Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7448,2,Mod(1,7448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7448, 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("7448.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7448.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: | \(59.4725794254\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} - x^{5} + 66x^{4} + 4x^{3} - 76x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1064) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.34151\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7448.1 |
$q$-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 | ||||||||
\(3\) | 1.34151 | 0.774524 | 0.387262 | − | 0.921970i | \(-0.373421\pi\) | ||||
0.387262 | + | 0.921970i | \(0.373421\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.90869 | −1.30081 | −0.650403 | − | 0.759590i | \(-0.725400\pi\) | ||||
−0.650403 | + | 0.759590i | \(0.725400\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.20034 | −0.400113 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.99462 | 1.50594 | 0.752968 | − | 0.658057i | \(-0.228621\pi\) | ||||
0.752968 | + | 0.658057i | \(0.228621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55217 | −0.430495 | −0.215247 | − | 0.976560i | \(-0.569056\pi\) | ||||
−0.215247 | + | 0.976560i | \(0.569056\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.90205 | −1.00750 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.19129 | −1.50161 | −0.750804 | − | 0.660525i | \(-0.770334\pi\) | ||||
−0.750804 | + | 0.660525i | \(0.770334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.78397 | 1.41456 | 0.707278 | − | 0.706936i | \(-0.249923\pi\) | ||||
0.707278 | + | 0.706936i | \(0.249923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.46047 | 0.692095 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.63482 | −1.08442 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.707720 | 0.131420 | 0.0657102 | − | 0.997839i | \(-0.479069\pi\) | ||||
0.0657102 | + | 0.997839i | \(0.479069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.56989 | −1.71880 | −0.859401 | − | 0.511302i | \(-0.829164\pi\) | ||||
−0.859401 | + | 0.511302i | \(0.829164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.70036 | 1.16638 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.24407 | 0.697720 | 0.348860 | − | 0.937175i | \(-0.386569\pi\) | ||||
0.348860 | + | 0.937175i | \(0.386569\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.08226 | −0.333428 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.25818 | −0.191871 | −0.0959355 | − | 0.995388i | \(-0.530584\pi\) | ||||
−0.0959355 | + | 0.995388i | \(0.530584\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.49141 | 0.520469 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.3543 | 1.80206 | 0.901030 | − | 0.433757i | \(-0.142812\pi\) | ||||
0.901030 | + | 0.433757i | \(0.142812\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.30570 | −1.16303 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.891734 | 0.122489 | 0.0612445 | − | 0.998123i | \(-0.480493\pi\) | ||||
0.0612445 | + | 0.998123i | \(0.480493\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.5278 | −1.95893 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.34151 | −0.177688 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.5769 | −1.37700 | −0.688498 | − | 0.725238i | \(-0.741730\pi\) | ||||
−0.688498 | + | 0.725238i | \(0.741730\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8291 | 1.51457 | 0.757283 | − | 0.653086i | \(-0.226526\pi\) | ||||
0.757283 | + | 0.653086i | \(0.226526\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.51478 | 0.559990 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.98968 | 0.243078 | 0.121539 | − | 0.992587i | \(-0.461217\pi\) | ||||
0.121539 | + | 0.992587i | \(0.461217\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.10079 | 1.09561 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4174 | −1.47368 | −0.736839 | − | 0.676068i | \(-0.763683\pi\) | ||||
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00688 | 0.820094 | 0.410047 | − | 0.912064i | \(-0.365512\pi\) | ||||
0.410047 | + | 0.912064i | \(0.365512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.64228 | 0.536044 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9359 | 1.90544 | 0.952721 | − | 0.303845i | \(-0.0982706\pi\) | ||||
0.952721 | + | 0.303845i | \(0.0982706\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.95817 | −0.439796 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.494217 | 0.0542474 | 0.0271237 | − | 0.999632i | \(-0.491365\pi\) | ||||
0.0271237 | + | 0.999632i | \(0.491365\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0085 | 1.95330 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.949417 | 0.101788 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.38043 | 0.358325 | 0.179163 | − | 0.983819i | \(-0.442661\pi\) | ||||
0.179163 | + | 0.983819i | \(0.442661\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.8381 | −1.33125 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.90869 | 0.298425 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0685 | 1.02230 | 0.511152 | − | 0.859491i | \(-0.329219\pi\) | ||||
0.511152 | + | 0.859491i | \(0.329219\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.99524 | −0.602545 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.57231 | −0.255954 | −0.127977 | − | 0.991777i | \(-0.540848\pi\) | ||||
−0.127977 | + | 0.991777i | \(0.540848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.43706 | −0.634263 | −0.317131 | − | 0.948382i | \(-0.602720\pi\) | ||||
−0.317131 | + | 0.948382i | \(0.602720\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.39859 | 0.231881 | 0.115940 | − | 0.993256i | \(-0.463012\pi\) | ||||
