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: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 616) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) 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 | ||||||||
\(3\) | −0.414214 | −0.239146 | −0.119573 | − | 0.992825i | \(-0.538153\pi\) | ||||
−0.119573 | + | 0.992825i | \(0.538153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.41421 | −0.632456 | −0.316228 | − | 0.948683i | \(-0.602416\pi\) | ||||
−0.316228 | + | 0.948683i | \(0.602416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.585786 | 0.151249 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.58579 | −0.593220 | −0.296610 | − | 0.954999i | \(-0.595856\pi\) | ||||
−0.296610 | + | 0.954999i | \(0.595856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.41421 | −1.12894 | −0.564471 | − | 0.825453i | \(-0.690920\pi\) | ||||
−0.564471 | + | 0.825453i | \(0.690920\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41421 | 0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.65685 | −1.73442 | −0.867211 | − | 0.497941i | \(-0.834090\pi\) | ||||
−0.867211 | + | 0.497941i | \(0.834090\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.414214 | 0.0721053 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.07107 | −1.49127 | −0.745637 | − | 0.666352i | \(-0.767855\pi\) | ||||
−0.745637 | + | 0.666352i | \(0.767855\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.757359 | 0.121275 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.24264 | −0.974937 | −0.487468 | − | 0.873141i | \(-0.662080\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.00000 | 0.596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.82843 | 0.704298 | 0.352149 | − | 0.935944i | \(-0.385451\pi\) | ||||
0.352149 | + | 0.935944i | \(0.385451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.828427 | −0.116003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.58579 | 0.355185 | 0.177593 | − | 0.984104i | \(-0.443169\pi\) | ||||
0.177593 | + | 0.984104i | \(0.443169\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.41421 | 0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.07107 | 0.141866 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.41421 | 0.574682 | 0.287341 | − | 0.957828i | \(-0.407229\pi\) | ||||
0.287341 | + | 0.957828i | \(0.407229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.17157 | 1.04626 | 0.523131 | − | 0.852252i | \(-0.324764\pi\) | ||||
0.523131 | + | 0.852252i | \(0.324764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.58579 | 0.320727 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.07107 | −0.986038 | −0.493019 | − | 0.870019i | \(-0.664107\pi\) | ||||
−0.493019 | + | 0.870019i | \(0.664107\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.24264 | 0.269982 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.75736 | 0.683273 | 0.341636 | − | 0.939832i | \(-0.389019\pi\) | ||||
0.341636 | + | 0.939832i | \(0.389019\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.41421 | 0.399603 | 0.199802 | − | 0.979836i | \(-0.435970\pi\) | ||||
0.199802 | + | 0.979836i | \(0.435970\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.24264 | 0.143488 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.07107 | −0.908066 | −0.454033 | − | 0.890985i | \(-0.650015\pi\) | ||||
−0.454033 | + | 0.890985i | \(0.650015\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4853 | −1.15091 | −0.575455 | − | 0.817834i | \(-0.695175\pi\) | ||||
−0.575455 | + | 0.817834i | \(0.695175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82843 | −0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.414214 | −0.0444084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.17157 | 0.972185 | 0.486092 | − | 0.873907i | \(-0.338422\pi\) | ||||
0.486092 | + | 0.873907i | \(0.338422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.65685 | 0.375185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8284 | 1.60713 | 0.803567 | − | 0.595215i | \(-0.202933\pi\) | ||||
0.803567 | + | 0.595215i | \(0.202933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82843 | 0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.48528 | 0.744813 | 0.372407 | − | 0.928070i | \(-0.378533\pi\) | ||||
0.372407 | + | 0.928070i | \(0.378533\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8995 | −1.56662 | −0.783312 | − | 0.621629i | \(-0.786471\pi\) | ||||
−0.783312 | + | 0.621629i | \(0.786471\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5563 | −1.31054 | −0.655271 | − | 0.755394i | \(-0.727446\pi\) | ||||
−0.655271 | + | 0.755394i | \(0.727446\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.48528 | −0.812743 | −0.406371 | − | 0.913708i | \(-0.633206\pi\) | ||||
−0.406371 | + | 0.913708i | \(0.633206\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.75736 | 0.356633 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.48528 | −0.704156 | −0.352078 | − | 0.935971i | \(-0.614525\pi\) | ||||
−0.352078 | + | 0.935971i | \(0.614525\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.65685 | 0.714005 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.17157 | 0.478112 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.58579 | 0.233153 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3137 | 1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.41421 | −0.569169 | −0.284585 | − | 0.958651i | \(-0.591856\pi\) | ||||
