Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3732.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 13x + 19 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.20633\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.48688 | −1.69588 | −0.847941 | − | 0.530091i | \(-0.822158\pi\) | ||||
−0.847941 | + | 0.530091i | \(0.822158\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.20633 | −0.363722 | −0.181861 | − | 0.983324i | \(-0.558212\pi\) | ||||
−0.181861 | + | 0.983324i | \(0.558212\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.69321 | −1.76494 | −0.882472 | − | 0.470365i | \(-0.844122\pi\) | ||||
−0.882472 | + | 0.470365i | \(0.844122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.48688 | 0.979118 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.69321 | −1.18712 | −0.593558 | − | 0.804791i | \(-0.702277\pi\) | ||||
−0.593558 | + | 0.804791i | \(0.702277\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.41266 | −1.37650 | −0.688248 | − | 0.725475i | \(-0.741620\pi\) | ||||
−0.688248 | + | 0.725475i | \(0.741620\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.20633 | −0.216663 | −0.108332 | − | 0.994115i | \(-0.534551\pi\) | ||||
−0.108332 | + | 0.994115i | \(0.534551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.20633 | 0.209995 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.719448 | 0.118277 | 0.0591383 | − | 0.998250i | \(-0.481165\pi\) | ||||
0.0591383 | + | 0.998250i | \(0.481165\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.28055 | 0.199989 | 0.0999943 | − | 0.994988i | \(-0.468118\pi\) | ||||
0.0999943 | + | 0.994988i | \(0.468118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.28055 | −0.195282 | −0.0976412 | − | 0.995222i | \(-0.531130\pi\) | ||||
−0.0976412 | + | 0.995222i | \(0.531130\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.92578 | −0.864364 | −0.432182 | − | 0.901787i | \(-0.642256\pi\) | ||||
−0.432182 | + | 0.901787i | \(0.642256\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.1321 | 1.87602 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.69321 | −0.919383 | −0.459692 | − | 0.888079i | \(-0.652040\pi\) | ||||
−0.459692 | + | 0.888079i | \(0.652040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.69321 | 1.01899 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.92578 | 0.771471 | 0.385735 | − | 0.922609i | \(-0.373948\pi\) | ||||
0.385735 | + | 0.922609i | \(0.373948\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.41266 | 1.20517 | 0.602584 | − | 0.798056i | \(-0.294138\pi\) | ||||
0.602584 | + | 0.798056i | \(0.294138\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.48688 | −0.565294 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2063 | −1.36907 | −0.684536 | − | 0.728979i | \(-0.739995\pi\) | ||||
−0.684536 | + | 0.728979i | \(0.739995\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.69321 | 0.685382 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.13211 | 0.609069 | 0.304535 | − | 0.952501i | \(-0.401499\pi\) | ||||
0.304535 | + | 0.952501i | \(0.401499\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.13211 | −0.600668 | −0.300334 | − | 0.953834i | \(-0.597098\pi\) | ||||
−0.300334 | + | 0.953834i | \(0.597098\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.41266 | 0.616830 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.71945 | 0.305962 | 0.152981 | − | 0.988229i | \(-0.451113\pi\) | ||||
0.152981 | + | 0.988229i | \(0.451113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.89954 | −0.537795 | −0.268897 | − | 0.963169i | \(-0.586659\pi\) | ||||
−0.268897 | + | 0.963169i | \(0.586659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.41266 | 0.794721 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.412660 | −0.0437419 | −0.0218709 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218709 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.48688 | −0.470353 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.20633 | 0.125091 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9738 | −1.31729 | −0.658643 | − | 0.752456i | \(-0.728869\pi\) | ||||
−0.658643 | + | 0.752456i | \(0.728869\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.20633 | −0.121241 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6670 | 1.35991 | 0.679957 | − | 0.733252i | \(-0.261998\pi\) | ||||
0.679957 | + | 0.733252i | \(0.261998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.719448 | 0.0708893 | 0.0354447 | − | 0.999372i | \(-0.488715\pi\) | ||||
0.0354447 | + | 0.999372i | \(0.488715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7991 | 1.33401 | 0.667004 | − | 0.745054i | \(-0.267576\pi\) | ||||
0.667004 | + | 0.745054i | \(0.267576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.867892 | 0.0831290 | 0.0415645 | − | 0.999136i | \(-0.486766\pi\) | ||||
0.0415645 | + | 0.999136i | \(0.486766\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.719448 | −0.0682870 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.41266 | 0.603252 | 0.301626 | − | 0.953426i | \(-0.402471\pi\) | ||||
0.301626 | + | 0.953426i | \(0.402471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.4606 | 1.23394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.54477 | −0.867706 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.28055 | −0.115463 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1321 | −1.34276 | −0.671379 | − | 0.741114i | \(-0.734298\pi\) | ||||
