 | −0.271003 | −0.135502 | − | 0.990777i | \(-0.543265\pi\) | ||||
−0.135502 | + | 0.990777i | \(0.543265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.7980 | −1.29701 | −0.648504 | − | 0.761211i | \(-0.724605\pi\) | ||||
−0.648504 | + | 0.761211i | \(0.724605\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.44949 | −0.616417 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.20204 | −0.142438 | −0.0712191 | − | 0.997461i | \(-0.522689\pi\) | ||||
−0.0712191 | + | 0.997461i | \(0.522689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.69694 | −0.238141 | −0.119070 | − | 0.992886i | \(-0.537991\pi\) | ||||
−0.119070 | + | 0.992886i | \(0.537991\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.89898 | −0.312984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.89898 | −0.182982 | −0.0914910 | − | 0.995806i | \(-0.529163\pi\) | ||||
−0.0914910 | + | 0.995806i | \(0.529163\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.7980 | 1.73399 | 0.866995 | − | 0.498318i | \(-0.166049\pi\) | ||||
0.866995 | + | 0.498318i | \(0.166049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.6969 | 1.28605 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.0000 | −1.10993 | −0.554964 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.79796 | −0.479025 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.5959 | 1.37770 | 0.688849 | − | 0.724905i | \(-0.258116\pi\) | ||||
0.688849 | + | 0.724905i | \(0.258116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.8990 | −1.87698 | −0.938490 | − | 0.345307i | \(-0.887775\pi\) | ||||
−0.938490 | + | 0.345307i | \(0.887775\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0000 | −0.841178 | −0.420589 | − | 0.907251i | \(-0.638177\pi\) | ||||
−0.420589 | + | 0.907251i | \(0.638177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.10102 | −0.483266 | −0.241633 | − | 0.970368i | \(-0.577683\pi\) | ||||
−0.241633 | + | 0.970368i | \(0.577683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.65153 | 0.217061 | 0.108530 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108530 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.1464 | 2.01560 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.5959 | 1.02796 | 0.513982 | − | 0.857801i | \(-0.328170\pi\) | ||||
0.513982 | + | 0.857801i | \(0.328170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.10102 | −0.0641039 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 40.6969 | 2.34573 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | 0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.75255 | 0.271242 | 0.135621 | − | 0.990761i | \(-0.456697\pi\) | ||||
0.135621 | + | 0.990761i | \(0.456697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.89898 | 0.391205 | 0.195603 | − | 0.980683i | \(-0.437334\pi\) | ||||
0.195603 | + | 0.980683i | \(0.437334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5959 | −0.881533 | −0.440767 | − | 0.897622i | \(-0.645293\pi\) | ||||
−0.440767 | + | 0.897622i | \(0.645293\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.7980 | −1.44896 | −0.724479 | − | 0.689297i | \(-0.757920\pi\) | ||||
−0.724479 | + | 0.689297i | \(0.757920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.7980 | −0.767739 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −32.5959 | −1.79707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.89898 | 0.379202 | 0.189601 | − | 0.981861i | \(-0.439281\pi\) | ||||
0.189601 | + | 0.981861i | \(0.439281\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.2474 | −0.723785 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.7980 | −1.62320 | −0.811599 | − | 0.584215i | \(-0.801403\pi\) | ||||
−0.811599 | + | 0.584215i | \(0.801403\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.24745 | 0.391325 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.5959 | 1.37406 | 0.687030 | − | 0.726629i | \(-0.258914\pi\) | ||||
0.687030 | + | 0.726629i | \(0.258914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.30306 | −0.123280 | −0.0616400 | − | 0.998098i | \(-0.519633\pi\) | ||||
−0.0616400 | + | 0.998098i | \(0.519633\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.79796 | 0.520022 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.6969 | −1.51457 | −0.757283 | − | 0.653087i | \(-0.773474\pi\) | ||||
