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 | 1.2 | ||
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 | ||||||||
\(3\) | 2.41421 | 1.39385 | 0.696923 | − | 0.717146i | \(-0.254552\pi\) | ||||
0.696923 | + | 0.717146i | \(0.254552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.41421 | 0.632456 | 0.316228 | − | 0.948683i | \(-0.397584\pi\) | ||||
0.316228 | + | 0.948683i | \(0.397584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.82843 | 1.06181 | 0.530907 | − | 0.847430i | \(-0.321851\pi\) | ||||
0.530907 | + | 0.847430i | \(0.321851\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.41421 | −1.24211 | −0.621053 | − | 0.783769i | \(-0.713295\pi\) | ||||
−0.621053 | + | 0.783769i | \(0.713295\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.58579 | −0.539174 | −0.269587 | − | 0.962976i | \(-0.586887\pi\) | ||||
−0.269587 | + | 0.962976i | \(0.586887\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65685 | 0.297580 | 0.148790 | − | 0.988869i | \(-0.452462\pi\) | ||||
0.148790 | + | 0.988869i | \(0.452462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.41421 | −0.420261 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.07107 | 0.833678 | 0.416839 | − | 0.908980i | \(-0.363138\pi\) | ||||
0.416839 | + | 0.908980i | \(0.363138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.24264 | 1.48001 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.24264 | 0.350242 | 0.175121 | − | 0.984547i | \(-0.443968\pi\) | ||||
0.175121 | + | 0.984547i | \(0.443968\pi\) | |||||||
\(42\) | 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 | ||||||||
\(47\) | −0.828427 | −0.120839 | −0.0604193 | − | 0.998173i | \(-0.519244\pi\) | ||||
−0.0604193 | + | 0.998173i | \(0.519244\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.82843 | 0.676115 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.41421 | 0.743699 | 0.371850 | − | 0.928293i | \(-0.378724\pi\) | ||||
0.371850 | + | 0.928293i | \(0.378724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.0711 | −1.73131 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.58579 | 0.206452 | 0.103226 | − | 0.994658i | \(-0.467084\pi\) | ||||
0.103226 | + | 0.994658i | \(0.467084\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.8284 | 1.77055 | 0.885274 | − | 0.465069i | \(-0.153971\pi\) | ||||
0.885274 | + | 0.465069i | \(0.153971\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.41421 | 0.671551 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.07107 | 0.741699 | 0.370849 | − | 0.928693i | \(-0.379067\pi\) | ||||
0.370849 | + | 0.928693i | \(0.379067\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.24264 | −0.751526 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.2426 | 1.69029 | 0.845145 | − | 0.534537i | \(-0.179514\pi\) | ||||
0.845145 | + | 0.534537i | \(0.179514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.585786 | 0.0685611 | 0.0342806 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342806 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.24264 | −0.836308 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.07107 | 0.683048 | 0.341524 | − | 0.939873i | \(-0.389057\pi\) | ||||
0.341524 | + | 0.939873i | \(0.389057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.48528 | 0.711852 | 0.355926 | − | 0.934514i | \(-0.384165\pi\) | ||||
0.355926 | + | 0.934514i | \(0.384165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.82843 | 0.306786 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.41421 | 0.258831 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.8284 | 1.57181 | 0.785905 | − | 0.618347i | \(-0.212197\pi\) | ||||
0.785905 | + | 0.618347i | \(0.212197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.65685 | −0.785577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1716 | 1.03277 | 0.516383 | − | 0.856358i | \(-0.327278\pi\) | ||||
0.516383 | + | 0.856358i | \(0.327278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.48528 | −0.943821 | −0.471910 | − | 0.881647i | \(-0.656435\pi\) | ||||
−0.471910 | + | 0.881647i | \(0.656435\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.89949 | 0.384229 | 0.192114 | − | 0.981373i | \(-0.438466\pi\) | ||||
0.192114 | + | 0.981373i | \(0.438466\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.5563 | 1.69724 | 0.848618 | − | 0.529006i | \(-0.177435\pi\) | ||||
0.848618 | + | 0.529006i | \(0.177435\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.48528 | 0.812743 | 0.406371 | − | 0.913708i | \(-0.366794\pi\) | ||||
0.406371 | + | 0.913708i | \(0.366794\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.2426 | 1.16202 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.48528 | 0.892300 | 0.446150 | − | 0.894958i | \(-0.352795\pi\) | ||||
0.446150 | + | 0.894958i | \(0.352795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65685 | −0.341003 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.8284 | 1.00109 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.41421 | 0.488183 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.3137 | −1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.58579 | −0.318187 | −0.159094 | − | 0.987264i | \(-0.550857\pi\) | ||||
−0.159094 | + | 0.987264i | \(0.550857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.3137 | 1.70048 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.0711 | −1.66625 | −0.833123 | − | 0.553087i | \(-0.813450\pi\) | ||||
