Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6014,2,Mod(1,6014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6014 = 2 \cdot 31 \cdot 97 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6014.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: | \(48.0220317756\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.253397 | 0.146299 | 0.0731495 | − | 0.997321i | \(-0.476695\pi\) | ||||
0.0731495 | + | 0.997321i | \(0.476695\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.480250 | −0.214774 | −0.107387 | − | 0.994217i | \(-0.534248\pi\) | ||||
−0.107387 | + | 0.994217i | \(0.534248\pi\) | |||||||
\(6\) | −0.253397 | −0.103449 | ||||||||
\(7\) | 2.09789 | 0.792928 | 0.396464 | − | 0.918050i | \(-0.370237\pi\) | ||||
0.396464 | + | 0.918050i | \(0.370237\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.93579 | −0.978597 | ||||||||
\(10\) | 0.480250 | 0.151868 | ||||||||
\(11\) | −0.665471 | −0.200647 | −0.100324 | − | 0.994955i | \(-0.531988\pi\) | ||||
−0.100324 | + | 0.994955i | \(0.531988\pi\) | |||||||
\(12\) | 0.253397 | 0.0731495 | ||||||||
\(13\) | 2.39046 | 0.662995 | 0.331497 | − | 0.943456i | \(-0.392446\pi\) | ||||
0.331497 | + | 0.943456i | \(0.392446\pi\) | |||||||
\(14\) | −2.09789 | −0.560685 | ||||||||
\(15\) | −0.121694 | −0.0314213 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.40960 | −0.826951 | −0.413475 | − | 0.910515i | \(-0.635685\pi\) | ||||
−0.413475 | + | 0.910515i | \(0.635685\pi\) | |||||||
\(18\) | 2.93579 | 0.691972 | ||||||||
\(19\) | −1.80607 | −0.414341 | −0.207170 | − | 0.978305i | \(-0.566425\pi\) | ||||
−0.207170 | + | 0.978305i | \(0.566425\pi\) | |||||||
\(20\) | −0.480250 | −0.107387 | ||||||||
\(21\) | 0.531600 | 0.116005 | ||||||||
\(22\) | 0.665471 | 0.141879 | ||||||||
\(23\) | 7.76002 | 1.61808 | 0.809038 | − | 0.587757i | \(-0.199989\pi\) | ||||
0.809038 | + | 0.587757i | \(0.199989\pi\) | |||||||
\(24\) | −0.253397 | −0.0517245 | ||||||||
\(25\) | −4.76936 | −0.953872 | ||||||||
\(26\) | −2.39046 | −0.468808 | ||||||||
\(27\) | −1.50411 | −0.289467 | ||||||||
\(28\) | 2.09789 | 0.396464 | ||||||||
\(29\) | −4.82413 | −0.895818 | −0.447909 | − | 0.894079i | \(-0.647831\pi\) | ||||
−0.447909 | + | 0.894079i | \(0.647831\pi\) | |||||||
\(30\) | 0.121694 | 0.0222182 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.168629 | −0.0293545 | ||||||||
\(34\) | 3.40960 | 0.584742 | ||||||||
\(35\) | −1.00751 | −0.170300 | ||||||||
\(36\) | −2.93579 | −0.489298 | ||||||||
\(37\) | 5.29145 | 0.869909 | 0.434954 | − | 0.900453i | \(-0.356765\pi\) | ||||
0.434954 | + | 0.900453i | \(0.356765\pi\) | |||||||
\(38\) | 1.80607 | 0.292983 | ||||||||
\(39\) | 0.605737 | 0.0969955 | ||||||||
\(40\) | 0.480250 | 0.0759341 | ||||||||
\(41\) | 6.01318 | 0.939101 | 0.469550 | − | 0.882906i | \(-0.344416\pi\) | ||||
0.469550 | + | 0.882906i | \(0.344416\pi\) | |||||||
\(42\) | −0.531600 | −0.0820277 | ||||||||
\(43\) | −3.79195 | −0.578266 | −0.289133 | − | 0.957289i | \(-0.593367\pi\) | ||||
−0.289133 | + | 0.957289i | \(0.593367\pi\) | |||||||
\(44\) | −0.665471 | −0.100324 | ||||||||
\(45\) | 1.40991 | 0.210177 | ||||||||
\(46\) | −7.76002 | −1.14415 | ||||||||
\(47\) | 7.00498 | 1.02178 | 0.510891 | − | 0.859646i | \(-0.329316\pi\) | ||||
0.510891 | + | 0.859646i | \(0.329316\pi\) | |||||||
\(48\) | 0.253397 | 0.0365748 | ||||||||
\(49\) | −2.59886 | −0.371265 | ||||||||
\(50\) | 4.76936 | 0.674489 | ||||||||
\(51\) | −0.863985 | −0.120982 | ||||||||
\(52\) | 2.39046 | 0.331497 | ||||||||
\(53\) | −1.21348 | −0.166684 | −0.0833422 | − | 0.996521i | \(-0.526559\pi\) | ||||
−0.0833422 | + | 0.996521i | \(0.526559\pi\) | |||||||
\(54\) | 1.50411 | 0.204684 | ||||||||
\(55\) | 0.319592 | 0.0430938 | ||||||||
\(56\) | −2.09789 | −0.280342 | ||||||||
\(57\) | −0.457653 | −0.0606177 | ||||||||
\(58\) | 4.82413 | 0.633439 | ||||||||
\(59\) | 8.41980 | 1.09617 | 0.548083 | − | 0.836424i | \(-0.315358\pi\) | ||||
0.548083 | + | 0.836424i | \(0.315358\pi\) | |||||||
\(60\) | −0.121694 | −0.0157106 | ||||||||
\(61\) | −4.49726 | −0.575815 | −0.287908 | − | 0.957658i | \(-0.592960\pi\) | ||||
−0.287908 | + | 0.957658i | \(0.592960\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | −6.15897 | −0.775957 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.14802 | −0.142394 | ||||||||
\(66\) | 0.168629 | 0.0207568 | ||||||||
\(67\) | −15.5489 | −1.89960 | −0.949801 | − | 0.312854i | \(-0.898715\pi\) | ||||
−0.949801 | + | 0.312854i | \(0.898715\pi\) | |||||||
\(68\) | −3.40960 | −0.413475 | ||||||||
\(69\) | 1.96637 | 0.236723 | ||||||||
\(70\) | 1.00751 | 0.120421 | ||||||||
\(71\) | −12.1087 | −1.43704 | −0.718518 | − | 0.695508i | \(-0.755179\pi\) | ||||
−0.718518 | + | 0.695508i | \(0.755179\pi\) | |||||||
\(72\) | 2.93579 | 0.345986 | ||||||||
\(73\) | −1.77532 | −0.207785 | −0.103893 | − | 0.994589i | \(-0.533130\pi\) | ||||
−0.103893 | + | 0.994589i | \(0.533130\pi\) | |||||||
\(74\) | −5.29145 | −0.615118 | ||||||||
\(75\) | −1.20854 | −0.139551 | ||||||||
\(76\) | −1.80607 | −0.207170 | ||||||||
\(77\) | −1.39609 | −0.159099 | ||||||||
\(78\) | −0.605737 | −0.0685862 | ||||||||
\(79\) | −9.47170 | −1.06565 | −0.532824 | − | 0.846226i | \(-0.678869\pi\) | ||||
−0.532824 | + | 0.846226i | \(0.678869\pi\) | |||||||
\(80\) | −0.480250 | −0.0536935 | ||||||||
\(81\) | 8.42623 | 0.936248 | ||||||||
\(82\) | −6.01318 | −0.664044 | ||||||||
\(83\) | −6.01881 | −0.660650 | −0.330325 | − | 0.943867i | \(-0.607158\pi\) | ||||
−0.330325 | + | 0.943867i | \(0.607158\pi\) | |||||||
\(84\) | 0.531600 | 0.0580023 | ||||||||
\(85\) | 1.63746 | 0.177608 | ||||||||
\(86\) | 3.79195 | 0.408896 | ||||||||
\(87\) | −1.22242 | −0.131057 | ||||||||
\(88\) | 0.665471 | 0.0709395 | ||||||||
\(89\) | 14.3028 | 1.51610 | 0.758049 | − | 0.652198i | \(-0.226153\pi\) | ||||
0.758049 | + | 0.652198i | \(0.226153\pi\) | |||||||
\(90\) | −1.40991 | −0.148618 | ||||||||
\(91\) | 5.01493 | 0.525707 | ||||||||
\(92\) | 7.76002 | 0.809038 | ||||||||
\(93\) | 0.253397 | 0.0262761 | ||||||||
\(94\) | −7.00498 | −0.722508 | ||||||||
\(95\) | 0.867364 | 0.0889897 | ||||||||
\(96\) | −0.253397 | −0.0258623 | ||||||||
\(97\) | 1.00000 | 0.101535 | ||||||||
\(98\) | 2.59886 | 0.262524 | ||||||||
\(99\) | 1.95368 | 0.196353 | ||||||||
\(100\) | −4.76936 | −0.476936 | ||||||||
\(101\) | 16.3076 | 1.62267 | 0.811333 | − | 0.584584i | \(-0.198742\pi\) | ||||
0.811333 | + | 0.584584i | \(0.198742\pi\) | |||||||
\(102\) | 0.863985 | 0.0855473 | ||||||||
\(103\) | −4.25960 | −0.419711 | −0.209855 | − | 0.977732i | \(-0.567299\pi\) | ||||
−0.209855 | + | 0.977732i | \(0.567299\pi\) | |||||||
\(104\) | −2.39046 | −0.234404 | ||||||||
\(105\) | −0.255301 | −0.0249148 | ||||||||
\(106\) | 1.21348 | 0.117864 | ||||||||
\(107\) | −16.8783 | −1.63169 | −0.815844 | − | 0.578272i | \(-0.803727\pi\) | ||||
−0.815844 | + | 0.578272i | \(0.803727\pi\) | |||||||
\(108\) | −1.50411 | −0.144733 | ||||||||
\(109\) | 9.71703 | 0.930723 | 0.465361 | − | 0.885121i | \(-0.345924\pi\) | ||||
0.465361 | + | 0.885121i | \(0.345924\pi\) | |||||||
\(110\) | −0.319592 | −0.0304719 | ||||||||
\(111\) | 1.34084 | 0.127267 | ||||||||
\(112\) | 2.09789 | 0.198232 | ||||||||
