Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.49253 | −1.43906 | −0.719531 | − | 0.694461i | \(-0.755643\pi\) | ||||
−0.719531 | + | 0.694461i | \(0.755643\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.92718 | −1.75629 | −0.878144 | − | 0.478396i | \(-0.841218\pi\) | ||||
−0.878144 | + | 0.478396i | \(0.841218\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18622 | 0.826315 | 0.413157 | − | 0.910660i | \(-0.364426\pi\) | ||||
0.413157 | + | 0.910660i | \(0.364426\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.21269 | 1.07090 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.47715 | 1.04840 | 0.524199 | − | 0.851596i | \(-0.324365\pi\) | ||||
0.524199 | + | 0.851596i | \(0.324365\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.85586 | 1.06942 | 0.534711 | − | 0.845035i | \(-0.320421\pi\) | ||||
0.534711 | + | 0.845035i | \(0.320421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.78861 | 2.52741 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.14678 | −0.520671 | −0.260336 | − | 0.965518i | \(-0.583833\pi\) | ||||
−0.260336 | + | 0.965518i | \(0.583833\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.07416 | 1.62292 | 0.811462 | − | 0.584406i | \(-0.198672\pi\) | ||||
0.811462 | + | 0.584406i | \(0.198672\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.44922 | −1.18912 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.572069 | −0.119285 | −0.0596423 | − | 0.998220i | \(-0.518996\pi\) | ||||
−0.0596423 | + | 0.998220i | \(0.518996\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.4227 | 2.08455 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.530148 | −0.102027 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.29014 | 0.982354 | 0.491177 | − | 0.871060i | \(-0.336567\pi\) | ||||
0.491177 | + | 0.871060i | \(0.336567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.09240 | 1.45344 | 0.726719 | − | 0.686935i | \(-0.241044\pi\) | ||||
0.726719 | + | 0.686935i | \(0.241044\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.66688 | −1.50871 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.58569 | −1.45125 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.15971 | 0.683852 | 0.341926 | − | 0.939727i | \(-0.388921\pi\) | ||||
0.341926 | + | 0.939727i | \(0.388921\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.61083 | −1.53896 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.245191 | 0.0382924 | 0.0191462 | − | 0.999817i | \(-0.493905\pi\) | ||||
0.0191462 | + | 0.999817i | \(0.493905\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.43293 | 0.828514 | 0.414257 | − | 0.910160i | \(-0.364042\pi\) | ||||
0.414257 | + | 0.910160i | \(0.364042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.6168 | −1.88081 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.50042 | 0.218858 | 0.109429 | − | 0.993995i | \(-0.465098\pi\) | ||||
0.109429 | + | 0.993995i | \(0.465098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.22043 | −0.317204 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.35091 | 0.749278 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.38122 | −1.01389 | −0.506944 | − | 0.861979i | \(-0.669225\pi\) | ||||
−0.506944 | + | 0.861979i | \(0.669225\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.6554 | −1.84129 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −17.6325 | −2.33549 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.9107 | −1.42045 | −0.710227 | − | 0.703972i | \(-0.751408\pi\) | ||||
−0.710227 | + | 0.703972i | \(0.751408\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.32991 | 1.06654 | 0.533268 | − | 0.845946i | \(-0.320964\pi\) | ||||
0.533268 | + | 0.845946i | \(0.320964\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.02367 | 0.884899 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.1426 | −1.87821 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.93170 | 0.724673 | 0.362336 | − | 0.932047i | \(-0.381979\pi\) | ||||
0.362336 | + | 0.932047i | \(0.381979\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.42590 | 0.171658 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.26670 | −0.743721 | −0.371861 | − | 0.928289i | \(-0.621280\pi\) | ||||
−0.371861 | + | 0.928289i | \(0.621280\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.909284 | 0.106424 | 0.0532118 | − | 0.998583i | \(-0.483054\pi\) | ||||
0.0532118 | + | 0.998583i | \(0.483054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −25.9790 | −2.99980 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.60182 | 0.866307 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.07280 | −1.02077 | −0.510385 | − | 0.859946i | \(-0.670497\pi\) | ||||
−0.510385 | + | 0.859946i | \(0.670497\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.31668 | −0.924075 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2441 | 1.34396 | 0.671980 | − | 0.740569i | \(-0.265444\pi\) | ||||
0.671980 | + | 0.740569i | \(0.265444\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.43080 | 0.914449 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.1858 | −1.41367 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9607 | 1.16184 | 0.580918 | − | 0.813962i | \(-0.302694\pi\) | ||||
0.580918 | + | 0.813962i | \(0.302694\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.42976 | 0.883679 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.1705 | −2.09159 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27.7815 | −2.85032 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.29623 | −0.740820 | −0.370410 | − | 0.928868i | \(-0.620783\pi\) | ||||
−0.370410 | + | 0.928868i | \(0.620783\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.1710 | 1.12273 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.15477 | −0.214408 | −0.107204 | − | 0.994237i | \(-0.534190\pi\) | ||||
−0.107204 | + | 0.994237i | \(0.534190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.8738 | 1.56410 | 0.782048 | − | 0.623218i | \(-0.214175\pi\) | ||||
0.782048 | + | 0.623218i | \(0.214175\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.4001 | 2.08843 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.70889 | 0.938594 | 0.469297 | − | 0.883040i | \(-0.344507\pi\) | ||||