−0.833123 | + | 0.553087i | \(0.813450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.585786 | −0.0504165 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.0000 | 1.45241 | 0.726204 | − | 0.687479i | \(-0.241283\pi\) | ||||
0.726204 | + | 0.687479i | \(0.241283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.3137 | 1.63817 | 0.819084 | − | 0.573674i | \(-0.194482\pi\) | ||||
0.819084 | + | 0.573674i | \(0.194482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.82843 | −0.320149 | ||||||||
\(144\) | 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 | ||||||||
\(151\) | −8.41421 | −0.684739 | −0.342369 | − | 0.939565i | \(-0.611229\pi\) | ||||
−0.342369 | + | 0.939565i | \(0.611229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.65685 | 0.457330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.34315 | 0.188206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.3137 | −1.22217 | −0.611083 | − | 0.791566i | \(-0.709266\pi\) | ||||
−0.611083 | + | 0.791566i | \(0.709266\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.0711 | 1.03660 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24.8995 | −1.95028 | −0.975139 | − | 0.221592i | \(-0.928875\pi\) | ||||
−0.975139 | + | 0.221592i | \(0.928875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.41421 | −0.265796 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.7279 | −1.99089 | −0.995443 | − | 0.0953565i | \(-0.969601\pi\) | ||||
−0.995443 | + | 0.0953565i | \(0.969601\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.65685 | 0.127450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.3137 | −1.17107 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.82843 | −0.595184 | −0.297592 | − | 0.954693i | \(-0.596184\pi\) | ||||
−0.297592 | + | 0.954693i | \(0.596184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.82843 | 0.287762 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.899495 | 0.0672314 | 0.0336157 | − | 0.999435i | \(-0.489298\pi\) | ||||
0.0336157 | + | 0.999435i | \(0.489298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.31371 | −0.692283 | −0.346141 | − | 0.938182i | \(-0.612508\pi\) | ||||
−0.346141 | + | 0.938182i | \(0.612508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33.3848 | 2.46787 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.17157 | 0.527265 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | −0.146254 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.4853 | −0.758688 | −0.379344 | − | 0.925256i | \(-0.623850\pi\) | ||||
−0.379344 | + | 0.925256i | \(0.623850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.2132 | −1.38300 | −0.691498 | − | 0.722378i | \(-0.743049\pi\) | ||||
−0.691498 | + | 0.722378i | \(0.743049\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.0711 | 0.936039 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.1421 | 1.22133 | 0.610663 | − | 0.791890i | \(-0.290903\pi\) | ||||
0.610663 | + | 0.791890i | \(0.290903\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.0416 | −1.70427 | −0.852133 | − | 0.523325i | \(-0.824691\pi\) | ||||
−0.852133 | + | 0.523325i | \(0.824691\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.6569 | 1.03381 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.17157 | 0.221512 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.31371 | −0.508338 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.41421 | 0.374509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0711 | 1.31291 | 0.656453 | − | 0.754367i | \(-0.272056\pi\) | ||||
0.656453 | + | 0.754367i | \(0.272056\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.3848 | 2.35601 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.3137 | 0.771589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.41421 | 0.0955637 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.65685 | 0.515056 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.5563 | −0.773870 | −0.386935 | − | 0.922107i | \(-0.626466\pi\) | ||||
−0.386935 | + | 0.922107i | \(0.626466\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.48528 | −0.565685 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.142136 | 0.00943387 | 0.00471694 | − | 0.999989i | \(-0.498499\pi\) | ||||
0.00471694 | + | 0.999989i | \(0.498499\pi\) | |||||||
\(228\) | 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 | ||||||||
\(233\) | −16.3848 | −1.07340 | −0.536701 | − | 0.843772i | \(-0.680330\pi\) | ||||
−0.536701 | + | 0.843772i | \(0.680330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.17157 | −0.0764250 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.6569 | 0.952065 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.7279 | −0.887985 | −0.443993 | − | 0.896030i | \(-0.646438\pi\) | ||||
−0.443993 | + | 0.896030i | \(0.646438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.72792 | −0.175721 | −0.0878605 | − | 0.996133i | \(-0.528003\pi\) | ||||
−0.0878605 | + | 0.996133i | \(0.528003\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6569 | −1.38929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.7279 | −1.31889 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.6569 | 0.992213 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4853 | −1.04054 | −0.520271 | − | 0.854001i | \(-0.674169\pi\) | ||||