0.115940 | + | 0.993256i | \(0.463012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2546 | −1.36534 | −0.682670 | − | 0.730727i | \(-0.739181\pi\) | ||||
−0.682670 | + | 0.730727i | \(0.739181\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.69348 | 0.540401 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.713643 | −0.0671338 | −0.0335669 | − | 0.999436i | \(-0.510687\pi\) | ||||
−0.0335669 | + | 0.999436i | \(0.510687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.7325 | −1.84006 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.86313 | 0.172247 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.9463 | 1.26784 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.68303 | 0.241921 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.47800 | 0.400525 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.73364 | −0.774985 | −0.387493 | − | 0.921873i | \(-0.626659\pi\) | ||||
−0.387493 | + | 0.921873i | \(0.626659\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.68787 | −0.148609 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.20006 | 0.541702 | 0.270851 | − | 0.962621i | \(-0.412695\pi\) | ||||
0.270851 | + | 0.962621i | \(0.412695\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.3899 | 1.41062 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.8363 | 1.52386 | 0.761928 | − | 0.647662i | \(-0.224253\pi\) | ||||
0.761928 | + | 0.647662i | \(0.224253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.1484 | 1.28487 | 0.642435 | − | 0.766340i | \(-0.277924\pi\) | ||||
0.642435 | + | 0.766340i | \(0.277924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.5735 | 1.39574 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.75251 | −0.648297 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.05854 | −0.170952 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.61171 | 0.705499 | 0.352749 | − | 0.935718i | \(-0.385247\pi\) | ||||
0.352749 | + | 0.935718i | \(0.385247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2640 | 1.40492 | 0.702461 | − | 0.711722i | \(-0.252084\pi\) | ||||
0.702461 | + | 0.711722i | \(0.252084\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.43165 | 0.600813 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.8358 | 2.23583 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.9496 | 1.35273 | 0.676364 | − | 0.736567i | \(-0.263555\pi\) | ||||
0.676364 | + | 0.736567i | \(0.263555\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.19627 | 0.0948707 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2680 | −1.35253 | −0.676266 | − | 0.736657i | \(-0.736403\pi\) | ||||
−0.676266 | + | 0.736657i | \(0.736403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −19.4893 | −1.51724 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.74790 | −0.676933 | −0.338466 | − | 0.940979i | \(-0.609908\pi\) | ||||
−0.338466 | + | 0.940979i | \(0.609908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5908 | −0.814674 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.20034 | 0.0917922 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.99381 | −0.531730 | −0.265865 | − | 0.964010i | \(-0.585657\pi\) | ||||
−0.265865 | + | 0.964010i | \(0.585657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.1891 | −1.06652 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.4426 | 1.52795 | 0.763977 | − | 0.645243i | \(-0.223244\pi\) | ||||
0.763977 | + | 0.645243i | \(0.223244\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.96247 | −0.740505 | −0.370252 | − | 0.928931i | \(-0.620729\pi\) | ||||
−0.370252 | + | 0.928931i | \(0.620729\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.8690 | 1.17307 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.3447 | −0.907598 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.9232 | −2.26133 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.5416 | 1.05219 | 0.526097 | − | 0.850425i | \(-0.323655\pi\) | ||||
0.526097 | + | 0.850425i | \(0.323655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.7083 | −1.13071 | −0.565353 | − | 0.824849i | \(-0.691260\pi\) | ||||
−0.565353 | + | 0.824849i | \(0.691260\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.05665 | 0.433725 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.726728 | 0.0517772 | 0.0258886 | − | 0.999665i | \(-0.491758\pi\) | ||||
0.0258886 | + | 0.999665i | \(0.491758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3804 | 1.01940 | 0.509699 | − | 0.860353i | \(-0.329757\pi\) | ||||
0.509699 | + | 0.860353i | \(0.329757\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.66919 | 0.188270 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.81738 | −0.406303 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.14306 | −0.565982 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.99462 | −0.345485 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.8134 | −1.43285 | −0.716427 | − | 0.697662i | \(-0.754224\pi\) | ||||
−0.716427 | + | 0.697662i | \(0.754224\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.6582 | −1.14140 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.65966 | 0.249587 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.39984 | 0.635182 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.60993 | 0.646434 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.02432 | −0.403418 | −0.201709 | − | 0.979445i | \(-0.564650\pi\) | ||||
−0.201709 | + | 0.979445i | \(0.564650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.15374 | −0.276916 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.86625 | −0.522102 | −0.261051 | − | 0.965325i | \(-0.584069\pi\) | ||||
−0.261051 | + | 0.965325i | \(0.584069\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.6691 | 1.89450 | 0.947252 | − | 0.320488i | \(-0.103847\pi\) | ||||
