Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −2.56870 | −1.48304 | −0.741519 | − | 0.670931i | \(-0.765894\pi\) | ||||
−0.741519 | + | 0.670931i | \(0.765894\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.11955 | −0.500678 | −0.250339 | − | 0.968158i | \(-0.580542\pi\) | ||||
−0.250339 | + | 0.968158i | \(0.580542\pi\) | |||||||
\(6\) | −2.56870 | −1.04867 | ||||||||
\(7\) | −1.44974 | −0.547951 | −0.273975 | − | 0.961737i | \(-0.588339\pi\) | ||||
−0.273975 | + | 0.961737i | \(0.588339\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.59821 | 1.19940 | ||||||||
\(10\) | −1.11955 | −0.354033 | ||||||||
\(11\) | −1.59607 | −0.481234 | −0.240617 | − | 0.970620i | \(-0.577350\pi\) | ||||
−0.240617 | + | 0.970620i | \(0.577350\pi\) | |||||||
\(12\) | −2.56870 | −0.741519 | ||||||||
\(13\) | 3.12799 | 0.867549 | 0.433775 | − | 0.901021i | \(-0.357181\pi\) | ||||
0.433775 | + | 0.901021i | \(0.357181\pi\) | |||||||
\(14\) | −1.44974 | −0.387460 | ||||||||
\(15\) | 2.87579 | 0.742525 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.27438 | −1.27922 | −0.639612 | − | 0.768698i | \(-0.720905\pi\) | ||||
−0.639612 | + | 0.768698i | \(0.720905\pi\) | |||||||
\(18\) | 3.59821 | 0.848107 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −1.11955 | −0.250339 | ||||||||
\(21\) | 3.72395 | 0.812632 | ||||||||
\(22\) | −1.59607 | −0.340284 | ||||||||
\(23\) | −0.783250 | −0.163319 | −0.0816594 | − | 0.996660i | \(-0.526022\pi\) | ||||
−0.0816594 | + | 0.996660i | \(0.526022\pi\) | |||||||
\(24\) | −2.56870 | −0.524333 | ||||||||
\(25\) | −3.74661 | −0.749321 | ||||||||
\(26\) | 3.12799 | 0.613450 | ||||||||
\(27\) | −1.53663 | −0.295724 | ||||||||
\(28\) | −1.44974 | −0.273975 | ||||||||
\(29\) | 8.48094 | 1.57487 | 0.787435 | − | 0.616397i | \(-0.211408\pi\) | ||||
0.787435 | + | 0.616397i | \(0.211408\pi\) | |||||||
\(30\) | 2.87579 | 0.525044 | ||||||||
\(31\) | 4.24784 | 0.762934 | 0.381467 | − | 0.924382i | \(-0.375419\pi\) | ||||
0.381467 | + | 0.924382i | \(0.375419\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.09983 | 0.713689 | ||||||||
\(34\) | −5.27438 | −0.904548 | ||||||||
\(35\) | 1.62306 | 0.274347 | ||||||||
\(36\) | 3.59821 | 0.599702 | ||||||||
\(37\) | −7.23807 | −1.18993 | −0.594966 | − | 0.803751i | \(-0.702834\pi\) | ||||
−0.594966 | + | 0.803751i | \(0.702834\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −8.03487 | −1.28661 | ||||||||
\(40\) | −1.11955 | −0.177016 | ||||||||
\(41\) | −0.308723 | −0.0482144 | −0.0241072 | − | 0.999709i | \(-0.507674\pi\) | ||||
−0.0241072 | + | 0.999709i | \(0.507674\pi\) | |||||||
\(42\) | 3.72395 | 0.574618 | ||||||||
\(43\) | 10.5372 | 1.60690 | 0.803452 | − | 0.595370i | \(-0.202995\pi\) | ||||
0.803452 | + | 0.595370i | \(0.202995\pi\) | |||||||
\(44\) | −1.59607 | −0.240617 | ||||||||
\(45\) | −4.02838 | −0.600515 | ||||||||
\(46\) | −0.783250 | −0.115484 | ||||||||
\(47\) | 1.70974 | 0.249392 | 0.124696 | − | 0.992195i | \(-0.460204\pi\) | ||||
0.124696 | + | 0.992195i | \(0.460204\pi\) | |||||||
\(48\) | −2.56870 | −0.370760 | ||||||||
\(49\) | −4.89825 | −0.699750 | ||||||||
\(50\) | −3.74661 | −0.529850 | ||||||||
\(51\) | 13.5483 | 1.89714 | ||||||||
\(52\) | 3.12799 | 0.433775 | ||||||||
\(53\) | 6.97906 | 0.958647 | 0.479324 | − | 0.877638i | \(-0.340882\pi\) | ||||
0.479324 | + | 0.877638i | \(0.340882\pi\) | |||||||
\(54\) | −1.53663 | −0.209108 | ||||||||
\(55\) | 1.78689 | 0.240944 | ||||||||
\(56\) | −1.44974 | −0.193730 | ||||||||
\(57\) | −2.56870 | −0.340232 | ||||||||
\(58\) | 8.48094 | 1.11360 | ||||||||
\(59\) | −12.0572 | −1.56971 | −0.784854 | − | 0.619681i | \(-0.787262\pi\) | ||||
−0.784854 | + | 0.619681i | \(0.787262\pi\) | |||||||
\(60\) | 2.87579 | 0.371262 | ||||||||
\(61\) | −0.529483 | −0.0677934 | −0.0338967 | − | 0.999425i | \(-0.510792\pi\) | ||||
−0.0338967 | + | 0.999425i | \(0.510792\pi\) | |||||||
\(62\) | 4.24784 | 0.539476 | ||||||||
\(63\) | −5.21648 | −0.657215 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.50195 | −0.434363 | ||||||||
\(66\) | 4.09983 | 0.504655 | ||||||||
\(67\) | 4.61367 | 0.563649 | 0.281825 | − | 0.959466i | \(-0.409060\pi\) | ||||
0.281825 | + | 0.959466i | \(0.409060\pi\) | |||||||
\(68\) | −5.27438 | −0.639612 | ||||||||
\(69\) | 2.01193 | 0.242208 | ||||||||
\(70\) | 1.62306 | 0.193993 | ||||||||
\(71\) | −2.79282 | −0.331447 | −0.165723 | − | 0.986172i | \(-0.552996\pi\) | ||||
−0.165723 | + | 0.986172i | \(0.552996\pi\) | |||||||
\(72\) | 3.59821 | 0.424053 | ||||||||
\(73\) | 13.8081 | 1.61612 | 0.808058 | − | 0.589103i | \(-0.200519\pi\) | ||||
0.808058 | + | 0.589103i | \(0.200519\pi\) | |||||||
\(74\) | −7.23807 | −0.841409 | ||||||||
\(75\) | 9.62390 | 1.11127 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 2.31390 | 0.263693 | ||||||||
\(78\) | −8.03487 | −0.909770 | ||||||||
\(79\) | −5.27871 | −0.593901 | −0.296951 | − | 0.954893i | \(-0.595970\pi\) | ||||
−0.296951 | + | 0.954893i | \(0.595970\pi\) | |||||||
\(80\) | −1.11955 | −0.125170 | ||||||||
\(81\) | −6.84751 | −0.760834 | ||||||||
\(82\) | −0.308723 | −0.0340927 | ||||||||
\(83\) | 9.23497 | 1.01367 | 0.506835 | − | 0.862043i | \(-0.330815\pi\) | ||||
0.506835 | + | 0.862043i | \(0.330815\pi\) | |||||||
\(84\) | 3.72395 | 0.406316 | ||||||||
\(85\) | 5.90493 | 0.640480 | ||||||||
\(86\) | 10.5372 | 1.13625 | ||||||||
\(87\) | −21.7850 | −2.33559 | ||||||||
\(88\) | −1.59607 | −0.170142 | ||||||||
\(89\) | −4.76645 | −0.505243 | −0.252621 | − | 0.967565i | \(-0.581293\pi\) | ||||
−0.252621 | + | 0.967565i | \(0.581293\pi\) | |||||||
\(90\) | −4.02838 | −0.424628 | ||||||||
\(91\) | −4.53478 | −0.475374 | ||||||||
\(92\) | −0.783250 | −0.0816594 | ||||||||
\(93\) | −10.9114 | −1.13146 | ||||||||
\(94\) | 1.70974 | 0.176347 | ||||||||
\(95\) | −1.11955 | −0.114863 | ||||||||
\(96\) | −2.56870 | −0.262167 | ||||||||
\(97\) | −12.8257 | −1.30225 | −0.651125 | − | 0.758970i | \(-0.725703\pi\) | ||||
−0.651125 | + | 0.758970i | \(0.725703\pi\) | |||||||
\(98\) | −4.89825 | −0.494798 | ||||||||
\(99\) | −5.74301 | −0.577195 | ||||||||
\(100\) | −3.74661 | −0.374661 | ||||||||
\(101\) | 14.1213 | 1.40512 | 0.702560 | − | 0.711625i | \(-0.252040\pi\) | ||||
0.702560 | + | 0.711625i | \(0.252040\pi\) | |||||||
\(102\) | 13.5483 | 1.34148 | ||||||||
\(103\) | 10.7149 | 1.05577 | 0.527884 | − | 0.849316i | \(-0.322985\pi\) | ||||
0.527884 | + | 0.849316i | \(0.322985\pi\) | |||||||
\(104\) | 3.12799 | 0.306725 | ||||||||
\(105\) | −4.16915 | −0.406867 | ||||||||
\(106\) | 6.97906 | 0.677866 | ||||||||
\(107\) | −10.6703 | −1.03154 | −0.515770 | − | 0.856727i | \(-0.672494\pi\) | ||||
−0.515770 | + | 0.856727i | \(0.672494\pi\) | |||||||
\(108\) | −1.53663 | −0.147862 | ||||||||
\(109\) | −9.54223 | −0.913980 | −0.456990 | − | 0.889472i | \(-0.651072\pi\) | ||||
−0.456990 | + | 0.889472i | \(0.651072\pi\) | |||||||
\(110\) | 1.78689 | 0.170373 | ||||||||
\(111\) | 18.5924 | 1.76471 | ||||||||
\(112\) | −1.44974 | −0.136988 | ||||||||
\(113\) | 3.61727 | 0.340284 | 0.170142 | − | 0.985420i | \(-0.445577\pi\) | ||||
0.170142 | + | 0.985420i | \(0.445577\pi\) | |||||||