−0.520271 | + | 0.854001i | \(0.674169\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.58579 | 0.162567 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.82843 | 0.427613 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.51472 | 0.156864 | 0.0784319 | − | 0.996919i | \(-0.475009\pi\) | ||||
0.0784319 | + | 0.996919i | \(0.475009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.0416 | −1.54413 | −0.772067 | − | 0.635542i | \(-0.780777\pi\) | ||||
−0.772067 | + | 0.635542i | \(0.780777\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.65685 | 0.470357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 35.7990 | 2.19086 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.34315 | 0.142864 | 0.0714321 | − | 0.997445i | \(-0.477243\pi\) | ||||
0.0714321 | + | 0.997445i | \(0.477243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0711 | 0.854756 | 0.427378 | − | 0.904073i | \(-0.359437\pi\) | ||||
0.427378 | + | 0.904073i | \(0.359437\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | 0.180907 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7990 | 0.889185 | 0.444593 | − | 0.895733i | \(-0.353348\pi\) | ||||
0.444593 | + | 0.895733i | \(0.353348\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.68629 | 0.280561 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.89949 | 0.471244 | 0.235622 | − | 0.971845i | \(-0.424287\pi\) | ||||
0.235622 | + | 0.971845i | \(0.424287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.55635 | −0.211403 | −0.105702 | − | 0.994398i | \(-0.533709\pi\) | ||||
−0.105702 | + | 0.994398i | \(0.533709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.4853 | −1.09497 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.5563 | 1.43952 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.8284 | 1.09997 | 0.549984 | − | 0.835175i | \(-0.314634\pi\) | ||||
0.549984 | + | 0.835175i | \(0.314634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.24264 | 0.130572 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.414214 | 0.0240351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.89949 | −0.572503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.8995 | −1.31554 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.5563 | 1.11979 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4142 | 0.651444 | 0.325722 | − | 0.945466i | \(-0.394393\pi\) | ||||
0.325722 | + | 0.945466i | \(0.394393\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.41421 | 0.535556 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.2132 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.6569 | 1.16759 | 0.583797 | − | 0.811900i | \(-0.301566\pi\) | ||||
0.583797 | + | 0.811900i | \(0.301566\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.9706 | −0.728499 | −0.364250 | − | 0.931301i | \(-0.618675\pi\) | ||||
−0.364250 | + | 0.931301i | \(0.618675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00000 | −0.0559893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 42.3848 | 2.36569 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.8284 | −0.602510 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.4853 | −0.637089 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.4853 | 1.13284 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.3848 | −1.72506 | −0.862532 | − | 0.506003i | \(-0.831122\pi\) | ||||
−0.862532 | + | 0.506003i | \(0.831122\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.3431 | 0.786000 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.58579 | 0.469092 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.24264 | 0.340058 | 0.170029 | − | 0.985439i | \(-0.445614\pi\) | ||||
0.170029 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.8995 | 1.24373 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.65685 | −0.0897237 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.82843 | −0.475307 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.4142 | 0.612747 | 0.306374 | − | 0.951911i | \(-0.400884\pi\) | ||||
0.306374 | + | 0.951911i | \(0.400884\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.2843 | 1.72814 | 0.864069 | − | 0.503374i | \(-0.167908\pi\) | ||||
0.864069 | + | 0.503374i | \(0.167908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.58579 | −0.0846430 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.3137 | 1.34731 | 0.673656 | − | 0.739045i | \(-0.264723\pi\) | ||||
0.673656 | + | 0.739045i | \(0.264723\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.1421 | 1.06903 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.0711 | −1.48153 | −0.740767 | − | 0.671762i | \(-0.765538\pi\) | ||||
−0.740767 | + | 0.671762i | \(0.765538\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3137 | 0.542827 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.41421 | 0.126713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.828427 | 0.0433619 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.242641 | −0.0126657 | −0.00633287 | − | 0.999980i | \(-0.502016\pi\) | ||||
−0.00633287 | + | 0.999980i | \(0.502016\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.34315 | 0.330211 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.6274 | 1.63761 | 0.818803 | − | 0.574075i | \(-0.194638\pi\) | ||||
0.818803 | + | 0.574075i | \(0.194638\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −27.3137 | −1.41047 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.82843 | 0.197174 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3848 | −1.50939 | −0.754697 | − | 0.656073i | \(-0.772216\pi\) | ||||