0.469297 | + | 0.883040i | \(0.344507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.266281 | −0.0255051 | −0.0127525 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127525 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.3682 | −0.984105 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.96495 | −0.749280 | −0.374640 | − | 0.927170i | \(-0.622234\pi\) | ||||
−0.374640 | + | 0.927170i | \(0.622234\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.24662 | 0.209498 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.3877 | 1.14524 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.69334 | −0.430238 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.09054 | 0.0991398 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.611145 | −0.0551051 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −21.2961 | −1.90478 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.21230 | −0.551253 | −0.275626 | − | 0.961265i | \(-0.588885\pi\) | ||||
−0.275626 | + | 0.961265i | \(0.588885\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.5417 | −1.19228 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7337 | −1.28729 | −0.643645 | − | 0.765324i | \(-0.722579\pi\) | ||||
−0.643645 | + | 0.765324i | \(0.722579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.4657 | 1.34105 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.08199 | 0.179189 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.14072 | 0.780945 | 0.390472 | − | 0.920615i | \(-0.372312\pi\) | ||||
0.390472 | + | 0.920615i | \(0.372312\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.35070 | 0.114564 | 0.0572822 | − | 0.998358i | \(-0.481757\pi\) | ||||
0.0572822 | + | 0.998358i | \(0.481757\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.73983 | −0.314950 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.4074 | 1.12118 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.7753 | −1.72530 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.53448 | 0.456476 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.3909 | 1.01510 | 0.507552 | − | 0.861621i | \(-0.330550\pi\) | ||||
0.507552 | + | 0.861621i | \(0.330550\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7936 | −1.44802 | −0.724012 | − | 0.689788i | \(-0.757704\pi\) | ||||
−0.724012 | + | 0.689788i | \(0.757704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.89695 | −0.557586 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.7803 | −2.55266 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1429 | 1.04892 | 0.524459 | − | 0.851435i | \(-0.324267\pi\) | ||||
0.524459 | + | 0.851435i | \(0.324267\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.3979 | 1.45905 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.25067 | −0.0985667 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.93629 | 0.543292 | 0.271646 | − | 0.962397i | \(-0.412432\pi\) | ||||
0.271646 | + | 0.962397i | \(0.412432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 34.0364 | 2.64973 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.5044 | −0.967622 | −0.483811 | − | 0.875173i | \(-0.660748\pi\) | ||||
−0.483811 | + | 0.875173i | \(0.660748\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.86762 | 0.143663 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.7271 | 1.73799 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.2106 | 1.61261 | 0.806307 | − | 0.591497i | \(-0.201463\pi\) | ||||
0.806307 | + | 0.591497i | \(0.201463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.7865 | 1.72249 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.1953 | 2.04412 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.3274 | −1.36986 | −0.684929 | − | 0.728610i | \(-0.740167\pi\) | ||||
−0.684929 | + | 0.728610i | \(0.740167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4582 | 0.851685 | 0.425842 | − | 0.904797i | \(-0.359978\pi\) | ||||
0.425842 | + | 0.904797i | \(0.359978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.7625 | −1.53481 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.3359 | −1.20104 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.46467 | −0.545871 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.15902 | −0.0843064 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.23850 | −0.523759 | −0.261880 | − | 0.965101i | \(-0.584342\pi\) | ||||
−0.261880 | + | 0.965101i | \(0.584342\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.26334 | −0.450845 | −0.225423 | − | 0.974261i | \(-0.572376\pi\) | ||||
−0.225423 | + | 0.974261i | \(0.572376\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 37.7435 | 2.70286 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.18663 | 0.369532 | 0.184766 | − | 0.982783i | \(-0.440847\pi\) | ||||
0.184766 | + | 0.982783i | \(0.440847\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.9473 | −1.48491 | −0.742456 | − | 0.669895i | \(-0.766339\pi\) | ||||
−0.742456 | + | 0.669895i | \(0.766339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.7849 | −1.04285 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.5654 | 0.811734 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.962908 | −0.0672524 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.83788 | −0.127742 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.5979 | 1.70147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4373 | −1.20043 | −0.600217 | − | 0.799837i | \(-0.704919\pi\) | ||||
−0.600217 | + | 0.799837i | \(0.704919\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.6199 | 1.07026 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.3361 | −1.45511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.6918 | 1.20100 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.26642 | −0.153150 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.27768 | −0.556817 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.61026 | 0.509621 | 0.254810 | − | 0.966991i | \(-0.417987\pi\) | ||||
0.254810 | + | 0.966991i | \(0.417987\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 33.4851 | 2.23234 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 26.2180 | 1.74015 | 0.870074 | − | 0.492921i | \(-0.164071\pi\) | ||||
0.870074 | + | 0.492921i | \(0.164071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.1573 | 0.869462 | 0.434731 | − | 0.900560i | \(-0.356843\pi\) | ||||
0.434731 | + | 0.900560i | \(0.356843\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.9477 | −1.24667 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.87355 | 0.253764 | 0.126882 | − | 0.991918i | \(-0.459503\pi\) | ||||
