Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96907 | −1.39234 | −0.696172 | − | 0.717875i | \(-0.745115\pi\) | ||||
−0.696172 | + | 0.717875i | \(0.745115\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.87725 | 0.938623 | ||||||||
\(5\) | 4.10878 | 1.83750 | 0.918750 | − | 0.394839i | \(-0.129200\pi\) | ||||
0.918750 | + | 0.394839i | \(0.129200\pi\) | |||||||
\(6\) | 1.96907 | 0.803870 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.241710 | 0.0854575 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.09048 | −2.55843 | ||||||||
\(11\) | 4.87993 | 1.47136 | 0.735678 | − | 0.677332i | \(-0.236864\pi\) | ||||
0.735678 | + | 0.677332i | \(0.236864\pi\) | |||||||
\(12\) | −1.87725 | −0.541914 | ||||||||
\(13\) | 2.68737 | 0.745341 | 0.372671 | − | 0.927964i | \(-0.378442\pi\) | ||||
0.372671 | + | 0.927964i | \(0.378442\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.10878 | −1.06088 | ||||||||
\(16\) | −4.23044 | −1.05761 | ||||||||
\(17\) | 3.34460 | 0.811184 | 0.405592 | − | 0.914054i | \(-0.367065\pi\) | ||||
0.405592 | + | 0.914054i | \(0.367065\pi\) | |||||||
\(18\) | −1.96907 | −0.464115 | ||||||||
\(19\) | 0.186064 | 0.0426861 | 0.0213431 | − | 0.999772i | \(-0.493206\pi\) | ||||
0.0213431 | + | 0.999772i | \(0.493206\pi\) | |||||||
\(20\) | 7.71319 | 1.72472 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.60894 | −2.04863 | ||||||||
\(23\) | 5.74714 | 1.19836 | 0.599181 | − | 0.800614i | \(-0.295493\pi\) | ||||
0.599181 | + | 0.800614i | \(0.295493\pi\) | |||||||
\(24\) | −0.241710 | −0.0493389 | ||||||||
\(25\) | 11.8820 | 2.37641 | ||||||||
\(26\) | −5.29162 | −1.03777 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.28935 | 0.425121 | 0.212561 | − | 0.977148i | \(-0.431820\pi\) | ||||
0.212561 | + | 0.977148i | \(0.431820\pi\) | |||||||
\(30\) | 8.09048 | 1.47711 | ||||||||
\(31\) | −0.783246 | −0.140675 | −0.0703376 | − | 0.997523i | \(-0.522408\pi\) | ||||
−0.0703376 | + | 0.997523i | \(0.522408\pi\) | |||||||
\(32\) | 7.84662 | 1.38710 | ||||||||
\(33\) | −4.87993 | −0.849488 | ||||||||
\(34\) | −6.58576 | −1.12945 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.87725 | 0.312874 | ||||||||
\(37\) | 1.26983 | 0.208759 | 0.104380 | − | 0.994538i | \(-0.466714\pi\) | ||||
0.104380 | + | 0.994538i | \(0.466714\pi\) | |||||||
\(38\) | −0.366374 | −0.0594338 | ||||||||
\(39\) | −2.68737 | −0.430323 | ||||||||
\(40\) | 0.993134 | 0.157028 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2503 | −1.71565 | −0.857824 | − | 0.513944i | \(-0.828184\pi\) | ||||
−0.857824 | + | 0.513944i | \(0.828184\pi\) | |||||||
\(44\) | 9.16084 | 1.38105 | ||||||||
\(45\) | 4.10878 | 0.612500 | ||||||||
\(46\) | −11.3165 | −1.66853 | ||||||||
\(47\) | −2.29201 | −0.334324 | −0.167162 | − | 0.985929i | \(-0.553460\pi\) | ||||
−0.167162 | + | 0.985929i | \(0.553460\pi\) | |||||||
\(48\) | 4.23044 | 0.610611 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −23.3966 | −3.30878 | ||||||||
\(51\) | −3.34460 | −0.468338 | ||||||||
\(52\) | 5.04485 | 0.699595 | ||||||||
\(53\) | 11.2502 | 1.54533 | 0.772667 | − | 0.634812i | \(-0.218922\pi\) | ||||
0.772667 | + | 0.634812i | \(0.218922\pi\) | |||||||
\(54\) | 1.96907 | 0.267957 | ||||||||
\(55\) | 20.0506 | 2.70362 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.186064 | −0.0246448 | ||||||||
\(58\) | −4.50789 | −0.591915 | ||||||||
\(59\) | 11.9843 | 1.56023 | 0.780113 | − | 0.625639i | \(-0.215162\pi\) | ||||
0.780113 | + | 0.625639i | \(0.215162\pi\) | |||||||
\(60\) | −7.71319 | −0.995768 | ||||||||
\(61\) | 1.36157 | 0.174331 | 0.0871654 | − | 0.996194i | \(-0.472219\pi\) | ||||
0.0871654 | + | 0.996194i | \(0.472219\pi\) | |||||||
\(62\) | 1.54227 | 0.195868 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.98969 | −0.873711 | ||||||||
\(65\) | 11.0418 | 1.36957 | ||||||||
\(66\) | 9.60894 | 1.18278 | ||||||||
\(67\) | −2.74258 | −0.335059 | −0.167529 | − | 0.985867i | \(-0.553579\pi\) | ||||
−0.167529 | + | 0.985867i | \(0.553579\pi\) | |||||||
\(68\) | 6.27864 | 0.761397 | ||||||||
\(69\) | −5.74714 | −0.691875 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.59530 | 0.782719 | 0.391359 | − | 0.920238i | \(-0.372005\pi\) | ||||
0.391359 | + | 0.920238i | \(0.372005\pi\) | |||||||
\(72\) | 0.241710 | 0.0284858 | ||||||||
\(73\) | −3.81962 | −0.447053 | −0.223527 | − | 0.974698i | \(-0.571757\pi\) | ||||
−0.223527 | + | 0.974698i | \(0.571757\pi\) | |||||||
\(74\) | −2.50039 | −0.290665 | ||||||||
\(75\) | −11.8820 | −1.37202 | ||||||||
\(76\) | 0.349289 | 0.0400662 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.29162 | 0.599158 | ||||||||
\(79\) | −10.7548 | −1.21001 | −0.605003 | − | 0.796223i | \(-0.706828\pi\) | ||||
−0.605003 | + | 0.796223i | \(0.706828\pi\) | |||||||
\(80\) | −17.3819 | −1.94336 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.96907 | −0.217448 | ||||||||
\(83\) | −3.54877 | −0.389528 | −0.194764 | − | 0.980850i | \(-0.562394\pi\) | ||||
−0.194764 | + | 0.980850i | \(0.562394\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.7422 | 1.49055 | ||||||||
\(86\) | 22.1526 | 2.38877 | ||||||||
\(87\) | −2.28935 | −0.245444 | ||||||||
\(88\) | 1.17953 | 0.125738 | ||||||||
\(89\) | −9.08983 | −0.963520 | −0.481760 | − | 0.876303i | \(-0.660002\pi\) | ||||
−0.481760 | + | 0.876303i | \(0.660002\pi\) | |||||||
\(90\) | −8.09048 | −0.852811 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.7888 | 1.12481 | ||||||||
\(93\) | 0.783246 | 0.0812189 | ||||||||
\(94\) | 4.51313 | 0.465494 | ||||||||
\(95\) | 0.764497 | 0.0784357 | ||||||||
\(96\) | −7.84662 | −0.800842 | ||||||||
\(97\) | 10.0278 | 1.01817 | 0.509083 | − | 0.860717i | \(-0.329985\pi\) | ||||
0.509083 | + | 0.860717i | \(0.329985\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.87993 | 0.490452 | ||||||||
\(100\) | 22.3055 | 2.23055 | ||||||||
\(101\) | 5.67306 | 0.564490 | 0.282245 | − | 0.959342i | \(-0.408921\pi\) | ||||
0.282245 | + | 0.959342i | \(0.408921\pi\) | |||||||
\(102\) | 6.58576 | 0.652087 | ||||||||
\(103\) | 8.59023 | 0.846421 | 0.423210 | − | 0.906031i | \(-0.360903\pi\) | ||||
0.423210 | + | 0.906031i | \(0.360903\pi\) | |||||||
\(104\) | 0.649564 | 0.0636950 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.1525 | −2.15164 | ||||||||
\(107\) | −3.10612 | −0.300279 | −0.150140 | − | 0.988665i | \(-0.547972\pi\) | ||||
−0.150140 | + | 0.988665i | \(0.547972\pi\) | |||||||
\(108\) | −1.87725 | −0.180638 | ||||||||
\(109\) | 10.4576 | 1.00166 | 0.500830 | − | 0.865546i | \(-0.333028\pi\) | ||||
0.500830 | + | 0.865546i | \(0.333028\pi\) | |||||||
\(110\) | −39.4810 | −3.76437 | ||||||||
\(111\) | −1.26983 | −0.120527 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.24364 | −0.775497 | −0.387748 | − | 0.921765i | \(-0.626747\pi\) | ||||
−0.387748 | + | 0.921765i | \(0.626747\pi\) | |||||||
\(114\) | 0.366374 | 0.0343141 | ||||||||