−0.754697 | + | 0.656073i | \(0.772216\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.65685 | −0.443504 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.8995 | −1.42560 | −0.712799 | − | 0.701369i | \(-0.752573\pi\) | ||||
−0.712799 | + | 0.701369i | \(0.752573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.6274 | 1.15022 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.21320 | −0.467128 | −0.233564 | − | 0.972341i | \(-0.575039\pi\) | ||||
−0.233564 | + | 0.972341i | \(0.575039\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.17157 | −0.261538 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.0416 | −2.32249 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.58579 | 0.431998 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.3431 | −1.22175 | −0.610874 | − | 0.791728i | \(-0.709182\pi\) | ||||
−0.610874 | + | 0.791728i | \(0.709182\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 6.34315 | 0.315975 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.4142 | −0.666558 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.07107 | −0.251363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1005 | 0.697225 | 0.348613 | − | 0.937267i | \(-0.386653\pi\) | ||||
0.348613 | + | 0.937267i | \(0.386653\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.0416 | 2.02443 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.17157 | 0.450215 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 46.6274 | 2.28335 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.4558 | 1.24360 | 0.621800 | − | 0.783176i | \(-0.286402\pi\) | ||||
0.621800 | + | 0.783176i | \(0.286402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.65685 | −0.0807501 | −0.0403751 | − | 0.999185i | \(-0.512855\pi\) | ||||
−0.0403751 | + | 0.999185i | \(0.512855\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.34315 | −0.113928 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.24264 | −0.446239 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7279 | 0.853924 | 0.426962 | − | 0.904270i | \(-0.359584\pi\) | ||||
0.426962 | + | 0.904270i | \(0.359584\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.4558 | −1.80001 | −0.900006 | − | 0.435876i | \(-0.856438\pi\) | ||||
−0.900006 | + | 0.435876i | \(0.856438\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.41421 | 0.163699 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.0000 | 0.669711 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0711 | 0.767030 | 0.383515 | − | 0.923535i | \(-0.374713\pi\) | ||||
0.383515 | + | 0.923535i | \(0.374713\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3137 | 0.822599 | 0.411300 | − | 0.911500i | \(-0.365075\pi\) | ||||
0.411300 | + | 0.911500i | \(0.365075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.9706 | 0.994100 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −38.6274 | −1.82701 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.24264 | −0.105602 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.3137 | −0.954421 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.68629 | 0.312772 | 0.156386 | − | 0.987696i | \(-0.450016\pi\) | ||||
0.156386 | + | 0.987696i | \(0.450016\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.828427 | −0.0386677 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.0000 | 0.605470 | 0.302735 | − | 0.953075i | \(-0.402100\pi\) | ||||
0.302735 | + | 0.953075i | \(0.402100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.7990 | −1.19898 | −0.599490 | − | 0.800382i | \(-0.704630\pi\) | ||||
−0.599490 | + | 0.800382i | \(0.704630\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.65685 | 0.262330 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.9411 | −1.47806 | −0.739030 | − | 0.673673i | \(-0.764716\pi\) | ||||
−0.739030 | + | 0.673673i | \(0.764716\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.9706 | −1.70351 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.2426 | 0.745263 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.3137 | 0.701167 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.0710678 | −0.00324717 | −0.00162359 | − | 0.999999i | \(-0.500517\pi\) | ||||
−0.00162359 | + | 0.999999i | \(0.500517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.4142 | 0.885212 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3848 | 0.653179 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.686292 | 0.0310988 | 0.0155494 | − | 0.999879i | \(-0.495050\pi\) | ||||
0.0155494 | + | 0.999879i | \(0.495050\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −60.1127 | −2.71839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.82843 | −0.217904 | −0.108952 | − | 0.994047i | \(-0.534749\pi\) | ||||
−0.108952 | + | 0.994047i | \(0.534749\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | 0.0900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7990 | −0.707260 | −0.353630 | − | 0.935385i | \(-0.615053\pi\) | ||||
−0.353630 | + | 0.935385i | \(0.615053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −62.1127 | −2.77499 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.72792 | 0.255395 | 0.127698 | − | 0.991813i | \(-0.459241\pi\) | ||||
0.127698 | + | 0.991813i | \(0.459241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4142 | −0.596925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.00000 | 0.177646 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.3431 | −1.07899 | −0.539495 | − | 0.841988i | \(-0.681385\pi\) | ||||
