Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 | ||||||||
\(3\) | −1.30065 | −0.750928 | −0.375464 | − | 0.926837i | \(-0.622517\pi\) | ||||
−0.375464 | + | 0.926837i | \(0.622517\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.66833 | 1.19331 | 0.596657 | − | 0.802497i | \(-0.296495\pi\) | ||||
0.596657 | + | 0.802497i | \(0.296495\pi\) | |||||||
\(6\) | −1.30065 | −0.530986 | ||||||||
\(7\) | −4.20545 | −1.58951 | −0.794755 | − | 0.606931i | \(-0.792401\pi\) | ||||
−0.794755 | + | 0.606931i | \(0.792401\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.30832 | −0.436107 | ||||||||
\(10\) | 2.66833 | 0.843800 | ||||||||
\(11\) | −2.85367 | −0.860413 | −0.430207 | − | 0.902730i | \(-0.641559\pi\) | ||||
−0.430207 | + | 0.902730i | \(0.641559\pi\) | |||||||
\(12\) | −1.30065 | −0.375464 | ||||||||
\(13\) | 5.25232 | 1.45673 | 0.728365 | − | 0.685189i | \(-0.240280\pi\) | ||||
0.728365 | + | 0.685189i | \(0.240280\pi\) | |||||||
\(14\) | −4.20545 | −1.12395 | ||||||||
\(15\) | −3.47055 | −0.896093 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.66501 | −0.888896 | −0.444448 | − | 0.895805i | \(-0.646600\pi\) | ||||
−0.444448 | + | 0.895805i | \(0.646600\pi\) | |||||||
\(18\) | −1.30832 | −0.308374 | ||||||||
\(19\) | −2.56826 | −0.589199 | −0.294599 | − | 0.955621i | \(-0.595186\pi\) | ||||
−0.294599 | + | 0.955621i | \(0.595186\pi\) | |||||||
\(20\) | 2.66833 | 0.596657 | ||||||||
\(21\) | 5.46980 | 1.19361 | ||||||||
\(22\) | −2.85367 | −0.608404 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.30065 | −0.265493 | ||||||||
\(25\) | 2.11998 | 0.423997 | ||||||||
\(26\) | 5.25232 | 1.03006 | ||||||||
\(27\) | 5.60360 | 1.07841 | ||||||||
\(28\) | −4.20545 | −0.794755 | ||||||||
\(29\) | 1.86198 | 0.345761 | 0.172881 | − | 0.984943i | \(-0.444692\pi\) | ||||
0.172881 | + | 0.984943i | \(0.444692\pi\) | |||||||
\(30\) | −3.47055 | −0.633633 | ||||||||
\(31\) | 9.92467 | 1.78252 | 0.891262 | − | 0.453489i | \(-0.149821\pi\) | ||||
0.891262 | + | 0.453489i | \(0.149821\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.71161 | 0.646109 | ||||||||
\(34\) | −3.66501 | −0.628544 | ||||||||
\(35\) | −11.2215 | −1.89678 | ||||||||
\(36\) | −1.30832 | −0.218053 | ||||||||
\(37\) | 0.702891 | 0.115555 | 0.0577773 | − | 0.998329i | \(-0.481599\pi\) | ||||
0.0577773 | + | 0.998329i | \(0.481599\pi\) | |||||||
\(38\) | −2.56826 | −0.416626 | ||||||||
\(39\) | −6.83140 | −1.09390 | ||||||||
\(40\) | 2.66833 | 0.421900 | ||||||||
\(41\) | −1.57152 | −0.245430 | −0.122715 | − | 0.992442i | \(-0.539160\pi\) | ||||
−0.122715 | + | 0.992442i | \(0.539160\pi\) | |||||||
\(42\) | 5.46980 | 0.844008 | ||||||||
\(43\) | −3.65307 | −0.557088 | −0.278544 | − | 0.960424i | \(-0.589852\pi\) | ||||
−0.278544 | + | 0.960424i | \(0.589852\pi\) | |||||||
\(44\) | −2.85367 | −0.430207 | ||||||||
\(45\) | −3.49103 | −0.520412 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −9.81910 | −1.43226 | −0.716131 | − | 0.697966i | \(-0.754089\pi\) | ||||
−0.716131 | + | 0.697966i | \(0.754089\pi\) | |||||||
\(48\) | −1.30065 | −0.187732 | ||||||||
\(49\) | 10.6858 | 1.52654 | ||||||||
\(50\) | 2.11998 | 0.299811 | ||||||||
\(51\) | 4.76688 | 0.667497 | ||||||||
\(52\) | 5.25232 | 0.728365 | ||||||||
\(53\) | −1.81090 | −0.248746 | −0.124373 | − | 0.992236i | \(-0.539692\pi\) | ||||
−0.124373 | + | 0.992236i | \(0.539692\pi\) | |||||||
\(54\) | 5.60360 | 0.762553 | ||||||||
\(55\) | −7.61453 | −1.02674 | ||||||||
\(56\) | −4.20545 | −0.561977 | ||||||||
\(57\) | 3.34039 | 0.442446 | ||||||||
\(58\) | 1.86198 | 0.244490 | ||||||||
\(59\) | 7.25435 | 0.944437 | 0.472218 | − | 0.881482i | \(-0.343453\pi\) | ||||
0.472218 | + | 0.881482i | \(0.343453\pi\) | |||||||
\(60\) | −3.47055 | −0.448046 | ||||||||
\(61\) | 12.6714 | 1.62241 | 0.811205 | − | 0.584761i | \(-0.198812\pi\) | ||||
0.811205 | + | 0.584761i | \(0.198812\pi\) | |||||||
\(62\) | 9.92467 | 1.26043 | ||||||||
\(63\) | 5.50207 | 0.693196 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.0149 | 1.73834 | ||||||||
\(66\) | 3.71161 | 0.456868 | ||||||||
\(67\) | −15.7750 | −1.92722 | −0.963609 | − | 0.267316i | \(-0.913863\pi\) | ||||
−0.963609 | + | 0.267316i | \(0.913863\pi\) | |||||||
\(68\) | −3.66501 | −0.444448 | ||||||||
\(69\) | −1.30065 | −0.156579 | ||||||||
\(70\) | −11.2215 | −1.34123 | ||||||||
\(71\) | 0.378262 | 0.0448914 | 0.0224457 | − | 0.999748i | \(-0.492855\pi\) | ||||
0.0224457 | + | 0.999748i | \(0.492855\pi\) | |||||||
\(72\) | −1.30832 | −0.154187 | ||||||||
\(73\) | 11.9647 | 1.40037 | 0.700184 | − | 0.713963i | \(-0.253101\pi\) | ||||
0.700184 | + | 0.713963i | \(0.253101\pi\) | |||||||
\(74\) | 0.702891 | 0.0817094 | ||||||||
\(75\) | −2.75735 | −0.318391 | ||||||||
\(76\) | −2.56826 | −0.294599 | ||||||||
\(77\) | 12.0010 | 1.36764 | ||||||||
\(78\) | −6.83140 | −0.773504 | ||||||||
\(79\) | 12.9176 | 1.45335 | 0.726673 | − | 0.686984i | \(-0.241066\pi\) | ||||
0.726673 | + | 0.686984i | \(0.241066\pi\) | |||||||
\(80\) | 2.66833 | 0.298328 | ||||||||
\(81\) | −3.36334 | −0.373704 | ||||||||
\(82\) | −1.57152 | −0.173545 | ||||||||
\(83\) | 8.73622 | 0.958925 | 0.479463 | − | 0.877562i | \(-0.340832\pi\) | ||||
0.479463 | + | 0.877562i | \(0.340832\pi\) | |||||||
\(84\) | 5.46980 | 0.596804 | ||||||||
\(85\) | −9.77946 | −1.06073 | ||||||||
\(86\) | −3.65307 | −0.393921 | ||||||||
\(87\) | −2.42178 | −0.259642 | ||||||||
\(88\) | −2.85367 | −0.304202 | ||||||||
\(89\) | −4.30510 | −0.456339 | −0.228170 | − | 0.973621i | \(-0.573274\pi\) | ||||
−0.228170 | + | 0.973621i | \(0.573274\pi\) | |||||||
\(90\) | −3.49103 | −0.367987 | ||||||||
\(91\) | −22.0883 | −2.31549 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −12.9085 | −1.33855 | ||||||||
\(94\) | −9.81910 | −1.01276 | ||||||||
\(95\) | −6.85296 | −0.703099 | ||||||||
\(96\) | −1.30065 | −0.132747 | ||||||||
\(97\) | 17.8664 | 1.81406 | 0.907031 | − | 0.421063i | \(-0.138343\pi\) | ||||
0.907031 | + | 0.421063i | \(0.138343\pi\) | |||||||
\(98\) | 10.6858 | 1.07943 | ||||||||
\(99\) | 3.73351 | 0.375232 | ||||||||
\(100\) | 2.11998 | 0.211998 | ||||||||
\(101\) | 10.4315 | 1.03798 | 0.518988 | − | 0.854782i | \(-0.326309\pi\) | ||||
0.518988 | + | 0.854782i | \(0.326309\pi\) | |||||||
\(102\) | 4.76688 | 0.471992 | ||||||||
\(103\) | 10.7732 | 1.06151 | 0.530757 | − | 0.847524i | \(-0.321908\pi\) | ||||
0.530757 | + | 0.847524i | \(0.321908\pi\) | |||||||
\(104\) | 5.25232 | 0.515032 | ||||||||
\(105\) | 14.5952 | 1.42435 | ||||||||
\(106\) | −1.81090 | −0.175890 | ||||||||
\(107\) | −8.76351 | −0.847200 | −0.423600 | − | 0.905849i | \(-0.639234\pi\) | ||||
−0.423600 | + | 0.905849i | \(0.639234\pi\) | |||||||
\(108\) | 5.60360 | 0.539207 | ||||||||
\(109\) | 11.2050 | 1.07325 | 0.536624 | − | 0.843821i | \(-0.319699\pi\) | ||||
0.536624 | + | 0.843821i | \(0.319699\pi\) | |||||||
\(110\) | −7.61453 | −0.726017 | ||||||||
\(111\) | −0.914212 | −0.0867732 | ||||||||
\(112\) | −4.20545 | −0.397377 | ||||||||
\(113\) | −8.86378 | −0.833834 | −0.416917 | − | 0.908945i | \(-0.636889\pi\) | ||||
