Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, 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("3240.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.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: | \(25.8715302549\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 3240.1 |
$q$-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 | ||||||||
\(7\) | −1.44949 | −0.547856 | −0.273928 | − | 0.961750i | \(-0.588323\pi\) | ||||
−0.273928 | + | 0.961750i | \(0.588323\pi\) | |||||||
\(8\) | 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 | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.89898 | 0.665072 | 0.332536 | − | 0.943091i | \(-0.392096\pi\) | ||||
0.332536 | + | 0.943091i | \(0.392096\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.55051 | 0.531818 | 0.265909 | − | 0.963998i | \(-0.414328\pi\) | ||||
0.265909 | + | 0.963998i | \(0.414328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.89898 | −1.46680 | −0.733402 | − | 0.679795i | \(-0.762069\pi\) | ||||
−0.733402 | + | 0.679795i | \(0.762069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.8990 | 1.95751 | 0.978757 | − | 0.205023i | \(-0.0657268\pi\) | ||||
0.978757 | + | 0.205023i | \(0.0657268\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.44949 | −0.245008 | ||||||||
\(36\) | 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 | ||||||||
\(41\) | 0.101021 | 0.0157768 | 0.00788838 | − | 0.999969i | \(-0.497489\pi\) | ||||
0.00788838 | + | 0.999969i | \(0.497489\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.79796 | −1.18918 | −0.594589 | − | 0.804030i | \(-0.702685\pi\) | ||||
−0.594589 | + | 0.804030i | \(0.702685\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.55051 | 0.663760 | 0.331880 | − | 0.943322i | \(-0.392317\pi\) | ||||
0.331880 | + | 0.943322i | \(0.392317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.89898 | −0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.7980 | 1.62057 | 0.810287 | − | 0.586033i | \(-0.199311\pi\) | ||||
0.810287 | + | 0.586033i | \(0.199311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.8990 | 1.41893 | 0.709463 | − | 0.704743i | \(-0.248937\pi\) | ||||
0.709463 | + | 0.704743i | \(0.248937\pi\) | |||||||
\(60\) | 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 | ||||||||
\(67\) | 11.2474 | 1.37409 | 0.687047 | − | 0.726613i | \(-0.258907\pi\) | ||||
0.687047 | + | 0.726613i | \(0.258907\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.79796 | 1.16280 | 0.581402 | − | 0.813617i | \(-0.302504\pi\) | ||||
0.581402 | + | 0.813617i | \(0.302504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.79796 | −0.678600 | −0.339300 | − | 0.940678i | \(-0.610190\pi\) | ||||
−0.339300 | + | 0.940678i | \(0.610190\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.89898 | 0.326161 | 0.163080 | − | 0.986613i | \(-0.447857\pi\) | ||||
0.163080 | + | 0.986613i | \(0.447857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.550510 | 0.0604264 | 0.0302132 | − | 0.999543i | \(-0.490381\pi\) | ||||
0.0302132 | + | 0.999543i | \(0.490381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000 | 0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.7980 | 1.78058 | 0.890290 | − | 0.455394i | \(-0.150502\pi\) | ||||
0.890290 | + | 0.455394i | \(0.150502\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.89898 | 0.297429 | ||||||||
\(96\) | 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 | \(-0.468274\pi\) | ||||
0.0995037 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.34847 | −0.227035 | −0.113518 | − | 0.993536i | \(-0.536212\pi\) | ||||
−0.113518 | + | 0.993536i | \(0.536212\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.79796 | 0.842692 | 0.421346 | − | 0.906900i | \(-0.361558\pi\) | ||||
0.421346 | + | 0.906900i | \(0.361558\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 2.55051 | 0.237836 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.89898 | −0.265749 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3485 | −1.27322 | −0.636610 | − | 0.771186i | \(-0.719664\pi\) | ||||
−0.636610 | + | 0.771186i | \(0.719664\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.89898 | 0.602767 | 0.301383 | − | 0.953503i | \(-0.402552\pi\) | ||||
0.301383 | + | 0.953503i | \(0.402552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.20204 | −0.364363 | ||||||||
\(134\) | 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 | ||||||||
\(145\) | −7.89898 | −0.655975 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.0000 | 1.72039 | 0.860194 | − | 0.509968i | \(-0.170343\pi\) | ||||
