Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8014,2,Mod(1,8014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8014 = 2 \cdot 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8014.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: | \(63.9921121799\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 8014.1 |
$q$-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 | ||||||||
\(3\) | −3.16888 | −1.82955 | −0.914777 | − | 0.403960i | \(-0.867634\pi\) | ||||
−0.914777 | + | 0.403960i | \(0.867634\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.03965 | −1.35937 | −0.679686 | − | 0.733503i | \(-0.737884\pi\) | ||||
−0.679686 | + | 0.733503i | \(0.737884\pi\) | |||||||
\(6\) | −3.16888 | −1.29369 | ||||||||
\(7\) | −1.28246 | −0.484723 | −0.242361 | − | 0.970186i | \(-0.577922\pi\) | ||||
−0.242361 | + | 0.970186i | \(0.577922\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.04180 | 2.34727 | ||||||||
\(10\) | −3.03965 | −0.961221 | ||||||||
\(11\) | 3.46314 | 1.04418 | 0.522088 | − | 0.852892i | \(-0.325153\pi\) | ||||
0.522088 | + | 0.852892i | \(0.325153\pi\) | |||||||
\(12\) | −3.16888 | −0.914777 | ||||||||
\(13\) | −4.50722 | −1.25008 | −0.625039 | − | 0.780594i | \(-0.714917\pi\) | ||||
−0.625039 | + | 0.780594i | \(0.714917\pi\) | |||||||
\(14\) | −1.28246 | −0.342751 | ||||||||
\(15\) | 9.63228 | 2.48704 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.23801 | 0.785332 | 0.392666 | − | 0.919681i | \(-0.371553\pi\) | ||||
0.392666 | + | 0.919681i | \(0.371553\pi\) | |||||||
\(18\) | 7.04180 | 1.65977 | ||||||||
\(19\) | −0.846917 | −0.194296 | −0.0971480 | − | 0.995270i | \(-0.530972\pi\) | ||||
−0.0971480 | + | 0.995270i | \(0.530972\pi\) | |||||||
\(20\) | −3.03965 | −0.679686 | ||||||||
\(21\) | 4.06395 | 0.886826 | ||||||||
\(22\) | 3.46314 | 0.738344 | ||||||||
\(23\) | −0.287066 | −0.0598574 | −0.0299287 | − | 0.999552i | \(-0.509528\pi\) | ||||
−0.0299287 | + | 0.999552i | \(0.509528\pi\) | |||||||
\(24\) | −3.16888 | −0.646845 | ||||||||
\(25\) | 4.23946 | 0.847891 | ||||||||
\(26\) | −4.50722 | −0.883939 | ||||||||
\(27\) | −12.8080 | −2.46489 | ||||||||
\(28\) | −1.28246 | −0.242361 | ||||||||
\(29\) | 1.25694 | 0.233407 | 0.116704 | − | 0.993167i | \(-0.462767\pi\) | ||||
0.116704 | + | 0.993167i | \(0.462767\pi\) | |||||||
\(30\) | 9.63228 | 1.75860 | ||||||||
\(31\) | −6.14846 | −1.10430 | −0.552148 | − | 0.833746i | \(-0.686192\pi\) | ||||
−0.552148 | + | 0.833746i | \(0.686192\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −10.9743 | −1.91038 | ||||||||
\(34\) | 3.23801 | 0.555313 | ||||||||
\(35\) | 3.89821 | 0.658919 | ||||||||
\(36\) | 7.04180 | 1.17363 | ||||||||
\(37\) | 7.21847 | 1.18671 | 0.593354 | − | 0.804941i | \(-0.297803\pi\) | ||||
0.593354 | + | 0.804941i | \(0.297803\pi\) | |||||||
\(38\) | −0.846917 | −0.137388 | ||||||||
\(39\) | 14.2828 | 2.28708 | ||||||||
\(40\) | −3.03965 | −0.480610 | ||||||||
\(41\) | −4.83235 | −0.754686 | −0.377343 | − | 0.926074i | \(-0.623162\pi\) | ||||
−0.377343 | + | 0.926074i | \(0.623162\pi\) | |||||||
\(42\) | 4.06395 | 0.627081 | ||||||||
\(43\) | 1.61059 | 0.245613 | 0.122807 | − | 0.992431i | \(-0.460811\pi\) | ||||
0.122807 | + | 0.992431i | \(0.460811\pi\) | |||||||
\(44\) | 3.46314 | 0.522088 | ||||||||
\(45\) | −21.4046 | −3.19081 | ||||||||
\(46\) | −0.287066 | −0.0423256 | ||||||||
\(47\) | 3.12714 | 0.456141 | 0.228070 | − | 0.973645i | \(-0.426758\pi\) | ||||
0.228070 | + | 0.973645i | \(0.426758\pi\) | |||||||
\(48\) | −3.16888 | −0.457388 | ||||||||
\(49\) | −5.35531 | −0.765044 | ||||||||
\(50\) | 4.23946 | 0.599549 | ||||||||
\(51\) | −10.2608 | −1.43681 | ||||||||
\(52\) | −4.50722 | −0.625039 | ||||||||
\(53\) | −6.99757 | −0.961190 | −0.480595 | − | 0.876943i | \(-0.659579\pi\) | ||||
−0.480595 | + | 0.876943i | \(0.659579\pi\) | |||||||
\(54\) | −12.8080 | −1.74294 | ||||||||
\(55\) | −10.5267 | −1.41942 | ||||||||
\(56\) | −1.28246 | −0.171375 | ||||||||
\(57\) | 2.68378 | 0.355475 | ||||||||
\(58\) | 1.25694 | 0.165044 | ||||||||
\(59\) | 8.82489 | 1.14890 | 0.574451 | − | 0.818539i | \(-0.305215\pi\) | ||||
0.574451 | + | 0.818539i | \(0.305215\pi\) | |||||||
\(60\) | 9.63228 | 1.24352 | ||||||||
\(61\) | 9.09016 | 1.16388 | 0.581938 | − | 0.813233i | \(-0.302295\pi\) | ||||
0.581938 | + | 0.813233i | \(0.302295\pi\) | |||||||
\(62\) | −6.14846 | −0.780855 | ||||||||
\(63\) | −9.03080 | −1.13777 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.7004 | 1.69932 | ||||||||
\(66\) | −10.9743 | −1.35084 | ||||||||
\(67\) | 0.507256 | 0.0619712 | 0.0309856 | − | 0.999520i | \(-0.490135\pi\) | ||||
0.0309856 | + | 0.999520i | \(0.490135\pi\) | |||||||
\(68\) | 3.23801 | 0.392666 | ||||||||
\(69\) | 0.909678 | 0.109512 | ||||||||
\(70\) | 3.89821 | 0.465926 | ||||||||
\(71\) | −8.65604 | −1.02728 | −0.513642 | − | 0.858005i | \(-0.671704\pi\) | ||||
−0.513642 | + | 0.858005i | \(0.671704\pi\) | |||||||
\(72\) | 7.04180 | 0.829884 | ||||||||
\(73\) | 0.231430 | 0.0270868 | 0.0135434 | − | 0.999908i | \(-0.495689\pi\) | ||||
0.0135434 | + | 0.999908i | \(0.495689\pi\) | |||||||
\(74\) | 7.21847 | 0.839130 | ||||||||
\(75\) | −13.4343 | −1.55126 | ||||||||
\(76\) | −0.846917 | −0.0971480 | ||||||||
\(77\) | −4.44133 | −0.506136 | ||||||||
\(78\) | 14.2828 | 1.61721 | ||||||||
\(79\) | 3.00674 | 0.338285 | 0.169142 | − | 0.985592i | \(-0.445900\pi\) | ||||
0.169142 | + | 0.985592i | \(0.445900\pi\) | |||||||
\(80\) | −3.03965 | −0.339843 | ||||||||
\(81\) | 19.4615 | 2.16239 | ||||||||
\(82\) | −4.83235 | −0.533644 | ||||||||
\(83\) | −14.5534 | −1.59745 | −0.798723 | − | 0.601698i | \(-0.794491\pi\) | ||||
−0.798723 | + | 0.601698i | \(0.794491\pi\) | |||||||
\(84\) | 4.06395 | 0.443413 | ||||||||
\(85\) | −9.84239 | −1.06756 | ||||||||
\(86\) | 1.61059 | 0.173675 | ||||||||
\(87\) | −3.98308 | −0.427031 | ||||||||
\(88\) | 3.46314 | 0.369172 | ||||||||
\(89\) | −17.1962 | −1.82279 | −0.911396 | − | 0.411530i | \(-0.864994\pi\) | ||||
−0.911396 | + | 0.411530i | \(0.864994\pi\) | |||||||
\(90\) | −21.4046 | −2.25624 | ||||||||
\(91\) | 5.78031 | 0.605941 | ||||||||
\(92\) | −0.287066 | −0.0299287 | ||||||||
\(93\) | 19.4837 | 2.02037 | ||||||||
\(94\) | 3.12714 | 0.322540 | ||||||||
\(95\) | 2.57433 | 0.264120 | ||||||||
\(96\) | −3.16888 | −0.323422 | ||||||||
\(97\) | −12.2668 | −1.24550 | −0.622752 | − | 0.782419i | \(-0.713986\pi\) | ||||
−0.622752 | + | 0.782419i | \(0.713986\pi\) | |||||||
\(98\) | −5.35531 | −0.540968 | ||||||||
\(99\) | 24.3867 | 2.45096 | ||||||||
\(100\) | 4.23946 | 0.423946 | ||||||||
\(101\) | 6.75003 | 0.671653 | 0.335826 | − | 0.941924i | \(-0.390984\pi\) | ||||
0.335826 | + | 0.941924i | \(0.390984\pi\) | |||||||
\(102\) | −10.2608 | −1.01598 | ||||||||
\(103\) | 0.260264 | 0.0256445 | 0.0128223 | − | 0.999918i | \(-0.495918\pi\) | ||||
0.0128223 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(104\) | −4.50722 | −0.441969 | ||||||||
\(105\) | −12.3530 | −1.20553 | ||||||||
\(106\) | −6.99757 | −0.679664 | ||||||||
\(107\) | −12.2796 | −1.18712 | −0.593558 | − | 0.804791i | \(-0.702277\pi\) | ||||
−0.593558 | + | 0.804791i | \(0.702277\pi\) | |||||||