\(114\) | −2.56870 | −0.240581 | ||||||||
\(115\) | 0.876887 | 0.0817702 | ||||||||
\(116\) | 8.48094 | 0.787435 | ||||||||
\(117\) | 11.2552 | 1.04054 | ||||||||
\(118\) | −12.0572 | −1.10995 | ||||||||
\(119\) | 7.64649 | 0.700952 | ||||||||
\(120\) | 2.87579 | 0.262522 | ||||||||
\(121\) | −8.45255 | −0.768413 | ||||||||
\(122\) | −0.529483 | −0.0479372 | ||||||||
\(123\) | 0.793016 | 0.0715038 | ||||||||
\(124\) | 4.24784 | 0.381467 | ||||||||
\(125\) | 9.79227 | 0.875847 | ||||||||
\(126\) | −5.21648 | −0.464721 | ||||||||
\(127\) | −8.96922 | −0.795890 | −0.397945 | − | 0.917409i | \(-0.630277\pi\) | ||||
−0.397945 | + | 0.917409i | \(0.630277\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −27.0668 | −2.38310 | ||||||||
\(130\) | −3.50195 | −0.307141 | ||||||||
\(131\) | 19.2311 | 1.68023 | 0.840115 | − | 0.542408i | \(-0.182487\pi\) | ||||
0.840115 | + | 0.542408i | \(0.182487\pi\) | |||||||
\(132\) | 4.09983 | 0.356845 | ||||||||
\(133\) | −1.44974 | −0.125709 | ||||||||
\(134\) | 4.61367 | 0.398560 | ||||||||
\(135\) | 1.72033 | 0.148062 | ||||||||
\(136\) | −5.27438 | −0.452274 | ||||||||
\(137\) | 8.29430 | 0.708630 | 0.354315 | − | 0.935126i | \(-0.384714\pi\) | ||||
0.354315 | + | 0.935126i | \(0.384714\pi\) | |||||||
\(138\) | 2.01193 | 0.171267 | ||||||||
\(139\) | 2.58268 | 0.219060 | 0.109530 | − | 0.993983i | \(-0.465065\pi\) | ||||
0.109530 | + | 0.993983i | \(0.465065\pi\) | |||||||
\(140\) | 1.62306 | 0.137174 | ||||||||
\(141\) | −4.39182 | −0.369858 | ||||||||
\(142\) | −2.79282 | −0.234368 | ||||||||
\(143\) | −4.99251 | −0.417495 | ||||||||
\(144\) | 3.59821 | 0.299851 | ||||||||
\(145\) | −9.49484 | −0.788503 | ||||||||
\(146\) | 13.8081 | 1.14277 | ||||||||
\(147\) | 12.5821 | 1.03776 | ||||||||
\(148\) | −7.23807 | −0.594966 | ||||||||
\(149\) | −3.79596 | −0.310977 | −0.155489 | − | 0.987838i | \(-0.549695\pi\) | ||||
−0.155489 | + | 0.987838i | \(0.549695\pi\) | |||||||
\(150\) | 9.62390 | 0.785789 | ||||||||
\(151\) | −4.42526 | −0.360122 | −0.180061 | − | 0.983655i | \(-0.557630\pi\) | ||||
−0.180061 | + | 0.983655i | \(0.557630\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −18.9783 | −1.53431 | ||||||||
\(154\) | 2.31390 | 0.186459 | ||||||||
\(155\) | −4.75567 | −0.381984 | ||||||||
\(156\) | −8.03487 | −0.643305 | ||||||||
\(157\) | −10.9439 | −0.873422 | −0.436711 | − | 0.899602i | \(-0.643857\pi\) | ||||
−0.436711 | + | 0.899602i | \(0.643857\pi\) | |||||||
\(158\) | −5.27871 | −0.419951 | ||||||||
\(159\) | −17.9271 | −1.42171 | ||||||||
\(160\) | −1.11955 | −0.0885082 | ||||||||
\(161\) | 1.13551 | 0.0894907 | ||||||||
\(162\) | −6.84751 | −0.537991 | ||||||||
\(163\) | −7.68585 | −0.602002 | −0.301001 | − | 0.953624i | \(-0.597321\pi\) | ||||
−0.301001 | + | 0.953624i | \(0.597321\pi\) | |||||||
\(164\) | −0.308723 | −0.0241072 | ||||||||
\(165\) | −4.58997 | −0.357329 | ||||||||
\(166\) | 9.23497 | 0.716773 | ||||||||
\(167\) | 12.0757 | 0.934447 | 0.467223 | − | 0.884139i | \(-0.345254\pi\) | ||||
0.467223 | + | 0.884139i | \(0.345254\pi\) | |||||||
\(168\) | 3.72395 | 0.287309 | ||||||||
\(169\) | −3.21566 | −0.247358 | ||||||||
\(170\) | 5.90493 | 0.452887 | ||||||||
\(171\) | 3.59821 | 0.275162 | ||||||||
\(172\) | 10.5372 | 0.803452 | ||||||||
\(173\) | −12.7449 | −0.968976 | −0.484488 | − | 0.874798i | \(-0.660994\pi\) | ||||
−0.484488 | + | 0.874798i | \(0.660994\pi\) | |||||||
\(174\) | −21.7850 | −1.65151 | ||||||||
\(175\) | 5.43161 | 0.410591 | ||||||||
\(176\) | −1.59607 | −0.120309 | ||||||||
\(177\) | 30.9712 | 2.32794 | ||||||||
\(178\) | −4.76645 | −0.357260 | ||||||||
\(179\) | 20.9073 | 1.56269 | 0.781344 | − | 0.624101i | \(-0.214535\pi\) | ||||
0.781344 | + | 0.624101i | \(0.214535\pi\) | |||||||
\(180\) | −4.02838 | −0.300258 | ||||||||
\(181\) | 1.33857 | 0.0994954 | 0.0497477 | − | 0.998762i | \(-0.484158\pi\) | ||||
0.0497477 | + | 0.998762i | \(0.484158\pi\) | |||||||
\(182\) | −4.53478 | −0.336140 | ||||||||
\(183\) | 1.36008 | 0.100540 | ||||||||
\(184\) | −0.783250 | −0.0577419 | ||||||||
\(185\) | 8.10338 | 0.595773 | ||||||||
\(186\) | −10.9114 | −0.800063 | ||||||||
\(187\) | 8.41830 | 0.615607 | ||||||||
\(188\) | 1.70974 | 0.124696 | ||||||||
\(189\) | 2.22771 | 0.162042 | ||||||||
\(190\) | −1.11955 | −0.0812207 | ||||||||
\(191\) | −21.7762 | −1.57567 | −0.787834 | − | 0.615888i | \(-0.788797\pi\) | ||||
−0.787834 | + | 0.615888i | \(0.788797\pi\) | |||||||
\(192\) | −2.56870 | −0.185380 | ||||||||
\(193\) | −4.51037 | −0.324663 | −0.162332 | − | 0.986736i | \(-0.551901\pi\) | ||||
−0.162332 | + | 0.986736i | \(0.551901\pi\) | |||||||
\(194\) | −12.8257 | −0.920830 | ||||||||
\(195\) | 8.99544 | 0.644177 | ||||||||
\(196\) | −4.89825 | −0.349875 | ||||||||
\(197\) | −6.26163 | −0.446122 | −0.223061 | − | 0.974804i | \(-0.571605\pi\) | ||||
−0.223061 | + | 0.974804i | \(0.571605\pi\) | |||||||
\(198\) | −5.74301 | −0.408138 | ||||||||
\(199\) | −6.13531 | −0.434921 | −0.217460 | − | 0.976069i | \(-0.569777\pi\) | ||||
−0.217460 | + | 0.976069i | \(0.569777\pi\) | |||||||
\(200\) | −3.74661 | −0.264925 | ||||||||
\(201\) | −11.8511 | −0.835914 | ||||||||
\(202\) | 14.1213 | 0.993569 | ||||||||
\(203\) | −12.2952 | −0.862952 | ||||||||
\(204\) | 13.5483 | 0.948570 | ||||||||
\(205\) | 0.345631 | 0.0241399 | ||||||||
\(206\) | 10.7149 | 0.746541 | ||||||||
\(207\) | −2.81830 | −0.195885 | ||||||||
\(208\) | 3.12799 | 0.216887 | ||||||||
\(209\) | −1.59607 | −0.110403 | ||||||||
\(210\) | −4.16915 | −0.287699 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 6.97906 | 0.479324 | ||||||||
\(213\) | 7.17391 | 0.491548 | ||||||||
\(214\) | −10.6703 | −0.729409 | ||||||||
\(215\) | −11.7969 | −0.804541 | ||||||||
\(216\) | −1.53663 | −0.104554 | ||||||||
\(217\) | −6.15827 | −0.418050 | ||||||||
\(218\) | −9.54223 | −0.646281 | ||||||||
\(219\) | −35.4688 | −2.39676 | ||||||||
\(220\) | 1.78689 | 0.120472 | ||||||||
\(221\) | −16.4982 | −1.10979 | ||||||||
\(222\) | 18.5924 | 1.24784 | ||||||||
\(223\) | −13.4467 | −0.900459 | −0.450229 | − | 0.892913i | \(-0.648658\pi\) | ||||
−0.450229 | + | 0.892913i | \(0.648658\pi\) | |||||||
\(224\) | −1.44974 | −0.0968650 | ||||||||
\(225\) | −13.4811 | −0.898739 | ||||||||
\(226\) | 3.61727 | 0.240617 | ||||||||
\(227\) | −14.0539 | −0.932790 | −0.466395 | − | 0.884577i | \(-0.654447\pi\) | ||||
−0.466395 | + | 0.884577i | \(0.654447\pi\) | |||||||
\(228\) | −2.56870 | −0.170116 | ||||||||
\(229\) | 3.54804 | 0.234461 | 0.117230 | − | 0.993105i | \(-0.462598\pi\) | ||||
0.117230 | + | 0.993105i | \(0.462598\pi\) | |||||||
\(230\) | 0.876887 | 0.0578202 | ||||||||
\(231\) | −5.94370 | −0.391067 | ||||||||
\(232\) | 8.48094 | 0.556801 | ||||||||
\(233\) | −26.5635 | −1.74024 | −0.870118 | − | 0.492844i | \(-0.835957\pi\) | ||||
−0.870118 | + | 0.492844i | \(0.835957\pi\) | |||||||
\(234\) | 11.2552 | 0.735774 | ||||||||
\(235\) | −1.91414 | −0.124865 | ||||||||
\(236\) | −12.0572 | −0.784854 | ||||||||
\(237\) | 13.5594 | 0.880778 | ||||||||
\(238\) | 7.64649 | 0.495648 | ||||||||
\(239\) | −4.33166 | −0.280192 | −0.140096 | − | 0.990138i | \(-0.544741\pi\) | ||||