\(113\) | −8.10723 | −0.762664 | −0.381332 | − | 0.924438i | \(-0.624535\pi\) | ||||
−0.381332 | + | 0.924438i | \(0.624535\pi\) | |||||||
\(114\) | 0.457653 | 0.0428632 | ||||||||
\(115\) | −3.72675 | −0.347521 | ||||||||
\(116\) | −4.82413 | −0.447909 | ||||||||
\(117\) | −7.01789 | −0.648804 | ||||||||
\(118\) | −8.41980 | −0.775106 | ||||||||
\(119\) | −7.15298 | −0.655712 | ||||||||
\(120\) | 0.121694 | 0.0111091 | ||||||||
\(121\) | −10.5571 | −0.959741 | ||||||||
\(122\) | 4.49726 | 0.407163 | ||||||||
\(123\) | 1.52372 | 0.137390 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 4.69173 | 0.419641 | ||||||||
\(126\) | 6.15897 | 0.548684 | ||||||||
\(127\) | −14.5625 | −1.29221 | −0.646107 | − | 0.763247i | \(-0.723604\pi\) | ||||
−0.646107 | + | 0.763247i | \(0.723604\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.960870 | −0.0845998 | ||||||||
\(130\) | 1.14802 | 0.100688 | ||||||||
\(131\) | 13.9631 | 1.21996 | 0.609982 | − | 0.792416i | \(-0.291177\pi\) | ||||
0.609982 | + | 0.792416i | \(0.291177\pi\) | |||||||
\(132\) | −0.168629 | −0.0146772 | ||||||||
\(133\) | −3.78894 | −0.328542 | ||||||||
\(134\) | 15.5489 | 1.34322 | ||||||||
\(135\) | 0.722350 | 0.0621700 | ||||||||
\(136\) | 3.40960 | 0.292371 | ||||||||
\(137\) | 9.13671 | 0.780602 | 0.390301 | − | 0.920687i | \(-0.372371\pi\) | ||||
0.390301 | + | 0.920687i | \(0.372371\pi\) | |||||||
\(138\) | −1.96637 | −0.167388 | ||||||||
\(139\) | −1.94326 | −0.164825 | −0.0824125 | − | 0.996598i | \(-0.526262\pi\) | ||||
−0.0824125 | + | 0.996598i | \(0.526262\pi\) | |||||||
\(140\) | −1.00751 | −0.0851502 | ||||||||
\(141\) | 1.77504 | 0.149486 | ||||||||
\(142\) | 12.1087 | 1.01614 | ||||||||
\(143\) | −1.59078 | −0.133028 | ||||||||
\(144\) | −2.93579 | −0.244649 | ||||||||
\(145\) | 2.31679 | 0.192399 | ||||||||
\(146\) | 1.77532 | 0.146926 | ||||||||
\(147\) | −0.658543 | −0.0543157 | ||||||||
\(148\) | 5.29145 | 0.434954 | ||||||||
\(149\) | −17.7125 | −1.45106 | −0.725532 | − | 0.688189i | \(-0.758406\pi\) | ||||
−0.725532 | + | 0.688189i | \(0.758406\pi\) | |||||||
\(150\) | 1.20854 | 0.0986772 | ||||||||
\(151\) | −9.88828 | −0.804697 | −0.402348 | − | 0.915487i | \(-0.631806\pi\) | ||||
−0.402348 | + | 0.915487i | \(0.631806\pi\) | |||||||
\(152\) | 1.80607 | 0.146492 | ||||||||
\(153\) | 10.0099 | 0.809251 | ||||||||
\(154\) | 1.39609 | 0.112500 | ||||||||
\(155\) | −0.480250 | −0.0385746 | ||||||||
\(156\) | 0.605737 | 0.0484978 | ||||||||
\(157\) | −8.35754 | −0.667004 | −0.333502 | − | 0.942749i | \(-0.608230\pi\) | ||||
−0.333502 | + | 0.942749i | \(0.608230\pi\) | |||||||
\(158\) | 9.47170 | 0.753528 | ||||||||
\(159\) | −0.307493 | −0.0243858 | ||||||||
\(160\) | 0.480250 | 0.0379671 | ||||||||
\(161\) | 16.2797 | 1.28302 | ||||||||
\(162\) | −8.42623 | −0.662027 | ||||||||
\(163\) | 2.88088 | 0.225648 | 0.112824 | − | 0.993615i | \(-0.464010\pi\) | ||||
0.112824 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(164\) | 6.01318 | 0.469550 | ||||||||
\(165\) | 0.0809839 | 0.00630458 | ||||||||
\(166\) | 6.01881 | 0.467150 | ||||||||
\(167\) | 6.55783 | 0.507460 | 0.253730 | − | 0.967275i | \(-0.418343\pi\) | ||||
0.253730 | + | 0.967275i | \(0.418343\pi\) | |||||||
\(168\) | −0.531600 | −0.0410138 | ||||||||
\(169\) | −7.28569 | −0.560438 | ||||||||
\(170\) | −1.63746 | −0.125588 | ||||||||
\(171\) | 5.30224 | 0.405472 | ||||||||
\(172\) | −3.79195 | −0.289133 | ||||||||
\(173\) | 0.606282 | 0.0460948 | 0.0230474 | − | 0.999734i | \(-0.492663\pi\) | ||||
0.0230474 | + | 0.999734i | \(0.492663\pi\) | |||||||
\(174\) | 1.22242 | 0.0926715 | ||||||||
\(175\) | −10.0056 | −0.756352 | ||||||||
\(176\) | −0.665471 | −0.0501618 | ||||||||
\(177\) | 2.13356 | 0.160368 | ||||||||
\(178\) | −14.3028 | −1.07204 | ||||||||
\(179\) | −7.22701 | −0.540172 | −0.270086 | − | 0.962836i | \(-0.587052\pi\) | ||||
−0.270086 | + | 0.962836i | \(0.587052\pi\) | |||||||
\(180\) | 1.40991 | 0.105089 | ||||||||
\(181\) | −22.3379 | −1.66036 | −0.830180 | − | 0.557496i | \(-0.811762\pi\) | ||||
−0.830180 | + | 0.557496i | \(0.811762\pi\) | |||||||
\(182\) | −5.01493 | −0.371731 | ||||||||
\(183\) | −1.13959 | −0.0842412 | ||||||||
\(184\) | −7.76002 | −0.572076 | ||||||||
\(185\) | −2.54122 | −0.186834 | ||||||||
\(186\) | −0.253397 | −0.0185800 | ||||||||
\(187\) | 2.26899 | 0.165925 | ||||||||
\(188\) | 7.00498 | 0.510891 | ||||||||
\(189\) | −3.15547 | −0.229526 | ||||||||
\(190\) | −0.867364 | −0.0629252 | ||||||||
\(191\) | −17.6757 | −1.27897 | −0.639486 | − | 0.768803i | \(-0.720853\pi\) | ||||
−0.639486 | + | 0.768803i | \(0.720853\pi\) | |||||||
\(192\) | 0.253397 | 0.0182874 | ||||||||
\(193\) | −8.72407 | −0.627973 | −0.313986 | − | 0.949428i | \(-0.601665\pi\) | ||||
−0.313986 | + | 0.949428i | \(0.601665\pi\) | |||||||
\(194\) | −1.00000 | −0.0717958 | ||||||||
\(195\) | −0.290905 | −0.0208321 | ||||||||
\(196\) | −2.59886 | −0.185633 | ||||||||
\(197\) | −5.40889 | −0.385368 | −0.192684 | − | 0.981261i | \(-0.561719\pi\) | ||||
−0.192684 | + | 0.981261i | \(0.561719\pi\) | |||||||
\(198\) | −1.95368 | −0.138842 | ||||||||
\(199\) | −27.9355 | −1.98029 | −0.990147 | − | 0.140033i | \(-0.955279\pi\) | ||||
−0.990147 | + | 0.140033i | \(0.955279\pi\) | |||||||
\(200\) | 4.76936 | 0.337245 | ||||||||
\(201\) | −3.94006 | −0.277910 | ||||||||
\(202\) | −16.3076 | −1.14740 | ||||||||
\(203\) | −10.1205 | −0.710319 | ||||||||
\(204\) | −0.863985 | −0.0604910 | ||||||||
\(205\) | −2.88783 | −0.201695 | ||||||||
\(206\) | 4.25960 | 0.296780 | ||||||||
\(207\) | −22.7818 | −1.58344 | ||||||||
\(208\) | 2.39046 | 0.165749 | ||||||||
\(209\) | 1.20189 | 0.0831363 | ||||||||
\(210\) | 0.255301 | 0.0176174 | ||||||||
\(211\) | 19.7703 | 1.36104 | 0.680522 | − | 0.732728i | \(-0.261753\pi\) | ||||
0.680522 | + | 0.732728i | \(0.261753\pi\) | |||||||
\(212\) | −1.21348 | −0.0833422 | ||||||||
\(213\) | −3.06831 | −0.210237 | ||||||||
\(214\) | 16.8783 | 1.15378 | ||||||||
\(215\) | 1.82108 | 0.124197 | ||||||||
\(216\) | 1.50411 | 0.102342 | ||||||||
\(217\) | 2.09789 | 0.142414 | ||||||||
\(218\) | −9.71703 | −0.658120 | ||||||||
\(219\) | −0.449861 | −0.0303988 | ||||||||
\(220\) | 0.319592 | 0.0215469 | ||||||||
\(221\) | −8.15053 | −0.548264 | ||||||||
\(222\) | −1.34084 | −0.0899912 | ||||||||
\(223\) | −2.47720 | −0.165886 | −0.0829428 | − | 0.996554i | \(-0.526432\pi\) | ||||
−0.0829428 | + | 0.996554i | \(0.526432\pi\) | |||||||
\(224\) | −2.09789 | −0.140171 | ||||||||
\(225\) | 14.0018 | 0.933456 | ||||||||
\(226\) | 8.10723 | 0.539285 | ||||||||
\(227\) | 21.2988 | 1.41365 | 0.706827 | − | 0.707387i | \(-0.250126\pi\) | ||||
0.706827 | + | 0.707387i | \(0.250126\pi\) | |||||||
\(228\) | −0.457653 | −0.0303088 | ||||||||
\(229\) | 10.3502 | 0.683962 | 0.341981 | − | 0.939707i | \(-0.388902\pi\) | ||||
0.341981 | + | 0.939707i | \(0.388902\pi\) | |||||||
\(230\) | 3.72675 | 0.245734 | ||||||||
\(231\) | −0.353764 | −0.0232760 | ||||||||
\(232\) | 4.82413 | 0.316720 | ||||||||
\(233\) | 7.70459 | 0.504745 | 0.252372 | − | 0.967630i | \(-0.418789\pi\) | ||||
0.252372 | + | 0.967630i | \(0.418789\pi\) | |||||||
\(234\) | 7.01789 | 0.458774 | ||||||||