0.947252 | + | 0.320488i | \(0.103847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.04304 | 0.199356 | 0.0996781 | − | 0.995020i | \(-0.468219\pi\) | ||||
0.0996781 | + | 0.995020i | \(0.468219\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −35.9348 | −2.34413 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.7198 | 1.47581 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.23545 | 0.597392 | 0.298696 | − | 0.954348i | \(-0.403448\pi\) | ||||
0.298696 | + | 0.954348i | \(0.403448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.03850 | 0.582221 | 0.291110 | − | 0.956689i | \(-0.405975\pi\) | ||||
0.291110 | + | 0.956689i | \(0.405975\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.5945 | 0.743788 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.55217 | 0.0987622 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.663000 | 0.0420159 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.91027 | 0.183695 | 0.0918473 | − | 0.995773i | \(-0.470723\pi\) | ||||
0.0918473 | + | 0.995773i | \(0.470723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.8834 | 2.13023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 24.1587 | 1.51288 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.9088 | −1.42901 | −0.714505 | − | 0.699631i | \(-0.753348\pi\) | ||||
−0.714505 | + | 0.699631i | \(0.753348\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.849504 | −0.0525830 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.6699 | 1.08957 | 0.544787 | − | 0.838574i | \(-0.316610\pi\) | ||||
0.544787 | + | 0.838574i | \(0.316610\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.59378 | −0.159334 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.53490 | 0.277531 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.4234 | 0.696497 | 0.348248 | − | 0.937402i | \(-0.386777\pi\) | ||||
0.348248 | + | 0.937402i | \(0.386777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.04922 | 0.306719 | 0.153359 | − | 0.988170i | \(-0.450991\pi\) | ||||
0.153359 | + | 0.988170i | \(0.450991\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.2838 | 1.04225 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.45687 | 0.387956 | 0.193978 | − | 0.981006i | \(-0.437861\pi\) | ||||
0.193978 | + | 0.981006i | \(0.437861\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.4871 | 0.687715 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2877 | −0.613711 | −0.306856 | − | 0.951756i | \(-0.599277\pi\) | ||||
−0.306856 | + | 0.951756i | \(0.599277\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0500 | 1.31074 | 0.655368 | − | 0.755310i | \(-0.272514\pi\) | ||||
0.655368 | + | 0.755310i | \(0.272514\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.90205 | 0.231137 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.3320 | 1.25483 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.5071 | 0.791798 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.5297 | 1.19936 | 0.599680 | − | 0.800240i | \(-0.295295\pi\) | ||||
0.599680 | + | 0.800240i | \(0.295295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.7649 | 1.79120 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.1438 | −1.63307 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5299 | −0.608958 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.45079 | −0.198242 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −34.4073 | −1.97016 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.5830 | −1.23181 | −0.615904 | − | 0.787821i | \(-0.711209\pi\) | ||||
−0.615904 | + | 0.787821i | \(0.711209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.63541 | −0.491251 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6510 | 1.34112 | 0.670562 | − | 0.741853i | \(-0.266053\pi\) | ||||
0.670562 | + | 0.741853i | \(0.266053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.7120 | 1.50985 | 0.754927 | − | 0.655809i | \(-0.227672\pi\) | ||||
0.754927 | + | 0.655809i | \(0.227672\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.0740 | −1.52063 | −0.760314 | − | 0.649555i | \(-0.774955\pi\) | ||||
−0.760314 | + | 0.649555i | \(0.774955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.53480 | 0.197911 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.21775 | 0.179597 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.19129 | 0.344492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.37125 | −0.297943 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.1227 | −1.05749 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.14003 | 0.172591 | 0.0862957 | − | 0.996270i | \(-0.472497\pi\) | ||||
0.0862957 | + | 0.996270i | \(0.472497\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.09432 | −0.279167 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.78737 | −0.316198 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6417 | 1.17890 | 0.589449 | − | 0.807805i | \(-0.299345\pi\) | ||||
0.589449 | + | 0.807805i | \(0.299345\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.957362 | −0.0519968 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −47.7980 | −2.58841 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.4714 | −1.42517 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.56676 | −0.137791 | −0.0688955 | − | 0.997624i | \(-0.521948\pi\) | ||||
−0.0688955 | + | 0.997624i | \(0.521948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.91567 | −0.102543 | −0.0512716 | − | 0.998685i | \(-0.516327\pi\) | ||||
−0.0512716 | + | 0.998685i | \(0.516327\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.74619 | 0.466837 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.8777 | 0.845087 | 0.422543 | − | 0.906343i | \(-0.361137\pi\) | ||||
