Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5850,2,Mod(1,5850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5850.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: | \(46.7124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1950) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.70156 | −1.77702 | −0.888512 | − | 0.458854i | \(-0.848260\pi\) | ||||
−0.888512 | + | 0.458854i | \(0.848260\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.70156 | −1.41757 | −0.708787 | − | 0.705422i | \(-0.750757\pi\) | ||||
−0.708787 | + | 0.705422i | \(0.750757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −4.70156 | −1.25655 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.701562 | −0.170154 | −0.0850769 | − | 0.996374i | \(-0.527114\pi\) | ||||
−0.0850769 | + | 0.996374i | \(0.527114\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.70156 | −0.390365 | −0.195183 | − | 0.980767i | \(-0.562530\pi\) | ||||
−0.195183 | + | 0.980767i | \(0.562530\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.70156 | −1.00238 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.70156 | −0.888512 | ||||||||
\(29\) | 6.40312 | 1.18903 | 0.594515 | − | 0.804084i | \(-0.297344\pi\) | ||||
0.594515 | + | 0.804084i | \(0.297344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1047 | −1.81486 | −0.907428 | − | 0.420208i | \(-0.861957\pi\) | ||||
−0.907428 | + | 0.420208i | \(0.861957\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.701562 | −0.120317 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.70156 | 0.279735 | 0.139868 | − | 0.990170i | \(-0.455332\pi\) | ||||
0.139868 | + | 0.990170i | \(0.455332\pi\) | |||||||
\(38\) | −1.70156 | −0.276030 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.70156 | 0.578087 | 0.289043 | − | 0.957316i | \(-0.406663\pi\) | ||||
0.289043 | + | 0.957316i | \(0.406663\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4031 | 1.73896 | 0.869480 | − | 0.493968i | \(-0.164454\pi\) | ||||
0.869480 | + | 0.493968i | \(0.164454\pi\) | |||||||
\(44\) | −4.70156 | −0.708787 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00000 | 1.02105 | 0.510527 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510527 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.1047 | 2.15781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 2.40312 | 0.330095 | 0.165047 | − | 0.986286i | \(-0.447222\pi\) | ||||
0.165047 | + | 0.986286i | \(0.447222\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.70156 | −0.628273 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.40312 | 0.840771 | ||||||||
\(59\) | −2.70156 | −0.351713 | −0.175857 | − | 0.984416i | \(-0.556270\pi\) | ||||
−0.175857 | + | 0.984416i | \(0.556270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1047 | 1.80592 | 0.902960 | − | 0.429725i | \(-0.141389\pi\) | ||||
0.902960 | + | 0.429725i | \(0.141389\pi\) | |||||||
\(62\) | −10.1047 | −1.28330 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.40312 | 0.782266 | 0.391133 | − | 0.920334i | \(-0.372083\pi\) | ||||
0.391133 | + | 0.920334i | \(0.372083\pi\) | |||||||
\(68\) | −0.701562 | −0.0850769 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70156 | 0.201938 | 0.100969 | − | 0.994890i | \(-0.467806\pi\) | ||||
0.100969 | + | 0.994890i | \(0.467806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0000 | 1.40449 | 0.702247 | − | 0.711934i | \(-0.252180\pi\) | ||||
0.702247 | + | 0.711934i | \(0.252180\pi\) | |||||||
\(74\) | 1.70156 | 0.197803 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.70156 | −0.195183 | ||||||||
\(77\) | 22.1047 | 2.51906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.70156 | −0.641476 | −0.320738 | − | 0.947168i | \(-0.603931\pi\) | ||||
−0.320738 | + | 0.947168i | \(0.603931\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.70156 | 0.408769 | ||||||||
\(83\) | −10.7016 | −1.17465 | −0.587325 | − | 0.809352i | \(-0.699819\pi\) | ||||
−0.587325 | + | 0.809352i | \(0.699819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.4031 | 1.22963 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.70156 | −0.501188 | ||||||||
\(89\) | −11.4031 | −1.20873 | −0.604364 | − | 0.796708i | \(-0.706573\pi\) | ||||
−0.604364 | + | 0.796708i | \(0.706573\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.70156 | −0.492858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.00000 | 0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.59688 | 0.263673 | 0.131836 | − | 0.991271i | \(-0.457913\pi\) | ||||
0.131836 | + | 0.991271i | \(0.457913\pi\) | |||||||
\(98\) | 15.1047 | 1.52580 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.70156 | −0.666830 | −0.333415 | − | 0.942780i | \(-0.608201\pi\) | ||||
−0.333415 | + | 0.942780i | \(0.608201\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.40312 | −0.138254 | −0.0691270 | − | 0.997608i | \(-0.522021\pi\) | ||||
−0.0691270 | + | 0.997608i | \(0.522021\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.40312 | 0.233412 | ||||||||
\(107\) | 19.1047 | 1.84692 | 0.923460 | − | 0.383695i | \(-0.125349\pi\) | ||||
0.923460 | + | 0.383695i | \(0.125349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.29844 | 0.411716 | 0.205858 | − | 0.978582i | \(-0.434002\pi\) | ||||
0.205858 | + | 0.978582i | \(0.434002\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.70156 | −0.444256 | ||||||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.40312 | 0.594515 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.70156 | −0.248699 | ||||||||