\(235\) | −3.36414 | −0.219452 | ||||||||
\(236\) | 8.41980 | 0.548083 | ||||||||
\(237\) | −2.40010 | −0.155903 | ||||||||
\(238\) | 7.15298 | 0.463659 | ||||||||
\(239\) | 10.8586 | 0.702387 | 0.351193 | − | 0.936303i | \(-0.385776\pi\) | ||||
0.351193 | + | 0.936303i | \(0.385776\pi\) | |||||||
\(240\) | −0.121694 | −0.00785532 | ||||||||
\(241\) | 20.4943 | 1.32016 | 0.660078 | − | 0.751197i | \(-0.270523\pi\) | ||||
0.660078 | + | 0.751197i | \(0.270523\pi\) | |||||||
\(242\) | 10.5571 | 0.678639 | ||||||||
\(243\) | 6.64753 | 0.426439 | ||||||||
\(244\) | −4.49726 | −0.287908 | ||||||||
\(245\) | 1.24810 | 0.0797382 | ||||||||
\(246\) | −1.52372 | −0.0971491 | ||||||||
\(247\) | −4.31734 | −0.274706 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | −1.52515 | −0.0966525 | ||||||||
\(250\) | −4.69173 | −0.296731 | ||||||||
\(251\) | 15.1004 | 0.953126 | 0.476563 | − | 0.879140i | \(-0.341882\pi\) | ||||
0.476563 | + | 0.879140i | \(0.341882\pi\) | |||||||
\(252\) | −6.15897 | −0.387978 | ||||||||
\(253\) | −5.16407 | −0.324662 | ||||||||
\(254\) | 14.5625 | 0.913733 | ||||||||
\(255\) | 0.414929 | 0.0259838 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.8607 | −0.989362 | −0.494681 | − | 0.869075i | \(-0.664715\pi\) | ||||
−0.494681 | + | 0.869075i | \(0.664715\pi\) | |||||||
\(258\) | 0.960870 | 0.0598211 | ||||||||
\(259\) | 11.1009 | 0.689775 | ||||||||
\(260\) | −1.14802 | −0.0711971 | ||||||||
\(261\) | 14.1626 | 0.876645 | ||||||||
\(262\) | −13.9631 | −0.862644 | ||||||||
\(263\) | −19.7908 | −1.22035 | −0.610177 | − | 0.792266i | \(-0.708901\pi\) | ||||
−0.610177 | + | 0.792266i | \(0.708901\pi\) | |||||||
\(264\) | 0.168629 | 0.0103784 | ||||||||
\(265\) | 0.582774 | 0.0357995 | ||||||||
\(266\) | 3.78894 | 0.232315 | ||||||||
\(267\) | 3.62430 | 0.221804 | ||||||||
\(268\) | −15.5489 | −0.949801 | ||||||||
\(269\) | 8.55109 | 0.521369 | 0.260684 | − | 0.965424i | \(-0.416052\pi\) | ||||
0.260684 | + | 0.965424i | \(0.416052\pi\) | |||||||
\(270\) | −0.722350 | −0.0439608 | ||||||||
\(271\) | −16.8411 | −1.02303 | −0.511513 | − | 0.859275i | \(-0.670915\pi\) | ||||
−0.511513 | + | 0.859275i | \(0.670915\pi\) | |||||||
\(272\) | −3.40960 | −0.206738 | ||||||||
\(273\) | 1.27077 | 0.0769105 | ||||||||
\(274\) | −9.13671 | −0.551969 | ||||||||
\(275\) | 3.17387 | 0.191392 | ||||||||
\(276\) | 1.96637 | 0.118361 | ||||||||
\(277\) | −2.36156 | −0.141892 | −0.0709462 | − | 0.997480i | \(-0.522602\pi\) | ||||
−0.0709462 | + | 0.997480i | \(0.522602\pi\) | |||||||
\(278\) | 1.94326 | 0.116549 | ||||||||
\(279\) | −2.93579 | −0.175761 | ||||||||
\(280\) | 1.00751 | 0.0602103 | ||||||||
\(281\) | 0.346952 | 0.0206974 | 0.0103487 | − | 0.999946i | \(-0.496706\pi\) | ||||
0.0103487 | + | 0.999946i | \(0.496706\pi\) | |||||||
\(282\) | −1.77504 | −0.105702 | ||||||||
\(283\) | 17.4821 | 1.03920 | 0.519602 | − | 0.854408i | \(-0.326080\pi\) | ||||
0.519602 | + | 0.854408i | \(0.326080\pi\) | |||||||
\(284\) | −12.1087 | −0.718518 | ||||||||
\(285\) | 0.219788 | 0.0130191 | ||||||||
\(286\) | 1.59078 | 0.0940650 | ||||||||
\(287\) | 12.6150 | 0.744639 | ||||||||
\(288\) | 2.93579 | 0.172993 | ||||||||
\(289\) | −5.37460 | −0.316153 | ||||||||
\(290\) | −2.31679 | −0.136046 | ||||||||
\(291\) | 0.253397 | 0.0148544 | ||||||||
\(292\) | −1.77532 | −0.103893 | ||||||||
\(293\) | −15.7681 | −0.921179 | −0.460590 | − | 0.887613i | \(-0.652362\pi\) | ||||
−0.460590 | + | 0.887613i | \(0.652362\pi\) | |||||||
\(294\) | 0.658543 | 0.0384070 | ||||||||
\(295\) | −4.04361 | −0.235428 | ||||||||
\(296\) | −5.29145 | −0.307559 | ||||||||
\(297\) | 1.00094 | 0.0580807 | ||||||||
\(298\) | 17.7125 | 1.02606 | ||||||||
\(299\) | 18.5500 | 1.07278 | ||||||||
\(300\) | −1.20854 | −0.0697753 | ||||||||
\(301\) | −7.95509 | −0.458524 | ||||||||
\(302\) | 9.88828 | 0.569007 | ||||||||
\(303\) | 4.13230 | 0.237395 | ||||||||
\(304\) | −1.80607 | −0.103585 | ||||||||
\(305\) | 2.15981 | 0.123670 | ||||||||
\(306\) | −10.0099 | −0.572227 | ||||||||
\(307\) | −8.89454 | −0.507638 | −0.253819 | − | 0.967252i | \(-0.581687\pi\) | ||||
−0.253819 | + | 0.967252i | \(0.581687\pi\) | |||||||
\(308\) | −1.39609 | −0.0795493 | ||||||||
\(309\) | −1.07937 | −0.0614033 | ||||||||
\(310\) | 0.480250 | 0.0272764 | ||||||||
\(311\) | 22.2407 | 1.26116 | 0.630579 | − | 0.776125i | \(-0.282818\pi\) | ||||
0.630579 | + | 0.776125i | \(0.282818\pi\) | |||||||
\(312\) | −0.605737 | −0.0342931 | ||||||||
\(313\) | −19.7898 | −1.11859 | −0.559293 | − | 0.828970i | \(-0.688927\pi\) | ||||
−0.559293 | + | 0.828970i | \(0.688927\pi\) | |||||||
\(314\) | 8.35754 | 0.471643 | ||||||||
\(315\) | 2.95784 | 0.166655 | ||||||||
\(316\) | −9.47170 | −0.532824 | ||||||||
\(317\) | −23.3646 | −1.31228 | −0.656142 | − | 0.754637i | \(-0.727813\pi\) | ||||
−0.656142 | + | 0.754637i | \(0.727813\pi\) | |||||||
\(318\) | 0.307493 | 0.0172433 | ||||||||
\(319\) | 3.21032 | 0.179743 | ||||||||
\(320\) | −0.480250 | −0.0268468 | ||||||||
\(321\) | −4.27692 | −0.238714 | ||||||||
\(322\) | −16.2797 | −0.907230 | ||||||||
\(323\) | 6.15798 | 0.342639 | ||||||||
\(324\) | 8.42623 | 0.468124 | ||||||||
\(325\) | −11.4010 | −0.632412 | ||||||||
\(326\) | −2.88088 | −0.159557 | ||||||||
\(327\) | 2.46227 | 0.136164 | ||||||||
\(328\) | −6.01318 | −0.332022 | ||||||||
\(329\) | 14.6957 | 0.810199 | ||||||||
\(330\) | −0.0809839 | −0.00445801 | ||||||||
\(331\) | 20.1711 | 1.10870 | 0.554352 | − | 0.832282i | \(-0.312966\pi\) | ||||
0.554352 | + | 0.832282i | \(0.312966\pi\) | |||||||
\(332\) | −6.01881 | −0.330325 | ||||||||
\(333\) | −15.5346 | −0.851290 | ||||||||
\(334\) | −6.55783 | −0.358828 | ||||||||
\(335\) | 7.46736 | 0.407986 | ||||||||
\(336\) | 0.531600 | 0.0290012 | ||||||||
\(337\) | −5.83412 | −0.317804 | −0.158902 | − | 0.987294i | \(-0.550795\pi\) | ||||
−0.158902 | + | 0.987294i | \(0.550795\pi\) | |||||||
\(338\) | 7.28569 | 0.396289 | ||||||||
\(339\) | −2.05435 | −0.111577 | ||||||||
\(340\) | 1.63746 | 0.0888038 | ||||||||
\(341\) | −0.665471 | −0.0360373 | ||||||||
\(342\) | −5.30224 | −0.286712 | ||||||||
\(343\) | −20.1373 | −1.08731 | ||||||||
\(344\) | 3.79195 | 0.204448 | ||||||||
\(345\) | −0.944348 | −0.0508420 | ||||||||
\(346\) | −0.606282 | −0.0325939 | ||||||||
\(347\) | −22.8780 | −1.22816 | −0.614078 | − | 0.789246i | \(-0.710472\pi\) | ||||
−0.614078 | + | 0.789246i | \(0.710472\pi\) | |||||||
\(348\) | −1.22242 | −0.0655287 | ||||||||
\(349\) | −1.33157 | −0.0712772 | −0.0356386 | − | 0.999365i | \(-0.511347\pi\) | ||||
−0.0356386 | + | 0.999365i | \(0.511347\pi\) | |||||||
\(350\) | 10.0056 | 0.534822 | ||||||||
\(351\) | −3.59553 | −0.191915 | ||||||||
\(352\) | 0.665471 | 0.0354697 | ||||||||
\(353\) | −10.3020 | −0.548318 | −0.274159 | − | 0.961684i | \(-0.588399\pi\) | ||||
−0.274159 | + | 0.961684i | \(0.588399\pi\) | |||||||
\(354\) | −2.13356 | −0.113397 | ||||||||
\(355\) | 5.81519 | 0.308638 | ||||||||
\(356\) | 14.3028 | 0.758049 | ||||||||
\(357\) | −1.81255 | −0.0959301 | ||||||||
\(358\) | 7.22701 | 0.381960 | ||||||||
\(359\) | −2.16605 | −0.114320 | −0.0571598 | − | 0.998365i | \(-0.518204\pi\) | ||||
−0.0571598 | + | 0.998365i | \(0.518204\pi\) | |||||||