−0.416917 | + | 0.908945i | \(0.636889\pi\) | |||||||
\(114\) | 3.34039 | 0.312856 | ||||||||
\(115\) | 2.66833 | 0.248823 | ||||||||
\(116\) | 1.86198 | 0.172881 | ||||||||
\(117\) | −6.87171 | −0.635290 | ||||||||
\(118\) | 7.25435 | 0.667817 | ||||||||
\(119\) | 15.4130 | 1.41291 | ||||||||
\(120\) | −3.47055 | −0.316817 | ||||||||
\(121\) | −2.85658 | −0.259689 | ||||||||
\(122\) | 12.6714 | 1.14722 | ||||||||
\(123\) | 2.04399 | 0.184301 | ||||||||
\(124\) | 9.92467 | 0.891262 | ||||||||
\(125\) | −7.68483 | −0.687352 | ||||||||
\(126\) | 5.50207 | 0.490163 | ||||||||
\(127\) | −6.68674 | −0.593352 | −0.296676 | − | 0.954978i | \(-0.595878\pi\) | ||||
−0.296676 | + | 0.954978i | \(0.595878\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.75135 | 0.418333 | ||||||||
\(130\) | 14.0149 | 1.22919 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 3.71161 | 0.323054 | ||||||||
\(133\) | 10.8007 | 0.936537 | ||||||||
\(134\) | −15.7750 | −1.36275 | ||||||||
\(135\) | 14.9523 | 1.28688 | ||||||||
\(136\) | −3.66501 | −0.314272 | ||||||||
\(137\) | 18.7955 | 1.60581 | 0.802904 | − | 0.596109i | \(-0.203287\pi\) | ||||
0.802904 | + | 0.596109i | \(0.203287\pi\) | |||||||
\(138\) | −1.30065 | −0.110718 | ||||||||
\(139\) | 13.2145 | 1.12084 | 0.560418 | − | 0.828210i | \(-0.310640\pi\) | ||||
0.560418 | + | 0.828210i | \(0.310640\pi\) | |||||||
\(140\) | −11.2215 | −0.948392 | ||||||||
\(141\) | 12.7712 | 1.07553 | ||||||||
\(142\) | 0.378262 | 0.0317430 | ||||||||
\(143\) | −14.9884 | −1.25339 | ||||||||
\(144\) | −1.30832 | −0.109027 | ||||||||
\(145\) | 4.96838 | 0.412602 | ||||||||
\(146\) | 11.9647 | 0.990209 | ||||||||
\(147\) | −13.8984 | −1.14632 | ||||||||
\(148\) | 0.702891 | 0.0577773 | ||||||||
\(149\) | −19.3153 | −1.58237 | −0.791186 | − | 0.611576i | \(-0.790536\pi\) | ||||
−0.791186 | + | 0.611576i | \(0.790536\pi\) | |||||||
\(150\) | −2.75735 | −0.225137 | ||||||||
\(151\) | 12.8549 | 1.04612 | 0.523059 | − | 0.852296i | \(-0.324791\pi\) | ||||
0.523059 | + | 0.852296i | \(0.324791\pi\) | |||||||
\(152\) | −2.56826 | −0.208313 | ||||||||
\(153\) | 4.79501 | 0.387654 | ||||||||
\(154\) | 12.0010 | 0.967064 | ||||||||
\(155\) | 26.4823 | 2.12711 | ||||||||
\(156\) | −6.83140 | −0.546950 | ||||||||
\(157\) | 15.1710 | 1.21078 | 0.605390 | − | 0.795929i | \(-0.293017\pi\) | ||||
0.605390 | + | 0.795929i | \(0.293017\pi\) | |||||||
\(158\) | 12.9176 | 1.02767 | ||||||||
\(159\) | 2.35534 | 0.186790 | ||||||||
\(160\) | 2.66833 | 0.210950 | ||||||||
\(161\) | −4.20545 | −0.331436 | ||||||||
\(162\) | −3.36334 | −0.264249 | ||||||||
\(163\) | 23.0022 | 1.80167 | 0.900837 | − | 0.434158i | \(-0.142954\pi\) | ||||
0.900837 | + | 0.434158i | \(0.142954\pi\) | |||||||
\(164\) | −1.57152 | −0.122715 | ||||||||
\(165\) | 9.90381 | 0.771010 | ||||||||
\(166\) | 8.73622 | 0.678063 | ||||||||
\(167\) | −10.1821 | −0.787915 | −0.393957 | − | 0.919129i | \(-0.628894\pi\) | ||||
−0.393957 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(168\) | 5.46980 | 0.422004 | ||||||||
\(169\) | 14.5868 | 1.12206 | ||||||||
\(170\) | −9.77946 | −0.750051 | ||||||||
\(171\) | 3.36010 | 0.256953 | ||||||||
\(172\) | −3.65307 | −0.278544 | ||||||||
\(173\) | 15.3418 | 1.16641 | 0.583207 | − | 0.812324i | \(-0.301798\pi\) | ||||
0.583207 | + | 0.812324i | \(0.301798\pi\) | |||||||
\(174\) | −2.42178 | −0.183595 | ||||||||
\(175\) | −8.91548 | −0.673947 | ||||||||
\(176\) | −2.85367 | −0.215103 | ||||||||
\(177\) | −9.43535 | −0.709204 | ||||||||
\(178\) | −4.30510 | −0.322681 | ||||||||
\(179\) | −3.34395 | −0.249939 | −0.124969 | − | 0.992161i | \(-0.539883\pi\) | ||||
−0.124969 | + | 0.992161i | \(0.539883\pi\) | |||||||
\(180\) | −3.49103 | −0.260206 | ||||||||
\(181\) | −13.3129 | −0.989540 | −0.494770 | − | 0.869024i | \(-0.664748\pi\) | ||||
−0.494770 | + | 0.869024i | \(0.664748\pi\) | |||||||
\(182\) | −22.0883 | −1.63730 | ||||||||
\(183\) | −16.4810 | −1.21831 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 1.87554 | 0.137893 | ||||||||
\(186\) | −12.9085 | −0.946496 | ||||||||
\(187\) | 10.4587 | 0.764818 | ||||||||
\(188\) | −9.81910 | −0.716131 | ||||||||
\(189\) | −23.5656 | −1.71415 | ||||||||
\(190\) | −6.85296 | −0.497166 | ||||||||
\(191\) | −16.8178 | −1.21689 | −0.608446 | − | 0.793595i | \(-0.708207\pi\) | ||||
−0.608446 | + | 0.793595i | \(0.708207\pi\) | |||||||
\(192\) | −1.30065 | −0.0938660 | ||||||||
\(193\) | −14.2903 | −1.02864 | −0.514318 | − | 0.857599i | \(-0.671955\pi\) | ||||
−0.514318 | + | 0.857599i | \(0.671955\pi\) | |||||||
\(194\) | 17.8664 | 1.28274 | ||||||||
\(195\) | −18.2284 | −1.30537 | ||||||||
\(196\) | 10.6858 | 0.763270 | ||||||||
\(197\) | 14.1738 | 1.00984 | 0.504922 | − | 0.863165i | \(-0.331521\pi\) | ||||
0.504922 | + | 0.863165i | \(0.331521\pi\) | |||||||
\(198\) | 3.73351 | 0.265329 | ||||||||
\(199\) | 10.1475 | 0.719334 | 0.359667 | − | 0.933081i | \(-0.382890\pi\) | ||||
0.359667 | + | 0.933081i | \(0.382890\pi\) | |||||||
\(200\) | 2.11998 | 0.149906 | ||||||||
\(201\) | 20.5176 | 1.44720 | ||||||||
\(202\) | 10.4315 | 0.733959 | ||||||||
\(203\) | −7.83047 | −0.549591 | ||||||||
\(204\) | 4.76688 | 0.333749 | ||||||||
\(205\) | −4.19334 | −0.292875 | ||||||||
\(206\) | 10.7732 | 0.750604 | ||||||||
\(207\) | −1.30832 | −0.0909345 | ||||||||
\(208\) | 5.25232 | 0.364183 | ||||||||
\(209\) | 7.32895 | 0.506954 | ||||||||
\(210\) | 14.5952 | 1.00717 | ||||||||
\(211\) | 20.9748 | 1.44397 | 0.721984 | − | 0.691910i | \(-0.243230\pi\) | ||||
0.721984 | + | 0.691910i | \(0.243230\pi\) | |||||||
\(212\) | −1.81090 | −0.124373 | ||||||||
\(213\) | −0.491985 | −0.0337103 | ||||||||
\(214\) | −8.76351 | −0.599061 | ||||||||
\(215\) | −9.74759 | −0.664780 | ||||||||
\(216\) | 5.60360 | 0.381277 | ||||||||
\(217\) | −41.7377 | −2.83334 | ||||||||
\(218\) | 11.2050 | 0.758901 | ||||||||
\(219\) | −15.5619 | −1.05158 | ||||||||
\(220\) | −7.61453 | −0.513371 | ||||||||
\(221\) | −19.2498 | −1.29488 | ||||||||
\(222\) | −0.914212 | −0.0613579 | ||||||||
\(223\) | 12.8028 | 0.857337 | 0.428669 | − | 0.903462i | \(-0.358983\pi\) | ||||
0.428669 | + | 0.903462i | \(0.358983\pi\) | |||||||
\(224\) | −4.20545 | −0.280988 | ||||||||
\(225\) | −2.77362 | −0.184908 | ||||||||
\(226\) | −8.86378 | −0.589610 | ||||||||
\(227\) | −15.5102 | −1.02945 | −0.514724 | − | 0.857356i | \(-0.672106\pi\) | ||||
−0.514724 | + | 0.857356i | \(0.672106\pi\) | |||||||
\(228\) | 3.34039 | 0.221223 | ||||||||
\(229\) | 12.3368 | 0.815237 | 0.407619 | − | 0.913152i | \(-0.366359\pi\) | ||||
0.407619 | + | 0.913152i | \(0.366359\pi\) | |||||||
\(230\) | 2.66833 | 0.175944 | ||||||||
\(231\) | −15.6090 | −1.02700 | ||||||||
\(232\) | 1.86198 | 0.122245 | ||||||||
\(233\) | −6.15840 | −0.403450 | −0.201725 | − | 0.979442i | \(-0.564655\pi\) | ||||
−0.201725 | + | 0.979442i | \(0.564655\pi\) | |||||||
\(234\) | −6.87171 | −0.449218 | ||||||||
\(235\) | −26.2006 | −1.70914 | ||||||||
\(236\) | 7.25435 | 0.472218 | ||||||||
\(237\) | −16.8012 | −1.09136 | ||||||||
\(238\) | 15.4130 | 0.999077 | ||||||||