−0.284585 | + | 0.958651i | \(0.591856\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.31371 | −0.291756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.92893 | −0.430643 | −0.215321 | − | 0.976543i | \(-0.569080\pi\) | ||||
−0.215321 | + | 0.976543i | \(0.569080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.41421 | −0.293849 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.0000 | 1.45241 | 0.726204 | − | 0.687479i | \(-0.241283\pi\) | ||||
0.726204 | + | 0.687479i | \(0.241283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.31371 | −0.281065 | −0.140533 | − | 0.990076i | \(-0.544881\pi\) | ||||
−0.140533 | + | 0.990076i | \(0.544881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.82843 | 0.152901 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.41421 | −0.117444 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0000 | −1.31077 | −0.655386 | − | 0.755295i | \(-0.727494\pi\) | ||||
−0.655386 | + | 0.755295i | \(0.727494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.58579 | −0.454565 | −0.227282 | − | 0.973829i | \(-0.572984\pi\) | ||||
−0.227282 | + | 0.973829i | \(0.572984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.65685 | −0.457330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6569 | 1.09694 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.31371 | 0.583697 | 0.291849 | − | 0.956464i | \(-0.405730\pi\) | ||||
0.291849 | + | 0.956464i | \(0.405730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.07107 | −0.0849412 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.10051 | −0.399502 | −0.199751 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199751 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.585786 | −0.0456034 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.272078 | −0.0210540 | −0.0105270 | − | 0.999945i | \(-0.503351\pi\) | ||||
−0.0105270 | + | 0.999945i | \(0.503351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.31371 | 0.559293 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.17157 | −0.165102 | −0.0825508 | − | 0.996587i | \(-0.526307\pi\) | ||||
−0.0825508 | + | 0.996587i | \(0.526307\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.82843 | −0.137433 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.8995 | −1.41261 | −0.706307 | − | 0.707905i | \(-0.749640\pi\) | ||||
−0.706307 | + | 0.707905i | \(0.749640\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3137 | 0.989600 | 0.494800 | − | 0.869007i | \(-0.335241\pi\) | ||||
0.494800 | + | 0.869007i | \(0.335241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.38478 | −0.250210 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.8284 | 0.943165 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | −0.146254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.48528 | 0.469258 | 0.234629 | − | 0.972085i | \(-0.424612\pi\) | ||||
0.234629 | + | 0.972085i | \(0.424612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.2132 | 1.67092 | 0.835461 | − | 0.549549i | \(-0.185200\pi\) | ||||
0.835461 | + | 0.549549i | \(0.185200\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.07107 | −0.0767008 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.1421 | −0.793844 | −0.396922 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396922 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0416 | 1.70427 | 0.852133 | − | 0.523325i | \(-0.175309\pi\) | ||||
0.852133 | + | 0.523325i | \(0.175309\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.34315 | 0.235807 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.82843 | 0.616604 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.3137 | 1.06438 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.58579 | 0.178863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.92893 | 0.339322 | 0.169661 | − | 0.985503i | \(-0.445733\pi\) | ||||
0.169661 | + | 0.985503i | \(0.445733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.38478 | −0.163402 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.3137 | −0.771589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.41421 | −0.0955637 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.65685 | −0.245987 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.5563 | 1.30959 | 0.654795 | − | 0.755807i | \(-0.272755\pi\) | ||||
0.654795 | + | 0.755807i | \(0.272755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.48528 | 0.565685 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.1421 | −1.86786 | −0.933930 | − | 0.357457i | \(-0.883644\pi\) | ||||
−0.933930 | + | 0.357457i | \(0.883644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | 0.264327 | 0.132164 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132164 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3848 | 1.33545 | 0.667726 | − | 0.744408i | \(-0.267268\pi\) | ||||
0.667726 | + | 0.744408i | \(0.267268\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.82843 | −0.445437 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.34315 | 0.217161 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.7279 | 0.758616 | 0.379308 | − | 0.925270i | \(-0.376162\pi\) | ||||
0.379308 | + | 0.925270i | \(0.376162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7279 | 1.46403 | 0.732017 | − | 0.681286i | \(-0.238579\pi\) | ||||
0.732017 | + | 0.681286i | \(0.238579\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.3431 | −0.663513 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.72792 | 0.300830 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.34315 | 0.275236 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.485281 | 0.0306307 | 0.0153153 | − | 0.999883i | \(-0.495125\pi\) | ||||