−0.140096 | + | 0.990138i | \(0.544741\pi\) | |||||||
\(240\) | 2.87579 | 0.185631 | ||||||||
\(241\) | 17.5154 | 1.12827 | 0.564135 | − | 0.825683i | \(-0.309210\pi\) | ||||
0.564135 | + | 0.825683i | \(0.309210\pi\) | |||||||
\(242\) | −8.45255 | −0.543350 | ||||||||
\(243\) | 22.1991 | 1.42407 | ||||||||
\(244\) | −0.529483 | −0.0338967 | ||||||||
\(245\) | 5.48383 | 0.350349 | ||||||||
\(246\) | 0.793016 | 0.0505608 | ||||||||
\(247\) | 3.12799 | 0.199029 | ||||||||
\(248\) | 4.24784 | 0.269738 | ||||||||
\(249\) | −23.7218 | −1.50331 | ||||||||
\(250\) | 9.79227 | 0.619317 | ||||||||
\(251\) | 17.9688 | 1.13418 | 0.567091 | − | 0.823655i | \(-0.308069\pi\) | ||||
0.567091 | + | 0.823655i | \(0.308069\pi\) | |||||||
\(252\) | −5.21648 | −0.328607 | ||||||||
\(253\) | 1.25012 | 0.0785947 | ||||||||
\(254\) | −8.96922 | −0.562779 | ||||||||
\(255\) | −15.1680 | −0.949856 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.8193 | −0.862023 | −0.431011 | − | 0.902346i | \(-0.641843\pi\) | ||||
−0.431011 | + | 0.902346i | \(0.641843\pi\) | |||||||
\(258\) | −27.0668 | −1.68511 | ||||||||
\(259\) | 10.4933 | 0.652024 | ||||||||
\(260\) | −3.50195 | −0.217181 | ||||||||
\(261\) | 30.5162 | 1.88891 | ||||||||
\(262\) | 19.2311 | 1.18810 | ||||||||
\(263\) | 19.3564 | 1.19357 | 0.596783 | − | 0.802402i | \(-0.296445\pi\) | ||||
0.596783 | + | 0.802402i | \(0.296445\pi\) | |||||||
\(264\) | 4.09983 | 0.252327 | ||||||||
\(265\) | −7.81341 | −0.479974 | ||||||||
\(266\) | −1.44974 | −0.0888894 | ||||||||
\(267\) | 12.2436 | 0.749294 | ||||||||
\(268\) | 4.61367 | 0.281825 | ||||||||
\(269\) | −7.48232 | −0.456205 | −0.228103 | − | 0.973637i | \(-0.573252\pi\) | ||||
−0.228103 | + | 0.973637i | \(0.573252\pi\) | |||||||
\(270\) | 1.72033 | 0.104696 | ||||||||
\(271\) | 22.9387 | 1.39343 | 0.696713 | − | 0.717350i | \(-0.254645\pi\) | ||||
0.696713 | + | 0.717350i | \(0.254645\pi\) | |||||||
\(272\) | −5.27438 | −0.319806 | ||||||||
\(273\) | 11.6485 | 0.704999 | ||||||||
\(274\) | 8.29430 | 0.501077 | ||||||||
\(275\) | 5.97986 | 0.360599 | ||||||||
\(276\) | 2.01193 | 0.121104 | ||||||||
\(277\) | −22.6938 | −1.36354 | −0.681770 | − | 0.731567i | \(-0.738789\pi\) | ||||
−0.681770 | + | 0.731567i | \(0.738789\pi\) | |||||||
\(278\) | 2.58268 | 0.154899 | ||||||||
\(279\) | 15.2846 | 0.915066 | ||||||||
\(280\) | 1.62306 | 0.0969963 | ||||||||
\(281\) | 11.2472 | 0.670951 | 0.335475 | − | 0.942049i | \(-0.391103\pi\) | ||||
0.335475 | + | 0.942049i | \(0.391103\pi\) | |||||||
\(282\) | −4.39182 | −0.261529 | ||||||||
\(283\) | −33.5810 | −1.99618 | −0.998091 | − | 0.0617538i | \(-0.980331\pi\) | ||||
−0.998091 | + | 0.0617538i | \(0.980331\pi\) | |||||||
\(284\) | −2.79282 | −0.165723 | ||||||||
\(285\) | 2.87579 | 0.170347 | ||||||||
\(286\) | −4.99251 | −0.295213 | ||||||||
\(287\) | 0.447568 | 0.0264191 | ||||||||
\(288\) | 3.59821 | 0.212027 | ||||||||
\(289\) | 10.8191 | 0.636415 | ||||||||
\(290\) | −9.49484 | −0.557556 | ||||||||
\(291\) | 32.9453 | 1.93129 | ||||||||
\(292\) | 13.8081 | 0.808058 | ||||||||
\(293\) | −16.6218 | −0.971057 | −0.485528 | − | 0.874221i | \(-0.661373\pi\) | ||||
−0.485528 | + | 0.874221i | \(0.661373\pi\) | |||||||
\(294\) | 12.5821 | 0.733804 | ||||||||
\(295\) | 13.4986 | 0.785918 | ||||||||
\(296\) | −7.23807 | −0.420704 | ||||||||
\(297\) | 2.45257 | 0.142312 | ||||||||
\(298\) | −3.79596 | −0.219894 | ||||||||
\(299\) | −2.45000 | −0.141687 | ||||||||
\(300\) | 9.62390 | 0.555636 | ||||||||
\(301\) | −15.2762 | −0.880504 | ||||||||
\(302\) | −4.42526 | −0.254645 | ||||||||
\(303\) | −36.2733 | −2.08385 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0.592783 | 0.0339427 | ||||||||
\(306\) | −18.9783 | −1.08492 | ||||||||
\(307\) | −23.7172 | −1.35361 | −0.676806 | − | 0.736162i | \(-0.736636\pi\) | ||||
−0.676806 | + | 0.736162i | \(0.736636\pi\) | |||||||
\(308\) | 2.31390 | 0.131846 | ||||||||
\(309\) | −27.5233 | −1.56575 | ||||||||
\(310\) | −4.75567 | −0.270104 | ||||||||
\(311\) | −31.4708 | −1.78454 | −0.892272 | − | 0.451498i | \(-0.850890\pi\) | ||||
−0.892272 | + | 0.451498i | \(0.850890\pi\) | |||||||
\(312\) | −8.03487 | −0.454885 | ||||||||
\(313\) | −20.0011 | −1.13053 | −0.565265 | − | 0.824910i | \(-0.691226\pi\) | ||||
−0.565265 | + | 0.824910i | \(0.691226\pi\) | |||||||
\(314\) | −10.9439 | −0.617603 | ||||||||
\(315\) | 5.84011 | 0.329053 | ||||||||
\(316\) | −5.27871 | −0.296951 | ||||||||
\(317\) | −20.0539 | −1.12634 | −0.563169 | − | 0.826341i | \(-0.690418\pi\) | ||||
−0.563169 | + | 0.826341i | \(0.690418\pi\) | |||||||
\(318\) | −17.9271 | −1.00530 | ||||||||
\(319\) | −13.5362 | −0.757882 | ||||||||
\(320\) | −1.11955 | −0.0625848 | ||||||||
\(321\) | 27.4089 | 1.52981 | ||||||||
\(322\) | 1.13551 | 0.0632795 | ||||||||
\(323\) | −5.27438 | −0.293474 | ||||||||
\(324\) | −6.84751 | −0.380417 | ||||||||
\(325\) | −11.7194 | −0.650073 | ||||||||
\(326\) | −7.68585 | −0.425680 | ||||||||
\(327\) | 24.5111 | 1.35547 | ||||||||
\(328\) | −0.308723 | −0.0170464 | ||||||||
\(329\) | −2.47869 | −0.136654 | ||||||||
\(330\) | −4.58997 | −0.252669 | ||||||||
\(331\) | 6.26128 | 0.344151 | 0.172075 | − | 0.985084i | \(-0.444953\pi\) | ||||
0.172075 | + | 0.985084i | \(0.444953\pi\) | |||||||
\(332\) | 9.23497 | 0.506835 | ||||||||
\(333\) | −26.0441 | −1.42721 | ||||||||
\(334\) | 12.0757 | 0.660754 | ||||||||
\(335\) | −5.16523 | −0.282207 | ||||||||
\(336\) | 3.72395 | 0.203158 | ||||||||
\(337\) | −14.6756 | −0.799431 | −0.399715 | − | 0.916639i | \(-0.630891\pi\) | ||||
−0.399715 | + | 0.916639i | \(0.630891\pi\) | |||||||
\(338\) | −3.21566 | −0.174909 | ||||||||
\(339\) | −9.29168 | −0.504655 | ||||||||
\(340\) | 5.90493 | 0.320240 | ||||||||
\(341\) | −6.77986 | −0.367150 | ||||||||
\(342\) | 3.59821 | 0.194569 | ||||||||
\(343\) | 17.2494 | 0.931380 | ||||||||
\(344\) | 10.5372 | 0.568126 | ||||||||
\(345\) | −2.25246 | −0.121268 | ||||||||
\(346\) | −12.7449 | −0.685170 | ||||||||
\(347\) | −31.6736 | −1.70033 | −0.850163 | − | 0.526520i | \(-0.823497\pi\) | ||||
−0.850163 | + | 0.526520i | \(0.823497\pi\) | |||||||
\(348\) | −21.7850 | −1.16780 | ||||||||
\(349\) | −4.24754 | −0.227366 | −0.113683 | − | 0.993517i | \(-0.536265\pi\) | ||||
−0.113683 | + | 0.993517i | \(0.536265\pi\) | |||||||
\(350\) | 5.43161 | 0.290332 | ||||||||
\(351\) | −4.80655 | −0.256555 | ||||||||
\(352\) | −1.59607 | −0.0850710 | ||||||||
\(353\) | 24.0277 | 1.27886 | 0.639432 | − | 0.768848i | \(-0.279169\pi\) | ||||
0.639432 | + | 0.768848i | \(0.279169\pi\) | |||||||
\(354\) | 30.9712 | 1.64610 | ||||||||
\(355\) | 3.12670 | 0.165948 | ||||||||
\(356\) | −4.76645 | −0.252621 | ||||||||
\(357\) | −19.6415 | −1.03954 | ||||||||
\(358\) | 20.9073 | 1.10499 | ||||||||
\(359\) | 23.1048 | 1.21943 | 0.609713 | − | 0.792622i | \(-0.291285\pi\) | ||||
0.609713 | + | 0.792622i | \(0.291285\pi\) | |||||||
\(360\) | −4.02838 | −0.212314 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 1.33857 | 0.0703539 | ||||||||
\(363\) | 21.7120 | 1.13959 | ||||||||
\(364\) | −4.53478 | −0.237687 | ||||||||