−0.671379 | + | 0.741114i | \(0.734298\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.28055 | 0.112746 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.69321 | −0.672159 | −0.336080 | − | 0.941834i | \(-0.609101\pi\) | ||||
−0.336080 | + | 0.941834i | \(0.609101\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34.5185 | 2.99314 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.7991 | −1.69155 | −0.845775 | − | 0.533540i | \(-0.820861\pi\) | ||||
−0.845775 | + | 0.533540i | \(0.820861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.9475 | −1.69193 | −0.845964 | − | 0.533241i | \(-0.820974\pi\) | ||||
−0.845964 | + | 0.533241i | \(0.820974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.92578 | 0.499041 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.20633 | −0.100878 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.1321 | −1.08312 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.85156 | 0.315532 | 0.157766 | − | 0.987477i | \(-0.449571\pi\) | ||||
0.157766 | + | 0.987477i | \(0.449571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0742 | −0.982586 | −0.491293 | − | 0.870994i | \(-0.663476\pi\) | ||||
−0.491293 | + | 0.870994i | \(0.663476\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | −0.242536 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.69321 | −0.534176 | −0.267088 | − | 0.963672i | \(-0.586062\pi\) | ||||
−0.267088 | + | 0.963672i | \(0.586062\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.69321 | 0.530806 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.5448 | 2.01321 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2543 | 0.803180 | 0.401590 | − | 0.915820i | \(-0.368458\pi\) | ||||
0.401590 | + | 0.915820i | \(0.368458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.71945 | −0.365202 | −0.182601 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182601 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.69321 | −0.588315 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.280552 | −0.0213300 | −0.0106650 | − | 0.999943i | \(-0.503395\pi\) | ||||
−0.0106650 | + | 0.999943i | \(0.503395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.92578 | −0.445409 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.15834 | −0.161322 | −0.0806611 | − | 0.996742i | \(-0.525703\pi\) | ||||
−0.0806611 | + | 0.996742i | \(0.525703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.10587 | −0.379516 | −0.189758 | − | 0.981831i | \(-0.560770\pi\) | ||||
−0.189758 | + | 0.981831i | \(0.560770\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.41266 | −0.695804 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.61899 | 0.264647 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.48688 | 0.326373 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.2543 | 1.45794 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.1059 | −1.00500 | −0.502501 | − | 0.864577i | \(-0.667587\pi\) | ||||
−0.502501 | + | 0.864577i | \(0.667587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.3864 | 0.948938 | 0.474469 | − | 0.880272i | \(-0.342640\pi\) | ||||
0.474469 | + | 0.880272i | \(0.342640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2063 | 0.790434 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 33.2597 | 2.33438 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.69321 | −0.395706 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.28055 | 0.641949 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1321 | 1.04174 | 0.520869 | − | 0.853637i | \(-0.325608\pi\) | ||||
0.520869 | + | 0.853637i | \(0.325608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.13211 | −0.351646 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.41266 | 0.367435 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.13211 | 0.346796 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0796 | 1.27767 | 0.638833 | − | 0.769345i | \(-0.279417\pi\) | ||||
0.638833 | + | 0.769345i | \(0.279417\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.7674 | −1.17927 | −0.589633 | − | 0.807671i | \(-0.700728\pi\) | ||||
−0.589633 | + | 0.807671i | \(0.700728\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.41266 | −0.356127 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.4127 | −0.944205 | −0.472102 | − | 0.881544i | \(-0.656505\pi\) | ||||
−0.472102 | + | 0.881544i | \(0.656505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.71945 | −0.176647 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.0217 | 1.68321 | 0.841604 | − | 0.540096i | \(-0.181612\pi\) | ||||
0.841604 | + | 0.540096i | \(0.181612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.74568 | 0.241281 | 0.120640 | − | 0.992696i | \(-0.461505\pi\) | ||||
0.120640 | + | 0.992696i | \(0.461505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.69321 | −0.489507 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.89954 | 0.310496 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.66698 | −0.420816 | −0.210408 | − | 0.977614i | \(-0.567479\pi\) | ||||