\(108\) | −12.8080 | −1.23245 | ||||||||
\(109\) | −3.06057 | −0.293150 | −0.146575 | − | 0.989200i | \(-0.546825\pi\) | ||||
−0.146575 | + | 0.989200i | \(0.546825\pi\) | |||||||
\(110\) | −10.5267 | −1.00368 | ||||||||
\(111\) | −22.8744 | −2.17115 | ||||||||
\(112\) | −1.28246 | −0.121181 | ||||||||
\(113\) | −14.6944 | −1.38233 | −0.691165 | − | 0.722697i | \(-0.742902\pi\) | ||||
−0.691165 | + | 0.722697i | \(0.742902\pi\) | |||||||
\(114\) | 2.68378 | 0.251359 | ||||||||
\(115\) | 0.872580 | 0.0813685 | ||||||||
\(116\) | 1.25694 | 0.116704 | ||||||||
\(117\) | −31.7389 | −2.93426 | ||||||||
\(118\) | 8.82489 | 0.812397 | ||||||||
\(119\) | −4.15260 | −0.380668 | ||||||||
\(120\) | 9.63228 | 0.879302 | ||||||||
\(121\) | 0.993337 | 0.0903034 | ||||||||
\(122\) | 9.09016 | 0.822984 | ||||||||
\(123\) | 15.3131 | 1.38074 | ||||||||
\(124\) | −6.14846 | −0.552148 | ||||||||
\(125\) | 2.31179 | 0.206773 | ||||||||
\(126\) | −9.03080 | −0.804527 | ||||||||
\(127\) | −10.8892 | −0.966259 | −0.483130 | − | 0.875549i | \(-0.660500\pi\) | ||||
−0.483130 | + | 0.875549i | \(0.660500\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.10377 | −0.449362 | ||||||||
\(130\) | 13.7004 | 1.20160 | ||||||||
\(131\) | 3.51410 | 0.307028 | 0.153514 | − | 0.988146i | \(-0.450941\pi\) | ||||
0.153514 | + | 0.988146i | \(0.450941\pi\) | |||||||
\(132\) | −10.9743 | −0.955188 | ||||||||
\(133\) | 1.08613 | 0.0941797 | ||||||||
\(134\) | 0.507256 | 0.0438203 | ||||||||
\(135\) | 38.9317 | 3.35071 | ||||||||
\(136\) | 3.23801 | 0.277657 | ||||||||
\(137\) | −16.2368 | −1.38720 | −0.693600 | − | 0.720360i | \(-0.743976\pi\) | ||||
−0.693600 | + | 0.720360i | \(0.743976\pi\) | |||||||
\(138\) | 0.909678 | 0.0774369 | ||||||||
\(139\) | 7.68972 | 0.652234 | 0.326117 | − | 0.945329i | \(-0.394260\pi\) | ||||
0.326117 | + | 0.945329i | \(0.394260\pi\) | |||||||
\(140\) | 3.89821 | 0.329459 | ||||||||
\(141\) | −9.90954 | −0.834534 | ||||||||
\(142\) | −8.65604 | −0.726399 | ||||||||
\(143\) | −15.6091 | −1.30530 | ||||||||
\(144\) | 7.04180 | 0.586816 | ||||||||
\(145\) | −3.82064 | −0.317287 | ||||||||
\(146\) | 0.231430 | 0.0191533 | ||||||||
\(147\) | 16.9703 | 1.39969 | ||||||||
\(148\) | 7.21847 | 0.593354 | ||||||||
\(149\) | 8.62106 | 0.706265 | 0.353132 | − | 0.935573i | \(-0.385117\pi\) | ||||
0.353132 | + | 0.935573i | \(0.385117\pi\) | |||||||
\(150\) | −13.4343 | −1.09691 | ||||||||
\(151\) | 21.3163 | 1.73469 | 0.867346 | − | 0.497706i | \(-0.165824\pi\) | ||||
0.867346 | + | 0.497706i | \(0.165824\pi\) | |||||||
\(152\) | −0.846917 | −0.0686940 | ||||||||
\(153\) | 22.8014 | 1.84338 | ||||||||
\(154\) | −4.44133 | −0.357892 | ||||||||
\(155\) | 18.6892 | 1.50115 | ||||||||
\(156\) | 14.2828 | 1.14354 | ||||||||
\(157\) | −6.99959 | −0.558628 | −0.279314 | − | 0.960200i | \(-0.590107\pi\) | ||||
−0.279314 | + | 0.960200i | \(0.590107\pi\) | |||||||
\(158\) | 3.00674 | 0.239203 | ||||||||
\(159\) | 22.1745 | 1.75855 | ||||||||
\(160\) | −3.03965 | −0.240305 | ||||||||
\(161\) | 0.368150 | 0.0290143 | ||||||||
\(162\) | 19.4615 | 1.52904 | ||||||||
\(163\) | 22.6419 | 1.77345 | 0.886725 | − | 0.462296i | \(-0.152974\pi\) | ||||
0.886725 | + | 0.462296i | \(0.152974\pi\) | |||||||
\(164\) | −4.83235 | −0.377343 | ||||||||
\(165\) | 33.3579 | 2.59691 | ||||||||
\(166\) | −14.5534 | −1.12957 | ||||||||
\(167\) | 0.707537 | 0.0547508 | 0.0273754 | − | 0.999625i | \(-0.491285\pi\) | ||||
0.0273754 | + | 0.999625i | \(0.491285\pi\) | |||||||
\(168\) | 4.06395 | 0.313541 | ||||||||
\(169\) | 7.31503 | 0.562695 | ||||||||
\(170\) | −9.84239 | −0.754877 | ||||||||
\(171\) | −5.96381 | −0.456064 | ||||||||
\(172\) | 1.61059 | 0.122807 | ||||||||
\(173\) | 6.92283 | 0.526333 | 0.263166 | − | 0.964750i | \(-0.415233\pi\) | ||||
0.263166 | + | 0.964750i | \(0.415233\pi\) | |||||||
\(174\) | −3.98308 | −0.301957 | ||||||||
\(175\) | −5.43692 | −0.410992 | ||||||||
\(176\) | 3.46314 | 0.261044 | ||||||||
\(177\) | −27.9650 | −2.10198 | ||||||||
\(178\) | −17.1962 | −1.28891 | ||||||||
\(179\) | 5.27002 | 0.393900 | 0.196950 | − | 0.980414i | \(-0.436896\pi\) | ||||
0.196950 | + | 0.980414i | \(0.436896\pi\) | |||||||
\(180\) | −21.4046 | −1.59540 | ||||||||
\(181\) | −10.2356 | −0.760804 | −0.380402 | − | 0.924821i | \(-0.624214\pi\) | ||||
−0.380402 | + | 0.924821i | \(0.624214\pi\) | |||||||
\(182\) | 5.78031 | 0.428465 | ||||||||
\(183\) | −28.8056 | −2.12937 | ||||||||
\(184\) | −0.287066 | −0.0211628 | ||||||||
\(185\) | −21.9416 | −1.61318 | ||||||||
\(186\) | 19.4837 | 1.42862 | ||||||||
\(187\) | 11.2137 | 0.820024 | ||||||||
\(188\) | 3.12714 | 0.228070 | ||||||||
\(189\) | 16.4257 | 1.19479 | ||||||||
\(190\) | 2.57433 | 0.186761 | ||||||||
\(191\) | 4.00758 | 0.289979 | 0.144989 | − | 0.989433i | \(-0.453685\pi\) | ||||
0.144989 | + | 0.989433i | \(0.453685\pi\) | |||||||
\(192\) | −3.16888 | −0.228694 | ||||||||
\(193\) | 10.0430 | 0.722911 | 0.361455 | − | 0.932389i | \(-0.382280\pi\) | ||||
0.361455 | + | 0.932389i | \(0.382280\pi\) | |||||||
\(194\) | −12.2668 | −0.880705 | ||||||||
\(195\) | −43.4148 | −3.10900 | ||||||||
\(196\) | −5.35531 | −0.382522 | ||||||||
\(197\) | 20.1963 | 1.43892 | 0.719462 | − | 0.694531i | \(-0.244388\pi\) | ||||
0.719462 | + | 0.694531i | \(0.244388\pi\) | |||||||
\(198\) | 24.3867 | 1.73309 | ||||||||
\(199\) | 8.46992 | 0.600417 | 0.300208 | − | 0.953874i | \(-0.402944\pi\) | ||||
0.300208 | + | 0.953874i | \(0.402944\pi\) | |||||||
\(200\) | 4.23946 | 0.299775 | ||||||||
\(201\) | −1.60743 | −0.113380 | ||||||||
\(202\) | 6.75003 | 0.474930 | ||||||||
\(203\) | −1.61197 | −0.113138 | ||||||||
\(204\) | −10.2608 | −0.718403 | ||||||||
\(205\) | 14.6886 | 1.02590 | ||||||||
\(206\) | 0.260264 | 0.0181334 | ||||||||
\(207\) | −2.02146 | −0.140501 | ||||||||
\(208\) | −4.50722 | −0.312519 | ||||||||
\(209\) | −2.93299 | −0.202879 | ||||||||
\(210\) | −12.3530 | −0.852436 | ||||||||
\(211\) | 7.40185 | 0.509564 | 0.254782 | − | 0.966998i | \(-0.417996\pi\) | ||||
0.254782 | + | 0.966998i | \(0.417996\pi\) | |||||||
\(212\) | −6.99757 | −0.480595 | ||||||||
\(213\) | 27.4300 | 1.87947 | ||||||||
\(214\) | −12.2796 | −0.839418 | ||||||||
\(215\) | −4.89563 | −0.333879 | ||||||||
\(216\) | −12.8080 | −0.871472 | ||||||||
\(217\) | 7.88513 | 0.535278 | ||||||||
\(218\) | −3.06057 | −0.207288 | ||||||||
\(219\) | −0.733373 | −0.0495567 | ||||||||
\(220\) | −10.5267 | −0.709712 | ||||||||
\(221\) | −14.5944 | −0.981726 | ||||||||
\(222\) | −22.8744 | −1.53523 | ||||||||
\(223\) | −4.66593 | −0.312454 | −0.156227 | − | 0.987721i | \(-0.549933\pi\) | ||||
−0.156227 | + | 0.987721i | \(0.549933\pi\) | |||||||
\(224\) | −1.28246 | −0.0856877 | ||||||||
\(225\) | 29.8534 | 1.99023 | ||||||||
\(226\) | −14.6944 | −0.977455 | ||||||||
\(227\) | −25.5637 | −1.69672 | −0.848361 | − | 0.529418i | \(-0.822410\pi\) | ||||
−0.848361 | + | 0.529418i | \(0.822410\pi\) | |||||||
\(228\) | 2.68378 | 0.177737 | ||||||||
\(229\) | 16.8881 | 1.11600 | 0.558000 | − | 0.829841i | \(-0.311569\pi\) | ||||
0.558000 | + | 0.829841i | \(0.311569\pi\) | |||||||
\(230\) | 0.872580 | 0.0575362 | ||||||||
\(231\) | 14.0740 | 0.926003 | ||||||||