−0.539495 | + | 0.841988i | \(0.681385\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.24264 | 0.0990150 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.51472 | 0.243008 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.828427 | 0.0364342 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8995 | −0.829596 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.07107 | 0.0468345 | 0.0234173 | − | 0.999726i | \(-0.492545\pi\) | ||||
0.0234173 | + | 0.999726i | \(0.492545\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.31371 | 0.144347 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.3137 | −0.709292 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.48528 | 0.194645 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.58579 | 0.371892 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.8284 | 1.07343 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.17157 | 0.0937103 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.1421 | −1.59687 | −0.798433 | − | 0.602084i | \(-0.794337\pi\) | ||||
−0.798433 | + | 0.602084i | \(0.794337\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.4853 | −0.964936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | 0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.6985 | −0.671219 | −0.335609 | − | 0.942001i | \(-0.608942\pi\) | ||||
−0.335609 | + | 0.942001i | \(0.608942\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 39.1127 | 1.66929 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.41421 | −0.230653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.3137 | 0.734926 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.1716 | −0.558097 | −0.279049 | − | 0.960277i | \(-0.590019\pi\) | ||||
−0.279049 | + | 0.960277i | \(0.590019\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.6274 | 1.29540 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.82843 | −0.203856 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 45.2132 | 1.90551 | 0.952755 | − | 0.303741i | \(-0.0982357\pi\) | ||||
0.952755 | + | 0.303741i | \(0.0982357\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.4142 | 0.564340 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.9706 | 0.879132 | 0.439566 | − | 0.898210i | \(-0.355132\pi\) | ||||
0.439566 | + | 0.898210i | \(0.355132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.58579 | −0.191909 | −0.0959546 | − | 0.995386i | \(-0.530590\pi\) | ||||
−0.0959546 | + | 0.995386i | \(0.530590\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.3137 | −1.05750 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.75736 | 0.323504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.9706 | 0.748124 | 0.374062 | − | 0.927404i | \(-0.377965\pi\) | ||||
0.374062 | + | 0.927404i | \(0.377965\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −46.3848 | −1.92769 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.41421 | −0.224234 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.3137 | 0.633144 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.2132 | −1.08193 | −0.540967 | − | 0.841044i | \(-0.681942\pi\) | ||||
−0.540967 | + | 0.841044i | \(0.681942\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.97056 | −0.369626 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.3848 | 1.70234 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.4142 | 0.550856 | 0.275428 | − | 0.961322i | \(-0.411180\pi\) | ||||
0.275428 | + | 0.961322i | \(0.411180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −58.0416 | −2.37549 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.0294 | −0.450651 | −0.225325 | − | 0.974284i | \(-0.572344\pi\) | ||||
−0.225325 | + | 0.974284i | \(0.572344\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3431 | 0.503487 | 0.251744 | − | 0.967794i | \(-0.418996\pi\) | ||||
0.251744 | + | 0.967794i | \(0.418996\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.1716 | 0.699281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.41421 | 0.0574960 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.2843 | −1.39156 | −0.695778 | − | 0.718257i | \(-0.744940\pi\) | ||||
−0.695778 | + | 0.718257i | \(0.744940\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.17157 | −0.128308 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.6274 | −0.671575 | −0.335788 | − | 0.941938i | \(-0.609002\pi\) | ||||
−0.335788 | + | 0.941938i | \(0.609002\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.65685 | 0.308754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6274 | −0.468102 | −0.234051 | − | 0.972224i | \(-0.575198\pi\) | ||||
−0.234051 | + | 0.972224i | \(0.575198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.3137 | 0.937057 | 0.468529 | − | 0.883448i | \(-0.344784\pi\) | ||||
0.468529 | + | 0.883448i | \(0.344784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07107 | 0.0429805 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.0711 | 0.522008 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1421 | 0.404393 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.3848 | −1.28922 | −0.644609 | − | 0.764513i | \(-0.722980\pi\) | ||||