\(365\) | −15.4589 | −0.809154 | ||||||||
\(366\) | 1.36008 | 0.0710927 | ||||||||
\(367\) | 9.79259 | 0.511169 | 0.255584 | − | 0.966787i | \(-0.417732\pi\) | ||||
0.255584 | + | 0.966787i | \(0.417732\pi\) | |||||||
\(368\) | −0.783250 | −0.0408297 | ||||||||
\(369\) | −1.11085 | −0.0578285 | ||||||||
\(370\) | 8.10338 | 0.421275 | ||||||||
\(371\) | −10.1178 | −0.525292 | ||||||||
\(372\) | −10.9114 | −0.565730 | ||||||||
\(373\) | −14.7854 | −0.765561 | −0.382781 | − | 0.923839i | \(-0.625033\pi\) | ||||
−0.382781 | + | 0.923839i | \(0.625033\pi\) | |||||||
\(374\) | 8.41830 | 0.435300 | ||||||||
\(375\) | −25.1534 | −1.29891 | ||||||||
\(376\) | 1.70974 | 0.0881733 | ||||||||
\(377\) | 26.5283 | 1.36628 | ||||||||
\(378\) | 2.22771 | 0.114581 | ||||||||
\(379\) | −32.9460 | −1.69232 | −0.846160 | − | 0.532929i | \(-0.821091\pi\) | ||||
−0.846160 | + | 0.532929i | \(0.821091\pi\) | |||||||
\(380\) | −1.11955 | −0.0574317 | ||||||||
\(381\) | 23.0392 | 1.18034 | ||||||||
\(382\) | −21.7762 | −1.11416 | ||||||||
\(383\) | −2.22797 | −0.113844 | −0.0569220 | − | 0.998379i | \(-0.518129\pi\) | ||||
−0.0569220 | + | 0.998379i | \(0.518129\pi\) | |||||||
\(384\) | −2.56870 | −0.131083 | ||||||||
\(385\) | −2.59052 | −0.132025 | ||||||||
\(386\) | −4.51037 | −0.229572 | ||||||||
\(387\) | 37.9150 | 1.92733 | ||||||||
\(388\) | −12.8257 | −0.651125 | ||||||||
\(389\) | −15.9564 | −0.809022 | −0.404511 | − | 0.914533i | \(-0.632558\pi\) | ||||
−0.404511 | + | 0.914533i | \(0.632558\pi\) | |||||||
\(390\) | 8.99544 | 0.455502 | ||||||||
\(391\) | 4.13115 | 0.208921 | ||||||||
\(392\) | −4.89825 | −0.247399 | ||||||||
\(393\) | −49.3989 | −2.49185 | ||||||||
\(394\) | −6.26163 | −0.315456 | ||||||||
\(395\) | 5.90978 | 0.297353 | ||||||||
\(396\) | −5.74301 | −0.288597 | ||||||||
\(397\) | −16.5148 | −0.828855 | −0.414427 | − | 0.910082i | \(-0.636018\pi\) | ||||
−0.414427 | + | 0.910082i | \(0.636018\pi\) | |||||||
\(398\) | −6.13531 | −0.307535 | ||||||||
\(399\) | 3.72395 | 0.186431 | ||||||||
\(400\) | −3.74661 | −0.187330 | ||||||||
\(401\) | −1.36916 | −0.0683726 | −0.0341863 | − | 0.999415i | \(-0.510884\pi\) | ||||
−0.0341863 | + | 0.999415i | \(0.510884\pi\) | |||||||
\(402\) | −11.8511 | −0.591080 | ||||||||
\(403\) | 13.2872 | 0.661883 | ||||||||
\(404\) | 14.1213 | 0.702560 | ||||||||
\(405\) | 7.66613 | 0.380933 | ||||||||
\(406\) | −12.2952 | −0.610199 | ||||||||
\(407\) | 11.5525 | 0.572636 | ||||||||
\(408\) | 13.5483 | 0.670740 | ||||||||
\(409\) | −33.9138 | −1.67693 | −0.838464 | − | 0.544958i | \(-0.816546\pi\) | ||||
−0.838464 | + | 0.544958i | \(0.816546\pi\) | |||||||
\(410\) | 0.345631 | 0.0170695 | ||||||||
\(411\) | −21.3056 | −1.05093 | ||||||||
\(412\) | 10.7149 | 0.527884 | ||||||||
\(413\) | 17.4798 | 0.860123 | ||||||||
\(414\) | −2.81830 | −0.138512 | ||||||||
\(415\) | −10.3390 | −0.507522 | ||||||||
\(416\) | 3.12799 | 0.153362 | ||||||||
\(417\) | −6.63413 | −0.324875 | ||||||||
\(418\) | −1.59607 | −0.0780665 | ||||||||
\(419\) | −4.70812 | −0.230007 | −0.115003 | − | 0.993365i | \(-0.536688\pi\) | ||||
−0.115003 | + | 0.993365i | \(0.536688\pi\) | |||||||
\(420\) | −4.16915 | −0.203434 | ||||||||
\(421\) | −5.43867 | −0.265065 | −0.132532 | − | 0.991179i | \(-0.542311\pi\) | ||||
−0.132532 | + | 0.991179i | \(0.542311\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 6.15202 | 0.299121 | ||||||||
\(424\) | 6.97906 | 0.338933 | ||||||||
\(425\) | 19.7610 | 0.958550 | ||||||||
\(426\) | 7.17391 | 0.347577 | ||||||||
\(427\) | 0.767614 | 0.0371474 | ||||||||
\(428\) | −10.6703 | −0.515770 | ||||||||
\(429\) | 12.8243 | 0.619161 | ||||||||
\(430\) | −11.7969 | −0.568897 | ||||||||
\(431\) | 24.7539 | 1.19235 | 0.596177 | − | 0.802853i | \(-0.296686\pi\) | ||||
0.596177 | + | 0.802853i | \(0.296686\pi\) | |||||||
\(432\) | −1.53663 | −0.0739309 | ||||||||
\(433\) | −17.4451 | −0.838360 | −0.419180 | − | 0.907903i | \(-0.637682\pi\) | ||||
−0.419180 | + | 0.907903i | \(0.637682\pi\) | |||||||
\(434\) | −6.15827 | −0.295606 | ||||||||
\(435\) | 24.3894 | 1.16938 | ||||||||
\(436\) | −9.54223 | −0.456990 | ||||||||
\(437\) | −0.783250 | −0.0374679 | ||||||||
\(438\) | −35.4688 | −1.69477 | ||||||||
\(439\) | 27.0520 | 1.29112 | 0.645561 | − | 0.763708i | \(-0.276623\pi\) | ||||
0.645561 | + | 0.763708i | \(0.276623\pi\) | |||||||
\(440\) | 1.78689 | 0.0851864 | ||||||||
\(441\) | −17.6249 | −0.839283 | ||||||||
\(442\) | −16.4982 | −0.784740 | ||||||||
\(443\) | −11.9016 | −0.565460 | −0.282730 | − | 0.959199i | \(-0.591240\pi\) | ||||
−0.282730 | + | 0.959199i | \(0.591240\pi\) | |||||||
\(444\) | 18.5924 | 0.882357 | ||||||||
\(445\) | 5.33628 | 0.252964 | ||||||||
\(446\) | −13.4467 | −0.636721 | ||||||||
\(447\) | 9.75068 | 0.461191 | ||||||||
\(448\) | −1.44974 | −0.0684939 | ||||||||
\(449\) | −10.4434 | −0.492855 | −0.246427 | − | 0.969161i | \(-0.579257\pi\) | ||||
−0.246427 | + | 0.969161i | \(0.579257\pi\) | |||||||
\(450\) | −13.4811 | −0.635505 | ||||||||
\(451\) | 0.492745 | 0.0232024 | ||||||||
\(452\) | 3.61727 | 0.170142 | ||||||||
\(453\) | 11.3672 | 0.534075 | ||||||||
\(454\) | −14.0539 | −0.659582 | ||||||||
\(455\) | 5.07692 | 0.238010 | ||||||||
\(456\) | −2.56870 | −0.120290 | ||||||||
\(457\) | −6.79423 | −0.317821 | −0.158910 | − | 0.987293i | \(-0.550798\pi\) | ||||
−0.158910 | + | 0.987293i | \(0.550798\pi\) | |||||||
\(458\) | 3.54804 | 0.165789 | ||||||||
\(459\) | 8.10474 | 0.378297 | ||||||||
\(460\) | 0.876887 | 0.0408851 | ||||||||
\(461\) | −16.7365 | −0.779498 | −0.389749 | − | 0.920921i | \(-0.627438\pi\) | ||||
−0.389749 | + | 0.920921i | \(0.627438\pi\) | |||||||
\(462\) | −5.94370 | −0.276526 | ||||||||
\(463\) | 1.46440 | 0.0680564 | 0.0340282 | − | 0.999421i | \(-0.489166\pi\) | ||||
0.0340282 | + | 0.999421i | \(0.489166\pi\) | |||||||
\(464\) | 8.48094 | 0.393718 | ||||||||
\(465\) | 12.2159 | 0.566497 | ||||||||
\(466\) | −26.5635 | −1.23053 | ||||||||
\(467\) | −10.8327 | −0.501278 | −0.250639 | − | 0.968081i | \(-0.580641\pi\) | ||||
−0.250639 | + | 0.968081i | \(0.580641\pi\) | |||||||
\(468\) | 11.2552 | 0.520271 | ||||||||
\(469\) | −6.68863 | −0.308852 | ||||||||
\(470\) | −1.91414 | −0.0882929 | ||||||||
\(471\) | 28.1117 | 1.29532 | ||||||||
\(472\) | −12.0572 | −0.554975 | ||||||||
\(473\) | −16.8181 | −0.773297 | ||||||||
\(474\) | 13.5594 | 0.622804 | ||||||||
\(475\) | −3.74661 | −0.171906 | ||||||||
\(476\) | 7.64649 | 0.350476 | ||||||||
\(477\) | 25.1121 | 1.14981 | ||||||||
\(478\) | −4.33166 | −0.198125 | ||||||||
\(479\) | −20.9816 | −0.958672 | −0.479336 | − | 0.877631i | \(-0.659123\pi\) | ||||
−0.479336 | + | 0.877631i | \(0.659123\pi\) | |||||||
\(480\) | 2.87579 | 0.131261 | ||||||||
\(481\) | −22.6406 | −1.03232 | ||||||||
\(482\) | 17.5154 | 0.797807 | ||||||||
\(483\) | −2.91678 | −0.132718 | ||||||||
\(484\) | −8.45255 | −0.384207 | ||||||||
\(485\) | 14.3590 | 0.652008 | ||||||||
\(486\) | 22.1991 | 1.00697 | ||||||||
\(487\) | −19.9002 | −0.901764 | −0.450882 | − | 0.892584i | \(-0.648890\pi\) | ||||
−0.450882 | + | 0.892584i | \(0.648890\pi\) | |||||||