\(115\) | 23.6137 | 2.20199 | ||||||||
\(116\) | 4.29767 | 0.399029 | ||||||||
\(117\) | 2.68737 | 0.248447 | ||||||||
\(118\) | −23.5980 | −2.17237 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.993134 | −0.0906603 | ||||||||
\(121\) | 12.8138 | 1.16489 | ||||||||
\(122\) | −2.68103 | −0.242729 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −1.47035 | −0.132041 | ||||||||
\(125\) | 28.2768 | 2.52915 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7620 | 1.57612 | 0.788060 | − | 0.615598i | \(-0.211086\pi\) | ||||
0.788060 | + | 0.615598i | \(0.211086\pi\) | |||||||
\(128\) | −1.93004 | −0.170593 | ||||||||
\(129\) | 11.2503 | 0.990530 | ||||||||
\(130\) | −21.7421 | −1.90691 | ||||||||
\(131\) | −12.1215 | −1.05906 | −0.529529 | − | 0.848292i | \(-0.677631\pi\) | ||||
−0.529529 | + | 0.848292i | \(0.677631\pi\) | |||||||
\(132\) | −9.16084 | −0.797349 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.40033 | 0.466517 | ||||||||
\(135\) | −4.10878 | −0.353627 | ||||||||
\(136\) | 0.808424 | 0.0693218 | ||||||||
\(137\) | 13.6412 | 1.16545 | 0.582725 | − | 0.812669i | \(-0.301986\pi\) | ||||
0.582725 | + | 0.812669i | \(0.301986\pi\) | |||||||
\(138\) | 11.3165 | 0.963328 | ||||||||
\(139\) | 7.04836 | 0.597834 | 0.298917 | − | 0.954279i | \(-0.403375\pi\) | ||||
0.298917 | + | 0.954279i | \(0.403375\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.29201 | 0.193022 | ||||||||
\(142\) | −12.9866 | −1.08981 | ||||||||
\(143\) | 13.1142 | 1.09666 | ||||||||
\(144\) | −4.23044 | −0.352537 | ||||||||
\(145\) | 9.40642 | 0.781161 | ||||||||
\(146\) | 7.52112 | 0.622452 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.38379 | 0.195946 | ||||||||
\(149\) | −22.0836 | −1.80916 | −0.904579 | − | 0.426305i | \(-0.859815\pi\) | ||||
−0.904579 | + | 0.426305i | \(0.859815\pi\) | |||||||
\(150\) | 23.3966 | 1.91032 | ||||||||
\(151\) | −13.9955 | −1.13894 | −0.569469 | − | 0.822013i | \(-0.692851\pi\) | ||||
−0.569469 | + | 0.822013i | \(0.692851\pi\) | |||||||
\(152\) | 0.0449737 | 0.00364785 | ||||||||
\(153\) | 3.34460 | 0.270395 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.21818 | −0.258491 | ||||||||
\(156\) | −5.04485 | −0.403911 | ||||||||
\(157\) | −22.2994 | −1.77968 | −0.889841 | − | 0.456270i | \(-0.849185\pi\) | ||||
−0.889841 | + | 0.456270i | \(0.849185\pi\) | |||||||
\(158\) | 21.1769 | 1.68475 | ||||||||
\(159\) | −11.2502 | −0.892199 | ||||||||
\(160\) | 32.2400 | 2.54880 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.96907 | −0.154705 | ||||||||
\(163\) | −12.0403 | −0.943070 | −0.471535 | − | 0.881847i | \(-0.656300\pi\) | ||||
−0.471535 | + | 0.881847i | \(0.656300\pi\) | |||||||
\(164\) | 1.87725 | 0.146588 | ||||||||
\(165\) | −20.0506 | −1.56093 | ||||||||
\(166\) | 6.98778 | 0.542357 | ||||||||
\(167\) | −8.09156 | −0.626144 | −0.313072 | − | 0.949729i | \(-0.601358\pi\) | ||||
−0.313072 | + | 0.949729i | \(0.601358\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.77806 | −0.444466 | ||||||||
\(170\) | −27.0594 | −2.07536 | ||||||||
\(171\) | 0.186064 | 0.0142287 | ||||||||
\(172\) | −21.1195 | −1.61035 | ||||||||
\(173\) | 6.27533 | 0.477104 | 0.238552 | − | 0.971130i | \(-0.423327\pi\) | ||||
0.238552 | + | 0.971130i | \(0.423327\pi\) | |||||||
\(174\) | 4.50789 | 0.341743 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.6443 | −1.55612 | ||||||||
\(177\) | −11.9843 | −0.900797 | ||||||||
\(178\) | 17.8985 | 1.34155 | ||||||||
\(179\) | 20.9156 | 1.56331 | 0.781654 | − | 0.623712i | \(-0.214376\pi\) | ||||
0.781654 | + | 0.623712i | \(0.214376\pi\) | |||||||
\(180\) | 7.71319 | 0.574907 | ||||||||
\(181\) | −1.55997 | −0.115952 | −0.0579758 | − | 0.998318i | \(-0.518465\pi\) | ||||
−0.0579758 | + | 0.998318i | \(0.518465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.36157 | −0.100650 | ||||||||
\(184\) | 1.38914 | 0.102409 | ||||||||
\(185\) | 5.21746 | 0.383595 | ||||||||
\(186\) | −1.54227 | −0.113085 | ||||||||
\(187\) | 16.3214 | 1.19354 | ||||||||
\(188\) | −4.30267 | −0.313804 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.50535 | −0.109210 | ||||||||
\(191\) | −17.2164 | −1.24574 | −0.622868 | − | 0.782327i | \(-0.714033\pi\) | ||||
−0.622868 | + | 0.782327i | \(0.714033\pi\) | |||||||
\(192\) | 6.98969 | 0.504437 | ||||||||
\(193\) | −15.9807 | −1.15031 | −0.575157 | − | 0.818043i | \(-0.695059\pi\) | ||||
−0.575157 | + | 0.818043i | \(0.695059\pi\) | |||||||
\(194\) | −19.7454 | −1.41764 | ||||||||
\(195\) | −11.0418 | −0.790719 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.32916 | 0.664675 | 0.332337 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332337 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(198\) | −9.60894 | −0.682878 | ||||||||
\(199\) | 12.6095 | 0.893866 | 0.446933 | − | 0.894567i | \(-0.352516\pi\) | ||||
0.446933 | + | 0.894567i | \(0.352516\pi\) | |||||||
\(200\) | 2.87201 | 0.203082 | ||||||||
\(201\) | 2.74258 | 0.193446 | ||||||||
\(202\) | −11.1707 | −0.785965 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.27864 | −0.439593 | ||||||||
\(205\) | 4.10878 | 0.286969 | ||||||||
\(206\) | −16.9148 | −1.17851 | ||||||||
\(207\) | 5.74714 | 0.399454 | ||||||||
\(208\) | −11.3687 | −0.788280 | ||||||||
\(209\) | 0.907982 | 0.0628064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9027 | −1.09479 | −0.547394 | − | 0.836875i | \(-0.684380\pi\) | ||||
−0.547394 | + | 0.836875i | \(0.684380\pi\) | |||||||
\(212\) | 21.1194 | 1.45049 | ||||||||
\(213\) | −6.59530 | −0.451903 | ||||||||
\(214\) | 6.11617 | 0.418092 | ||||||||
\(215\) | −46.2248 | −3.15250 | ||||||||
\(216\) | −0.241710 | −0.0164463 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.5918 | −1.39465 | ||||||||
\(219\) | 3.81962 | 0.258106 | ||||||||
\(220\) | 37.6398 | 2.53768 | ||||||||
\(221\) | 8.98816 | 0.604609 | ||||||||
\(222\) | 2.50039 | 0.167815 | ||||||||
\(223\) | −29.0062 | −1.94240 | −0.971199 | − | 0.238268i | \(-0.923420\pi\) | ||||
−0.971199 | + | 0.238268i | \(0.923420\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.8820 | 0.792136 | ||||||||
\(226\) | 16.2323 | 1.07976 | ||||||||
\(227\) | −20.3453 | −1.35036 | −0.675182 | − | 0.737651i | \(-0.735935\pi\) | ||||
−0.675182 | + | 0.737651i | \(0.735935\pi\) | |||||||
\(228\) | −0.349289 | −0.0231322 | ||||||||
\(229\) | −24.6741 | −1.63051 | −0.815257 | − | 0.579100i | \(-0.803404\pi\) | ||||
−0.815257 | + | 0.579100i | \(0.803404\pi\) | |||||||
\(230\) | −46.4971 | −3.06593 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.553359 | 0.0363298 | ||||||||
\(233\) | 7.08960 | 0.464455 | 0.232227 | − | 0.972661i | \(-0.425399\pi\) | ||||
0.232227 | + | 0.972661i | \(0.425399\pi\) | |||||||
\(234\) | −5.29162 | −0.345924 | ||||||||
\(235\) | −9.41736 | −0.614321 | ||||||||
\(236\) | 22.4975 | 1.46446 | ||||||||
\(237\) | 10.7548 | 0.698598 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3453 | −1.25134 | −0.625672 | − | 0.780086i | \(-0.715175\pi\) | ||||