0.860194 | + | 0.509968i | \(0.170343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.8990 | 0.875427 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.20204 | −0.335359 | −0.167680 | − | 0.985842i | \(-0.553627\pi\) | ||||
−0.167680 | + | 0.985842i | \(0.553627\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.69694 | −0.291360 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.7980 | 0.924087 | 0.462044 | − | 0.886857i | \(-0.347116\pi\) | ||||
0.462044 | + | 0.886857i | \(0.347116\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.34847 | 0.491259 | 0.245630 | − | 0.969364i | \(-0.421005\pi\) | ||||
0.245630 | + | 0.969364i | \(0.421005\pi\) | |||||||
\(168\) | 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 | \(-0.349220\pi\) | ||||
0.456172 | + | 0.889892i | \(0.349220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.44949 | −0.109571 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.79796 | −0.433360 | −0.216680 | − | 0.976243i | \(-0.569523\pi\) | ||||
−0.216680 | + | 0.976243i | \(0.569523\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.6969 | 1.46406 | 0.732031 | − | 0.681271i | \(-0.238573\pi\) | ||||
0.732031 | + | 0.681271i | \(0.238573\pi\) | |||||||
\(182\) | 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 | ||||||||
\(191\) | 5.10102 | 0.369097 | 0.184548 | − | 0.982823i | \(-0.440918\pi\) | ||||
0.184548 | + | 0.982823i | \(0.440918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.7980 | −1.56905 | −0.784526 | − | 0.620096i | \(-0.787094\pi\) | ||||
−0.784526 | + | 0.620096i | \(0.787094\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.5959 | −1.68114 | −0.840570 | − | 0.541703i | \(-0.817780\pi\) | ||||
−0.840570 | + | 0.541703i | \(0.817780\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1010 | 0.928707 | 0.464353 | − | 0.885650i | \(-0.346287\pi\) | ||||
0.464353 | + | 0.885650i | \(0.346287\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4495 | 0.803597 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.101021 | 0.00705558 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.79796 | −0.531816 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.7980 | −1.07244 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.550510 | 0.0368649 | 0.0184324 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184324 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.7980 | 1.84502 | 0.922508 | − | 0.385979i | \(-0.126136\pi\) | ||||
0.922508 | + | 0.385979i | \(0.126136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.8990 | −0.918470 | −0.459235 | − | 0.888315i | \(-0.651876\pi\) | ||||
−0.459235 | + | 0.888315i | \(0.651876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.202041 | 0.0132361 | 0.00661807 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00661807 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.55051 | 0.296843 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.7980 | −1.40999 | −0.704996 | − | 0.709211i | \(-0.749051\pi\) | ||||
−0.704996 | + | 0.709211i | \(0.749051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.6969 | 1.65529 | 0.827643 | − | 0.561255i | \(-0.189681\pi\) | ||||
0.827643 | + | 0.561255i | \(0.189681\pi\) | |||||||
\(242\) | 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 | ||||||||
\(251\) | 6.89898 | 0.435460 | 0.217730 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217730 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.20204 | −0.511629 | −0.255815 | − | 0.966726i | \(-0.582344\pi\) | ||||
−0.255815 | + | 0.966726i | \(0.582344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.69694 | 0.540401 | ||||||||
\(260\) | 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 | ||||||||
\(265\) | 11.7980 | 0.724743 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5959 | 1.01187 | 0.505935 | − | 0.862571i | \(-0.331147\pi\) | ||||
0.505935 | + | 0.862571i | \(0.331147\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1010 | 1.28180 | 0.640898 | − | 0.767626i | \(-0.278562\pi\) | ||||
0.640898 | + | 0.767626i | \(0.278562\pi\) | |||||||
\(272\) | 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 | ||||||||
\(281\) | 17.8990 | 1.06776 | 0.533882 | − | 0.845559i | \(-0.320733\pi\) | ||||
0.533882 | + | 0.845559i | \(0.320733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3485 | −1.09070 | −0.545352 | − | 0.838207i | \(-0.683604\pi\) | ||||
−0.545352 | + | 0.838207i | \(0.683604\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.146428 | −0.00864338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.5959 | 1.26165 | 0.630823 | − | 0.775926i | \(-0.282717\pi\) | ||||