−0.644609 | + | 0.764513i | \(0.722980\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 46.0416 | 1.82999 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.07107 | −0.201239 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 40.2843 | 1.59362 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.2548 | −1.82696 | −0.913478 | − | 0.406888i | \(-0.866614\pi\) | ||||
−0.913478 | + | 0.406888i | \(0.866614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.4142 | 1.51491 | 0.757454 | − | 0.652888i | \(-0.226443\pi\) | ||||
0.757454 | + | 0.652888i | \(0.226443\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27.3137 | 1.07548 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.07107 | 0.0421080 | 0.0210540 | − | 0.999778i | \(-0.493298\pi\) | ||||
0.0210540 | + | 0.999778i | \(0.493298\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.58579 | −0.0622476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −34.9289 | −1.36687 | −0.683437 | − | 0.730009i | \(-0.739516\pi\) | ||||
−0.683437 | + | 0.730009i | \(0.739516\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.9706 | −1.05383 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.65685 | 0.0646400 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.68629 | −0.338370 | −0.169185 | − | 0.985584i | \(-0.554114\pi\) | ||||
−0.169185 | + | 0.985584i | \(0.554114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.6274 | −1.58022 | −0.790112 | − | 0.612963i | \(-0.789978\pi\) | ||||
−0.790112 | + | 0.612963i | \(0.789978\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.4853 | 0.717909 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.58579 | −0.100122 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.8995 | −1.07866 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8284 | −0.533841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.75736 | 0.299024 | 0.149512 | − | 0.988760i | \(-0.452230\pi\) | ||||
0.149512 | + | 0.988760i | \(0.452230\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.24264 | 0.0478293 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.2843 | 1.85572 | 0.927858 | − | 0.372935i | \(-0.121648\pi\) | ||||
0.927858 | + | 0.372935i | \(0.121648\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.343146 | 0.0131494 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.89949 | 0.187474 | 0.0937370 | − | 0.995597i | \(-0.470119\pi\) | ||||
0.0937370 | + | 0.995597i | \(0.470119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0416 | 0.918583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.65685 | 0.368432 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.7279 | 0.789671 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.38478 | −0.280930 | −0.140465 | − | 0.990086i | \(-0.544860\pi\) | ||||
−0.140465 | + | 0.990086i | \(0.544860\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.3137 | 1.03607 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.48528 | 0.169892 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.5563 | −1.49616 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.45584 | −0.319373 | −0.159686 | − | 0.987168i | \(-0.551048\pi\) | ||||
−0.159686 | + | 0.987168i | \(0.551048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.4558 | −1.03552 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.82843 | −0.106525 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.0711 | 1.24201 | 0.621005 | − | 0.783807i | \(-0.286725\pi\) | ||||
0.621005 | + | 0.783807i | \(0.286725\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.1716 | 0.643984 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.28427 | −0.160447 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.41421 | −0.202480 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.1421 | −1.23772 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.1716 | 0.864154 | 0.432077 | − | 0.901837i | \(-0.357781\pi\) | ||||
0.432077 | + | 0.901837i | \(0.357781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.58579 | −0.244928 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.00000 | −0.111417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.7990 | 0.956832 | 0.478416 | − | 0.878133i | \(-0.341211\pi\) | ||||
0.478416 | + | 0.878133i | \(0.341211\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | 0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3431 | −0.640584 | −0.320292 | − | 0.947319i | \(-0.603781\pi\) | ||||
−0.320292 | + | 0.947319i | \(0.603781\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.07107 | −0.223631 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.4264 | 1.78139 | 0.890697 | − | 0.454597i | \(-0.150217\pi\) | ||||
0.890697 | + | 0.454597i | \(0.150217\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −50.0416 | −1.83833 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 18.3431 | 0.671141 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.3137 | 0.412843 | 0.206422 | − | 0.978463i | \(-0.433818\pi\) | ||||
0.206422 | + | 0.978463i | \(0.433818\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −39.7990 | −1.45036 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.8995 | −0.433067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.31371 | −0.193130 | −0.0965650 | − | 0.995327i | \(-0.530786\pi\) | ||||
−0.0965650 | + | 0.995327i | \(0.530786\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.24264 | 0.226594 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9411 | −1.44786 | −0.723932 | − | 0.689871i | \(-0.757667\pi\) | ||||