−0.625672 | + | 0.780086i | \(0.715175\pi\) | |||||||
\(240\) | 17.3819 | 1.12200 | ||||||||
\(241\) | 26.5629 | 1.71107 | 0.855534 | − | 0.517747i | \(-0.173229\pi\) | ||||
0.855534 | + | 0.517747i | \(0.173229\pi\) | |||||||
\(242\) | −25.2312 | −1.62192 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.55600 | 0.163631 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.96907 | 0.125543 | ||||||||
\(247\) | 0.500023 | 0.0318157 | ||||||||
\(248\) | −0.189319 | −0.0120218 | ||||||||
\(249\) | 3.54877 | 0.224894 | ||||||||
\(250\) | −55.6790 | −3.52145 | ||||||||
\(251\) | −25.9956 | −1.64083 | −0.820414 | − | 0.571770i | \(-0.806257\pi\) | ||||
−0.820414 | + | 0.571770i | \(0.806257\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.0457 | 1.76322 | ||||||||
\(254\) | −34.9746 | −2.19450 | ||||||||
\(255\) | −13.7422 | −0.860570 | ||||||||
\(256\) | 17.7798 | 1.11124 | ||||||||
\(257\) | −21.1096 | −1.31678 | −0.658391 | − | 0.752676i | \(-0.728763\pi\) | ||||
−0.658391 | + | 0.752676i | \(0.728763\pi\) | |||||||
\(258\) | −22.1526 | −1.37916 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 20.7282 | 1.28551 | ||||||||
\(261\) | 2.28935 | 0.141707 | ||||||||
\(262\) | 23.8681 | 1.47457 | ||||||||
\(263\) | −10.5110 | −0.648136 | −0.324068 | − | 0.946034i | \(-0.605051\pi\) | ||||
−0.324068 | + | 0.946034i | \(0.605051\pi\) | |||||||
\(264\) | −1.17953 | −0.0725951 | ||||||||
\(265\) | 46.2245 | 2.83955 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.08983 | 0.556288 | ||||||||
\(268\) | −5.14849 | −0.314494 | ||||||||
\(269\) | −21.1796 | −1.29135 | −0.645673 | − | 0.763614i | \(-0.723423\pi\) | ||||
−0.645673 | + | 0.763614i | \(0.723423\pi\) | |||||||
\(270\) | 8.09048 | 0.492371 | ||||||||
\(271\) | 2.53803 | 0.154175 | 0.0770873 | − | 0.997024i | \(-0.475438\pi\) | ||||
0.0770873 | + | 0.997024i | \(0.475438\pi\) | |||||||
\(272\) | −14.1491 | −0.857916 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.8606 | −1.62271 | ||||||||
\(275\) | 57.9836 | 3.49654 | ||||||||
\(276\) | −10.7888 | −0.649410 | ||||||||
\(277\) | 20.2870 | 1.21893 | 0.609465 | − | 0.792813i | \(-0.291384\pi\) | ||||
0.609465 | + | 0.792813i | \(0.291384\pi\) | |||||||
\(278\) | −13.8787 | −0.832390 | ||||||||
\(279\) | −0.783246 | −0.0468917 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.2747 | −1.09018 | −0.545088 | − | 0.838379i | \(-0.683504\pi\) | ||||
−0.545088 | + | 0.838379i | \(0.683504\pi\) | |||||||
\(282\) | −4.51313 | −0.268753 | ||||||||
\(283\) | 4.14431 | 0.246354 | 0.123177 | − | 0.992385i | \(-0.460692\pi\) | ||||
0.123177 | + | 0.992385i | \(0.460692\pi\) | |||||||
\(284\) | 12.3810 | 0.734678 | ||||||||
\(285\) | −0.764497 | −0.0452849 | ||||||||
\(286\) | −25.8228 | −1.52693 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.84662 | 0.462366 | ||||||||
\(289\) | −5.81366 | −0.341980 | ||||||||
\(290\) | −18.5219 | −1.08765 | ||||||||
\(291\) | −10.0278 | −0.587839 | ||||||||
\(292\) | −7.17038 | −0.419615 | ||||||||
\(293\) | −2.08588 | −0.121859 | −0.0609293 | − | 0.998142i | \(-0.519406\pi\) | ||||
−0.0609293 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 49.2409 | 2.86692 | ||||||||
\(296\) | 0.306932 | 0.0178401 | ||||||||
\(297\) | −4.87993 | −0.283163 | ||||||||
\(298\) | 43.4842 | 2.51897 | ||||||||
\(299\) | 15.4447 | 0.893189 | ||||||||
\(300\) | −22.3055 | −1.28781 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 27.5582 | 1.58579 | ||||||||
\(303\) | −5.67306 | −0.325909 | ||||||||
\(304\) | −0.787134 | −0.0451452 | ||||||||
\(305\) | 5.59438 | 0.320333 | ||||||||
\(306\) | −6.58576 | −0.376483 | ||||||||
\(307\) | −6.30305 | −0.359734 | −0.179867 | − | 0.983691i | \(-0.557567\pi\) | ||||
−0.179867 | + | 0.983691i | \(0.557567\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.59023 | −0.488681 | ||||||||
\(310\) | 6.33684 | 0.359908 | ||||||||
\(311\) | −16.3846 | −0.929083 | −0.464541 | − | 0.885551i | \(-0.653781\pi\) | ||||
−0.464541 | + | 0.885551i | \(0.653781\pi\) | |||||||
\(312\) | −0.649564 | −0.0367743 | ||||||||
\(313\) | 14.1093 | 0.797504 | 0.398752 | − | 0.917059i | \(-0.369443\pi\) | ||||
0.398752 | + | 0.917059i | \(0.369443\pi\) | |||||||
\(314\) | 43.9091 | 2.47793 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.1894 | −1.13574 | ||||||||
\(317\) | 6.97987 | 0.392029 | 0.196014 | − | 0.980601i | \(-0.437200\pi\) | ||||
0.196014 | + | 0.980601i | \(0.437200\pi\) | |||||||
\(318\) | 22.1525 | 1.24225 | ||||||||
\(319\) | 11.1719 | 0.625505 | ||||||||
\(320\) | −28.7191 | −1.60544 | ||||||||
\(321\) | 3.10612 | 0.173366 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.622311 | 0.0346263 | ||||||||
\(324\) | 1.87725 | 0.104291 | ||||||||
\(325\) | 31.9314 | 1.77124 | ||||||||
\(326\) | 23.7082 | 1.31308 | ||||||||
\(327\) | −10.4576 | −0.578308 | ||||||||
\(328\) | 0.241710 | 0.0133462 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 39.4810 | 2.17336 | ||||||||
\(331\) | 10.6727 | 0.586626 | 0.293313 | − | 0.956016i | \(-0.405242\pi\) | ||||
0.293313 | + | 0.956016i | \(0.405242\pi\) | |||||||
\(332\) | −6.66192 | −0.365620 | ||||||||
\(333\) | 1.26983 | 0.0695864 | ||||||||
\(334\) | 15.9329 | 0.871808 | ||||||||
\(335\) | −11.2686 | −0.615671 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.30369 | −0.288910 | −0.144455 | − | 0.989511i | \(-0.546143\pi\) | ||||
−0.144455 | + | 0.989511i | \(0.546143\pi\) | |||||||
\(338\) | 11.3774 | 0.618850 | ||||||||
\(339\) | 8.24364 | 0.447733 | ||||||||
\(340\) | 25.7975 | 1.39907 | ||||||||
\(341\) | −3.82219 | −0.206983 | ||||||||
\(342\) | −0.366374 | −0.0198113 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.71930 | −0.146615 | ||||||||
\(345\) | −23.6137 | −1.27132 | ||||||||
\(346\) | −12.3566 | −0.664293 | ||||||||
\(347\) | 5.01085 | 0.268996 | 0.134498 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134498 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(348\) | −4.29767 | −0.230379 | ||||||||
\(349\) | −30.8522 | −1.65148 | −0.825740 | − | 0.564051i | \(-0.809242\pi\) | ||||
−0.825740 | + | 0.564051i | \(0.809242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.68737 | −0.143441 | ||||||||
\(352\) | 38.2910 | 2.04092 | ||||||||
\(353\) | 6.06809 | 0.322972 | 0.161486 | − | 0.986875i | \(-0.448371\pi\) | ||||
0.161486 | + | 0.986875i | \(0.448371\pi\) | |||||||
\(354\) | 23.5980 | 1.25422 | ||||||||
\(355\) | 27.0986 | 1.43825 | ||||||||
\(356\) | −17.0638 | −0.904382 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.1844 | −2.17666 | ||||||||
\(359\) | 14.9483 | 0.788940 | 0.394470 | − | 0.918909i | \(-0.370928\pi\) | ||||
0.394470 | + | 0.918909i | \(0.370928\pi\) | |||||||
\(360\) | 0.993134 | 0.0523427 | ||||||||
\(361\) | −18.9654 | −0.998178 | ||||||||
\(362\) | 3.07169 | 0.161445 | ||||||||