0.422543 | + | 0.906343i | \(0.361137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.1185 | 1.91697 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.0794 | 1.05975 | 0.529875 | − | 0.848076i | \(-0.322239\pi\) | ||||
0.529875 | + | 0.848076i | \(0.322239\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.7091 | 0.981975 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.3808 | −1.06678 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.58480 | −0.187125 | −0.0935626 | − | 0.995613i | \(-0.529826\pi\) | ||||
−0.0935626 | + | 0.995613i | \(0.529826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.40068 | −0.124974 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.6745 | 1.38115 | 0.690576 | − | 0.723260i | \(-0.257357\pi\) | ||||
0.690576 | + | 0.723260i | \(0.257357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.00730 | 0.310216 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.09850 | −0.0565758 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.9451 | 0.973146 | 0.486573 | − | 0.873640i | \(-0.338247\pi\) | ||||
0.486573 | + | 0.873640i | \(0.338247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.7163 | −0.600244 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.9515 | 0.763988 | 0.381994 | − | 0.924165i | \(-0.375238\pi\) | ||||
0.381994 | + | 0.924165i | \(0.375238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.51025 | 0.0767701 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.6168 | 1.85655 | 0.928273 | − | 0.371900i | \(-0.121294\pi\) | ||||
0.928273 | + | 0.371900i | \(0.121294\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.0015 | −2.12411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.31748 | 0.419561 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −49.2614 | −2.47861 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.8520 | 0.996346 | 0.498173 | − | 0.867078i | \(-0.334004\pi\) | ||||
0.498173 | + | 0.867078i | \(0.334004\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.63008 | 0.231215 | 0.115608 | − | 0.993295i | \(-0.463118\pi\) | ||||
0.115608 | + | 0.993295i | \(0.463118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.8541 | 0.739935 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.5131 | 0.572090 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.1975 | 1.05072 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.41274 | −0.218196 | −0.109098 | − | 0.994031i | \(-0.534796\pi\) | ||||
−0.109098 | + | 0.994031i | \(0.534796\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.9276 | 1.18026 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.43752 | −0.0705653 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.3218 | 0.995162 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.8148 | −1.60311 | −0.801554 | − | 0.597922i | \(-0.795993\pi\) | ||||
−0.801554 | + | 0.597922i | \(0.795993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.3765 | 0.505721 | 0.252861 | − | 0.967503i | \(-0.418629\pi\) | ||||
0.252861 | + | 0.967503i | \(0.418629\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.8294 | −0.721028 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.4248 | −1.03926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.4001 | −0.502122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.11967 | −0.102101 | −0.0510505 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510505 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.23274 | 0.203413 | 0.101706 | − | 0.994814i | \(-0.467570\pi\) | ||||
0.101706 | + | 0.994814i | \(0.467570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.76156 | −0.132407 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.78397 | −0.324521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7380 | 1.13295 | 0.566476 | − | 0.824078i | \(-0.308306\pi\) | ||||
0.566476 | + | 0.824078i | \(0.308306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.6401 | −0.505529 | −0.252764 | − | 0.967528i | \(-0.581340\pi\) | ||||
−0.252764 | + | 0.967528i | \(0.581340\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.83263 | −0.466111 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.5527 | 0.546426 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.4650 | 0.871418 | 0.435709 | − | 0.900088i | \(-0.356498\pi\) | ||||
0.435709 | + | 0.900088i | \(0.356498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.98925 | 0.470375 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.1599 | 1.08815 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.43795 | −0.394711 | −0.197355 | − | 0.980332i | \(-0.563235\pi\) | ||||
−0.197355 | + | 0.980332i | \(0.563235\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34.8868 | 1.62837 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8951 | 0.880034 | 0.440017 | − | 0.897990i | \(-0.354972\pi\) | ||||
0.440017 | + | 0.897990i | \(0.354972\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.5602 | 1.28083 | 0.640415 | − | 0.768029i | \(-0.278762\pi\) | ||||
0.640415 | + | 0.768029i | \(0.278762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.3422 | 1.73170 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.2741 | −1.07700 | −0.538498 | − | 0.842627i | \(-0.681008\pi\) | ||||
−0.538498 | + | 0.842627i | \(0.681008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.7382 | 1.04772 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.28415 | −0.288945 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.46047 | −0.158777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.07038 | −0.0490095 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.40293 | −0.201175 | −0.100588 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100588 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.58751 | −0.300365 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −29.2862 | −1.32982 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.2497 | −1.09886 | −0.549429 | − | 0.835541i | \(-0.685155\pi\) | ||||