0.0153153 | + | 0.999883i | \(0.495125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.41421 | 0.340389 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.17157 | 0.0733667 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.4853 | 1.21546 | 0.607729 | − | 0.794144i | \(-0.292081\pi\) | ||||
0.607729 | + | 0.794144i | \(0.292081\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.82843 | −0.175075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.0416 | 1.42081 | 0.710404 | − | 0.703794i | \(-0.248512\pi\) | ||||
0.710404 | + | 0.703794i | \(0.248512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.65685 | −0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.79899 | −0.232494 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.6569 | 0.832673 | 0.416337 | − | 0.909211i | \(-0.363314\pi\) | ||||
0.416337 | + | 0.909211i | \(0.363314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0710678 | −0.00431706 | −0.00215853 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215853 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | 0.180907 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.7990 | −1.49003 | −0.745013 | − | 0.667049i | \(-0.767557\pi\) | ||||
−0.745013 | + | 0.667049i | \(0.767557\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.3137 | 1.63523 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.8995 | −0.709864 | −0.354932 | − | 0.934892i | \(-0.615496\pi\) | ||||
−0.354932 | + | 0.934892i | \(0.615496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.5563 | 1.63805 | 0.819027 | − | 0.573754i | \(-0.194514\pi\) | ||||
0.819027 | + | 0.573754i | \(0.194514\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.51472 | −0.0897242 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.55635 | −0.384340 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.1716 | 0.769492 | 0.384746 | − | 0.923023i | \(-0.374289\pi\) | ||||
0.384746 | + | 0.923023i | \(0.374289\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.24264 | −0.363461 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.41421 | −0.140087 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.89949 | 0.572503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.10051 | −0.178119 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.5563 | −0.661715 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.58579 | 0.490017 | 0.245008 | − | 0.969521i | \(-0.421209\pi\) | ||||
0.245008 | + | 0.969521i | \(0.421209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.58579 | 0.374652 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.2132 | −1.54312 | −0.771560 | − | 0.636157i | \(-0.780523\pi\) | ||||
−0.771560 | + | 0.636157i | \(0.780523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.34315 | 0.528106 | 0.264053 | − | 0.964508i | \(-0.414941\pi\) | ||||
0.264053 | + | 0.964508i | \(0.414941\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.9706 | 1.17782 | 0.588912 | − | 0.808197i | \(-0.299556\pi\) | ||||
0.588912 | + | 0.808197i | \(0.299556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00000 | −0.0559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.61522 | 0.313411 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.17157 | −0.287754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.48528 | 0.304269 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.51472 | 0.194364 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.38478 | 0.295974 | 0.147987 | − | 0.988989i | \(-0.452721\pi\) | ||||
0.147987 | + | 0.988989i | \(0.452721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.6569 | 1.40599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.4142 | 0.623625 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.24264 | −0.122164 | −0.0610822 | − | 0.998133i | \(-0.519455\pi\) | ||||
−0.0610822 | + | 0.998133i | \(0.519455\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.10051 | 0.168396 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.65685 | 0.522948 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.17157 | −0.170752 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.58579 | 0.460909 | 0.230455 | − | 0.973083i | \(-0.425979\pi\) | ||||
0.230455 | + | 0.973083i | \(0.425979\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.2843 | −1.29991 | −0.649954 | − | 0.759974i | \(-0.725212\pi\) | ||||
−0.649954 | + | 0.759974i | \(0.725212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.41421 | −0.235613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.68629 | 0.142977 | 0.0714884 | − | 0.997441i | \(-0.477225\pi\) | ||||
0.0714884 | + | 0.997441i | \(0.477225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.14214 | −0.432140 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.9289 | −0.735141 | −0.367570 | − | 0.929996i | \(-0.619810\pi\) | ||||
−0.367570 | + | 0.929996i | \(0.619810\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3137 | −0.648090 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.414214 | −0.0217406 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.82843 | −0.252731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.24264 | 0.430262 | 0.215131 | − | 0.976585i | \(-0.430982\pi\) | ||||
0.215131 | + | 0.976585i | \(0.430982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.6569 | 0.919179 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6274 | −0.705601 | −0.352800 | − | 0.935699i | \(-0.614771\pi\) | ||||
