Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.54327 | 0.891007 | 0.445504 | − | 0.895280i | \(-0.353025\pi\) | ||||
0.445504 | + | 0.895280i | \(0.353025\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.0183668 | −0.00821387 | −0.00410694 | − | 0.999992i | \(-0.501307\pi\) | ||||
−0.00410694 | + | 0.999992i | \(0.501307\pi\) | |||||||
\(6\) | 1.54327 | 0.630037 | ||||||||
\(7\) | −4.28156 | −1.61828 | −0.809138 | − | 0.587618i | \(-0.800066\pi\) | ||||
−0.809138 | + | 0.587618i | \(0.800066\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.618317 | −0.206106 | ||||||||
\(10\) | −0.0183668 | −0.00580809 | ||||||||
\(11\) | 2.99582 | 0.903274 | 0.451637 | − | 0.892202i | \(-0.350840\pi\) | ||||
0.451637 | + | 0.892202i | \(0.350840\pi\) | |||||||
\(12\) | 1.54327 | 0.445504 | ||||||||
\(13\) | 4.32372 | 1.19918 | 0.599592 | − | 0.800306i | \(-0.295329\pi\) | ||||
0.599592 | + | 0.800306i | \(0.295329\pi\) | |||||||
\(14\) | −4.28156 | −1.14429 | ||||||||
\(15\) | −0.0283449 | −0.00731862 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.98650 | −1.20940 | −0.604702 | − | 0.796452i | \(-0.706708\pi\) | ||||
−0.604702 | + | 0.796452i | \(0.706708\pi\) | |||||||
\(18\) | −0.618317 | −0.145739 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.0183668 | −0.00410694 | ||||||||
\(21\) | −6.60760 | −1.44190 | ||||||||
\(22\) | 2.99582 | 0.638711 | ||||||||
\(23\) | −3.35613 | −0.699801 | −0.349900 | − | 0.936787i | \(-0.613785\pi\) | ||||
−0.349900 | + | 0.936787i | \(0.613785\pi\) | |||||||
\(24\) | 1.54327 | 0.315019 | ||||||||
\(25\) | −4.99966 | −0.999933 | ||||||||
\(26\) | 4.32372 | 0.847951 | ||||||||
\(27\) | −5.58404 | −1.07465 | ||||||||
\(28\) | −4.28156 | −0.809138 | ||||||||
\(29\) | 3.45887 | 0.642295 | 0.321148 | − | 0.947029i | \(-0.395931\pi\) | ||||
0.321148 | + | 0.947029i | \(0.395931\pi\) | |||||||
\(30\) | −0.0283449 | −0.00517505 | ||||||||
\(31\) | −7.49814 | −1.34671 | −0.673353 | − | 0.739321i | \(-0.735147\pi\) | ||||
−0.673353 | + | 0.739321i | \(0.735147\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.62336 | 0.804824 | ||||||||
\(34\) | −4.98650 | −0.855177 | ||||||||
\(35\) | 0.0786384 | 0.0132923 | ||||||||
\(36\) | −0.618317 | −0.103053 | ||||||||
\(37\) | 0.329578 | 0.0541823 | 0.0270911 | − | 0.999633i | \(-0.491376\pi\) | ||||
0.0270911 | + | 0.999633i | \(0.491376\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 6.67267 | 1.06848 | ||||||||
\(40\) | −0.0183668 | −0.00290404 | ||||||||
\(41\) | 11.3967 | 1.77986 | 0.889930 | − | 0.456098i | \(-0.150753\pi\) | ||||
0.889930 | + | 0.456098i | \(0.150753\pi\) | |||||||