\(232\) | 1.25694 | 0.0825219 | ||||||||
\(233\) | 17.2278 | 1.12863 | 0.564314 | − | 0.825560i | \(-0.309141\pi\) | ||||
0.564314 | + | 0.825560i | \(0.309141\pi\) | |||||||
\(234\) | −31.7389 | −2.07484 | ||||||||
\(235\) | −9.50542 | −0.620065 | ||||||||
\(236\) | 8.82489 | 0.574451 | ||||||||
\(237\) | −9.52800 | −0.618910 | ||||||||
\(238\) | −4.15260 | −0.269173 | ||||||||
\(239\) | 10.2780 | 0.664827 | 0.332414 | − | 0.943134i | \(-0.392137\pi\) | ||||
0.332414 | + | 0.943134i | \(0.392137\pi\) | |||||||
\(240\) | 9.63228 | 0.621761 | ||||||||
\(241\) | 1.86449 | 0.120102 | 0.0600512 | − | 0.998195i | \(-0.480874\pi\) | ||||
0.0600512 | + | 0.998195i | \(0.480874\pi\) | |||||||
\(242\) | 0.993337 | 0.0638541 | ||||||||
\(243\) | −23.2473 | −1.49131 | ||||||||
\(244\) | 9.09016 | 0.581938 | ||||||||
\(245\) | 16.2782 | 1.03998 | ||||||||
\(246\) | 15.3131 | 0.976330 | ||||||||
\(247\) | 3.81724 | 0.242885 | ||||||||
\(248\) | −6.14846 | −0.390428 | ||||||||
\(249\) | 46.1181 | 2.92261 | ||||||||
\(250\) | 2.31179 | 0.146210 | ||||||||
\(251\) | 6.05456 | 0.382161 | 0.191080 | − | 0.981574i | \(-0.438801\pi\) | ||||
0.191080 | + | 0.981574i | \(0.438801\pi\) | |||||||
\(252\) | −9.03080 | −0.568887 | ||||||||
\(253\) | −0.994150 | −0.0625017 | ||||||||
\(254\) | −10.8892 | −0.683248 | ||||||||
\(255\) | 31.1894 | 1.95315 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.6654 | 0.852425 | 0.426213 | − | 0.904623i | \(-0.359848\pi\) | ||||
0.426213 | + | 0.904623i | \(0.359848\pi\) | |||||||
\(258\) | −5.10377 | −0.317747 | ||||||||
\(259\) | −9.25737 | −0.575225 | ||||||||
\(260\) | 13.7004 | 0.849660 | ||||||||
\(261\) | 8.85109 | 0.547869 | ||||||||
\(262\) | 3.51410 | 0.217102 | ||||||||
\(263\) | 0.256730 | 0.0158306 | 0.00791531 | − | 0.999969i | \(-0.497480\pi\) | ||||
0.00791531 | + | 0.999969i | \(0.497480\pi\) | |||||||
\(264\) | −10.9743 | −0.675420 | ||||||||
\(265\) | 21.2701 | 1.30661 | ||||||||
\(266\) | 1.08613 | 0.0665951 | ||||||||
\(267\) | 54.4926 | 3.33490 | ||||||||
\(268\) | 0.507256 | 0.0309856 | ||||||||
\(269\) | 25.7916 | 1.57254 | 0.786271 | − | 0.617882i | \(-0.212009\pi\) | ||||
0.786271 | + | 0.617882i | \(0.212009\pi\) | |||||||
\(270\) | 38.9317 | 2.36931 | ||||||||
\(271\) | 27.6172 | 1.67763 | 0.838813 | − | 0.544419i | \(-0.183250\pi\) | ||||
0.838813 | + | 0.544419i | \(0.183250\pi\) | |||||||
\(272\) | 3.23801 | 0.196333 | ||||||||
\(273\) | −18.3171 | −1.10860 | ||||||||
\(274\) | −16.2368 | −0.980899 | ||||||||
\(275\) | 14.6818 | 0.885347 | ||||||||
\(276\) | 0.909678 | 0.0547562 | ||||||||
\(277\) | 15.0027 | 0.901426 | 0.450713 | − | 0.892669i | \(-0.351170\pi\) | ||||
0.450713 | + | 0.892669i | \(0.351170\pi\) | |||||||
\(278\) | 7.68972 | 0.461199 | ||||||||
\(279\) | −43.2962 | −2.59208 | ||||||||
\(280\) | 3.89821 | 0.232963 | ||||||||
\(281\) | 14.0305 | 0.836988 | 0.418494 | − | 0.908220i | \(-0.362558\pi\) | ||||
0.418494 | + | 0.908220i | \(0.362558\pi\) | |||||||
\(282\) | −9.90954 | −0.590105 | ||||||||
\(283\) | 2.91971 | 0.173559 | 0.0867794 | − | 0.996228i | \(-0.472342\pi\) | ||||
0.0867794 | + | 0.996228i | \(0.472342\pi\) | |||||||
\(284\) | −8.65604 | −0.513642 | ||||||||
\(285\) | −8.15773 | −0.483222 | ||||||||
\(286\) | −15.6091 | −0.922987 | ||||||||
\(287\) | 6.19728 | 0.365814 | ||||||||
\(288\) | 7.04180 | 0.414942 | ||||||||
\(289\) | −6.51532 | −0.383254 | ||||||||
\(290\) | −3.82064 | −0.224356 | ||||||||
\(291\) | 38.8720 | 2.27872 | ||||||||
\(292\) | 0.231430 | 0.0135434 | ||||||||
\(293\) | 12.7936 | 0.747413 | 0.373706 | − | 0.927547i | \(-0.378087\pi\) | ||||
0.373706 | + | 0.927547i | \(0.378087\pi\) | |||||||
\(294\) | 16.9703 | 0.989729 | ||||||||
\(295\) | −26.8246 | −1.56179 | ||||||||
\(296\) | 7.21847 | 0.419565 | ||||||||
\(297\) | −44.3558 | −2.57378 | ||||||||
\(298\) | 8.62106 | 0.499405 | ||||||||
\(299\) | 1.29387 | 0.0748264 | ||||||||
\(300\) | −13.4343 | −0.775631 | ||||||||
\(301\) | −2.06552 | −0.119054 | ||||||||
\(302\) | 21.3163 | 1.22661 | ||||||||
\(303\) | −21.3900 | −1.22882 | ||||||||
\(304\) | −0.846917 | −0.0485740 | ||||||||
\(305\) | −27.6309 | −1.58214 | ||||||||
\(306\) | 22.8014 | 1.30347 | ||||||||
\(307\) | −0.792900 | −0.0452532 | −0.0226266 | − | 0.999744i | \(-0.507203\pi\) | ||||
−0.0226266 | + | 0.999744i | \(0.507203\pi\) | |||||||
\(308\) | −4.44133 | −0.253068 | ||||||||
\(309\) | −0.824744 | −0.0469180 | ||||||||
\(310\) | 18.6892 | 1.06147 | ||||||||
\(311\) | 13.3358 | 0.756204 | 0.378102 | − | 0.925764i | \(-0.376577\pi\) | ||||
0.378102 | + | 0.925764i | \(0.376577\pi\) | |||||||
\(312\) | 14.2828 | 0.808606 | ||||||||
\(313\) | −12.1971 | −0.689423 | −0.344712 | − | 0.938709i | \(-0.612023\pi\) | ||||
−0.344712 | + | 0.938709i | \(0.612023\pi\) | |||||||
\(314\) | −6.99959 | −0.395010 | ||||||||
\(315\) | 27.4504 | 1.54666 | ||||||||
\(316\) | 3.00674 | 0.169142 | ||||||||
\(317\) | 16.9958 | 0.954580 | 0.477290 | − | 0.878746i | \(-0.341619\pi\) | ||||
0.477290 | + | 0.878746i | \(0.341619\pi\) | |||||||
\(318\) | 22.1745 | 1.24348 | ||||||||
\(319\) | 4.35295 | 0.243718 | ||||||||
\(320\) | −3.03965 | −0.169921 | ||||||||
\(321\) | 38.9126 | 2.17189 | ||||||||
\(322\) | 0.368150 | 0.0205162 | ||||||||
\(323\) | −2.74232 | −0.152587 | ||||||||
\(324\) | 19.4615 | 1.08119 | ||||||||
\(325\) | −19.1082 | −1.05993 | ||||||||
\(326\) | 22.6419 | 1.25402 | ||||||||
\(327\) | 9.69859 | 0.536333 | ||||||||
\(328\) | −4.83235 | −0.266822 | ||||||||
\(329\) | −4.01043 | −0.221102 | ||||||||
\(330\) | 33.3579 | 1.83629 | ||||||||
\(331\) | −7.05932 | −0.388015 | −0.194008 | − | 0.981000i | \(-0.562149\pi\) | ||||
−0.194008 | + | 0.981000i | \(0.562149\pi\) | |||||||
\(332\) | −14.5534 | −0.798723 | ||||||||
\(333\) | 50.8310 | 2.78552 | ||||||||
\(334\) | 0.707537 | 0.0387147 | ||||||||
\(335\) | −1.54188 | −0.0842419 | ||||||||
\(336\) | 4.06395 | 0.221707 | ||||||||
\(337\) | 1.85496 | 0.101046 | 0.0505230 | − | 0.998723i | \(-0.483911\pi\) | ||||
0.0505230 | + | 0.998723i | \(0.483911\pi\) | |||||||
\(338\) | 7.31503 | 0.397885 | ||||||||
\(339\) | 46.5647 | 2.52905 | ||||||||
\(340\) | −9.84239 | −0.533779 | ||||||||
\(341\) | −21.2930 | −1.15308 | ||||||||
\(342\) | −5.96381 | −0.322486 | ||||||||
\(343\) | 15.8451 | 0.855557 | ||||||||
\(344\) | 1.61059 | 0.0868373 | ||||||||
\(345\) | −2.76510 | −0.148868 | ||||||||
\(346\) | 6.92283 | 0.372173 | ||||||||
\(347\) | −1.49193 | −0.0800912 | −0.0400456 | − | 0.999198i | \(-0.512750\pi\) | ||||
−0.0400456 | + | 0.999198i | \(0.512750\pi\) | |||||||
\(348\) | −3.98308 | −0.213515 | ||||||||
\(349\) | 6.00693 | 0.321544 | 0.160772 | − | 0.986992i | \(-0.448602\pi\) | ||||
0.160772 | + | 0.986992i | \(0.448602\pi\) | |||||||
\(350\) | −5.43692 | −0.290615 | ||||||||
\(351\) | 57.7283 | 3.08131 | ||||||||
\(352\) | 3.46314 | 0.184586 | ||||||||
\(353\) | 25.6381 | 1.36458 | 0.682290 | − | 0.731082i | \(-0.260984\pi\) | ||||
0.682290 | + | 0.731082i | \(0.260984\pi\) | |||||||
\(354\) | −27.9650 | −1.48632 | ||||||||
\(355\) | 26.3113 | 1.39646 | ||||||||
\(356\) | −17.1962 | −0.911396 | ||||||||
\(357\) | 13.1591 | 0.696453 | ||||||||
\(358\) | 5.27002 | 0.278529 | ||||||||
