Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8624,2,Mod(1,8624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8624, 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("8624.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8624 = 2^{4} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8624.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: | \(68.8629867032\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8624.1 |
$q$-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 | ||||||||
\(3\) | 3.23607 | 1.86834 | 0.934172 | − | 0.356822i | \(-0.116140\pi\) | ||||
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23607 | 0.342824 | 0.171412 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.47214 | 1.67110 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.23607 | −0.299791 | −0.149895 | − | 0.988702i | \(-0.547894\pi\) | ||||
−0.149895 | + | 0.988702i | \(0.547894\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.47214 | −0.567147 | −0.283573 | − | 0.958951i | \(-0.591520\pi\) | ||||
−0.283573 | + | 0.958951i | \(0.591520\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.47214 | 1.34953 | 0.674767 | − | 0.738031i | \(-0.264244\pi\) | ||||
0.674767 | + | 0.738031i | \(0.264244\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.4721 | 2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.472136 | −0.0876734 | −0.0438367 | − | 0.999039i | \(-0.513958\pi\) | ||||
−0.0438367 | + | 0.999039i | \(0.513958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.23607 | −1.29964 | −0.649818 | − | 0.760090i | \(-0.725155\pi\) | ||||
−0.649818 | + | 0.760090i | \(0.725155\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.23607 | 0.563327 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.472136 | 0.0776187 | 0.0388093 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388093 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.76393 | 1.05635 | 0.528174 | − | 0.849136i | \(-0.322877\pi\) | ||||
0.528174 | + | 0.849136i | \(0.322877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.9443 | 2.22776 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.23607 | 1.05549 | 0.527744 | − | 0.849403i | \(-0.323038\pi\) | ||||
0.527744 | + | 0.849403i | \(0.323038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.47214 | 1.16374 | 0.581869 | − | 0.813283i | \(-0.302322\pi\) | ||||
0.581869 | + | 0.813283i | \(0.302322\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.23607 | 0.421300 | 0.210650 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210650 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.76393 | 0.353885 | 0.176943 | − | 0.984221i | \(-0.443379\pi\) | ||||
0.176943 | + | 0.984221i | \(0.443379\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.47214 | 0.306631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.52786 | −0.675336 | −0.337668 | − | 0.941265i | \(-0.609638\pi\) | ||||
−0.337668 | + | 0.941265i | \(0.609638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.9443 | 2.52139 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.52786 | 0.181324 | 0.0906621 | − | 0.995882i | \(-0.471102\pi\) | ||||
0.0906621 | + | 0.995882i | \(0.471102\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.23607 | 0.612835 | 0.306418 | − | 0.951897i | \(-0.400870\pi\) | ||||
0.306418 | + | 0.951897i | \(0.400870\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.23607 | −0.373669 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.4164 | 1.69217 | 0.846085 | − | 0.533048i | \(-0.178953\pi\) | ||||
0.846085 | + | 0.533048i | \(0.178953\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.47214 | −0.268141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.52786 | −0.163804 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −23.4164 | −2.42817 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.94427 | −0.507272 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.41641 | 0.956091 | 0.478046 | − | 0.878335i | \(-0.341345\pi\) | ||||
0.478046 | + | 0.878335i | \(0.341345\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.47214 | 0.750978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.23607 | 0.919023 | 0.459512 | − | 0.888172i | \(-0.348024\pi\) | ||||
0.459512 | + | 0.888172i | \(0.348024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.70820 | −0.562446 | −0.281223 | − | 0.959642i | \(-0.590740\pi\) | ||||
−0.281223 | + | 0.959642i | \(0.590740\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.47214 | 0.428353 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.52786 | 0.145018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9443 | 1.20706 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.23607 | 0.853875 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.8885 | 1.97362 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.9443 | −1.85850 | −0.929252 | − | 0.369447i | \(-0.879547\pi\) | ||||
−0.929252 | + | 0.369447i | \(0.879547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.8885 | −2.27936 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8885 | −1.21345 | −0.606724 | − | 0.794913i | \(-0.707517\pi\) | ||||
−0.606724 | + | 0.794913i | \(0.707517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 28.9443 | 2.49113 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.52786 | 0.643149 | 0.321574 | − | 0.946884i | \(-0.395788\pi\) | ||||
0.321574 | + | 0.946884i | \(0.395788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4721 | −0.888235 | −0.444117 | − | 0.895969i | \(-0.646483\pi\) | ||||