0.630823 | + | 0.775926i | \(0.282717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8990 | 0.634563 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.3031 | 0.651498 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00000 | −0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.2474 | −1.66924 | −0.834620 | − | 0.550826i | \(-0.814313\pi\) | ||||
−0.834620 | + | 0.550826i | \(0.814313\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.89898 | −0.164386 | −0.0821930 | − | 0.996616i | \(-0.526192\pi\) | ||||
−0.0821930 | + | 0.996616i | \(0.526192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.5959 | 1.33372 | 0.666860 | − | 0.745183i | \(-0.267638\pi\) | ||||
0.666860 | + | 0.745183i | \(0.267638\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.20204 | 0.348341 | 0.174171 | − | 0.984715i | \(-0.444276\pi\) | ||||
0.174171 | + | 0.984715i | \(0.444276\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.79796 | 0.322607 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.59592 | −0.363645 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.89898 | 0.159342 | 0.0796712 | − | 0.996821i | \(-0.474613\pi\) | ||||
0.0796712 | + | 0.996821i | \(0.474613\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.2474 | 0.614514 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.2020 | −0.555741 | −0.277870 | − | 0.960619i | \(-0.589629\pi\) | ||||
−0.277870 | + | 0.960619i | \(0.589629\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2474 | 0.931275 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5959 | −0.729867 | −0.364934 | − | 0.931034i | \(-0.618908\pi\) | ||||
−0.364934 | + | 0.931034i | \(0.618908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.6969 | −1.69670 | −0.848349 | − | 0.529437i | \(-0.822403\pi\) | ||||
−0.848349 | + | 0.529437i | \(0.822403\pi\) | |||||||
\(350\) | 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 | ||||||||
\(359\) | 0.696938 | 0.0367830 | 0.0183915 | − | 0.999831i | \(-0.494145\pi\) | ||||
0.0183915 | + | 0.999831i | \(0.494145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5959 | −0.557680 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.79796 | −0.303479 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0000 | 1.14839 | 0.574195 | − | 0.818718i | \(-0.305315\pi\) | ||||
0.574195 | + | 0.818718i | \(0.305315\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.1010 | −0.887841 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.5959 | −0.911082 | −0.455541 | − | 0.890215i | \(-0.650554\pi\) | ||||
−0.455541 | + | 0.890215i | \(0.650554\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.1010 | 0.878420 | 0.439210 | − | 0.898384i | \(-0.355258\pi\) | ||||
0.439210 | + | 0.898384i | \(0.355258\pi\) | |||||||
\(380\) | 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 | ||||||||
\(389\) | −22.5959 | −1.14566 | −0.572829 | − | 0.819675i | \(-0.694154\pi\) | ||||
−0.572829 | + | 0.819675i | \(0.694154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.10102 | 0.257970 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.89898 | 0.145863 | ||||||||
\(396\) | 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 | ||||||||
\(401\) | 13.5959 | 0.678948 | 0.339474 | − | 0.940615i | \(-0.389751\pi\) | ||||
0.339474 | + | 0.940615i | \(0.389751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.5959 | 1.46342 | 0.731712 | − | 0.681614i | \(-0.238722\pi\) | ||||
0.731712 | + | 0.681614i | \(0.238722\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.7980 | −0.777367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.550510 | 0.0270235 | ||||||||
\(416\) | 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 | ||||||||
\(421\) | −13.5959 | −0.662624 | −0.331312 | − | 0.943521i | \(-0.607491\pi\) | ||||
−0.331312 | + | 0.943521i | \(0.607491\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.34847 | 0.210437 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.10102 | −0.245708 | −0.122854 | − | 0.992425i | \(-0.539205\pi\) | ||||
−0.122854 | + | 0.992425i | \(0.539205\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.79796 | 0.374746 | 0.187373 | − | 0.982289i | \(-0.440003\pi\) | ||||
0.187373 | + | 0.982289i | \(0.440003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.39388 | 0.353697 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.79796 | 0.0858119 | 0.0429059 | − | 0.999079i | \(-0.486338\pi\) | ||||
0.0429059 | + | 0.999079i | \(0.486338\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.1464 | −1.24225 | −0.621127 | − | 0.783710i | \(-0.713325\pi\) | ||||