\(359\) | −27.1825 | −1.43464 | −0.717319 | − | 0.696745i | \(-0.754631\pi\) | ||||
−0.717319 | + | 0.696745i | \(0.754631\pi\) | |||||||
\(360\) | −21.4046 | −1.12812 | ||||||||
\(361\) | −18.2827 | −0.962249 | ||||||||
\(362\) | −10.2356 | −0.537970 | ||||||||
\(363\) | −3.14776 | −0.165215 | ||||||||
\(364\) | 5.78031 | 0.302971 | ||||||||
\(365\) | −0.703465 | −0.0368210 | ||||||||
\(366\) | −28.8056 | −1.50569 | ||||||||
\(367\) | −14.6711 | −0.765828 | −0.382914 | − | 0.923784i | \(-0.625079\pi\) | ||||
−0.382914 | + | 0.923784i | \(0.625079\pi\) | |||||||
\(368\) | −0.287066 | −0.0149644 | ||||||||
\(369\) | −34.0284 | −1.77145 | ||||||||
\(370\) | −21.9416 | −1.14069 | ||||||||
\(371\) | 8.97408 | 0.465911 | ||||||||
\(372\) | 19.4837 | 1.01018 | ||||||||
\(373\) | −0.602150 | −0.0311781 | −0.0155891 | − | 0.999878i | \(-0.504962\pi\) | ||||
−0.0155891 | + | 0.999878i | \(0.504962\pi\) | |||||||
\(374\) | 11.2137 | 0.579845 | ||||||||
\(375\) | −7.32578 | −0.378302 | ||||||||
\(376\) | 3.12714 | 0.161270 | ||||||||
\(377\) | −5.66529 | −0.291777 | ||||||||
\(378\) | 16.4257 | 0.844845 | ||||||||
\(379\) | −4.61086 | −0.236844 | −0.118422 | − | 0.992963i | \(-0.537784\pi\) | ||||
−0.118422 | + | 0.992963i | \(0.537784\pi\) | |||||||
\(380\) | 2.57433 | 0.132060 | ||||||||
\(381\) | 34.5065 | 1.76782 | ||||||||
\(382\) | 4.00758 | 0.205046 | ||||||||
\(383\) | −18.2631 | −0.933200 | −0.466600 | − | 0.884468i | \(-0.654521\pi\) | ||||
−0.466600 | + | 0.884468i | \(0.654521\pi\) | |||||||
\(384\) | −3.16888 | −0.161711 | ||||||||
\(385\) | 13.5001 | 0.688027 | ||||||||
\(386\) | 10.0430 | 0.511175 | ||||||||
\(387\) | 11.3415 | 0.576519 | ||||||||
\(388\) | −12.2668 | −0.622752 | ||||||||
\(389\) | −29.0706 | −1.47394 | −0.736969 | − | 0.675926i | \(-0.763744\pi\) | ||||
−0.736969 | + | 0.675926i | \(0.763744\pi\) | |||||||
\(390\) | −43.4148 | −2.19839 | ||||||||
\(391\) | −0.929522 | −0.0470079 | ||||||||
\(392\) | −5.35531 | −0.270484 | ||||||||
\(393\) | −11.1357 | −0.561724 | ||||||||
\(394\) | 20.1963 | 1.01747 | ||||||||
\(395\) | −9.13943 | −0.459855 | ||||||||
\(396\) | 24.3867 | 1.22548 | ||||||||
\(397\) | −8.41968 | −0.422571 | −0.211286 | − | 0.977424i | \(-0.567765\pi\) | ||||
−0.211286 | + | 0.977424i | \(0.567765\pi\) | |||||||
\(398\) | 8.46992 | 0.424559 | ||||||||
\(399\) | −3.44183 | −0.172307 | ||||||||
\(400\) | 4.23946 | 0.211973 | ||||||||
\(401\) | −2.69017 | −0.134340 | −0.0671702 | − | 0.997742i | \(-0.521397\pi\) | ||||
−0.0671702 | + | 0.997742i | \(0.521397\pi\) | |||||||
\(402\) | −1.60743 | −0.0801715 | ||||||||
\(403\) | 27.7125 | 1.38046 | ||||||||
\(404\) | 6.75003 | 0.335826 | ||||||||
\(405\) | −59.1561 | −2.93949 | ||||||||
\(406\) | −1.61197 | −0.0800005 | ||||||||
\(407\) | 24.9986 | 1.23913 | ||||||||
\(408\) | −10.2608 | −0.507988 | ||||||||
\(409\) | 36.9422 | 1.82668 | 0.913338 | − | 0.407203i | \(-0.133496\pi\) | ||||
0.913338 | + | 0.407203i | \(0.133496\pi\) | |||||||
\(410\) | 14.6886 | 0.725420 | ||||||||
\(411\) | 51.4523 | 2.53796 | ||||||||
\(412\) | 0.260264 | 0.0128223 | ||||||||
\(413\) | −11.3175 | −0.556900 | ||||||||
\(414\) | −2.02146 | −0.0993494 | ||||||||
\(415\) | 44.2373 | 2.17152 | ||||||||
\(416\) | −4.50722 | −0.220985 | ||||||||
\(417\) | −24.3678 | −1.19330 | ||||||||
\(418\) | −2.93299 | −0.143457 | ||||||||
\(419\) | 24.3255 | 1.18838 | 0.594190 | − | 0.804325i | \(-0.297473\pi\) | ||||
0.594190 | + | 0.804325i | \(0.297473\pi\) | |||||||
\(420\) | −12.3530 | −0.602763 | ||||||||
\(421\) | −13.7992 | −0.672532 | −0.336266 | − | 0.941767i | \(-0.609164\pi\) | ||||
−0.336266 | + | 0.941767i | \(0.609164\pi\) | |||||||
\(422\) | 7.40185 | 0.360316 | ||||||||
\(423\) | 22.0207 | 1.07068 | ||||||||
\(424\) | −6.99757 | −0.339832 | ||||||||
\(425\) | 13.7274 | 0.665876 | ||||||||
\(426\) | 27.4300 | 1.32899 | ||||||||
\(427\) | −11.6577 | −0.564157 | ||||||||
\(428\) | −12.2796 | −0.593558 | ||||||||
\(429\) | 49.4635 | 2.38812 | ||||||||
\(430\) | −4.89563 | −0.236088 | ||||||||
\(431\) | 7.63843 | 0.367930 | 0.183965 | − | 0.982933i | \(-0.441107\pi\) | ||||
0.183965 | + | 0.982933i | \(0.441107\pi\) | |||||||
\(432\) | −12.8080 | −0.616224 | ||||||||
\(433\) | −0.237432 | −0.0114103 | −0.00570514 | − | 0.999984i | \(-0.501816\pi\) | ||||
−0.00570514 | + | 0.999984i | \(0.501816\pi\) | |||||||
\(434\) | 7.88513 | 0.378498 | ||||||||
\(435\) | 12.1072 | 0.580494 | ||||||||
\(436\) | −3.06057 | −0.146575 | ||||||||
\(437\) | 0.243121 | 0.0116301 | ||||||||
\(438\) | −0.733373 | −0.0350419 | ||||||||
\(439\) | 22.7203 | 1.08438 | 0.542190 | − | 0.840256i | \(-0.317595\pi\) | ||||
0.542190 | + | 0.840256i | \(0.317595\pi\) | |||||||
\(440\) | −10.5267 | −0.501842 | ||||||||
\(441\) | −37.7110 | −1.79576 | ||||||||
\(442\) | −14.5944 | −0.694185 | ||||||||
\(443\) | 31.7608 | 1.50900 | 0.754500 | − | 0.656300i | \(-0.227880\pi\) | ||||
0.754500 | + | 0.656300i | \(0.227880\pi\) | |||||||
\(444\) | −22.8744 | −1.08557 | ||||||||
\(445\) | 52.2703 | 2.47785 | ||||||||
\(446\) | −4.66593 | −0.220938 | ||||||||
\(447\) | −27.3191 | −1.29215 | ||||||||
\(448\) | −1.28246 | −0.0605904 | ||||||||
\(449\) | −10.4783 | −0.494503 | −0.247252 | − | 0.968951i | \(-0.579527\pi\) | ||||
−0.247252 | + | 0.968951i | \(0.579527\pi\) | |||||||
\(450\) | 29.8534 | 1.40730 | ||||||||
\(451\) | −16.7351 | −0.788025 | ||||||||
\(452\) | −14.6944 | −0.691165 | ||||||||
\(453\) | −67.5486 | −3.17371 | ||||||||
\(454\) | −25.5637 | −1.19976 | ||||||||
\(455\) | −17.5701 | −0.823700 | ||||||||
\(456\) | 2.68378 | 0.125679 | ||||||||
\(457\) | −29.2012 | −1.36598 | −0.682988 | − | 0.730430i | \(-0.739320\pi\) | ||||
−0.682988 | + | 0.730430i | \(0.739320\pi\) | |||||||
\(458\) | 16.8881 | 0.789131 | ||||||||
\(459\) | −41.4723 | −1.93576 | ||||||||
\(460\) | 0.872580 | 0.0406842 | ||||||||
\(461\) | −14.6740 | −0.683437 | −0.341719 | − | 0.939802i | \(-0.611009\pi\) | ||||
−0.341719 | + | 0.939802i | \(0.611009\pi\) | |||||||
\(462\) | 14.0740 | 0.654783 | ||||||||
\(463\) | −8.79064 | −0.408536 | −0.204268 | − | 0.978915i | \(-0.565481\pi\) | ||||
−0.204268 | + | 0.978915i | \(0.565481\pi\) | |||||||
\(464\) | 1.25694 | 0.0583518 | ||||||||
\(465\) | −59.2237 | −2.74643 | ||||||||
\(466\) | 17.2278 | 0.798060 | ||||||||
\(467\) | 3.63604 | 0.168256 | 0.0841279 | − | 0.996455i | \(-0.473190\pi\) | ||||
0.0841279 | + | 0.996455i | \(0.473190\pi\) | |||||||
\(468\) | −31.7389 | −1.46713 | ||||||||
\(469\) | −0.650534 | −0.0300389 | ||||||||
\(470\) | −9.50542 | −0.438452 | ||||||||
\(471\) | 22.1809 | 1.02204 | ||||||||
\(472\) | 8.82489 | 0.406198 | ||||||||
\(473\) | 5.57771 | 0.256463 | ||||||||
\(474\) | −9.52800 | −0.437636 | ||||||||
\(475\) | −3.59047 | −0.164742 | ||||||||
\(476\) | −4.15260 | −0.190334 | ||||||||
\(477\) | −49.2755 | −2.25617 | ||||||||
\(478\) | 10.2780 | 0.470104 | ||||||||
\(479\) | 0.241336 | 0.0110269 | 0.00551347 | − | 0.999985i | \(-0.498245\pi\) | ||||
0.00551347 | + | 0.999985i | \(0.498245\pi\) | |||||||
\(480\) | 9.63228 | 0.439651 | ||||||||
\(481\) | −32.5352 | −1.48348 | ||||||||
\(482\) | 1.86449 | 0.0849252 | ||||||||