\(42\) | −6.60760 | −1.01957 | ||||||||
\(43\) | −9.79706 | −1.49404 | −0.747019 | − | 0.664803i | \(-0.768516\pi\) | ||||
−0.747019 | + | 0.664803i | \(0.768516\pi\) | |||||||
\(44\) | 2.99582 | 0.451637 | ||||||||
\(45\) | 0.0113565 | 0.00169293 | ||||||||
\(46\) | −3.35613 | −0.494834 | ||||||||
\(47\) | −1.16608 | −0.170091 | −0.0850453 | − | 0.996377i | \(-0.527103\pi\) | ||||
−0.0850453 | + | 0.996377i | \(0.527103\pi\) | |||||||
\(48\) | 1.54327 | 0.222752 | ||||||||
\(49\) | 11.3317 | 1.61882 | ||||||||
\(50\) | −4.99966 | −0.707059 | ||||||||
\(51\) | −7.69551 | −1.07759 | ||||||||
\(52\) | 4.32372 | 0.599592 | ||||||||
\(53\) | −13.1012 | −1.79959 | −0.899793 | − | 0.436317i | \(-0.856283\pi\) | ||||
−0.899793 | + | 0.436317i | \(0.856283\pi\) | |||||||
\(54\) | −5.58404 | −0.759892 | ||||||||
\(55\) | −0.0550236 | −0.00741938 | ||||||||
\(56\) | −4.28156 | −0.572147 | ||||||||
\(57\) | 1.54327 | 0.204411 | ||||||||
\(58\) | 3.45887 | 0.454171 | ||||||||
\(59\) | −8.47759 | −1.10369 | −0.551844 | − | 0.833947i | \(-0.686076\pi\) | ||||
−0.551844 | + | 0.833947i | \(0.686076\pi\) | |||||||
\(60\) | −0.0283449 | −0.00365931 | ||||||||
\(61\) | 1.61162 | 0.206347 | 0.103173 | − | 0.994663i | \(-0.467100\pi\) | ||||
0.103173 | + | 0.994663i | \(0.467100\pi\) | |||||||
\(62\) | −7.49814 | −0.952265 | ||||||||
\(63\) | 2.64736 | 0.333536 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0794128 | −0.00984995 | ||||||||
\(66\) | 4.62336 | 0.569096 | ||||||||
\(67\) | 10.1292 | 1.23748 | 0.618738 | − | 0.785598i | \(-0.287644\pi\) | ||||
0.618738 | + | 0.785598i | \(0.287644\pi\) | |||||||
\(68\) | −4.98650 | −0.604702 | ||||||||
\(69\) | −5.17941 | −0.623528 | ||||||||
\(70\) | 0.0786384 | 0.00939909 | ||||||||
\(71\) | 4.96060 | 0.588715 | 0.294357 | − | 0.955695i | \(-0.404894\pi\) | ||||
0.294357 | + | 0.955695i | \(0.404894\pi\) | |||||||
\(72\) | −0.618317 | −0.0728693 | ||||||||
\(73\) | −16.4077 | −1.92038 | −0.960190 | − | 0.279348i | \(-0.909882\pi\) | ||||
−0.960190 | + | 0.279348i | \(0.909882\pi\) | |||||||
\(74\) | 0.329578 | 0.0383127 | ||||||||
\(75\) | −7.71583 | −0.890947 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −12.8268 | −1.46175 | ||||||||
\(78\) | 6.67267 | 0.755531 | ||||||||
\(79\) | 8.25238 | 0.928466 | 0.464233 | − | 0.885713i | \(-0.346330\pi\) | ||||
0.464233 | + | 0.885713i | \(0.346330\pi\) | |||||||
\(80\) | −0.0183668 | −0.00205347 | ||||||||
\(81\) | −6.76273 | −0.751415 | ||||||||
\(82\) | 11.3967 | 1.25855 | ||||||||
\(83\) | −3.64838 | −0.400462 | −0.200231 | − | 0.979749i | \(-0.564169\pi\) | ||||