−0.210408 | + | 0.977614i | \(0.567479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.86789 | 0.431781 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.1321 | 1.13105 | 0.565525 | − | 0.824731i | \(-0.308674\pi\) | ||||
0.565525 | + | 0.824731i | \(0.308674\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.22808 | −0.200583 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.41266 | −0.458832 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.28055 | 0.202287 | 0.101144 | − | 0.994872i | \(-0.467750\pi\) | ||||
0.101144 | + | 0.994872i | \(0.467750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.412660 | 0.0252544 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.9475 | −1.52108 | −0.760539 | − | 0.649293i | \(-0.775065\pi\) | ||||
−0.760539 | + | 0.649293i | \(0.775065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.31220 | 0.444185 | 0.222092 | − | 0.975026i | \(-0.428711\pi\) | ||||
0.222092 | + | 0.975026i | \(0.428711\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.48688 | 0.271558 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9738 | 0.779518 | 0.389759 | − | 0.920917i | \(-0.372558\pi\) | ||||
0.389759 | + | 0.920917i | \(0.372558\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.20633 | −0.0722211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 33.3864 | 1.99167 | 0.995834 | − | 0.0911899i | \(-0.0290670\pi\) | ||||
0.995834 | + | 0.0911899i | \(0.0290670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.3864 | 1.74684 | 0.873421 | − | 0.486966i | \(-0.161897\pi\) | ||||
0.873421 | + | 0.486966i | \(0.161897\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.74568 | −0.339157 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.9738 | 0.760535 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8253 | −0.632422 | −0.316211 | − | 0.948689i | \(-0.602411\pi\) | ||||
−0.316211 | + | 0.948689i | \(0.602411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.20633 | 0.0699984 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.69321 | −0.329247 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.74568 | 0.331176 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.6670 | −0.785147 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5448 | 0.773041 | 0.386520 | − | 0.922281i | \(-0.373677\pi\) | ||||
0.386520 | + | 0.922281i | \(0.373677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.719448 | −0.0409280 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.26422 | −0.468621 | −0.234310 | − | 0.972162i | \(-0.575283\pi\) | ||||
−0.234310 | + | 0.972162i | \(0.575283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.3068 | 0.639097 | 0.319549 | − | 0.947570i | \(-0.396469\pi\) | ||||
0.319549 | + | 0.947570i | \(0.396469\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.6407 | 1.21546 | 0.607732 | − | 0.794142i | \(-0.292079\pi\) | ||||
0.607732 | + | 0.794142i | \(0.292079\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.94211 | 0.500662 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.7991 | −0.770190 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.0796 | 1.28419 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.867892 | −0.0479945 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.5883 | 1.46586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5185 | −1.56752 | −0.783760 | − | 0.621064i | \(-0.786701\pi\) | ||||
−0.783760 | + | 0.621064i | \(0.786701\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.719448 | 0.0394255 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.6145 | 1.83110 | 0.915549 | − | 0.402206i | \(-0.131756\pi\) | ||||
0.915549 | + | 0.402206i | \(0.131756\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.41266 | −0.348288 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.45523 | 0.0788052 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −27.5140 | −1.48562 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.8253 | −1.86952 | −0.934761 | − | 0.355278i | \(-0.884386\pi\) | ||||
−0.934761 | + | 0.355278i | \(0.884386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.66698 | −0.142760 | −0.0713800 | − | 0.997449i | \(-0.522740\pi\) | ||||
−0.0713800 | + | 0.997449i | \(0.522740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.45523 | −0.237128 | −0.118564 | − | 0.992946i | \(-0.537829\pi\) | ||||
−0.118564 | + | 0.992946i | \(0.537829\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.4606 | −0.712413 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.92578 | 0.418307 | 0.209153 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209153 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.1855 | 2.11503 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.54477 | 0.500970 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.7728 | 0.979935 | 0.489967 | − | 0.871741i | \(-0.337009\pi\) | ||||
0.489967 | + | 0.871741i | \(0.337009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.28055 | 0.0666629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.0316 | 1.55917 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.2281 | 1.56515 | 0.782575 | − | 0.622556i | \(-0.213906\pi\) | ||||
0.782575 | + | 0.622556i | \(0.213906\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.41266 | −0.381771 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0579 | 0.568005 | 0.284003 | − | 0.958823i | \(-0.408338\pi\) | ||||