\(119\) | 3.29844 | 0.302367 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.1047 | 1.00952 | ||||||||
\(122\) | 14.1047 | 1.27698 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.1047 | −0.907428 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.29844 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.5078 | −1.96652 | −0.983258 | − | 0.182217i | \(-0.941673\pi\) | ||||
−0.983258 | + | 0.182217i | \(0.941673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000 | 0.693688 | ||||||||
\(134\) | 6.40312 | 0.553146 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.701562 | −0.0601585 | ||||||||
\(137\) | 13.7016 | 1.17060 | 0.585302 | − | 0.810816i | \(-0.300976\pi\) | ||||
0.585302 | + | 0.810816i | \(0.300976\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.40312 | 0.797563 | 0.398781 | − | 0.917046i | \(-0.369433\pi\) | ||||
0.398781 | + | 0.917046i | \(0.369433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.70156 | 0.142792 | ||||||||
\(143\) | −4.70156 | −0.393164 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.0000 | 0.993127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.70156 | 0.139868 | ||||||||
\(149\) | −6.59688 | −0.540437 | −0.270219 | − | 0.962799i | \(-0.587096\pi\) | ||||
−0.270219 | + | 0.962799i | \(0.587096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1047 | −1.14782 | −0.573912 | − | 0.818917i | \(-0.694575\pi\) | ||||
−0.573912 | + | 0.818917i | \(0.694575\pi\) | |||||||
\(152\) | −1.70156 | −0.138015 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 22.1047 | 1.78125 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7016 | 1.81178 | 0.905891 | − | 0.423511i | \(-0.139203\pi\) | ||||
0.905891 | + | 0.423511i | \(0.139203\pi\) | |||||||
\(158\) | −5.70156 | −0.453592 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.8062 | 1.47302 | 0.736510 | − | 0.676427i | \(-0.236473\pi\) | ||||
0.736510 | + | 0.676427i | \(0.236473\pi\) | |||||||
\(164\) | 3.70156 | 0.289043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.7016 | −0.830602 | ||||||||
\(167\) | −1.10469 | −0.0854832 | −0.0427416 | − | 0.999086i | \(-0.513609\pi\) | ||||
−0.0427416 | + | 0.999086i | \(0.513609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.4031 | 0.869480 | ||||||||
\(173\) | −0.193752 | −0.0147307 | −0.00736533 | − | 0.999973i | \(-0.502344\pi\) | ||||
−0.00736533 | + | 0.999973i | \(0.502344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.70156 | −0.354394 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.4031 | −0.854700 | ||||||||
\(179\) | 24.2094 | 1.80949 | 0.904747 | − | 0.425950i | \(-0.140060\pi\) | ||||
0.904747 | + | 0.425950i | \(0.140060\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2984 | 0.839806 | 0.419903 | − | 0.907569i | \(-0.362064\pi\) | ||||
0.419903 | + | 0.907569i | \(0.362064\pi\) | |||||||
\(182\) | −4.70156 | −0.348503 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.29844 | 0.241206 | ||||||||
\(188\) | 7.00000 | 0.510527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8062 | 0.926628 | 0.463314 | − | 0.886194i | \(-0.346660\pi\) | ||||
0.463314 | + | 0.886194i | \(0.346660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2094 | −1.16678 | −0.583388 | − | 0.812194i | \(-0.698273\pi\) | ||||
−0.583388 | + | 0.812194i | \(0.698273\pi\) | |||||||
\(194\) | 2.59688 | 0.186445 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.1047 | 1.07891 | ||||||||
\(197\) | −5.40312 | −0.384957 | −0.192478 | − | 0.981301i | \(-0.561653\pi\) | ||||
−0.192478 | + | 0.981301i | \(0.561653\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.29844 | 0.588261 | 0.294130 | − | 0.955765i | \(-0.404970\pi\) | ||||
0.294130 | + | 0.955765i | \(0.404970\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.70156 | −0.471520 | ||||||||
\(203\) | −30.1047 | −2.11293 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.40312 | −0.0977603 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.80625 | 0.468561 | 0.234281 | − | 0.972169i | \(-0.424727\pi\) | ||||
0.234281 | + | 0.972169i | \(0.424727\pi\) | |||||||
\(212\) | 2.40312 | 0.165047 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.1047 | 1.30597 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47.5078 | 3.22504 | ||||||||
\(218\) | 4.29844 | 0.291127 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.701562 | −0.0471922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4031 | −0.763610 | −0.381805 | − | 0.924243i | \(-0.624697\pi\) | ||||
−0.381805 | + | 0.924243i | \(0.624697\pi\) | |||||||
\(224\) | −4.70156 | −0.314136 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | −16.1047 | −1.06891 | −0.534453 | − | 0.845198i | \(-0.679482\pi\) | ||||
−0.534453 | + | 0.845198i | \(0.679482\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.7016 | 1.03759 | 0.518794 | − | 0.854899i | \(-0.326381\pi\) | ||||
0.518794 | + | 0.854899i | \(0.326381\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.40312 | 0.420386 | ||||||||
\(233\) | −20.2094 | −1.32396 | −0.661980 | − | 0.749521i | \(-0.730284\pi\) | ||||
−0.661980 | + | 0.749521i | \(0.730284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.70156 | −0.175857 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.29844 | 0.213806 | ||||||||
\(239\) | −6.10469 | −0.394879 | −0.197440 | − | 0.980315i | \(-0.563263\pi\) | ||||
−0.197440 | + | 0.980315i | \(0.563263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.59688 | −0.167279 | −0.0836397 | − | 0.996496i | \(-0.526654\pi\) | ||||
−0.0836397 | + | 0.996496i | \(0.526654\pi\) | |||||||