\(363\) | −12.8138 | −0.672548 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6940 | −0.821461 | ||||||||
\(366\) | 2.68103 | 0.140139 | ||||||||
\(367\) | −24.3316 | −1.27010 | −0.635051 | − | 0.772470i | \(-0.719021\pi\) | ||||
−0.635051 | + | 0.772470i | \(0.719021\pi\) | |||||||
\(368\) | −24.3129 | −1.26740 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −10.2736 | −0.534097 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.47035 | 0.0762339 | ||||||||
\(373\) | −24.1138 | −1.24856 | −0.624281 | − | 0.781200i | \(-0.714608\pi\) | ||||
−0.624281 | + | 0.781200i | \(0.714608\pi\) | |||||||
\(374\) | −32.1381 | −1.66182 | ||||||||
\(375\) | −28.2768 | −1.46021 | ||||||||
\(376\) | −0.554003 | −0.0285705 | ||||||||
\(377\) | 6.15232 | 0.316861 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.8760 | 1.99692 | 0.998462 | − | 0.0554442i | \(-0.0176575\pi\) | ||||
0.998462 | + | 0.0554442i | \(0.0176575\pi\) | |||||||
\(380\) | 1.43515 | 0.0736216 | ||||||||
\(381\) | −17.7620 | −0.909973 | ||||||||
\(382\) | 33.9004 | 1.73449 | ||||||||
\(383\) | −2.85283 | −0.145773 | −0.0728865 | − | 0.997340i | \(-0.523221\pi\) | ||||
−0.0728865 | + | 0.997340i | \(0.523221\pi\) | |||||||
\(384\) | 1.93004 | 0.0984920 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.4671 | 1.60163 | ||||||||
\(387\) | −11.2503 | −0.571882 | ||||||||
\(388\) | 18.8246 | 0.955675 | ||||||||
\(389\) | 3.62480 | 0.183785 | 0.0918924 | − | 0.995769i | \(-0.470708\pi\) | ||||
0.0918924 | + | 0.995769i | \(0.470708\pi\) | |||||||
\(390\) | 21.7421 | 1.10095 | ||||||||
\(391\) | 19.2219 | 0.972093 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.1215 | 0.611448 | ||||||||
\(394\) | −18.3698 | −0.925456 | ||||||||
\(395\) | −44.1890 | −2.22339 | ||||||||
\(396\) | 9.16084 | 0.460350 | ||||||||
\(397\) | 24.5418 | 1.23172 | 0.615859 | − | 0.787857i | \(-0.288809\pi\) | ||||
0.615859 | + | 0.787857i | \(0.288809\pi\) | |||||||
\(398\) | −24.8291 | −1.24457 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −50.2662 | −2.51331 | ||||||||
\(401\) | −16.6130 | −0.829612 | −0.414806 | − | 0.909910i | \(-0.636151\pi\) | ||||
−0.414806 | + | 0.909910i | \(0.636151\pi\) | |||||||
\(402\) | −5.40033 | −0.269344 | ||||||||
\(403\) | −2.10487 | −0.104851 | ||||||||
\(404\) | 10.6497 | 0.529844 | ||||||||
\(405\) | 4.10878 | 0.204167 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.19670 | 0.307159 | ||||||||
\(408\) | −0.808424 | −0.0400230 | ||||||||
\(409\) | −6.47251 | −0.320045 | −0.160023 | − | 0.987113i | \(-0.551157\pi\) | ||||
−0.160023 | + | 0.987113i | \(0.551157\pi\) | |||||||
\(410\) | −8.09048 | −0.399560 | ||||||||
\(411\) | −13.6412 | −0.672873 | ||||||||
\(412\) | 16.1260 | 0.794470 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −11.3165 | −0.556178 | ||||||||
\(415\) | −14.5811 | −0.715758 | ||||||||
\(416\) | 21.0867 | 1.03386 | ||||||||
\(417\) | −7.04836 | −0.345159 | ||||||||
\(418\) | −1.78788 | −0.0874482 | ||||||||
\(419\) | −36.5645 | −1.78629 | −0.893145 | − | 0.449768i | \(-0.851507\pi\) | ||||
−0.893145 | + | 0.449768i | \(0.851507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.5817 | 0.954352 | 0.477176 | − | 0.878808i | \(-0.341660\pi\) | ||||
0.477176 | + | 0.878808i | \(0.341660\pi\) | |||||||
\(422\) | 31.3136 | 1.52432 | ||||||||
\(423\) | −2.29201 | −0.111441 | ||||||||
\(424\) | 2.71929 | 0.132060 | ||||||||
\(425\) | 39.7407 | 1.92771 | ||||||||
\(426\) | 12.9866 | 0.629204 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.83094 | −0.281849 | ||||||||
\(429\) | −13.1142 | −0.633158 | ||||||||
\(430\) | 91.0199 | 4.38937 | ||||||||
\(431\) | −14.7266 | −0.709358 | −0.354679 | − | 0.934988i | \(-0.615410\pi\) | ||||
−0.354679 | + | 0.934988i | \(0.615410\pi\) | |||||||
\(432\) | 4.23044 | 0.203537 | ||||||||
\(433\) | −36.9867 | −1.77747 | −0.888734 | − | 0.458423i | \(-0.848414\pi\) | ||||
−0.888734 | + | 0.458423i | \(0.848414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.40642 | −0.451003 | ||||||||
\(436\) | 19.6316 | 0.940181 | ||||||||
\(437\) | 1.06934 | 0.0511534 | ||||||||
\(438\) | −7.52112 | −0.359373 | ||||||||
\(439\) | −37.3318 | −1.78175 | −0.890875 | − | 0.454248i | \(-0.849908\pi\) | ||||
−0.890875 | + | 0.454248i | \(0.849908\pi\) | |||||||
\(440\) | 4.84643 | 0.231044 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.6983 | −0.841824 | ||||||||
\(443\) | 12.9322 | 0.614427 | 0.307214 | − | 0.951641i | \(-0.400603\pi\) | ||||
0.307214 | + | 0.951641i | \(0.400603\pi\) | |||||||
\(444\) | −2.38379 | −0.113130 | ||||||||
\(445\) | −37.3481 | −1.77047 | ||||||||
\(446\) | 57.1153 | 2.70449 | ||||||||
\(447\) | 22.0836 | 1.04452 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.2013 | 0.764585 | 0.382293 | − | 0.924041i | \(-0.375135\pi\) | ||||
0.382293 | + | 0.924041i | \(0.375135\pi\) | |||||||
\(450\) | −23.3966 | −1.10293 | ||||||||
\(451\) | 4.87993 | 0.229787 | ||||||||
\(452\) | −15.4754 | −0.727899 | ||||||||
\(453\) | 13.9955 | 0.657566 | ||||||||
\(454\) | 40.0613 | 1.88017 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.0449737 | −0.00210609 | ||||||||
\(457\) | 34.1158 | 1.59587 | 0.797934 | − | 0.602745i | \(-0.205926\pi\) | ||||
0.797934 | + | 0.602745i | \(0.205926\pi\) | |||||||
\(458\) | 48.5852 | 2.27024 | ||||||||
\(459\) | −3.34460 | −0.156113 | ||||||||
\(460\) | 44.3288 | 2.06684 | ||||||||
\(461\) | 4.85915 | 0.226313 | 0.113157 | − | 0.993577i | \(-0.463904\pi\) | ||||
0.113157 | + | 0.993577i | \(0.463904\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.8794 | 0.691505 | 0.345752 | − | 0.938326i | \(-0.387624\pi\) | ||||
0.345752 | + | 0.938326i | \(0.387624\pi\) | |||||||
\(464\) | −9.68495 | −0.449612 | ||||||||
\(465\) | 3.21818 | 0.149240 | ||||||||
\(466\) | −13.9599 | −0.646681 | ||||||||
\(467\) | 10.9481 | 0.506616 | 0.253308 | − | 0.967386i | \(-0.418481\pi\) | ||||
0.253308 | + | 0.967386i | \(0.418481\pi\) | |||||||
\(468\) | 5.04485 | 0.233198 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.5435 | 0.855346 | ||||||||
\(471\) | 22.2994 | 1.02750 | ||||||||
\(472\) | 2.89673 | 0.133333 | ||||||||
\(473\) | −54.9005 | −2.52433 | ||||||||
\(474\) | −21.1769 | −0.972689 | ||||||||
\(475\) | 2.21083 | 0.101440 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.2502 | 0.515111 | ||||||||
\(478\) | 38.0923 | 1.74230 | ||||||||
\(479\) | −12.9076 | −0.589765 | −0.294882 | − | 0.955534i | \(-0.595281\pi\) | ||||
−0.294882 | + | 0.955534i | \(0.595281\pi\) | |||||||
\(480\) | −32.2400 | −1.47155 | ||||||||
\(481\) | 3.41251 | 0.155597 | ||||||||
\(482\) | −52.3043 | −2.38239 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.0546 | 1.09339 | ||||||||
\(485\) | 41.2019 | 1.87088 | ||||||||
\(486\) | 1.96907 | 0.0893189 | ||||||||
\(487\) | 36.1750 | 1.63925 | 0.819623 | − | 0.572903i | \(-0.194183\pi\) | ||||
0.819623 | + | 0.572903i | \(0.194183\pi\) | |||||||