−0.352800 | + | 0.935699i | \(0.614771\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.68629 | −0.241999 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.82843 | −0.0941688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.38478 | 0.379330 | 0.189665 | − | 0.981849i | \(-0.439260\pi\) | ||||
0.189665 | + | 0.981849i | \(0.439260\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.65685 | 0.136115 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.10051 | −0.413916 | −0.206958 | − | 0.978350i | \(-0.566356\pi\) | ||||
−0.206958 | + | 0.978350i | \(0.566356\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.6274 | −1.15022 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.2132 | 1.68398 | 0.841988 | − | 0.539496i | \(-0.181385\pi\) | ||||
0.841988 | + | 0.539496i | \(0.181385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8284 | −0.547617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.04163 | 0.102987 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.4142 | 0.574311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.6569 | −1.78957 | −0.894783 | − | 0.446501i | \(-0.852670\pi\) | ||||
−0.894783 | + | 0.446501i | \(0.852670\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.0000 | −1.24844 | −0.624220 | − | 0.781248i | \(-0.714583\pi\) | ||||
−0.624220 | + | 0.781248i | \(0.714583\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.6569 | 0.879551 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.5858 | −0.526012 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.07107 | 0.449636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.8995 | 1.67622 | 0.838111 | − | 0.545500i | \(-0.183660\pi\) | ||||
0.838111 | + | 0.545500i | \(0.183660\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.04163 | −0.347338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8284 | 0.727899 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.37258 | 0.0672157 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4558 | −1.24360 | −0.621800 | − | 0.783176i | \(-0.713598\pi\) | ||||
−0.621800 | + | 0.783176i | \(0.713598\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.65685 | 0.470646 | 0.235323 | − | 0.971917i | \(-0.424385\pi\) | ||||
0.235323 | + | 0.971917i | \(0.424385\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.6569 | −0.664019 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.757359 | −0.0365657 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.72792 | −0.372241 | −0.186120 | − | 0.982527i | \(-0.559591\pi\) | ||||
−0.186120 | + | 0.982527i | \(0.559591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4558 | 0.646647 | 0.323323 | − | 0.946289i | \(-0.395200\pi\) | ||||
0.323323 | + | 0.946289i | \(0.395200\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.585786 | 0.0280863 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.0000 | 0.669711 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.92893 | 0.0920629 | 0.0460315 | − | 0.998940i | \(-0.485343\pi\) | ||||
0.0460315 | + | 0.998940i | \(0.485343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.31371 | −0.252462 | −0.126231 | − | 0.992001i | \(-0.540288\pi\) | ||||
−0.126231 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.9706 | −0.614864 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.62742 | 0.313466 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.24264 | 0.293954 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.31371 | 0.108708 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3137 | 1.37124 | 0.685619 | − | 0.727961i | \(-0.259532\pi\) | ||||
0.685619 | + | 0.727961i | \(0.259532\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.82843 | 0.225372 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0000 | 0.605470 | 0.302735 | − | 0.953075i | \(-0.402100\pi\) | ||||
0.302735 | + | 0.953075i | \(0.402100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.7990 | 0.641293 | 0.320647 | − | 0.947199i | \(-0.396100\pi\) | ||||
0.320647 | + | 0.947199i | \(0.396100\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.65685 | −0.262330 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.9411 | 1.66316 | 0.831578 | − | 0.555407i | \(-0.187438\pi\) | ||||
0.831578 | + | 0.555407i | \(0.187438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.02944 | −0.139589 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.75736 | 0.355932 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.31371 | −0.334872 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0711 | 0.642923 | 0.321462 | − | 0.946923i | \(-0.395826\pi\) | ||||
0.321462 | + | 0.946923i | \(0.395826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.5858 | 0.756247 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.3848 | −1.01644 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.3137 | 1.05644 | 0.528222 | − | 0.849106i | \(-0.322859\pi\) | ||||
0.528222 | + | 0.849106i | \(0.322859\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.11270 | 0.0955395 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.828427 | 0.0373864 | 0.0186932 | − | 0.999825i | \(-0.494049\pi\) | ||||
0.0186932 | + | 0.999825i | \(0.494049\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | 0.0900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.7990 | 1.06539 | 0.532695 | − | 0.846308i | \(-0.321179\pi\) | ||||
0.532695 | + | 0.846308i | \(0.321179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.112698 | 0.00503499 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.7279 | −0.879625 | −0.439812 | − | 0.898090i | \(-0.644955\pi\) | ||||