−0.200231 | + | 0.979749i | \(0.564169\pi\) | |||||||
\(84\) | −6.60760 | −0.720948 | ||||||||
\(85\) | 0.0915859 | 0.00993389 | ||||||||
\(86\) | −9.79706 | −1.05644 | ||||||||
\(87\) | 5.33796 | 0.572290 | ||||||||
\(88\) | 2.99582 | 0.319356 | ||||||||
\(89\) | −8.09860 | −0.858450 | −0.429225 | − | 0.903198i | \(-0.641213\pi\) | ||||
−0.429225 | + | 0.903198i | \(0.641213\pi\) | |||||||
\(90\) | 0.0113565 | 0.00119708 | ||||||||
\(91\) | −18.5123 | −1.94061 | ||||||||
\(92\) | −3.35613 | −0.349900 | ||||||||
\(93\) | −11.5717 | −1.19993 | ||||||||
\(94\) | −1.16608 | −0.120272 | ||||||||
\(95\) | −0.0183668 | −0.00188439 | ||||||||
\(96\) | 1.54327 | 0.157509 | ||||||||
\(97\) | 2.65533 | 0.269608 | 0.134804 | − | 0.990872i | \(-0.456960\pi\) | ||||
0.134804 | + | 0.990872i | \(0.456960\pi\) | |||||||
\(98\) | 11.3317 | 1.14468 | ||||||||
\(99\) | −1.85237 | −0.186170 | ||||||||
\(100\) | −4.99966 | −0.499966 | ||||||||
\(101\) | −7.01241 | −0.697760 | −0.348880 | − | 0.937167i | \(-0.613438\pi\) | ||||
−0.348880 | + | 0.937167i | \(0.613438\pi\) | |||||||
\(102\) | −7.69551 | −0.761969 | ||||||||
\(103\) | 6.04519 | 0.595650 | 0.297825 | − | 0.954620i | \(-0.403739\pi\) | ||||
0.297825 | + | 0.954620i | \(0.403739\pi\) | |||||||
\(104\) | 4.32372 | 0.423976 | ||||||||
\(105\) | 0.121360 | 0.0118436 | ||||||||
\(106\) | −13.1012 | −1.27250 | ||||||||
\(107\) | 6.69195 | 0.646936 | 0.323468 | − | 0.946239i | \(-0.395151\pi\) | ||||
0.323468 | + | 0.946239i | \(0.395151\pi\) | |||||||
\(108\) | −5.58404 | −0.537325 | ||||||||
\(109\) | −6.28126 | −0.601636 | −0.300818 | − | 0.953682i | \(-0.597260\pi\) | ||||
−0.300818 | + | 0.953682i | \(0.597260\pi\) | |||||||
\(110\) | −0.0550236 | −0.00524629 | ||||||||
\(111\) | 0.508628 | 0.0482768 | ||||||||
\(112\) | −4.28156 | −0.404569 | ||||||||
\(113\) | −8.76071 | −0.824138 | −0.412069 | − | 0.911153i | \(-0.635194\pi\) | ||||
−0.412069 | + | 0.911153i | \(0.635194\pi\) | |||||||
\(114\) | 1.54327 | 0.144541 | ||||||||
\(115\) | 0.0616412 | 0.00574808 | ||||||||
\(116\) | 3.45887 | 0.321148 | ||||||||
\(117\) | −2.67343 | −0.247159 | ||||||||
\(118\) | −8.47759 | −0.780426 | ||||||||
\(119\) | 21.3500 | 1.95715 | ||||||||
\(120\) | −0.0283449 | −0.00258752 | ||||||||
\(121\) | −2.02506 | −0.184096 | ||||||||
\(122\) | 1.61162 | 0.145909 | ||||||||
\(123\) | 17.5881 | 1.58587 | ||||||||
\(124\) | −7.49814 | −0.673353 | ||||||||
\(125\) | 0.183662 | 0.0164272 | ||||||||
\(126\) | 2.64736 | 0.235846 | ||||||||
\(127\) | −7.07855 | −0.628119 | −0.314060 | − | 0.949403i | \(-0.601689\pi\) | ||||