−0.549429 | + | 0.835541i | \(0.685155\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.1652 | −1.04757 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.0129 | −1.21908 | −0.609538 | − | 0.792757i | \(-0.708645\pi\) | ||||
−0.609538 | + | 0.792757i | \(0.708645\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.38170 | −0.197342 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.4383 | 0.783793 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.6939 | 0.881621 | 0.440810 | − | 0.897600i | \(-0.354691\pi\) | ||||
0.440810 | + | 0.897600i | \(0.354691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.7354 | −0.524300 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.561980 | −0.0250574 | −0.0125287 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125287 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.48204 | 0.332946 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.2077 | −0.630985 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.6989 | 0.784490 | 0.392245 | − | 0.919861i | \(-0.371699\pi\) | ||||
0.392245 | + | 0.919861i | \(0.371699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.63482 | 0.248783 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.7234 | 0.825052 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 61.7051 | 2.71379 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.38230 | −0.411837 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.3035 | −1.76573 | −0.882863 | − | 0.469630i | \(-0.844387\pi\) | ||||
−0.882863 | + | 0.469630i | \(0.844387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.95670 | −0.0855606 | −0.0427803 | − | 0.999085i | \(-0.513622\pi\) | ||||
−0.0427803 | + | 0.999085i | \(0.513622\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 59.2499 | 2.58097 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0222 | 1.00097 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6959 | 0.550954 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.10434 | −0.134464 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.97677 | −0.301632 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.4241 | 1.18344 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.0688 | −1.33575 | −0.667877 | − | 0.744272i | \(-0.732797\pi\) | ||||
−0.667877 | + | 0.744272i | \(0.732797\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.3648 | −0.573538 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 41.4621 | 1.77604 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.8556 | 1.57583 | 0.787917 | − | 0.615782i | \(-0.211160\pi\) | ||||
0.787917 | + | 0.615782i | \(0.211160\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.1990 | −0.605998 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.707720 | −0.0301499 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.5606 | −0.702956 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.2272 | 0.984167 | 0.492083 | − | 0.870548i | \(-0.336236\pi\) | ||||
0.492083 | + | 0.870548i | \(0.336236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.95291 | 0.0825994 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −41.4839 | −1.75145 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.0547 | −1.01378 | −0.506891 | − | 0.862010i | \(-0.669206\pi\) | ||||
−0.506891 | + | 0.862010i | \(0.669206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.07576 | 0.0873281 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.5761 | −1.23989 | −0.619946 | − | 0.784644i | \(-0.712846\pi\) | ||||
−0.619946 | + | 0.784644i | \(0.712846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.4925 | −1.10867 | −0.554337 | − | 0.832292i | \(-0.687028\pi\) | ||||
−0.554337 | + | 0.832292i | \(0.687028\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.5078 | 0.814949 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.4757 | 0.979006 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.5816 | −1.06497 | −0.532487 | − | 0.846438i | \(-0.678743\pi\) | ||||
−0.532487 | + | 0.846438i | \(0.678743\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.0729 | −0.875759 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.45388 | 0.184461 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.41927 | −0.224059 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.2213 | −1.12354 | −0.561771 | − | 0.827293i | \(-0.689880\pi\) | ||||
−0.561771 | + | 0.827293i | \(0.689880\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.56989 | 0.394320 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.974916 | 0.0401027 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.90598 | −0.0782690 | −0.0391345 | − | 0.999234i | \(-0.512460\pi\) | ||||
−0.0391345 | + | 0.999234i | \(0.512460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.2915 | 0.789548 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.0500 | −0.819221 | −0.409610 | − | 0.912261i | \(-0.634335\pi\) | ||||
−0.409610 | + | 0.912261i | \(0.634335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.6961 | 0.599466 | 0.299733 | − | 0.954023i | \(-0.403102\pi\) | ||||
0.299733 | + | 0.954023i | \(0.403102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.38829 | −0.0972589 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.5654 | −1.64922 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.4800 | −0.953025 | −0.476512 | − | 0.879168i | \(-0.658099\pi\) | ||||
−0.476512 | + | 0.879168i | \(0.658099\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.1760 | −0.775777 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.3278 | 1.10376 | 0.551880 | − | 0.833924i | \(-0.313911\pi\) | ||||