0.126882 | + | 0.991918i | \(0.459503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.89241 | −0.384378 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 22.6142 | 1.46895 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.4227 | −1.32103 | −0.660517 | − | 0.750812i | \(-0.729663\pi\) | ||||
−0.660517 | + | 0.750812i | \(0.729663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.40360 | 0.605739 | 0.302870 | − | 0.953032i | \(-0.402055\pi\) | ||||
0.302870 | + | 0.953032i | \(0.402055\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3200 | 1.43183 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.72002 | 0.557101 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.2769 | 1.73559 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −30.5186 | −1.93404 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.3902 | −1.66573 | −0.832866 | − | 0.553475i | \(-0.813301\pi\) | ||||
−0.832866 | + | 0.553475i | \(0.813301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.98917 | −0.125058 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −21.0140 | −1.31595 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.8601 | 1.23884 | 0.619420 | − | 0.785060i | \(-0.287368\pi\) | ||||
0.619420 | + | 0.785060i | \(0.287368\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.09405 | 0.565077 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.9956 | 1.05200 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.7481 | 1.34105 | 0.670523 | − | 0.741889i | \(-0.266070\pi\) | ||||
0.670523 | + | 0.741889i | \(0.266070\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.9874 | 1.78068 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.3200 | −1.67195 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 29.7942 | 1.81658 | 0.908291 | − | 0.418339i | \(-0.137388\pi\) | ||||
0.908291 | + | 0.418339i | \(0.137388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.81290 | 0.292363 | 0.146181 | − | 0.989258i | \(-0.453302\pi\) | ||||
0.146181 | + | 0.989258i | \(0.453302\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.0114 | −1.27167 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 36.2414 | 2.18544 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.87943 | −0.112924 | −0.0564620 | − | 0.998405i | \(-0.517982\pi\) | ||||
−0.0564620 | + | 0.998405i | \(0.517982\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.9984 | 1.55648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0500 | 0.778498 | 0.389249 | − | 0.921133i | \(-0.372735\pi\) | ||||
0.389249 | + | 0.921133i | \(0.372735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.75429 | 0.401501 | 0.200751 | − | 0.979642i | \(-0.435662\pi\) | ||||
0.200751 | + | 0.979642i | \(0.435662\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 69.2462 | 4.10179 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.536042 | 0.0316415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3913 | −0.728902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.1861 | 1.06609 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.1411 | −1.17666 | −0.588329 | − | 0.808622i | \(-0.700214\pi\) | ||||
−0.588329 | + | 0.808622i | \(0.700214\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 42.8484 | 2.49473 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.84340 | −0.106965 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.20582 | −0.127566 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.8776 | 0.684613 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.37083 | 0.308546 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.7131 | −1.87314 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.70210 | 0.268363 | 0.134182 | − | 0.990957i | \(-0.457159\pi\) | ||||
0.134182 | + | 0.990957i | \(0.457159\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −39.5660 | −2.25083 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.6084 | 1.84905 | 0.924527 | − | 0.381115i | \(-0.124460\pi\) | ||||
0.924527 | + | 0.381115i | \(0.124460\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.32504 | 0.131419 | 0.0657096 | − | 0.997839i | \(-0.479069\pi\) | ||||
0.0657096 | + | 0.997839i | \(0.479069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −27.5832 | −1.55414 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.3206 | −0.748160 | −0.374080 | − | 0.927396i | \(-0.622041\pi\) | ||||
−0.374080 | + | 0.927396i | \(0.622041\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.3946 | 1.02990 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.1997 | −1.35069 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.1867 | −0.845009 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40.1886 | 2.22926 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.663712 | 0.0367034 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.28025 | 0.180846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.14348 | −0.0628516 | −0.0314258 | − | 0.999506i | \(-0.510005\pi\) | ||||
−0.0314258 | + | 0.999506i | \(0.510005\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.3639 | 0.732336 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.2949 | −1.27273 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.33761 | −0.345232 | −0.172616 | − | 0.984989i | \(-0.555222\pi\) | ||||
−0.172616 | + | 0.984989i | \(0.555222\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.8529 | 1.07826 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.1385 | 1.52378 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1579 | −1.08843 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.59976 | −0.301481 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.93567 | 0.264961 | 0.132480 | − | 0.991186i | \(-0.457706\pi\) | ||||
0.132480 | + | 0.991186i | \(0.457706\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.75307 | −0.468541 | −0.234270 | − | 0.972171i | \(-0.575270\pi\) | ||||
−0.234270 | + | 0.972171i | \(0.575270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.04417 | −0.109110 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.01433 | 0.266886 | 0.133443 | − | 0.991056i | \(-0.457397\pi\) | ||||
0.133443 | + | 0.991056i | \(0.457397\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.6105 | 1.30619 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.6983 | 0.619139 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.8687 | 1.68197 | 0.840984 | − | 0.541060i | \(-0.181977\pi\) | ||||