\(488\) | 0.329105 | 0.0148979 | ||||||||
\(489\) | 12.0403 | 0.544482 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.5961 | −1.20027 | −0.600134 | − | 0.799900i | \(-0.704886\pi\) | ||||
−0.600134 | + | 0.799900i | \(0.704886\pi\) | |||||||
\(492\) | −1.87725 | −0.0846328 | ||||||||
\(493\) | 7.65695 | 0.344852 | ||||||||
\(494\) | −0.984582 | −0.0442984 | ||||||||
\(495\) | 20.0506 | 0.901206 | ||||||||
\(496\) | 3.31348 | 0.148779 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.98778 | −0.313130 | ||||||||
\(499\) | 2.92760 | 0.131058 | 0.0655288 | − | 0.997851i | \(-0.479127\pi\) | ||||
0.0655288 | + | 0.997851i | \(0.479127\pi\) | |||||||
\(500\) | 53.0825 | 2.37392 | ||||||||
\(501\) | 8.09156 | 0.361504 | ||||||||
\(502\) | 51.1872 | 2.28460 | ||||||||
\(503\) | −24.7773 | −1.10477 | −0.552383 | − | 0.833590i | \(-0.686281\pi\) | ||||
−0.552383 | + | 0.833590i | \(0.686281\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.3093 | 1.03725 | ||||||||
\(506\) | −55.2240 | −2.45501 | ||||||||
\(507\) | 5.77806 | 0.256613 | ||||||||
\(508\) | 33.3436 | 1.47938 | ||||||||
\(509\) | −0.0377927 | −0.00167513 | −0.000837566 | − | 1.00000i | \(-0.500267\pi\) | ||||
−0.000837566 | 1.00000i | \(0.500267\pi\) | ||||||||
\(510\) | 27.0594 | 1.19821 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −31.1496 | −1.37663 | ||||||||
\(513\) | −0.186064 | −0.00821494 | ||||||||
\(514\) | 41.5664 | 1.83341 | ||||||||
\(515\) | 35.2953 | 1.55530 | ||||||||
\(516\) | 21.1195 | 0.929734 | ||||||||
\(517\) | −11.1849 | −0.491910 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.27533 | −0.275456 | ||||||||
\(520\) | 2.66891 | 0.117040 | ||||||||
\(521\) | 31.0842 | 1.36182 | 0.680911 | − | 0.732366i | \(-0.261584\pi\) | ||||
0.680911 | + | 0.732366i | \(0.261584\pi\) | |||||||
\(522\) | −4.50789 | −0.197305 | ||||||||
\(523\) | 3.42589 | 0.149804 | 0.0749018 | − | 0.997191i | \(-0.476136\pi\) | ||||
0.0749018 | + | 0.997191i | \(0.476136\pi\) | |||||||
\(524\) | −22.7550 | −0.994057 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.6969 | 0.902428 | ||||||||
\(527\) | −2.61965 | −0.114114 | ||||||||
\(528\) | 20.6443 | 0.898426 | ||||||||
\(529\) | 10.0297 | 0.436072 | ||||||||
\(530\) | −91.0195 | −3.95363 | ||||||||
\(531\) | 11.9843 | 0.520075 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.68737 | 0.116403 | ||||||||
\(534\) | −17.8985 | −0.774545 | ||||||||
\(535\) | −12.7623 | −0.551764 | ||||||||
\(536\) | −0.662909 | −0.0286333 | ||||||||
\(537\) | −20.9156 | −0.902576 | ||||||||
\(538\) | 41.7042 | 1.79800 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.71319 | −0.331923 | ||||||||
\(541\) | −18.9563 | −0.814996 | −0.407498 | − | 0.913206i | \(-0.633599\pi\) | ||||
−0.407498 | + | 0.913206i | \(0.633599\pi\) | |||||||
\(542\) | −4.99757 | −0.214664 | ||||||||
\(543\) | 1.55997 | 0.0669447 | ||||||||
\(544\) | 26.2438 | 1.12519 | ||||||||
\(545\) | 42.9681 | 1.84055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.9021 | 1.27852 | 0.639261 | − | 0.768989i | \(-0.279240\pi\) | ||||
0.639261 | + | 0.768989i | \(0.279240\pi\) | |||||||
\(548\) | 25.6080 | 1.09392 | ||||||||
\(549\) | 1.36157 | 0.0581103 | ||||||||
\(550\) | −114.174 | −4.86839 | ||||||||
\(551\) | 0.425966 | 0.0181468 | ||||||||
\(552\) | −1.38914 | −0.0591259 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −39.9466 | −1.69717 | ||||||||
\(555\) | −5.21746 | −0.221469 | ||||||||
\(556\) | 13.2315 | 0.561141 | ||||||||
\(557\) | 39.7964 | 1.68623 | 0.843114 | − | 0.537735i | \(-0.180720\pi\) | ||||
0.843114 | + | 0.537735i | \(0.180720\pi\) | |||||||
\(558\) | 1.54227 | 0.0652895 | ||||||||
\(559\) | −30.2335 | −1.27874 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.3214 | −0.689091 | ||||||||
\(562\) | 35.9842 | 1.51790 | ||||||||
\(563\) | −19.6406 | −0.827754 | −0.413877 | − | 0.910333i | \(-0.635826\pi\) | ||||
−0.413877 | + | 0.910333i | \(0.635826\pi\) | |||||||
\(564\) | 4.30267 | 0.181175 | ||||||||
\(565\) | −33.8713 | −1.42498 | ||||||||
\(566\) | −8.16044 | −0.343009 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.59415 | 0.0668892 | ||||||||
\(569\) | 19.4591 | 0.815766 | 0.407883 | − | 0.913034i | \(-0.366267\pi\) | ||||
0.407883 | + | 0.913034i | \(0.366267\pi\) | |||||||
\(570\) | 1.50535 | 0.0630522 | ||||||||
\(571\) | −12.9550 | −0.542150 | −0.271075 | − | 0.962558i | \(-0.587379\pi\) | ||||
−0.271075 | + | 0.962558i | \(0.587379\pi\) | |||||||
\(572\) | 24.6185 | 1.02935 | ||||||||
\(573\) | 17.2164 | 0.719226 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 68.2878 | 2.84780 | ||||||||
\(576\) | −6.98969 | −0.291237 | ||||||||
\(577\) | −16.9641 | −0.706225 | −0.353113 | − | 0.935581i | \(-0.614877\pi\) | ||||
−0.353113 | + | 0.935581i | \(0.614877\pi\) | |||||||
\(578\) | 11.4475 | 0.476154 | ||||||||
\(579\) | 15.9807 | 0.664134 | ||||||||
\(580\) | 17.6582 | 0.733216 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 19.7454 | 0.818474 | ||||||||
\(583\) | 54.9002 | 2.27373 | ||||||||
\(584\) | −0.923243 | −0.0382041 | ||||||||
\(585\) | 11.0418 | 0.456522 | ||||||||
\(586\) | 4.10725 | 0.169669 | ||||||||
\(587\) | 39.4502 | 1.62828 | 0.814142 | − | 0.580667i | \(-0.197208\pi\) | ||||
0.814142 | + | 0.580667i | \(0.197208\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.145734 | −0.00600488 | ||||||||
\(590\) | −96.9589 | −3.99173 | ||||||||
\(591\) | −9.32916 | −0.383750 | ||||||||
\(592\) | −5.37195 | −0.220786 | ||||||||
\(593\) | 12.4924 | 0.513003 | 0.256501 | − | 0.966544i | \(-0.417430\pi\) | ||||
0.256501 | + | 0.966544i | \(0.417430\pi\) | |||||||
\(594\) | 9.60894 | 0.394260 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −41.4564 | −1.69812 | ||||||||
\(597\) | −12.6095 | −0.516074 | ||||||||
\(598\) | −30.4117 | −1.24363 | ||||||||
\(599\) | −42.6285 | −1.74175 | −0.870876 | − | 0.491502i | \(-0.836448\pi\) | ||||
−0.870876 | + | 0.491502i | \(0.836448\pi\) | |||||||
\(600\) | −2.87201 | −0.117249 | ||||||||
\(601\) | 45.6087 | 1.86042 | 0.930210 | − | 0.367028i | \(-0.119625\pi\) | ||||
0.930210 | + | 0.367028i | \(0.119625\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.74258 | −0.111686 | ||||||||
\(604\) | −26.2730 | −1.06903 | ||||||||
\(605\) | 52.6489 | 2.14048 | ||||||||
\(606\) | 11.1707 | 0.453777 | ||||||||
\(607\) | 14.2458 | 0.578220 | 0.289110 | − | 0.957296i | \(-0.406641\pi\) | ||||
0.289110 | + | 0.957296i | \(0.406641\pi\) | |||||||
\(608\) | 1.45998 | 0.0592099 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.0157 | −0.446014 | ||||||||
\(611\) | −6.15947 | −0.249186 | ||||||||
\(612\) | 6.27864 | 0.253799 | ||||||||
\(613\) | 43.8828 | 1.77241 | 0.886206 | − | 0.463292i | \(-0.153332\pi\) | ||||
0.886206 | + | 0.463292i | \(0.153332\pi\) | |||||||
\(614\) | 12.4112 | 0.500874 | ||||||||
\(615\) | −4.10878 | −0.165682 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.1419 | 1.65631 | 0.828154 | − | 0.560500i | \(-0.189391\pi\) | ||||