0.284003 | + | 0.958823i | \(0.408338\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.1321 | 0.775241 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.2543 | 1.13714 | 0.568571 | − | 0.822634i | \(-0.307496\pi\) | ||||
0.568571 | + | 0.822634i | \(0.307496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.28055 | −0.0650941 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.2380 | 1.17821 | 0.589106 | − | 0.808056i | \(-0.299480\pi\) | ||||
0.589106 | + | 0.808056i | \(0.299480\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.0796 | 0.863754 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.69321 | 0.388071 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.36019 | −0.218832 | −0.109416 | − | 0.993996i | \(-0.534898\pi\) | ||||
−0.109416 | + | 0.993996i | \(0.534898\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −34.5185 | −1.72809 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.8787 | −1.54201 | −0.771005 | − | 0.636829i | \(-0.780246\pi\) | ||||
−0.771005 | + | 0.636829i | \(0.780246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.20633 | −0.0600916 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.867892 | −0.0430198 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.8787 | −1.62575 | −0.812874 | − | 0.582440i | \(-0.802098\pi\) | ||||
−0.812874 | + | 0.582440i | \(0.802098\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.7991 | 0.976617 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.5883 | −1.30832 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.9475 | 0.976835 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.7194 | 1.01221 | 0.506106 | − | 0.862471i | \(-0.331085\pi\) | ||||
0.506106 | + | 0.862471i | \(0.331085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2117 | −1.18001 | −0.590004 | − | 0.807400i | \(-0.700874\pi\) | ||||
−0.590004 | + | 0.807400i | \(0.700874\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.92578 | −0.288121 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.2335 | −2.04382 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.20633 | 0.0582422 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.920365 | 0.0443324 | 0.0221662 | − | 0.999754i | \(-0.492944\pi\) | ||||
0.0221662 | + | 0.999754i | \(0.492944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.7991 | −0.663142 | −0.331571 | − | 0.943430i | \(-0.607579\pi\) | ||||
−0.331571 | + | 0.943430i | \(0.607579\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.7991 | 2.09519 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3765 | 1.02025 | 0.510123 | − | 0.860102i | \(-0.329600\pi\) | ||||
0.510123 | + | 0.860102i | \(0.329600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.1321 | 0.625338 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.1059 | −0.480144 | −0.240072 | − | 0.970755i | \(-0.577171\pi\) | ||||
−0.240072 | + | 0.970755i | \(0.577171\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.85156 | −0.182172 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.5086 | −1.34541 | −0.672703 | − | 0.739913i | \(-0.734867\pi\) | ||||
−0.672703 | + | 0.739913i | \(0.734867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54477 | −0.0727403 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0742 | 0.567296 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.4923 | 1.37959 | 0.689796 | − | 0.724004i | \(-0.257700\pi\) | ||||
0.689796 | + | 0.724004i | \(0.257700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.00000 | 0.140028 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.73578 | 0.173993 | 0.0869964 | − | 0.996209i | \(-0.472273\pi\) | ||||
0.0869964 | + | 0.996209i | \(0.472273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.00541 | −0.325569 | −0.162785 | − | 0.986662i | \(-0.552048\pi\) | ||||
−0.162785 | + | 0.986662i | \(0.552048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5349 | −1.18161 | −0.590806 | − | 0.806813i | \(-0.701190\pi\) | ||||
−0.590806 | + | 0.806813i | \(0.701190\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 50.2815 | 2.32178 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.69321 | 0.308407 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.54477 | 0.0710285 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.69321 | −0.306461 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.23257 | 0.102009 | 0.0510043 | − | 0.998698i | \(-0.483758\pi\) | ||||
0.0510043 | + | 0.998698i | \(0.483758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.719448 | 0.0328040 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.5448 | −1.16233 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.4443 | −1.19831 | −0.599153 | − | 0.800635i | \(-0.704496\pi\) | ||||
−0.599153 | + | 0.800635i | \(0.704496\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.2543 | −0.463716 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0000 | 0.992846 | 0.496423 | − | 0.868081i | \(-0.334646\pi\) | ||||
0.496423 | + | 0.868081i | \(0.334646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.2380 | 1.00155 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −23.0272 | −1.03291 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.2597 | 1.84704 | 0.923520 | − | 0.383551i | \(-0.125299\pi\) | ||||