0.840984 | + | 0.541060i | \(0.181977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.0437 | 1.63388 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.71820 | −0.142668 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.57092 | −0.186911 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.03363 | 0.106155 | 0.0530773 | − | 0.998590i | \(-0.483097\pi\) | ||||
0.0530773 | + | 0.998590i | \(0.483097\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.787723 | 0.0410072 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.1370 | −0.837791 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.3372 | −1.20835 | −0.604176 | − | 0.796851i | \(-0.706498\pi\) | ||||
−0.604176 | + | 0.796851i | \(0.706498\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 53.0811 | 2.74110 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.3980 | 1.05055 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.0205 | −1.38795 | −0.693975 | − | 0.719999i | \(-0.744142\pi\) | ||||
−0.693975 | + | 0.719999i | \(0.744142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.4843 | 0.793287 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.47464 | −0.433034 | −0.216517 | − | 0.976279i | \(-0.569470\pi\) | ||||
−0.216517 | + | 0.976279i | \(0.569470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.8537 | −1.52149 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.4543 | 0.887254 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.56427 | 0.282120 | 0.141060 | − | 0.990001i | \(-0.454949\pi\) | ||||
0.141060 | + | 0.990001i | \(0.454949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.22811 | 0.0621081 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.7242 | 1.85249 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.6305 | 1.79277 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.8815 | −0.847257 | −0.423628 | − | 0.905836i | \(-0.639244\pi\) | ||||
−0.423628 | + | 0.905836i | \(0.639244\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −38.5487 | −1.92985 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.8108 | 1.68843 | 0.844215 | − | 0.536005i | \(-0.180067\pi\) | ||||
0.844215 | + | 0.536005i | \(0.180067\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.2031 | 1.55434 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 32.6611 | 1.62294 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.4639 | 0.716949 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.34695 | 0.116049 | 0.0580247 | − | 0.998315i | \(-0.481520\pi\) | ||||
0.0580247 | + | 0.998315i | \(0.481520\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.7835 | −1.12383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.8533 | −1.17374 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −48.0846 | −2.36038 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.36665 | −0.164865 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.68586 | 0.228919 | 0.114460 | − | 0.993428i | \(-0.463486\pi\) | ||||
0.114460 | + | 0.993428i | \(0.463486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.06792 | −0.246996 | −0.123498 | − | 0.992345i | \(-0.539411\pi\) | ||||
−0.123498 | + | 0.992345i | \(0.539411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.82038 | 0.234375 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.3754 | −1.08536 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.2110 | 0.881294 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33.4182 | −1.61345 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.8409 | 0.811196 | 0.405598 | − | 0.914052i | \(-0.367063\pi\) | ||||
0.405598 | + | 0.914052i | \(0.367063\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.0307 | 0.914556 | 0.457278 | − | 0.889324i | \(-0.348825\pi\) | ||||
0.457278 | + | 0.889324i | \(0.348825\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 51.7831 | 2.48281 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.04691 | −0.193590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.0666 | −1.67364 | −0.836819 | − | 0.547479i | \(-0.815587\pi\) | ||||
−0.836819 | + | 0.547479i | \(0.815587\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.13355 | −0.339693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.7054 | −1.03126 | −0.515628 | − | 0.856812i | \(-0.672441\pi\) | ||||
−0.515628 | + | 0.856812i | \(0.672441\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43.0448 | −2.04052 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −30.8847 | −1.46080 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.7769 | −1.31087 | −0.655436 | − | 0.755251i | \(-0.727515\pi\) | ||||
−0.655436 | + | 0.755251i | \(0.727515\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.852564 | 0.0401457 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 44.3511 | 2.08380 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.1052 | −1.55200 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.78593 | −0.0835421 | −0.0417710 | − | 0.999127i | \(-0.513300\pi\) | ||||
−0.0417710 | + | 0.999127i | \(0.513300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.13811 | 0.0531225 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.4279 | 0.625400 | 0.312700 | − | 0.949852i | \(-0.398766\pi\) | ||||
0.312700 | + | 0.949852i | \(0.398766\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.4010 | −1.78465 | −0.892323 | − | 0.451398i | \(-0.850926\pi\) | ||||
−0.892323 | + | 0.451398i | \(0.850926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 79.2133 | 3.67343 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.1437 | −1.57998 | −0.789991 | − | 0.613118i | \(-0.789915\pi\) | ||||
−0.789991 | + | 0.613118i | \(0.789915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9680 | 0.598808 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.7591 | −1.50946 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.8911 | 0.868613 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 73.7322 | 3.38306 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.7136 | −1.08577 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.7021 | 0.763139 | 0.381569 | − | 0.924340i | \(-0.375384\pi\) | ||||