−0.757283 | + | 0.653087i | \(0.773474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.5959 | 1.50505 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.7980 | −0.722218 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0000 | −1.14839 | −0.574195 | − | 0.818718i | \(-0.694685\pi\) | ||||
−0.574195 | + | 0.818718i | \(0.694685\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.8990 | −1.39653 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.5959 | 1.11819 | 0.559097 | − | 0.829102i | \(-0.311148\pi\) | ||||
0.559097 | + | 0.829102i | \(0.311148\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.8990 | −1.38171 | −0.690854 | − | 0.722994i | \(-0.742765\pi\) | ||||
−0.690854 | + | 0.722994i | \(0.742765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.00000 | −0.102195 | −0.0510976 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510976 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5959 | −0.841446 | −0.420723 | − | 0.907189i | \(-0.638224\pi\) | ||||
−0.420723 | + | 0.907189i | \(0.638224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.8990 | −0.753474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.89898 | −0.347125 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0000 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.5959 | 1.27820 | 0.639100 | − | 0.769124i | \(-0.279307\pi\) | ||||
0.639100 | + | 0.769124i | \(0.279307\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.59592 | −0.474488 | −0.237244 | − | 0.971450i | \(-0.576244\pi\) | ||||
−0.237244 | + | 0.971450i | \(0.576244\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.79796 | −0.186885 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.44949 | −0.267505 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.5959 | 1.24747 | 0.623734 | − | 0.781636i | \(-0.285615\pi\) | ||||
0.623734 | + | 0.781636i | \(0.285615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3485 | 0.500798 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8990 | −0.717659 | −0.358829 | − | 0.933403i | \(-0.616824\pi\) | ||||
−0.358829 | + | 0.933403i | \(0.616824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7980 | −0.566974 | −0.283487 | − | 0.958976i | \(-0.591491\pi\) | ||||
−0.283487 | + | 0.958976i | \(0.591491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 51.3939 | 2.45850 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7980 | 0.849450 | 0.424725 | − | 0.905322i | \(-0.360371\pi\) | ||||
0.424725 | + | 0.905322i | \(0.360371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.14643 | 0.387048 | 0.193524 | − | 0.981095i | \(-0.438008\pi\) | ||||
0.193524 | + | 0.981095i | \(0.438008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.79796 | −0.132636 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.5959 | 1.01917 | 0.509587 | − | 0.860419i | \(-0.329798\pi\) | ||||
0.509587 | + | 0.860419i | \(0.329798\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.5959 | 0.823102 | 0.411551 | − | 0.911387i | \(-0.364987\pi\) | ||||
0.411551 | + | 0.911387i | \(0.364987\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.1010 | 0.563601 | 0.281800 | − | 0.959473i | \(-0.409068\pi\) | ||||
0.281800 | + | 0.959473i | \(0.409068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2020 | −0.567077 | −0.283538 | − | 0.958961i | \(-0.591508\pi\) | ||||
−0.283538 | + | 0.958961i | \(0.591508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.79796 | −0.360847 | −0.180423 | − | 0.983589i | \(-0.557747\pi\) | ||||
−0.180423 | + | 0.983589i | \(0.557747\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.6969 | −2.11009 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.89898 | 0.316547 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.4949 | −1.39335 | −0.696674 | − | 0.717388i | \(-0.745337\pi\) | ||||
−0.696674 | + | 0.717388i | \(0.745337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | −0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5959 | 0.616090 | 0.308045 | − | 0.951372i | \(-0.400325\pi\) | ||||
0.308045 | + | 0.951372i | \(0.400325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.7980 | 0.622693 | 0.311347 | − | 0.950296i | \(-0.399220\pi\) | ||||