\(239\) | −11.3501 | −0.734174 | −0.367087 | − | 0.930187i | \(-0.619645\pi\) | ||||
−0.367087 | + | 0.930187i | \(0.619645\pi\) | |||||||
\(240\) | −3.47055 | −0.224023 | ||||||||
\(241\) | −3.47734 | −0.223995 | −0.111998 | − | 0.993708i | \(-0.535725\pi\) | ||||
−0.111998 | + | 0.993708i | \(0.535725\pi\) | |||||||
\(242\) | −2.85658 | −0.183628 | ||||||||
\(243\) | −12.4363 | −0.797788 | ||||||||
\(244\) | 12.6714 | 0.811205 | ||||||||
\(245\) | 28.5132 | 1.82164 | ||||||||
\(246\) | 2.04399 | 0.130320 | ||||||||
\(247\) | −13.4893 | −0.858303 | ||||||||
\(248\) | 9.92467 | 0.630217 | ||||||||
\(249\) | −11.3627 | −0.720084 | ||||||||
\(250\) | −7.68483 | −0.486031 | ||||||||
\(251\) | −3.32774 | −0.210045 | −0.105022 | − | 0.994470i | \(-0.533491\pi\) | ||||
−0.105022 | + | 0.994470i | \(0.533491\pi\) | |||||||
\(252\) | 5.50207 | 0.346598 | ||||||||
\(253\) | −2.85367 | −0.179409 | ||||||||
\(254\) | −6.68674 | −0.419564 | ||||||||
\(255\) | 12.7196 | 0.796533 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.07096 | −0.253939 | −0.126970 | − | 0.991907i | \(-0.540525\pi\) | ||||
−0.126970 | + | 0.991907i | \(0.540525\pi\) | |||||||
\(258\) | 4.75135 | 0.295806 | ||||||||
\(259\) | −2.95597 | −0.183675 | ||||||||
\(260\) | 14.0149 | 0.869168 | ||||||||
\(261\) | −2.43607 | −0.150789 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 3.14816 | 0.194124 | 0.0970621 | − | 0.995278i | \(-0.469055\pi\) | ||||
0.0970621 | + | 0.995278i | \(0.469055\pi\) | |||||||
\(264\) | 3.71161 | 0.228434 | ||||||||
\(265\) | −4.83207 | −0.296832 | ||||||||
\(266\) | 10.8007 | 0.662232 | ||||||||
\(267\) | 5.59940 | 0.342678 | ||||||||
\(268\) | −15.7750 | −0.963609 | ||||||||
\(269\) | 28.7046 | 1.75015 | 0.875075 | − | 0.483987i | \(-0.160812\pi\) | ||||
0.875075 | + | 0.483987i | \(0.160812\pi\) | |||||||
\(270\) | 14.9523 | 0.909965 | ||||||||
\(271\) | −14.4065 | −0.875130 | −0.437565 | − | 0.899187i | \(-0.644159\pi\) | ||||
−0.437565 | + | 0.899187i | \(0.644159\pi\) | |||||||
\(272\) | −3.66501 | −0.222224 | ||||||||
\(273\) | 28.7291 | 1.73876 | ||||||||
\(274\) | 18.7955 | 1.13548 | ||||||||
\(275\) | −6.04973 | −0.364813 | ||||||||
\(276\) | −1.30065 | −0.0782897 | ||||||||
\(277\) | 17.3840 | 1.04450 | 0.522251 | − | 0.852792i | \(-0.325092\pi\) | ||||
0.522251 | + | 0.852792i | \(0.325092\pi\) | |||||||
\(278\) | 13.2145 | 0.792551 | ||||||||
\(279\) | −12.9846 | −0.777371 | ||||||||
\(280\) | −11.2215 | −0.670614 | ||||||||
\(281\) | 11.6114 | 0.692678 | 0.346339 | − | 0.938109i | \(-0.387425\pi\) | ||||
0.346339 | + | 0.938109i | \(0.387425\pi\) | |||||||
\(282\) | 12.7712 | 0.760512 | ||||||||
\(283\) | 12.2581 | 0.728669 | 0.364335 | − | 0.931268i | \(-0.381296\pi\) | ||||
0.364335 | + | 0.931268i | \(0.381296\pi\) | |||||||
\(284\) | 0.378262 | 0.0224457 | ||||||||
\(285\) | 8.91327 | 0.527977 | ||||||||
\(286\) | −14.9884 | −0.886281 | ||||||||
\(287\) | 6.60895 | 0.390114 | ||||||||
\(288\) | −1.30832 | −0.0770935 | ||||||||
\(289\) | −3.56768 | −0.209864 | ||||||||
\(290\) | 4.96838 | 0.291753 | ||||||||
\(291\) | −23.2379 | −1.36223 | ||||||||
\(292\) | 11.9647 | 0.700184 | ||||||||
\(293\) | 13.1720 | 0.769517 | 0.384759 | − | 0.923017i | \(-0.374285\pi\) | ||||
0.384759 | + | 0.923017i | \(0.374285\pi\) | |||||||
\(294\) | −13.8984 | −0.810573 | ||||||||
\(295\) | 19.3570 | 1.12701 | ||||||||
\(296\) | 0.702891 | 0.0408547 | ||||||||
\(297\) | −15.9908 | −0.927881 | ||||||||
\(298\) | −19.3153 | −1.11891 | ||||||||
\(299\) | 5.25232 | 0.303749 | ||||||||
\(300\) | −2.75735 | −0.159196 | ||||||||
\(301\) | 15.3628 | 0.885496 | ||||||||
\(302\) | 12.8549 | 0.739717 | ||||||||
\(303\) | −13.5677 | −0.779445 | ||||||||
\(304\) | −2.56826 | −0.147300 | ||||||||
\(305\) | 33.8116 | 1.93604 | ||||||||
\(306\) | 4.79501 | 0.274112 | ||||||||
\(307\) | −12.3317 | −0.703805 | −0.351902 | − | 0.936037i | \(-0.614465\pi\) | ||||
−0.351902 | + | 0.936037i | \(0.614465\pi\) | |||||||
\(308\) | 12.0010 | 0.683818 | ||||||||
\(309\) | −14.0121 | −0.797121 | ||||||||
\(310\) | 26.4823 | 1.50409 | ||||||||
\(311\) | 1.57092 | 0.0890787 | 0.0445393 | − | 0.999008i | \(-0.485818\pi\) | ||||
0.0445393 | + | 0.999008i | \(0.485818\pi\) | |||||||
\(312\) | −6.83140 | −0.386752 | ||||||||
\(313\) | 2.11509 | 0.119552 | 0.0597759 | − | 0.998212i | \(-0.480961\pi\) | ||||
0.0597759 | + | 0.998212i | \(0.480961\pi\) | |||||||
\(314\) | 15.1710 | 0.856151 | ||||||||
\(315\) | 14.6813 | 0.827200 | ||||||||
\(316\) | 12.9176 | 0.726673 | ||||||||
\(317\) | −17.5972 | −0.988357 | −0.494178 | − | 0.869361i | \(-0.664531\pi\) | ||||
−0.494178 | + | 0.869361i | \(0.664531\pi\) | |||||||
\(318\) | 2.35534 | 0.132081 | ||||||||
\(319\) | −5.31348 | −0.297498 | ||||||||
\(320\) | 2.66833 | 0.149164 | ||||||||
\(321\) | 11.3982 | 0.636187 | ||||||||
\(322\) | −4.20545 | −0.234360 | ||||||||
\(323\) | 9.41270 | 0.523736 | ||||||||
\(324\) | −3.36334 | −0.186852 | ||||||||
\(325\) | 11.1348 | 0.617649 | ||||||||
\(326\) | 23.0022 | 1.27398 | ||||||||
\(327\) | −14.5738 | −0.805932 | ||||||||
\(328\) | −1.57152 | −0.0867727 | ||||||||
\(329\) | 41.2937 | 2.27660 | ||||||||
\(330\) | 9.90381 | 0.545187 | ||||||||
\(331\) | −18.0421 | −0.991681 | −0.495840 | − | 0.868414i | \(-0.665140\pi\) | ||||
−0.495840 | + | 0.868414i | \(0.665140\pi\) | |||||||
\(332\) | 8.73622 | 0.479463 | ||||||||
\(333\) | −0.919606 | −0.0503941 | ||||||||
\(334\) | −10.1821 | −0.557140 | ||||||||
\(335\) | −42.0928 | −2.29978 | ||||||||
\(336\) | 5.46980 | 0.298402 | ||||||||
\(337\) | −21.5947 | −1.17634 | −0.588168 | − | 0.808739i | \(-0.700151\pi\) | ||||
−0.588168 | + | 0.808739i | \(0.700151\pi\) | |||||||
\(338\) | 14.5868 | 0.793419 | ||||||||
\(339\) | 11.5286 | 0.626150 | ||||||||
\(340\) | −9.77946 | −0.530366 | ||||||||
\(341\) | −28.3217 | −1.53371 | ||||||||
\(342\) | 3.36010 | 0.181694 | ||||||||
\(343\) | −15.5004 | −0.836942 | ||||||||
\(344\) | −3.65307 | −0.196960 | ||||||||
\(345\) | −3.47055 | −0.186848 | ||||||||
\(346\) | 15.3418 | 0.824779 | ||||||||
\(347\) | 13.8264 | 0.742240 | 0.371120 | − | 0.928585i | \(-0.378974\pi\) | ||||
0.371120 | + | 0.928585i | \(0.378974\pi\) | |||||||
\(348\) | −2.42178 | −0.129821 | ||||||||
\(349\) | 5.65619 | 0.302769 | 0.151384 | − | 0.988475i | \(-0.451627\pi\) | ||||
0.151384 | + | 0.988475i | \(0.451627\pi\) | |||||||
\(350\) | −8.91548 | −0.476553 | ||||||||
\(351\) | 29.4319 | 1.57096 | ||||||||
\(352\) | −2.85367 | −0.152101 | ||||||||
\(353\) | 20.0562 | 1.06749 | 0.533743 | − | 0.845647i | \(-0.320785\pi\) | ||||
0.533743 | + | 0.845647i | \(0.320785\pi\) | |||||||
\(354\) | −9.43535 | −0.501483 | ||||||||
\(355\) | 1.00933 | 0.0535696 | ||||||||
\(356\) | −4.30510 | −0.228170 | ||||||||
\(357\) | −20.0469 | −1.06099 | ||||||||
\(358\) | −3.34395 | −0.176733 | ||||||||
\(359\) | −11.6364 | −0.614145 | −0.307073 | − | 0.951686i | \(-0.599349\pi\) | ||||
−0.307073 | + | 0.951686i | \(0.599349\pi\) | |||||||
\(360\) | −3.49103 | −0.183993 | ||||||||
\(361\) | −12.4041 | −0.652845 | ||||||||
\(362\) | −13.3129 | −0.699710 | ||||||||
\(363\) | 3.71539 | 0.195008 | ||||||||