0.551880 | + | 0.833924i | \(0.313911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.80410 | −0.314692 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.5796 | −1.02980 | −0.514898 | − | 0.857252i | \(-0.672170\pi\) | ||||
−0.514898 | + | 0.857252i | \(0.672170\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.49116 | −0.0599350 | −0.0299675 | − | 0.999551i | \(-0.509540\pi\) | ||||
−0.0299675 | + | 0.999551i | \(0.509540\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −38.2264 | −1.53397 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3275 | −1.21310 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.70036 | −0.267587 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −26.2762 | −1.04770 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0819 | −0.879066 | −0.439533 | − | 0.898226i | \(-0.644856\pi\) | ||||
−0.439533 | + | 0.898226i | \(0.644856\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.9215 | −1.10978 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.4034 | 1.00810 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.9051 | 0.589638 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.80334 | −0.110725 | −0.0553627 | − | 0.998466i | \(-0.517632\pi\) | ||||
−0.0553627 | + | 0.998466i | \(0.517632\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.0640 | 1.06730 | 0.533649 | − | 0.845706i | \(-0.320820\pi\) | ||||
0.533649 | + | 0.845706i | \(0.320820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.90949 | 0.193311 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.37572 | −0.211341 | −0.105671 | − | 0.994401i | \(-0.533699\pi\) | ||||
−0.105671 | + | 0.994401i | \(0.533699\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −52.8277 | −2.07367 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.1250 | −1.10062 | −0.550308 | − | 0.834962i | \(-0.685490\pi\) | ||||
−0.550308 | + | 0.834962i | \(0.685490\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.0341 | −0.704649 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.41064 | −0.328130 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.3753 | 1.37802 | 0.689012 | − | 0.724750i | \(-0.258045\pi\) | ||||
0.689012 | + | 0.724750i | \(0.258045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −43.4717 | −1.69085 | −0.845426 | − | 0.534093i | \(-0.820653\pi\) | ||||
−0.845426 | + | 0.534093i | \(0.820653\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.8919 | 0.500679 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.80115 | 0.185901 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.08171 | −0.312457 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59.0821 | 2.28084 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.7175 | 0.682961 | 0.341481 | − | 0.939889i | \(-0.389072\pi\) | ||||
0.341481 | + | 0.939889i | \(0.389072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.4991 | −0.750522 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.8447 | −1.72352 | −0.861761 | − | 0.507314i | \(-0.830638\pi\) | ||||
−0.861761 | + | 0.507314i | \(0.830638\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5527 | −0.404380 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.0471 | −1.14972 | −0.574861 | − | 0.818251i | \(-0.694944\pi\) | ||||
−0.574861 | + | 0.818251i | \(0.694944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −51.8802 | −1.98224 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.4600 | 1.46734 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.38412 | −0.0527309 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.4930 | 0.703508 | 0.351754 | − | 0.936092i | \(-0.385585\pi\) | ||||
0.351754 | + | 0.936092i | \(0.385585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44.0620 | −1.67137 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.3826 | −0.469023 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.08228 | 0.154406 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.5282 | −1.00196 | −0.500978 | − | 0.865460i | \(-0.667026\pi\) | ||||
−0.500978 | + | 0.865460i | \(0.667026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.24407 | −0.160068 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −48.2071 | −1.81558 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.9319 | 1.42456 | 0.712281 | − | 0.701894i | \(-0.247662\pi\) | ||||
0.712281 | + | 0.701894i | \(0.247662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.3289 | −0.762393 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −64.9218 | −2.43134 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.5496 | 0.843309 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.3895 | 0.462694 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.431495 | 0.0160921 | 0.00804603 | − | 0.999968i | \(-0.497439\pi\) | ||||
0.00804603 | + | 0.999968i | \(0.497439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.1253 | 0.450944 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44905 | 0.0909554 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.14690 | 0.116712 | 0.0583560 | − | 0.998296i | \(-0.481414\pi\) | ||||
0.0583560 | + | 0.998296i | \(0.481414\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.4287 | 1.01588 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.78977 | 0.288115 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7044 | 0.543119 | 0.271559 | − | 0.962422i | \(-0.412461\pi\) | ||||
0.271559 | + | 0.962422i | \(0.412461\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.93772 | 0.366061 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.9990 | −0.551747 | −0.275873 | − | 0.961194i | \(-0.588967\pi\) | ||||
−0.275873 | + | 0.961194i | \(0.588967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.08226 | 0.0764937 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.3454 | −1.14995 | −0.574975 | − | 0.818171i | \(-0.694988\pi\) | ||||