−0.723932 | + | 0.689871i | \(0.757667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.00000 | 0.289241 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.07107 | 0.219214 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.97056 | 0.107121 | 0.0535606 | − | 0.998565i | \(-0.482943\pi\) | ||||
0.0535606 | + | 0.998565i | \(0.482943\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.07107 | 0.218644 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6274 | 0.382242 | 0.191121 | − | 0.981567i | \(-0.438788\pi\) | ||||
0.191121 | + | 0.981567i | \(0.438788\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.97056 | −0.178548 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.1421 | −0.435037 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.2426 | −0.509642 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.414214 | −0.0148028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.6569 | −0.772966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.3848 | 1.51085 | 0.755427 | − | 0.655233i | \(-0.227429\pi\) | ||||
0.755427 | + | 0.655233i | \(0.227429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −60.4558 | −2.15229 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.9411 | 1.87999 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.4853 | 0.655605 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.3137 | 0.471596 | 0.235798 | − | 0.971802i | \(-0.424230\pi\) | ||||
0.235798 | + | 0.971802i | \(0.424230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.65685 | −0.0586153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.9411 | 1.48192 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.585786 | −0.0206720 | ||||||||
\(804\) | 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 | ||||||||
\(811\) | 38.3431 | 1.34641 | 0.673205 | − | 0.739456i | \(-0.264917\pi\) | ||||
0.673205 | + | 0.739456i | \(0.264917\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.9706 | 1.19140 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.2132 | −1.23346 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.3137 | −1.51535 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.8284 | −0.971219 | −0.485609 | − | 0.874176i | \(-0.661402\pi\) | ||||
−0.485609 | + | 0.874176i | \(0.661402\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.8284 | 1.14433 | 0.572164 | − | 0.820140i | \(-0.306104\pi\) | ||||
0.572164 | + | 0.820140i | \(0.306104\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.24264 | 0.252156 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.5269 | 1.13107 | 0.565536 | − | 0.824724i | \(-0.308669\pi\) | ||||
0.565536 | + | 0.824724i | \(0.308669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.5858 | −1.20121 | −0.600607 | − | 0.799544i | \(-0.705074\pi\) | ||||
−0.600607 | + | 0.799544i | \(0.705074\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.7279 | 1.23939 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −36.3848 | −1.25915 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.686292 | −0.0237217 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.51472 | 0.328485 | 0.164242 | − | 0.986420i | \(-0.447482\pi\) | ||||
0.164242 | + | 0.986420i | \(0.447482\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.0711 | 0.656842 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.34315 | 0.0806067 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.58579 | −0.294663 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.1127 | −0.449498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 50.0000 | 1.71197 | 0.855984 | − | 0.517003i | \(-0.172952\pi\) | ||||
0.855984 | + | 0.517003i | \(0.172952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.6569 | −0.740649 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.28427 | −0.282985 | −0.141493 | − | 0.989939i | \(-0.545190\pi\) | ||||
−0.141493 | + | 0.989939i | \(0.545190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.58579 | −0.327063 | −0.163531 | − | 0.986538i | \(-0.552289\pi\) | ||||
−0.163531 | + | 0.986538i | \(0.552289\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.3848 | −0.353502 | −0.176751 | − | 0.984256i | \(-0.556559\pi\) | ||||
−0.176751 | + | 0.984256i | \(0.556559\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0711 | −0.376428 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −31.3848 | −1.06588 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.07107 | −0.205947 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.2426 | 0.787547 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.7696 | 0.973702 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43.2843 | −1.46161 | −0.730803 | − | 0.682588i | \(-0.760854\pi\) | ||||
−0.730803 | + | 0.682588i | \(0.760854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.4558 | 1.53319 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.1716 | −0.477452 | −0.238726 | − | 0.971087i | \(-0.576730\pi\) | ||||
−0.238726 | + | 0.971087i | \(0.576730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.6690 | 1.80611 | 0.903054 | − | 0.429528i | \(-0.141320\pi\) | ||||
0.903054 | + | 0.429528i | \(0.141320\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.41421 | 0.181997 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.27208 | −0.210596 | −0.105298 | − | 0.994441i | \(-0.533580\pi\) | ||||