−0.439812 | + | 0.898090i | \(0.644955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5858 | −0.471061 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.00000 | 0.177646 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.6569 | −1.58046 | −0.790231 | − | 0.612809i | \(-0.790040\pi\) | ||||
−0.790231 | + | 0.612809i | \(0.790040\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.24264 | −0.275619 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.4853 | 0.990820 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.82843 | −0.212354 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.899495 | 0.0394834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0711 | −0.571558 | −0.285779 | − | 0.958296i | \(-0.592252\pi\) | ||||
−0.285779 | + | 0.958296i | \(0.592252\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.3137 | −0.841318 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.31371 | 0.274509 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.4853 | −0.541815 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.4142 | 0.494404 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.1716 | 0.828859 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.82843 | 0.337822 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.85786 | −0.380829 | −0.190415 | − | 0.981704i | \(-0.560983\pi\) | ||||
−0.190415 | + | 0.981704i | \(0.560983\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.51472 | −0.236659 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | 0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.6985 | 1.86841 | 0.934206 | − | 0.356734i | \(-0.116110\pi\) | ||||
0.934206 | + | 0.356734i | \(0.116110\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.1127 | −0.986426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.58579 | −0.110158 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.31371 | −0.225554 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.8284 | −0.797786 | −0.398893 | − | 0.916997i | \(-0.630606\pi\) | ||||
−0.398893 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6274 | −0.618674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.828427 | 0.0349762 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.78680 | 0.117449 | 0.0587247 | − | 0.998274i | \(-0.481297\pi\) | ||||
0.0587247 | + | 0.998274i | \(0.481297\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.5858 | 0.445347 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.9706 | −0.543754 | −0.271877 | − | 0.962332i | \(-0.587644\pi\) | ||||
−0.271877 | + | 0.962332i | \(0.587644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.41421 | −0.310275 | −0.155138 | − | 0.987893i | \(-0.549582\pi\) | ||||
−0.155138 | + | 0.987893i | \(0.549582\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.68629 | −0.112221 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.2426 | 0.677365 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.9706 | −0.664863 | −0.332432 | − | 0.943127i | \(-0.607869\pi\) | ||||
−0.332432 | + | 0.943127i | \(0.607869\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.61522 | −0.399595 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.58579 | −0.107092 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.31371 | −0.302385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.2132 | 0.669191 | 0.334595 | − | 0.942362i | \(-0.391400\pi\) | ||||
0.334595 | + | 0.942362i | \(0.391400\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.9706 | 1.02889 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.61522 | 0.189845 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5858 | 0.434706 | 0.217353 | − | 0.976093i | \(-0.430258\pi\) | ||||
0.217353 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.95837 | −0.407569 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.9706 | −1.83745 | −0.918724 | − | 0.394901i | \(-0.870779\pi\) | ||||
−0.918724 | + | 0.394901i | \(0.870779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.6569 | 0.964983 | 0.482492 | − | 0.875901i | \(-0.339732\pi\) | ||||
0.482492 | + | 0.875901i | \(0.339732\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.8284 | 0.929645 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.41421 | −0.0574960 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.2843 | 0.904491 | 0.452245 | − | 0.891894i | \(-0.350623\pi\) | ||||
0.452245 | + | 0.891894i | \(0.350623\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.82843 | −0.357160 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.6274 | 1.15625 | 0.578125 | − | 0.815948i | \(-0.303785\pi\) | ||||
0.578125 | + | 0.815948i | \(0.303785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.65685 | −0.147459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.6274 | 1.35379 | 0.676894 | − | 0.736080i | \(-0.263325\pi\) | ||||
0.676894 | + | 0.736080i | \(0.263325\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.686292 | 0.0275844 | 0.0137922 | − | 0.999905i | \(-0.495610\pi\) | ||||
0.0137922 | + | 0.999905i | \(0.495610\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13.0711 | −0.524524 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.07107 | −0.0427743 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.1421 | −0.723374 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.38478 | 0.174555 | 0.0872776 | − | 0.996184i | \(-0.472183\pi\) | ||||