\(364\) | −22.0883 | −1.15774 | ||||||||
\(365\) | 31.9259 | 1.67108 | ||||||||
\(366\) | −16.4810 | −0.861478 | ||||||||
\(367\) | −27.0101 | −1.40991 | −0.704957 | − | 0.709250i | \(-0.749034\pi\) | ||||
−0.704957 | + | 0.709250i | \(0.749034\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 2.05605 | 0.107034 | ||||||||
\(370\) | 1.87554 | 0.0975049 | ||||||||
\(371\) | 7.61563 | 0.395384 | ||||||||
\(372\) | −12.9085 | −0.669274 | ||||||||
\(373\) | −1.84894 | −0.0957345 | −0.0478672 | − | 0.998854i | \(-0.515242\pi\) | ||||
−0.0478672 | + | 0.998854i | \(0.515242\pi\) | |||||||
\(374\) | 10.4587 | 0.540808 | ||||||||
\(375\) | 9.99524 | 0.516152 | ||||||||
\(376\) | −9.81910 | −0.506381 | ||||||||
\(377\) | 9.77972 | 0.503681 | ||||||||
\(378\) | −23.5656 | −1.21209 | ||||||||
\(379\) | 10.7898 | 0.554234 | 0.277117 | − | 0.960836i | \(-0.410621\pi\) | ||||
0.277117 | + | 0.960836i | \(0.410621\pi\) | |||||||
\(380\) | −6.85296 | −0.351549 | ||||||||
\(381\) | 8.69708 | 0.445565 | ||||||||
\(382\) | −16.8178 | −0.860472 | ||||||||
\(383\) | 10.4496 | 0.533952 | 0.266976 | − | 0.963703i | \(-0.413976\pi\) | ||||
0.266976 | + | 0.963703i | \(0.413976\pi\) | |||||||
\(384\) | −1.30065 | −0.0663733 | ||||||||
\(385\) | 32.0225 | 1.63202 | ||||||||
\(386\) | −14.2903 | −0.727356 | ||||||||
\(387\) | 4.77938 | 0.242950 | ||||||||
\(388\) | 17.8664 | 0.907031 | ||||||||
\(389\) | −2.54826 | −0.129202 | −0.0646010 | − | 0.997911i | \(-0.520577\pi\) | ||||
−0.0646010 | + | 0.997911i | \(0.520577\pi\) | |||||||
\(390\) | −18.2284 | −0.923033 | ||||||||
\(391\) | −3.66501 | −0.185348 | ||||||||
\(392\) | 10.6858 | 0.539714 | ||||||||
\(393\) | −1.30065 | −0.0656089 | ||||||||
\(394\) | 14.1738 | 0.714068 | ||||||||
\(395\) | 34.4685 | 1.73430 | ||||||||
\(396\) | 3.73351 | 0.187616 | ||||||||
\(397\) | 11.9449 | 0.599499 | 0.299750 | − | 0.954018i | \(-0.403097\pi\) | ||||
0.299750 | + | 0.954018i | \(0.403097\pi\) | |||||||
\(398\) | 10.1475 | 0.508646 | ||||||||
\(399\) | −14.0478 | −0.703272 | ||||||||
\(400\) | 2.11998 | 0.105999 | ||||||||
\(401\) | 26.9570 | 1.34617 | 0.673083 | − | 0.739567i | \(-0.264970\pi\) | ||||
0.673083 | + | 0.739567i | \(0.264970\pi\) | |||||||
\(402\) | 20.5176 | 1.02333 | ||||||||
\(403\) | 52.1275 | 2.59666 | ||||||||
\(404\) | 10.4315 | 0.518988 | ||||||||
\(405\) | −8.97449 | −0.445946 | ||||||||
\(406\) | −7.83047 | −0.388620 | ||||||||
\(407\) | −2.00582 | −0.0994247 | ||||||||
\(408\) | 4.76688 | 0.235996 | ||||||||
\(409\) | 29.9678 | 1.48181 | 0.740907 | − | 0.671607i | \(-0.234396\pi\) | ||||
0.740907 | + | 0.671607i | \(0.234396\pi\) | |||||||
\(410\) | −4.19334 | −0.207094 | ||||||||
\(411\) | −24.4463 | −1.20585 | ||||||||
\(412\) | 10.7732 | 0.530757 | ||||||||
\(413\) | −30.5078 | −1.50119 | ||||||||
\(414\) | −1.30832 | −0.0643004 | ||||||||
\(415\) | 23.3111 | 1.14430 | ||||||||
\(416\) | 5.25232 | 0.257516 | ||||||||
\(417\) | −17.1873 | −0.841668 | ||||||||
\(418\) | 7.32895 | 0.358471 | ||||||||
\(419\) | −18.6662 | −0.911902 | −0.455951 | − | 0.890005i | \(-0.650701\pi\) | ||||
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(420\) | 14.5952 | 0.712174 | ||||||||
\(421\) | −3.04689 | −0.148496 | −0.0742481 | − | 0.997240i | \(-0.523656\pi\) | ||||
−0.0742481 | + | 0.997240i | \(0.523656\pi\) | |||||||
\(422\) | 20.9748 | 1.02104 | ||||||||
\(423\) | 12.8465 | 0.624619 | ||||||||
\(424\) | −1.81090 | −0.0879449 | ||||||||
\(425\) | −7.76977 | −0.376889 | ||||||||
\(426\) | −0.491985 | −0.0238367 | ||||||||
\(427\) | −53.2890 | −2.57884 | ||||||||
\(428\) | −8.76351 | −0.423600 | ||||||||
\(429\) | 19.4946 | 0.941206 | ||||||||
\(430\) | −9.74759 | −0.470071 | ||||||||
\(431\) | 2.00453 | 0.0965547 | 0.0482774 | − | 0.998834i | \(-0.484627\pi\) | ||||
0.0482774 | + | 0.998834i | \(0.484627\pi\) | |||||||
\(432\) | 5.60360 | 0.269603 | ||||||||
\(433\) | 9.17585 | 0.440963 | 0.220482 | − | 0.975391i | \(-0.429237\pi\) | ||||
0.220482 | + | 0.975391i | \(0.429237\pi\) | |||||||
\(434\) | −41.7377 | −2.00347 | ||||||||
\(435\) | −6.46211 | −0.309834 | ||||||||
\(436\) | 11.2050 | 0.536624 | ||||||||
\(437\) | −2.56826 | −0.122856 | ||||||||
\(438\) | −15.5619 | −0.743576 | ||||||||
\(439\) | −21.4540 | −1.02394 | −0.511972 | − | 0.859002i | \(-0.671085\pi\) | ||||
−0.511972 | + | 0.859002i | \(0.671085\pi\) | |||||||
\(440\) | −7.61453 | −0.363008 | ||||||||
\(441\) | −13.9804 | −0.665735 | ||||||||
\(442\) | −19.2498 | −0.915620 | ||||||||
\(443\) | 38.1606 | 1.81306 | 0.906531 | − | 0.422139i | \(-0.138720\pi\) | ||||
0.906531 | + | 0.422139i | \(0.138720\pi\) | |||||||
\(444\) | −0.914212 | −0.0433866 | ||||||||
\(445\) | −11.4874 | −0.544556 | ||||||||
\(446\) | 12.8028 | 0.606229 | ||||||||
\(447\) | 25.1224 | 1.18825 | ||||||||
\(448\) | −4.20545 | −0.198689 | ||||||||
\(449\) | −11.8880 | −0.561029 | −0.280515 | − | 0.959850i | \(-0.590505\pi\) | ||||
−0.280515 | + | 0.959850i | \(0.590505\pi\) | |||||||
\(450\) | −2.77362 | −0.130750 | ||||||||
\(451\) | 4.48460 | 0.211171 | ||||||||
\(452\) | −8.86378 | −0.416917 | ||||||||
\(453\) | −16.7197 | −0.785560 | ||||||||
\(454\) | −15.5102 | −0.727930 | ||||||||
\(455\) | −58.9390 | −2.76310 | ||||||||
\(456\) | 3.34039 | 0.156428 | ||||||||
\(457\) | −20.4974 | −0.958828 | −0.479414 | − | 0.877589i | \(-0.659151\pi\) | ||||
−0.479414 | + | 0.877589i | \(0.659151\pi\) | |||||||
\(458\) | 12.3368 | 0.576460 | ||||||||
\(459\) | −20.5373 | −0.958597 | ||||||||
\(460\) | 2.66833 | 0.124412 | ||||||||
\(461\) | 18.5868 | 0.865673 | 0.432837 | − | 0.901472i | \(-0.357513\pi\) | ||||
0.432837 | + | 0.901472i | \(0.357513\pi\) | |||||||
\(462\) | −15.6090 | −0.726196 | ||||||||
\(463\) | −32.0652 | −1.49020 | −0.745099 | − | 0.666954i | \(-0.767598\pi\) | ||||
−0.745099 | + | 0.666954i | \(0.767598\pi\) | |||||||
\(464\) | 1.86198 | 0.0864403 | ||||||||
\(465\) | −34.4441 | −1.59731 | ||||||||
\(466\) | −6.15840 | −0.285282 | ||||||||
\(467\) | −22.3931 | −1.03623 | −0.518115 | − | 0.855311i | \(-0.673366\pi\) | ||||
−0.518115 | + | 0.855311i | \(0.673366\pi\) | |||||||
\(468\) | −6.87171 | −0.317645 | ||||||||
\(469\) | 66.3408 | 3.06333 | ||||||||
\(470\) | −26.2006 | −1.20854 | ||||||||
\(471\) | −19.7321 | −0.909209 | ||||||||
\(472\) | 7.25435 | 0.333909 | ||||||||
\(473\) | 10.4246 | 0.479326 | ||||||||
\(474\) | −16.8012 | −0.771707 | ||||||||
\(475\) | −5.44467 | −0.249818 | ||||||||
\(476\) | 15.4130 | 0.706454 | ||||||||
\(477\) | 2.36923 | 0.108480 | ||||||||
\(478\) | −11.3501 | −0.519140 | ||||||||
\(479\) | −35.9014 | −1.64037 | −0.820187 | − | 0.572095i | \(-0.806131\pi\) | ||||
−0.820187 | + | 0.572095i | \(0.806131\pi\) | |||||||
\(480\) | −3.47055 | −0.158408 | ||||||||
\(481\) | 3.69180 | 0.168332 | ||||||||
\(482\) | −3.47734 | −0.158388 | ||||||||
\(483\) | 5.46980 | 0.248884 | ||||||||
\(484\) | −2.85658 | −0.129844 | ||||||||
\(485\) | 47.6736 | 2.16475 | ||||||||
\(486\) | −12.4363 | −0.564121 | ||||||||
\(487\) | −16.9582 | −0.768449 | −0.384225 | − | 0.923240i | \(-0.625531\pi\) | ||||