\(360\) | −1.40991 | −0.0743089 | ||||||||
\(361\) | −15.7381 | −0.828322 | ||||||||
\(362\) | 22.3379 | 1.17405 | ||||||||
\(363\) | −2.67515 | −0.140409 | ||||||||
\(364\) | 5.01493 | 0.262854 | ||||||||
\(365\) | 0.852595 | 0.0446269 | ||||||||
\(366\) | 1.13959 | 0.0595676 | ||||||||
\(367\) | −3.83617 | −0.200247 | −0.100123 | − | 0.994975i | \(-0.531924\pi\) | ||||
−0.100123 | + | 0.994975i | \(0.531924\pi\) | |||||||
\(368\) | 7.76002 | 0.404519 | ||||||||
\(369\) | −17.6534 | −0.919001 | ||||||||
\(370\) | 2.54122 | 0.132112 | ||||||||
\(371\) | −2.54575 | −0.132169 | ||||||||
\(372\) | 0.253397 | 0.0131380 | ||||||||
\(373\) | −2.13167 | −0.110374 | −0.0551869 | − | 0.998476i | \(-0.517575\pi\) | ||||
−0.0551869 | + | 0.998476i | \(0.517575\pi\) | |||||||
\(374\) | −2.26899 | −0.117327 | ||||||||
\(375\) | 1.18887 | 0.0613931 | ||||||||
\(376\) | −7.00498 | −0.361254 | ||||||||
\(377\) | −11.5319 | −0.593923 | ||||||||
\(378\) | 3.15547 | 0.162300 | ||||||||
\(379\) | −34.3867 | −1.76632 | −0.883162 | − | 0.469068i | \(-0.844590\pi\) | ||||
−0.883162 | + | 0.469068i | \(0.844590\pi\) | |||||||
\(380\) | 0.867364 | 0.0444949 | ||||||||
\(381\) | −3.69010 | −0.189050 | ||||||||
\(382\) | 17.6757 | 0.904370 | ||||||||
\(383\) | 35.0921 | 1.79312 | 0.896562 | − | 0.442918i | \(-0.146057\pi\) | ||||
0.896562 | + | 0.442918i | \(0.146057\pi\) | |||||||
\(384\) | −0.253397 | −0.0129311 | ||||||||
\(385\) | 0.670470 | 0.0341703 | ||||||||
\(386\) | 8.72407 | 0.444044 | ||||||||
\(387\) | 11.1324 | 0.565890 | ||||||||
\(388\) | 1.00000 | 0.0507673 | ||||||||
\(389\) | −25.7587 | −1.30602 | −0.653009 | − | 0.757350i | \(-0.726494\pi\) | ||||
−0.653009 | + | 0.757350i | \(0.726494\pi\) | |||||||
\(390\) | 0.290905 | 0.0147305 | ||||||||
\(391\) | −26.4586 | −1.33807 | ||||||||
\(392\) | 2.59886 | 0.131262 | ||||||||
\(393\) | 3.53822 | 0.178480 | ||||||||
\(394\) | 5.40889 | 0.272496 | ||||||||
\(395\) | 4.54878 | 0.228874 | ||||||||
\(396\) | 1.95368 | 0.0981763 | ||||||||
\(397\) | 5.10599 | 0.256262 | 0.128131 | − | 0.991757i | \(-0.459102\pi\) | ||||
0.128131 | + | 0.991757i | \(0.459102\pi\) | |||||||
\(398\) | 27.9355 | 1.40028 | ||||||||
\(399\) | −0.960107 | −0.0480654 | ||||||||
\(400\) | −4.76936 | −0.238468 | ||||||||
\(401\) | 17.9374 | 0.895750 | 0.447875 | − | 0.894096i | \(-0.352181\pi\) | ||||
0.447875 | + | 0.894096i | \(0.352181\pi\) | |||||||
\(402\) | 3.94006 | 0.196512 | ||||||||
\(403\) | 2.39046 | 0.119077 | ||||||||
\(404\) | 16.3076 | 0.811333 | ||||||||
\(405\) | −4.04669 | −0.201082 | ||||||||
\(406\) | 10.1205 | 0.502272 | ||||||||
\(407\) | −3.52130 | −0.174545 | ||||||||
\(408\) | 0.863985 | 0.0427736 | ||||||||
\(409\) | 15.1426 | 0.748753 | 0.374376 | − | 0.927277i | \(-0.377857\pi\) | ||||
0.374376 | + | 0.927277i | \(0.377857\pi\) | |||||||
\(410\) | 2.88783 | 0.142620 | ||||||||
\(411\) | 2.31522 | 0.114201 | ||||||||
\(412\) | −4.25960 | −0.209855 | ||||||||
\(413\) | 17.6638 | 0.869180 | ||||||||
\(414\) | 22.7818 | 1.11966 | ||||||||
\(415\) | 2.89053 | 0.141891 | ||||||||
\(416\) | −2.39046 | −0.117202 | ||||||||
\(417\) | −0.492416 | −0.0241137 | ||||||||
\(418\) | −1.20189 | −0.0587862 | ||||||||
\(419\) | −38.8018 | −1.89559 | −0.947796 | − | 0.318877i | \(-0.896694\pi\) | ||||
−0.947796 | + | 0.318877i | \(0.896694\pi\) | |||||||
\(420\) | −0.255301 | −0.0124574 | ||||||||
\(421\) | 35.1430 | 1.71276 | 0.856382 | − | 0.516343i | \(-0.172707\pi\) | ||||
0.856382 | + | 0.516343i | \(0.172707\pi\) | |||||||
\(422\) | −19.7703 | −0.962403 | ||||||||
\(423\) | −20.5651 | −0.999911 | ||||||||
\(424\) | 1.21348 | 0.0589318 | ||||||||
\(425\) | 16.2616 | 0.788805 | ||||||||
\(426\) | 3.06831 | 0.148660 | ||||||||
\(427\) | −9.43476 | −0.456580 | ||||||||
\(428\) | −16.8783 | −0.815844 | ||||||||
\(429\) | −0.403100 | −0.0194619 | ||||||||
\(430\) | −1.82108 | −0.0878203 | ||||||||
\(431\) | −6.10231 | −0.293938 | −0.146969 | − | 0.989141i | \(-0.546952\pi\) | ||||
−0.146969 | + | 0.989141i | \(0.546952\pi\) | |||||||
\(432\) | −1.50411 | −0.0723667 | ||||||||
\(433\) | −6.73716 | −0.323767 | −0.161884 | − | 0.986810i | \(-0.551757\pi\) | ||||
−0.161884 | + | 0.986810i | \(0.551757\pi\) | |||||||
\(434\) | −2.09789 | −0.100702 | ||||||||
\(435\) | 0.587068 | 0.0281477 | ||||||||
\(436\) | 9.71703 | 0.465361 | ||||||||
\(437\) | −14.0151 | −0.670434 | ||||||||
\(438\) | 0.449861 | 0.0214952 | ||||||||
\(439\) | 25.4609 | 1.21518 | 0.607591 | − | 0.794250i | \(-0.292136\pi\) | ||||
0.607591 | + | 0.794250i | \(0.292136\pi\) | |||||||
\(440\) | −0.319592 | −0.0152360 | ||||||||
\(441\) | 7.62969 | 0.363319 | ||||||||
\(442\) | 8.15053 | 0.387681 | ||||||||
\(443\) | −6.20495 | −0.294806 | −0.147403 | − | 0.989077i | \(-0.547091\pi\) | ||||
−0.147403 | + | 0.989077i | \(0.547091\pi\) | |||||||
\(444\) | 1.34084 | 0.0636334 | ||||||||
\(445\) | −6.86893 | −0.325619 | ||||||||
\(446\) | 2.47720 | 0.117299 | ||||||||
\(447\) | −4.48830 | −0.212289 | ||||||||
\(448\) | 2.09789 | 0.0991160 | ||||||||
\(449\) | −0.0172868 | −0.000815817 0 | −0.000407908 | − | 1.00000i | \(-0.500130\pi\) | ||||
−0.000407908 | 1.00000i | \(0.500130\pi\) | ||||||||
\(450\) | −14.0018 | −0.660053 | ||||||||
\(451\) | −4.00160 | −0.188428 | ||||||||
\(452\) | −8.10723 | −0.381332 | ||||||||
\(453\) | −2.50566 | −0.117726 | ||||||||
\(454\) | −21.2988 | −0.999604 | ||||||||
\(455\) | −2.40842 | −0.112908 | ||||||||
\(456\) | 0.457653 | 0.0214316 | ||||||||
\(457\) | −16.3152 | −0.763192 | −0.381596 | − | 0.924329i | \(-0.624625\pi\) | ||||
−0.381596 | + | 0.924329i | \(0.624625\pi\) | |||||||
\(458\) | −10.3502 | −0.483634 | ||||||||
\(459\) | 5.12843 | 0.239375 | ||||||||
\(460\) | −3.72675 | −0.173760 | ||||||||
\(461\) | −2.90217 | −0.135167 | −0.0675837 | − | 0.997714i | \(-0.521529\pi\) | ||||
−0.0675837 | + | 0.997714i | \(0.521529\pi\) | |||||||
\(462\) | 0.353764 | 0.0164586 | ||||||||
\(463\) | 3.78789 | 0.176038 | 0.0880190 | − | 0.996119i | \(-0.471946\pi\) | ||||
0.0880190 | + | 0.996119i | \(0.471946\pi\) | |||||||
\(464\) | −4.82413 | −0.223955 | ||||||||
\(465\) | −0.121694 | −0.00564343 | ||||||||
\(466\) | −7.70459 | −0.356908 | ||||||||
\(467\) | −22.2445 | −1.02935 | −0.514675 | − | 0.857385i | \(-0.672087\pi\) | ||||
−0.514675 | + | 0.857385i | \(0.672087\pi\) | |||||||
\(468\) | −7.01789 | −0.324402 | ||||||||
\(469\) | −32.6199 | −1.50625 | ||||||||
\(470\) | 3.36414 | 0.155176 | ||||||||
\(471\) | −2.11778 | −0.0975821 | ||||||||
\(472\) | −8.41980 | −0.387553 | ||||||||
\(473\) | 2.52343 | 0.116027 | ||||||||
\(474\) | 2.40010 | 0.110240 | ||||||||
\(475\) | 8.61380 | 0.395228 | ||||||||
\(476\) | −7.15298 | −0.327856 | ||||||||
\(477\) | 3.56252 | 0.163117 | ||||||||
\(478\) | −10.8586 | −0.496662 | ||||||||
\(479\) | 0.457308 | 0.0208950 | 0.0104475 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104475 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(480\) | 0.121694 | 0.00555455 | ||||||||
\(481\) | 12.6490 | 0.576745 | ||||||||
\(482\) | −20.4943 | −0.933491 | ||||||||
\(483\) | 4.12522 | 0.187704 | ||||||||
\(484\) | −10.5571 | −0.479870 | ||||||||
\(485\) | −0.480250 | −0.0218070 | ||||||||
\(486\) | −6.64753 | −0.301538 | ||||||||