−0.444117 | + | 0.895969i | \(0.646483\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.4164 | 1.97202 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.23607 | 0.103365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.944272 | −0.0784175 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.94427 | 0.727875 | 0.363937 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363937 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.23607 | −0.746692 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.4721 | −1.16243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.94427 | 0.554213 | 0.277107 | − | 0.960839i | \(-0.410624\pi\) | ||||
0.277107 | + | 0.960839i | \(0.410624\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.4164 | 2.17426 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.4164 | −1.83411 | −0.917057 | − | 0.398755i | \(-0.869442\pi\) | ||||
−0.917057 | + | 0.398755i | \(0.869442\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.47214 | 0.503855 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.9443 | −1.00166 | −0.500829 | − | 0.865546i | \(-0.666971\pi\) | ||||
−0.500829 | + | 0.865546i | \(0.666971\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4721 | −0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.4721 | −1.41260 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.2361 | 1.31043 | 0.655217 | − | 0.755441i | \(-0.272577\pi\) | ||||
0.655217 | + | 0.755441i | \(0.272577\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.4721 | 0.787134 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.94427 | −0.668526 | −0.334263 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334263 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.41641 | −0.105281 | −0.0526404 | − | 0.998614i | \(-0.516764\pi\) | ||||
−0.0526404 | + | 0.998614i | \(0.516764\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.94427 | 0.661180 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.944272 | 0.0694243 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.23607 | −0.0903902 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9443 | 1.51547 | 0.757737 | − | 0.652560i | \(-0.226305\pi\) | ||||
0.757737 | + | 0.652560i | \(0.226305\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.8885 | −1.71954 | −0.859768 | − | 0.510686i | \(-0.829392\pi\) | ||||
−0.859768 | + | 0.510686i | \(0.829392\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.00000 | 0.572892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1803 | 1.43055 | 0.715273 | − | 0.698845i | \(-0.246302\pi\) | ||||
0.715273 | + | 0.698845i | \(0.246302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.8885 | −1.26176 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5279 | 0.944827 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 48.3607 | 3.36130 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.47214 | −0.171001 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.8885 | −1.50687 | −0.753435 | − | 0.657523i | \(-0.771604\pi\) | ||||
−0.753435 | + | 0.657523i | \(0.771604\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.94427 | 0.338776 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.0000 | −1.09119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.9443 | 1.14499 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.52786 | −0.102775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1803 | 0.815656 | 0.407828 | − | 0.913059i | \(-0.366286\pi\) | ||||
0.407828 | + | 0.913059i | \(0.366286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.47214 | −0.498142 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.8885 | −1.98377 | −0.991886 | − | 0.127129i | \(-0.959424\pi\) | ||||
−0.991886 | + | 0.127129i | \(0.959424\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.47214 | −0.295527 | −0.147764 | − | 0.989023i | \(-0.547207\pi\) | ||||
−0.147764 | + | 0.989023i | \(0.547207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.4164 | −1.14099 | −0.570493 | − | 0.821302i | \(-0.693248\pi\) | ||||
−0.570493 | + | 0.821302i | \(0.693248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.4721 | 0.944058 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.9443 | −1.88013 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.8885 | −1.67459 | −0.837295 | − | 0.546751i | \(-0.815864\pi\) | ||||
−0.837295 | + | 0.546751i | \(0.815864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.1246 | −1.74725 | −0.873625 | − | 0.486600i | \(-0.838237\pi\) | ||||
−0.873625 | + | 0.486600i | \(0.838237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 35.5967 | 2.28353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.05573 | −0.194431 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 49.8885 | 3.16156 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.7082 | 1.11773 | 0.558866 | − | 0.829258i | \(-0.311237\pi\) | ||||
0.558866 | + | 0.829258i | \(0.311237\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.47214 | 0.406900 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.52786 | −0.218369 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.9443 | 1.04088 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.47214 | −0.396088 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4164 | 0.818013 | 0.409006 | − | 0.912532i | \(-0.365875\pi\) | ||||