\(488\) | −0.529483 | −0.0239686 | ||||||||
\(489\) | 19.7426 | 0.892792 | ||||||||
\(490\) | 5.48383 | 0.247734 | ||||||||
\(491\) | 41.2744 | 1.86269 | 0.931345 | − | 0.364139i | \(-0.118637\pi\) | ||||
0.931345 | + | 0.364139i | \(0.118637\pi\) | |||||||
\(492\) | 0.793016 | 0.0357519 | ||||||||
\(493\) | −44.7317 | −2.01461 | ||||||||
\(494\) | 3.12799 | 0.140735 | ||||||||
\(495\) | 6.42959 | 0.288989 | ||||||||
\(496\) | 4.24784 | 0.190733 | ||||||||
\(497\) | 4.04887 | 0.181617 | ||||||||
\(498\) | −23.7218 | −1.06300 | ||||||||
\(499\) | −21.2431 | −0.950972 | −0.475486 | − | 0.879723i | \(-0.657728\pi\) | ||||
−0.475486 | + | 0.879723i | \(0.657728\pi\) | |||||||
\(500\) | 9.79227 | 0.437923 | ||||||||
\(501\) | −31.0189 | −1.38582 | ||||||||
\(502\) | 17.9688 | 0.801988 | ||||||||
\(503\) | 24.6494 | 1.09906 | 0.549531 | − | 0.835473i | \(-0.314806\pi\) | ||||
0.549531 | + | 0.835473i | \(0.314806\pi\) | |||||||
\(504\) | −5.21648 | −0.232360 | ||||||||
\(505\) | −15.8095 | −0.703512 | ||||||||
\(506\) | 1.25012 | 0.0555748 | ||||||||
\(507\) | 8.26006 | 0.366842 | ||||||||
\(508\) | −8.96922 | −0.397945 | ||||||||
\(509\) | −32.1847 | −1.42656 | −0.713281 | − | 0.700878i | \(-0.752792\pi\) | ||||
−0.713281 | + | 0.700878i | \(0.752792\pi\) | |||||||
\(510\) | −15.1680 | −0.671650 | ||||||||
\(511\) | −20.0182 | −0.885552 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.53663 | −0.0678437 | ||||||||
\(514\) | −13.8193 | −0.609542 | ||||||||
\(515\) | −11.9958 | −0.528600 | ||||||||
\(516\) | −27.0668 | −1.19155 | ||||||||
\(517\) | −2.72888 | −0.120016 | ||||||||
\(518\) | 10.4933 | 0.461051 | ||||||||
\(519\) | 32.7378 | 1.43703 | ||||||||
\(520\) | −3.50195 | −0.153570 | ||||||||
\(521\) | 30.9918 | 1.35777 | 0.678887 | − | 0.734243i | \(-0.262463\pi\) | ||||
0.678887 | + | 0.734243i | \(0.262463\pi\) | |||||||
\(522\) | 30.5162 | 1.33566 | ||||||||
\(523\) | 19.9724 | 0.873332 | 0.436666 | − | 0.899624i | \(-0.356159\pi\) | ||||
0.436666 | + | 0.899624i | \(0.356159\pi\) | |||||||
\(524\) | 19.2311 | 0.840115 | ||||||||
\(525\) | −13.9522 | −0.608923 | ||||||||
\(526\) | 19.3564 | 0.843979 | ||||||||
\(527\) | −22.4047 | −0.975963 | ||||||||
\(528\) | 4.09983 | 0.178422 | ||||||||
\(529\) | −22.3865 | −0.973327 | ||||||||
\(530\) | −7.81341 | −0.339393 | ||||||||
\(531\) | −43.3842 | −1.88271 | ||||||||
\(532\) | −1.44974 | −0.0628543 | ||||||||
\(533\) | −0.965683 | −0.0418284 | ||||||||
\(534\) | 12.2436 | 0.529831 | ||||||||
\(535\) | 11.9460 | 0.516470 | ||||||||
\(536\) | 4.61367 | 0.199280 | ||||||||
\(537\) | −53.7046 | −2.31753 | ||||||||
\(538\) | −7.48232 | −0.322586 | ||||||||
\(539\) | 7.81797 | 0.336744 | ||||||||
\(540\) | 1.72033 | 0.0740312 | ||||||||
\(541\) | −19.8748 | −0.854483 | −0.427242 | − | 0.904137i | \(-0.640515\pi\) | ||||
−0.427242 | + | 0.904137i | \(0.640515\pi\) | |||||||
\(542\) | 22.9387 | 0.985300 | ||||||||
\(543\) | −3.43839 | −0.147556 | ||||||||
\(544\) | −5.27438 | −0.226137 | ||||||||
\(545\) | 10.6830 | 0.457610 | ||||||||
\(546\) | 11.6485 | 0.498509 | ||||||||
\(547\) | −3.92524 | −0.167831 | −0.0839156 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839156 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(548\) | 8.29430 | 0.354315 | ||||||||
\(549\) | −1.90519 | −0.0813116 | ||||||||
\(550\) | 5.97986 | 0.254982 | ||||||||
\(551\) | 8.48094 | 0.361300 | ||||||||
\(552\) | 2.01193 | 0.0856335 | ||||||||
\(553\) | 7.65277 | 0.325429 | ||||||||
\(554\) | −22.6938 | −0.964168 | ||||||||
\(555\) | −20.8151 | −0.883554 | ||||||||
\(556\) | 2.58268 | 0.109530 | ||||||||
\(557\) | 16.5212 | 0.700027 | 0.350014 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350014 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(558\) | 15.2846 | 0.647049 | ||||||||
\(559\) | 32.9602 | 1.39407 | ||||||||
\(560\) | 1.62306 | 0.0685868 | ||||||||
\(561\) | −21.6241 | −0.912969 | ||||||||
\(562\) | 11.2472 | 0.474434 | ||||||||
\(563\) | −25.7588 | −1.08560 | −0.542801 | − | 0.839861i | \(-0.682636\pi\) | ||||
−0.542801 | + | 0.839861i | \(0.682636\pi\) | |||||||
\(564\) | −4.39182 | −0.184929 | ||||||||
\(565\) | −4.04972 | −0.170373 | ||||||||
\(566\) | −33.5810 | −1.41151 | ||||||||
\(567\) | 9.92712 | 0.416900 | ||||||||
\(568\) | −2.79282 | −0.117184 | ||||||||
\(569\) | 27.8785 | 1.16873 | 0.584364 | − | 0.811492i | \(-0.301344\pi\) | ||||
0.584364 | + | 0.811492i | \(0.301344\pi\) | |||||||
\(570\) | 2.87579 | 0.120453 | ||||||||
\(571\) | −9.63791 | −0.403334 | −0.201667 | − | 0.979454i | \(-0.564636\pi\) | ||||
−0.201667 | + | 0.979454i | \(0.564636\pi\) | |||||||
\(572\) | −4.99251 | −0.208747 | ||||||||
\(573\) | 55.9364 | 2.33678 | ||||||||
\(574\) | 0.447568 | 0.0186811 | ||||||||
\(575\) | 2.93453 | 0.122378 | ||||||||
\(576\) | 3.59821 | 0.149925 | ||||||||
\(577\) | −10.3302 | −0.430052 | −0.215026 | − | 0.976608i | \(-0.568984\pi\) | ||||
−0.215026 | + | 0.976608i | \(0.568984\pi\) | |||||||
\(578\) | 10.8191 | 0.450013 | ||||||||
\(579\) | 11.5858 | 0.481488 | ||||||||
\(580\) | −9.49484 | −0.394252 | ||||||||
\(581\) | −13.3883 | −0.555441 | ||||||||
\(582\) | 32.9453 | 1.36563 | ||||||||
\(583\) | −11.1391 | −0.461334 | ||||||||
\(584\) | 13.8081 | 0.571383 | ||||||||
\(585\) | −12.6007 | −0.520977 | ||||||||
\(586\) | −16.6218 | −0.686641 | ||||||||
\(587\) | 42.4384 | 1.75162 | 0.875810 | − | 0.482655i | \(-0.160328\pi\) | ||||
0.875810 | + | 0.482655i | \(0.160328\pi\) | |||||||
\(588\) | 12.5821 | 0.518878 | ||||||||
\(589\) | 4.24784 | 0.175029 | ||||||||
\(590\) | 13.4986 | 0.555728 | ||||||||
\(591\) | 16.0842 | 0.661617 | ||||||||
\(592\) | −7.23807 | −0.297483 | ||||||||
\(593\) | −13.3131 | −0.546702 | −0.273351 | − | 0.961914i | \(-0.588132\pi\) | ||||
−0.273351 | + | 0.961914i | \(0.588132\pi\) | |||||||
\(594\) | 2.45257 | 0.100630 | ||||||||
\(595\) | −8.56062 | −0.350951 | ||||||||
\(596\) | −3.79596 | −0.155489 | ||||||||
\(597\) | 15.7598 | 0.645004 | ||||||||
\(598\) | −2.45000 | −0.100188 | ||||||||
\(599\) | 7.22746 | 0.295306 | 0.147653 | − | 0.989039i | \(-0.452828\pi\) | ||||
0.147653 | + | 0.989039i | \(0.452828\pi\) | |||||||
\(600\) | 9.62390 | 0.392894 | ||||||||
\(601\) | 11.0629 | 0.451264 | 0.225632 | − | 0.974213i | \(-0.427555\pi\) | ||||
0.225632 | + | 0.974213i | \(0.427555\pi\) | |||||||
\(602\) | −15.2762 | −0.622610 | ||||||||
\(603\) | 16.6010 | 0.676043 | ||||||||
\(604\) | −4.42526 | −0.180061 | ||||||||
\(605\) | 9.46305 | 0.384728 | ||||||||
\(606\) | −36.2733 | −1.47350 | ||||||||
\(607\) | −18.4308 | −0.748083 | −0.374041 | − | 0.927412i | \(-0.622028\pi\) | ||||
−0.374041 | + | 0.927412i | \(0.622028\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 31.5826 | 1.27979 | ||||||||
\(610\) | 0.592783 | 0.0240011 | ||||||||
\(611\) | 5.34807 | 0.216360 | ||||||||
\(612\) | −18.9783 | −0.767153 | ||||||||
\(613\) | −6.26812 | −0.253167 | −0.126583 | − | 0.991956i | \(-0.540401\pi\) | ||||
−0.126583 | + | 0.991956i | \(0.540401\pi\) | |||||||
\(614\) | −23.7172 | −0.957148 | ||||||||
\(615\) | −0.887821 | −0.0358004 | ||||||||
\(616\) | 2.31390 | 0.0932295 | ||||||||