\(487\) | −35.1270 | −1.59176 | −0.795879 | − | 0.605456i | \(-0.792991\pi\) | ||||
−0.795879 | + | 0.605456i | \(0.792991\pi\) | |||||||
\(488\) | 4.49726 | 0.203581 | ||||||||
\(489\) | 0.730007 | 0.0330120 | ||||||||
\(490\) | −1.24810 | −0.0563834 | ||||||||
\(491\) | −17.4311 | −0.786653 | −0.393326 | − | 0.919399i | \(-0.628676\pi\) | ||||
−0.393326 | + | 0.919399i | \(0.628676\pi\) | |||||||
\(492\) | 1.52372 | 0.0686948 | ||||||||
\(493\) | 16.4484 | 0.740797 | ||||||||
\(494\) | 4.31734 | 0.194246 | ||||||||
\(495\) | −0.938256 | −0.0421715 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −25.4027 | −1.13947 | ||||||||
\(498\) | 1.52515 | 0.0683437 | ||||||||
\(499\) | 10.6225 | 0.475528 | 0.237764 | − | 0.971323i | \(-0.423586\pi\) | ||||
0.237764 | + | 0.971323i | \(0.423586\pi\) | |||||||
\(500\) | 4.69173 | 0.209821 | ||||||||
\(501\) | 1.66174 | 0.0742409 | ||||||||
\(502\) | −15.1004 | −0.673962 | ||||||||
\(503\) | 23.4766 | 1.04677 | 0.523385 | − | 0.852096i | \(-0.324669\pi\) | ||||
0.523385 | + | 0.852096i | \(0.324669\pi\) | |||||||
\(504\) | 6.15897 | 0.274342 | ||||||||
\(505\) | −7.83172 | −0.348507 | ||||||||
\(506\) | 5.16407 | 0.229571 | ||||||||
\(507\) | −1.84618 | −0.0819915 | ||||||||
\(508\) | −14.5625 | −0.646107 | ||||||||
\(509\) | −4.93509 | −0.218744 | −0.109372 | − | 0.994001i | \(-0.534884\pi\) | ||||
−0.109372 | + | 0.994001i | \(0.534884\pi\) | |||||||
\(510\) | −0.414929 | −0.0183733 | ||||||||
\(511\) | −3.72442 | −0.164759 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.71653 | 0.119938 | ||||||||
\(514\) | 15.8607 | 0.699585 | ||||||||
\(515\) | 2.04567 | 0.0901430 | ||||||||
\(516\) | −0.960870 | −0.0422999 | ||||||||
\(517\) | −4.66161 | −0.205017 | ||||||||
\(518\) | −11.1009 | −0.487745 | ||||||||
\(519\) | 0.153630 | 0.00674362 | ||||||||
\(520\) | 1.14802 | 0.0503439 | ||||||||
\(521\) | −14.8713 | −0.651523 | −0.325761 | − | 0.945452i | \(-0.605621\pi\) | ||||
−0.325761 | + | 0.945452i | \(0.605621\pi\) | |||||||
\(522\) | −14.1626 | −0.619881 | ||||||||
\(523\) | −11.2282 | −0.490977 | −0.245488 | − | 0.969400i | \(-0.578948\pi\) | ||||
−0.245488 | + | 0.969400i | \(0.578948\pi\) | |||||||
\(524\) | 13.9631 | 0.609982 | ||||||||
\(525\) | −2.53539 | −0.110654 | ||||||||
\(526\) | 19.7908 | 0.862920 | ||||||||
\(527\) | −3.40960 | −0.148525 | ||||||||
\(528\) | −0.168629 | −0.00733862 | ||||||||
\(529\) | 37.2178 | 1.61817 | ||||||||
\(530\) | −0.582774 | −0.0253141 | ||||||||
\(531\) | −24.7188 | −1.07270 | ||||||||
\(532\) | −3.78894 | −0.164271 | ||||||||
\(533\) | 14.3743 | 0.622619 | ||||||||
\(534\) | −3.62430 | −0.156839 | ||||||||
\(535\) | 8.10581 | 0.350445 | ||||||||
\(536\) | 15.5489 | 0.671611 | ||||||||
\(537\) | −1.83131 | −0.0790267 | ||||||||
\(538\) | −8.55109 | −0.368664 | ||||||||
\(539\) | 1.72946 | 0.0744933 | ||||||||
\(540\) | 0.722350 | 0.0310850 | ||||||||
\(541\) | −8.65172 | −0.371967 | −0.185983 | − | 0.982553i | \(-0.559547\pi\) | ||||
−0.185983 | + | 0.982553i | \(0.559547\pi\) | |||||||
\(542\) | 16.8411 | 0.723389 | ||||||||
\(543\) | −5.66036 | −0.242909 | ||||||||
\(544\) | 3.40960 | 0.146186 | ||||||||
\(545\) | −4.66660 | −0.199895 | ||||||||
\(546\) | −1.27077 | −0.0543839 | ||||||||
\(547\) | −25.9434 | −1.10926 | −0.554630 | − | 0.832097i | \(-0.687140\pi\) | ||||
−0.554630 | + | 0.832097i | \(0.687140\pi\) | |||||||
\(548\) | 9.13671 | 0.390301 | ||||||||
\(549\) | 13.2030 | 0.563491 | ||||||||
\(550\) | −3.17387 | −0.135334 | ||||||||
\(551\) | 8.71271 | 0.371174 | ||||||||
\(552\) | −1.96637 | −0.0836942 | ||||||||
\(553\) | −19.8706 | −0.844983 | ||||||||
\(554\) | 2.36156 | 0.100333 | ||||||||
\(555\) | −0.643938 | −0.0273336 | ||||||||
\(556\) | −1.94326 | −0.0824125 | ||||||||
\(557\) | 16.8703 | 0.714817 | 0.357408 | − | 0.933948i | \(-0.383660\pi\) | ||||
0.357408 | + | 0.933948i | \(0.383660\pi\) | |||||||
\(558\) | 2.93579 | 0.124282 | ||||||||
\(559\) | −9.06450 | −0.383388 | ||||||||
\(560\) | −1.00751 | −0.0425751 | ||||||||
\(561\) | 0.574957 | 0.0242747 | ||||||||
\(562\) | −0.346952 | −0.0146353 | ||||||||
\(563\) | 34.3415 | 1.44732 | 0.723662 | − | 0.690155i | \(-0.242458\pi\) | ||||
0.723662 | + | 0.690155i | \(0.242458\pi\) | |||||||
\(564\) | 1.77504 | 0.0747428 | ||||||||
\(565\) | 3.89350 | 0.163801 | ||||||||
\(566\) | −17.4821 | −0.734829 | ||||||||
\(567\) | 17.6773 | 0.742377 | ||||||||
\(568\) | 12.1087 | 0.508069 | ||||||||
\(569\) | −42.7601 | −1.79260 | −0.896298 | − | 0.443453i | \(-0.853753\pi\) | ||||
−0.896298 | + | 0.443453i | \(0.853753\pi\) | |||||||
\(570\) | −0.219788 | −0.00920590 | ||||||||
\(571\) | 40.7917 | 1.70708 | 0.853539 | − | 0.521029i | \(-0.174452\pi\) | ||||
0.853539 | + | 0.521029i | \(0.174452\pi\) | |||||||
\(572\) | −1.59078 | −0.0665140 | ||||||||
\(573\) | −4.47899 | −0.187112 | ||||||||
\(574\) | −12.6150 | −0.526540 | ||||||||
\(575\) | −37.0103 | −1.54344 | ||||||||
\(576\) | −2.93579 | −0.122325 | ||||||||
\(577\) | 8.55741 | 0.356249 | 0.178125 | − | 0.984008i | \(-0.442997\pi\) | ||||
0.178125 | + | 0.984008i | \(0.442997\pi\) | |||||||
\(578\) | 5.37460 | 0.223554 | ||||||||
\(579\) | −2.21066 | −0.0918718 | ||||||||
\(580\) | 2.31679 | 0.0961993 | ||||||||
\(581\) | −12.6268 | −0.523848 | ||||||||
\(582\) | −0.253397 | −0.0105037 | ||||||||
\(583\) | 0.807536 | 0.0334447 | ||||||||
\(584\) | 1.77532 | 0.0734631 | ||||||||
\(585\) | 3.37034 | 0.139346 | ||||||||
\(586\) | 15.7681 | 0.651372 | ||||||||
\(587\) | −3.12283 | −0.128893 | −0.0644466 | − | 0.997921i | \(-0.520528\pi\) | ||||
−0.0644466 | + | 0.997921i | \(0.520528\pi\) | |||||||
\(588\) | −0.658543 | −0.0271579 | ||||||||
\(589\) | −1.80607 | −0.0744178 | ||||||||
\(590\) | 4.04361 | 0.166473 | ||||||||
\(591\) | −1.37060 | −0.0563789 | ||||||||
\(592\) | 5.29145 | 0.217477 | ||||||||
\(593\) | 31.3115 | 1.28581 | 0.642905 | − | 0.765946i | \(-0.277729\pi\) | ||||
0.642905 | + | 0.765946i | \(0.277729\pi\) | |||||||
\(594\) | −1.00094 | −0.0410692 | ||||||||
\(595\) | 3.43522 | 0.140830 | ||||||||
\(596\) | −17.7125 | −0.725532 | ||||||||
\(597\) | −7.07878 | −0.289715 | ||||||||
\(598\) | −18.5500 | −0.758567 | ||||||||
\(599\) | −26.1835 | −1.06983 | −0.534914 | − | 0.844907i | \(-0.679656\pi\) | ||||
−0.534914 | + | 0.844907i | \(0.679656\pi\) | |||||||
\(600\) | 1.20854 | 0.0493386 | ||||||||
\(601\) | −28.5941 | −1.16638 | −0.583189 | − | 0.812337i | \(-0.698195\pi\) | ||||
−0.583189 | + | 0.812337i | \(0.698195\pi\) | |||||||
\(602\) | 7.95509 | 0.324225 | ||||||||
\(603\) | 45.6483 | 1.85894 | ||||||||
\(604\) | −9.88828 | −0.402348 | ||||||||
\(605\) | 5.07007 | 0.206128 | ||||||||
\(606\) | −4.13230 | −0.167863 | ||||||||
\(607\) | −23.9524 | −0.972198 | −0.486099 | − | 0.873904i | \(-0.661581\pi\) | ||||
−0.486099 | + | 0.873904i | \(0.661581\pi\) | |||||||
\(608\) | 1.80607 | 0.0732458 | ||||||||
\(609\) | −2.56451 | −0.103919 | ||||||||
\(610\) | −2.15981 | −0.0874481 | ||||||||
\(611\) | 16.7451 | 0.677436 | ||||||||
\(612\) | 10.0099 | 0.404626 | ||||||||
\(613\) | −1.07263 | −0.0433231 | −0.0216616 | − | 0.999765i | \(-0.506896\pi\) | ||||
−0.0216616 | + | 0.999765i | \(0.506896\pi\) | |||||||