0.923520 | + | 0.383551i | \(0.125299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.71945 | 0.210849 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.1321 | −1.12059 | −0.560293 | − | 0.828295i | \(-0.689311\pi\) | ||||
−0.560293 | + | 0.828295i | \(0.689311\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.2018 | −1.51597 | −0.757985 | − | 0.652272i | \(-0.773816\pi\) | ||||
−0.757985 | + | 0.652272i | \(0.773816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.0272 | 1.01866 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.69321 | 0.339664 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.14844 | 0.314388 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.280552 | 0.0123149 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.17468 | −0.0514637 | −0.0257318 | − | 0.999669i | \(-0.508192\pi\) | ||||
−0.0257318 | + | 0.999669i | \(0.508192\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.20092 | 0.0962394 | 0.0481197 | − | 0.998842i | \(-0.484677\pi\) | ||||
0.0481197 | + | 0.998842i | \(0.484677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.61899 | 0.157646 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.41266 | 0.409246 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.92578 | 0.257157 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.28055 | 0.0554669 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.15834 | 0.0931394 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.8417 | −0.682348 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.13211 | −0.392620 | −0.196310 | − | 0.980542i | \(-0.562896\pi\) | ||||
−0.196310 | + | 0.980542i | \(0.562896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.10587 | 0.219114 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.0534 | −1.62705 | −0.813523 | − | 0.581533i | \(-0.802453\pi\) | ||||
−0.813523 | + | 0.581533i | \(0.802453\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.41266 | 0.401723 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 57.0272 | 2.42944 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.2018 | −0.518875 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.2543 | 0.688717 | 0.344359 | − | 0.938838i | \(-0.388096\pi\) | ||||
0.344359 | + | 0.938838i | \(0.388096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.28055 | −0.0541616 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.61899 | −0.152794 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.95743 | 0.335366 | 0.167683 | − | 0.985841i | \(-0.446372\pi\) | ||||
0.167683 | + | 0.985841i | \(0.446372\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.48688 | −0.188431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.2806 | −1.26943 | −0.634713 | − | 0.772748i | \(-0.718882\pi\) | ||||
−0.634713 | + | 0.772748i | \(0.718882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.6407 | 0.654545 | 0.327272 | − | 0.944930i | \(-0.393871\pi\) | ||||
0.327272 | + | 0.944930i | \(0.393871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.00000 | −0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.67688 | −0.361223 | −0.180612 | − | 0.983555i | \(-0.557808\pi\) | ||||
−0.180612 | + | 0.983555i | \(0.557808\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.2543 | −0.841741 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.9837 | 0.912036 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.07422 | 0.334400 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.7150 | −1.47411 | −0.737057 | − | 0.675830i | \(-0.763785\pi\) | ||||
−0.737057 | + | 0.675830i | \(0.763785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.28055 | 0.382398 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.1059 | 0.580238 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.5086 | −1.08858 | −0.544289 | − | 0.838897i | \(-0.683201\pi\) | ||||
−0.544289 | + | 0.838897i | \(0.683201\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.3864 | −0.547870 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.9050 | −1.46704 | −0.733518 | − | 0.679670i | \(-0.762123\pi\) | ||||
−0.733518 | + | 0.679670i | \(0.762123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.5185 | 1.12250 | 0.561252 | − | 0.827645i | \(-0.310320\pi\) | ||||
0.561252 | + | 0.827645i | \(0.310320\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.2063 | −0.456357 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.53487 | −0.305831 | −0.152915 | − | 0.988239i | \(-0.548866\pi\) | ||||
−0.152915 | + | 0.988239i | \(0.548866\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.2597 | −1.34775 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.92578 | −0.239731 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.8253 | 0.921906 | 0.460953 | − | 0.887425i | \(-0.347508\pi\) | ||||
0.460953 | + | 0.887425i | \(0.347508\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.5349 | −1.59161 | −0.795807 | − | 0.605550i | \(-0.792953\pi\) | ||||
−0.795807 | + | 0.605550i | \(0.792953\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.9837 | −0.441471 | −0.220735 | − | 0.975334i | \(-0.570846\pi\) | ||||