\(242\) | 11.1047 | 0.713836 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.1047 | 0.902960 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.70156 | −0.108268 | ||||||||
\(248\) | −10.1047 | −0.641648 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.298438 | −0.0188372 | −0.00941862 | − | 0.999956i | \(-0.502998\pi\) | ||||
−0.00941862 | + | 0.999956i | \(0.502998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.29844 | 0.395199 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.2984 | −0.954290 | −0.477145 | − | 0.878824i | \(-0.658328\pi\) | ||||
−0.477145 | + | 0.878824i | \(0.658328\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.5078 | −1.39054 | ||||||||
\(263\) | 2.00000 | 0.123325 | 0.0616626 | − | 0.998097i | \(-0.480360\pi\) | ||||
0.0616626 | + | 0.998097i | \(0.480360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.40312 | 0.391133 | ||||||||
\(269\) | −31.2094 | −1.90287 | −0.951435 | − | 0.307851i | \(-0.900390\pi\) | ||||
−0.951435 | + | 0.307851i | \(0.900390\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.5078 | 1.18502 | 0.592508 | − | 0.805565i | \(-0.298138\pi\) | ||||
0.592508 | + | 0.805565i | \(0.298138\pi\) | |||||||
\(272\) | −0.701562 | −0.0425385 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.7016 | 0.827742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 9.40312 | 0.563962 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.9109 | 1.30710 | 0.653548 | − | 0.756885i | \(-0.273280\pi\) | ||||
0.653548 | + | 0.756885i | \(0.273280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.4031 | −1.27228 | −0.636142 | − | 0.771572i | \(-0.719471\pi\) | ||||
−0.636142 | + | 0.771572i | \(0.719471\pi\) | |||||||
\(284\) | 1.70156 | 0.100969 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.70156 | −0.278009 | ||||||||
\(287\) | −17.4031 | −1.02727 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5078 | −0.971048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.0000 | 0.702247 | ||||||||
\(293\) | 21.4031 | 1.25038 | 0.625192 | − | 0.780471i | \(-0.285021\pi\) | ||||
0.625192 | + | 0.780471i | \(0.285021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.70156 | 0.0989013 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.59688 | −0.382147 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −53.6125 | −3.09017 | ||||||||
\(302\) | −14.1047 | −0.811633 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.70156 | −0.0975913 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.70156 | 0.325405 | 0.162703 | − | 0.986675i | \(-0.447979\pi\) | ||||
0.162703 | + | 0.986675i | \(0.447979\pi\) | |||||||
\(308\) | 22.1047 | 1.25953 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.0000 | −1.70114 | −0.850572 | − | 0.525859i | \(-0.823744\pi\) | ||||
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2094 | 1.19882 | 0.599412 | − | 0.800440i | \(-0.295401\pi\) | ||||
0.599412 | + | 0.800440i | \(0.295401\pi\) | |||||||
\(314\) | 22.7016 | 1.28112 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.70156 | −0.320738 | ||||||||
\(317\) | 1.19375 | 0.0670478 | 0.0335239 | − | 0.999438i | \(-0.489327\pi\) | ||||
0.0335239 | + | 0.999438i | \(0.489327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.1047 | −1.68554 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.19375 | 0.0664221 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.8062 | 1.04158 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.70156 | 0.204385 | ||||||||
\(329\) | −32.9109 | −1.81444 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | −10.7016 | −0.587325 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.10469 | −0.0604457 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.10469 | −0.441490 | −0.220745 | − | 0.975332i | \(-0.570849\pi\) | ||||
−0.220745 | + | 0.975332i | \(0.570849\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 47.5078 | 2.57269 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −38.1047 | −2.05746 | ||||||||
\(344\) | 11.4031 | 0.614815 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.193752 | −0.0104161 | ||||||||
\(347\) | 10.5078 | 0.564089 | 0.282044 | − | 0.959401i | \(-0.408987\pi\) | ||||
0.282044 | + | 0.959401i | \(0.408987\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4031 | −0.610395 | −0.305198 | − | 0.952289i | \(-0.598723\pi\) | ||||
−0.305198 | + | 0.952289i | \(0.598723\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.70156 | −0.250594 | ||||||||
\(353\) | 14.5078 | 0.772173 | 0.386086 | − | 0.922463i | \(-0.373827\pi\) | ||||
0.386086 | + | 0.922463i | \(0.373827\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.4031 | −0.604364 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24.2094 | 1.27951 | ||||||||
\(359\) | 34.6125 | 1.82678 | 0.913389 | − | 0.407088i | \(-0.133456\pi\) | ||||
0.913389 | + | 0.407088i | \(0.133456\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1047 | −0.847615 | ||||||||
\(362\) | 11.2984 | 0.593833 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.70156 | −0.246429 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.29844 | 0.119977 | 0.0599887 | − | 0.998199i | \(-0.480894\pi\) | ||||
0.0599887 | + | 0.998199i | \(0.480894\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.2984 | −0.586586 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.29844 | −0.274343 | −0.137171 | − | 0.990547i | \(-0.543801\pi\) | ||||
−0.137171 | + | 0.990547i | \(0.543801\pi\) | |||||||