0.311347 | + | 0.950296i | \(0.399220\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.79796 | 0.171051 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.7980 | 1.51605 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0000 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.0454 | −1.11672 | −0.558360 | − | 0.829599i | \(-0.688569\pi\) | ||||
−0.558360 | + | 0.829599i | \(0.688569\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.10102 | −0.181775 | −0.0908873 | − | 0.995861i | \(-0.528970\pi\) | ||||
−0.0908873 | + | 0.995861i | \(0.528970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −47.5959 | −2.10552 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.0000 | 0.440653 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.20204 | 0.403149 | 0.201574 | − | 0.979473i | \(-0.435394\pi\) | ||||
0.201574 | + | 0.979473i | \(0.435394\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.3485 | 1.50195 | 0.750977 | − | 0.660329i | \(-0.229583\pi\) | ||||
0.750977 | + | 0.660329i | \(0.229583\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.20204 | 0.0959224 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.4949 | 1.41282 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3485 | −0.533871 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1010 | 0.520264 | 0.260132 | − | 0.965573i | \(-0.416234\pi\) | ||||
0.260132 | + | 0.965573i | \(0.416234\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.7980 | 0.462534 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7526 | 0.716287 | 0.358144 | − | 0.933666i | \(-0.383410\pi\) | ||||
0.358144 | + | 0.933666i | \(0.383410\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.1010 | −0.558122 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.7980 | −1.01199 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.7980 | 1.85578 | 0.927890 | − | 0.372855i | \(-0.121621\pi\) | ||||
0.927890 | + | 0.372855i | \(0.121621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.3485 | 0.436136 | 0.218068 | − | 0.975934i | \(-0.430025\pi\) | ||||
0.218068 | + | 0.975934i | \(0.430025\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.79796 | 0.412203 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.0000 | 0.419222 | 0.209611 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209611 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.7980 | −1.07961 | −0.539805 | − | 0.841790i | \(-0.681502\pi\) | ||||
−0.539805 | + | 0.841790i | \(0.681502\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.44949 | 0.310665 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.0000 | −1.08239 | −0.541197 | − | 0.840896i | \(-0.682029\pi\) | ||||
−0.541197 | + | 0.840896i | \(0.682029\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.7980 | −0.779871 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.65153 | −0.315812 | −0.157906 | − | 0.987454i | \(-0.550474\pi\) | ||||
−0.157906 | + | 0.987454i | \(0.550474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.59592 | −0.312984 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.3939 | −1.28919 | −0.644596 | − | 0.764523i | \(-0.722974\pi\) | ||||
−0.644596 | + | 0.764523i | \(0.722974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.89898 | −0.282831 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.6969 | 1.00909 | 0.504545 | − | 0.863386i | \(-0.331660\pi\) | ||||
0.504545 | + | 0.863386i | \(0.331660\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0000 | 0.447214 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.14643 | −0.0871208 | −0.0435604 | − | 0.999051i | \(-0.513870\pi\) | ||||
−0.0435604 | + | 0.999051i | \(0.513870\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5959 | −1.19537 | −0.597684 | − | 0.801732i | \(-0.703912\pi\) | ||||
−0.597684 | + | 0.801732i | \(0.703912\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.1918 | −1.41677 | −0.708385 | − | 0.705826i | \(-0.750576\pi\) | ||||
−0.708385 | + | 0.705826i | \(0.750576\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.6969 | 0.992654 | 0.496327 | − | 0.868136i | \(-0.334682\pi\) | ||||
0.496327 | + | 0.868136i | \(0.334682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.65153 | −0.386680 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5959 | 0.620864 | 0.310432 | − | 0.950596i | \(-0.399526\pi\) | ||||
0.310432 | + | 0.950596i | \(0.399526\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.348469 | 0.0138286 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.8990 | −0.548977 | −0.274488 | − | 0.961590i | \(-0.588508\pi\) | ||||