−0.314060 | + | 0.949403i | \(0.601689\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −15.1195 | −1.33120 | ||||||||
\(130\) | −0.0794128 | −0.00696496 | ||||||||
\(131\) | 11.2562 | 0.983457 | 0.491729 | − | 0.870748i | \(-0.336365\pi\) | ||||
0.491729 | + | 0.870748i | \(0.336365\pi\) | |||||||
\(132\) | 4.62336 | 0.402412 | ||||||||
\(133\) | −4.28156 | −0.371258 | ||||||||
\(134\) | 10.1292 | 0.875027 | ||||||||
\(135\) | 0.102561 | 0.00882703 | ||||||||
\(136\) | −4.98650 | −0.427589 | ||||||||
\(137\) | −1.46424 | −0.125098 | −0.0625492 | − | 0.998042i | \(-0.519923\pi\) | ||||
−0.0625492 | + | 0.998042i | \(0.519923\pi\) | |||||||
\(138\) | −5.17941 | −0.440901 | ||||||||
\(139\) | −18.8318 | −1.59729 | −0.798647 | − | 0.601800i | \(-0.794451\pi\) | ||||
−0.798647 | + | 0.601800i | \(0.794451\pi\) | |||||||
\(140\) | 0.0786384 | 0.00664616 | ||||||||
\(141\) | −1.79958 | −0.151552 | ||||||||
\(142\) | 4.96060 | 0.416284 | ||||||||
\(143\) | 12.9531 | 1.08319 | ||||||||
\(144\) | −0.618317 | −0.0515264 | ||||||||
\(145\) | −0.0635282 | −0.00527573 | ||||||||
\(146\) | −16.4077 | −1.35791 | ||||||||
\(147\) | 17.4879 | 1.44238 | ||||||||
\(148\) | 0.329578 | 0.0270911 | ||||||||
\(149\) | −23.1725 | −1.89837 | −0.949183 | − | 0.314725i | \(-0.898088\pi\) | ||||
−0.949183 | + | 0.314725i | \(0.898088\pi\) | |||||||
\(150\) | −7.71583 | −0.629995 | ||||||||
\(151\) | 7.66353 | 0.623650 | 0.311825 | − | 0.950140i | \(-0.399060\pi\) | ||||
0.311825 | + | 0.950140i | \(0.399060\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 3.08324 | 0.249265 | ||||||||
\(154\) | −12.8268 | −1.03361 | ||||||||
\(155\) | 0.137717 | 0.0110617 | ||||||||
\(156\) | 6.67267 | 0.534241 | ||||||||
\(157\) | 9.09348 | 0.725739 | 0.362869 | − | 0.931840i | \(-0.381797\pi\) | ||||
0.362869 | + | 0.931840i | \(0.381797\pi\) | |||||||
\(158\) | 8.25238 | 0.656524 | ||||||||
\(159\) | −20.2187 | −1.60344 | ||||||||
\(160\) | −0.0183668 | −0.00145202 | ||||||||
\(161\) | 14.3695 | 1.13247 | ||||||||
\(162\) | −6.76273 | −0.531331 | ||||||||
\(163\) | 10.6542 | 0.834500 | 0.417250 | − | 0.908792i | \(-0.362994\pi\) | ||||
0.417250 | + | 0.908792i | \(0.362994\pi\) | |||||||
\(164\) | 11.3967 | 0.889930 | ||||||||
\(165\) | −0.0849163 | −0.00661072 | ||||||||
\(166\) | −3.64838 | −0.283169 | ||||||||
\(167\) | −11.4669 | −0.887337 | −0.443669 | − | 0.896191i | \(-0.646323\pi\) | ||||
−0.443669 | + | 0.896191i | \(0.646323\pi\) | |||||||
\(168\) | −6.60760 | −0.509787 | ||||||||
\(169\) | 5.69456 | 0.438043 | ||||||||
\(170\) | 0.0915859 | 0.00702432 | ||||||||
\(171\) | −0.618317 | −0.0472839 | ||||||||