0.0872776 | + | 0.996184i | \(0.472183\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.04163 | −0.0811475 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.07107 | 0.359974 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.2843 | −0.644196 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.2548 | 1.74796 | 0.873980 | − | 0.485961i | \(-0.161530\pi\) | ||||
0.873980 | + | 0.485961i | \(0.161530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.5858 | 1.40337 | 0.701683 | − | 0.712489i | \(-0.252432\pi\) | ||||
0.701683 | + | 0.712489i | \(0.252432\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.68629 | 0.184523 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.0711 | −0.513877 | −0.256938 | − | 0.966428i | \(-0.582714\pi\) | ||||
−0.256938 | + | 0.966428i | \(0.582714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.41421 | −0.173273 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −49.0711 | −1.92030 | −0.960150 | − | 0.279486i | \(-0.909836\pi\) | ||||
−0.960150 | + | 0.279486i | \(0.909836\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.97056 | 0.272362 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.65685 | −0.376750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.3137 | −1.21981 | −0.609904 | − | 0.792475i | \(-0.708792\pi\) | ||||
−0.609904 | + | 0.792475i | \(0.708792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.62742 | 0.179986 | 0.0899928 | − | 0.995942i | \(-0.471316\pi\) | ||||
0.0899928 | + | 0.995942i | \(0.471316\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.51472 | 0.0588268 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.41421 | −0.209639 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.10051 | −0.313184 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.17157 | −0.315460 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2426 | 0.626108 | 0.313054 | − | 0.949735i | \(-0.398648\pi\) | ||||
0.313054 | + | 0.949735i | \(0.398648\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.24264 | −0.278769 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.28427 | −0.318390 | −0.159195 | − | 0.987247i | \(-0.550890\pi\) | ||||
−0.159195 | + | 0.987247i | \(0.550890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.6569 | 0.446692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.8995 | −0.570113 | −0.285057 | − | 0.958511i | \(-0.592012\pi\) | ||||
−0.285057 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.0416 | −0.918583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.65685 | −0.0632129 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.72792 | −0.180119 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.3848 | 1.11785 | 0.558925 | − | 0.829218i | \(-0.311214\pi\) | ||||
0.558925 | + | 0.829218i | \(0.311214\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.68629 | 0.177761 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4853 | −0.472914 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.44365 | −0.319368 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.4558 | 1.60354 | 0.801768 | − | 0.597636i | \(-0.203893\pi\) | ||||
0.801768 | + | 0.597636i | \(0.203893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.4558 | 0.884654 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.82843 | 0.106525 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.9289 | 0.710891 | 0.355445 | − | 0.934697i | \(-0.384329\pi\) | ||||
0.355445 | + | 0.934697i | \(0.384329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.8284 | 0.856133 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.2843 | 1.95806 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.58579 | −0.0967029 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.85786 | −0.181420 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.8284 | 1.07512 | 0.537559 | − | 0.843226i | \(-0.319346\pi\) | ||||
0.537559 | + | 0.843226i | \(0.319346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.41421 | −0.350118 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | −0.111417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7990 | −0.511776 | −0.255888 | − | 0.966706i | \(-0.582368\pi\) | ||||
−0.255888 | + | 0.966706i | \(0.582368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | 0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.6569 | −1.05847 | −0.529233 | − | 0.848477i | \(-0.677520\pi\) | ||||
−0.529233 | + | 0.848477i | \(0.677520\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.07107 | 0.297302 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.4264 | −1.33997 | −0.669984 | − | 0.742376i | \(-0.733699\pi\) | ||||
−0.669984 | + | 0.742376i | \(0.733699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.95837 | −0.0719425 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.0000 | −1.24734 | −0.623670 | − | 0.781688i | \(-0.714359\pi\) | ||||
−0.623670 | + | 0.781688i | \(0.714359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.6274 | 0.829004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 29.6569 | 1.08509 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3137 | −0.412843 | −0.206422 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206422 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.201010 | −0.00732522 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.89949 | 0.287492 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3137 | 0.629277 | 0.314639 | − | 0.949212i | \(-0.398117\pi\) | ||||
0.314639 | + | 0.949212i | \(0.398117\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.24264 | −0.0814027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.9411 | 1.01287 | 0.506433 | − | 0.862280i | \(-0.330964\pi\) | ||||