−0.274488 | + | 0.961590i | \(0.588508\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1464 | 0.794498 | 0.397249 | − | 0.917711i | \(-0.369965\pi\) | ||||
0.397249 | + | 0.917711i | \(0.369965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.55051 | −0.257527 | −0.128764 | − | 0.991675i | \(-0.541101\pi\) | ||||
−0.128764 | + | 0.991675i | \(0.541101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.7980 | 1.08782 | 0.543909 | − | 0.839144i | \(-0.316944\pi\) | ||||
0.543909 | + | 0.839144i | \(0.316944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.89898 | 0.113273 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.2020 | −0.397415 | −0.198708 | − | 0.980059i | \(-0.563674\pi\) | ||||
−0.198708 | + | 0.980059i | \(0.563674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0000 | 0.388955 | 0.194477 | − | 0.980907i | \(-0.437699\pi\) | ||||
0.194477 | + | 0.980907i | \(0.437699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.7980 | 0.922845 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.1464 | −0.547752 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.0000 | −0.616755 | −0.308377 | − | 0.951264i | \(-0.599786\pi\) | ||||
−0.308377 | + | 0.951264i | \(0.599786\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2020 | 0.545829 | 0.272914 | − | 0.962038i | \(-0.412012\pi\) | ||||
0.272914 | + | 0.962038i | \(0.412012\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.89898 | −0.264759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.3939 | −0.895142 | −0.447571 | − | 0.894248i | \(-0.647711\pi\) | ||||
−0.447571 | + | 0.894248i | \(0.647711\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5959 | −0.748722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.8990 | −1.47979 | −0.739893 | − | 0.672724i | \(-0.765124\pi\) | ||||
−0.739893 | + | 0.672724i | \(0.765124\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.5959 | 0.743316 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7980 | 0.749901 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3939 | 1.14796 | 0.573980 | − | 0.818869i | \(-0.305399\pi\) | ||||
0.573980 | + | 0.818869i | \(0.305399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.3939 | −1.56120 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.89898 | 0.259463 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.69694 | 0.364176 | 0.182088 | − | 0.983282i | \(-0.441714\pi\) | ||||
0.182088 | + | 0.983282i | \(0.441714\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.20204 | −0.307169 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.2929 | 1.05515 | 0.527573 | − | 0.849510i | \(-0.323102\pi\) | ||||
0.527573 | + | 0.849510i | \(0.323102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.4949 | 1.28466 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.89898 | −0.0705263 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.2474 | 1.15890 | 0.579452 | − | 0.815006i | \(-0.303267\pi\) | ||||
0.579452 | + | 0.815006i | \(0.303267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.5959 | 0.872727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.5959 | −1.09315 | −0.546575 | − | 0.837410i | \(-0.684069\pi\) | ||||
−0.546575 | + | 0.837410i | \(0.684069\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1010 | 1.21764 | 0.608820 | − | 0.793308i | \(-0.291643\pi\) | ||||
0.608820 | + | 0.793308i | \(0.291643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.04541 | 0.258471 | 0.129235 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129235 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.0000 | 0.769380 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.5959 | −1.55642 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.2020 | −0.956126 | −0.478063 | − | 0.878326i | \(-0.658661\pi\) | ||||
−0.478063 | + | 0.878326i | \(0.658661\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.5959 | 1.14837 | 0.574187 | − | 0.818724i | \(-0.305318\pi\) | ||||
0.574187 | + | 0.818724i | \(0.305318\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.0000 | 1.26875 | 0.634375 | − | 0.773026i | \(-0.281258\pi\) | ||||
0.634375 | + | 0.773026i | \(0.281258\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.2474 | 1.34845 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.20204 | −0.187590 | −0.0937952 | − | 0.995592i | \(-0.529900\pi\) | ||||