\(617\) | −7.67738 | −0.309080 | −0.154540 | − | 0.987987i | \(-0.549390\pi\) | ||||
−0.154540 | + | 0.987987i | \(0.549390\pi\) | |||||||
\(618\) | −27.5233 | −1.10715 | ||||||||
\(619\) | 20.6025 | 0.828086 | 0.414043 | − | 0.910257i | \(-0.364116\pi\) | ||||
0.414043 | + | 0.910257i | \(0.364116\pi\) | |||||||
\(620\) | −4.75567 | −0.190992 | ||||||||
\(621\) | 1.20356 | 0.0482973 | ||||||||
\(622\) | −31.4708 | −1.26186 | ||||||||
\(623\) | 6.91012 | 0.276848 | ||||||||
\(624\) | −8.03487 | −0.321652 | ||||||||
\(625\) | 7.77010 | 0.310804 | ||||||||
\(626\) | −20.0011 | −0.799405 | ||||||||
\(627\) | 4.09983 | 0.163732 | ||||||||
\(628\) | −10.9439 | −0.436711 | ||||||||
\(629\) | 38.1763 | 1.52219 | ||||||||
\(630\) | 5.84011 | 0.232676 | ||||||||
\(631\) | −20.8444 | −0.829803 | −0.414901 | − | 0.909866i | \(-0.636184\pi\) | ||||
−0.414901 | + | 0.909866i | \(0.636184\pi\) | |||||||
\(632\) | −5.27871 | −0.209976 | ||||||||
\(633\) | 2.56870 | 0.102097 | ||||||||
\(634\) | −20.0539 | −0.796442 | ||||||||
\(635\) | 10.0415 | 0.398485 | ||||||||
\(636\) | −17.9271 | −0.710856 | ||||||||
\(637\) | −15.3217 | −0.607067 | ||||||||
\(638\) | −13.5362 | −0.535904 | ||||||||
\(639\) | −10.0492 | −0.397538 | ||||||||
\(640\) | −1.11955 | −0.0442541 | ||||||||
\(641\) | 13.9591 | 0.551350 | 0.275675 | − | 0.961251i | \(-0.411099\pi\) | ||||
0.275675 | + | 0.961251i | \(0.411099\pi\) | |||||||
\(642\) | 27.4089 | 1.08174 | ||||||||
\(643\) | 15.3604 | 0.605756 | 0.302878 | − | 0.953029i | \(-0.402052\pi\) | ||||
0.302878 | + | 0.953029i | \(0.402052\pi\) | |||||||
\(644\) | 1.13551 | 0.0447454 | ||||||||
\(645\) | 30.3027 | 1.19317 | ||||||||
\(646\) | −5.27438 | −0.207518 | ||||||||
\(647\) | −27.6543 | −1.08720 | −0.543602 | − | 0.839343i | \(-0.682940\pi\) | ||||
−0.543602 | + | 0.839343i | \(0.682940\pi\) | |||||||
\(648\) | −6.84751 | −0.268996 | ||||||||
\(649\) | 19.2441 | 0.755397 | ||||||||
\(650\) | −11.7194 | −0.459671 | ||||||||
\(651\) | 15.8187 | 0.619985 | ||||||||
\(652\) | −7.68585 | −0.301001 | ||||||||
\(653\) | 1.42887 | 0.0559159 | 0.0279580 | − | 0.999609i | \(-0.491100\pi\) | ||||
0.0279580 | + | 0.999609i | \(0.491100\pi\) | |||||||
\(654\) | 24.5111 | 0.958460 | ||||||||
\(655\) | −21.5302 | −0.841255 | ||||||||
\(656\) | −0.308723 | −0.0120536 | ||||||||
\(657\) | 49.6845 | 1.93838 | ||||||||
\(658\) | −2.47869 | −0.0966293 | ||||||||
\(659\) | −11.5309 | −0.449180 | −0.224590 | − | 0.974453i | \(-0.572104\pi\) | ||||
−0.224590 | + | 0.974453i | \(0.572104\pi\) | |||||||
\(660\) | −4.58997 | −0.178664 | ||||||||
\(661\) | 19.5495 | 0.760386 | 0.380193 | − | 0.924907i | \(-0.375858\pi\) | ||||
0.380193 | + | 0.924907i | \(0.375858\pi\) | |||||||
\(662\) | 6.26128 | 0.243351 | ||||||||
\(663\) | 42.3789 | 1.64586 | ||||||||
\(664\) | 9.23497 | 0.358386 | ||||||||
\(665\) | 1.62306 | 0.0629395 | ||||||||
\(666\) | −26.0441 | −1.00919 | ||||||||
\(667\) | −6.64269 | −0.257206 | ||||||||
\(668\) | 12.0757 | 0.467223 | ||||||||
\(669\) | 34.5406 | 1.33542 | ||||||||
\(670\) | −5.16523 | −0.199550 | ||||||||
\(671\) | 0.845094 | 0.0326245 | ||||||||
\(672\) | 3.72395 | 0.143654 | ||||||||
\(673\) | 27.2522 | 1.05050 | 0.525248 | − | 0.850949i | \(-0.323972\pi\) | ||||
0.525248 | + | 0.850949i | \(0.323972\pi\) | |||||||
\(674\) | −14.6756 | −0.565283 | ||||||||
\(675\) | 5.75713 | 0.221592 | ||||||||
\(676\) | −3.21566 | −0.123679 | ||||||||
\(677\) | −22.8576 | −0.878489 | −0.439245 | − | 0.898367i | \(-0.644754\pi\) | ||||
−0.439245 | + | 0.898367i | \(0.644754\pi\) | |||||||
\(678\) | −9.29168 | −0.356845 | ||||||||
\(679\) | 18.5939 | 0.713569 | ||||||||
\(680\) | 5.90493 | 0.226444 | ||||||||
\(681\) | 36.1002 | 1.38336 | ||||||||
\(682\) | −6.77986 | −0.259614 | ||||||||
\(683\) | 1.86134 | 0.0712221 | 0.0356111 | − | 0.999366i | \(-0.488662\pi\) | ||||
0.0356111 | + | 0.999366i | \(0.488662\pi\) | |||||||
\(684\) | 3.59821 | 0.137581 | ||||||||
\(685\) | −9.28589 | −0.354796 | ||||||||
\(686\) | 17.2494 | 0.658585 | ||||||||
\(687\) | −9.11384 | −0.347715 | ||||||||
\(688\) | 10.5372 | 0.401726 | ||||||||
\(689\) | 21.8304 | 0.831674 | ||||||||
\(690\) | −2.25246 | −0.0857497 | ||||||||
\(691\) | 40.4717 | 1.53962 | 0.769808 | − | 0.638276i | \(-0.220352\pi\) | ||||
0.769808 | + | 0.638276i | \(0.220352\pi\) | |||||||
\(692\) | −12.7449 | −0.484488 | ||||||||
\(693\) | 8.32589 | 0.316274 | ||||||||
\(694\) | −31.6736 | −1.20231 | ||||||||
\(695\) | −2.89144 | −0.109679 | ||||||||
\(696\) | −21.7850 | −0.825757 | ||||||||
\(697\) | 1.62832 | 0.0616770 | ||||||||
\(698\) | −4.24754 | −0.160772 | ||||||||
\(699\) | 68.2337 | 2.58084 | ||||||||
\(700\) | 5.43161 | 0.205296 | ||||||||
\(701\) | −6.54368 | −0.247151 | −0.123576 | − | 0.992335i | \(-0.539436\pi\) | ||||
−0.123576 | + | 0.992335i | \(0.539436\pi\) | |||||||
\(702\) | −4.80655 | −0.181412 | ||||||||
\(703\) | −7.23807 | −0.272989 | ||||||||
\(704\) | −1.59607 | −0.0601543 | ||||||||
\(705\) | 4.91686 | 0.185180 | ||||||||
\(706\) | 24.0277 | 0.904294 | ||||||||
\(707\) | −20.4722 | −0.769936 | ||||||||
\(708\) | 30.9712 | 1.16397 | ||||||||
\(709\) | −37.5896 | −1.41171 | −0.705854 | − | 0.708358i | \(-0.749436\pi\) | ||||
−0.705854 | + | 0.708358i | \(0.749436\pi\) | |||||||
\(710\) | 3.12670 | 0.117343 | ||||||||
\(711\) | −18.9939 | −0.712327 | ||||||||
\(712\) | −4.76645 | −0.178630 | ||||||||
\(713\) | −3.32712 | −0.124601 | ||||||||
\(714\) | −19.6415 | −0.735065 | ||||||||
\(715\) | 5.58936 | 0.209030 | ||||||||
\(716\) | 20.9073 | 0.781344 | ||||||||
\(717\) | 11.1267 | 0.415535 | ||||||||
\(718\) | 23.1048 | 0.862264 | ||||||||
\(719\) | 41.8677 | 1.56140 | 0.780702 | − | 0.624904i | \(-0.214862\pi\) | ||||
0.780702 | + | 0.624904i | \(0.214862\pi\) | |||||||
\(720\) | −4.02838 | −0.150129 | ||||||||
\(721\) | −15.5338 | −0.578509 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −44.9919 | −1.67327 | ||||||||
\(724\) | 1.33857 | 0.0497477 | ||||||||
\(725\) | −31.7747 | −1.18008 | ||||||||
\(726\) | 21.7120 | 0.805810 | ||||||||
\(727\) | −31.8289 | −1.18047 | −0.590234 | − | 0.807232i | \(-0.700965\pi\) | ||||
−0.590234 | + | 0.807232i | \(0.700965\pi\) | |||||||
\(728\) | −4.53478 | −0.168070 | ||||||||
\(729\) | −36.4802 | −1.35112 | ||||||||
\(730\) | −15.4589 | −0.572158 | ||||||||
\(731\) | −55.5770 | −2.05559 | ||||||||
\(732\) | 1.36008 | 0.0502701 | ||||||||
\(733\) | 0.782883 | 0.0289164 | 0.0144582 | − | 0.999895i | \(-0.495398\pi\) | ||||
0.0144582 | + | 0.999895i | \(0.495398\pi\) | |||||||
\(734\) | 9.79259 | 0.361451 | ||||||||
\(735\) | −14.0863 | −0.519582 | ||||||||
\(736\) | −0.783250 | −0.0288710 | ||||||||
\(737\) | −7.36376 | −0.271247 | ||||||||
\(738\) | −1.11085 | −0.0408910 | ||||||||
\(739\) | −12.9409 | −0.476038 | −0.238019 | − | 0.971260i | \(-0.576498\pi\) | ||||
−0.238019 | + | 0.971260i | \(0.576498\pi\) | |||||||
\(740\) | 8.10338 | 0.297886 | ||||||||
\(741\) | −8.03487 | −0.295168 | ||||||||
\(742\) | −10.1178 | −0.371437 | ||||||||
\(743\) | −21.3676 | −0.783901 | −0.391950 | − | 0.919986i | \(-0.628199\pi\) | ||||