0.381569 | + | 0.924340i | \(0.375384\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0392 | 0.731326 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.11733 | 0.141844 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.6536 | 1.30109 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0061 | 1.54096 | 0.770482 | − | 0.637462i | \(-0.220016\pi\) | ||||
0.770482 | + | 0.637462i | \(0.220016\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.2889 | −0.781831 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.4410 | −1.64456 | −0.822280 | − | 0.569083i | \(-0.807298\pi\) | ||||
−0.822280 | + | 0.569083i | \(0.807298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3568 | −0.511483 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −43.8706 | −1.97183 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.7004 | −0.614548 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.7536 | 0.884294 | 0.442147 | − | 0.896943i | \(-0.354217\pi\) | ||||
0.442147 | + | 0.896943i | \(0.354217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.1676 | 1.39247 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.7793 | 1.14944 | 0.574721 | − | 0.818350i | \(-0.305111\pi\) | ||||
0.574721 | + | 0.818350i | \(0.305111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.46218 | 0.376562 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.65509 | −0.206740 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.7842 | −0.522324 | −0.261162 | − | 0.965295i | \(-0.584106\pi\) | ||||
−0.261162 | + | 0.965295i | \(0.584106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.98790 | 0.0879395 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.75035 | −0.165582 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −62.3395 | −2.74700 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.21717 | 0.229451 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −52.8681 | −2.32065 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.0809 | −0.835949 | −0.417974 | − | 0.908459i | \(-0.637260\pi\) | ||||
−0.417974 | + | 0.908459i | \(0.637260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.20785 | −0.183997 | −0.0919983 | − | 0.995759i | \(-0.529325\pi\) | ||||
−0.0919983 | + | 0.995759i | \(0.529325\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −56.7959 | −2.47878 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.3726 | −0.756763 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6727 | −0.985771 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.0528 | −1.52116 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.945420 | 0.0409507 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.1286 | −1.64844 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.6817 | 1.97131 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.72075 | −0.332556 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.17651 | 0.0505820 | 0.0252910 | − | 0.999680i | \(-0.491949\pi\) | ||||
0.0252910 | + | 0.999680i | \(0.491949\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −28.5600 | −1.22563 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.04573 | 0.0447943 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.24925 | 0.0534141 | 0.0267071 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267071 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.7615 | 1.14215 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.4233 | 1.59429 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.8352 | −0.843477 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 40.7178 | 1.72837 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.66180 | 0.197527 | 0.0987635 | − | 0.995111i | \(-0.468511\pi\) | ||||
0.0987635 | + | 0.995111i | \(0.468511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.9486 | 0.886031 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.6059 | 0.785542 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.89653 | −0.417089 | −0.208545 | − | 0.978013i | \(-0.566873\pi\) | ||||
−0.208545 | + | 0.978013i | \(0.566873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.2798 | 1.31595 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.1821 | −0.763577 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.5155 | 0.608521 | 0.304260 | − | 0.952589i | \(-0.401591\pi\) | ||||
0.304260 | + | 0.952589i | \(0.401591\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.2594 | 1.14077 | 0.570385 | − | 0.821377i | \(-0.306794\pi\) | ||||
0.570385 | + | 0.821377i | \(0.306794\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0422 | 0.753722 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.96253 | −0.248655 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.2339 | −1.55007 | −0.775033 | − | 0.631920i | \(-0.782267\pi\) | ||||
−0.775033 | + | 0.631920i | \(0.782267\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.6116 | 0.648794 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.7682 | 1.11053 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.6656 | −1.06296 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −48.6487 | −2.01138 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.9918 | −0.825152 | −0.412576 | − | 0.910923i | \(-0.635371\pi\) | ||||
−0.412576 | + | 0.910923i | \(0.635371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.2469 | 2.35882 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9278 | −0.531780 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.6630 | −1.50557 | −0.752785 | − | 0.658266i | \(-0.771290\pi\) | ||||
−0.752785 | + | 0.658266i | \(0.771290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.4316 | 0.755622 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 52.2116 | 2.13688 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.8396 | 0.892343 | 0.446172 | − | 0.894947i | \(-0.352787\pi\) | ||||
0.446172 | + | 0.894947i | \(0.352787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.564099 | −0.0230101 | −0.0115050 | − | 0.999934i | \(-0.503662\pi\) | ||||
−0.0115050 | + | 0.999934i | \(0.503662\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.0568 | 0.776051 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.28274 | −0.174118 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.3256 | 1.71794 | 0.858972 | − | 0.512022i | \(-0.171103\pi\) | ||||
0.858972 | + | 0.512022i | \(0.171103\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.8271 | −1.16814 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.78539 | 0.234052 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.1984 | −0.775416 | −0.387708 | − | 0.921782i | \(-0.626733\pi\) | ||||