−0.220735 | + | 0.975334i | \(0.570846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.69321 | 0.228461 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.85156 | 0.0741810 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.28055 | −0.370630 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.15834 | −0.0860588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.6670 | −1.38007 | −0.690035 | − | 0.723776i | \(-0.742405\pi\) | ||||
−0.690035 | + | 0.723776i | \(0.742405\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.1321 | −0.601447 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.1321 | 0.520313 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.13211 | 0.203023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.1222 | 0.399803 | 0.199902 | − | 0.979816i | \(-0.435938\pi\) | ||||
0.199902 | + | 0.979816i | \(0.435938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5710 | 0.574624 | 0.287312 | − | 0.957837i | \(-0.407238\pi\) | ||||
0.287312 | + | 0.957837i | \(0.407238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.1855 | 1.69780 | 0.848899 | − | 0.528556i | \(-0.177266\pi\) | ||||
0.848899 | + | 0.528556i | \(0.177266\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.14844 | −0.280601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.41266 | −0.212139 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00000 | 0.352197 | 0.176099 | − | 0.984373i | \(-0.443652\pi\) | ||||
0.176099 | + | 0.984373i | \(0.443652\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.13211 | −0.200223 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.7892 | −1.00460 | −0.502302 | − | 0.864692i | \(-0.667513\pi\) | ||||
−0.502302 | + | 0.864692i | \(0.667513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.6670 | 1.11502 | 0.557508 | − | 0.830172i | \(-0.311758\pi\) | ||||
0.557508 | + | 0.830172i | \(0.311758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.00000 | 0.116510 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.2018 | 1.63406 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.0796 | −0.737661 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.3548 | −0.438346 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.40276 | −0.285355 | −0.142678 | − | 0.989769i | \(-0.545571\pi\) | ||||
−0.142678 | + | 0.989769i | \(0.545571\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.3864 | 1.74434 | 0.872171 | − | 0.489201i | \(-0.162712\pi\) | ||||
0.872171 | + | 0.489201i | \(0.162712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 58.2117 | 2.23396 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.7674 | 0.680850 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.5403 | 1.85734 | 0.928671 | − | 0.370904i | \(-0.120952\pi\) | ||||
0.928671 | + | 0.370904i | \(0.120952\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.00000 | −0.0763048 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.69321 | −0.254991 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.803571 | −0.0305693 | −0.0152846 | − | 0.999883i | \(-0.504865\pi\) | ||||
−0.0152846 | + | 0.999883i | \(0.504865\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.41266 | 0.205610 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.84166 | −0.145513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.4127 | 0.545137 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.6571 | −1.19567 | −0.597836 | − | 0.801619i | \(-0.703972\pi\) | ||||
−0.597836 | + | 0.801619i | \(0.703972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.53487 | −0.208751 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −61.3221 | −2.30626 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.66698 | −0.325495 | −0.162748 | − | 0.986668i | \(-0.552036\pi\) | ||||
−0.162748 | + | 0.986668i | \(0.552036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.71945 | 0.101987 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.86789 | 0.257205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.0217 | −0.971800 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.9312 | 0.780602 | 0.390301 | − | 0.920687i | \(-0.372371\pi\) | ||||
0.390301 | + | 0.920687i | \(0.372371\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.22808 | −0.120220 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.74568 | −0.139304 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.6670 | 1.58243 | 0.791215 | − | 0.611538i | \(-0.209449\pi\) | ||||
0.791215 | + | 0.611538i | \(0.209449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.84166 | 0.142089 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.2117 | −0.746538 | −0.373269 | − | 0.927723i | \(-0.621763\pi\) | ||||
−0.373269 | + | 0.927723i | \(0.621763\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.5185 | 0.497962 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.0054 | 1.43484 | 0.717419 | − | 0.696642i | \(-0.245324\pi\) | ||||
0.717419 | + | 0.696642i | \(0.245324\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.69321 | 0.282617 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.3548 | −1.29704 | −0.648520 | − | 0.761197i | \(-0.724612\pi\) | ||||
−0.648520 | + | 0.761197i | \(0.724612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.89954 | −0.179265 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −61.9149 | −2.26232 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.4661 | −1.33067 | −0.665333 | − | 0.746547i | \(-0.731710\pi\) | ||||