0.409006 | + | 0.912532i | \(0.365875\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.52786 | −0.0928111 | −0.0464056 | − | 0.998923i | \(-0.514777\pi\) | ||||
−0.0464056 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8885 | 0.954650 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −54.0689 | −3.23702 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4721 | −0.744025 | −0.372013 | − | 0.928228i | \(-0.621332\pi\) | ||||
−0.372013 | + | 0.928228i | \(0.621332\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.88854 | −0.350038 | −0.175019 | − | 0.984565i | \(-0.555999\pi\) | ||||
−0.175019 | + | 0.984565i | \(0.555999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.0000 | −0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4721 | −0.910126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.4721 | 1.78631 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.1246 | −0.883589 | −0.441795 | − | 0.897116i | \(-0.645658\pi\) | ||||
−0.441795 | + | 0.897116i | \(0.645658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.47214 | 0.376822 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.4721 | 0.839759 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00000 | 0.462652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 29.8885 | 1.71705 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.52786 | 0.316525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.94427 | 0.510477 | 0.255238 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255238 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4721 | −1.05084 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.7082 | −1.23096 | −0.615480 | − | 0.788153i | \(-0.711038\pi\) | ||||
−0.615480 | + | 0.788153i | \(0.711038\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.94427 | 0.166420 | 0.0832100 | − | 0.996532i | \(-0.473483\pi\) | ||||
0.0832100 | + | 0.996532i | \(0.473483\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.472136 | −0.0264345 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.9443 | 0.722479 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.05573 | 0.170025 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.23607 | −0.0685647 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.4721 | 0.800311 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.8885 | −1.20310 | −0.601552 | − | 0.798834i | \(-0.705451\pi\) | ||||
−0.601552 | + | 0.798834i | \(0.705451\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.52786 | 0.193326 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0557 | −0.604039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.4721 | −1.11519 | −0.557594 | − | 0.830114i | \(-0.688275\pi\) | ||||
−0.557594 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.47214 | 0.351518 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.23607 | −0.391855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 41.8885 | 2.25520 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.05573 | −0.164040 | −0.0820200 | − | 0.996631i | \(-0.526137\pi\) | ||||
−0.0820200 | + | 0.996631i | \(0.526137\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.76393 | 0.147950 | 0.0739749 | − | 0.997260i | \(-0.476432\pi\) | ||||
0.0739749 | + | 0.997260i | \(0.476432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8885 | 0.954820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8885 | 0.845662 | 0.422831 | − | 0.906209i | \(-0.361036\pi\) | ||||
0.422831 | + | 0.906209i | \(0.361036\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.05573 | 0.162181 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.05573 | 0.372387 | 0.186194 | − | 0.982513i | \(-0.440385\pi\) | ||||
0.186194 | + | 0.982513i | \(0.440385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.23607 | 0.169850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4721 | 0.548137 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.1246 | 0.893897 | 0.446949 | − | 0.894560i | \(-0.352511\pi\) | ||||
0.446949 | + | 0.894560i | \(0.352511\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 50.5410 | 2.63106 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −38.8328 | −2.00532 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.583592 | −0.0300565 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.3050 | 1.29983 | 0.649914 | − | 0.760008i | \(-0.274805\pi\) | ||||
0.649914 | + | 0.760008i | \(0.274805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −67.7771 | −3.47233 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.6525 | 1.36188 | 0.680939 | − | 0.732340i | \(-0.261572\pi\) | ||||
0.680939 | + | 0.732340i | \(0.261572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −59.7771 | −3.03864 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.8885 | −1.00839 | −0.504195 | − | 0.863590i | \(-0.668211\pi\) | ||||
−0.504195 | + | 0.863590i | \(0.668211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.9443 | −2.26714 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.8885 | −0.900070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.111456 | 0.00559383 | 0.00279691 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279691 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.05573 | 0.252471 | 0.126236 | − | 0.992000i | \(-0.459710\pi\) | ||||
0.126236 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.94427 | −0.445546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 48.8328 | 2.42652 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.472136 | 0.0234029 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.1246 | 1.53901 | 0.769507 | − | 0.638639i | \(-0.220502\pi\) | ||||