\(374\) | 3.29844 | 0.170558 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 6.40312 | 0.329778 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.8953 | −0.713754 | −0.356877 | − | 0.934151i | \(-0.616159\pi\) | ||||
−0.356877 | + | 0.934151i | \(0.616159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.8062 | 0.655225 | ||||||||
\(383\) | 32.5078 | 1.66107 | 0.830536 | − | 0.556965i | \(-0.188034\pi\) | ||||
0.830536 | + | 0.556965i | \(0.188034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.2094 | −0.825035 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.59688 | 0.131836 | ||||||||
\(389\) | 27.1047 | 1.37426 | 0.687131 | − | 0.726533i | \(-0.258870\pi\) | ||||
0.687131 | + | 0.726533i | \(0.258870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15.1047 | 0.762902 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.40312 | −0.272205 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9109 | 1.09968 | 0.549839 | − | 0.835271i | \(-0.314689\pi\) | ||||
0.549839 | + | 0.835271i | \(0.314689\pi\) | |||||||
\(398\) | 8.29844 | 0.415963 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.2094 | −0.909333 | −0.454666 | − | 0.890662i | \(-0.650241\pi\) | ||||
−0.454666 | + | 0.890662i | \(0.650241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.1047 | −0.503350 | ||||||||
\(404\) | −6.70156 | −0.333415 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30.1047 | −1.49407 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.4031 | 1.45389 | 0.726945 | − | 0.686695i | \(-0.240939\pi\) | ||||
0.726945 | + | 0.686695i | \(0.240939\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.40312 | −0.0691270 | ||||||||
\(413\) | 12.7016 | 0.625003 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.00000 | 0.391293 | ||||||||
\(419\) | −9.91093 | −0.484181 | −0.242090 | − | 0.970254i | \(-0.577833\pi\) | ||||
−0.242090 | + | 0.970254i | \(0.577833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.596876 | −0.0290899 | −0.0145450 | − | 0.999894i | \(-0.504630\pi\) | ||||
−0.0145450 | + | 0.999894i | \(0.504630\pi\) | |||||||
\(422\) | 6.80625 | 0.331323 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.40312 | 0.116706 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −66.3141 | −3.20916 | ||||||||
\(428\) | 19.1047 | 0.923460 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.3141 | −1.70102 | −0.850509 | − | 0.525960i | \(-0.823706\pi\) | ||||
−0.850509 | + | 0.525960i | \(0.823706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.1047 | 0.533657 | 0.266829 | − | 0.963744i | \(-0.414024\pi\) | ||||
0.266829 | + | 0.963744i | \(0.414024\pi\) | |||||||
\(434\) | 47.5078 | 2.28045 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.29844 | 0.205858 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.2984 | −0.491518 | −0.245759 | − | 0.969331i | \(-0.579037\pi\) | ||||
−0.245759 | + | 0.969331i | \(0.579037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.701562 | −0.0333699 | ||||||||
\(443\) | 32.5078 | 1.54449 | 0.772246 | − | 0.635323i | \(-0.219133\pi\) | ||||
0.772246 | + | 0.635323i | \(0.219133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.4031 | −0.539954 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.70156 | −0.222128 | ||||||||
\(449\) | −2.29844 | −0.108470 | −0.0542350 | − | 0.998528i | \(-0.517272\pi\) | ||||
−0.0542350 | + | 0.998528i | \(0.517272\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.4031 | −0.819481 | ||||||||
\(452\) | −14.0000 | −0.658505 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.1047 | −0.755830 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.59688 | 0.121477 | 0.0607384 | − | 0.998154i | \(-0.480654\pi\) | ||||
0.0607384 | + | 0.998154i | \(0.480654\pi\) | |||||||
\(458\) | 15.7016 | 0.733686 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.2094 | −1.68644 | −0.843219 | − | 0.537570i | \(-0.819342\pi\) | ||||
−0.843219 | + | 0.537570i | \(0.819342\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.2984 | 0.989822 | 0.494911 | − | 0.868944i | \(-0.335201\pi\) | ||||
0.494911 | + | 0.868944i | \(0.335201\pi\) | |||||||
\(464\) | 6.40312 | 0.297258 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.2094 | −0.936181 | ||||||||
\(467\) | 30.2984 | 1.40204 | 0.701022 | − | 0.713139i | \(-0.252727\pi\) | ||||
0.701022 | + | 0.713139i | \(0.252727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.1047 | −1.39011 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.70156 | −0.124349 | ||||||||
\(473\) | −53.6125 | −2.46511 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.29844 | 0.151184 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.10469 | −0.279222 | ||||||||
\(479\) | 40.6125 | 1.85563 | 0.927816 | − | 0.373038i | \(-0.121684\pi\) | ||||
0.927816 | + | 0.373038i | \(0.121684\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.70156 | 0.0775846 | ||||||||
\(482\) | −2.59688 | −0.118284 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.1047 | 0.504758 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.89531 | 0.357771 | 0.178885 | − | 0.983870i | \(-0.442751\pi\) | ||||
0.178885 | + | 0.983870i | \(0.442751\pi\) | |||||||
\(488\) | 14.1047 | 0.638489 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.4031 | −1.50746 | −0.753731 | − | 0.657183i | \(-0.771748\pi\) | ||||
−0.753731 | + | 0.657183i | \(0.771748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.49219 | −0.202318 | ||||||||
\(494\) | −1.70156 | −0.0765569 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.1047 | −0.453714 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.2094 | 0.770397 | 0.385199 | − | 0.922834i | \(-0.374133\pi\) | ||||