−0.621127 | + | 0.783710i | \(0.713325\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.7980 | 0.796300 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 17.5959 | 0.830403 | 0.415201 | − | 0.909730i | \(-0.363711\pi\) | ||||
0.415201 | + | 0.909730i | \(0.363711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.5959 | −1.01021 | −0.505107 | − | 0.863057i | \(-0.668547\pi\) | ||||
−0.505107 | + | 0.863057i | \(0.668547\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.8990 | −1.01994 | −0.509969 | − | 0.860193i | \(-0.670343\pi\) | ||||
−0.509969 | + | 0.860193i | \(0.670343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.7980 | 1.47778 | 0.738888 | − | 0.673828i | \(-0.235351\pi\) | ||||
0.738888 | + | 0.673828i | \(0.235351\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.7980 | 0.545944 | 0.272972 | − | 0.962022i | \(-0.411993\pi\) | ||||
0.272972 | + | 0.962022i | \(0.411993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3031 | −0.752805 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.89898 | 0.133014 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.4949 | 0.845053 | 0.422527 | − | 0.906350i | \(-0.361143\pi\) | ||||
0.422527 | + | 0.906350i | \(0.361143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.00000 | 0.0908153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.5959 | 1.15986 | 0.579931 | − | 0.814666i | \(-0.303080\pi\) | ||||
0.579931 | + | 0.814666i | \(0.303080\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.79796 | −0.261658 | −0.130829 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130829 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.7980 | −0.711504 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.2020 | −0.637049 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.0000 | −1.25345 | −0.626726 | − | 0.779240i | \(-0.715605\pi\) | ||||
−0.626726 | + | 0.779240i | \(0.715605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.0454 | 0.849193 | 0.424596 | − | 0.905383i | \(-0.360416\pi\) | ||||
0.424596 | + | 0.905383i | \(0.360416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.8990 | 0.616061 | 0.308031 | − | 0.951376i | \(-0.400330\pi\) | ||||
0.308031 | + | 0.951376i | \(0.400330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.40408 | 0.371775 | ||||||||
\(512\) | 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 | ||||||||
\(521\) | −28.7980 | −1.26166 | −0.630831 | − | 0.775920i | \(-0.717286\pi\) | ||||
−0.630831 | + | 0.775920i | \(0.717286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.6515 | −0.859301 | −0.429651 | − | 0.902995i | \(-0.641363\pi\) | ||||
−0.429651 | + | 0.902995i | \(0.641363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.7980 | 0.949534 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.4949 | −0.717169 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.34847 | −0.101533 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.8990 | 0.941511 | 0.470755 | − | 0.882264i | \(-0.343981\pi\) | ||||
0.470755 | + | 0.882264i | \(0.343981\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.79796 | 0.376863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.2474 | −1.76361 | −0.881807 | − | 0.471611i | \(-0.843673\pi\) | ||||
−0.881807 | + | 0.471611i | \(0.843673\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.8990 | −0.975529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.20204 | −0.178689 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.2020 | −1.02547 | −0.512737 | − | 0.858546i | \(-0.671368\pi\) | ||||
−0.512737 | + | 0.858546i | \(0.671368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.34847 | −0.183266 | −0.0916331 | − | 0.995793i | \(-0.529209\pi\) | ||||
−0.0916331 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(564\) | 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 | \(-0.567220\pi\) | ||||
−0.209611 | + | 0.977785i | \(0.567220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.20204 | 0.259547 | 0.129774 | − | 0.991544i | \(-0.458575\pi\) | ||||
0.129774 | + | 0.991544i | \(0.458575\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.55051 | 0.106364 | ||||||||
\(576\) | 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 | ||||||||
\(581\) | −0.797959 | −0.0331049 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.3485 | −0.922420 | −0.461210 | − | 0.887291i | \(-0.652585\pi\) | ||||
−0.461210 | + | 0.887291i | \(0.652585\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.5959 | 1.30189 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.3939 | −1.12493 | −0.562466 | − | 0.826821i | \(-0.690147\pi\) | ||||