\(172\) | −9.79706 | −0.747019 | ||||||||
\(173\) | −1.51469 | −0.115160 | −0.0575799 | − | 0.998341i | \(-0.518338\pi\) | ||||
−0.0575799 | + | 0.998341i | \(0.518338\pi\) | |||||||
\(174\) | 5.33796 | 0.404670 | ||||||||
\(175\) | 21.4063 | 1.61817 | ||||||||
\(176\) | 2.99582 | 0.225818 | ||||||||
\(177\) | −13.0832 | −0.983395 | ||||||||
\(178\) | −8.09860 | −0.607016 | ||||||||
\(179\) | 11.9286 | 0.891586 | 0.445793 | − | 0.895136i | \(-0.352922\pi\) | ||||
0.445793 | + | 0.895136i | \(0.352922\pi\) | |||||||
\(180\) | 0.0113565 | 0.000846463 0 | ||||||||
\(181\) | −10.4087 | −0.773676 | −0.386838 | − | 0.922148i | \(-0.626433\pi\) | ||||
−0.386838 | + | 0.922148i | \(0.626433\pi\) | |||||||
\(182\) | −18.5123 | −1.37222 | ||||||||
\(183\) | 2.48716 | 0.183856 | ||||||||
\(184\) | −3.35613 | −0.247417 | ||||||||
\(185\) | −0.00605328 | −0.000445046 0 | ||||||||
\(186\) | −11.5717 | −0.848476 | ||||||||
\(187\) | −14.9387 | −1.09242 | ||||||||
\(188\) | −1.16608 | −0.0850453 | ||||||||
\(189\) | 23.9084 | 1.73908 | ||||||||
\(190\) | −0.0183668 | −0.00133247 | ||||||||
\(191\) | −6.81941 | −0.493435 | −0.246718 | − | 0.969087i | \(-0.579352\pi\) | ||||
−0.246718 | + | 0.969087i | \(0.579352\pi\) | |||||||
\(192\) | 1.54327 | 0.111376 | ||||||||
\(193\) | −0.388352 | −0.0279542 | −0.0139771 | − | 0.999902i | \(-0.504449\pi\) | ||||
−0.0139771 | + | 0.999902i | \(0.504449\pi\) | |||||||
\(194\) | 2.65533 | 0.190641 | ||||||||
\(195\) | −0.122555 | −0.00877638 | ||||||||
\(196\) | 11.3317 | 0.809410 | ||||||||
\(197\) | −7.14947 | −0.509379 | −0.254689 | − | 0.967023i | \(-0.581973\pi\) | ||||
−0.254689 | + | 0.967023i | \(0.581973\pi\) | |||||||
\(198\) | −1.85237 | −0.131642 | ||||||||
\(199\) | 15.4828 | 1.09755 | 0.548774 | − | 0.835971i | \(-0.315095\pi\) | ||||
0.548774 | + | 0.835971i | \(0.315095\pi\) | |||||||
\(200\) | −4.99966 | −0.353530 | ||||||||
\(201\) | 15.6320 | 1.10260 | ||||||||
\(202\) | −7.01241 | −0.493391 | ||||||||
\(203\) | −14.8093 | −1.03941 | ||||||||
\(204\) | −7.69551 | −0.538794 | ||||||||
\(205\) | −0.209320 | −0.0146195 | ||||||||
\(206\) | 6.04519 | 0.421188 | ||||||||
\(207\) | 2.07515 | 0.144233 | ||||||||
\(208\) | 4.32372 | 0.299796 | ||||||||
\(209\) | 2.99582 | 0.207225 | ||||||||
\(210\) | 0.121360 | 0.00837466 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −13.1012 | −0.899793 | ||||||||
\(213\) | 7.65555 | 0.524549 | ||||||||
\(214\) | 6.69195 | 0.457453 | ||||||||
\(215\) | 0.179940 | 0.0122718 | ||||||||
\(216\) | −5.58404 | −0.379946 | ||||||||
\(217\) | 32.1037 | 2.17934 | ||||||||
\(218\) | −6.28126 | −0.425421 | ||||||||