−0.384225 | + | 0.923240i | \(0.625531\pi\) | |||||||
\(488\) | 12.6714 | 0.573609 | ||||||||
\(489\) | −29.9178 | −1.35293 | ||||||||
\(490\) | 28.5132 | 1.28810 | ||||||||
\(491\) | 35.5842 | 1.60589 | 0.802947 | − | 0.596051i | \(-0.203264\pi\) | ||||
0.802947 | + | 0.596051i | \(0.203264\pi\) | |||||||
\(492\) | 2.04399 | 0.0921503 | ||||||||
\(493\) | −6.82419 | −0.307346 | ||||||||
\(494\) | −13.4893 | −0.606912 | ||||||||
\(495\) | 9.96224 | 0.447769 | ||||||||
\(496\) | 9.92467 | 0.445631 | ||||||||
\(497\) | −1.59076 | −0.0713554 | ||||||||
\(498\) | −11.3627 | −0.509176 | ||||||||
\(499\) | 14.9594 | 0.669676 | 0.334838 | − | 0.942276i | \(-0.391318\pi\) | ||||
0.334838 | + | 0.942276i | \(0.391318\pi\) | |||||||
\(500\) | −7.68483 | −0.343676 | ||||||||
\(501\) | 13.2433 | 0.591667 | ||||||||
\(502\) | −3.32774 | −0.148524 | ||||||||
\(503\) | −4.93850 | −0.220197 | −0.110098 | − | 0.993921i | \(-0.535117\pi\) | ||||
−0.110098 | + | 0.993921i | \(0.535117\pi\) | |||||||
\(504\) | 5.50207 | 0.245082 | ||||||||
\(505\) | 27.8347 | 1.23863 | ||||||||
\(506\) | −2.85367 | −0.126861 | ||||||||
\(507\) | −18.9723 | −0.842589 | ||||||||
\(508\) | −6.68674 | −0.296676 | ||||||||
\(509\) | 38.1329 | 1.69021 | 0.845106 | − | 0.534599i | \(-0.179537\pi\) | ||||
0.845106 | + | 0.534599i | \(0.179537\pi\) | |||||||
\(510\) | 12.7196 | 0.563234 | ||||||||
\(511\) | −50.3171 | −2.22590 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −14.3915 | −0.635400 | ||||||||
\(514\) | −4.07096 | −0.179562 | ||||||||
\(515\) | 28.7464 | 1.26672 | ||||||||
\(516\) | 4.75135 | 0.209166 | ||||||||
\(517\) | 28.0204 | 1.23234 | ||||||||
\(518\) | −2.95597 | −0.129878 | ||||||||
\(519\) | −19.9542 | −0.875893 | ||||||||
\(520\) | 14.0149 | 0.614595 | ||||||||
\(521\) | 16.9751 | 0.743693 | 0.371846 | − | 0.928294i | \(-0.378725\pi\) | ||||
0.371846 | + | 0.928294i | \(0.378725\pi\) | |||||||
\(522\) | −2.43607 | −0.106624 | ||||||||
\(523\) | 35.9553 | 1.57222 | 0.786109 | − | 0.618088i | \(-0.212093\pi\) | ||||
0.786109 | + | 0.618088i | \(0.212093\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 11.5959 | 0.506086 | ||||||||
\(526\) | 3.14816 | 0.137267 | ||||||||
\(527\) | −36.3740 | −1.58448 | ||||||||
\(528\) | 3.71161 | 0.161527 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.83207 | −0.209892 | ||||||||
\(531\) | −9.49102 | −0.411875 | ||||||||
\(532\) | 10.8007 | 0.468268 | ||||||||
\(533\) | −8.25412 | −0.357526 | ||||||||
\(534\) | 5.59940 | 0.242310 | ||||||||
\(535\) | −23.3839 | −1.01098 | ||||||||
\(536\) | −15.7750 | −0.681374 | ||||||||
\(537\) | 4.34930 | 0.187686 | ||||||||
\(538\) | 28.7046 | 1.23754 | ||||||||
\(539\) | −30.4937 | −1.31346 | ||||||||
\(540\) | 14.9523 | 0.643442 | ||||||||
\(541\) | −32.1060 | −1.38035 | −0.690173 | − | 0.723644i | \(-0.742466\pi\) | ||||
−0.690173 | + | 0.723644i | \(0.742466\pi\) | |||||||
\(542\) | −14.4065 | −0.618811 | ||||||||
\(543\) | 17.3154 | 0.743074 | ||||||||
\(544\) | −3.66501 | −0.157136 | ||||||||
\(545\) | 29.8987 | 1.28072 | ||||||||
\(546\) | 28.7291 | 1.22949 | ||||||||
\(547\) | 27.7705 | 1.18738 | 0.593690 | − | 0.804694i | \(-0.297670\pi\) | ||||
0.593690 | + | 0.804694i | \(0.297670\pi\) | |||||||
\(548\) | 18.7955 | 0.802904 | ||||||||
\(549\) | −16.5783 | −0.707544 | ||||||||
\(550\) | −6.04973 | −0.257962 | ||||||||
\(551\) | −4.78205 | −0.203722 | ||||||||
\(552\) | −1.30065 | −0.0553592 | ||||||||
\(553\) | −54.3243 | −2.31011 | ||||||||
\(554\) | 17.3840 | 0.738574 | ||||||||
\(555\) | −2.43942 | −0.103548 | ||||||||
\(556\) | 13.2145 | 0.560418 | ||||||||
\(557\) | −5.14927 | −0.218181 | −0.109091 | − | 0.994032i | \(-0.534794\pi\) | ||||
−0.109091 | + | 0.994032i | \(0.534794\pi\) | |||||||
\(558\) | −12.9846 | −0.549684 | ||||||||
\(559\) | −19.1871 | −0.811527 | ||||||||
\(560\) | −11.2215 | −0.474196 | ||||||||
\(561\) | −13.6031 | −0.574324 | ||||||||
\(562\) | 11.6114 | 0.489797 | ||||||||
\(563\) | −38.5209 | −1.62346 | −0.811731 | − | 0.584031i | \(-0.801475\pi\) | ||||
−0.811731 | + | 0.584031i | \(0.801475\pi\) | |||||||
\(564\) | 12.7712 | 0.537763 | ||||||||
\(565\) | −23.6515 | −0.995026 | ||||||||
\(566\) | 12.2581 | 0.515247 | ||||||||
\(567\) | 14.1443 | 0.594006 | ||||||||
\(568\) | 0.378262 | 0.0158715 | ||||||||
\(569\) | 10.8903 | 0.456546 | 0.228273 | − | 0.973597i | \(-0.426692\pi\) | ||||
0.228273 | + | 0.973597i | \(0.426692\pi\) | |||||||
\(570\) | 8.91327 | 0.373336 | ||||||||
\(571\) | −6.01142 | −0.251570 | −0.125785 | − | 0.992058i | \(-0.540145\pi\) | ||||
−0.125785 | + | 0.992058i | \(0.540145\pi\) | |||||||
\(572\) | −14.9884 | −0.626695 | ||||||||
\(573\) | 21.8740 | 0.913798 | ||||||||
\(574\) | 6.60895 | 0.275852 | ||||||||
\(575\) | 2.11998 | 0.0884095 | ||||||||
\(576\) | −1.30832 | −0.0545133 | ||||||||
\(577\) | −12.9805 | −0.540387 | −0.270194 | − | 0.962806i | \(-0.587088\pi\) | ||||
−0.270194 | + | 0.962806i | \(0.587088\pi\) | |||||||
\(578\) | −3.56768 | −0.148396 | ||||||||
\(579\) | 18.5866 | 0.772432 | ||||||||
\(580\) | 4.96838 | 0.206301 | ||||||||
\(581\) | −36.7397 | −1.52422 | ||||||||
\(582\) | −23.2379 | −0.963243 | ||||||||
\(583\) | 5.16770 | 0.214024 | ||||||||
\(584\) | 11.9647 | 0.495105 | ||||||||
\(585\) | −18.3360 | −0.758100 | ||||||||
\(586\) | 13.1720 | 0.544131 | ||||||||
\(587\) | 2.20337 | 0.0909427 | 0.0454714 | − | 0.998966i | \(-0.485521\pi\) | ||||
0.0454714 | + | 0.998966i | \(0.485521\pi\) | |||||||
\(588\) | −13.8984 | −0.573161 | ||||||||
\(589\) | −25.4891 | −1.05026 | ||||||||
\(590\) | 19.3570 | 0.796916 | ||||||||
\(591\) | −18.4352 | −0.758321 | ||||||||
\(592\) | 0.702891 | 0.0288886 | ||||||||
\(593\) | 31.9688 | 1.31280 | 0.656401 | − | 0.754412i | \(-0.272078\pi\) | ||||
0.656401 | + | 0.754412i | \(0.272078\pi\) | |||||||
\(594\) | −15.9908 | −0.656111 | ||||||||
\(595\) | 41.1270 | 1.68604 | ||||||||
\(596\) | −19.3153 | −0.791186 | ||||||||
\(597\) | −13.1983 | −0.540169 | ||||||||
\(598\) | 5.25232 | 0.214783 | ||||||||
\(599\) | 12.5338 | 0.512117 | 0.256058 | − | 0.966661i | \(-0.417576\pi\) | ||||
0.256058 | + | 0.966661i | \(0.417576\pi\) | |||||||
\(600\) | −2.75735 | −0.112568 | ||||||||
\(601\) | 15.9943 | 0.652421 | 0.326211 | − | 0.945297i | \(-0.394228\pi\) | ||||
0.326211 | + | 0.945297i | \(0.394228\pi\) | |||||||
\(602\) | 15.3628 | 0.626140 | ||||||||
\(603\) | 20.6387 | 0.840473 | ||||||||
\(604\) | 12.8549 | 0.523059 | ||||||||
\(605\) | −7.62229 | −0.309890 | ||||||||
\(606\) | −13.5677 | −0.551151 | ||||||||
\(607\) | −29.5180 | −1.19810 | −0.599049 | − | 0.800712i | \(-0.704454\pi\) | ||||
−0.599049 | + | 0.800712i | \(0.704454\pi\) | |||||||
\(608\) | −2.56826 | −0.104157 | ||||||||
\(609\) | 10.1847 | 0.412703 | ||||||||
\(610\) | 33.8116 | 1.36899 | ||||||||
\(611\) | −51.5730 | −2.08642 | ||||||||
\(612\) | 4.79501 | 0.193827 | ||||||||
\(613\) | −5.06021 | −0.204380 | −0.102190 | − | 0.994765i | \(-0.532585\pi\) | ||||
−0.102190 | + | 0.994765i | \(0.532585\pi\) | |||||||
\(614\) | −12.3317 | −0.497665 | ||||||||
\(615\) | 5.45404 | 0.219928 | ||||||||
\(616\) | 12.0010 | 0.483532 | ||||||||