0.769507 | + | 0.638639i | \(0.220502\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.3607 | 1.20162 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.8328 | 1.51352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −33.8885 | −1.65953 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.65248 | −0.324995 | −0.162497 | − | 0.986709i | \(-0.551955\pi\) | ||||
−0.162497 | + | 0.986709i | \(0.551955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.3607 | −1.08979 | −0.544896 | − | 0.838503i | \(-0.683431\pi\) | ||||
−0.544896 | + | 0.838503i | \(0.683431\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 54.0689 | 2.62892 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.23607 | 0.0599581 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | −0.578020 | −0.289010 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289010 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.472136 | −0.0226894 | −0.0113447 | − | 0.999936i | \(-0.503611\pi\) | ||||
−0.0113447 | + | 0.999936i | \(0.503611\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.05573 | −0.146511 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.52786 | 0.0729210 | 0.0364605 | − | 0.999335i | \(-0.488392\pi\) | ||||
0.0364605 | + | 0.999335i | \(0.488392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.05573 | 0.335228 | 0.167614 | − | 0.985853i | \(-0.446394\pi\) | ||||
0.167614 | + | 0.985853i | \(0.446394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 45.3050 | 2.14285 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5279 | −0.921577 | −0.460788 | − | 0.887510i | \(-0.652433\pi\) | ||||
−0.460788 | + | 0.887510i | \(0.652433\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.76393 | 0.318501 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.9443 | 1.35992 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.8328 | 1.16163 | 0.580815 | − | 0.814036i | \(-0.302734\pi\) | ||||
0.580815 | + | 0.814036i | \(0.302734\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.8885 | −0.834966 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1803 | −0.474146 | −0.237073 | − | 0.971492i | \(-0.576188\pi\) | ||||
−0.237073 | + | 0.971492i | \(0.576188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.4721 | 0.672577 | 0.336289 | − | 0.941759i | \(-0.390828\pi\) | ||||
0.336289 | + | 0.941759i | \(0.390828\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −46.8328 | −2.17182 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.0689 | −1.57652 | −0.788260 | − | 0.615342i | \(-0.789018\pi\) | ||||
−0.788260 | + | 0.615342i | \(0.789018\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.4721 | 1.03546 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.47214 | 0.113429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 63.3050 | 2.89853 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.4721 | 1.02678 | 0.513389 | − | 0.858156i | \(-0.328390\pi\) | ||||
0.513389 | + | 0.858156i | \(0.328390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.583592 | 0.0266095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.8328 | 0.855154 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.36068 | −0.378859 | −0.189429 | − | 0.981894i | \(-0.560664\pi\) | ||||
−0.189429 | + | 0.981894i | \(0.560664\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −75.7771 | −3.42676 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.583592 | 0.0262837 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.9443 | 0.671695 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4721 | −0.468797 | −0.234399 | − | 0.972141i | \(-0.575312\pi\) | ||||
−0.234399 | + | 0.972141i | \(0.575312\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.8885 | −1.87144 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.41641 | −0.152330 | −0.0761650 | − | 0.997095i | \(-0.524268\pi\) | ||||
−0.0761650 | + | 0.997095i | \(0.524268\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.4721 | 0.821999 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.1246 | −1.64876 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.5279 | −1.39745 | −0.698724 | − | 0.715391i | \(-0.746248\pi\) | ||||
−0.698724 | + | 0.715391i | \(0.746248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.7771 | −1.57960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.4164 | −0.503067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.23607 | 0.318242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 55.7771 | 2.44834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.3607 | 0.629153 | 0.314576 | − | 0.949232i | \(-0.398138\pi\) | ||||
0.314576 | + | 0.949232i | \(0.398138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 44.0000 | 1.92399 | 0.961993 | − | 0.273075i | \(-0.0880406\pi\) | ||||
0.961993 | + | 0.273075i | \(0.0880406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.94427 | 0.389619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.1803 | 1.04934 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.36068 | 0.362141 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.9443 | −1.24904 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.8328 | −1.41159 | −0.705797 | − | 0.708415i | \(-0.749411\pi\) | ||||