0.385199 | + | 0.922834i | \(0.374133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.298438 | −0.0133199 | ||||||||
\(503\) | −12.2094 | −0.544389 | −0.272195 | − | 0.962242i | \(-0.587749\pi\) | ||||
−0.272195 | + | 0.962242i | \(0.587749\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.29844 | 0.279448 | ||||||||
\(509\) | 5.40312 | 0.239489 | 0.119745 | − | 0.992805i | \(-0.461792\pi\) | ||||
0.119745 | + | 0.992805i | \(0.461792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −56.4187 | −2.49582 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.2984 | −0.674785 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.9109 | −1.44742 | ||||||||
\(518\) | −8.00000 | −0.351500 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.2094 | 1.58636 | 0.793181 | − | 0.608986i | \(-0.208424\pi\) | ||||
0.793181 | + | 0.608986i | \(0.208424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8062 | 1.08470 | 0.542351 | − | 0.840152i | \(-0.317534\pi\) | ||||
0.542351 | + | 0.840152i | \(0.317534\pi\) | |||||||
\(524\) | −22.5078 | −0.983258 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00000 | 0.0872041 | ||||||||
\(527\) | 7.08907 | 0.308805 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | 3.70156 | 0.160332 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.40312 | 0.276573 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −31.2094 | −1.34553 | ||||||||
\(539\) | −71.0156 | −3.05886 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.79063 | −0.0769851 | −0.0384925 | − | 0.999259i | \(-0.512256\pi\) | ||||
−0.0384925 | + | 0.999259i | \(0.512256\pi\) | |||||||
\(542\) | 19.5078 | 0.837932 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.701562 | −0.0300792 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.6125 | 1.35165 | 0.675826 | − | 0.737061i | \(-0.263787\pi\) | ||||
0.675826 | + | 0.737061i | \(0.263787\pi\) | |||||||
\(548\) | 13.7016 | 0.585302 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.8953 | −0.464156 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.8062 | 1.13992 | ||||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.40312 | 0.398781 | ||||||||
\(557\) | 16.8062 | 0.712104 | 0.356052 | − | 0.934466i | \(-0.384123\pi\) | ||||
0.356052 | + | 0.934466i | \(0.384123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.4031 | 0.482301 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.9109 | 0.924257 | ||||||||
\(563\) | −32.5078 | −1.37004 | −0.685020 | − | 0.728524i | \(-0.740207\pi\) | ||||
−0.685020 | + | 0.728524i | \(0.740207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.4031 | −0.899640 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.70156 | 0.0713960 | ||||||||
\(569\) | 11.2984 | 0.473655 | 0.236828 | − | 0.971552i | \(-0.423892\pi\) | ||||
0.236828 | + | 0.971552i | \(0.423892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0000 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(572\) | −4.70156 | −0.196582 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −17.4031 | −0.726392 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.2094 | −1.00785 | −0.503925 | − | 0.863748i | \(-0.668111\pi\) | ||||
−0.503925 | + | 0.863748i | \(0.668111\pi\) | |||||||
\(578\) | −16.5078 | −0.686634 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.3141 | 2.08738 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.2984 | −0.467933 | ||||||||
\(584\) | 12.0000 | 0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.4031 | 0.884155 | ||||||||
\(587\) | −7.50781 | −0.309881 | −0.154940 | − | 0.987924i | \(-0.549519\pi\) | ||||
−0.154940 | + | 0.987924i | \(0.549519\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1938 | 0.708456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.70156 | 0.0699338 | ||||||||
\(593\) | 17.9109 | 0.735514 | 0.367757 | − | 0.929922i | \(-0.380126\pi\) | ||||
0.367757 | + | 0.929922i | \(0.380126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.59688 | −0.270219 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.20937 | −0.335426 | −0.167713 | − | 0.985836i | \(-0.553638\pi\) | ||||
−0.167713 | + | 0.985836i | \(0.553638\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6125 | 0.432893 | 0.216446 | − | 0.976295i | \(-0.430553\pi\) | ||||
0.216446 | + | 0.976295i | \(0.430553\pi\) | |||||||
\(602\) | −53.6125 | −2.18508 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.1047 | −0.573912 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.1047 | 1.42486 | 0.712428 | − | 0.701746i | \(-0.247596\pi\) | ||||
0.712428 | + | 0.701746i | \(0.247596\pi\) | |||||||
\(608\) | −1.70156 | −0.0690075 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.00000 | 0.283190 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.8062 | 0.517240 | 0.258620 | − | 0.965979i | \(-0.416732\pi\) | ||||
0.258620 | + | 0.965979i | \(0.416732\pi\) | |||||||
\(614\) | 5.70156 | 0.230096 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.1047 | 0.890623 | ||||||||
\(617\) | −27.1047 | −1.09119 | −0.545597 | − | 0.838048i | \(-0.683697\pi\) | ||||
−0.545597 | + | 0.838048i | \(0.683697\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1938 | −0.530302 | −0.265151 | − | 0.964207i | \(-0.585422\pi\) | ||||
−0.265151 | + | 0.964207i | \(0.585422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.0000 | −1.20289 | ||||||||
\(623\) | 53.6125 | 2.14794 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.2094 | 0.847697 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.7016 | 0.905891 | ||||||||