0.506433 | + | 0.862280i | \(0.330964\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.00000 | 0.289241 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.07107 | −0.291429 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.9706 | −1.11683 | −0.558414 | − | 0.829563i | \(-0.688590\pi\) | ||||
−0.558414 | + | 0.829563i | \(0.688590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.07107 | −0.290672 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.6274 | −1.24546 | −0.622731 | − | 0.782436i | \(-0.713977\pi\) | ||||
−0.622731 | + | 0.782436i | \(0.713977\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.9706 | 1.04065 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.1421 | 0.578352 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.75736 | −0.206015 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.41421 | 0.0862770 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.3431 | −0.369163 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.61522 | 0.200161 | 0.100081 | − | 0.994979i | \(-0.468090\pi\) | ||||
0.100081 | + | 0.994979i | \(0.468090\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.54416 | −0.339781 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.9411 | −0.530575 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.51472 | 0.0537215 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.31371 | −0.329908 | −0.164954 | − | 0.986301i | \(-0.552748\pi\) | ||||
−0.164954 | + | 0.986301i | \(0.552748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.65685 | 0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.9411 | −0.916585 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.41421 | −0.120485 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.65685 | −0.199131 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.00000 | −0.281265 | −0.140633 | − | 0.990062i | \(-0.544914\pi\) | ||||
−0.140633 | + | 0.990062i | \(0.544914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.6569 | 1.74369 | 0.871844 | − | 0.489784i | \(-0.162924\pi\) | ||||
0.871844 | + | 0.489784i | \(0.162924\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0294373 | 0.00103241 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.21320 | 0.252667 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.6863 | −0.723722 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.1716 | −0.773793 | −0.386897 | − | 0.922123i | \(-0.626453\pi\) | ||||
−0.386897 | + | 0.922123i | \(0.626453\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.1716 | 0.947141 | 0.473571 | − | 0.880756i | \(-0.342965\pi\) | ||||
0.473571 | + | 0.880756i | \(0.342965\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.24264 | −0.0432632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.5269 | −1.13107 | −0.565536 | − | 0.824724i | \(-0.691331\pi\) | ||||
−0.565536 | + | 0.824724i | \(0.691331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.4142 | −1.29945 | −0.649725 | − | 0.760170i | \(-0.725116\pi\) | ||||
−0.649725 | + | 0.760170i | \(0.725116\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.2721 | 0.356334 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.384776 | 0.0133157 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.3137 | −0.805840 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.4853 | 0.914373 | 0.457187 | − | 0.889371i | \(-0.348857\pi\) | ||||
0.457187 | + | 0.889371i | \(0.348857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.92893 | 0.169761 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.6569 | 0.469810 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.4142 | −0.391735 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49.1127 | 1.68356 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.0000 | 1.71197 | 0.855984 | − | 0.517003i | \(-0.172952\pi\) | ||||
0.855984 | + | 0.517003i | \(0.172952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3431 | −0.353728 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.2843 | 1.64936 | 0.824680 | − | 0.565600i | \(-0.191355\pi\) | ||||
0.824680 | + | 0.565600i | \(0.191355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.4142 | −0.423568 | −0.211784 | − | 0.977317i | \(-0.567927\pi\) | ||||
−0.211784 | + | 0.977317i | \(0.567927\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.3848 | 0.898148 | 0.449074 | − | 0.893495i | \(-0.351754\pi\) | ||||
0.449074 | + | 0.893495i | \(0.351754\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.07107 | 0.104419 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.38478 | 0.182877 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.07107 | 0.273792 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.7574 | 0.500034 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −44.7696 | −1.51522 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.2843 | 0.448578 | 0.224289 | − | 0.974523i | \(-0.427994\pi\) | ||||
0.224289 | + | 0.974523i | \(0.427994\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.45584 | −0.184021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.8284 | −0.668037 | −0.334018 | − | 0.942567i | \(-0.608405\pi\) | ||||
−0.334018 | + | 0.942567i | \(0.608405\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.6690 | −1.33497 | −0.667485 | − | 0.744623i | \(-0.732629\pi\) | ||||
−0.667485 | + | 0.744623i | \(0.732629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.58579 | 0.0869203 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31.7279 | −1.06532 | −0.532660 | − | 0.846330i | \(-0.678807\pi\) | ||||