−0.705797 | + | 0.708415i | \(0.749411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.58359 | −0.196701 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.94427 | 0.383131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.6525 | 0.881426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.16718 | 0.0497237 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.05573 | 0.129708 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0557 | −0.892160 | −0.446080 | − | 0.894993i | \(-0.647180\pi\) | ||||
−0.446080 | + | 0.894993i | \(0.647180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.88854 | −0.418241 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.4164 | 1.66120 | 0.830602 | − | 0.556867i | \(-0.187997\pi\) | ||||
0.830602 | + | 0.556867i | \(0.187997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | 0.168281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.4721 | 0.690548 | 0.345274 | − | 0.938502i | \(-0.387786\pi\) | ||||
0.345274 | + | 0.938502i | \(0.387786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.9443 | 1.37867 | 0.689337 | − | 0.724440i | \(-0.257902\pi\) | ||||
0.689337 | + | 0.724440i | \(0.257902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 67.7771 | 2.83143 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.47214 | −0.269907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4721 | 1.18531 | 0.592655 | − | 0.805456i | \(-0.298080\pi\) | ||||
0.592655 | + | 0.805456i | \(0.298080\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −77.3050 | −3.21268 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.47214 | 0.350880 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.4721 | 0.763729 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.1246 | −0.541711 | −0.270855 | − | 0.962620i | \(-0.587307\pi\) | ||||
−0.270855 | + | 0.962620i | \(0.587307\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.8885 | 0.737085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.47214 | −0.266228 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.2918 | 1.32607 | 0.663033 | − | 0.748591i | \(-0.269269\pi\) | ||||
0.663033 | + | 0.748591i | \(0.269269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 65.3050 | 2.67275 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.41641 | −0.139591 | −0.0697953 | − | 0.997561i | \(-0.522235\pi\) | ||||
−0.0697953 | + | 0.997561i | \(0.522235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.12461 | −0.127456 | −0.0637278 | − | 0.997967i | \(-0.520299\pi\) | ||||
−0.0637278 | + | 0.997967i | \(0.520299\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −41.3050 | −1.68207 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.94427 | −0.200682 | −0.100341 | − | 0.994953i | \(-0.531993\pi\) | ||||
−0.100341 | + | 0.994953i | \(0.531993\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.94427 | 0.361847 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.3050 | −1.91063 | −0.955315 | − | 0.295591i | \(-0.904483\pi\) | ||||
−0.955315 | + | 0.295591i | \(0.904483\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 43.7771 | 1.76526 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4164 | 1.34529 | 0.672647 | − | 0.739964i | \(-0.265157\pi\) | ||||
0.672647 | + | 0.739964i | \(0.265157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.1246 | −1.17062 | −0.585308 | − | 0.810811i | \(-0.699027\pi\) | ||||
−0.585308 | + | 0.810811i | \(0.699027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 93.6656 | 3.75867 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.00000 | −0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.583592 | −0.0232693 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.0000 | 0.955425 | 0.477712 | − | 0.878516i | \(-0.341466\pi\) | ||||
0.477712 | + | 0.878516i | \(0.341466\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −70.8328 | −2.81535 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −41.8885 | −1.66230 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.4164 | 0.451626 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.4721 | −0.966591 | −0.483296 | − | 0.875457i | \(-0.660560\pi\) | ||||
−0.483296 | + | 0.875457i | \(0.660560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.1246 | −1.14856 | −0.574281 | − | 0.818658i | \(-0.694718\pi\) | ||||
−0.574281 | + | 0.818658i | \(0.694718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −51.7771 | −2.03872 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.0689 | −0.867617 | −0.433809 | − | 0.901005i | \(-0.642831\pi\) | ||||
−0.433809 | + | 0.901005i | \(0.642831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.23607 | 0.127027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.9443 | 1.68054 | 0.840270 | − | 0.542169i | \(-0.182397\pi\) | ||||
0.840270 | + | 0.542169i | \(0.182397\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.7771 | −1.08534 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 39.1246 | 1.52640 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8328 | −0.499139 | −0.249569 | − | 0.968357i | \(-0.580289\pi\) | ||||
−0.249569 | + | 0.968357i | \(0.580289\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.94427 | −0.192020 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.05573 | −0.118318 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 39.4164 | 1.52393 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.76393 | 0.106700 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.41641 | 0.208787 | 0.104394 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104394 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.4721 | −0.557033 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.70820 | −0.142518 | −0.0712589 | − | 0.997458i | \(-0.522702\pi\) | ||||