\(483\) | −1.16662 | −0.0530831 | ||||||||
\(484\) | 0.993337 | 0.0451517 | ||||||||
\(485\) | 37.2867 | 1.69310 | ||||||||
\(486\) | −23.2473 | −1.05452 | ||||||||
\(487\) | −8.08526 | −0.366378 | −0.183189 | − | 0.983078i | \(-0.558642\pi\) | ||||
−0.183189 | + | 0.983078i | \(0.558642\pi\) | |||||||
\(488\) | 9.09016 | 0.411492 | ||||||||
\(489\) | −71.7495 | −3.24462 | ||||||||
\(490\) | 16.2782 | 0.735376 | ||||||||
\(491\) | 10.1812 | 0.459470 | 0.229735 | − | 0.973253i | \(-0.426214\pi\) | ||||
0.229735 | + | 0.973253i | \(0.426214\pi\) | |||||||
\(492\) | 15.3131 | 0.690369 | ||||||||
\(493\) | 4.06997 | 0.183302 | ||||||||
\(494\) | 3.81724 | 0.171746 | ||||||||
\(495\) | −74.1270 | −3.33176 | ||||||||
\(496\) | −6.14846 | −0.276074 | ||||||||
\(497\) | 11.1010 | 0.497948 | ||||||||
\(498\) | 46.1181 | 2.06660 | ||||||||
\(499\) | 15.1985 | 0.680380 | 0.340190 | − | 0.940357i | \(-0.389509\pi\) | ||||
0.340190 | + | 0.940357i | \(0.389509\pi\) | |||||||
\(500\) | 2.31179 | 0.103386 | ||||||||
\(501\) | −2.24210 | −0.100170 | ||||||||
\(502\) | 6.05456 | 0.270228 | ||||||||
\(503\) | 19.8713 | 0.886018 | 0.443009 | − | 0.896517i | \(-0.353911\pi\) | ||||
0.443009 | + | 0.896517i | \(0.353911\pi\) | |||||||
\(504\) | −9.03080 | −0.402264 | ||||||||
\(505\) | −20.5177 | −0.913026 | ||||||||
\(506\) | −0.994150 | −0.0441954 | ||||||||
\(507\) | −23.1804 | −1.02948 | ||||||||
\(508\) | −10.8892 | −0.483130 | ||||||||
\(509\) | −21.0381 | −0.932496 | −0.466248 | − | 0.884654i | \(-0.654394\pi\) | ||||
−0.466248 | + | 0.884654i | \(0.654394\pi\) | |||||||
\(510\) | 31.1894 | 1.38109 | ||||||||
\(511\) | −0.296799 | −0.0131296 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 10.8473 | 0.478919 | ||||||||
\(514\) | 13.6654 | 0.602756 | ||||||||
\(515\) | −0.791110 | −0.0348605 | ||||||||
\(516\) | −5.10377 | −0.224681 | ||||||||
\(517\) | 10.8297 | 0.476291 | ||||||||
\(518\) | −9.25737 | −0.406745 | ||||||||
\(519\) | −21.9376 | −0.962954 | ||||||||
\(520\) | 13.7004 | 0.600800 | ||||||||
\(521\) | −26.2594 | −1.15045 | −0.575224 | − | 0.817996i | \(-0.695085\pi\) | ||||
−0.575224 | + | 0.817996i | \(0.695085\pi\) | |||||||
\(522\) | 8.85109 | 0.387402 | ||||||||
\(523\) | −31.3689 | −1.37166 | −0.685832 | − | 0.727760i | \(-0.740562\pi\) | ||||
−0.685832 | + | 0.727760i | \(0.740562\pi\) | |||||||
\(524\) | 3.51410 | 0.153514 | ||||||||
\(525\) | 17.2289 | 0.751932 | ||||||||
\(526\) | 0.256730 | 0.0111939 | ||||||||
\(527\) | −19.9087 | −0.867239 | ||||||||
\(528\) | −10.9743 | −0.477594 | ||||||||
\(529\) | −22.9176 | −0.996417 | ||||||||
\(530\) | 21.2701 | 0.923916 | ||||||||
\(531\) | 62.1431 | 2.69678 | ||||||||
\(532\) | 1.08613 | 0.0470899 | ||||||||
\(533\) | 21.7805 | 0.943417 | ||||||||
\(534\) | 54.4926 | 2.35813 | ||||||||
\(535\) | 37.3257 | 1.61373 | ||||||||
\(536\) | 0.507256 | 0.0219101 | ||||||||
\(537\) | −16.7001 | −0.720661 | ||||||||
\(538\) | 25.7916 | 1.11195 | ||||||||
\(539\) | −18.5462 | −0.798840 | ||||||||
\(540\) | 38.9317 | 1.67535 | ||||||||
\(541\) | −9.67287 | −0.415869 | −0.207935 | − | 0.978143i | \(-0.566674\pi\) | ||||
−0.207935 | + | 0.978143i | \(0.566674\pi\) | |||||||
\(542\) | 27.6172 | 1.18626 | ||||||||
\(543\) | 32.4353 | 1.39193 | ||||||||
\(544\) | 3.23801 | 0.138828 | ||||||||
\(545\) | 9.30307 | 0.398500 | ||||||||
\(546\) | −18.3171 | −0.783900 | ||||||||
\(547\) | 23.8349 | 1.01911 | 0.509554 | − | 0.860439i | \(-0.329810\pi\) | ||||
0.509554 | + | 0.860439i | \(0.329810\pi\) | |||||||
\(548\) | −16.2368 | −0.693600 | ||||||||
\(549\) | 64.0110 | 2.73192 | ||||||||
\(550\) | 14.6818 | 0.626035 | ||||||||
\(551\) | −1.06452 | −0.0453501 | ||||||||
\(552\) | 0.909678 | 0.0387185 | ||||||||
\(553\) | −3.85601 | −0.163974 | ||||||||
\(554\) | 15.0027 | 0.637405 | ||||||||
\(555\) | 69.5303 | 2.95139 | ||||||||
\(556\) | 7.68972 | 0.326117 | ||||||||
\(557\) | −8.59867 | −0.364337 | −0.182169 | − | 0.983267i | \(-0.558312\pi\) | ||||
−0.182169 | + | 0.983267i | \(0.558312\pi\) | |||||||
\(558\) | −43.2962 | −1.83287 | ||||||||
\(559\) | −7.25930 | −0.307036 | ||||||||
\(560\) | 3.89821 | 0.164730 | ||||||||
\(561\) | −35.5348 | −1.50028 | ||||||||
\(562\) | 14.0305 | 0.591840 | ||||||||
\(563\) | 18.3220 | 0.772182 | 0.386091 | − | 0.922461i | \(-0.373825\pi\) | ||||
0.386091 | + | 0.922461i | \(0.373825\pi\) | |||||||
\(564\) | −9.90954 | −0.417267 | ||||||||
\(565\) | 44.6657 | 1.87910 | ||||||||
\(566\) | 2.91971 | 0.122725 | ||||||||
\(567\) | −24.9585 | −1.04816 | ||||||||
\(568\) | −8.65604 | −0.363200 | ||||||||
\(569\) | 10.6598 | 0.446883 | 0.223442 | − | 0.974717i | \(-0.428271\pi\) | ||||
0.223442 | + | 0.974717i | \(0.428271\pi\) | |||||||
\(570\) | −8.15773 | −0.341690 | ||||||||
\(571\) | 7.63681 | 0.319591 | 0.159795 | − | 0.987150i | \(-0.448917\pi\) | ||||
0.159795 | + | 0.987150i | \(0.448917\pi\) | |||||||
\(572\) | −15.6091 | −0.652651 | ||||||||
\(573\) | −12.6996 | −0.530531 | ||||||||
\(574\) | 6.19728 | 0.258669 | ||||||||
\(575\) | −1.21700 | −0.0507526 | ||||||||
\(576\) | 7.04180 | 0.293408 | ||||||||
\(577\) | −28.3404 | −1.17983 | −0.589914 | − | 0.807466i | \(-0.700838\pi\) | ||||
−0.589914 | + | 0.807466i | \(0.700838\pi\) | |||||||
\(578\) | −6.51532 | −0.271002 | ||||||||
\(579\) | −31.8250 | −1.32260 | ||||||||
\(580\) | −3.82064 | −0.158644 | ||||||||
\(581\) | 18.6641 | 0.774319 | ||||||||
\(582\) | 38.8720 | 1.61130 | ||||||||
\(583\) | −24.2336 | −1.00365 | ||||||||
\(584\) | 0.231430 | 0.00957663 | ||||||||
\(585\) | 96.4751 | 3.98876 | ||||||||
\(586\) | 12.7936 | 0.528501 | ||||||||
\(587\) | 16.3759 | 0.675907 | 0.337954 | − | 0.941163i | \(-0.390265\pi\) | ||||
0.337954 | + | 0.941163i | \(0.390265\pi\) | |||||||
\(588\) | 16.9703 | 0.699844 | ||||||||
\(589\) | 5.20723 | 0.214560 | ||||||||
\(590\) | −26.8246 | −1.10435 | ||||||||
\(591\) | −63.9996 | −2.63259 | ||||||||
\(592\) | 7.21847 | 0.296677 | ||||||||
\(593\) | 35.7370 | 1.46754 | 0.733771 | − | 0.679397i | \(-0.237759\pi\) | ||||
0.733771 | + | 0.679397i | \(0.237759\pi\) | |||||||
\(594\) | −44.3558 | −1.81994 | ||||||||
\(595\) | 12.6224 | 0.517470 | ||||||||
\(596\) | 8.62106 | 0.353132 | ||||||||
\(597\) | −26.8402 | −1.09849 | ||||||||
\(598\) | 1.29387 | 0.0529103 | ||||||||
\(599\) | 17.5971 | 0.718999 | 0.359500 | − | 0.933145i | \(-0.382947\pi\) | ||||
0.359500 | + | 0.933145i | \(0.382947\pi\) | |||||||
\(600\) | −13.4343 | −0.548454 | ||||||||
\(601\) | −18.2459 | −0.744266 | −0.372133 | − | 0.928179i | \(-0.621373\pi\) | ||||
−0.372133 | + | 0.928179i | \(0.621373\pi\) | |||||||
\(602\) | −2.06552 | −0.0841841 | ||||||||
\(603\) | 3.57200 | 0.145463 | ||||||||
\(604\) | 21.3163 | 0.867346 | ||||||||
\(605\) | −3.01939 | −0.122756 | ||||||||
\(606\) | −21.3900 | −0.868910 | ||||||||
\(607\) | 8.32651 | 0.337962 | 0.168981 | − | 0.985619i | \(-0.445952\pi\) | ||||
0.168981 | + | 0.985619i | \(0.445952\pi\) | |||||||
\(608\) | −0.846917 | −0.0343470 | ||||||||
\(609\) | 5.10813 | 0.206992 | ||||||||
\(610\) | −27.6309 | −1.11874 | ||||||||
\(611\) | −14.0947 | −0.570212 | ||||||||
\(612\) | 22.8014 | 0.921691 | ||||||||
\(613\) | 25.0195 | 1.01053 | 0.505265 | − | 0.862964i | \(-0.331395\pi\) | ||||