\(629\) | −1.19375 | −0.0475980 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.6125 | 1.33809 | 0.669046 | − | 0.743221i | \(-0.266703\pi\) | ||||
0.669046 | + | 0.743221i | \(0.266703\pi\) | |||||||
\(632\) | −5.70156 | −0.226796 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.19375 | 0.0474099 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.1047 | 0.598469 | ||||||||
\(638\) | −30.1047 | −1.19186 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.50781 | −0.217545 | −0.108773 | − | 0.994067i | \(-0.534692\pi\) | ||||
−0.108773 | + | 0.994067i | \(0.534692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2984 | 0.406131 | 0.203065 | − | 0.979165i | \(-0.434910\pi\) | ||||
0.203065 | + | 0.979165i | \(0.434910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.19375 | 0.0469675 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.7016 | 0.498580 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.8062 | 0.736510 | ||||||||
\(653\) | −21.2984 | −0.833472 | −0.416736 | − | 0.909027i | \(-0.636826\pi\) | ||||
−0.416736 | + | 0.909027i | \(0.636826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.70156 | 0.144522 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −32.9109 | −1.28300 | ||||||||
\(659\) | 19.3141 | 0.752369 | 0.376184 | − | 0.926545i | \(-0.377236\pi\) | ||||
0.376184 | + | 0.926545i | \(0.377236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.1203 | −1.56050 | −0.780250 | − | 0.625468i | \(-0.784908\pi\) | ||||
−0.780250 | + | 0.625468i | \(0.784908\pi\) | |||||||
\(662\) | −12.0000 | −0.466393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.7016 | −0.415301 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.10469 | −0.0427416 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −66.3141 | −2.56003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0156 | −1.38830 | −0.694150 | − | 0.719830i | \(-0.744220\pi\) | ||||
−0.694150 | + | 0.719830i | \(0.744220\pi\) | |||||||
\(674\) | −8.10469 | −0.312181 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 31.6125 | 1.21497 | 0.607483 | − | 0.794332i | \(-0.292179\pi\) | ||||
0.607483 | + | 0.794332i | \(0.292179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2094 | −0.468553 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 47.5078 | 1.81917 | ||||||||
\(683\) | 44.7016 | 1.71046 | 0.855229 | − | 0.518251i | \(-0.173417\pi\) | ||||
0.855229 | + | 0.518251i | \(0.173417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −38.1047 | −1.45484 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.4031 | 0.434740 | ||||||||
\(689\) | 2.40312 | 0.0915517 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.1938 | −0.844290 | −0.422145 | − | 0.906528i | \(-0.638723\pi\) | ||||
−0.422145 | + | 0.906528i | \(0.638723\pi\) | |||||||
\(692\) | −0.193752 | −0.00736533 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.5078 | 0.398871 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.59688 | −0.0983637 | ||||||||
\(698\) | −11.4031 | −0.431615 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9109 | −1.16749 | −0.583745 | − | 0.811937i | \(-0.698413\pi\) | ||||
−0.583745 | + | 0.811937i | \(0.698413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.89531 | −0.109199 | ||||||||
\(704\) | −4.70156 | −0.177197 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5078 | 0.546009 | ||||||||
\(707\) | 31.5078 | 1.18497 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6125 | 0.586340 | 0.293170 | − | 0.956060i | \(-0.405290\pi\) | ||||
0.293170 | + | 0.956060i | \(0.405290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.4031 | −0.427350 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.2094 | 0.904747 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34.6125 | 1.29173 | ||||||||
\(719\) | 11.0156 | 0.410813 | 0.205407 | − | 0.978677i | \(-0.434148\pi\) | ||||
0.205407 | + | 0.978677i | \(0.434148\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.59688 | 0.245680 | ||||||||
\(722\) | −16.1047 | −0.599354 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.2984 | 0.419903 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.79063 | −0.288938 | −0.144469 | − | 0.989509i | \(-0.546147\pi\) | ||||
−0.144469 | + | 0.989509i | \(0.546147\pi\) | |||||||
\(728\) | −4.70156 | −0.174251 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.9109 | −1.76963 | −0.884815 | − | 0.465942i | \(-0.845716\pi\) | ||||
−0.884815 | + | 0.465942i | \(0.845716\pi\) | |||||||
\(734\) | 2.29844 | 0.0848369 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.1047 | −1.10892 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.61250 | 0.169673 | 0.0848367 | − | 0.996395i | \(-0.472963\pi\) | ||||
0.0848367 | + | 0.996395i | \(0.472963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.2984 | −0.414779 | ||||||||
\(743\) | −30.6125 | −1.12306 | −0.561532 | − | 0.827455i | \(-0.689788\pi\) | ||||
−0.561532 | + | 0.827455i | \(0.689788\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.29844 | −0.193990 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.29844 | 0.120603 | ||||||||
\(749\) | −89.8219 | −3.28202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.50781 | 0.310454 | 0.155227 | − | 0.987879i | \(-0.450389\pi\) | ||||
0.155227 | + | 0.987879i | \(0.450389\pi\) | |||||||
\(752\) | 7.00000 | 0.255264 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.40312 | 0.233188 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8953 | 0.650416 | 0.325208 | − | 0.945642i | \(-0.394566\pi\) | ||||
0.325208 | + | 0.945642i | \(0.394566\pi\) | |||||||