−0.391950 | + | 0.919986i | \(0.628199\pi\) | |||||||
\(744\) | −10.9114 | −0.400032 | ||||||||
\(745\) | 4.24977 | 0.155699 | ||||||||
\(746\) | −14.7854 | −0.541333 | ||||||||
\(747\) | 33.2294 | 1.21580 | ||||||||
\(748\) | 8.41830 | 0.307803 | ||||||||
\(749\) | 15.4692 | 0.565233 | ||||||||
\(750\) | −25.1534 | −0.918472 | ||||||||
\(751\) | 17.7401 | 0.647345 | 0.323673 | − | 0.946169i | \(-0.395082\pi\) | ||||
0.323673 | + | 0.946169i | \(0.395082\pi\) | |||||||
\(752\) | 1.70974 | 0.0623479 | ||||||||
\(753\) | −46.1565 | −1.68204 | ||||||||
\(754\) | 26.5283 | 0.966104 | ||||||||
\(755\) | 4.95430 | 0.180305 | ||||||||
\(756\) | 2.22771 | 0.0810210 | ||||||||
\(757\) | 7.83074 | 0.284613 | 0.142307 | − | 0.989823i | \(-0.454548\pi\) | ||||
0.142307 | + | 0.989823i | \(0.454548\pi\) | |||||||
\(758\) | −32.9460 | −1.19665 | ||||||||
\(759\) | −3.21119 | −0.116559 | ||||||||
\(760\) | −1.11955 | −0.0406104 | ||||||||
\(761\) | 24.5923 | 0.891469 | 0.445735 | − | 0.895165i | \(-0.352943\pi\) | ||||
0.445735 | + | 0.895165i | \(0.352943\pi\) | |||||||
\(762\) | 23.0392 | 0.834623 | ||||||||
\(763\) | 13.8338 | 0.500816 | ||||||||
\(764\) | −21.7762 | −0.787834 | ||||||||
\(765\) | 21.2472 | 0.768194 | ||||||||
\(766\) | −2.22797 | −0.0804999 | ||||||||
\(767\) | −37.7147 | −1.36180 | ||||||||
\(768\) | −2.56870 | −0.0926899 | ||||||||
\(769\) | 47.8044 | 1.72387 | 0.861936 | − | 0.507017i | \(-0.169252\pi\) | ||||
0.861936 | + | 0.507017i | \(0.169252\pi\) | |||||||
\(770\) | −2.59052 | −0.0933560 | ||||||||
\(771\) | 35.4976 | 1.27841 | ||||||||
\(772\) | −4.51037 | −0.162332 | ||||||||
\(773\) | −27.1576 | −0.976789 | −0.488395 | − | 0.872623i | \(-0.662417\pi\) | ||||
−0.488395 | + | 0.872623i | \(0.662417\pi\) | |||||||
\(774\) | 37.9150 | 1.36283 | ||||||||
\(775\) | −15.9150 | −0.571683 | ||||||||
\(776\) | −12.8257 | −0.460415 | ||||||||
\(777\) | −26.9542 | −0.966977 | ||||||||
\(778\) | −15.9564 | −0.572065 | ||||||||
\(779\) | −0.308723 | −0.0110611 | ||||||||
\(780\) | 8.99544 | 0.322088 | ||||||||
\(781\) | 4.45755 | 0.159504 | ||||||||
\(782\) | 4.13115 | 0.147730 | ||||||||
\(783\) | −13.0320 | −0.465727 | ||||||||
\(784\) | −4.89825 | −0.174937 | ||||||||
\(785\) | 12.2523 | 0.437303 | ||||||||
\(786\) | −49.3989 | −1.76200 | ||||||||
\(787\) | −31.5415 | −1.12433 | −0.562167 | − | 0.827024i | \(-0.690032\pi\) | ||||
−0.562167 | + | 0.827024i | \(0.690032\pi\) | |||||||
\(788\) | −6.26163 | −0.223061 | ||||||||
\(789\) | −49.7208 | −1.77011 | ||||||||
\(790\) | 5.90978 | 0.210261 | ||||||||
\(791\) | −5.24411 | −0.186459 | ||||||||
\(792\) | −5.74301 | −0.204069 | ||||||||
\(793\) | −1.65622 | −0.0588141 | ||||||||
\(794\) | −16.5148 | −0.586089 | ||||||||
\(795\) | 20.0703 | 0.711820 | ||||||||
\(796\) | −6.13531 | −0.217460 | ||||||||
\(797\) | 23.5790 | 0.835210 | 0.417605 | − | 0.908629i | \(-0.362870\pi\) | ||||
0.417605 | + | 0.908629i | \(0.362870\pi\) | |||||||
\(798\) | 3.72395 | 0.131826 | ||||||||
\(799\) | −9.01783 | −0.319028 | ||||||||
\(800\) | −3.74661 | −0.132463 | ||||||||
\(801\) | −17.1507 | −0.605990 | ||||||||
\(802\) | −1.36916 | −0.0483467 | ||||||||
\(803\) | −22.0387 | −0.777731 | ||||||||
\(804\) | −11.8511 | −0.417957 | ||||||||
\(805\) | −1.27126 | −0.0448060 | ||||||||
\(806\) | 13.2872 | 0.468022 | ||||||||
\(807\) | 19.2198 | 0.676570 | ||||||||
\(808\) | 14.1213 | 0.496785 | ||||||||
\(809\) | −15.7494 | −0.553721 | −0.276861 | − | 0.960910i | \(-0.589294\pi\) | ||||
−0.276861 | + | 0.960910i | \(0.589294\pi\) | |||||||
\(810\) | 7.66613 | 0.269360 | ||||||||
\(811\) | 1.28089 | 0.0449780 | 0.0224890 | − | 0.999747i | \(-0.492841\pi\) | ||||
0.0224890 | + | 0.999747i | \(0.492841\pi\) | |||||||
\(812\) | −12.2952 | −0.431476 | ||||||||
\(813\) | −58.9225 | −2.06650 | ||||||||
\(814\) | 11.5525 | 0.404915 | ||||||||
\(815\) | 8.60469 | 0.301409 | ||||||||
\(816\) | 13.5483 | 0.474285 | ||||||||
\(817\) | 10.5372 | 0.368649 | ||||||||
\(818\) | −33.9138 | −1.18577 | ||||||||
\(819\) | −16.3171 | −0.570166 | ||||||||
\(820\) | 0.345631 | 0.0120699 | ||||||||
\(821\) | 5.21179 | 0.181893 | 0.0909464 | − | 0.995856i | \(-0.471011\pi\) | ||||
0.0909464 | + | 0.995856i | \(0.471011\pi\) | |||||||
\(822\) | −21.3056 | −0.743117 | ||||||||
\(823\) | 5.52758 | 0.192679 | 0.0963396 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963396 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(824\) | 10.7149 | 0.373271 | ||||||||
\(825\) | −15.3605 | −0.534783 | ||||||||
\(826\) | 17.4798 | 0.608199 | ||||||||
\(827\) | 7.72995 | 0.268797 | 0.134398 | − | 0.990927i | \(-0.457090\pi\) | ||||
0.134398 | + | 0.990927i | \(0.457090\pi\) | |||||||
\(828\) | −2.81830 | −0.0979426 | ||||||||
\(829\) | −24.6254 | −0.855277 | −0.427638 | − | 0.903950i | \(-0.640654\pi\) | ||||
−0.427638 | + | 0.903950i | \(0.640654\pi\) | |||||||
\(830\) | −10.3390 | −0.358872 | ||||||||
\(831\) | 58.2936 | 2.02218 | ||||||||
\(832\) | 3.12799 | 0.108444 | ||||||||
\(833\) | 25.8352 | 0.895137 | ||||||||
\(834\) | −6.63413 | −0.229721 | ||||||||
\(835\) | −13.5194 | −0.467857 | ||||||||
\(836\) | −1.59607 | −0.0552014 | ||||||||
\(837\) | −6.52733 | −0.225618 | ||||||||
\(838\) | −4.70812 | −0.162639 | ||||||||
\(839\) | 41.7298 | 1.44067 | 0.720337 | − | 0.693624i | \(-0.243987\pi\) | ||||
0.720337 | + | 0.693624i | \(0.243987\pi\) | |||||||
\(840\) | −4.16915 | −0.143849 | ||||||||
\(841\) | 42.9263 | 1.48022 | ||||||||
\(842\) | −5.43867 | −0.187429 | ||||||||
\(843\) | −28.8906 | −0.995046 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 3.60009 | 0.123847 | ||||||||
\(846\) | 6.15202 | 0.211511 | ||||||||
\(847\) | 12.2540 | 0.421053 | ||||||||
\(848\) | 6.97906 | 0.239662 | ||||||||
\(849\) | 86.2594 | 2.96042 | ||||||||
\(850\) | 19.7610 | 0.677797 | ||||||||
\(851\) | 5.66922 | 0.194338 | ||||||||
\(852\) | 7.17391 | 0.245774 | ||||||||
\(853\) | −38.6648 | −1.32386 | −0.661929 | − | 0.749566i | \(-0.730262\pi\) | ||||
−0.661929 | + | 0.749566i | \(0.730262\pi\) | |||||||
\(854\) | 0.767614 | 0.0262672 | ||||||||
\(855\) | −4.02838 | −0.137768 | ||||||||
\(856\) | −10.6703 | −0.364705 | ||||||||
\(857\) | 10.7384 | 0.366815 | 0.183408 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183408 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(858\) | 12.8243 | 0.437813 | ||||||||
\(859\) | 43.6837 | 1.49047 | 0.745235 | − | 0.666802i | \(-0.232337\pi\) | ||||
0.745235 | + | 0.666802i | \(0.232337\pi\) | |||||||
\(860\) | −11.7969 | −0.402271 | ||||||||
\(861\) | −1.14967 | −0.0391806 | ||||||||
\(862\) | 24.7539 | 0.843121 | ||||||||
\(863\) | −31.2451 | −1.06360 | −0.531798 | − | 0.846871i | \(-0.678483\pi\) | ||||
−0.531798 | + | 0.846871i | \(0.678483\pi\) | |||||||
\(864\) | −1.53663 | −0.0522771 | ||||||||
\(865\) | 14.2685 | 0.485145 | ||||||||
\(866\) | −17.4451 | −0.592810 | ||||||||
\(867\) | −27.7909 | −0.943828 | ||||||||
\(868\) | −6.15827 | −0.209025 | ||||||||
\(869\) | 8.42521 | 0.285806 | ||||||||
\(870\) | 24.3894 | 0.826877 | ||||||||
\(871\) | 14.4315 | 0.488993 | ||||||||
\(872\) | −9.54223 | −0.323141 | ||||||||