0.505265 | + | 0.862964i | \(0.331395\pi\) | |||||||
\(614\) | −0.792900 | −0.0319989 | ||||||||
\(615\) | −46.5465 | −1.87694 | ||||||||
\(616\) | −4.44133 | −0.178946 | ||||||||
\(617\) | 22.9530 | 0.924052 | 0.462026 | − | 0.886866i | \(-0.347123\pi\) | ||||
0.462026 | + | 0.886866i | \(0.347123\pi\) | |||||||
\(618\) | −0.824744 | −0.0331761 | ||||||||
\(619\) | 37.2680 | 1.49793 | 0.748963 | − | 0.662612i | \(-0.230552\pi\) | ||||
0.748963 | + | 0.662612i | \(0.230552\pi\) | |||||||
\(620\) | 18.6892 | 0.750574 | ||||||||
\(621\) | 3.67673 | 0.147542 | ||||||||
\(622\) | 13.3358 | 0.534717 | ||||||||
\(623\) | 22.0534 | 0.883549 | ||||||||
\(624\) | 14.2828 | 0.571771 | ||||||||
\(625\) | −28.2243 | −1.12897 | ||||||||
\(626\) | −12.1971 | −0.487496 | ||||||||
\(627\) | 9.29429 | 0.371178 | ||||||||
\(628\) | −6.99959 | −0.279314 | ||||||||
\(629\) | 23.3734 | 0.931960 | ||||||||
\(630\) | 27.4504 | 1.09365 | ||||||||
\(631\) | −1.08594 | −0.0432306 | −0.0216153 | − | 0.999766i | \(-0.506881\pi\) | ||||
−0.0216153 | + | 0.999766i | \(0.506881\pi\) | |||||||
\(632\) | 3.00674 | 0.119602 | ||||||||
\(633\) | −23.4556 | −0.932275 | ||||||||
\(634\) | 16.9958 | 0.674990 | ||||||||
\(635\) | 33.0993 | 1.31351 | ||||||||
\(636\) | 22.1745 | 0.879274 | ||||||||
\(637\) | 24.1375 | 0.956364 | ||||||||
\(638\) | 4.35295 | 0.172335 | ||||||||
\(639\) | −60.9541 | −2.41131 | ||||||||
\(640\) | −3.03965 | −0.120153 | ||||||||
\(641\) | −33.9464 | −1.34080 | −0.670401 | − | 0.741999i | \(-0.733878\pi\) | ||||
−0.670401 | + | 0.741999i | \(0.733878\pi\) | |||||||
\(642\) | 38.9126 | 1.53576 | ||||||||
\(643\) | 27.0846 | 1.06811 | 0.534055 | − | 0.845449i | \(-0.320667\pi\) | ||||
0.534055 | + | 0.845449i | \(0.320667\pi\) | |||||||
\(644\) | 0.368150 | 0.0145071 | ||||||||
\(645\) | 15.5137 | 0.610850 | ||||||||
\(646\) | −2.74232 | −0.107895 | ||||||||
\(647\) | −25.8657 | −1.01688 | −0.508442 | − | 0.861096i | \(-0.669778\pi\) | ||||
−0.508442 | + | 0.861096i | \(0.669778\pi\) | |||||||
\(648\) | 19.4615 | 0.764520 | ||||||||
\(649\) | 30.5618 | 1.19966 | ||||||||
\(650\) | −19.1082 | −0.749484 | ||||||||
\(651\) | −24.9870 | −0.979319 | ||||||||
\(652\) | 22.6419 | 0.886725 | ||||||||
\(653\) | 33.5998 | 1.31486 | 0.657432 | − | 0.753514i | \(-0.271643\pi\) | ||||
0.657432 | + | 0.753514i | \(0.271643\pi\) | |||||||
\(654\) | 9.69859 | 0.379245 | ||||||||
\(655\) | −10.6816 | −0.417365 | ||||||||
\(656\) | −4.83235 | −0.188672 | ||||||||
\(657\) | 1.62968 | 0.0635799 | ||||||||
\(658\) | −4.01043 | −0.156343 | ||||||||
\(659\) | 33.4850 | 1.30439 | 0.652196 | − | 0.758050i | \(-0.273848\pi\) | ||||
0.652196 | + | 0.758050i | \(0.273848\pi\) | |||||||
\(660\) | 33.3579 | 1.29846 | ||||||||
\(661\) | −14.4870 | −0.563479 | −0.281739 | − | 0.959491i | \(-0.590911\pi\) | ||||
−0.281739 | + | 0.959491i | \(0.590911\pi\) | |||||||
\(662\) | −7.05932 | −0.274368 | ||||||||
\(663\) | 46.2479 | 1.79612 | ||||||||
\(664\) | −14.5534 | −0.564783 | ||||||||
\(665\) | −3.30146 | −0.128025 | ||||||||
\(666\) | 50.8310 | 1.96966 | ||||||||
\(667\) | −0.360824 | −0.0139712 | ||||||||
\(668\) | 0.707537 | 0.0273754 | ||||||||
\(669\) | 14.7858 | 0.571650 | ||||||||
\(670\) | −1.54188 | −0.0595680 | ||||||||
\(671\) | 31.4805 | 1.21529 | ||||||||
\(672\) | 4.06395 | 0.156770 | ||||||||
\(673\) | −4.39816 | −0.169537 | −0.0847683 | − | 0.996401i | \(-0.527015\pi\) | ||||
−0.0847683 | + | 0.996401i | \(0.527015\pi\) | |||||||
\(674\) | 1.85496 | 0.0714503 | ||||||||
\(675\) | −54.2988 | −2.08996 | ||||||||
\(676\) | 7.31503 | 0.281347 | ||||||||
\(677\) | −20.3723 | −0.782969 | −0.391485 | − | 0.920185i | \(-0.628038\pi\) | ||||
−0.391485 | + | 0.920185i | \(0.628038\pi\) | |||||||
\(678\) | 46.5647 | 1.78831 | ||||||||
\(679\) | 15.7316 | 0.603725 | ||||||||
\(680\) | −9.84239 | −0.377439 | ||||||||
\(681\) | 81.0083 | 3.10424 | ||||||||
\(682\) | −21.2930 | −0.815350 | ||||||||
\(683\) | −30.1909 | −1.15522 | −0.577611 | − | 0.816312i | \(-0.696015\pi\) | ||||
−0.577611 | + | 0.816312i | \(0.696015\pi\) | |||||||
\(684\) | −5.96381 | −0.228032 | ||||||||
\(685\) | 49.3540 | 1.88572 | ||||||||
\(686\) | 15.8451 | 0.604970 | ||||||||
\(687\) | −53.5165 | −2.04178 | ||||||||
\(688\) | 1.61059 | 0.0614033 | ||||||||
\(689\) | 31.5396 | 1.20156 | ||||||||
\(690\) | −2.76510 | −0.105266 | ||||||||
\(691\) | 18.4334 | 0.701239 | 0.350619 | − | 0.936518i | \(-0.385971\pi\) | ||||
0.350619 | + | 0.936518i | \(0.385971\pi\) | |||||||
\(692\) | 6.92283 | 0.263166 | ||||||||
\(693\) | −31.2749 | −1.18804 | ||||||||
\(694\) | −1.49193 | −0.0566331 | ||||||||
\(695\) | −23.3740 | −0.886628 | ||||||||
\(696\) | −3.98308 | −0.150978 | ||||||||
\(697\) | −15.6472 | −0.592679 | ||||||||
\(698\) | 6.00693 | 0.227366 | ||||||||
\(699\) | −54.5927 | −2.06488 | ||||||||
\(700\) | −5.43692 | −0.205496 | ||||||||
\(701\) | −48.4633 | −1.83043 | −0.915217 | − | 0.402962i | \(-0.867981\pi\) | ||||
−0.915217 | + | 0.402962i | \(0.867981\pi\) | |||||||
\(702\) | 57.7283 | 2.17881 | ||||||||
\(703\) | −6.11344 | −0.230573 | ||||||||
\(704\) | 3.46314 | 0.130522 | ||||||||
\(705\) | 30.1215 | 1.13444 | ||||||||
\(706\) | 25.6381 | 0.964904 | ||||||||
\(707\) | −8.65661 | −0.325565 | ||||||||
\(708\) | −27.9650 | −1.05099 | ||||||||
\(709\) | 51.5335 | 1.93538 | 0.967691 | − | 0.252138i | \(-0.0811338\pi\) | ||||
0.967691 | + | 0.252138i | \(0.0811338\pi\) | |||||||
\(710\) | 26.3113 | 0.987446 | ||||||||
\(711\) | 21.1729 | 0.794044 | ||||||||
\(712\) | −17.1962 | −0.644454 | ||||||||
\(713\) | 1.76501 | 0.0661003 | ||||||||
\(714\) | 13.1591 | 0.492467 | ||||||||
\(715\) | 47.4463 | 1.77439 | ||||||||
\(716\) | 5.27002 | 0.196950 | ||||||||
\(717\) | −32.5697 | −1.21634 | ||||||||
\(718\) | −27.1825 | −1.01444 | ||||||||
\(719\) | −6.06661 | −0.226246 | −0.113123 | − | 0.993581i | \(-0.536085\pi\) | ||||
−0.113123 | + | 0.993581i | \(0.536085\pi\) | |||||||
\(720\) | −21.4046 | −0.797701 | ||||||||
\(721\) | −0.333777 | −0.0124305 | ||||||||
\(722\) | −18.2827 | −0.680413 | ||||||||
\(723\) | −5.90835 | −0.219734 | ||||||||
\(724\) | −10.2356 | −0.380402 | ||||||||
\(725\) | 5.32873 | 0.197904 | ||||||||
\(726\) | −3.14776 | −0.116825 | ||||||||
\(727\) | 26.8418 | 0.995506 | 0.497753 | − | 0.867319i | \(-0.334159\pi\) | ||||
0.497753 | + | 0.867319i | \(0.334159\pi\) | |||||||
\(728\) | 5.78031 | 0.214233 | ||||||||
\(729\) | 15.2833 | 0.566048 | ||||||||
\(730\) | −0.703465 | −0.0260364 | ||||||||
\(731\) | 5.21511 | 0.192888 | ||||||||
\(732\) | −28.8056 | −1.06469 | ||||||||
\(733\) | −51.8368 | −1.91464 | −0.957319 | − | 0.289034i | \(-0.906666\pi\) | ||||
−0.957319 | + | 0.289034i | \(0.906666\pi\) | |||||||
\(734\) | −14.6711 | −0.541522 | ||||||||
\(735\) | −51.5838 | −1.90270 | ||||||||
\(736\) | −0.287066 | −0.0105814 | ||||||||
\(737\) | 1.75670 | 0.0647089 | ||||||||
\(738\) | −34.0284 | −1.25260 | ||||||||
\(739\) | 17.2741 | 0.635437 | 0.317719 | − | 0.948185i | \(-0.397083\pi\) | ||||
0.317719 | + | 0.948185i | \(0.397083\pi\) | |||||||
\(740\) | −21.9416 | −0.806589 | ||||||||
\(741\) | −12.0964 | −0.444371 | ||||||||