−0.574975 | + | 0.818171i | \(0.694988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.0488 | −0.917717 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.593228 | −0.0217051 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.43909 | 0.161985 | 0.0809923 | − | 0.996715i | \(-0.474191\pi\) | ||||
0.0809923 | + | 0.996715i | \(0.474191\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.90417 | 0.142276 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50.2155 | −1.82753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.60936 | 0.276567 | 0.138283 | − | 0.990393i | \(-0.455841\pi\) | ||||
0.138283 | + | 0.990393i | \(0.455841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 45.4550 | 1.64991 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.4829 | −0.488755 | −0.244378 | − | 0.969680i | \(-0.578584\pi\) | ||||
−0.244378 | + | 0.969680i | \(0.578584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −21.6163 | −0.781541 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.4172 | 0.592789 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3561 | −0.770121 | −0.385061 | − | 0.922891i | \(-0.625819\pi\) | ||||
−0.385061 | + | 0.922891i | \(0.625819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.7324 | −1.10680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.4207 | 1.48980 | 0.744900 | − | 0.667176i | \(-0.232497\pi\) | ||||
0.744900 | + | 0.667176i | \(0.232497\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.1164 | −1.18957 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.00000 | −0.0716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −62.0204 | −2.21927 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.98787 | −0.142515 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49.3012 | −1.75964 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.3559 | 1.29595 | 0.647974 | − | 0.761662i | \(-0.275616\pi\) | ||||
0.647974 | + | 0.761662i | \(0.275616\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.7045 | 0.843901 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.3608 | −0.652013 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.47959 | −0.123408 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.65901 | −0.306718 | −0.153359 | − | 0.988171i | \(-0.549009\pi\) | ||||
−0.153359 | + | 0.988171i | \(0.549009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −76.4890 | −2.70599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.05766 | −0.143371 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.9968 | 1.23501 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3247 | 0.539453 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.1306 | −1.27028 | −0.635142 | − | 0.772395i | \(-0.719059\pi\) | ||||
−0.635142 | + | 0.772395i | \(0.719059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.7940 | −1.08133 | −0.540663 | − | 0.841240i | \(-0.681826\pi\) | ||||
−0.540663 | + | 0.841240i | \(0.681826\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.77361 | 0.237561 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 50.2272 | 1.75938 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.25818 | 0.0440182 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.3877 | 0.432333 | 0.216166 | − | 0.976357i | \(-0.430645\pi\) | ||||
0.216166 | + | 0.976357i | \(0.430645\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.475455 | −0.0165733 | −0.00828665 | − | 0.999966i | \(-0.502638\pi\) | ||||
−0.00828665 | + | 0.999966i | \(0.502638\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.1864 | 0.807248 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8510 | 1.03802 | 0.519010 | − | 0.854768i | \(-0.326301\pi\) | ||||
0.519010 | + | 0.854768i | \(0.326301\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.0129 | −1.04239 | −0.521196 | − | 0.853437i | \(-0.674514\pi\) | ||||
−0.521196 | + | 0.853437i | \(0.674514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.66199 | 0.300481 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.4449 | 0.880558 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 53.9246 | 1.86391 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.3155 | 1.18470 | 0.592351 | − | 0.805680i | \(-0.298200\pi\) | ||||
0.592351 | + | 0.805680i | \(0.298200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4991 | −0.982729 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.8011 | −0.475334 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.8053 | 1.05973 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.5804 | 1.01520 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.7916 | 0.986964 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.59556 | 0.225828 | 0.112914 | − | 0.993605i | \(-0.463982\pi\) | ||||
0.112914 | + | 0.993605i | \(0.463982\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.49141 | −0.119404 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.7037 | −1.52705 | −0.763525 | − | 0.645779i | \(-0.776533\pi\) | ||||
−0.763525 | + | 0.645779i | \(0.776533\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.0696 | 1.81071 | 0.905356 | − | 0.424653i | \(-0.139604\pi\) | ||||
0.905356 | + | 0.424653i | \(0.139604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.4050 | −1.30732 | −0.653661 | − | 0.756788i | \(-0.726768\pi\) | ||||
−0.653661 | + | 0.756788i | \(0.726768\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.3428 | 0.691677 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.6172 | 0.971893 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 84.5887 | 2.86948 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.08833 | −0.104644 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.0856 | −0.409037 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.7329 | 0.700099 | 0.350050 | − | 0.936731i | \(-0.386165\pi\) | ||||