0.828154 | + | 0.560500i | \(0.189391\pi\) | |||||||
\(618\) | 16.9148 | 0.680413 | ||||||||
\(619\) | −17.9272 | −0.720556 | −0.360278 | − | 0.932845i | \(-0.617318\pi\) | ||||
−0.360278 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(620\) | −6.04133 | −0.242625 | ||||||||
\(621\) | −5.74714 | −0.230625 | ||||||||
\(622\) | 32.2624 | 1.29360 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11.3687 | 0.455114 | ||||||||
\(625\) | 56.7727 | 2.27091 | ||||||||
\(626\) | −27.7822 | −1.11040 | ||||||||
\(627\) | −0.907982 | −0.0362613 | ||||||||
\(628\) | −41.8614 | −1.67045 | ||||||||
\(629\) | 4.24708 | 0.169342 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2409 | 0.407685 | 0.203843 | − | 0.979004i | \(-0.434657\pi\) | ||||
0.203843 | + | 0.979004i | \(0.434657\pi\) | |||||||
\(632\) | −2.59954 | −0.103404 | ||||||||
\(633\) | 15.9027 | 0.632077 | ||||||||
\(634\) | −13.7439 | −0.545839 | ||||||||
\(635\) | 72.9800 | 2.89612 | ||||||||
\(636\) | −21.1194 | −0.837438 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21.9982 | −0.870918 | ||||||||
\(639\) | 6.59530 | 0.260906 | ||||||||
\(640\) | −7.93010 | −0.313465 | ||||||||
\(641\) | 26.1190 | 1.03164 | 0.515819 | − | 0.856697i | \(-0.327488\pi\) | ||||
0.515819 | + | 0.856697i | \(0.327488\pi\) | |||||||
\(642\) | −6.11617 | −0.241386 | ||||||||
\(643\) | −21.4692 | −0.846662 | −0.423331 | − | 0.905975i | \(-0.639139\pi\) | ||||
−0.423331 | + | 0.905975i | \(0.639139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 46.2248 | 1.82010 | ||||||||
\(646\) | −1.22538 | −0.0482117 | ||||||||
\(647\) | −0.229609 | −0.00902684 | −0.00451342 | − | 0.999990i | \(-0.501437\pi\) | ||||
−0.00451342 | + | 0.999990i | \(0.501437\pi\) | |||||||
\(648\) | 0.241710 | 0.00949528 | ||||||||
\(649\) | 58.4827 | 2.29565 | ||||||||
\(650\) | −62.8752 | −2.46617 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.6026 | −0.885187 | ||||||||
\(653\) | 15.5172 | 0.607234 | 0.303617 | − | 0.952794i | \(-0.401806\pi\) | ||||
0.303617 | + | 0.952794i | \(0.401806\pi\) | |||||||
\(654\) | 20.5918 | 0.805204 | ||||||||
\(655\) | −49.8044 | −1.94602 | ||||||||
\(656\) | −4.23044 | −0.165171 | ||||||||
\(657\) | −3.81962 | −0.149018 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.0279 | 1.67613 | 0.838064 | − | 0.545571i | \(-0.183687\pi\) | ||||
0.838064 | + | 0.545571i | \(0.183687\pi\) | |||||||
\(660\) | −37.6398 | −1.46513 | ||||||||
\(661\) | −43.4018 | −1.68814 | −0.844068 | − | 0.536236i | \(-0.819846\pi\) | ||||
−0.844068 | + | 0.536236i | \(0.819846\pi\) | |||||||
\(662\) | −21.0154 | −0.816786 | ||||||||
\(663\) | −8.98816 | −0.349071 | ||||||||
\(664\) | −0.857774 | −0.0332881 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.50039 | −0.0968883 | ||||||||
\(667\) | 13.1572 | 0.509449 | ||||||||
\(668\) | −15.1899 | −0.587713 | ||||||||
\(669\) | 29.0062 | 1.12144 | ||||||||
\(670\) | 22.1887 | 0.857226 | ||||||||
\(671\) | 6.64436 | 0.256503 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.47233 | −0.249490 | −0.124745 | − | 0.992189i | \(-0.539811\pi\) | ||||
−0.124745 | + | 0.992189i | \(0.539811\pi\) | |||||||
\(674\) | 10.4433 | 0.402263 | ||||||||
\(675\) | −11.8820 | −0.457340 | ||||||||
\(676\) | −10.8468 | −0.417187 | ||||||||
\(677\) | −27.7353 | −1.06595 | −0.532977 | − | 0.846130i | \(-0.678927\pi\) | ||||
−0.532977 | + | 0.846130i | \(0.678927\pi\) | |||||||
\(678\) | −16.2323 | −0.623399 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.32163 | 0.127379 | ||||||||
\(681\) | 20.3453 | 0.779633 | ||||||||
\(682\) | 7.52617 | 0.288192 | ||||||||
\(683\) | 20.3012 | 0.776803 | 0.388401 | − | 0.921490i | \(-0.373027\pi\) | ||||
0.388401 | + | 0.921490i | \(0.373027\pi\) | |||||||
\(684\) | 0.349289 | 0.0133554 | ||||||||
\(685\) | 56.0488 | 2.14151 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.6741 | 0.941378 | ||||||||
\(688\) | 47.5935 | 1.81449 | ||||||||
\(689\) | 30.2334 | 1.15180 | ||||||||
\(690\) | 46.4971 | 1.77012 | ||||||||
\(691\) | −38.7781 | −1.47519 | −0.737593 | − | 0.675245i | \(-0.764038\pi\) | ||||
−0.737593 | + | 0.675245i | \(0.764038\pi\) | |||||||
\(692\) | 11.7803 | 0.447821 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.86672 | −0.374535 | ||||||||
\(695\) | 28.9601 | 1.09852 | ||||||||
\(696\) | −0.553359 | −0.0209750 | ||||||||
\(697\) | 3.34460 | 0.126686 | ||||||||
\(698\) | 60.7502 | 2.29943 | ||||||||
\(699\) | −7.08960 | −0.268153 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.57108 | 0.210417 | 0.105208 | − | 0.994450i | \(-0.466449\pi\) | ||||
0.105208 | + | 0.994450i | \(0.466449\pi\) | |||||||
\(702\) | 5.29162 | 0.199719 | ||||||||
\(703\) | 0.236271 | 0.00891112 | ||||||||
\(704\) | −34.1092 | −1.28554 | ||||||||
\(705\) | 9.41736 | 0.354678 | ||||||||
\(706\) | −11.9485 | −0.449688 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −22.4975 | −0.845509 | ||||||||
\(709\) | −17.4267 | −0.654473 | −0.327236 | − | 0.944942i | \(-0.606117\pi\) | ||||
−0.327236 | + | 0.944942i | \(0.606117\pi\) | |||||||
\(710\) | −53.3592 | −2.00253 | ||||||||
\(711\) | −10.7548 | −0.403336 | ||||||||
\(712\) | −2.19710 | −0.0823400 | ||||||||
\(713\) | −4.50143 | −0.168580 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 53.8832 | 2.01512 | ||||||||
\(716\) | 39.2638 | 1.46736 | ||||||||
\(717\) | 19.3453 | 0.722464 | ||||||||
\(718\) | −29.4343 | −1.09848 | ||||||||
\(719\) | 43.7743 | 1.63250 | 0.816252 | − | 0.577696i | \(-0.196048\pi\) | ||||
0.816252 | + | 0.577696i | \(0.196048\pi\) | |||||||
\(720\) | −17.3819 | −0.647786 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37.3442 | 1.38981 | ||||||||
\(723\) | −26.5629 | −0.987885 | ||||||||
\(724\) | −2.92845 | −0.108835 | ||||||||
\(725\) | 27.2021 | 1.01026 | ||||||||
\(726\) | 25.2312 | 0.936418 | ||||||||
\(727\) | 34.2841 | 1.27153 | 0.635763 | − | 0.771885i | \(-0.280686\pi\) | ||||
0.635763 | + | 0.771885i | \(0.280686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 30.9026 | 1.14376 | ||||||||
\(731\) | −37.6276 | −1.39171 | ||||||||
\(732\) | −2.55600 | −0.0944724 | ||||||||
\(733\) | −20.6748 | −0.763640 | −0.381820 | − | 0.924237i | \(-0.624703\pi\) | ||||
−0.381820 | + | 0.924237i | \(0.624703\pi\) | |||||||
\(734\) | 47.9108 | 1.76842 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 45.0956 | 1.66225 | ||||||||
\(737\) | −13.3836 | −0.492991 | ||||||||
\(738\) | −1.96907 | −0.0724826 | ||||||||
\(739\) | −45.0202 | −1.65610 | −0.828048 | − | 0.560657i | \(-0.810549\pi\) | ||||
−0.828048 | + | 0.560657i | \(0.810549\pi\) | |||||||
\(740\) | 9.79446 | 0.360052 | ||||||||
\(741\) | −0.500023 | −0.0183688 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.4216 | −0.859256 | −0.429628 | − | 0.903006i | \(-0.641355\pi\) | ||||
−0.429628 | + | 0.903006i | \(0.641355\pi\) | |||||||