−0.562466 | + | 0.826821i | \(0.690147\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.89898 | −0.118847 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.69694 | −0.191912 | −0.0959559 | − | 0.995386i | \(-0.530591\pi\) | ||||
−0.0959559 | + | 0.995386i | \(0.530591\pi\) | |||||||
\(600\) | 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 | ||||||||
\(607\) | −32.1464 | −1.30478 | −0.652392 | − | 0.757882i | \(-0.726234\pi\) | ||||
−0.652392 | + | 0.757882i | \(0.726234\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.59592 | 0.387575 | 0.193788 | − | 0.981043i | \(-0.437923\pi\) | ||||
0.193788 | + | 0.981043i | \(0.437923\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.1918 | −1.73884 | −0.869419 | − | 0.494076i | \(-0.835507\pi\) | ||||
−0.869419 | + | 0.494076i | \(0.835507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.69694 | 0.188786 | 0.0943929 | − | 0.995535i | \(-0.469909\pi\) | ||||
0.0943929 | + | 0.995535i | \(0.469909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.3485 | −0.975501 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5959 | 0.939339 | 0.469669 | − | 0.882842i | \(-0.344373\pi\) | ||||
0.469669 | + | 0.882842i | \(0.344373\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.3485 | −0.569402 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.10102 | 0.161981 | 0.0809903 | − | 0.996715i | \(-0.474192\pi\) | ||||
0.0809903 | + | 0.996715i | \(0.474192\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.1464 | 0.557881 | 0.278940 | − | 0.960308i | \(-0.410017\pi\) | ||||
0.278940 | + | 0.960308i | \(0.410017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.4495 | −0.450126 | −0.225063 | − | 0.974344i | \(-0.572259\pi\) | ||||
−0.225063 | + | 0.974344i | \(0.572259\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.20204 | −0.320971 | −0.160485 | − | 0.987038i | \(-0.551306\pi\) | ||||
−0.160485 | + | 0.987038i | \(0.551306\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.89898 | 0.269565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.7980 | −1.16076 | −0.580382 | − | 0.814344i | \(-0.697097\pi\) | ||||
−0.580382 | + | 0.814344i | \(0.697097\pi\) | |||||||
\(660\) | 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 | ||||||||
\(665\) | −4.20204 | −0.162948 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.1464 | −0.780073 | ||||||||
\(668\) | 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 | ||||||||
\(677\) | −33.7980 | −1.29896 | −0.649481 | − | 0.760378i | \(-0.725014\pi\) | ||||
−0.649481 | + | 0.760378i | \(0.725014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.89898 | −0.111253 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.3939 | 1.35431 | 0.677155 | − | 0.735841i | \(-0.263213\pi\) | ||||
0.677155 | + | 0.735841i | \(0.263213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.5959 | 0.748722 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.1010 | 1.10705 | 0.553527 | − | 0.832831i | \(-0.313281\pi\) | ||||
0.553527 | + | 0.832831i | \(0.313281\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.5959 | −0.743316 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.202041 | 0.00765285 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.3939 | 1.07242 | 0.536211 | − | 0.844084i | \(-0.319855\pi\) | ||||
0.536211 | + | 0.844084i | \(0.319855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.3939 | −0.656022 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.89898 | −0.109027 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.6969 | −0.739734 | −0.369867 | − | 0.929085i | \(-0.620597\pi\) | ||||
−0.369867 | + | 0.929085i | \(0.620597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.7980 | 1.04104 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.2929 | −1.50267 | −0.751335 | − | 0.659921i | \(-0.770590\pi\) | ||||
−0.751335 | + | 0.659921i | \(0.770590\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4949 | −0.539818 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.89898 | −0.293361 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.75255 | −0.250438 | −0.125219 | − | 0.992129i | \(-0.539963\pi\) | ||||
−0.125219 | + | 0.992129i | \(0.539963\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.5959 | −0.576836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.59592 | 0.354433 | 0.177217 | − | 0.984172i | \(-0.443291\pi\) | ||||
0.177217 | + | 0.984172i | \(0.443291\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.8990 | −1.57806 | −0.789032 | − | 0.614352i | \(-0.789418\pi\) | ||||
−0.789032 | + | 0.614352i | \(0.789418\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.0454 | −1.35906 | −0.679532 | − | 0.733646i | \(-0.737817\pi\) | ||||