−0.105298 | + | 0.994441i | \(0.533580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.48528 | 0.317769 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.48528 | 0.150094 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.27208 | 0.0425209 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.8995 | −0.797981 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.65685 | 0.0552592 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.8284 | 0.360747 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.1716 | −0.437838 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.6274 | −1.08338 | −0.541688 | − | 0.840580i | \(-0.682214\pi\) | ||||
−0.541688 | + | 0.840580i | \(0.682214\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.8284 | −0.889843 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.5147 | −0.712814 | −0.356407 | − | 0.934331i | \(-0.615998\pi\) | ||||
−0.356407 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.48528 | −0.214631 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 47.2132 | 1.56082 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.4558 | 1.49945 | 0.749725 | − | 0.661750i | \(-0.230186\pi\) | ||||
0.749725 | + | 0.661750i | \(0.230186\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.5563 | 0.908013 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 54.5269 | 1.79478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.2132 | −0.500207 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.0294 | 0.362254 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.4264 | −1.42477 | −0.712387 | − | 0.701787i | \(-0.752386\pi\) | ||||
−0.712387 | + | 0.701787i | \(0.752386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.7279 | 1.20242 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.82843 | −0.0924995 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5858 | 0.607171 | 0.303586 | − | 0.952804i | \(-0.401816\pi\) | ||||
0.303586 | + | 0.952804i | \(0.401816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49.8701 | 1.62745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.9411 | −0.552265 | −0.276132 | − | 0.961120i | \(-0.589053\pi\) | ||||
−0.276132 | + | 0.961120i | \(0.589053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.79899 | −0.188841 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.7990 | −1.29329 | −0.646647 | − | 0.762790i | \(-0.723829\pi\) | ||||
−0.646647 | + | 0.762790i | \(0.723829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.24264 | 0.0727992 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.3137 | −1.01542 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.3848 | 1.76170 | 0.880848 | − | 0.473399i | \(-0.156973\pi\) | ||||
0.880848 | + | 0.473399i | \(0.156973\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.8284 | −0.479837 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.41421 | −0.0780404 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.2548 | −0.911446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 49.6569 | 1.60017 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.1716 | −0.874684 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6569 | 0.953700 | 0.476850 | − | 0.878985i | \(-0.341778\pi\) | ||||
0.476850 | + | 0.878985i | \(0.341778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.1421 | −0.839806 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.2132 | −0.391940 | −0.195970 | − | 0.980610i | \(-0.562786\pi\) | ||||
−0.195970 | + | 0.980610i | \(0.562786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.7279 | −0.888004 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.9706 | 1.18279 | 0.591397 | − | 0.806381i | \(-0.298577\pi\) | ||||
0.591397 | + | 0.806381i | \(0.298577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.8284 | −0.473919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.0000 | 0.766261 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.4853 | −1.48265 | −0.741325 | − | 0.671146i | \(-0.765802\pi\) | ||||
−0.741325 | + | 0.671146i | \(0.765802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.2426 | 0.772435 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.6863 | −0.657786 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.8995 | −0.632128 | −0.316064 | − | 0.948738i | \(-0.602361\pi\) | ||||
−0.316064 | + | 0.948738i | \(0.602361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −75.7696 | −2.40447 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −34.0000 | −1.07787 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.45584 | 0.299470 | 0.149735 | − | 0.988726i | \(-0.452158\pi\) | ||||
0.149735 | + | 0.988726i | \(0.452158\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.10051 | −0.0664570 |
(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.1.2 | 2 | ||
4.3 | odd | 2 | 4312.2.a.m.1.1 | 2 | |||
7.3 | odd | 6 | 1232.2.q.h.177.2 | 4 | |||
7.5 | odd | 6 | 1232.2.q.h.529.2 | 4 | |||
7.6 | odd | 2 | 8624.2.a.bg.1.1 | 2 | |||
28.3 | even | 6 | 616.2.q.b.177.1 | ✓ | 4 | ||
28.19 | even | 6 | 616.2.q.b.529.1 | yes | 4 | ||
28.27 | even | 2 | 4312.2.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.q.b.177.1 | ✓ | 4 | 28.3 | even | 6 | ||
616.2.q.b.529.1 | yes | 4 | 28.19 | even | 6 | ||
1232.2.q.h.177.2 | 4 | 7.3 | odd | 6 | |||
1232.2.q.h.529.2 | 4 | 7.5 | odd | 6 | |||
4312.2.a.m.1.1 | 2 | 4.3 | odd | 2 | |||
4312.2.a.u.1.2 | 2 | 28.27 | even | 2 | |||
8624.2.a.bg.1.1 | 2 | 7.6 | odd | 2 | |||
8624.2.a.cd.1.2 | 2 | 1.1 | even | 1 | trivial |