\(614\) | 8.89454 | 0.358954 | ||||||||
\(615\) | −0.731768 | −0.0295077 | ||||||||
\(616\) | 1.39609 | 0.0562499 | ||||||||
\(617\) | 11.3134 | 0.455461 | 0.227731 | − | 0.973724i | \(-0.426869\pi\) | ||||
0.227731 | + | 0.973724i | \(0.426869\pi\) | |||||||
\(618\) | 1.07937 | 0.0434187 | ||||||||
\(619\) | 23.0385 | 0.925994 | 0.462997 | − | 0.886360i | \(-0.346774\pi\) | ||||
0.462997 | + | 0.886360i | \(0.346774\pi\) | |||||||
\(620\) | −0.480250 | −0.0192873 | ||||||||
\(621\) | −11.6719 | −0.468379 | ||||||||
\(622\) | −22.2407 | −0.891773 | ||||||||
\(623\) | 30.0058 | 1.20216 | ||||||||
\(624\) | 0.605737 | 0.0242489 | ||||||||
\(625\) | 21.5936 | 0.863744 | ||||||||
\(626\) | 19.7898 | 0.790959 | ||||||||
\(627\) | 0.304555 | 0.0121628 | ||||||||
\(628\) | −8.35754 | −0.333502 | ||||||||
\(629\) | −18.0417 | −0.719371 | ||||||||
\(630\) | −2.95784 | −0.117843 | ||||||||
\(631\) | −2.62007 | −0.104303 | −0.0521517 | − | 0.998639i | \(-0.516608\pi\) | ||||
−0.0521517 | + | 0.998639i | \(0.516608\pi\) | |||||||
\(632\) | 9.47170 | 0.376764 | ||||||||
\(633\) | 5.00974 | 0.199119 | ||||||||
\(634\) | 23.3646 | 0.927926 | ||||||||
\(635\) | 6.99364 | 0.277534 | ||||||||
\(636\) | −0.307493 | −0.0121929 | ||||||||
\(637\) | −6.21247 | −0.246147 | ||||||||
\(638\) | −3.21032 | −0.127098 | ||||||||
\(639\) | 35.5486 | 1.40628 | ||||||||
\(640\) | 0.480250 | 0.0189835 | ||||||||
\(641\) | −26.9489 | −1.06442 | −0.532209 | − | 0.846613i | \(-0.678638\pi\) | ||||
−0.532209 | + | 0.846613i | \(0.678638\pi\) | |||||||
\(642\) | 4.27692 | 0.168797 | ||||||||
\(643\) | −43.6704 | −1.72219 | −0.861096 | − | 0.508442i | \(-0.830221\pi\) | ||||
−0.861096 | + | 0.508442i | \(0.830221\pi\) | |||||||
\(644\) | 16.2797 | 0.641509 | ||||||||
\(645\) | 0.461457 | 0.0181699 | ||||||||
\(646\) | −6.15798 | −0.242283 | ||||||||
\(647\) | −23.3294 | −0.917172 | −0.458586 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458586 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(648\) | −8.42623 | −0.331014 | ||||||||
\(649\) | −5.60314 | −0.219942 | ||||||||
\(650\) | 11.4010 | 0.447183 | ||||||||
\(651\) | 0.531600 | 0.0208350 | ||||||||
\(652\) | 2.88088 | 0.112824 | ||||||||
\(653\) | −24.5466 | −0.960585 | −0.480292 | − | 0.877109i | \(-0.659469\pi\) | ||||
−0.480292 | + | 0.877109i | \(0.659469\pi\) | |||||||
\(654\) | −2.46227 | −0.0962824 | ||||||||
\(655\) | −6.70578 | −0.262017 | ||||||||
\(656\) | 6.01318 | 0.234775 | ||||||||
\(657\) | 5.21196 | 0.203338 | ||||||||
\(658\) | −14.6957 | −0.572897 | ||||||||
\(659\) | 5.45628 | 0.212547 | 0.106273 | − | 0.994337i | \(-0.466108\pi\) | ||||
0.106273 | + | 0.994337i | \(0.466108\pi\) | |||||||
\(660\) | 0.0809839 | 0.00315229 | ||||||||
\(661\) | −11.0906 | −0.431373 | −0.215686 | − | 0.976463i | \(-0.569199\pi\) | ||||
−0.215686 | + | 0.976463i | \(0.569199\pi\) | |||||||
\(662\) | −20.1711 | −0.783972 | ||||||||
\(663\) | −2.06532 | −0.0802105 | ||||||||
\(664\) | 6.01881 | 0.233575 | ||||||||
\(665\) | 1.81964 | 0.0705624 | ||||||||
\(666\) | 15.5346 | 0.601953 | ||||||||
\(667\) | −37.4353 | −1.44950 | ||||||||
\(668\) | 6.55783 | 0.253730 | ||||||||
\(669\) | −0.627716 | −0.0242689 | ||||||||
\(670\) | −7.46736 | −0.288489 | ||||||||
\(671\) | 2.99280 | 0.115536 | ||||||||
\(672\) | −0.531600 | −0.0205069 | ||||||||
\(673\) | 36.1899 | 1.39502 | 0.697509 | − | 0.716576i | \(-0.254292\pi\) | ||||
0.697509 | + | 0.716576i | \(0.254292\pi\) | |||||||
\(674\) | 5.83412 | 0.224722 | ||||||||
\(675\) | 7.17366 | 0.276114 | ||||||||
\(676\) | −7.28569 | −0.280219 | ||||||||
\(677\) | −19.4724 | −0.748385 | −0.374193 | − | 0.927351i | \(-0.622080\pi\) | ||||
−0.374193 | + | 0.927351i | \(0.622080\pi\) | |||||||
\(678\) | 2.05435 | 0.0788969 | ||||||||
\(679\) | 2.09789 | 0.0805096 | ||||||||
\(680\) | −1.63746 | −0.0627938 | ||||||||
\(681\) | 5.39707 | 0.206816 | ||||||||
\(682\) | 0.665471 | 0.0254822 | ||||||||
\(683\) | 0.876644 | 0.0335438 | 0.0167719 | − | 0.999859i | \(-0.494661\pi\) | ||||
0.0167719 | + | 0.999859i | \(0.494661\pi\) | |||||||
\(684\) | 5.30224 | 0.202736 | ||||||||
\(685\) | −4.38790 | −0.167653 | ||||||||
\(686\) | 20.1373 | 0.768848 | ||||||||
\(687\) | 2.62272 | 0.100063 | ||||||||
\(688\) | −3.79195 | −0.144567 | ||||||||
\(689\) | −2.90078 | −0.110511 | ||||||||
\(690\) | 0.944348 | 0.0359507 | ||||||||
\(691\) | −18.1992 | −0.692330 | −0.346165 | − | 0.938174i | \(-0.612516\pi\) | ||||
−0.346165 | + | 0.938174i | \(0.612516\pi\) | |||||||
\(692\) | 0.606282 | 0.0230474 | ||||||||
\(693\) | 4.09861 | 0.155693 | ||||||||
\(694\) | 22.8780 | 0.868437 | ||||||||
\(695\) | 0.933249 | 0.0354001 | ||||||||
\(696\) | 1.22242 | 0.0463358 | ||||||||
\(697\) | −20.5026 | −0.776590 | ||||||||
\(698\) | 1.33157 | 0.0504006 | ||||||||
\(699\) | 1.95232 | 0.0738437 | ||||||||
\(700\) | −10.0056 | −0.378176 | ||||||||
\(701\) | −16.3165 | −0.616266 | −0.308133 | − | 0.951343i | \(-0.599704\pi\) | ||||
−0.308133 | + | 0.951343i | \(0.599704\pi\) | |||||||
\(702\) | 3.59553 | 0.135704 | ||||||||
\(703\) | −9.55672 | −0.360439 | ||||||||
\(704\) | −0.665471 | −0.0250809 | ||||||||
\(705\) | −0.852464 | −0.0321057 | ||||||||
\(706\) | 10.3020 | 0.387719 | ||||||||
\(707\) | 34.2116 | 1.28666 | ||||||||
\(708\) | 2.13356 | 0.0801840 | ||||||||
\(709\) | 25.1933 | 0.946156 | 0.473078 | − | 0.881021i | \(-0.343143\pi\) | ||||
0.473078 | + | 0.881021i | \(0.343143\pi\) | |||||||
\(710\) | −5.81519 | −0.218240 | ||||||||
\(711\) | 27.8069 | 1.04284 | ||||||||
\(712\) | −14.3028 | −0.536021 | ||||||||
\(713\) | 7.76002 | 0.290615 | ||||||||
\(714\) | 1.81255 | 0.0678328 | ||||||||
\(715\) | 0.763973 | 0.0285710 | ||||||||
\(716\) | −7.22701 | −0.270086 | ||||||||
\(717\) | 2.75155 | 0.102759 | ||||||||
\(718\) | 2.16605 | 0.0808361 | ||||||||
\(719\) | −49.1968 | −1.83473 | −0.917366 | − | 0.398044i | \(-0.869689\pi\) | ||||
−0.917366 | + | 0.398044i | \(0.869689\pi\) | |||||||
\(720\) | 1.40991 | 0.0525443 | ||||||||
\(721\) | −8.93617 | −0.332800 | ||||||||
\(722\) | 15.7381 | 0.585712 | ||||||||
\(723\) | 5.19321 | 0.193138 | ||||||||
\(724\) | −22.3379 | −0.830180 | ||||||||
\(725\) | 23.0080 | 0.854496 | ||||||||
\(726\) | 2.67515 | 0.0992843 | ||||||||
\(727\) | 35.7304 | 1.32517 | 0.662584 | − | 0.748988i | \(-0.269460\pi\) | ||||
0.662584 | + | 0.748988i | \(0.269460\pi\) | |||||||
\(728\) | −5.01493 | −0.185866 | ||||||||
\(729\) | −23.5942 | −0.873860 | ||||||||
\(730\) | −0.852595 | −0.0315560 | ||||||||
\(731\) | 12.9290 | 0.478198 | ||||||||
\(732\) | −1.13959 | −0.0421206 | ||||||||
\(733\) | −13.7271 | −0.507022 | −0.253511 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253511 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(734\) | 3.83617 | 0.141596 | ||||||||
\(735\) | 0.316265 | 0.0116656 | ||||||||
\(736\) | −7.76002 | −0.286038 | ||||||||
\(737\) | 10.3474 | 0.381150 | ||||||||
\(738\) | 17.6534 | 0.649832 | ||||||||
\(739\) | −41.6904 | −1.53361 | −0.766804 | − | 0.641881i | \(-0.778154\pi\) | ||||
−0.766804 | + | 0.641881i | \(0.778154\pi\) | |||||||
\(740\) | −2.54122 | −0.0934170 | ||||||||
\(741\) | −1.09400 | −0.0401892 | ||||||||
\(742\) | 2.54575 | 0.0934574 | ||||||||