−0.679532 | + | 0.733646i | \(0.737817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.0000 | 0.769380 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.40408 | 0.124382 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.7980 | 1.67119 | 0.835596 | − | 0.549345i | \(-0.185123\pi\) | ||||
0.835596 | + | 0.549345i | \(0.185123\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.59592 | −0.276078 | −0.138039 | − | 0.990427i | \(-0.544080\pi\) | ||||
−0.138039 | + | 0.990427i | \(0.544080\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.0000 | −1.26875 | −0.634375 | − | 0.773026i | \(-0.718742\pi\) | ||||
−0.634375 | + | 0.773026i | \(0.718742\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.7526 | −0.461673 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.7980 | −0.894237 | −0.447119 | − | 0.894475i | \(-0.647550\pi\) | ||||
−0.447119 | + | 0.894475i | \(0.647550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.7980 | −0.927888 | −0.463944 | − | 0.885865i | \(-0.653566\pi\) | ||||
−0.463944 | + | 0.885865i | \(0.653566\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.8990 | 0.391503 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.292856 | 0.0104927 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.20204 | −0.149977 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.4041 | −0.370865 | −0.185433 | − | 0.982657i | \(-0.559369\pi\) | ||||
−0.185433 | + | 0.982657i | \(0.559369\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.2020 | 0.504966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.00000 | 0.283375 | 0.141687 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141687 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.10102 | 0.321971 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.69694 | −0.130300 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.8990 | 0.804092 | 0.402046 | − | 0.915619i | \(-0.368299\pi\) | ||||
0.402046 | + | 0.915619i | \(0.368299\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.7980 | 0.413264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.6061 | −0.790888 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.7980 | 0.586253 | 0.293126 | − | 0.956074i | \(-0.405304\pi\) | ||||
0.293126 | + | 0.956074i | \(0.405304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.34847 | 0.221294 | 0.110647 | − | 0.993860i | \(-0.464708\pi\) | ||||
0.110647 | + | 0.993860i | \(0.464708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.5403 | 1.37495 | 0.687476 | − | 0.726208i | \(-0.258719\pi\) | ||||
0.687476 | + | 0.726208i | \(0.258719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.1918 | −0.979143 | −0.489571 | − | 0.871963i | \(-0.662847\pi\) | ||||
−0.489571 | + | 0.871963i | \(0.662847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.79796 | −0.339479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.34847 | 0.219698 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.6969 | 0.852633 | 0.426317 | − | 0.904574i | \(-0.359811\pi\) | ||||
0.426317 | + | 0.904574i | \(0.359811\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33.3939 | 1.15151 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.0000 | −0.447214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.9444 | 0.547856 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.3031 | −0.524582 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7980 | 1.29418 | 0.647089 | − | 0.762415i | \(-0.275986\pi\) | ||||
0.647089 | + | 0.762415i | \(0.275986\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.5959 | −1.35257 | −0.676285 | − | 0.736640i | \(-0.736411\pi\) | ||||
−0.676285 | + | 0.736640i | \(0.736411\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | −52.5505 | −1.78884 | −0.894420 | − | 0.447228i | \(-0.852411\pi\) | ||||
−0.894420 | + | 0.447228i | \(0.852411\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | −1.44949 | −0.0490017 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.5959 | −1.33706 | −0.668530 | − | 0.743686i | \(-0.733076\pi\) | ||||
−0.668530 | + | 0.743686i | \(0.733076\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.8990 | −0.535650 | −0.267825 | − | 0.963468i | \(-0.586305\pi\) | ||||
−0.267825 | + | 0.963468i | \(0.586305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.0454 | −1.51590 | −0.757949 | − | 0.652313i | \(-0.773799\pi\) | ||||
−0.757949 | + | 0.652313i | \(0.773799\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.5959 | 1.26235 | 0.631174 | − | 0.775642i | \(-0.282574\pi\) | ||||