−0.665333 | + | 0.746547i | \(0.731710\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.66698 | 0.242958 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.82532 | −0.139034 | −0.0695168 | − | 0.997581i | \(-0.522146\pi\) | ||||
−0.0695168 | + | 0.997581i | \(0.522146\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.86789 | −0.249289 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.2543 | 1.09672 | 0.548359 | − | 0.836243i | \(-0.315253\pi\) | ||||
0.548359 | + | 0.836243i | \(0.315253\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.89413 | −0.140977 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.92578 | 0.213967 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.9738 | −1.40543 | −0.702715 | − | 0.711472i | \(-0.748029\pi\) | ||||
−0.702715 | + | 0.711472i | \(0.748029\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1321 | −0.653012 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.9213 | 0.968292 | 0.484146 | − | 0.874987i | \(-0.339130\pi\) | ||||
0.484146 | + | 0.874987i | \(0.339130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.22808 | 0.115807 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.85156 | −0.352969 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.19102 | −0.221532 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.41266 | 0.264907 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0316 | −0.785344 | −0.392672 | − | 0.919679i | \(-0.628449\pi\) | ||||
−0.392672 | + | 0.919679i | \(0.628449\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.28055 | −0.116791 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.7728 | −1.02304 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.41266 | 0.334253 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.7466 | 1.72669 | 0.863347 | − | 0.504611i | \(-0.168364\pi\) | ||||
0.863347 | + | 0.504611i | \(0.168364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.7773 | 0.628917 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.412660 | −0.0145806 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.19102 | 0.218476 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.9475 | 0.878195 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.7991 | −0.907047 | −0.453524 | − | 0.891244i | \(-0.649833\pi\) | ||||
−0.453524 | + | 0.891244i | \(0.649833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.1375 | 1.40942 | 0.704710 | − | 0.709496i | \(-0.251077\pi\) | ||||
0.704710 | + | 0.709496i | \(0.251077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.31220 | −0.256450 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.85156 | 0.344662 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.48688 | −0.156784 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.3176 | 1.68630 | 0.843148 | − | 0.537681i | \(-0.180700\pi\) | ||||
0.843148 | + | 0.537681i | \(0.180700\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.0633 | 0.629647 | 0.314824 | − | 0.949150i | \(-0.398055\pi\) | ||||
0.314824 | + | 0.949150i | \(0.398055\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.2696 | −1.36554 | −0.682769 | − | 0.730634i | \(-0.739225\pi\) | ||||
−0.682769 | + | 0.730634i | \(0.739225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 55.9213 | 1.94223 | 0.971113 | − | 0.238619i | \(-0.0766946\pi\) | ||||
0.971113 | + | 0.238619i | \(0.0766946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.9738 | −0.450055 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.3963 | −1.36500 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.20633 | 0.0416969 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.9574 | −1.58663 | −0.793313 | − | 0.608814i | \(-0.791646\pi\) | ||||
−0.793313 | + | 0.608814i | \(0.791646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.9475 | 0.894742 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −33.3864 | −1.14989 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.8262 | 1.47153 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.3864 | −1.00854 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.09597 | −0.140408 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.7204 | −1.12032 | −0.560162 | − | 0.828383i | \(-0.689261\pi\) | ||||
−0.560162 | + | 0.828383i | \(0.689261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.8951 | −0.884558 | −0.442279 | − | 0.896877i | \(-0.645830\pi\) | ||||
−0.442279 | + | 0.896877i | \(0.645830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.57744 | 0.0538215 | 0.0269108 | − | 0.999638i | \(-0.491433\pi\) | ||||
0.0269108 | + | 0.999638i | \(0.491433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.74568 | 0.195812 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.2761 | −1.09869 | −0.549345 | − | 0.835596i | \(-0.685123\pi\) | ||||
−0.549345 | + | 0.835596i | \(0.685123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.28055 | −0.111285 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2063 | −0.379712 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.9738 | −0.439095 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7991 | 0.398427 | 0.199213 | − | 0.979956i | \(-0.436161\pi\) | ||||