−0.0712589 | + | 0.997458i | \(0.522702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −96.7214 | −3.70637 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.8885 | −1.14365 | −0.571827 | − | 0.820374i | \(-0.693765\pi\) | ||||
−0.571827 | + | 0.820374i | \(0.693765\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.0557 | 0.575250 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.4721 | −0.552146 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.4721 | 0.398957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.5410 | −1.84659 | −0.923294 | − | 0.384095i | \(-0.874514\pi\) | ||||
−0.923294 | + | 0.384095i | \(0.874514\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.9443 | −0.794462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.36068 | −0.316683 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −56.3607 | −2.13176 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.4721 | −0.924300 | −0.462150 | − | 0.886802i | \(-0.652922\pi\) | ||||
−0.462150 | + | 0.886802i | \(0.652922\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.16718 | −0.0440212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 46.8328 | 1.76383 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.94427 | 0.110574 | 0.0552872 | − | 0.998470i | \(-0.482393\pi\) | ||||
0.0552872 | + | 0.998470i | \(0.482393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −66.8328 | −2.50643 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −46.8328 | −1.75390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.47214 | 0.0924526 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −83.7771 | −3.12871 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.4853 | 1.24879 | 0.624395 | − | 0.781108i | \(-0.285345\pi\) | ||||
0.624395 | + | 0.781108i | \(0.285345\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −87.7771 | −3.26447 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.472136 | 0.0175347 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.0132 | −1.89197 | −0.945987 | − | 0.324206i | \(-0.894903\pi\) | ||||
−0.945987 | + | 0.324206i | \(0.894903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.88854 | 0.365741 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.2361 | −0.488885 | −0.244443 | − | 0.969664i | \(-0.578605\pi\) | ||||
−0.244443 | + | 0.969664i | \(0.578605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.52786 | −0.203621 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.05573 | −0.259549 | −0.129775 | − | 0.991544i | \(-0.541425\pi\) | ||||
−0.129775 | + | 0.991544i | \(0.541425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.88854 | −0.363265 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.8885 | 1.24325 | 0.621625 | − | 0.783315i | \(-0.286473\pi\) | ||||
0.621625 | + | 0.783315i | \(0.286473\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.0000 | 1.02584 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 115.193 | 4.21471 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.4721 | −1.40387 | −0.701934 | − | 0.712242i | \(-0.747680\pi\) | ||||
−0.701934 | + | 0.712242i | \(0.747680\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 57.3050 | 2.08831 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.8885 | 0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.8885 | −0.722861 | −0.361431 | − | 0.932399i | \(-0.617712\pi\) | ||||
−0.361431 | + | 0.932399i | \(0.617712\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.9443 | 0.760229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.5967 | −0.637882 | −0.318941 | − | 0.947775i | \(-0.603327\pi\) | ||||
−0.318941 | + | 0.947775i | \(0.603327\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.4721 | −0.667861 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.00000 | 0.144432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.7082 | −1.14343 | −0.571714 | − | 0.820453i | \(-0.693721\pi\) | ||||
−0.571714 | + | 0.820453i | \(0.693721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.4164 | 0.699265 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.36068 | −0.228778 | −0.114389 | − | 0.993436i | \(-0.536491\pi\) | ||||
−0.114389 | + | 0.993436i | \(0.536491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.23607 | 0.259927 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.7214 | −0.599105 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.52786 | 0.0546713 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.83282 | −0.244185 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.8885 | 0.495703 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.5836 | −0.591141 | −0.295571 | − | 0.955321i | \(-0.595510\pi\) | ||||
−0.295571 | + | 0.955321i | \(0.595510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.41641 | 0.121320 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 54.8328 | 1.94472 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.94427 | −0.104291 | −0.0521457 | − | 0.998639i | \(-0.516606\pi\) | ||||
−0.0521457 | + | 0.998639i | \(0.516606\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.94427 | −0.316426 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.9443 | −0.528030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.23607 | 0.184777 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43.4164 | 1.52833 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.9443 | 1.36921 | 0.684604 | − | 0.728915i | \(-0.259975\pi\) | ||||