0.350050 | + | 0.936731i | \(0.386165\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.5409 | 0.928933 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3452 | −1.32557 | −0.662786 | − | 0.748809i | \(-0.730626\pi\) | ||||
−0.662786 | + | 0.748809i | \(0.730626\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.7816 | 0.901272 | 0.450636 | − | 0.892708i | \(-0.351197\pi\) | ||||
0.450636 | + | 0.892708i | \(0.351197\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41.2716 | 1.38733 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.93418 | −0.333557 | −0.166779 | − | 0.985994i | \(-0.553337\pi\) | ||||
−0.166779 | + | 0.985994i | \(0.553337\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.7696 | −0.662305 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.3543 | −0.413421 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −59.4613 | −1.98757 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.1260 | −0.471653 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.77280 | −0.225886 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.52098 | −0.183931 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.9777 | 0.963252 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.1589 | 0.636162 | 0.318081 | − | 0.948064i | \(-0.396962\pi\) | ||||
0.318081 | + | 0.948064i | \(0.396962\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.08764 | 0.102411 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53.0363 | −1.75717 | −0.878586 | − | 0.477584i | \(-0.841513\pi\) | ||||
−0.878586 | + | 0.477584i | \(0.841513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.46843 | 0.0816931 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46.1579 | −1.52593 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.7974 | 1.41176 | 0.705878 | − | 0.708334i | \(-0.250553\pi\) | ||||
0.705878 | + | 0.708334i | \(0.250553\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.9539 | −0.954065 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.2740 | 0.634411 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.6865 | 0.482889 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.72666 | 0.253777 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.3584 | −0.667938 | −0.333969 | − | 0.942584i | \(-0.608388\pi\) | ||||
−0.333969 | + | 0.942584i | \(0.608388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.7282 | 1.03873 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 89.9459 | 2.94154 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.5032 | −1.51919 | −0.759596 | − | 0.650395i | \(-0.774604\pi\) | ||||
−0.759596 | + | 0.650395i | \(0.774604\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.8346 | 1.16942 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.8300 | 1.29842 | 0.649211 | − | 0.760609i | \(-0.275099\pi\) | ||||
0.649211 | + | 0.760609i | \(0.275099\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5679 | 0.441833 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.34847 | −0.238793 | −0.119397 | − | 0.992847i | \(-0.538096\pi\) | ||||
−0.119397 | + | 0.992847i | \(0.538096\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.8759 | −0.353046 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.3202 | −1.17776 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.7557 | 0.899094 | 0.449547 | − | 0.893257i | \(-0.351585\pi\) | ||||
0.449547 | + | 0.893257i | \(0.351585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.2970 | −1.36870 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.74198 | 0.153286 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.5828 | 1.95428 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.87913 | −0.0927786 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.6905 | 1.47083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.6002 | −1.36993 | −0.684965 | − | 0.728576i | \(-0.740183\pi\) | ||||
−0.684965 | + | 0.728576i | \(0.740183\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.30570 | 0.266818 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.4695 | −1.39500 | −0.697501 | − | 0.716584i | \(-0.745705\pi\) | ||||
−0.697501 | + | 0.716584i | \(0.745705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.20560 | −0.230764 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.1705 | −0.805275 | −0.402637 | − | 0.915360i | \(-0.631906\pi\) | ||||
−0.402637 | + | 0.915360i | \(0.631906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.8840 | 0.539615 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.1103 | 0.546291 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.9857 | 1.05208 | 0.526041 | − | 0.850459i | \(-0.323676\pi\) | ||||
0.526041 | + | 0.850459i | \(0.323676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.11383 | −0.0673521 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.53547 | −0.271412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.2891 | 1.31159 | 0.655796 | − | 0.754938i | \(-0.272333\pi\) | ||||
0.655796 | + | 0.754938i | \(0.272333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.21239 | 0.133676 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.8281 | −1.32604 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5184 | 0.333122 | 0.166561 | − | 0.986031i | \(-0.446734\pi\) | ||||
0.166561 | + | 0.986031i | \(0.446734\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.9145 | −0.756622 |
(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 | 7448.2.a.br.1.6 | 8 | ||
7.3 | odd | 6 | 1064.2.q.n.457.6 | yes | 16 | ||
7.5 | odd | 6 | 1064.2.q.n.305.6 | ✓ | 16 | ||
7.6 | odd | 2 | 7448.2.a.bq.1.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1064.2.q.n.305.6 | ✓ | 16 | 7.5 | odd | 6 | ||
1064.2.q.n.457.6 | yes | 16 | 7.3 | odd | 6 | ||
7448.2.a.bq.1.3 | 8 | 7.6 | odd | 2 | |||
7448.2.a.br.1.6 | 8 | 1.1 | even | 1 | trivial |