0.199213 | + | 0.979956i | \(0.436161\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.8253 | 0.365129 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.0796 | −1.55246 | −0.776231 | − | 0.630448i | \(-0.782871\pi\) | ||||
−0.776231 | + | 0.630448i | \(0.782871\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.32312 | 0.313748 | 0.156874 | − | 0.987619i | \(-0.449858\pi\) | ||||
0.156874 | + | 0.987619i | \(0.449858\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.1954 | −1.78613 | −0.893063 | − | 0.449931i | \(-0.851449\pi\) | ||||
−0.893063 | + | 0.449931i | \(0.851449\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 67.8960 | 2.27716 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.20633 | −0.0404136 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.5883 | 1.52555 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.69321 | 0.190091 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.94211 | 0.298236 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0796 | 0.668950 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.74568 | −0.191204 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.7204 | 1.88337 | 0.941685 | − | 0.336497i | \(-0.109242\pi\) | ||||
0.941685 | + | 0.336497i | \(0.109242\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.6670 | 0.453305 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5883 | 1.11283 | 0.556414 | − | 0.830905i | \(-0.312177\pi\) | ||||
0.556414 | + | 0.830905i | \(0.312177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.91046 | 0.195608 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 34.5185 | 1.13990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.58734 | −0.184309 | −0.0921547 | − | 0.995745i | \(-0.529375\pi\) | ||||
−0.0921547 | + | 0.995745i | \(0.529375\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.5448 | −0.446315 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.13211 | 0.168925 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.719448 | 0.0236298 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.2117 | 0.728744 | 0.364372 | − | 0.931254i | \(-0.381284\pi\) | ||||
0.364372 | + | 0.931254i | \(0.381284\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −101.028 | −3.31106 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.26422 | 0.270558 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.23798 | −0.203786 | −0.101893 | − | 0.994795i | \(-0.532490\pi\) | ||||
−0.101893 | + | 0.994795i | \(0.532490\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.3068 | −0.368983 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.1846 | −0.364607 | −0.182303 | − | 0.983242i | \(-0.558355\pi\) | ||||
−0.182303 | + | 0.983242i | \(0.558355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.29045 | −0.237410 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.9094 | 0.354509 | 0.177255 | − | 0.984165i | \(-0.443278\pi\) | ||||
0.177255 | + | 0.984165i | \(0.443278\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.13211 | −0.166595 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.6407 | −0.701749 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.2806 | −0.851311 | −0.425655 | − | 0.904885i | \(-0.639956\pi\) | ||||
−0.425655 | + | 0.904885i | \(0.639956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.94211 | −0.289057 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 88.8361 | 2.86867 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5448 | −0.953057 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.7991 | 0.444669 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.4705 | 0.433184 | 0.216592 | − | 0.976262i | \(-0.430506\pi\) | ||||
0.216592 | + | 0.976262i | \(0.430506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.0796 | −0.741425 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.5349 | −0.370172 | −0.185086 | − | 0.982722i | \(-0.559256\pi\) | ||||
−0.185086 | + | 0.982722i | \(0.559256\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 89.5022 | 2.86931 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.2117 | −0.518660 | −0.259330 | − | 0.965789i | \(-0.583502\pi\) | ||||
−0.259330 | + | 0.965789i | \(0.583502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.497804 | 0.0159099 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.867892 | 0.0277097 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.1014 | 0.545449 | 0.272725 | − | 0.962092i | \(-0.412075\pi\) | ||||
0.272725 | + | 0.962092i | \(0.412075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.5883 | −0.846314 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.29045 | 0.231823 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.0470 | −1.87569 | −0.937844 | − | 0.347056i | \(-0.887181\pi\) | ||||
−0.937844 | + | 0.347056i | \(0.887181\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.5185 | 0.905008 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.5195 | −1.50496 | −0.752478 | − | 0.658617i | \(-0.771142\pi\) | ||||
−0.752478 | + | 0.658617i | \(0.771142\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.719448 | −0.0227623 |
(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 | 7800.2.a.bh.1.1 | ✓ | 3 | |
5.4 | even | 2 | 7800.2.a.bs.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bh.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7800.2.a.bs.1.3 | yes | 3 | 5.4 | even | 2 |