−0.387708 | + | 0.921782i | \(0.626733\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.40008 | 0.0967804 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.4840 | 1.26750 | 0.633750 | − | 0.773538i | \(-0.281515\pi\) | ||||
0.633750 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.3771 | −1.06019 | −0.530093 | − | 0.847939i | \(-0.677843\pi\) | ||||
−0.530093 | + | 0.847939i | \(0.677843\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.303281 | 0.0121703 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.9626 | 0.960042 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.5199 | 1.26080 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −61.3109 | −2.44852 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.92999 | −0.356062 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.85443 | 0.392298 | 0.196149 | − | 0.980574i | \(-0.437156\pi\) | ||||
0.196149 | + | 0.980574i | \(0.437156\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 43.4630 | 1.72750 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.3968 | 0.968159 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.56164 | −0.339225 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.1330 | −0.796450 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.555236 | −0.0219305 | −0.0109652 | − | 0.999940i | \(-0.503490\pi\) | ||||
−0.0109652 | + | 0.999940i | \(0.503490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.8519 | −0.625136 | −0.312568 | − | 0.949895i | \(-0.601189\pi\) | ||||
−0.312568 | + | 0.949895i | \(0.601189\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 53.1808 | 2.09399 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.4741 | −1.27669 | −0.638345 | − | 0.769751i | \(-0.720380\pi\) | ||||
−0.638345 | + | 0.769751i | \(0.720380\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.9382 | −1.48920 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −44.0973 | −1.72831 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.1028 | 1.21715 | 0.608573 | − | 0.793498i | \(-0.291742\pi\) | ||||
0.608573 | + | 0.793498i | \(0.291742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.8619 | 2.26085 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.92125 | 0.113969 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.9780 | 0.505551 | 0.252776 | − | 0.967525i | \(-0.418657\pi\) | ||||
0.252776 | + | 0.967525i | \(0.418657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.6740 | 0.998603 | 0.499301 | − | 0.866428i | \(-0.333590\pi\) | ||||
0.499301 | + | 0.866428i | \(0.333590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.6323 | 0.801294 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −60.7366 | −2.35526 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.02633 | −0.117180 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.9688 | −0.733376 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.9643 | 1.11815 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.25271 | −0.356666 | −0.178333 | − | 0.983970i | \(-0.557070\pi\) | ||||
−0.178333 | + | 0.983970i | \(0.557070\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.52559 | −0.212680 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 49.2561 | 1.89307 | 0.946533 | − | 0.322607i | \(-0.104559\pi\) | ||||
0.946533 | + | 0.322607i | \(0.104559\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.9512 | −0.612151 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −65.3490 | −2.50418 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.1109 | −0.425148 | −0.212574 | − | 0.977145i | \(-0.568185\pi\) | ||||
−0.212574 | + | 0.977145i | \(0.568185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.8973 | −1.37156 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.7950 | −1.25121 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.4609 | −1.08427 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.2131 | 1.79607 | 0.898036 | − | 0.439922i | \(-0.144994\pi\) | ||||
0.898036 | + | 0.439922i | \(0.144994\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.4223 | 0.927727 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.30442 | −0.201208 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.526371 | −0.0199377 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.65492 | −0.365183 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.3819 | −0.392119 | −0.196060 | − | 0.980592i | \(-0.562815\pi\) | ||||
−0.196060 | + | 0.980592i | \(0.562815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.4264 | 1.10984 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.6870 | 0.553144 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.71082 | −0.177168 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.3544 | −0.576648 | −0.288324 | − | 0.957533i | \(-0.593098\pi\) | ||||
−0.288324 | + | 0.957533i | \(0.593098\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.1481 | −1.09314 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.62941 | −0.173373 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.6532 | −1.96912 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 50.9041 | 1.90105 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.3370 | −0.571974 | −0.285987 | − | 0.958233i | \(-0.592321\pi\) | ||||
−0.285987 | + | 0.958233i | \(0.592321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.7038 | 1.29244 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.4387 | −0.871696 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 55.1378 | 2.04777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.20666 | 0.304368 | 0.152184 | − | 0.988352i | \(-0.451369\pi\) | ||||
0.152184 | + | 0.988352i | \(0.451369\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.6832 | −1.13641 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.6633 | −0.431383 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.9200 | 0.551082 | 0.275541 | − | 0.961289i | \(-0.411143\pi\) | ||||
0.275541 | + | 0.961289i | \(0.411143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.7349 | −0.801703 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.6254 | 0.759746 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.3144 | −1.44620 | −0.723102 | − | 0.690742i | \(-0.757284\pi\) | ||||