\(617\) | −34.3285 | −1.38201 | −0.691006 | − | 0.722849i | \(-0.742832\pi\) | ||||
−0.691006 | + | 0.722849i | \(0.742832\pi\) | |||||||
\(618\) | −14.0121 | −0.563650 | ||||||||
\(619\) | 37.8126 | 1.51982 | 0.759909 | − | 0.650030i | \(-0.225244\pi\) | ||||
0.759909 | + | 0.650030i | \(0.225244\pi\) | |||||||
\(620\) | 26.4823 | 1.06355 | ||||||||
\(621\) | 5.60360 | 0.224865 | ||||||||
\(622\) | 1.57092 | 0.0629881 | ||||||||
\(623\) | 18.1048 | 0.725355 | ||||||||
\(624\) | −6.83140 | −0.273475 | ||||||||
\(625\) | −31.1056 | −1.24422 | ||||||||
\(626\) | 2.11509 | 0.0845360 | ||||||||
\(627\) | −9.53238 | −0.380686 | ||||||||
\(628\) | 15.1710 | 0.605390 | ||||||||
\(629\) | −2.57610 | −0.102716 | ||||||||
\(630\) | 14.6813 | 0.584919 | ||||||||
\(631\) | 29.9115 | 1.19076 | 0.595378 | − | 0.803446i | \(-0.297002\pi\) | ||||
0.595378 | + | 0.803446i | \(0.297002\pi\) | |||||||
\(632\) | 12.9176 | 0.513835 | ||||||||
\(633\) | −27.2809 | −1.08432 | ||||||||
\(634\) | −17.5972 | −0.698874 | ||||||||
\(635\) | −17.8424 | −0.708055 | ||||||||
\(636\) | 2.35534 | 0.0933951 | ||||||||
\(637\) | 56.1251 | 2.22376 | ||||||||
\(638\) | −5.31348 | −0.210363 | ||||||||
\(639\) | −0.494888 | −0.0195775 | ||||||||
\(640\) | 2.66833 | 0.105475 | ||||||||
\(641\) | 10.0568 | 0.397221 | 0.198610 | − | 0.980079i | \(-0.436357\pi\) | ||||
0.198610 | + | 0.980079i | \(0.436357\pi\) | |||||||
\(642\) | 11.3982 | 0.449852 | ||||||||
\(643\) | 27.2073 | 1.07295 | 0.536476 | − | 0.843915i | \(-0.319755\pi\) | ||||
0.536476 | + | 0.843915i | \(0.319755\pi\) | |||||||
\(644\) | −4.20545 | −0.165718 | ||||||||
\(645\) | 12.6782 | 0.499202 | ||||||||
\(646\) | 9.41270 | 0.370338 | ||||||||
\(647\) | 38.3899 | 1.50926 | 0.754632 | − | 0.656148i | \(-0.227815\pi\) | ||||
0.754632 | + | 0.656148i | \(0.227815\pi\) | |||||||
\(648\) | −3.36334 | −0.132124 | ||||||||
\(649\) | −20.7015 | −0.812606 | ||||||||
\(650\) | 11.1348 | 0.436744 | ||||||||
\(651\) | 54.2859 | 2.12763 | ||||||||
\(652\) | 23.0022 | 0.900837 | ||||||||
\(653\) | −17.8023 | −0.696658 | −0.348329 | − | 0.937372i | \(-0.613251\pi\) | ||||
−0.348329 | + | 0.937372i | \(0.613251\pi\) | |||||||
\(654\) | −14.5738 | −0.569880 | ||||||||
\(655\) | 2.66833 | 0.104260 | ||||||||
\(656\) | −1.57152 | −0.0613576 | ||||||||
\(657\) | −15.6537 | −0.610710 | ||||||||
\(658\) | 41.2937 | 1.60980 | ||||||||
\(659\) | −2.86094 | −0.111446 | −0.0557232 | − | 0.998446i | \(-0.517746\pi\) | ||||
−0.0557232 | + | 0.998446i | \(0.517746\pi\) | |||||||
\(660\) | 9.90381 | 0.385505 | ||||||||
\(661\) | 30.1564 | 1.17295 | 0.586473 | − | 0.809969i | \(-0.300516\pi\) | ||||
0.586473 | + | 0.809969i | \(0.300516\pi\) | |||||||
\(662\) | −18.0421 | −0.701224 | ||||||||
\(663\) | 25.0372 | 0.972363 | ||||||||
\(664\) | 8.73622 | 0.339031 | ||||||||
\(665\) | 28.8198 | 1.11758 | ||||||||
\(666\) | −0.919606 | −0.0356340 | ||||||||
\(667\) | 1.86198 | 0.0720962 | ||||||||
\(668\) | −10.1821 | −0.393957 | ||||||||
\(669\) | −16.6519 | −0.643799 | ||||||||
\(670\) | −42.0928 | −1.62619 | ||||||||
\(671\) | −36.1601 | −1.39594 | ||||||||
\(672\) | 5.46980 | 0.211002 | ||||||||
\(673\) | −42.1563 | −1.62500 | −0.812502 | − | 0.582958i | \(-0.801895\pi\) | ||||
−0.812502 | + | 0.582958i | \(0.801895\pi\) | |||||||
\(674\) | −21.5947 | −0.831796 | ||||||||
\(675\) | 11.8795 | 0.457244 | ||||||||
\(676\) | 14.5868 | 0.561032 | ||||||||
\(677\) | 14.4134 | 0.553953 | 0.276977 | − | 0.960877i | \(-0.410668\pi\) | ||||
0.276977 | + | 0.960877i | \(0.410668\pi\) | |||||||
\(678\) | 11.5286 | 0.442755 | ||||||||
\(679\) | −75.1364 | −2.88347 | ||||||||
\(680\) | −9.77946 | −0.375025 | ||||||||
\(681\) | 20.1733 | 0.773042 | ||||||||
\(682\) | −28.3217 | −1.08449 | ||||||||
\(683\) | −18.0549 | −0.690852 | −0.345426 | − | 0.938446i | \(-0.612266\pi\) | ||||
−0.345426 | + | 0.938446i | \(0.612266\pi\) | |||||||
\(684\) | 3.36010 | 0.128477 | ||||||||
\(685\) | 50.1526 | 1.91623 | ||||||||
\(686\) | −15.5004 | −0.591807 | ||||||||
\(687\) | −16.0458 | −0.612185 | ||||||||
\(688\) | −3.65307 | −0.139272 | ||||||||
\(689\) | −9.51140 | −0.362356 | ||||||||
\(690\) | −3.47055 | −0.132122 | ||||||||
\(691\) | 7.78487 | 0.296150 | 0.148075 | − | 0.988976i | \(-0.452692\pi\) | ||||
0.148075 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(692\) | 15.3418 | 0.583207 | ||||||||
\(693\) | −15.7011 | −0.596435 | ||||||||
\(694\) | 13.8264 | 0.524843 | ||||||||
\(695\) | 35.2606 | 1.33751 | ||||||||
\(696\) | −2.42178 | −0.0917973 | ||||||||
\(697\) | 5.75964 | 0.218162 | ||||||||
\(698\) | 5.65619 | 0.214090 | ||||||||
\(699\) | 8.00990 | 0.302962 | ||||||||
\(700\) | −8.91548 | −0.336974 | ||||||||
\(701\) | 21.2195 | 0.801451 | 0.400726 | − | 0.916198i | \(-0.368758\pi\) | ||||
0.400726 | + | 0.916198i | \(0.368758\pi\) | |||||||
\(702\) | 29.4319 | 1.11083 | ||||||||
\(703\) | −1.80520 | −0.0680846 | ||||||||
\(704\) | −2.85367 | −0.107552 | ||||||||
\(705\) | 34.0777 | 1.28344 | ||||||||
\(706\) | 20.0562 | 0.754826 | ||||||||
\(707\) | −43.8692 | −1.64987 | ||||||||
\(708\) | −9.43535 | −0.354602 | ||||||||
\(709\) | −17.7505 | −0.666635 | −0.333318 | − | 0.942815i | \(-0.608168\pi\) | ||||
−0.333318 | + | 0.942815i | \(0.608168\pi\) | |||||||
\(710\) | 1.00933 | 0.0378794 | ||||||||
\(711\) | −16.9004 | −0.633814 | ||||||||
\(712\) | −4.30510 | −0.161340 | ||||||||
\(713\) | 9.92467 | 0.371682 | ||||||||
\(714\) | −20.0469 | −0.750236 | ||||||||
\(715\) | −39.9939 | −1.49569 | ||||||||
\(716\) | −3.34395 | −0.124969 | ||||||||
\(717\) | 14.7624 | 0.551312 | ||||||||
\(718\) | −11.6364 | −0.434266 | ||||||||
\(719\) | −35.6917 | −1.33108 | −0.665538 | − | 0.746364i | \(-0.731798\pi\) | ||||
−0.665538 | + | 0.746364i | \(0.731798\pi\) | |||||||
\(720\) | −3.49103 | −0.130103 | ||||||||
\(721\) | −45.3061 | −1.68729 | ||||||||
\(722\) | −12.4041 | −0.461631 | ||||||||
\(723\) | 4.52279 | 0.168204 | ||||||||
\(724\) | −13.3129 | −0.494770 | ||||||||
\(725\) | 3.94737 | 0.146602 | ||||||||
\(726\) | 3.71539 | 0.137891 | ||||||||
\(727\) | 35.9271 | 1.33246 | 0.666232 | − | 0.745745i | \(-0.267906\pi\) | ||||
0.666232 | + | 0.745745i | \(0.267906\pi\) | |||||||
\(728\) | −22.0883 | −0.818648 | ||||||||
\(729\) | 26.2652 | 0.972786 | ||||||||
\(730\) | 31.9259 | 1.18163 | ||||||||
\(731\) | 13.3885 | 0.495193 | ||||||||
\(732\) | −16.4810 | −0.609157 | ||||||||
\(733\) | −11.7726 | −0.434829 | −0.217415 | − | 0.976079i | \(-0.569762\pi\) | ||||
−0.217415 | + | 0.976079i | \(0.569762\pi\) | |||||||
\(734\) | −27.0101 | −0.996960 | ||||||||
\(735\) | −37.0856 | −1.36792 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 45.0165 | 1.65820 | ||||||||
\(738\) | 2.05605 | 0.0756843 | ||||||||
\(739\) | −20.5475 | −0.755853 | −0.377926 | − | 0.925836i | \(-0.623363\pi\) | ||||
−0.377926 | + | 0.925836i | \(0.623363\pi\) | |||||||
\(740\) | 1.87554 | 0.0689464 | ||||||||
\(741\) | 17.5448 | 0.644524 | ||||||||
\(742\) | 7.61563 | 0.279579 | ||||||||
\(743\) | −18.8448 | −0.691348 | −0.345674 | − | 0.938355i | \(-0.612350\pi\) | ||||