\(743\) | −44.2893 | −1.62482 | −0.812409 | − | 0.583089i | \(-0.801844\pi\) | ||||
−0.812409 | + | 0.583089i | \(0.801844\pi\) | |||||||
\(744\) | −0.253397 | −0.00929000 | ||||||||
\(745\) | 8.50642 | 0.311651 | ||||||||
\(746\) | 2.13167 | 0.0780460 | ||||||||
\(747\) | 17.6700 | 0.646510 | ||||||||
\(748\) | 2.26899 | 0.0829626 | ||||||||
\(749\) | −35.4089 | −1.29381 | ||||||||
\(750\) | −1.18887 | −0.0434115 | ||||||||
\(751\) | −35.9614 | −1.31225 | −0.656126 | − | 0.754652i | \(-0.727806\pi\) | ||||
−0.656126 | + | 0.754652i | \(0.727806\pi\) | |||||||
\(752\) | 7.00498 | 0.255445 | ||||||||
\(753\) | 3.82639 | 0.139441 | ||||||||
\(754\) | 11.5319 | 0.419967 | ||||||||
\(755\) | 4.74884 | 0.172828 | ||||||||
\(756\) | −3.15547 | −0.114763 | ||||||||
\(757\) | 14.7318 | 0.535436 | 0.267718 | − | 0.963497i | \(-0.413730\pi\) | ||||
0.267718 | + | 0.963497i | \(0.413730\pi\) | |||||||
\(758\) | 34.3867 | 1.24898 | ||||||||
\(759\) | −1.30856 | −0.0474978 | ||||||||
\(760\) | −0.867364 | −0.0314626 | ||||||||
\(761\) | −8.87719 | −0.321798 | −0.160899 | − | 0.986971i | \(-0.551439\pi\) | ||||
−0.160899 | + | 0.986971i | \(0.551439\pi\) | |||||||
\(762\) | 3.69010 | 0.133678 | ||||||||
\(763\) | 20.3853 | 0.737996 | ||||||||
\(764\) | −17.6757 | −0.639486 | ||||||||
\(765\) | −4.80724 | −0.173806 | ||||||||
\(766\) | −35.0921 | −1.26793 | ||||||||
\(767\) | 20.1272 | 0.726752 | ||||||||
\(768\) | 0.253397 | 0.00914369 | ||||||||
\(769\) | −7.85063 | −0.283101 | −0.141551 | − | 0.989931i | \(-0.545209\pi\) | ||||
−0.141551 | + | 0.989931i | \(0.545209\pi\) | |||||||
\(770\) | −0.670470 | −0.0241620 | ||||||||
\(771\) | −4.01905 | −0.144743 | ||||||||
\(772\) | −8.72407 | −0.313986 | ||||||||
\(773\) | −15.4815 | −0.556832 | −0.278416 | − | 0.960461i | \(-0.589809\pi\) | ||||
−0.278416 | + | 0.960461i | \(0.589809\pi\) | |||||||
\(774\) | −11.1324 | −0.400144 | ||||||||
\(775\) | −4.76936 | −0.171320 | ||||||||
\(776\) | −1.00000 | −0.0358979 | ||||||||
\(777\) | 2.81293 | 0.100913 | ||||||||
\(778\) | 25.7587 | 0.923495 | ||||||||
\(779\) | −10.8602 | −0.389108 | ||||||||
\(780\) | −0.290905 | −0.0104161 | ||||||||
\(781\) | 8.05798 | 0.288337 | ||||||||
\(782\) | 26.4586 | 0.946157 | ||||||||
\(783\) | 7.25604 | 0.259310 | ||||||||
\(784\) | −2.59886 | −0.0928163 | ||||||||
\(785\) | 4.01371 | 0.143255 | ||||||||
\(786\) | −3.53822 | −0.126204 | ||||||||
\(787\) | 22.0604 | 0.786367 | 0.393184 | − | 0.919460i | \(-0.371374\pi\) | ||||
0.393184 | + | 0.919460i | \(0.371374\pi\) | |||||||
\(788\) | −5.40889 | −0.192684 | ||||||||
\(789\) | −5.01494 | −0.178537 | ||||||||
\(790\) | −4.54878 | −0.161838 | ||||||||
\(791\) | −17.0081 | −0.604738 | ||||||||
\(792\) | −1.95368 | −0.0694211 | ||||||||
\(793\) | −10.7505 | −0.381763 | ||||||||
\(794\) | −5.10599 | −0.181205 | ||||||||
\(795\) | 0.147673 | 0.00523743 | ||||||||
\(796\) | −27.9355 | −0.990147 | ||||||||
\(797\) | −8.38083 | −0.296864 | −0.148432 | − | 0.988923i | \(-0.547423\pi\) | ||||
−0.148432 | + | 0.988923i | \(0.547423\pi\) | |||||||
\(798\) | 0.960107 | 0.0339874 | ||||||||
\(799\) | −23.8842 | −0.844962 | ||||||||
\(800\) | 4.76936 | 0.168622 | ||||||||
\(801\) | −41.9901 | −1.48365 | ||||||||
\(802\) | −17.9374 | −0.633391 | ||||||||
\(803\) | 1.18142 | 0.0416915 | ||||||||
\(804\) | −3.94006 | −0.138955 | ||||||||
\(805\) | −7.81830 | −0.275559 | ||||||||
\(806\) | −2.39046 | −0.0842004 | ||||||||
\(807\) | 2.16682 | 0.0762758 | ||||||||
\(808\) | −16.3076 | −0.573699 | ||||||||
\(809\) | −2.44509 | −0.0859648 | −0.0429824 | − | 0.999076i | \(-0.513686\pi\) | ||||
−0.0429824 | + | 0.999076i | \(0.513686\pi\) | |||||||
\(810\) | 4.04669 | 0.142186 | ||||||||
\(811\) | 21.7333 | 0.763158 | 0.381579 | − | 0.924336i | \(-0.375380\pi\) | ||||
0.381579 | + | 0.924336i | \(0.375380\pi\) | |||||||
\(812\) | −10.1205 | −0.355160 | ||||||||
\(813\) | −4.26750 | −0.149668 | ||||||||
\(814\) | 3.52130 | 0.123422 | ||||||||
\(815\) | −1.38354 | −0.0484633 | ||||||||
\(816\) | −0.863985 | −0.0302455 | ||||||||
\(817\) | 6.84852 | 0.239599 | ||||||||
\(818\) | −15.1426 | −0.529448 | ||||||||
\(819\) | −14.7228 | −0.514455 | ||||||||
\(820\) | −2.88783 | −0.100847 | ||||||||
\(821\) | −52.4951 | −1.83209 | −0.916046 | − | 0.401073i | \(-0.868638\pi\) | ||||
−0.916046 | + | 0.401073i | \(0.868638\pi\) | |||||||
\(822\) | −2.31522 | −0.0807525 | ||||||||
\(823\) | 16.4214 | 0.572412 | 0.286206 | − | 0.958168i | \(-0.407606\pi\) | ||||
0.286206 | + | 0.958168i | \(0.407606\pi\) | |||||||
\(824\) | 4.25960 | 0.148390 | ||||||||
\(825\) | 0.804251 | 0.0280004 | ||||||||
\(826\) | −17.6638 | −0.614603 | ||||||||
\(827\) | 4.43183 | 0.154110 | 0.0770550 | − | 0.997027i | \(-0.475448\pi\) | ||||
0.0770550 | + | 0.997027i | \(0.475448\pi\) | |||||||
\(828\) | −22.7818 | −0.791721 | ||||||||
\(829\) | 19.0009 | 0.659930 | 0.329965 | − | 0.943993i | \(-0.392963\pi\) | ||||
0.329965 | + | 0.943993i | \(0.392963\pi\) | |||||||
\(830\) | −2.89053 | −0.100332 | ||||||||
\(831\) | −0.598414 | −0.0207587 | ||||||||
\(832\) | 2.39046 | 0.0828744 | ||||||||
\(833\) | 8.86107 | 0.307018 | ||||||||
\(834\) | 0.492416 | 0.0170510 | ||||||||
\(835\) | −3.14939 | −0.108989 | ||||||||
\(836\) | 1.20189 | 0.0415681 | ||||||||
\(837\) | −1.50411 | −0.0519898 | ||||||||
\(838\) | 38.8018 | 1.34039 | ||||||||
\(839\) | 10.0355 | 0.346464 | 0.173232 | − | 0.984881i | \(-0.444579\pi\) | ||||
0.173232 | + | 0.984881i | \(0.444579\pi\) | |||||||
\(840\) | 0.255301 | 0.00880871 | ||||||||
\(841\) | −5.72779 | −0.197510 | ||||||||
\(842\) | −35.1430 | −1.21111 | ||||||||
\(843\) | 0.0879167 | 0.00302801 | ||||||||
\(844\) | 19.7703 | 0.680522 | ||||||||
\(845\) | 3.49895 | 0.120368 | ||||||||
\(846\) | 20.5651 | 0.707044 | ||||||||
\(847\) | −22.1477 | −0.761005 | ||||||||
\(848\) | −1.21348 | −0.0416711 | ||||||||
\(849\) | 4.42993 | 0.152035 | ||||||||
\(850\) | −16.2616 | −0.557769 | ||||||||
\(851\) | 41.0617 | 1.40758 | ||||||||
\(852\) | −3.06831 | −0.105119 | ||||||||
\(853\) | 33.5645 | 1.14923 | 0.574613 | − | 0.818425i | \(-0.305152\pi\) | ||||
0.574613 | + | 0.818425i | \(0.305152\pi\) | |||||||
\(854\) | 9.43476 | 0.322851 | ||||||||
\(855\) | −2.54640 | −0.0870850 | ||||||||
\(856\) | 16.8783 | 0.576889 | ||||||||
\(857\) | −18.1898 | −0.621353 | −0.310677 | − | 0.950516i | \(-0.600556\pi\) | ||||
−0.310677 | + | 0.950516i | \(0.600556\pi\) | |||||||
\(858\) | 0.403100 | 0.0137616 | ||||||||
\(859\) | −35.0211 | −1.19491 | −0.597453 | − | 0.801904i | \(-0.703820\pi\) | ||||
−0.597453 | + | 0.801904i | \(0.703820\pi\) | |||||||
\(860\) | 1.82108 | 0.0620984 | ||||||||
\(861\) | 3.19661 | 0.108940 | ||||||||
\(862\) | 6.10231 | 0.207845 | ||||||||
\(863\) | 50.2598 | 1.71086 | 0.855432 | − | 0.517916i | \(-0.173292\pi\) | ||||
0.855432 | + | 0.517916i | \(0.173292\pi\) | |||||||
\(864\) | 1.50411 | 0.0511710 | ||||||||
\(865\) | −0.291167 | −0.00989997 | ||||||||
\(866\) | 6.73716 | 0.228938 | ||||||||
\(867\) | −1.36191 | −0.0462529 | ||||||||
\(868\) | 2.09789 | 0.0712070 | ||||||||
\(869\) | 6.30314 | 0.213819 | ||||||||
\(870\) | −0.587068 | −0.0199035 | ||||||||
\(871\) | −37.1691 | −1.25943 | ||||||||