\(742\) | 8.97408 | 0.329449 | ||||||||
\(743\) | −26.0173 | −0.954482 | −0.477241 | − | 0.878773i | \(-0.658363\pi\) | ||||
−0.477241 | + | 0.878773i | \(0.658363\pi\) | |||||||
\(744\) | 19.4837 | 0.714308 | ||||||||
\(745\) | −26.2050 | −0.960076 | ||||||||
\(746\) | −0.602150 | −0.0220463 | ||||||||
\(747\) | −102.482 | −3.74963 | ||||||||
\(748\) | 11.2137 | 0.410012 | ||||||||
\(749\) | 15.7481 | 0.575422 | ||||||||
\(750\) | −7.32578 | −0.267500 | ||||||||
\(751\) | 50.8700 | 1.85627 | 0.928136 | − | 0.372240i | \(-0.121410\pi\) | ||||
0.928136 | + | 0.372240i | \(0.121410\pi\) | |||||||
\(752\) | 3.12714 | 0.114035 | ||||||||
\(753\) | −19.1862 | −0.699183 | ||||||||
\(754\) | −5.66529 | −0.206318 | ||||||||
\(755\) | −64.7939 | −2.35809 | ||||||||
\(756\) | 16.4257 | 0.597395 | ||||||||
\(757\) | −28.4707 | −1.03479 | −0.517393 | − | 0.855748i | \(-0.673098\pi\) | ||||
−0.517393 | + | 0.855748i | \(0.673098\pi\) | |||||||
\(758\) | −4.61086 | −0.167474 | ||||||||
\(759\) | 3.15034 | 0.114350 | ||||||||
\(760\) | 2.57433 | 0.0933807 | ||||||||
\(761\) | 33.6279 | 1.21901 | 0.609505 | − | 0.792782i | \(-0.291368\pi\) | ||||
0.609505 | + | 0.792782i | \(0.291368\pi\) | |||||||
\(762\) | 34.5065 | 1.25004 | ||||||||
\(763\) | 3.92505 | 0.142096 | ||||||||
\(764\) | 4.00758 | 0.144989 | ||||||||
\(765\) | −69.3081 | −2.50584 | ||||||||
\(766\) | −18.2631 | −0.659872 | ||||||||
\(767\) | −39.7757 | −1.43622 | ||||||||
\(768\) | −3.16888 | −0.114347 | ||||||||
\(769\) | 23.8916 | 0.861553 | 0.430777 | − | 0.902459i | \(-0.358240\pi\) | ||||
0.430777 | + | 0.902459i | \(0.358240\pi\) | |||||||
\(770\) | 13.5001 | 0.486508 | ||||||||
\(771\) | −43.3041 | −1.55956 | ||||||||
\(772\) | 10.0430 | 0.361455 | ||||||||
\(773\) | 2.84455 | 0.102311 | 0.0511557 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511557 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(774\) | 11.3415 | 0.407661 | ||||||||
\(775\) | −26.0661 | −0.936323 | ||||||||
\(776\) | −12.2668 | −0.440352 | ||||||||
\(777\) | 29.3355 | 1.05240 | ||||||||
\(778\) | −29.0706 | −1.04223 | ||||||||
\(779\) | 4.09260 | 0.146633 | ||||||||
\(780\) | −43.4148 | −1.55450 | ||||||||
\(781\) | −29.9771 | −1.07266 | ||||||||
\(782\) | −0.929522 | −0.0332396 | ||||||||
\(783\) | −16.0988 | −0.575324 | ||||||||
\(784\) | −5.35531 | −0.191261 | ||||||||
\(785\) | 21.2763 | 0.759384 | ||||||||
\(786\) | −11.1357 | −0.397199 | ||||||||
\(787\) | 7.49094 | 0.267023 | 0.133512 | − | 0.991047i | \(-0.457375\pi\) | ||||
0.133512 | + | 0.991047i | \(0.457375\pi\) | |||||||
\(788\) | 20.1963 | 0.719462 | ||||||||
\(789\) | −0.813545 | −0.0289630 | ||||||||
\(790\) | −9.13943 | −0.325166 | ||||||||
\(791\) | 18.8449 | 0.670047 | ||||||||
\(792\) | 24.3867 | 0.866545 | ||||||||
\(793\) | −40.9713 | −1.45493 | ||||||||
\(794\) | −8.41968 | −0.298803 | ||||||||
\(795\) | −67.4025 | −2.39052 | ||||||||
\(796\) | 8.46992 | 0.300208 | ||||||||
\(797\) | −31.0123 | −1.09851 | −0.549256 | − | 0.835654i | \(-0.685089\pi\) | ||||
−0.549256 | + | 0.835654i | \(0.685089\pi\) | |||||||
\(798\) | −3.44183 | −0.121839 | ||||||||
\(799\) | 10.1257 | 0.358222 | ||||||||
\(800\) | 4.23946 | 0.149887 | ||||||||
\(801\) | −121.092 | −4.27858 | ||||||||
\(802\) | −2.69017 | −0.0949930 | ||||||||
\(803\) | 0.801474 | 0.0282834 | ||||||||
\(804\) | −1.60743 | −0.0566898 | ||||||||
\(805\) | −1.11905 | −0.0394412 | ||||||||
\(806\) | 27.7125 | 0.976130 | ||||||||
\(807\) | −81.7305 | −2.87705 | ||||||||
\(808\) | 6.75003 | 0.237465 | ||||||||
\(809\) | 16.1090 | 0.566363 | 0.283181 | − | 0.959066i | \(-0.408610\pi\) | ||||
0.283181 | + | 0.959066i | \(0.408610\pi\) | |||||||
\(810\) | −59.1561 | −2.07853 | ||||||||
\(811\) | −0.142698 | −0.00501080 | −0.00250540 | − | 0.999997i | \(-0.500797\pi\) | ||||
−0.00250540 | + | 0.999997i | \(0.500797\pi\) | |||||||
\(812\) | −1.61197 | −0.0565689 | ||||||||
\(813\) | −87.5156 | −3.06931 | ||||||||
\(814\) | 24.9986 | 0.876199 | ||||||||
\(815\) | −68.8234 | −2.41078 | ||||||||
\(816\) | −10.2608 | −0.359202 | ||||||||
\(817\) | −1.36404 | −0.0477216 | ||||||||
\(818\) | 36.9422 | 1.29165 | ||||||||
\(819\) | 40.7038 | 1.42231 | ||||||||
\(820\) | 14.6886 | 0.512950 | ||||||||
\(821\) | 3.18240 | 0.111067 | 0.0555333 | − | 0.998457i | \(-0.482314\pi\) | ||||
0.0555333 | + | 0.998457i | \(0.482314\pi\) | |||||||
\(822\) | 51.4523 | 1.79461 | ||||||||
\(823\) | 33.6306 | 1.17229 | 0.586145 | − | 0.810206i | \(-0.300645\pi\) | ||||
0.586145 | + | 0.810206i | \(0.300645\pi\) | |||||||
\(824\) | 0.260264 | 0.00906671 | ||||||||
\(825\) | −46.5249 | −1.61979 | ||||||||
\(826\) | −11.3175 | −0.393787 | ||||||||
\(827\) | −44.6141 | −1.55138 | −0.775692 | − | 0.631111i | \(-0.782599\pi\) | ||||
−0.775692 | + | 0.631111i | \(0.782599\pi\) | |||||||
\(828\) | −2.02146 | −0.0702506 | ||||||||
\(829\) | −0.397951 | −0.0138214 | −0.00691070 | − | 0.999976i | \(-0.502200\pi\) | ||||
−0.00691070 | + | 0.999976i | \(0.502200\pi\) | |||||||
\(830\) | 44.2373 | 1.53550 | ||||||||
\(831\) | −47.5418 | −1.64921 | ||||||||
\(832\) | −4.50722 | −0.156260 | ||||||||
\(833\) | −17.3405 | −0.600813 | ||||||||
\(834\) | −24.3678 | −0.843788 | ||||||||
\(835\) | −2.15066 | −0.0744267 | ||||||||
\(836\) | −2.93299 | −0.101440 | ||||||||
\(837\) | 78.7493 | 2.72197 | ||||||||
\(838\) | 24.3255 | 0.840312 | ||||||||
\(839\) | 43.1968 | 1.49132 | 0.745660 | − | 0.666326i | \(-0.232134\pi\) | ||||
0.745660 | + | 0.666326i | \(0.232134\pi\) | |||||||
\(840\) | −12.3530 | −0.426218 | ||||||||
\(841\) | −27.4201 | −0.945521 | ||||||||
\(842\) | −13.7992 | −0.475552 | ||||||||
\(843\) | −44.4609 | −1.53131 | ||||||||
\(844\) | 7.40185 | 0.254782 | ||||||||
\(845\) | −22.2351 | −0.764911 | ||||||||
\(846\) | 22.0207 | 0.757088 | ||||||||
\(847\) | −1.27391 | −0.0437721 | ||||||||
\(848\) | −6.99757 | −0.240298 | ||||||||
\(849\) | −9.25221 | −0.317535 | ||||||||
\(850\) | 13.7274 | 0.470845 | ||||||||
\(851\) | −2.07218 | −0.0710333 | ||||||||
\(852\) | 27.4300 | 0.939735 | ||||||||
\(853\) | −6.47898 | −0.221836 | −0.110918 | − | 0.993830i | \(-0.535379\pi\) | ||||
−0.110918 | + | 0.993830i | \(0.535379\pi\) | |||||||
\(854\) | −11.6577 | −0.398919 | ||||||||
\(855\) | 18.1279 | 0.619961 | ||||||||
\(856\) | −12.2796 | −0.419709 | ||||||||
\(857\) | 9.63433 | 0.329102 | 0.164551 | − | 0.986369i | \(-0.447382\pi\) | ||||
0.164551 | + | 0.986369i | \(0.447382\pi\) | |||||||
\(858\) | 49.4635 | 1.68865 | ||||||||
\(859\) | 39.4243 | 1.34514 | 0.672570 | − | 0.740034i | \(-0.265190\pi\) | ||||
0.672570 | + | 0.740034i | \(0.265190\pi\) | |||||||
\(860\) | −4.89563 | −0.166940 | ||||||||
\(861\) | −19.6384 | −0.669276 | ||||||||
\(862\) | 7.63843 | 0.260166 | ||||||||
\(863\) | 12.5077 | 0.425768 | 0.212884 | − | 0.977077i | \(-0.431714\pi\) | ||||
0.212884 | + | 0.977077i | \(0.431714\pi\) | |||||||
\(864\) | −12.8080 | −0.435736 | ||||||||
\(865\) | −21.0429 | −0.715482 | ||||||||
\(866\) | −0.237432 | −0.00806828 | ||||||||
\(867\) | 20.6463 | 0.701184 | ||||||||
\(868\) | 7.88513 | 0.267639 | ||||||||
\(869\) | 10.4128 | 0.353229 | ||||||||
\(870\) | 12.1072 | 0.410471 | ||||||||
\(871\) | −2.28632 | −0.0774689 | ||||||||