\(744\) | 0.189319 | 0.00694076 | ||||||||
\(745\) | −90.7366 | −3.32433 | ||||||||
\(746\) | 47.4817 | 1.73843 | ||||||||
\(747\) | −3.54877 | −0.129843 | ||||||||
\(748\) | 30.6393 | 1.12029 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 55.6790 | 2.03311 | ||||||||
\(751\) | 24.0476 | 0.877509 | 0.438754 | − | 0.898607i | \(-0.355420\pi\) | ||||
0.438754 | + | 0.898607i | \(0.355420\pi\) | |||||||
\(752\) | 9.69621 | 0.353584 | ||||||||
\(753\) | 25.9956 | 0.947333 | ||||||||
\(754\) | −12.1144 | −0.441179 | ||||||||
\(755\) | −57.5044 | −2.09280 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.0114 | −1.89039 | −0.945194 | − | 0.326510i | \(-0.894127\pi\) | ||||
−0.945194 | + | 0.326510i | \(0.894127\pi\) | |||||||
\(758\) | −76.5496 | −2.78041 | ||||||||
\(759\) | −28.0457 | −1.01799 | ||||||||
\(760\) | 0.184787 | 0.00670292 | ||||||||
\(761\) | −16.0058 | −0.580209 | −0.290104 | − | 0.956995i | \(-0.593690\pi\) | ||||
−0.290104 | + | 0.956995i | \(0.593690\pi\) | |||||||
\(762\) | 34.9746 | 1.26700 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −32.3195 | −1.16928 | ||||||||
\(765\) | 13.7422 | 0.496851 | ||||||||
\(766\) | 5.61743 | 0.202966 | ||||||||
\(767\) | 32.2063 | 1.16290 | ||||||||
\(768\) | −17.7798 | −0.641572 | ||||||||
\(769\) | −42.7047 | −1.53997 | −0.769985 | − | 0.638062i | \(-0.779737\pi\) | ||||
−0.769985 | + | 0.638062i | \(0.779737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.1096 | 0.760244 | ||||||||
\(772\) | −29.9997 | −1.07971 | ||||||||
\(773\) | 13.8164 | 0.496943 | 0.248471 | − | 0.968639i | \(-0.420072\pi\) | ||||
0.248471 | + | 0.968639i | \(0.420072\pi\) | |||||||
\(774\) | 22.1526 | 0.796257 | ||||||||
\(775\) | −9.30657 | −0.334302 | ||||||||
\(776\) | 2.42382 | 0.0870100 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.13750 | −0.255892 | ||||||||
\(779\) | 0.186064 | 0.00666645 | ||||||||
\(780\) | −20.7282 | −0.742187 | ||||||||
\(781\) | 32.1847 | 1.15166 | ||||||||
\(782\) | −37.8493 | −1.35349 | ||||||||
\(783\) | −2.28935 | −0.0818147 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −91.6231 | −3.27017 | ||||||||
\(786\) | −23.8681 | −0.851346 | ||||||||
\(787\) | 5.73213 | 0.204328 | 0.102164 | − | 0.994768i | \(-0.467423\pi\) | ||||
0.102164 | + | 0.994768i | \(0.467423\pi\) | |||||||
\(788\) | 17.5131 | 0.623879 | ||||||||
\(789\) | 10.5110 | 0.374201 | ||||||||
\(790\) | 87.0113 | 3.09572 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.17953 | 0.0419128 | ||||||||
\(793\) | 3.65903 | 0.129936 | ||||||||
\(794\) | −48.3246 | −1.71498 | ||||||||
\(795\) | −46.2245 | −1.63942 | ||||||||
\(796\) | 23.6712 | 0.839004 | ||||||||
\(797\) | 4.96900 | 0.176011 | 0.0880055 | − | 0.996120i | \(-0.471951\pi\) | ||||
0.0880055 | + | 0.996120i | \(0.471951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.66586 | −0.271198 | ||||||||
\(800\) | 93.2339 | 3.29631 | ||||||||
\(801\) | −9.08983 | −0.321173 | ||||||||
\(802\) | 32.7121 | 1.15511 | ||||||||
\(803\) | −18.6395 | −0.657774 | ||||||||
\(804\) | 5.14849 | 0.181573 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.14464 | 0.145989 | ||||||||
\(807\) | 21.1796 | 0.745559 | ||||||||
\(808\) | 1.37124 | 0.0482399 | ||||||||
\(809\) | 48.0152 | 1.68813 | 0.844063 | − | 0.536244i | \(-0.180157\pi\) | ||||
0.844063 | + | 0.536244i | \(0.180157\pi\) | |||||||
\(810\) | −8.09048 | −0.284270 | ||||||||
\(811\) | 15.3782 | 0.540003 | 0.270001 | − | 0.962860i | \(-0.412976\pi\) | ||||
0.270001 | + | 0.962860i | \(0.412976\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.53803 | −0.0890127 | ||||||||
\(814\) | −12.2018 | −0.427671 | ||||||||
\(815\) | −49.4709 | −1.73289 | ||||||||
\(816\) | 14.1491 | 0.495318 | ||||||||
\(817\) | −2.09327 | −0.0732343 | ||||||||
\(818\) | 12.7449 | 0.445613 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.71319 | 0.269356 | ||||||||
\(821\) | −8.08265 | −0.282086 | −0.141043 | − | 0.990003i | \(-0.545046\pi\) | ||||
−0.141043 | + | 0.990003i | \(0.545046\pi\) | |||||||
\(822\) | 26.8606 | 0.936871 | ||||||||
\(823\) | 37.3193 | 1.30087 | 0.650435 | − | 0.759562i | \(-0.274587\pi\) | ||||
0.650435 | + | 0.759562i | \(0.274587\pi\) | |||||||
\(824\) | 2.07635 | 0.0723330 | ||||||||
\(825\) | −57.9836 | −2.01873 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.4901 | −0.712510 | −0.356255 | − | 0.934389i | \(-0.615947\pi\) | ||||
−0.356255 | + | 0.934389i | \(0.615947\pi\) | |||||||
\(828\) | 10.7888 | 0.374937 | ||||||||
\(829\) | −32.8011 | −1.13923 | −0.569614 | − | 0.821912i | \(-0.692907\pi\) | ||||
−0.569614 | + | 0.821912i | \(0.692907\pi\) | |||||||
\(830\) | 28.7112 | 0.996582 | ||||||||
\(831\) | −20.2870 | −0.703749 | ||||||||
\(832\) | −18.7838 | −0.651213 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.8787 | 0.480581 | ||||||||
\(835\) | −33.2464 | −1.15054 | ||||||||
\(836\) | 1.70451 | 0.0589516 | ||||||||
\(837\) | 0.783246 | 0.0270730 | ||||||||
\(838\) | 71.9981 | 2.48713 | ||||||||
\(839\) | −10.1261 | −0.349591 | −0.174796 | − | 0.984605i | \(-0.555926\pi\) | ||||
−0.174796 | + | 0.984605i | \(0.555926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7589 | −0.819272 | ||||||||
\(842\) | −38.5577 | −1.32879 | ||||||||
\(843\) | 18.2747 | 0.629413 | ||||||||
\(844\) | −29.8533 | −1.02759 | ||||||||
\(845\) | −23.7408 | −0.816707 | ||||||||
\(846\) | 4.51313 | 0.155165 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −47.5933 | −1.63436 | ||||||||
\(849\) | −4.14431 | −0.142232 | ||||||||
\(850\) | −78.2523 | −2.68403 | ||||||||
\(851\) | 7.29791 | 0.250169 | ||||||||
\(852\) | −12.3810 | −0.424167 | ||||||||
\(853\) | 5.07879 | 0.173894 | 0.0869472 | − | 0.996213i | \(-0.472289\pi\) | ||||
0.0869472 | + | 0.996213i | \(0.472289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.764497 | 0.0261452 | ||||||||
\(856\) | −0.750780 | −0.0256611 | ||||||||
\(857\) | 8.24571 | 0.281668 | 0.140834 | − | 0.990033i | \(-0.455022\pi\) | ||||
0.140834 | + | 0.990033i | \(0.455022\pi\) | |||||||
\(858\) | 25.8228 | 0.881574 | ||||||||
\(859\) | 55.2489 | 1.88507 | 0.942533 | − | 0.334112i | \(-0.108436\pi\) | ||||
0.942533 | + | 0.334112i | \(0.108436\pi\) | |||||||
\(860\) | −86.7753 | −2.95901 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.9978 | 0.987670 | ||||||||
\(863\) | 17.2958 | 0.588757 | 0.294378 | − | 0.955689i | \(-0.404887\pi\) | ||||
0.294378 | + | 0.955689i | \(0.404887\pi\) | |||||||
\(864\) | −7.84662 | −0.266947 | ||||||||
\(865\) | 25.7839 | 0.876679 | ||||||||
\(866\) | 72.8295 | 2.47485 | ||||||||
\(867\) | 5.81366 | 0.197442 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.4826 | −1.78035 | ||||||||
\(870\) | 18.5219 | 0.627952 | ||||||||
\(871\) | −7.37030 | −0.249733 | ||||||||
\(872\) | 2.52772 | 0.0855993 | ||||||||
\(873\) | 10.0278 | 0.339389 | ||||||||
\(874\) | −2.10561 | −0.0712232 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.17038 | 0.242265 | ||||||||