−0.723102 | + | 0.690742i | \(0.757284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −67.9885 | −2.49762 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −43.4766 | −1.59500 | −0.797500 | − | 0.603319i | \(-0.793845\pi\) | ||||
−0.797500 | + | 0.603319i | \(0.793845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.6614 | −1.78282 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.3364 | 1.43924 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.2258 | 0.775574 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 65.7782 | 2.39709 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 69.8787 | 2.54315 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.0740 | 0.729600 | 0.364800 | − | 0.931086i | \(-0.381137\pi\) | ||||
0.364800 | + | 0.931086i | \(0.381137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.95805 | 0.179966 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.5998 | 0.601742 | 0.300871 | − | 0.953665i | \(-0.402723\pi\) | ||||
0.300871 | + | 0.953665i | \(0.402723\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.582149 | −0.0210752 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 27.0856 | 0.979281 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.0702 | −1.51907 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.4487 | −0.881641 | −0.440821 | − | 0.897595i | \(-0.645313\pi\) | ||||
−0.440821 | + | 0.897595i | \(0.645313\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.5019 | −1.78277 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −33.8832 | −1.21869 | −0.609347 | − | 0.792903i | \(-0.708569\pi\) | ||||
−0.609347 | + | 0.792903i | \(0.708569\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 84.3451 | 3.02976 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.6672 | −0.813181 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.73452 | 0.0621455 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.7902 | −0.779716 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.80455 | −0.100227 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −51.6146 | −1.84220 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.39663 | −0.299307 | −0.149654 | − | 0.988738i | \(-0.547816\pi\) | ||||
−0.149654 | + | 0.988738i | \(0.547816\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54.2078 | −1.92985 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.4132 | −0.619141 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.1189 | 1.14058 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −72.2519 | −2.56251 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.8862 | 0.739826 | 0.369913 | − | 0.929066i | \(-0.379387\pi\) | ||||
0.369913 | + | 0.929066i | \(0.379387\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.22107 | −0.113953 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.2135 | 1.24421 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.16171 | 0.111574 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.91161 | 0.173112 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −74.2628 | −2.61417 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.28498 | −0.0803355 | −0.0401678 | − | 0.999193i | \(-0.512789\pi\) | ||||
−0.0401678 | + | 0.999193i | \(0.512789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.5733 | −0.652198 | −0.326099 | − | 0.945336i | \(-0.605734\pi\) | ||||
−0.326099 | + | 0.945336i | \(0.605734\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.9963 | −0.420728 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.2401 | −0.954178 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 38.4334 | 1.34461 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.0823 | 0.946330 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.4261 | −0.468575 | −0.234287 | − | 0.972167i | \(-0.575276\pi\) | ||||
−0.234287 | + | 0.972167i | \(0.575276\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 56.5702 | 1.97191 | 0.985957 | − | 0.167001i | \(-0.0534082\pi\) | ||||
0.985957 | + | 0.167001i | \(0.0534082\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −90.3327 | −3.14498 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.4792 | 0.816450 | 0.408225 | − | 0.912881i | \(-0.366148\pi\) | ||||
0.408225 | + | 0.912881i | \(0.366148\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.60961 | 0.0906356 | 0.0453178 | − | 0.998973i | \(-0.485570\pi\) | ||||
0.0453178 | + | 0.998973i | \(0.485570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.68453 | 0.162504 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.76677 | 0.165159 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.1072 | 1.69942 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.29017 | −0.148290 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.9247 | −1.17121 | −0.585606 | − | 0.810596i | \(-0.699143\pi\) | ||||
−0.585606 | + | 0.810596i | \(0.699143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.01442 | −0.0349802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.5275 | −1.12031 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.33448 | −0.252314 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.38416 | 0.0819207 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.8353 | −0.577785 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.37964 | −0.0815730 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.2402 | −0.829970 | −0.414985 | − | 0.909828i | \(-0.636213\pi\) | ||||
−0.414985 | + | 0.909828i | \(0.636213\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −89.2535 | −3.05240 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.8125 | −0.710941 | −0.355470 | − | 0.934688i | \(-0.615679\pi\) | ||||
−0.355470 | + | 0.934688i | \(0.615679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.8237 | −1.05169 | −0.525846 | − | 0.850580i | \(-0.676251\pi\) | ||||
−0.525846 | + | 0.850580i | \(0.676251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.33610 | −0.0455341 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.5436 | −1.48224 | −0.741121 | − | 0.671372i | \(-0.765705\pi\) | ||||
−0.741121 | + | 0.671372i | \(0.765705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −83.2980 | −2.83222 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.8857 | 1.04893 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.5474 | −1.07017 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.8718 | 0.774981 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23.4406 | −0.793343 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −46.5581 | −1.57395 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.6566 | −1.87939 | −0.939695 | − | 0.342014i | \(-0.888891\pi\) | ||||