0.631174 | + | 0.775642i | \(0.282574\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.7980 | 0.697541 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.1918 | 0.441448 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.79796 | −0.193804 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −86.0908 | −2.87129 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.5959 | 0.786094 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.6969 | 0.654748 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.3485 | −1.20693 | −0.603466 | − | 0.797389i | \(-0.706214\pi\) | ||||
−0.603466 | + | 0.797389i | \(0.706214\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.4949 | 1.27539 | 0.637696 | − | 0.770288i | \(-0.279887\pi\) | ||||
0.637696 | + | 0.770288i | \(0.279887\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.0000 | −0.330229 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.69694 | −0.154938 | −0.0774689 | − | 0.996995i | \(-0.524684\pi\) | ||||
−0.0774689 | + | 0.996995i | \(0.524684\pi\) | |||||||
\(920\) | 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 | ||||||||
\(929\) | 1.59592 | 0.0523604 | 0.0261802 | − | 0.999657i | \(-0.491666\pi\) | ||||
0.0261802 | + | 0.999657i | \(0.491666\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.2020 | −0.465453 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.9898 | 1.86178 | 0.930888 | − | 0.365305i | \(-0.119035\pi\) | ||||
0.930888 | + | 0.365305i | \(0.119035\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.6969 | −0.902894 | −0.451447 | − | 0.892298i | \(-0.649092\pi\) | ||||
−0.451447 | + | 0.892298i | \(0.649092\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.257654 | 0.00839036 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.1464 | 1.49956 | 0.749779 | − | 0.661689i | \(-0.230160\pi\) | ||||
0.749779 | + | 0.661689i | \(0.230160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.7980 | 1.09482 | 0.547412 | − | 0.836863i | \(-0.315613\pi\) | ||||
0.547412 | + | 0.836863i | \(0.315613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.10102 | 0.165065 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.4041 | −0.917216 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 87.7878 | 2.83186 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.7980 | −0.701701 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.8434 | −0.477330 | −0.238665 | − | 0.971102i | \(-0.576710\pi\) | ||||
−0.238665 | + | 0.971102i | \(0.576710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −60.6969 | −1.94786 | −0.973929 | − | 0.226854i | \(-0.927156\pi\) | ||||
−0.973929 | + | 0.226854i | \(0.927156\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.4041 | 0.910593 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.3939 | −1.45228 | −0.726139 | − | 0.687548i | \(-0.758687\pi\) | ||||
−0.726139 | + | 0.687548i | \(0.758687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.55051 | 0.208929 | 0.104464 | − | 0.994529i | \(-0.466687\pi\) | ||||
0.104464 | + | 0.994529i | \(0.466687\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.5959 | −0.751828 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19.8888 | −0.632426 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.696938 | −0.0221390 | −0.0110695 | − | 0.999939i | \(-0.503524\pi\) | ||||
−0.0110695 | + | 0.999939i | \(0.503524\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.1010 | 0.415330 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.3939 | 1.12094 | 0.560468 | − | 0.828176i | \(-0.310621\pi\) | ||||
0.560468 | + | 0.828176i | \(0.310621\pi\) | |||||||
\(998\) | 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 | 3240.2.a.o.1.1 | 2 | ||
3.2 | odd | 2 | 3240.2.a.j.1.1 | 2 | |||
4.3 | odd | 2 | 6480.2.a.bl.1.2 | 2 | |||
9.2 | odd | 6 | 360.2.q.c.121.2 | ✓ | 4 | ||
9.4 | even | 3 | 1080.2.q.c.721.2 | 4 | |||
9.5 | odd | 6 | 360.2.q.c.241.2 | yes | 4 | ||
9.7 | even | 3 | 1080.2.q.c.361.2 | 4 | |||
12.11 | even | 2 | 6480.2.a.bc.1.2 | 2 | |||
36.7 | odd | 6 | 2160.2.q.g.1441.1 | 4 | |||
36.11 | even | 6 | 720.2.q.g.481.1 | 4 | |||
36.23 | even | 6 | 720.2.q.g.241.1 | 4 | |||
36.31 | odd | 6 | 2160.2.q.g.721.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.q.c.121.2 | ✓ | 4 | 9.2 | odd | 6 | ||
360.2.q.c.241.2 | yes | 4 | 9.5 | odd | 6 | ||
720.2.q.g.241.1 | 4 | 36.23 | even | 6 | |||
720.2.q.g.481.1 | 4 | 36.11 | even | 6 | |||
1080.2.q.c.361.2 | 4 | 9.7 | even | 3 | |||
1080.2.q.c.721.2 | 4 | 9.4 | even | 3 | |||
2160.2.q.g.721.1 | 4 | 36.31 | odd | 6 | |||
2160.2.q.g.1441.1 | 4 | 36.7 | odd | 6 | |||
3240.2.a.j.1.1 | 2 | 3.2 | odd | 2 | |||
3240.2.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
6480.2.a.bc.1.2 | 2 | 12.11 | even | 2 | |||
6480.2.a.bl.1.2 | 2 | 4.3 | odd | 2 |