0.684604 | + | 0.728915i | \(0.259975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.8328 | 0.661310 | 0.330655 | − | 0.943752i | \(-0.392730\pi\) | ||||
0.330655 | + | 0.943752i | \(0.392730\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.94427 | −0.173403 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46.8328 | −1.64048 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.7771 | 0.691913 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.83282 | −0.308267 | −0.154134 | − | 0.988050i | \(-0.549259\pi\) | ||||
−0.154134 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.8885 | 1.73901 | 0.869503 | − | 0.493928i | \(-0.164439\pi\) | ||||
0.869503 | + | 0.493928i | \(0.164439\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.23607 | −0.112665 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.94427 | −0.171929 | −0.0859646 | − | 0.996298i | \(-0.527397\pi\) | ||||
−0.0859646 | + | 0.996298i | \(0.527397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.8328 | 0.584628 | 0.292314 | − | 0.956322i | \(-0.405575\pi\) | ||||
0.292314 | + | 0.956322i | \(0.405575\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 51.4164 | 1.78362 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.8885 | −0.895910 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −104.721 | −3.61970 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.0689 | −0.485712 | −0.242856 | − | 0.970062i | \(-0.578084\pi\) | ||||
−0.242856 | + | 0.970062i | \(0.578084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7771 | −0.992313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −40.3607 | −1.39010 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.9443 | −0.789307 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.0557 | −0.653991 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.05573 | 0.104749 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.652476 | −0.0223403 | −0.0111702 | − | 0.999938i | \(-0.503556\pi\) | ||||
−0.0111702 | + | 0.999938i | \(0.503556\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.9443 | −1.26347 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7639 | −0.367689 | −0.183844 | − | 0.982955i | \(-0.558854\pi\) | ||||
−0.183844 | + | 0.982955i | \(0.558854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.5410 | 1.38324 | 0.691621 | − | 0.722261i | \(-0.256897\pi\) | ||||
0.691621 | + | 0.722261i | \(0.256897\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.9443 | 0.712951 | 0.356476 | − | 0.934305i | \(-0.383978\pi\) | ||||
0.356476 | + | 0.934305i | \(0.383978\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.4721 | 1.17209 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −50.0689 | −1.70043 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.94427 | −0.303414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.83282 | −0.231521 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 70.3607 | 2.38135 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.4164 | 1.39853 | 0.699266 | − | 0.714861i | \(-0.253510\pi\) | ||||
0.699266 | + | 0.714861i | \(0.253510\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48.9443 | −1.65085 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.4164 | −0.991064 | −0.495532 | − | 0.868590i | \(-0.665027\pi\) | ||||
−0.495532 | + | 0.868590i | \(0.665027\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.94427 | −0.300999 | −0.150499 | − | 0.988610i | \(-0.548088\pi\) | ||||
−0.150499 | + | 0.988610i | \(0.548088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.9443 | 0.704034 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.3607 | 1.35518 | 0.677589 | − | 0.735440i | \(-0.263025\pi\) | ||||
0.677589 | + | 0.735440i | \(0.263025\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.4164 | 0.817980 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.8885 | −0.598617 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.8885 | −0.597948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.8885 | 0.864393 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.41641 | 0.113944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.4721 | −0.348877 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.83282 | −0.0941660 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.5279 | −0.449185 | −0.224593 | − | 0.974453i | \(-0.572105\pi\) | ||||
−0.224593 | + | 0.974453i | \(0.572105\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 69.0132 | 2.28902 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.5279 | −1.11083 | −0.555414 | − | 0.831574i | \(-0.687440\pi\) | ||||
−0.555414 | + | 0.831574i | \(0.687440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.4164 | 0.510209 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17.8885 | 0.591377 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.11146 | −0.201598 | −0.100799 | − | 0.994907i | \(-0.532140\pi\) | ||||
−0.100799 | + | 0.994907i | \(0.532140\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.9443 | 0.953746 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.88854 | 0.0621622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.472136 | −0.0155237 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42.6525 | −1.40089 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.2492 | −0.926827 | −0.463413 | − | 0.886142i | \(-0.653376\pi\) | ||||