\(872\) | −3.06057 | −0.103644 | ||||||||
\(873\) | −86.3803 | −2.92353 | ||||||||
\(874\) | 0.243121 | 0.00822369 | ||||||||
\(875\) | −2.96477 | −0.100227 | ||||||||
\(876\) | −0.733373 | −0.0247784 | ||||||||
\(877\) | −19.0268 | −0.642488 | −0.321244 | − | 0.946996i | \(-0.604101\pi\) | ||||
−0.321244 | + | 0.946996i | \(0.604101\pi\) | |||||||
\(878\) | 22.7203 | 0.766773 | ||||||||
\(879\) | −40.5415 | −1.36743 | ||||||||
\(880\) | −10.5267 | −0.354856 | ||||||||
\(881\) | 4.38011 | 0.147570 | 0.0737848 | − | 0.997274i | \(-0.476492\pi\) | ||||
0.0737848 | + | 0.997274i | \(0.476492\pi\) | |||||||
\(882\) | −37.7110 | −1.26979 | ||||||||
\(883\) | −1.03524 | −0.0348386 | −0.0174193 | − | 0.999848i | \(-0.505545\pi\) | ||||
−0.0174193 | + | 0.999848i | \(0.505545\pi\) | |||||||
\(884\) | −14.5944 | −0.490863 | ||||||||
\(885\) | 85.0038 | 2.85737 | ||||||||
\(886\) | 31.7608 | 1.06702 | ||||||||
\(887\) | 22.0410 | 0.740066 | 0.370033 | − | 0.929019i | \(-0.379346\pi\) | ||||
0.370033 | + | 0.929019i | \(0.379346\pi\) | |||||||
\(888\) | −22.8744 | −0.767616 | ||||||||
\(889\) | 13.9649 | 0.468368 | ||||||||
\(890\) | 52.2703 | 1.75211 | ||||||||
\(891\) | 67.3979 | 2.25792 | ||||||||
\(892\) | −4.66593 | −0.156227 | ||||||||
\(893\) | −2.64843 | −0.0886264 | ||||||||
\(894\) | −27.3191 | −0.913688 | ||||||||
\(895\) | −16.0190 | −0.535456 | ||||||||
\(896\) | −1.28246 | −0.0428439 | ||||||||
\(897\) | −4.10012 | −0.136899 | ||||||||
\(898\) | −10.4783 | −0.349667 | ||||||||
\(899\) | −7.72822 | −0.257751 | ||||||||
\(900\) | 29.8534 | 0.995113 | ||||||||
\(901\) | −22.6582 | −0.754853 | ||||||||
\(902\) | −16.7351 | −0.557218 | ||||||||
\(903\) | 6.54537 | 0.217816 | ||||||||
\(904\) | −14.6944 | −0.488727 | ||||||||
\(905\) | 31.1125 | 1.03422 | ||||||||
\(906\) | −67.5486 | −2.24415 | ||||||||
\(907\) | −29.3125 | −0.973306 | −0.486653 | − | 0.873595i | \(-0.661782\pi\) | ||||
−0.486653 | + | 0.873595i | \(0.661782\pi\) | |||||||
\(908\) | −25.5637 | −0.848361 | ||||||||
\(909\) | 47.5323 | 1.57655 | ||||||||
\(910\) | −17.5701 | −0.582444 | ||||||||
\(911\) | 9.90013 | 0.328006 | 0.164003 | − | 0.986460i | \(-0.447559\pi\) | ||||
0.164003 | + | 0.986460i | \(0.447559\pi\) | |||||||
\(912\) | 2.68378 | 0.0888687 | ||||||||
\(913\) | −50.4006 | −1.66802 | ||||||||
\(914\) | −29.2012 | −0.965891 | ||||||||
\(915\) | 87.5589 | 2.89461 | ||||||||
\(916\) | 16.8881 | 0.558000 | ||||||||
\(917\) | −4.50667 | −0.148823 | ||||||||
\(918\) | −41.4723 | −1.36879 | ||||||||
\(919\) | 0.357050 | 0.0117780 | 0.00588900 | − | 0.999983i | \(-0.498125\pi\) | ||||
0.00588900 | + | 0.999983i | \(0.498125\pi\) | |||||||
\(920\) | 0.872580 | 0.0287681 | ||||||||
\(921\) | 2.51261 | 0.0827932 | ||||||||
\(922\) | −14.6740 | −0.483263 | ||||||||
\(923\) | 39.0147 | 1.28418 | ||||||||
\(924\) | 14.0740 | 0.463001 | ||||||||
\(925\) | 30.6024 | 1.00620 | ||||||||
\(926\) | −8.79064 | −0.288878 | ||||||||
\(927\) | 1.83272 | 0.0601945 | ||||||||
\(928\) | 1.25694 | 0.0412610 | ||||||||
\(929\) | −7.81636 | −0.256446 | −0.128223 | − | 0.991745i | \(-0.540927\pi\) | ||||
−0.128223 | + | 0.991745i | \(0.540927\pi\) | |||||||
\(930\) | −59.2237 | −1.94202 | ||||||||
\(931\) | 4.53550 | 0.148645 | ||||||||
\(932\) | 17.2278 | 0.564314 | ||||||||
\(933\) | −42.2596 | −1.38352 | ||||||||
\(934\) | 3.63604 | 0.118975 | ||||||||
\(935\) | −34.0856 | −1.11472 | ||||||||
\(936\) | −31.7389 | −1.03742 | ||||||||
\(937\) | −21.7907 | −0.711873 | −0.355936 | − | 0.934510i | \(-0.615838\pi\) | ||||
−0.355936 | + | 0.934510i | \(0.615838\pi\) | |||||||
\(938\) | −0.650534 | −0.0212407 | ||||||||
\(939\) | 38.6513 | 1.26134 | ||||||||
\(940\) | −9.50542 | −0.310032 | ||||||||
\(941\) | 52.0794 | 1.69774 | 0.848869 | − | 0.528603i | \(-0.177284\pi\) | ||||
0.848869 | + | 0.528603i | \(0.177284\pi\) | |||||||
\(942\) | 22.1809 | 0.722692 | ||||||||
\(943\) | 1.38720 | 0.0451736 | ||||||||
\(944\) | 8.82489 | 0.287226 | ||||||||
\(945\) | −49.9282 | −1.62416 | ||||||||
\(946\) | 5.57771 | 0.181347 | ||||||||
\(947\) | 0.766172 | 0.0248973 | 0.0124486 | − | 0.999923i | \(-0.496037\pi\) | ||||
0.0124486 | + | 0.999923i | \(0.496037\pi\) | |||||||
\(948\) | −9.52800 | −0.309455 | ||||||||
\(949\) | −1.04310 | −0.0338606 | ||||||||
\(950\) | −3.59047 | −0.116490 | ||||||||
\(951\) | −53.8577 | −1.74646 | ||||||||
\(952\) | −4.15260 | −0.134587 | ||||||||
\(953\) | 23.4455 | 0.759473 | 0.379736 | − | 0.925095i | \(-0.376015\pi\) | ||||
0.379736 | + | 0.925095i | \(0.376015\pi\) | |||||||
\(954\) | −49.2755 | −1.59535 | ||||||||
\(955\) | −12.1816 | −0.394189 | ||||||||
\(956\) | 10.2780 | 0.332414 | ||||||||
\(957\) | −13.7940 | −0.445895 | ||||||||
\(958\) | 0.241336 | 0.00779722 | ||||||||
\(959\) | 20.8229 | 0.672408 | ||||||||
\(960\) | 9.63228 | 0.310880 | ||||||||
\(961\) | 6.80357 | 0.219470 | ||||||||
\(962\) | −32.5352 | −1.04898 | ||||||||
\(963\) | −86.4706 | −2.78648 | ||||||||
\(964\) | 1.86449 | 0.0600512 | ||||||||
\(965\) | −30.5272 | −0.982704 | ||||||||
\(966\) | −1.16662 | −0.0375355 | ||||||||
\(967\) | 12.5254 | 0.402789 | 0.201394 | − | 0.979510i | \(-0.435453\pi\) | ||||
0.201394 | + | 0.979510i | \(0.435453\pi\) | |||||||
\(968\) | 0.993337 | 0.0319271 | ||||||||
\(969\) | 8.69008 | 0.279166 | ||||||||
\(970\) | 37.2867 | 1.19721 | ||||||||
\(971\) | 54.2390 | 1.74061 | 0.870306 | − | 0.492511i | \(-0.163921\pi\) | ||||
0.870306 | + | 0.492511i | \(0.163921\pi\) | |||||||
\(972\) | −23.2473 | −0.745657 | ||||||||
\(973\) | −9.86173 | −0.316153 | ||||||||
\(974\) | −8.08526 | −0.259068 | ||||||||
\(975\) | 60.5514 | 1.93920 | ||||||||
\(976\) | 9.09016 | 0.290969 | ||||||||
\(977\) | 41.0382 | 1.31293 | 0.656464 | − | 0.754357i | \(-0.272051\pi\) | ||||
0.656464 | + | 0.754357i | \(0.272051\pi\) | |||||||
\(978\) | −71.7495 | −2.29429 | ||||||||
\(979\) | −59.5528 | −1.90332 | ||||||||
\(980\) | 16.2782 | 0.519989 | ||||||||
\(981\) | −21.5519 | −0.688101 | ||||||||
\(982\) | 10.1812 | 0.324895 | ||||||||
\(983\) | 37.4383 | 1.19410 | 0.597048 | − | 0.802206i | \(-0.296340\pi\) | ||||
0.597048 | + | 0.802206i | \(0.296340\pi\) | |||||||
\(984\) | 15.3131 | 0.488165 | ||||||||
\(985\) | −61.3895 | −1.95603 | ||||||||
\(986\) | 4.06997 | 0.129614 | ||||||||
\(987\) | 12.7086 | 0.404518 | ||||||||
\(988\) | 3.81724 | 0.121443 | ||||||||
\(989\) | −0.462347 | −0.0147018 | ||||||||
\(990\) | −74.1270 | −2.35591 | ||||||||
\(991\) | −52.5884 | −1.67053 | −0.835263 | − | 0.549851i | \(-0.814684\pi\) | ||||
−0.835263 | + | 0.549851i | \(0.814684\pi\) | |||||||
\(992\) | −6.14846 | −0.195214 | ||||||||
\(993\) | 22.3701 | 0.709895 | ||||||||
\(994\) | 11.1010 | 0.352102 | ||||||||
\(995\) | −25.7456 | −0.816190 | ||||||||
\(996\) | 46.1181 | 1.46131 | ||||||||
\(997\) | 17.8599 | 0.565628 | 0.282814 | − | 0.959175i | \(-0.408732\pi\) | ||||
0.282814 | + | 0.959175i | \(0.408732\pi\) | |||||||
\(998\) | 15.1985 | 0.481101 | ||||||||
\(999\) | −92.4539 | −2.92511 |
(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 | 8014.2.a.d.1.1 | ✓ | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8014.2.a.d.1.1 | ✓ | 88 | 1.1 | even | 1 | trivial |