−0.0937952 | + | 0.995592i | \(0.529900\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.20204 | 0.223072 | 0.111536 | − | 0.993760i | \(-0.464423\pi\) | ||||
0.111536 | + | 0.993760i | \(0.464423\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.10102 | −0.0395498 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −68.2929 | −2.44685 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.7980 | 0.849386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.5959 | 1.76790 | 0.883952 | − | 0.467578i | \(-0.154873\pi\) | ||||
0.883952 | + | 0.467578i | \(0.154873\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.7980 | 1.20172 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.8990 | −0.668598 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.6969 | 0.905698 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.0000 | −1.05474 | −0.527372 | − | 0.849635i | \(-0.676823\pi\) | ||||
−0.527372 | + | 0.849635i | \(0.676823\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1010 | −0.460039 | −0.230020 | − | 0.973186i | \(-0.573879\pi\) | ||||
−0.230020 | + | 0.973186i | \(0.573879\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.79796 | −0.273151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −81.3939 | −2.84761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.79796 | 0.0976494 | 0.0488247 | − | 0.998807i | \(-0.484452\pi\) | ||||
0.0488247 | + | 0.998807i | \(0.484452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.34847 | 0.291009 | 0.145505 | − | 0.989358i | \(-0.453519\pi\) | ||||
0.145505 | + | 0.989358i | \(0.453519\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −53.5403 | −1.86178 | −0.930889 | − | 0.365301i | \(-0.880966\pi\) | ||||
−0.930889 | + | 0.365301i | \(0.880966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.1918 | 1.74323 | 0.871617 | − | 0.490187i | \(-0.163072\pi\) | ||||
0.871617 | + | 0.490187i | \(0.163072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.79796 | −0.339479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.34847 | 0.288911 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.69694 | −0.162156 | −0.0810782 | − | 0.996708i | \(-0.525836\pi\) | ||||
−0.0810782 | + | 0.996708i | \(0.525836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3939 | −0.875651 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.0000 | 0.447214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.9444 | 1.30378 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −44.6969 | −1.53219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.2020 | 0.623226 | 0.311613 | − | 0.950209i | \(-0.399131\pi\) | ||||
0.311613 | + | 0.950209i | \(0.399131\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.404082 | 0.0138032 | 0.00690159 | − | 0.999976i | \(-0.497803\pi\) | ||||
0.00690159 | + | 0.999976i | \(0.497803\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.1918 | −1.33721 | −0.668604 | − | 0.743619i | \(-0.733108\pi\) | ||||
−0.668604 | + | 0.743619i | \(0.733108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −57.4495 | −1.95560 | −0.977802 | − | 0.209532i | \(-0.932806\pi\) | ||||
−0.977802 | + | 0.209532i | \(0.932806\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.44949 | 0.116614 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.404082 | −0.0136449 | −0.00682244 | − | 0.999977i | \(-0.502172\pi\) | ||||
−0.00682244 | + | 0.999977i | \(0.502172\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.10102 | 0.205549 | 0.102774 | − | 0.994705i | \(-0.467228\pi\) | ||||
0.102774 | + | 0.994705i | \(0.467228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.954592 | 0.0321246 | 0.0160623 | − | 0.999871i | \(-0.494887\pi\) | ||||
0.0160623 | + | 0.999871i | \(0.494887\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.59592 | −0.0535857 | −0.0267928 | − | 0.999641i | \(-0.508529\pi\) | ||||
−0.0267928 | + | 0.999641i | \(0.508529\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.20204 | 0.0403152 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 65.1918 | 2.18156 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.7980 | −0.461215 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.09082 | 0.0697326 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.5959 | −0.519575 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.69694 | 0.322337 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6515 | 0.718927 | 0.359464 | − | 0.933159i | \(-0.382960\pi\) | ||||