−0.345674 | + | 0.938355i | \(0.612350\pi\) | |||||||
\(744\) | −12.9085 | −0.473248 | ||||||||
\(745\) | −51.5396 | −1.88827 | ||||||||
\(746\) | −1.84894 | −0.0676945 | ||||||||
\(747\) | −11.4298 | −0.418194 | ||||||||
\(748\) | 10.4587 | 0.382409 | ||||||||
\(749\) | 36.8545 | 1.34663 | ||||||||
\(750\) | 9.99524 | 0.364975 | ||||||||
\(751\) | −15.1990 | −0.554619 | −0.277310 | − | 0.960781i | \(-0.589443\pi\) | ||||
−0.277310 | + | 0.960781i | \(0.589443\pi\) | |||||||
\(752\) | −9.81910 | −0.358066 | ||||||||
\(753\) | 4.32821 | 0.157729 | ||||||||
\(754\) | 9.77972 | 0.356156 | ||||||||
\(755\) | 34.3012 | 1.24835 | ||||||||
\(756\) | −23.5656 | −0.857074 | ||||||||
\(757\) | −44.6561 | −1.62305 | −0.811527 | − | 0.584315i | \(-0.801363\pi\) | ||||
−0.811527 | + | 0.584315i | \(0.801363\pi\) | |||||||
\(758\) | 10.7898 | 0.391903 | ||||||||
\(759\) | 3.71161 | 0.134723 | ||||||||
\(760\) | −6.85296 | −0.248583 | ||||||||
\(761\) | −19.1290 | −0.693427 | −0.346714 | − | 0.937971i | \(-0.612702\pi\) | ||||
−0.346714 | + | 0.937971i | \(0.612702\pi\) | |||||||
\(762\) | 8.69708 | 0.315062 | ||||||||
\(763\) | −47.1222 | −1.70594 | ||||||||
\(764\) | −16.8178 | −0.608446 | ||||||||
\(765\) | 12.7947 | 0.462592 | ||||||||
\(766\) | 10.4496 | 0.377561 | ||||||||
\(767\) | 38.1022 | 1.37579 | ||||||||
\(768\) | −1.30065 | −0.0469330 | ||||||||
\(769\) | 9.53986 | 0.344016 | 0.172008 | − | 0.985096i | \(-0.444974\pi\) | ||||
0.172008 | + | 0.985096i | \(0.444974\pi\) | |||||||
\(770\) | 32.0225 | 1.15401 | ||||||||
\(771\) | 5.29488 | 0.190690 | ||||||||
\(772\) | −14.2903 | −0.514318 | ||||||||
\(773\) | −30.7760 | −1.10694 | −0.553468 | − | 0.832871i | \(-0.686696\pi\) | ||||
−0.553468 | + | 0.832871i | \(0.686696\pi\) | |||||||
\(774\) | 4.77938 | 0.171791 | ||||||||
\(775\) | 21.0402 | 0.755785 | ||||||||
\(776\) | 17.8664 | 0.641368 | ||||||||
\(777\) | 3.84467 | 0.137927 | ||||||||
\(778\) | −2.54826 | −0.0913596 | ||||||||
\(779\) | 4.03607 | 0.144607 | ||||||||
\(780\) | −18.2284 | −0.652683 | ||||||||
\(781\) | −1.07943 | −0.0386252 | ||||||||
\(782\) | −3.66501 | −0.131061 | ||||||||
\(783\) | 10.4338 | 0.372874 | ||||||||
\(784\) | 10.6858 | 0.381635 | ||||||||
\(785\) | 40.4813 | 1.44484 | ||||||||
\(786\) | −1.30065 | −0.0463925 | ||||||||
\(787\) | 28.9575 | 1.03222 | 0.516112 | − | 0.856521i | \(-0.327379\pi\) | ||||
0.516112 | + | 0.856521i | \(0.327379\pi\) | |||||||
\(788\) | 14.1738 | 0.504922 | ||||||||
\(789\) | −4.09465 | −0.145773 | ||||||||
\(790\) | 34.4685 | 1.22633 | ||||||||
\(791\) | 37.2762 | 1.32539 | ||||||||
\(792\) | 3.73351 | 0.132665 | ||||||||
\(793\) | 66.5544 | 2.36342 | ||||||||
\(794\) | 11.9449 | 0.423910 | ||||||||
\(795\) | 6.28481 | 0.222899 | ||||||||
\(796\) | 10.1475 | 0.359667 | ||||||||
\(797\) | −20.3463 | −0.720704 | −0.360352 | − | 0.932816i | \(-0.617343\pi\) | ||||
−0.360352 | + | 0.932816i | \(0.617343\pi\) | |||||||
\(798\) | −14.0478 | −0.497288 | ||||||||
\(799\) | 35.9871 | 1.27313 | ||||||||
\(800\) | 2.11998 | 0.0749528 | ||||||||
\(801\) | 5.63244 | 0.199013 | ||||||||
\(802\) | 26.9570 | 0.951883 | ||||||||
\(803\) | −34.1434 | −1.20489 | ||||||||
\(804\) | 20.5176 | 0.723601 | ||||||||
\(805\) | −11.2215 | −0.395507 | ||||||||
\(806\) | 52.1275 | 1.83611 | ||||||||
\(807\) | −37.3345 | −1.31424 | ||||||||
\(808\) | 10.4315 | 0.366980 | ||||||||
\(809\) | −42.6845 | −1.50071 | −0.750353 | − | 0.661037i | \(-0.770116\pi\) | ||||
−0.750353 | + | 0.661037i | \(0.770116\pi\) | |||||||
\(810\) | −8.97449 | −0.315332 | ||||||||
\(811\) | 17.5640 | 0.616755 | 0.308377 | − | 0.951264i | \(-0.400214\pi\) | ||||
0.308377 | + | 0.951264i | \(0.400214\pi\) | |||||||
\(812\) | −7.83047 | −0.274796 | ||||||||
\(813\) | 18.7377 | 0.657160 | ||||||||
\(814\) | −2.00582 | −0.0703039 | ||||||||
\(815\) | 61.3775 | 2.14996 | ||||||||
\(816\) | 4.76688 | 0.166874 | ||||||||
\(817\) | 9.38202 | 0.328235 | ||||||||
\(818\) | 29.9678 | 1.04780 | ||||||||
\(819\) | 28.8986 | 1.00980 | ||||||||
\(820\) | −4.19334 | −0.146438 | ||||||||
\(821\) | −38.2203 | −1.33390 | −0.666949 | − | 0.745104i | \(-0.732400\pi\) | ||||
−0.666949 | + | 0.745104i | \(0.732400\pi\) | |||||||
\(822\) | −24.4463 | −0.852662 | ||||||||
\(823\) | 42.2945 | 1.47429 | 0.737146 | − | 0.675733i | \(-0.236173\pi\) | ||||
0.737146 | + | 0.675733i | \(0.236173\pi\) | |||||||
\(824\) | 10.7732 | 0.375302 | ||||||||
\(825\) | 7.86856 | 0.273948 | ||||||||
\(826\) | −30.5078 | −1.06150 | ||||||||
\(827\) | 47.3573 | 1.64677 | 0.823387 | − | 0.567481i | \(-0.192082\pi\) | ||||
0.823387 | + | 0.567481i | \(0.192082\pi\) | |||||||
\(828\) | −1.30832 | −0.0454673 | ||||||||
\(829\) | −39.9784 | −1.38851 | −0.694254 | − | 0.719731i | \(-0.744265\pi\) | ||||
−0.694254 | + | 0.719731i | \(0.744265\pi\) | |||||||
\(830\) | 23.3111 | 0.809141 | ||||||||
\(831\) | −22.6104 | −0.784346 | ||||||||
\(832\) | 5.25232 | 0.182091 | ||||||||
\(833\) | −39.1635 | −1.35694 | ||||||||
\(834\) | −17.1873 | −0.595149 | ||||||||
\(835\) | −27.1692 | −0.940229 | ||||||||
\(836\) | 7.32895 | 0.253477 | ||||||||
\(837\) | 55.6139 | 1.92230 | ||||||||
\(838\) | −18.6662 | −0.644812 | ||||||||
\(839\) | 23.1644 | 0.799722 | 0.399861 | − | 0.916576i | \(-0.369058\pi\) | ||||
0.399861 | + | 0.916576i | \(0.369058\pi\) | |||||||
\(840\) | 14.5952 | 0.503583 | ||||||||
\(841\) | −25.5330 | −0.880449 | ||||||||
\(842\) | −3.04689 | −0.105003 | ||||||||
\(843\) | −15.1023 | −0.520151 | ||||||||
\(844\) | 20.9748 | 0.721984 | ||||||||
\(845\) | 38.9225 | 1.33897 | ||||||||
\(846\) | 12.8465 | 0.441673 | ||||||||
\(847\) | 12.0132 | 0.412778 | ||||||||
\(848\) | −1.81090 | −0.0621865 | ||||||||
\(849\) | −15.9435 | −0.547179 | ||||||||
\(850\) | −7.76977 | −0.266501 | ||||||||
\(851\) | 0.702891 | 0.0240948 | ||||||||
\(852\) | −0.491985 | −0.0168551 | ||||||||
\(853\) | −7.34019 | −0.251323 | −0.125662 | − | 0.992073i | \(-0.540105\pi\) | ||||
−0.125662 | + | 0.992073i | \(0.540105\pi\) | |||||||
\(854\) | −53.2890 | −1.82351 | ||||||||
\(855\) | 8.96586 | 0.306626 | ||||||||
\(856\) | −8.76351 | −0.299531 | ||||||||
\(857\) | 29.2763 | 1.00006 | 0.500030 | − | 0.866008i | \(-0.333322\pi\) | ||||
0.500030 | + | 0.866008i | \(0.333322\pi\) | |||||||
\(858\) | 19.4946 | 0.665533 | ||||||||
\(859\) | 22.8807 | 0.780680 | 0.390340 | − | 0.920671i | \(-0.372357\pi\) | ||||
0.390340 | + | 0.920671i | \(0.372357\pi\) | |||||||
\(860\) | −9.74759 | −0.332390 | ||||||||
\(861\) | −8.59590 | −0.292947 | ||||||||
\(862\) | 2.00453 | 0.0682745 | ||||||||
\(863\) | −19.3138 | −0.657450 | −0.328725 | − | 0.944426i | \(-0.606619\pi\) | ||||
−0.328725 | + | 0.944426i | \(0.606619\pi\) | |||||||
\(864\) | 5.60360 | 0.190638 | ||||||||
\(865\) | 40.9369 | 1.39190 | ||||||||
\(866\) | 9.17585 | 0.311808 | ||||||||
\(867\) | 4.64029 | 0.157593 | ||||||||
\(868\) | −41.7377 | −1.41667 | ||||||||
\(869\) | −36.8626 | −1.25048 | ||||||||
\(870\) | −6.46211 | −0.219086 | ||||||||
\(871\) | −82.8551 | −2.80744 | ||||||||
\(872\) | 11.2050 | 0.379450 | ||||||||
\(873\) | −23.3750 | −0.791125 | ||||||||