\(758\) | −13.8953 | −0.504701 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.7172 | 0.968497 | 0.484249 | − | 0.874930i | \(-0.339093\pi\) | ||||
0.484249 | + | 0.874930i | \(0.339093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.2094 | −0.731628 | ||||||||
\(764\) | 12.8062 | 0.463314 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5078 | 1.17455 | ||||||||
\(767\) | −2.70156 | −0.0975478 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.00000 | −0.288487 | −0.144244 | − | 0.989542i | \(-0.546075\pi\) | ||||
−0.144244 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.2094 | −0.583388 | ||||||||
\(773\) | 26.5969 | 0.956623 | 0.478312 | − | 0.878190i | \(-0.341249\pi\) | ||||
0.478312 | + | 0.878190i | \(0.341249\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.59688 | 0.0932224 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 27.1047 | 0.971750 | ||||||||
\(779\) | −6.29844 | −0.225665 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.1047 | 0.539453 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.8953 | −1.20824 | −0.604119 | − | 0.796894i | \(-0.706475\pi\) | ||||
−0.604119 | + | 0.796894i | \(0.706475\pi\) | |||||||
\(788\) | −5.40312 | −0.192478 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 65.8219 | 2.34036 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1047 | 0.500872 | ||||||||
\(794\) | 21.9109 | 0.777590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.29844 | 0.294130 | ||||||||
\(797\) | 2.91093 | 0.103111 | 0.0515553 | − | 0.998670i | \(-0.483582\pi\) | ||||
0.0515553 | + | 0.998670i | \(0.483582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.91093 | −0.173736 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.2094 | −0.642995 | ||||||||
\(803\) | −56.4187 | −1.99097 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.1047 | −0.355922 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.70156 | −0.235760 | ||||||||
\(809\) | −7.19375 | −0.252919 | −0.126459 | − | 0.991972i | \(-0.540361\pi\) | ||||
−0.126459 | + | 0.991972i | \(0.540361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.7016 | 1.71014 | 0.855072 | − | 0.518510i | \(-0.173513\pi\) | ||||
0.855072 | + | 0.518510i | \(0.173513\pi\) | |||||||
\(812\) | −30.1047 | −1.05647 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.00000 | −0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.4031 | −0.678829 | ||||||||
\(818\) | 29.4031 | 1.02806 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5969 | 0.718836 | 0.359418 | − | 0.933177i | \(-0.382975\pi\) | ||||
0.359418 | + | 0.933177i | \(0.382975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.1047 | −0.596232 | −0.298116 | − | 0.954530i | \(-0.596358\pi\) | ||||
−0.298116 | + | 0.954530i | \(0.596358\pi\) | |||||||
\(824\) | −1.40312 | −0.0488801 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.7016 | 0.441944 | ||||||||
\(827\) | 20.7016 | 0.719864 | 0.359932 | − | 0.932979i | \(-0.382800\pi\) | ||||
0.359932 | + | 0.932979i | \(0.382800\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50781 | −0.191294 | −0.0956471 | − | 0.995415i | \(-0.530492\pi\) | ||||
−0.0956471 | + | 0.995415i | \(0.530492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −10.5969 | −0.367160 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.00000 | 0.276686 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.91093 | −0.342368 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.0000 | 0.413793 | ||||||||
\(842\) | −0.596876 | −0.0205697 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.80625 | 0.234281 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −52.2094 | −1.79394 | ||||||||
\(848\) | 2.40312 | 0.0825236 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.507811 | −0.0173871 | −0.00869355 | − | 0.999962i | \(-0.502767\pi\) | ||||
−0.00869355 | + | 0.999962i | \(0.502767\pi\) | |||||||
\(854\) | −66.3141 | −2.26922 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1047 | 0.652985 | ||||||||
\(857\) | −7.61250 | −0.260038 | −0.130019 | − | 0.991512i | \(-0.541504\pi\) | ||||
−0.130019 | + | 0.991512i | \(0.541504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.20937 | −0.211861 | −0.105931 | − | 0.994374i | \(-0.533782\pi\) | ||||
−0.105931 | + | 0.994374i | \(0.533782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −35.3141 | −1.20280 | ||||||||
\(863\) | 54.2250 | 1.84584 | 0.922920 | − | 0.384991i | \(-0.125796\pi\) | ||||
0.922920 | + | 0.384991i | \(0.125796\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.1047 | 0.377353 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 47.5078 | 1.61252 | ||||||||
\(869\) | 26.8062 | 0.909340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.40312 | 0.216962 | ||||||||
\(872\) | 4.29844 | 0.145563 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 42.7172 | 1.44246 | 0.721228 | − | 0.692697i | \(-0.243578\pi\) | ||||
0.721228 | + | 0.692697i | \(0.243578\pi\) | |||||||
\(878\) | −10.2984 | −0.347555 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.7172 | 1.33811 | 0.669053 | − | 0.743215i | \(-0.266700\pi\) | ||||
0.669053 | + | 0.743215i | \(0.266700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.6125 | −1.53498 | −0.767491 | − | 0.641059i | \(-0.778495\pi\) | ||||
−0.767491 | + | 0.641059i | \(0.778495\pi\) | |||||||
\(884\) | −0.701562 | −0.0235961 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.5078 | 1.09212 | ||||||||
\(887\) | −20.0000 | −0.671534 | −0.335767 | − | 0.941945i | \(-0.608996\pi\) | ||||