−0.463413 | + | 0.886142i | \(0.653376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −70.2492 | −2.29986 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.47214 | −0.0808475 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.6525 | −0.674687 | −0.337343 | − | 0.941382i | \(-0.609528\pi\) | ||||
−0.337343 | + | 0.941382i | \(0.609528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.52786 | 0.310930 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41.5967 | 1.35602 | 0.678008 | − | 0.735055i | \(-0.262844\pi\) | ||||
0.678008 | + | 0.735055i | \(0.262844\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.7771 | 1.42558 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 58.8328 | 1.91181 | 0.955905 | − | 0.293677i | \(-0.0948789\pi\) | ||||
0.955905 | + | 0.293677i | \(0.0948789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.47214 | 0.210094 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.3050 | 1.46911 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.05573 | 0.163771 | 0.0818855 | − | 0.996642i | \(-0.473906\pi\) | ||||
0.0818855 | + | 0.996642i | \(0.473906\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.8885 | 1.35548 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.52786 | −0.0493888 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.3607 | 0.689054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.8885 | 0.963145 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −47.7771 | −1.53800 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8885 | −0.703888 | −0.351944 | − | 0.936021i | \(-0.614479\pi\) | ||||
−0.351944 | + | 0.936021i | \(0.614479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.88854 | 0.317666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.1246 | −0.934653 | −0.467327 | − | 0.884085i | \(-0.654783\pi\) | ||||
−0.467327 | + | 0.884085i | \(0.654783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.00000 | −0.128103 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.05573 | 0.161747 | 0.0808735 | − | 0.996724i | \(-0.474229\pi\) | ||||
0.0808735 | + | 0.996724i | \(0.474229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.4164 | 1.06690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.1803 | 1.40913 | 0.704567 | − | 0.709637i | \(-0.251141\pi\) | ||||
0.704567 | + | 0.709637i | \(0.251141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.00000 | −0.127451 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.7771 | −1.64642 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.2492 | 0.833834 | 0.416917 | − | 0.908945i | \(-0.363111\pi\) | ||||
0.416917 | + | 0.908945i | \(0.363111\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −70.8328 | −2.24781 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.3607 | 1.27952 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.6525 | −1.03411 | −0.517057 | − | 0.855951i | \(-0.672973\pi\) | ||||
−0.517057 | + | 0.855951i | \(0.672973\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.83282 | 0.216181 |
(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 | 8624.2.a.ce.1.2 | 2 | ||
4.3 | odd | 2 | 539.2.a.f.1.1 | 2 | |||
7.6 | odd | 2 | 1232.2.a.m.1.1 | 2 | |||
12.11 | even | 2 | 4851.2.a.y.1.2 | 2 | |||
28.3 | even | 6 | 539.2.e.i.177.2 | 4 | |||
28.11 | odd | 6 | 539.2.e.j.177.2 | 4 | |||
28.19 | even | 6 | 539.2.e.i.67.2 | 4 | |||
28.23 | odd | 6 | 539.2.e.j.67.2 | 4 | |||
28.27 | even | 2 | 77.2.a.d.1.1 | ✓ | 2 | ||
44.43 | even | 2 | 5929.2.a.m.1.2 | 2 | |||
56.13 | odd | 2 | 4928.2.a.bv.1.2 | 2 | |||
56.27 | even | 2 | 4928.2.a.bm.1.1 | 2 | |||
84.83 | odd | 2 | 693.2.a.h.1.2 | 2 | |||
140.27 | odd | 4 | 1925.2.b.h.1849.1 | 4 | |||
140.83 | odd | 4 | 1925.2.b.h.1849.4 | 4 | |||
140.139 | even | 2 | 1925.2.a.r.1.2 | 2 | |||
308.27 | even | 10 | 847.2.f.n.729.1 | 4 | |||
308.83 | odd | 10 | 847.2.f.b.729.1 | 4 | |||
308.139 | odd | 10 | 847.2.f.m.148.1 | 4 | |||
308.167 | odd | 10 | 847.2.f.b.323.1 | 4 | |||
308.195 | odd | 10 | 847.2.f.m.372.1 | 4 | |||
308.223 | even | 10 | 847.2.f.a.372.1 | 4 | |||
308.251 | even | 10 | 847.2.f.n.323.1 | 4 | |||
308.279 | even | 10 | 847.2.f.a.148.1 | 4 | |||
308.307 | odd | 2 | 847.2.a.f.1.2 | 2 | |||
924.923 | even | 2 | 7623.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.1 | ✓ | 2 | 28.27 | even | 2 | ||
539.2.a.f.1.1 | 2 | 4.3 | odd | 2 | |||
539.2.e.i.67.2 | 4 | 28.19 | even | 6 | |||
539.2.e.i.177.2 | 4 | 28.3 | even | 6 | |||
539.2.e.j.67.2 | 4 | 28.23 | odd | 6 | |||
539.2.e.j.177.2 | 4 | 28.11 | odd | 6 | |||
693.2.a.h.1.2 | 2 | 84.83 | odd | 2 | |||
847.2.a.f.1.2 | 2 | 308.307 | odd | 2 | |||
847.2.f.a.148.1 | 4 | 308.279 | even | 10 | |||
847.2.f.a.372.1 | 4 | 308.223 | even | 10 | |||
847.2.f.b.323.1 | 4 | 308.167 | odd | 10 | |||
847.2.f.b.729.1 | 4 | 308.83 | odd | 10 | |||
847.2.f.m.148.1 | 4 | 308.139 | odd | 10 | |||
847.2.f.m.372.1 | 4 | 308.195 | odd | 10 | |||
847.2.f.n.323.1 | 4 | 308.251 | even | 10 | |||
847.2.f.n.729.1 | 4 | 308.27 | even | 10 | |||
1232.2.a.m.1.1 | 2 | 7.6 | odd | 2 | |||
1925.2.a.r.1.2 | 2 | 140.139 | even | 2 | |||
1925.2.b.h.1849.1 | 4 | 140.27 | odd | 4 | |||
1925.2.b.h.1849.4 | 4 | 140.83 | odd | 4 | |||
4851.2.a.y.1.2 | 2 | 12.11 | even | 2 | |||
4928.2.a.bm.1.1 | 2 | 56.27 | even | 2 | |||
4928.2.a.bv.1.2 | 2 | 56.13 | odd | 2 | |||
5929.2.a.m.1.2 | 2 | 44.43 | even | 2 | |||
7623.2.a.bl.1.1 | 2 | 924.923 | even | 2 | |||
8624.2.a.ce.1.2 | 2 | 1.1 | even | 1 | trivial |