\(877\) | 45.7039 | 1.54331 | 0.771656 | − | 0.636040i | \(-0.219429\pi\) | ||||
0.771656 | + | 0.636040i | \(0.219429\pi\) | |||||||
\(878\) | 73.5091 | 2.48081 | ||||||||
\(879\) | 2.08588 | 0.0703550 | ||||||||
\(880\) | −84.8227 | −2.85937 | ||||||||
\(881\) | 42.8769 | 1.44456 | 0.722279 | − | 0.691602i | \(-0.243095\pi\) | ||||
0.722279 | + | 0.691602i | \(0.243095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.6767 | 0.695826 | 0.347913 | − | 0.937527i | \(-0.386890\pi\) | ||||
0.347913 | + | 0.937527i | \(0.386890\pi\) | |||||||
\(884\) | 16.8730 | 0.567500 | ||||||||
\(885\) | −49.2409 | −1.65521 | ||||||||
\(886\) | −25.4644 | −0.855495 | ||||||||
\(887\) | 17.4997 | 0.587583 | 0.293791 | − | 0.955870i | \(-0.405083\pi\) | ||||
0.293791 | + | 0.955870i | \(0.405083\pi\) | |||||||
\(888\) | −0.306932 | −0.0103000 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 73.5410 | 2.46510 | ||||||||
\(891\) | 4.87993 | 0.163484 | ||||||||
\(892\) | −54.4518 | −1.82318 | ||||||||
\(893\) | −0.426462 | −0.0142710 | ||||||||
\(894\) | −43.4842 | −1.45433 | ||||||||
\(895\) | 85.9377 | 2.87258 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.4447 | −0.515683 | ||||||||
\(898\) | −31.9015 | −1.06457 | ||||||||
\(899\) | −1.79312 | −0.0598040 | ||||||||
\(900\) | 22.3055 | 0.743517 | ||||||||
\(901\) | 37.6274 | 1.25355 | ||||||||
\(902\) | −9.60894 | −0.319943 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.99257 | −0.0662720 | ||||||||
\(905\) | −6.40956 | −0.213061 | ||||||||
\(906\) | −27.5582 | −0.915559 | ||||||||
\(907\) | −23.9979 | −0.796837 | −0.398418 | − | 0.917204i | \(-0.630441\pi\) | ||||
−0.398418 | + | 0.917204i | \(0.630441\pi\) | |||||||
\(908\) | −38.1931 | −1.26748 | ||||||||
\(909\) | 5.67306 | 0.188163 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1362 | −0.435222 | −0.217611 | − | 0.976036i | \(-0.569826\pi\) | ||||
−0.217611 | + | 0.976036i | \(0.569826\pi\) | |||||||
\(912\) | 0.787134 | 0.0260646 | ||||||||
\(913\) | −17.3178 | −0.573134 | ||||||||
\(914\) | −67.1764 | −2.22200 | ||||||||
\(915\) | −5.59438 | −0.184944 | ||||||||
\(916\) | −46.3195 | −1.53044 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.58576 | 0.217362 | ||||||||
\(919\) | 30.7304 | 1.01370 | 0.506852 | − | 0.862033i | \(-0.330809\pi\) | ||||
0.506852 | + | 0.862033i | \(0.330809\pi\) | |||||||
\(920\) | 5.70768 | 0.188177 | ||||||||
\(921\) | 6.30305 | 0.207693 | ||||||||
\(922\) | −9.56803 | −0.315106 | ||||||||
\(923\) | 17.7240 | 0.583392 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0882 | 0.496097 | ||||||||
\(926\) | −29.2986 | −0.962813 | ||||||||
\(927\) | 8.59023 | 0.282140 | ||||||||
\(928\) | 17.9636 | 0.589686 | ||||||||
\(929\) | −30.6801 | −1.00658 | −0.503292 | − | 0.864117i | \(-0.667878\pi\) | ||||
−0.503292 | + | 0.864117i | \(0.667878\pi\) | |||||||
\(930\) | −6.33684 | −0.207793 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.3089 | 0.435948 | ||||||||
\(933\) | 16.3846 | 0.536406 | ||||||||
\(934\) | −21.5575 | −0.705384 | ||||||||
\(935\) | 67.0611 | 2.19313 | ||||||||
\(936\) | 0.649564 | 0.0212317 | ||||||||
\(937\) | −26.1785 | −0.855214 | −0.427607 | − | 0.903965i | \(-0.640643\pi\) | ||||
−0.427607 | + | 0.903965i | \(0.640643\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.1093 | −0.460439 | ||||||||
\(940\) | −17.6787 | −0.576616 | ||||||||
\(941\) | 19.3605 | 0.631135 | 0.315567 | − | 0.948903i | \(-0.397805\pi\) | ||||
0.315567 | + | 0.948903i | \(0.397805\pi\) | |||||||
\(942\) | −43.9091 | −1.43063 | ||||||||
\(943\) | 5.74714 | 0.187153 | ||||||||
\(944\) | −50.6989 | −1.65011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 108.103 | 3.51473 | ||||||||
\(947\) | 28.8451 | 0.937339 | 0.468670 | − | 0.883374i | \(-0.344733\pi\) | ||||
0.468670 | + | 0.883374i | \(0.344733\pi\) | |||||||
\(948\) | 20.1894 | 0.655720 | ||||||||
\(949\) | −10.2647 | −0.333207 | ||||||||
\(950\) | −4.35328 | −0.141239 | ||||||||
\(951\) | −6.97987 | −0.226338 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.3762 | −1.24313 | −0.621563 | − | 0.783364i | \(-0.713502\pi\) | ||||
−0.621563 | + | 0.783364i | \(0.713502\pi\) | |||||||
\(954\) | −22.1525 | −0.717212 | ||||||||
\(955\) | −70.7384 | −2.28904 | ||||||||
\(956\) | −36.3159 | −1.17454 | ||||||||
\(957\) | −11.1719 | −0.361135 | ||||||||
\(958\) | 25.4161 | 0.821156 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 28.7191 | 0.926904 | ||||||||
\(961\) | −30.3865 | −0.980210 | ||||||||
\(962\) | −6.71947 | −0.216645 | ||||||||
\(963\) | −3.10612 | −0.100093 | ||||||||
\(964\) | 49.8651 | 1.60605 | ||||||||
\(965\) | −65.6610 | −2.11370 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.5741 | −1.59419 | −0.797097 | − | 0.603851i | \(-0.793632\pi\) | ||||
−0.797097 | + | 0.603851i | \(0.793632\pi\) | |||||||
\(968\) | 3.09722 | 0.0995484 | ||||||||
\(969\) | −0.622311 | −0.0199915 | ||||||||
\(970\) | −81.1295 | −2.60491 | ||||||||
\(971\) | −13.3866 | −0.429596 | −0.214798 | − | 0.976658i | \(-0.568909\pi\) | ||||
−0.214798 | + | 0.976658i | \(0.568909\pi\) | |||||||
\(972\) | −1.87725 | −0.0602127 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −71.2312 | −2.28240 | ||||||||
\(975\) | −31.9314 | −1.02262 | ||||||||
\(976\) | −5.76003 | −0.184374 | ||||||||
\(977\) | −9.38029 | −0.300102 | −0.150051 | − | 0.988678i | \(-0.547944\pi\) | ||||
−0.150051 | + | 0.988678i | \(0.547944\pi\) | |||||||
\(978\) | −23.7082 | −0.758106 | ||||||||
\(979\) | −44.3578 | −1.41768 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.4576 | 0.333886 | ||||||||
\(982\) | 52.3697 | 1.67119 | ||||||||
\(983\) | 0.842818 | 0.0268817 | 0.0134409 | − | 0.999910i | \(-0.495722\pi\) | ||||
0.0134409 | + | 0.999910i | \(0.495722\pi\) | |||||||
\(984\) | −0.241710 | −0.00770544 | ||||||||
\(985\) | 38.3314 | 1.22134 | ||||||||
\(986\) | −15.0771 | −0.480153 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.938667 | 0.0298630 | ||||||||
\(989\) | −64.6568 | −2.05597 | ||||||||
\(990\) | −39.4810 | −1.25479 | ||||||||
\(991\) | −59.1465 | −1.87885 | −0.939425 | − | 0.342755i | \(-0.888640\pi\) | ||||
−0.939425 | + | 0.342755i | \(0.888640\pi\) | |||||||
\(992\) | −6.14584 | −0.195131 | ||||||||
\(993\) | −10.6727 | −0.338689 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 51.8097 | 1.64248 | ||||||||
\(996\) | 6.66192 | 0.211091 | ||||||||
\(997\) | 1.87911 | 0.0595121 | 0.0297560 | − | 0.999557i | \(-0.490527\pi\) | ||||
0.0297560 | + | 0.999557i | \(0.490527\pi\) | |||||||
\(998\) | −5.76467 | −0.182477 | ||||||||
\(999\) | −1.26983 | −0.0401758 |
(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 | 6027.2.a.bn.1.4 | ✓ | 24 | |
7.6 | odd | 2 | 6027.2.a.bo.1.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.4 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6027.2.a.bo.1.4 | yes | 24 | 7.6 | odd | 2 |