\(872\) | −9.71703 | −0.329060 | ||||||||
\(873\) | −2.93579 | −0.0993614 | ||||||||
\(874\) | 14.0151 | 0.474069 | ||||||||
\(875\) | 9.84274 | 0.332745 | ||||||||
\(876\) | −0.449861 | −0.0151994 | ||||||||
\(877\) | 15.5589 | 0.525385 | 0.262693 | − | 0.964880i | \(-0.415390\pi\) | ||||
0.262693 | + | 0.964880i | \(0.415390\pi\) | |||||||
\(878\) | −25.4609 | −0.859263 | ||||||||
\(879\) | −3.99558 | −0.134768 | ||||||||
\(880\) | 0.319592 | 0.0107735 | ||||||||
\(881\) | 50.7898 | 1.71115 | 0.855576 | − | 0.517678i | \(-0.173203\pi\) | ||||
0.855576 | + | 0.517678i | \(0.173203\pi\) | |||||||
\(882\) | −7.62969 | −0.256905 | ||||||||
\(883\) | −7.29434 | −0.245474 | −0.122737 | − | 0.992439i | \(-0.539167\pi\) | ||||
−0.122737 | + | 0.992439i | \(0.539167\pi\) | |||||||
\(884\) | −8.15053 | −0.274132 | ||||||||
\(885\) | −1.02464 | −0.0344429 | ||||||||
\(886\) | 6.20495 | 0.208459 | ||||||||
\(887\) | 21.1724 | 0.710898 | 0.355449 | − | 0.934696i | \(-0.384328\pi\) | ||||
0.355449 | + | 0.934696i | \(0.384328\pi\) | |||||||
\(888\) | −1.34084 | −0.0449956 | ||||||||
\(889\) | −30.5505 | −1.02463 | ||||||||
\(890\) | 6.86893 | 0.230247 | ||||||||
\(891\) | −5.60741 | −0.187855 | ||||||||
\(892\) | −2.47720 | −0.0829428 | ||||||||
\(893\) | −12.6515 | −0.423366 | ||||||||
\(894\) | 4.48830 | 0.150111 | ||||||||
\(895\) | 3.47077 | 0.116015 | ||||||||
\(896\) | −2.09789 | −0.0700856 | ||||||||
\(897\) | 4.70053 | 0.156946 | ||||||||
\(898\) | 0.0172868 | 0.000576869 0 | ||||||||
\(899\) | −4.82413 | −0.160894 | ||||||||
\(900\) | 14.0018 | 0.466728 | ||||||||
\(901\) | 4.13749 | 0.137840 | ||||||||
\(902\) | 4.00160 | 0.133239 | ||||||||
\(903\) | −2.01580 | −0.0670816 | ||||||||
\(904\) | 8.10723 | 0.269642 | ||||||||
\(905\) | 10.7277 | 0.356602 | ||||||||
\(906\) | 2.50566 | 0.0832451 | ||||||||
\(907\) | 36.1105 | 1.19903 | 0.599515 | − | 0.800364i | \(-0.295360\pi\) | ||||
0.599515 | + | 0.800364i | \(0.295360\pi\) | |||||||
\(908\) | 21.2988 | 0.706827 | ||||||||
\(909\) | −47.8757 | −1.58794 | ||||||||
\(910\) | 2.40842 | 0.0798383 | ||||||||
\(911\) | 29.2671 | 0.969663 | 0.484831 | − | 0.874608i | \(-0.338881\pi\) | ||||
0.484831 | + | 0.874608i | \(0.338881\pi\) | |||||||
\(912\) | −0.457653 | −0.0151544 | ||||||||
\(913\) | 4.00534 | 0.132558 | ||||||||
\(914\) | 16.3152 | 0.539658 | ||||||||
\(915\) | 0.547290 | 0.0180928 | ||||||||
\(916\) | 10.3502 | 0.341981 | ||||||||
\(917\) | 29.2931 | 0.967343 | ||||||||
\(918\) | −5.12843 | −0.169264 | ||||||||
\(919\) | 5.14714 | 0.169788 | 0.0848942 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848942 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(920\) | 3.72675 | 0.122867 | ||||||||
\(921\) | −2.25385 | −0.0742670 | ||||||||
\(922\) | 2.90217 | 0.0955778 | ||||||||
\(923\) | −28.9454 | −0.952748 | ||||||||
\(924\) | −0.353764 | −0.0116380 | ||||||||
\(925\) | −25.2368 | −0.829781 | ||||||||
\(926\) | −3.78789 | −0.124478 | ||||||||
\(927\) | 12.5053 | 0.410727 | ||||||||
\(928\) | 4.82413 | 0.158360 | ||||||||
\(929\) | −15.8998 | −0.521657 | −0.260828 | − | 0.965385i | \(-0.583996\pi\) | ||||
−0.260828 | + | 0.965385i | \(0.583996\pi\) | |||||||
\(930\) | 0.121694 | 0.00399050 | ||||||||
\(931\) | 4.69371 | 0.153830 | ||||||||
\(932\) | 7.70459 | 0.252372 | ||||||||
\(933\) | 5.63575 | 0.184506 | ||||||||
\(934\) | 22.2445 | 0.727861 | ||||||||
\(935\) | −1.08968 | −0.0356365 | ||||||||
\(936\) | 7.01789 | 0.229387 | ||||||||
\(937\) | −5.73068 | −0.187213 | −0.0936065 | − | 0.995609i | \(-0.529840\pi\) | ||||
−0.0936065 | + | 0.995609i | \(0.529840\pi\) | |||||||
\(938\) | 32.6199 | 1.06508 | ||||||||
\(939\) | −5.01468 | −0.163648 | ||||||||
\(940\) | −3.36414 | −0.109726 | ||||||||
\(941\) | −30.8897 | −1.00698 | −0.503488 | − | 0.864002i | \(-0.667950\pi\) | ||||
−0.503488 | + | 0.864002i | \(0.667950\pi\) | |||||||
\(942\) | 2.11778 | 0.0690010 | ||||||||
\(943\) | 46.6624 | 1.51954 | ||||||||
\(944\) | 8.41980 | 0.274041 | ||||||||
\(945\) | 1.51541 | 0.0492963 | ||||||||
\(946\) | −2.52343 | −0.0820438 | ||||||||
\(947\) | 26.5130 | 0.861556 | 0.430778 | − | 0.902458i | \(-0.358239\pi\) | ||||
0.430778 | + | 0.902458i | \(0.358239\pi\) | |||||||
\(948\) | −2.40010 | −0.0779517 | ||||||||
\(949\) | −4.24383 | −0.137760 | ||||||||
\(950\) | −8.61380 | −0.279468 | ||||||||
\(951\) | −5.92052 | −0.191986 | ||||||||
\(952\) | 7.15298 | 0.231829 | ||||||||
\(953\) | 3.93794 | 0.127562 | 0.0637811 | − | 0.997964i | \(-0.479684\pi\) | ||||
0.0637811 | + | 0.997964i | \(0.479684\pi\) | |||||||
\(954\) | −3.56252 | −0.115341 | ||||||||
\(955\) | 8.48877 | 0.274690 | ||||||||
\(956\) | 10.8586 | 0.351193 | ||||||||
\(957\) | 0.813486 | 0.0262963 | ||||||||
\(958\) | −0.457308 | −0.0147750 | ||||||||
\(959\) | 19.1678 | 0.618961 | ||||||||
\(960\) | −0.121694 | −0.00392766 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −12.6490 | −0.407820 | ||||||||
\(963\) | 49.5512 | 1.59676 | ||||||||
\(964\) | 20.4943 | 0.660078 | ||||||||
\(965\) | 4.18973 | 0.134872 | ||||||||
\(966\) | −4.12522 | −0.132727 | ||||||||
\(967\) | −14.8872 | −0.478740 | −0.239370 | − | 0.970928i | \(-0.576941\pi\) | ||||
−0.239370 | + | 0.970928i | \(0.576941\pi\) | |||||||
\(968\) | 10.5571 | 0.339320 | ||||||||
\(969\) | 1.56042 | 0.0501278 | ||||||||
\(970\) | 0.480250 | 0.0154199 | ||||||||
\(971\) | −23.2297 | −0.745477 | −0.372738 | − | 0.927937i | \(-0.621581\pi\) | ||||
−0.372738 | + | 0.927937i | \(0.621581\pi\) | |||||||
\(972\) | 6.64753 | 0.213220 | ||||||||
\(973\) | −4.07674 | −0.130694 | ||||||||
\(974\) | 35.1270 | 1.12554 | ||||||||
\(975\) | −2.88898 | −0.0925213 | ||||||||
\(976\) | −4.49726 | −0.143954 | ||||||||
\(977\) | 48.2004 | 1.54207 | 0.771034 | − | 0.636794i | \(-0.219740\pi\) | ||||
0.771034 | + | 0.636794i | \(0.219740\pi\) | |||||||
\(978\) | −0.730007 | −0.0233430 | ||||||||
\(979\) | −9.51812 | −0.304200 | ||||||||
\(980\) | 1.24810 | 0.0398691 | ||||||||
\(981\) | −28.5272 | −0.910802 | ||||||||
\(982\) | 17.4311 | 0.556248 | ||||||||
\(983\) | 1.76035 | 0.0561463 | 0.0280731 | − | 0.999606i | \(-0.491063\pi\) | ||||
0.0280731 | + | 0.999606i | \(0.491063\pi\) | |||||||
\(984\) | −1.52372 | −0.0485745 | ||||||||
\(985\) | 2.59762 | 0.0827671 | ||||||||
\(986\) | −16.4484 | −0.523823 | ||||||||
\(987\) | 3.72385 | 0.118531 | ||||||||
\(988\) | −4.31734 | −0.137353 | ||||||||
\(989\) | −29.4256 | −0.935679 | ||||||||
\(990\) | 0.938256 | 0.0298197 | ||||||||
\(991\) | −32.4972 | −1.03231 | −0.516153 | − | 0.856496i | \(-0.672636\pi\) | ||||
−0.516153 | + | 0.856496i | \(0.672636\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 5.11131 | 0.162202 | ||||||||
\(994\) | 25.4027 | 0.805725 | ||||||||
\(995\) | 13.4160 | 0.425316 | ||||||||
\(996\) | −1.52515 | −0.0483263 | ||||||||
\(997\) | −14.5994 | −0.462367 | −0.231183 | − | 0.972910i | \(-0.574260\pi\) | ||||
−0.231183 | + | 0.972910i | \(0.574260\pi\) | |||||||
\(998\) | −10.6225 | −0.336249 | ||||||||
\(999\) | −7.95894 | −0.251810 |
(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 | 6014.2.a.f.1.13 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6014.2.a.f.1.13 | ✓ | 22 | 1.1 | even | 1 | trivial |