\(874\) | −2.56826 | −0.0868726 | ||||||||
\(875\) | 32.3181 | 1.09255 | ||||||||
\(876\) | −15.5619 | −0.525788 | ||||||||
\(877\) | −40.2715 | −1.35987 | −0.679936 | − | 0.733272i | \(-0.737992\pi\) | ||||
−0.679936 | + | 0.733272i | \(0.737992\pi\) | |||||||
\(878\) | −21.4540 | −0.724038 | ||||||||
\(879\) | −17.1321 | −0.577852 | ||||||||
\(880\) | −7.61453 | −0.256686 | ||||||||
\(881\) | −19.1517 | −0.645238 | −0.322619 | − | 0.946529i | \(-0.604563\pi\) | ||||
−0.322619 | + | 0.946529i | \(0.604563\pi\) | |||||||
\(882\) | −13.9804 | −0.470746 | ||||||||
\(883\) | 9.21070 | 0.309965 | 0.154982 | − | 0.987917i | \(-0.450468\pi\) | ||||
0.154982 | + | 0.987917i | \(0.450468\pi\) | |||||||
\(884\) | −19.2498 | −0.647441 | ||||||||
\(885\) | −25.1766 | −0.846303 | ||||||||
\(886\) | 38.1606 | 1.28203 | ||||||||
\(887\) | 7.91081 | 0.265619 | 0.132810 | − | 0.991142i | \(-0.457600\pi\) | ||||
0.132810 | + | 0.991142i | \(0.457600\pi\) | |||||||
\(888\) | −0.914212 | −0.0306789 | ||||||||
\(889\) | 28.1207 | 0.943139 | ||||||||
\(890\) | −11.4874 | −0.385059 | ||||||||
\(891\) | 9.59785 | 0.321540 | ||||||||
\(892\) | 12.8028 | 0.428669 | ||||||||
\(893\) | 25.2180 | 0.843887 | ||||||||
\(894\) | 25.1224 | 0.840218 | ||||||||
\(895\) | −8.92276 | −0.298255 | ||||||||
\(896\) | −4.20545 | −0.140494 | ||||||||
\(897\) | −6.83140 | −0.228094 | ||||||||
\(898\) | −11.8880 | −0.396707 | ||||||||
\(899\) | 18.4796 | 0.616328 | ||||||||
\(900\) | −2.77362 | −0.0924540 | ||||||||
\(901\) | 6.63696 | 0.221109 | ||||||||
\(902\) | 4.48460 | 0.149321 | ||||||||
\(903\) | −19.9815 | −0.664944 | ||||||||
\(904\) | −8.86378 | −0.294805 | ||||||||
\(905\) | −35.5232 | −1.18083 | ||||||||
\(906\) | −16.7197 | −0.555475 | ||||||||
\(907\) | −47.8891 | −1.59013 | −0.795065 | − | 0.606524i | \(-0.792563\pi\) | ||||
−0.795065 | + | 0.606524i | \(0.792563\pi\) | |||||||
\(908\) | −15.5102 | −0.514724 | ||||||||
\(909\) | −13.6478 | −0.452668 | ||||||||
\(910\) | −58.9390 | −1.95381 | ||||||||
\(911\) | 5.14648 | 0.170510 | 0.0852552 | − | 0.996359i | \(-0.472829\pi\) | ||||
0.0852552 | + | 0.996359i | \(0.472829\pi\) | |||||||
\(912\) | 3.34039 | 0.110611 | ||||||||
\(913\) | −24.9303 | −0.825072 | ||||||||
\(914\) | −20.4974 | −0.677994 | ||||||||
\(915\) | −43.9769 | −1.45383 | ||||||||
\(916\) | 12.3368 | 0.407619 | ||||||||
\(917\) | −4.20545 | −0.138876 | ||||||||
\(918\) | −20.5373 | −0.677831 | ||||||||
\(919\) | −51.2148 | −1.68942 | −0.844710 | − | 0.535224i | \(-0.820227\pi\) | ||||
−0.844710 | + | 0.535224i | \(0.820227\pi\) | |||||||
\(920\) | 2.66833 | 0.0879722 | ||||||||
\(921\) | 16.0391 | 0.528507 | ||||||||
\(922\) | 18.5868 | 0.612124 | ||||||||
\(923\) | 1.98675 | 0.0653947 | ||||||||
\(924\) | −15.6090 | −0.513498 | ||||||||
\(925\) | 1.49012 | 0.0489948 | ||||||||
\(926\) | −32.0652 | −1.05373 | ||||||||
\(927\) | −14.0948 | −0.462934 | ||||||||
\(928\) | 1.86198 | 0.0611226 | ||||||||
\(929\) | −32.2420 | −1.05782 | −0.528912 | − | 0.848676i | \(-0.677400\pi\) | ||||
−0.528912 | + | 0.848676i | \(0.677400\pi\) | |||||||
\(930\) | −34.4441 | −1.12947 | ||||||||
\(931\) | −27.4438 | −0.899436 | ||||||||
\(932\) | −6.15840 | −0.201725 | ||||||||
\(933\) | −2.04321 | −0.0668917 | ||||||||
\(934\) | −22.3931 | −0.732725 | ||||||||
\(935\) | 27.9073 | 0.912668 | ||||||||
\(936\) | −6.87171 | −0.224609 | ||||||||
\(937\) | 33.8640 | 1.10629 | 0.553144 | − | 0.833086i | \(-0.313428\pi\) | ||||
0.553144 | + | 0.833086i | \(0.313428\pi\) | |||||||
\(938\) | 66.3408 | 2.16610 | ||||||||
\(939\) | −2.75098 | −0.0897749 | ||||||||
\(940\) | −26.2006 | −0.854569 | ||||||||
\(941\) | 16.6715 | 0.543475 | 0.271737 | − | 0.962371i | \(-0.412402\pi\) | ||||
0.271737 | + | 0.962371i | \(0.412402\pi\) | |||||||
\(942\) | −19.7321 | −0.642908 | ||||||||
\(943\) | −1.57152 | −0.0511757 | ||||||||
\(944\) | 7.25435 | 0.236109 | ||||||||
\(945\) | −62.8809 | −2.04552 | ||||||||
\(946\) | 10.4246 | 0.338935 | ||||||||
\(947\) | 2.48133 | 0.0806324 | 0.0403162 | − | 0.999187i | \(-0.487163\pi\) | ||||
0.0403162 | + | 0.999187i | \(0.487163\pi\) | |||||||
\(948\) | −16.8012 | −0.545679 | ||||||||
\(949\) | 62.8426 | 2.03996 | ||||||||
\(950\) | −5.44467 | −0.176648 | ||||||||
\(951\) | 22.8877 | 0.742185 | ||||||||
\(952\) | 15.4130 | 0.499539 | ||||||||
\(953\) | 17.6732 | 0.572491 | 0.286246 | − | 0.958156i | \(-0.407593\pi\) | ||||
0.286246 | + | 0.958156i | \(0.407593\pi\) | |||||||
\(954\) | 2.36923 | 0.0767068 | ||||||||
\(955\) | −44.8754 | −1.45213 | ||||||||
\(956\) | −11.3501 | −0.367087 | ||||||||
\(957\) | 6.91096 | 0.223399 | ||||||||
\(958\) | −35.9014 | −1.15992 | ||||||||
\(959\) | −79.0434 | −2.55245 | ||||||||
\(960\) | −3.47055 | −0.112012 | ||||||||
\(961\) | 67.4991 | 2.17739 | ||||||||
\(962\) | 3.69180 | 0.119029 | ||||||||
\(963\) | 11.4655 | 0.369470 | ||||||||
\(964\) | −3.47734 | −0.111998 | ||||||||
\(965\) | −38.1312 | −1.22749 | ||||||||
\(966\) | 5.46980 | 0.175988 | ||||||||
\(967\) | 28.4718 | 0.915590 | 0.457795 | − | 0.889058i | \(-0.348639\pi\) | ||||
0.457795 | + | 0.889058i | \(0.348639\pi\) | |||||||
\(968\) | −2.85658 | −0.0918138 | ||||||||
\(969\) | −12.2426 | −0.393288 | ||||||||
\(970\) | 47.6736 | 1.53071 | ||||||||
\(971\) | 59.6041 | 1.91279 | 0.956394 | − | 0.292081i | \(-0.0943477\pi\) | ||||
0.956394 | + | 0.292081i | \(0.0943477\pi\) | |||||||
\(972\) | −12.4363 | −0.398894 | ||||||||
\(973\) | −55.5728 | −1.78158 | ||||||||
\(974\) | −16.9582 | −0.543376 | ||||||||
\(975\) | −14.4825 | −0.463810 | ||||||||
\(976\) | 12.6714 | 0.405603 | ||||||||
\(977\) | 56.0328 | 1.79265 | 0.896323 | − | 0.443401i | \(-0.146228\pi\) | ||||
0.896323 | + | 0.443401i | \(0.146228\pi\) | |||||||
\(978\) | −29.9178 | −0.956664 | ||||||||
\(979\) | 12.2853 | 0.392640 | ||||||||
\(980\) | 28.5132 | 0.910821 | ||||||||
\(981\) | −14.6598 | −0.468051 | ||||||||
\(982\) | 35.5842 | 1.13554 | ||||||||
\(983\) | 52.4652 | 1.67338 | 0.836689 | − | 0.547678i | \(-0.184488\pi\) | ||||
0.836689 | + | 0.547678i | \(0.184488\pi\) | |||||||
\(984\) | 2.04399 | 0.0651601 | ||||||||
\(985\) | 37.8205 | 1.20506 | ||||||||
\(986\) | −6.82419 | −0.217326 | ||||||||
\(987\) | −53.7085 | −1.70956 | ||||||||
\(988\) | −13.4893 | −0.429152 | ||||||||
\(989\) | −3.65307 | −0.116161 | ||||||||
\(990\) | 9.96224 | 0.316621 | ||||||||
\(991\) | −15.2415 | −0.484161 | −0.242081 | − | 0.970256i | \(-0.577830\pi\) | ||||
−0.242081 | + | 0.970256i | \(0.577830\pi\) | |||||||
\(992\) | 9.92467 | 0.315109 | ||||||||
\(993\) | 23.4663 | 0.744681 | ||||||||
\(994\) | −1.59076 | −0.0504559 | ||||||||
\(995\) | 27.0768 | 0.858392 | ||||||||
\(996\) | −11.3627 | −0.360042 | ||||||||
\(997\) | −4.36515 | −0.138246 | −0.0691228 | − | 0.997608i | \(-0.522020\pi\) | ||||
−0.0691228 | + | 0.997608i | \(0.522020\pi\) | |||||||
\(998\) | 14.9594 | 0.473532 | ||||||||
\(999\) | 3.93872 | 0.124616 |
(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 | 6026.2.a.m.1.12 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.m.1.12 | ✓ | 41 | 1.1 | even | 1 | trivial |