0.359464 | + | 0.933159i | \(0.382960\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.4949 | −0.347711 | −0.173856 | − | 0.984771i | \(-0.555623\pi\) | ||||
−0.173856 | + | 0.984771i | \(0.555623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.0000 | 0.330229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.6969 | −0.814677 | −0.407338 | − | 0.913277i | \(-0.633543\pi\) | ||||
−0.407338 | + | 0.913277i | \(0.633543\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.5959 | 1.23348 | 0.616741 | − | 0.787166i | \(-0.288453\pi\) | ||||
0.616741 | + | 0.787166i | \(0.288453\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.7980 | 1.10768 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.9898 | −1.33908 | −0.669539 | − | 0.742777i | \(-0.733508\pi\) | ||||
−0.669539 | + | 0.742777i | \(0.733508\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.69694 | −0.0553186 | −0.0276593 | − | 0.999617i | \(-0.508805\pi\) | ||||
−0.0276593 | + | 0.999617i | \(0.508805\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −73.7423 | −2.40138 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.8536 | 0.385189 | 0.192595 | − | 0.981278i | \(-0.438310\pi\) | ||||
0.192595 | + | 0.981278i | \(0.438310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.2020 | −0.460049 | −0.230025 | − | 0.973185i | \(-0.573881\pi\) | ||||
−0.230025 | + | 0.973185i | \(0.573881\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.8990 | −0.482120 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −67.5959 | −2.18279 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.7878 | −0.960895 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.20204 | 0.0708862 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.8434 | −1.57070 | −0.785348 | − | 0.619054i | \(-0.787516\pi\) | ||||
−0.785348 | + | 0.619054i | \(0.787516\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.3031 | −1.00456 | −0.502282 | − | 0.864704i | \(-0.667506\pi\) | ||||
−0.502282 | + | 0.864704i | \(0.667506\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 67.5959 | 2.16703 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.3939 | −0.428508 | −0.214254 | − | 0.976778i | \(-0.568732\pi\) | ||||
−0.214254 | + | 0.976778i | \(0.568732\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.4495 | 0.365182 | 0.182591 | − | 0.983189i | \(-0.441552\pi\) | ||||
0.182591 | + | 0.983189i | \(0.441552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.5959 | 0.496927 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −87.8888 | −2.79470 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.6969 | −0.911588 | −0.455794 | − | 0.890085i | \(-0.650645\pi\) | ||||
−0.455794 | + | 0.890085i | \(0.650645\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.8990 | 0.725946 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.3939 | −0.740892 | −0.370446 | − | 0.928854i | \(-0.620795\pi\) | ||||
−0.370446 | + | 0.928854i | \(0.620795\pi\) | |||||||
\(998\) | 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 | 6480.2.a.bc.1.1 | 2 | ||
3.2 | odd | 2 | 6480.2.a.bl.1.1 | 2 | |||
4.3 | odd | 2 | 3240.2.a.j.1.2 | 2 | |||
9.2 | odd | 6 | 2160.2.q.g.1441.2 | 4 | |||
9.4 | even | 3 | 720.2.q.g.241.2 | 4 | |||
9.5 | odd | 6 | 2160.2.q.g.721.2 | 4 | |||
9.7 | even | 3 | 720.2.q.g.481.2 | 4 | |||
12.11 | even | 2 | 3240.2.a.o.1.2 | 2 | |||
36.7 | odd | 6 | 360.2.q.c.121.1 | ✓ | 4 | ||
36.11 | even | 6 | 1080.2.q.c.361.1 | 4 | |||
36.23 | even | 6 | 1080.2.q.c.721.1 | 4 | |||
36.31 | odd | 6 | 360.2.q.c.241.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.c.121.1 | ✓ | 4 | 36.7 | odd | 6 | ||
360.2.q.c.241.1 | yes | 4 | 36.31 | odd | 6 | ||
720.2.q.g.241.2 | 4 | 9.4 | even | 3 | |||
720.2.q.g.481.2 | 4 | 9.7 | even | 3 | |||
1080.2.q.c.361.1 | 4 | 36.11 | even | 6 | |||
1080.2.q.c.721.1 | 4 | 36.23 | even | 6 | |||
2160.2.q.g.721.2 | 4 | 9.5 | odd | 6 | |||
2160.2.q.g.1441.2 | 4 | 9.2 | odd | 6 | |||
3240.2.a.j.1.2 | 2 | 4.3 | odd | 2 | |||
3240.2.a.o.1.2 | 2 | 12.11 | even | 2 | |||
6480.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6480.2.a.bl.1.1 | 2 | 3.2 | odd | 2 |