−0.939695 | + | 0.342014i | \(0.888891\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.2024 | 1.69328 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.58474 | 0.0870821 | 0.0435411 | − | 0.999052i | \(-0.486136\pi\) | ||||
0.0435411 | + | 0.999052i | \(0.486136\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.56154 | −0.288119 | −0.144059 | − | 0.989569i | \(-0.546016\pi\) | ||||
−0.144059 | + | 0.989569i | \(0.546016\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −106.801 | −3.59007 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.2711 | −1.52006 | −0.760028 | − | 0.649891i | \(-0.774815\pi\) | ||||
−0.760028 | + | 0.649891i | \(0.774815\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.5815 | −0.455508 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.9183 | −0.968799 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.6142 | 0.355190 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.9752 | 2.40586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.49806 | 0.183575 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 42.8099 | 1.42779 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8459 | 0.527902 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.6052 | −0.985200 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44.9986 | −1.49580 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.5777 | 1.18134 | 0.590669 | − | 0.806914i | \(-0.298864\pi\) | ||||
0.590669 | + | 0.806914i | \(0.298864\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.92263 | −0.229609 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1500 | −0.435679 | −0.217839 | − | 0.975985i | \(-0.569901\pi\) | ||||
−0.217839 | + | 0.975985i | \(0.569901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.5744 | 1.40901 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 81.5382 | 2.69557 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.2112 | −1.06371 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.1987 | −0.765255 | −0.382628 | − | 0.923903i | \(-0.624981\pi\) | ||||
−0.382628 | + | 0.923903i | \(0.624981\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.7201 | −0.386191 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.1635 | −0.795351 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 43.3556 | 1.42552 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 50.9978 | 1.67499 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4634 | −0.343292 | −0.171646 | − | 0.985159i | \(-0.554909\pi\) | ||||
−0.171646 | + | 0.985159i | \(0.554909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7077 | −0.514797 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −81.2774 | −2.66090 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.3151 | 0.958707 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.5114 | −0.964094 | −0.482047 | − | 0.876145i | \(-0.660107\pi\) | ||||
−0.482047 | + | 0.876145i | \(0.660107\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.79523 | −0.189120 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.6333 | 1.45500 | 0.727502 | − | 0.686105i | \(-0.240681\pi\) | ||||
0.727502 | + | 0.686105i | \(0.240681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.140266 | −0.00456769 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.55169 | 0.148066 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.7330 | 1.42113 | 0.710566 | − | 0.703631i | \(-0.248439\pi\) | ||||
0.710566 | + | 0.703631i | \(0.248439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.50607 | 0.113812 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.2020 | 1.07665 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.2685 | 1.01289 | 0.506444 | − | 0.862273i | \(-0.330960\pi\) | ||||
0.506444 | + | 0.862273i | \(0.330960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.4269 | 0.919872 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −45.8490 | −1.48209 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.9837 | 0.645306 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.4870 | 1.11248 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.1917 | 1.00514 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.5973 | 0.791815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.81997 | 0.122842 | 0.0614210 | − | 0.998112i | \(-0.480437\pi\) | ||||
0.0614210 | + | 0.998112i | \(0.480437\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 37.8532 | 1.21602 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.4527 | 0.624268 | 0.312134 | − | 0.950038i | \(-0.398956\pi\) | ||||
0.312134 | + | 0.950038i | \(0.398956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.95292 | 0.0946663 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −100.171 | −3.20805 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 57.4235 | 1.83714 | 0.918571 | − | 0.395256i | \(-0.129344\pi\) | ||||
0.918571 | + | 0.395256i | \(0.129344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.1121 | 1.21807 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.855479 | −0.0273133 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.00696 | −0.223487 | −0.111744 | − | 0.993737i | \(-0.535644\pi\) | ||||
−0.111744 | + | 0.993737i | \(0.535644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.3688 | −0.649005 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.17610 | −0.260248 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.10801 | −0.0988290 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.87477 | −0.313682 | −0.156841 | − | 0.987624i | \(-0.550131\pi\) | ||||
−0.156841 | + | 0.987624i | \(0.550131\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.85017 | 0.0904473 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 82.2637 | 2.60793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.6262 | 1.44500 | 0.722498 | − | 0.691373i | \(-0.242994\pi\) | ||||
0.722498 | + | 0.691373i | \(0.242994\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.20526 | −0.0697713 |
(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 | 6008.2.a.e.1.8 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.8 | ✓ | 50 | 1.1 | even | 1 | trivial |