−0.335767 | + | 0.941945i | \(0.608996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.6125 | −0.993171 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.4031 | −0.381805 | ||||||||
\(893\) | −11.9109 | −0.398584 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.70156 | −0.157068 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.29844 | −0.0766999 | ||||||||
\(899\) | −64.7016 | −2.15792 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.68594 | −0.0561668 | ||||||||
\(902\) | −17.4031 | −0.579461 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0156 | 0.830630 | 0.415315 | − | 0.909678i | \(-0.363671\pi\) | ||||
0.415315 | + | 0.909678i | \(0.363671\pi\) | |||||||
\(908\) | −16.1047 | −0.534453 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.2094 | −1.39846 | −0.699229 | − | 0.714897i | \(-0.746473\pi\) | ||||
−0.699229 | + | 0.714897i | \(0.746473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 50.3141 | 1.66515 | ||||||||
\(914\) | 2.59688 | 0.0858970 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.7016 | 0.518794 | ||||||||
\(917\) | 105.822 | 3.49455 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.89531 | −0.161481 | −0.0807407 | − | 0.996735i | \(-0.525729\pi\) | ||||
−0.0807407 | + | 0.996735i | \(0.525729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.2094 | −1.19249 | ||||||||
\(923\) | 1.70156 | 0.0560076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.2984 | 0.699910 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.40312 | 0.210193 | ||||||||
\(929\) | −52.2984 | −1.71586 | −0.857928 | − | 0.513770i | \(-0.828249\pi\) | ||||
−0.857928 | + | 0.513770i | \(0.828249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.7016 | −0.842335 | ||||||||
\(932\) | −20.2094 | −0.661980 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.2984 | 0.991395 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.9109 | −0.487119 | −0.243560 | − | 0.969886i | \(-0.578315\pi\) | ||||
−0.243560 | + | 0.969886i | \(0.578315\pi\) | |||||||
\(938\) | −30.1047 | −0.982953 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.4187 | −0.926425 | −0.463212 | − | 0.886247i | \(-0.653303\pi\) | ||||
−0.463212 | + | 0.886247i | \(0.653303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −2.70156 | −0.0879284 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −53.6125 | −1.74309 | ||||||||
\(947\) | 47.5078 | 1.54380 | 0.771898 | − | 0.635746i | \(-0.219307\pi\) | ||||
0.771898 | + | 0.635746i | \(0.219307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000 | 0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.29844 | 0.106903 | ||||||||
\(953\) | −31.2984 | −1.01386 | −0.506928 | − | 0.861988i | \(-0.669219\pi\) | ||||
−0.506928 | + | 0.861988i | \(0.669219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.10469 | −0.197440 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.6125 | 1.31213 | ||||||||
\(959\) | −64.4187 | −2.08019 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71.1047 | 2.29370 | ||||||||
\(962\) | 1.70156 | 0.0548606 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.59688 | −0.0836397 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.8953 | −0.961368 | −0.480684 | − | 0.876894i | \(-0.659612\pi\) | ||||
−0.480684 | + | 0.876894i | \(0.659612\pi\) | |||||||
\(968\) | 11.1047 | 0.356918 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.8953 | 1.18403 | 0.592013 | − | 0.805928i | \(-0.298333\pi\) | ||||
0.592013 | + | 0.805928i | \(0.298333\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.2094 | −1.41729 | ||||||||
\(974\) | 7.89531 | 0.252982 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.1047 | 0.451480 | ||||||||
\(977\) | −23.4031 | −0.748732 | −0.374366 | − | 0.927281i | \(-0.622140\pi\) | ||||
−0.374366 | + | 0.927281i | \(0.622140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.6125 | 1.71346 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −33.4031 | −1.06594 | ||||||||
\(983\) | −7.50781 | −0.239462 | −0.119731 | − | 0.992806i | \(-0.538203\pi\) | ||||
−0.119731 | + | 0.992806i | \(0.538203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.49219 | −0.143060 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.70156 | −0.0541339 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.10469 | −0.289220 | −0.144610 | − | 0.989489i | \(-0.546193\pi\) | ||||
−0.144610 | + | 0.989489i | \(0.546193\pi\) | |||||||
\(992\) | −10.1047 | −0.320824 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.00000 | −0.253745 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.4922 | 0.332291 | 0.166145 | − | 0.986101i | \(-0.446868\pi\) | ||||
0.166145 | + | 0.986101i | \(0.446868\pi\) | |||||||
\(998\) | 17.2094 | 0.544753 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5850.2.a.cj.1.1 | 2 | ||
3.2 | odd | 2 | 1950.2.a.bc.1.1 | ✓ | 2 | ||
5.2 | odd | 4 | 5850.2.e.bi.5149.3 | 4 | |||
5.3 | odd | 4 | 5850.2.e.bi.5149.2 | 4 | |||
5.4 | even | 2 | 5850.2.a.cg.1.2 | 2 | |||
15.2 | even | 4 | 1950.2.e.p.1249.1 | 4 | |||
15.8 | even | 4 | 1950.2.e.p.1249.4 | 4 | |||
15.14 | odd | 2 | 1950.2.a.bg.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.a.bc.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
1950.2.a.bg.1.2 | yes | 2 | 15.14 | odd | 2 | ||
1950.2.e.p.1249.1 | 4 | 15.2 | even | 4 | |||
1950.2.e.p.1249.4 | 4 | 15.8 | even | 4 | |||
5850.2.a.cg.1.2 | 2 | 5.4 | even | 2 | |||
5850.2.a.cj.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5850.2.e.bi.5149.2 | 4 | 5.3 | odd | 4 | |||
5850.2.e.bi.5149.3 | 4 | 5.2 | odd | 4 |