−0.532660 | + | 0.846330i | \(0.678807\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.48528 | −0.250766 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.4853 | −0.417804 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.7279 | 0.893416 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.10051 | −0.136912 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.65685 | −0.322074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.17157 | 0.172290 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.8284 | −0.625878 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.6274 | 0.419286 | 0.209643 | − | 0.977778i | \(-0.432770\pi\) | ||||
0.209643 | + | 0.977778i | \(0.432770\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.1716 | −0.702217 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.4853 | −1.27507 | −0.637537 | − | 0.770420i | \(-0.720047\pi\) | ||||
−0.637537 | + | 0.770420i | \(0.720047\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.4853 | 0.347012 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.78680 | 0.158247 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.45584 | −0.179972 | −0.0899858 | − | 0.995943i | \(-0.528682\pi\) | ||||
−0.0899858 | + | 0.995943i | \(0.528682\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.55635 | −0.117186 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.5269 | −0.346498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.2132 | 0.894765 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 44.9706 | 1.47703 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.4264 | 1.35916 | 0.679578 | − | 0.733603i | \(-0.262163\pi\) | ||||
0.679578 | + | 0.733603i | \(0.262163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.2721 | 0.369031 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.82843 | 0.0924995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.4142 | 0.699572 | 0.349786 | − | 0.936830i | \(-0.386254\pi\) | ||||
0.349786 | + | 0.936830i | \(0.386254\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.87006 | −0.126295 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.9411 | 1.66063 | 0.830317 | − | 0.557292i | \(-0.188160\pi\) | ||||
0.830317 | + | 0.557292i | \(0.188160\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.7990 | 1.10065 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.201010 | −0.00653195 | −0.00326598 | − | 0.999995i | \(-0.501040\pi\) | ||||
−0.00326598 | + | 0.999995i | \(0.501040\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.24264 | −0.202645 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.68629 | −0.281672 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.6152 | 0.570613 | 0.285307 | − | 0.958436i | \(-0.407905\pi\) | ||||
0.285307 | + | 0.958436i | \(0.407905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.17157 | −0.296785 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.414214 | 0.0133896 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.2548 | 2.00822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.3431 | 1.23559 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.8284 | −1.05678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3431 | 0.589876 | 0.294938 | − | 0.955516i | \(-0.404701\pi\) | ||||
0.294938 | + | 0.955516i | \(0.404701\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.14214 | 0.0688153 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.2132 | 0.969588 | 0.484794 | − | 0.874628i | \(-0.338895\pi\) | ||||
0.484794 | + | 0.874628i | \(0.338895\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.27208 | −0.0727647 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.02944 | 0.0969203 | 0.0484601 | − | 0.998825i | \(-0.484569\pi\) | ||||
0.0484601 | + | 0.998825i | \(0.484569\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.17157 | −0.293125 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.0000 | 0.766261 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.5147 | −0.941373 | −0.470687 | − | 0.882300i | \(-0.655994\pi\) | ||||
−0.470687 | + | 0.882300i | \(0.655994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.7574 | 0.502071 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.3137 | −1.37730 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.100505 | −0.00319265 | −0.00159632 | − | 0.999999i | \(-0.500508\pi\) | ||||
−0.00159632 | + | 0.999999i | \(0.500508\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.23045 | −0.0707811 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.0000 | −1.07787 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.4558 | −1.31292 | −0.656460 | − | 0.754361i | \(-0.727947\pi\) | ||||
−0.656460 | + | 0.754361i | \(0.727947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.8995 | −0.692869 |
(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.cd.1.1 | 2 | ||
4.3 | odd | 2 | 4312.2.a.m.1.2 | 2 | |||
7.3 | odd | 6 | 1232.2.q.h.177.1 | 4 | |||
7.5 | odd | 6 | 1232.2.q.h.529.1 | 4 | |||
7.6 | odd | 2 | 8624.2.a.bg.1.2 | 2 | |||
28.3 | even | 6 | 616.2.q.b.177.2 | ✓ | 4 | ||
28.19 | even | 6 | 616.2.q.b.529.2 | yes | 4 | ||
28.27 | even | 2 | 4312.2.a.u.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.q.b.177.2 | ✓ | 4 | 28.3 | even | 6 | ||
616.2.q.b.529.2 | yes | 4 | 28.19 | even | 6 | ||
1232.2.q.h.177.1 | 4 | 7.3 | odd | 6 | |||
1232.2.q.h.529.1 | 4 | 7.5 | odd | 6 | |||
4312.2.a.m.1.2 | 2 | 4.3 | odd | 2 | |||
4312.2.a.u.1.1 | 2 | 28.27 | even | 2 | |||
8624.2.a.bg.1.2 | 2 | 7.6 | odd | 2 | |||
8624.2.a.cd.1.1 | 2 | 1.1 | even | 1 | trivial |