\(873\) | −46.1495 | −1.56192 | ||||||||
\(874\) | −0.783250 | −0.0264938 | ||||||||
\(875\) | −14.1963 | −0.479921 | ||||||||
\(876\) | −35.4688 | −1.19838 | ||||||||
\(877\) | 21.0182 | 0.709733 | 0.354866 | − | 0.934917i | \(-0.384526\pi\) | ||||
0.354866 | + | 0.934917i | \(0.384526\pi\) | |||||||
\(878\) | 27.0520 | 0.912962 | ||||||||
\(879\) | 42.6964 | 1.44011 | ||||||||
\(880\) | 1.78689 | 0.0602359 | ||||||||
\(881\) | 50.9134 | 1.71532 | 0.857658 | − | 0.514220i | \(-0.171919\pi\) | ||||
0.857658 | + | 0.514220i | \(0.171919\pi\) | |||||||
\(882\) | −17.6249 | −0.593462 | ||||||||
\(883\) | 48.8130 | 1.64269 | 0.821344 | − | 0.570434i | \(-0.193225\pi\) | ||||
0.821344 | + | 0.570434i | \(0.193225\pi\) | |||||||
\(884\) | −16.4982 | −0.554895 | ||||||||
\(885\) | −34.6738 | −1.16555 | ||||||||
\(886\) | −11.9016 | −0.399841 | ||||||||
\(887\) | −3.52130 | −0.118234 | −0.0591168 | − | 0.998251i | \(-0.518828\pi\) | ||||
−0.0591168 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(888\) | 18.5924 | 0.623921 | ||||||||
\(889\) | 13.0031 | 0.436109 | ||||||||
\(890\) | 5.33628 | 0.178872 | ||||||||
\(891\) | 10.9291 | 0.366140 | ||||||||
\(892\) | −13.4467 | −0.450229 | ||||||||
\(893\) | 1.70974 | 0.0572144 | ||||||||
\(894\) | 9.75068 | 0.326111 | ||||||||
\(895\) | −23.4068 | −0.782403 | ||||||||
\(896\) | −1.44974 | −0.0484325 | ||||||||
\(897\) | 6.29331 | 0.210128 | ||||||||
\(898\) | −10.4434 | −0.348501 | ||||||||
\(899\) | 36.0256 | 1.20152 | ||||||||
\(900\) | −13.4811 | −0.449370 | ||||||||
\(901\) | −36.8102 | −1.22633 | ||||||||
\(902\) | 0.492745 | 0.0164066 | ||||||||
\(903\) | 39.2399 | 1.30582 | ||||||||
\(904\) | 3.61727 | 0.120309 | ||||||||
\(905\) | −1.49860 | −0.0498152 | ||||||||
\(906\) | 11.3672 | 0.377648 | ||||||||
\(907\) | 48.9809 | 1.62639 | 0.813193 | − | 0.581994i | \(-0.197727\pi\) | ||||
0.813193 | + | 0.581994i | \(0.197727\pi\) | |||||||
\(908\) | −14.0539 | −0.466395 | ||||||||
\(909\) | 50.8113 | 1.68531 | ||||||||
\(910\) | 5.07692 | 0.168298 | ||||||||
\(911\) | −22.5447 | −0.746939 | −0.373470 | − | 0.927642i | \(-0.621832\pi\) | ||||
−0.373470 | + | 0.927642i | \(0.621832\pi\) | |||||||
\(912\) | −2.56870 | −0.0850581 | ||||||||
\(913\) | −14.7397 | −0.487813 | ||||||||
\(914\) | −6.79423 | −0.224733 | ||||||||
\(915\) | −1.52268 | −0.0503383 | ||||||||
\(916\) | 3.54804 | 0.117230 | ||||||||
\(917\) | −27.8802 | −0.920684 | ||||||||
\(918\) | 8.10474 | 0.267496 | ||||||||
\(919\) | −40.3174 | −1.32995 | −0.664975 | − | 0.746866i | \(-0.731558\pi\) | ||||
−0.664975 | + | 0.746866i | \(0.731558\pi\) | |||||||
\(920\) | 0.876887 | 0.0289101 | ||||||||
\(921\) | 60.9223 | 2.00746 | ||||||||
\(922\) | −16.7365 | −0.551188 | ||||||||
\(923\) | −8.73592 | −0.287546 | ||||||||
\(924\) | −5.94370 | −0.195533 | ||||||||
\(925\) | 27.1182 | 0.891641 | ||||||||
\(926\) | 1.46440 | 0.0481231 | ||||||||
\(927\) | 38.5544 | 1.26629 | ||||||||
\(928\) | 8.48094 | 0.278400 | ||||||||
\(929\) | −19.3473 | −0.634764 | −0.317382 | − | 0.948298i | \(-0.602804\pi\) | ||||
−0.317382 | + | 0.948298i | \(0.602804\pi\) | |||||||
\(930\) | 12.2159 | 0.400574 | ||||||||
\(931\) | −4.89825 | −0.160534 | ||||||||
\(932\) | −26.5635 | −0.870118 | ||||||||
\(933\) | 80.8390 | 2.64655 | ||||||||
\(934\) | −10.8327 | −0.354457 | ||||||||
\(935\) | −9.42471 | −0.308221 | ||||||||
\(936\) | 11.2552 | 0.367887 | ||||||||
\(937\) | 19.3382 | 0.631752 | 0.315876 | − | 0.948800i | \(-0.397702\pi\) | ||||
0.315876 | + | 0.948800i | \(0.397702\pi\) | |||||||
\(938\) | −6.68863 | −0.218391 | ||||||||
\(939\) | 51.3768 | 1.67662 | ||||||||
\(940\) | −1.91414 | −0.0624325 | ||||||||
\(941\) | 22.1728 | 0.722811 | 0.361406 | − | 0.932409i | \(-0.382297\pi\) | ||||
0.361406 | + | 0.932409i | \(0.382297\pi\) | |||||||
\(942\) | 28.1117 | 0.915929 | ||||||||
\(943\) | 0.241807 | 0.00787432 | ||||||||
\(944\) | −12.0572 | −0.392427 | ||||||||
\(945\) | −2.49403 | −0.0811309 | ||||||||
\(946\) | −16.8181 | −0.546804 | ||||||||
\(947\) | 49.7447 | 1.61648 | 0.808242 | − | 0.588850i | \(-0.200419\pi\) | ||||
0.808242 | + | 0.588850i | \(0.200419\pi\) | |||||||
\(948\) | 13.5594 | 0.440389 | ||||||||
\(949\) | 43.1916 | 1.40206 | ||||||||
\(950\) | −3.74661 | −0.121556 | ||||||||
\(951\) | 51.5124 | 1.67040 | ||||||||
\(952\) | 7.64649 | 0.247824 | ||||||||
\(953\) | −43.1522 | −1.39784 | −0.698918 | − | 0.715202i | \(-0.746335\pi\) | ||||
−0.698918 | + | 0.715202i | \(0.746335\pi\) | |||||||
\(954\) | 25.1121 | 0.813035 | ||||||||
\(955\) | 24.3795 | 0.788902 | ||||||||
\(956\) | −4.33166 | −0.140096 | ||||||||
\(957\) | 34.7704 | 1.12397 | ||||||||
\(958\) | −20.9816 | −0.677884 | ||||||||
\(959\) | −12.0246 | −0.388295 | ||||||||
\(960\) | 2.87579 | 0.0928156 | ||||||||
\(961\) | −12.9559 | −0.417932 | ||||||||
\(962\) | −22.6406 | −0.729963 | ||||||||
\(963\) | −38.3941 | −1.23723 | ||||||||
\(964\) | 17.5154 | 0.564135 | ||||||||
\(965\) | 5.04958 | 0.162552 | ||||||||
\(966\) | −2.91678 | −0.0938459 | ||||||||
\(967\) | −10.6831 | −0.343546 | −0.171773 | − | 0.985137i | \(-0.554950\pi\) | ||||
−0.171773 | + | 0.985137i | \(0.554950\pi\) | |||||||
\(968\) | −8.45255 | −0.271675 | ||||||||
\(969\) | 13.5483 | 0.435234 | ||||||||
\(970\) | 14.3590 | 0.461039 | ||||||||
\(971\) | −12.6516 | −0.406010 | −0.203005 | − | 0.979178i | \(-0.565071\pi\) | ||||
−0.203005 | + | 0.979178i | \(0.565071\pi\) | |||||||
\(972\) | 22.1991 | 0.712035 | ||||||||
\(973\) | −3.74422 | −0.120034 | ||||||||
\(974\) | −19.9002 | −0.637643 | ||||||||
\(975\) | 30.1035 | 0.964084 | ||||||||
\(976\) | −0.529483 | −0.0169483 | ||||||||
\(977\) | −17.7318 | −0.567291 | −0.283646 | − | 0.958929i | \(-0.591544\pi\) | ||||
−0.283646 | + | 0.958929i | \(0.591544\pi\) | |||||||
\(978\) | 19.7426 | 0.631299 | ||||||||
\(979\) | 7.60761 | 0.243140 | ||||||||
\(980\) | 5.48383 | 0.175175 | ||||||||
\(981\) | −34.3350 | −1.09623 | ||||||||
\(982\) | 41.2744 | 1.31712 | ||||||||
\(983\) | 25.9136 | 0.826516 | 0.413258 | − | 0.910614i | \(-0.364391\pi\) | ||||
0.413258 | + | 0.910614i | \(0.364391\pi\) | |||||||
\(984\) | 0.793016 | 0.0252804 | ||||||||
\(985\) | 7.01020 | 0.223364 | ||||||||
\(986\) | −44.7317 | −1.42455 | ||||||||
\(987\) | 6.36700 | 0.202664 | ||||||||
\(988\) | 3.12799 | 0.0995147 | ||||||||
\(989\) | −8.25324 | −0.262438 | ||||||||
\(990\) | 6.42959 | 0.204346 | ||||||||
\(991\) | −23.8788 | −0.758535 | −0.379267 | − | 0.925287i | \(-0.623824\pi\) | ||||
−0.379267 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(992\) | 4.24784 | 0.134869 | ||||||||
\(993\) | −16.0833 | −0.510389 | ||||||||
\(994\) | 4.04887 | 0.128422 | ||||||||
\(995\) | 6.86879 | 0.217755 | ||||||||
\(996\) | −23.7218 | −0.751656 | ||||||||
\(997\) | −36.2352 | −1.14758 | −0.573790 | − | 0.819003i | \(-0.694527\pi\) | ||||
−0.573790 | + | 0.819003i | \(0.694527\pi\) | |||||||
\(998\) | −21.2431 | −0.672439 | ||||||||
\(999\) | 11.1222 | 0.351891 |
(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 | 8018.2.a.d.1.4 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.4 | ✓ | 30 | 1.1 | even | 1 | trivial |