\(219\) | −25.3216 | −1.71107 | ||||||||
\(220\) | −0.0550236 | −0.00370969 | ||||||||
\(221\) | −21.5602 | −1.45030 | ||||||||
\(222\) | 0.508628 | 0.0341369 | ||||||||
\(223\) | −8.09141 | −0.541841 | −0.270921 | − | 0.962602i | \(-0.587328\pi\) | ||||
−0.270921 | + | 0.962602i | \(0.587328\pi\) | |||||||
\(224\) | −4.28156 | −0.286074 | ||||||||
\(225\) | 3.09138 | 0.206092 | ||||||||
\(226\) | −8.76071 | −0.582754 | ||||||||
\(227\) | 5.20647 | 0.345566 | 0.172783 | − | 0.984960i | \(-0.444724\pi\) | ||||
0.172783 | + | 0.984960i | \(0.444724\pi\) | |||||||
\(228\) | 1.54327 | 0.102206 | ||||||||
\(229\) | 17.2283 | 1.13848 | 0.569238 | − | 0.822173i | \(-0.307238\pi\) | ||||
0.569238 | + | 0.822173i | \(0.307238\pi\) | |||||||
\(230\) | 0.0616412 | 0.00406450 | ||||||||
\(231\) | −19.7952 | −1.30243 | ||||||||
\(232\) | 3.45887 | 0.227086 | ||||||||
\(233\) | −2.72435 | −0.178478 | −0.0892389 | − | 0.996010i | \(-0.528443\pi\) | ||||
−0.0892389 | + | 0.996010i | \(0.528443\pi\) | |||||||
\(234\) | −2.67343 | −0.174768 | ||||||||
\(235\) | 0.0214172 | 0.00139710 | ||||||||
\(236\) | −8.47759 | −0.551844 | ||||||||
\(237\) | 12.7357 | 0.827270 | ||||||||
\(238\) | 21.3500 | 1.38391 | ||||||||
\(239\) | −19.9630 | −1.29130 | −0.645650 | − | 0.763634i | \(-0.723413\pi\) | ||||
−0.645650 | + | 0.763634i | \(0.723413\pi\) | |||||||
\(240\) | −0.0283449 | −0.00182966 | ||||||||
\(241\) | −11.8516 | −0.763429 | −0.381714 | − | 0.924280i | \(-0.624666\pi\) | ||||
−0.381714 | + | 0.924280i | \(0.624666\pi\) | |||||||
\(242\) | −2.02506 | −0.130176 | ||||||||
\(243\) | 6.31540 | 0.405133 | ||||||||
\(244\) | 1.61162 | 0.103173 | ||||||||
\(245\) | −0.208128 | −0.0132968 | ||||||||
\(246\) | 17.5881 | 1.12138 | ||||||||
\(247\) | 4.32372 | 0.275112 | ||||||||
\(248\) | −7.49814 | −0.476133 | ||||||||
\(249\) | −5.63044 | −0.356815 | ||||||||
\(250\) | 0.183662 | 0.0116158 | ||||||||
\(251\) | 14.8904 | 0.939874 | 0.469937 | − | 0.882700i | \(-0.344277\pi\) | ||||
0.469937 | + | 0.882700i | \(0.344277\pi\) | |||||||
\(252\) | 2.64736 | 0.166768 | ||||||||
\(253\) | −10.0544 | −0.632112 | ||||||||
\(254\) | −7.07855 | −0.444148 | ||||||||
\(255\) | 0.141342 | 0.00885117 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.5355 | 1.40572 | 0.702862 | − | 0.711327i | \(-0.251905\pi\) | ||||
0.702862 | + | 0.711327i | \(0.251905\pi\) | |||||||
\(258\) | −15.1195 | −0.941300 | ||||||||
\(259\) | −1.41111 | −0.0876819 | ||||||||
\(260\) | −0.0794128 | −0.00492497 | ||||||||
\(261\) | −2.13868 | −0.132381 | ||||||||
\(262\) | 11.2562 | 0.695409 | ||||||||
\(263\) | −1.27361 | −0.0785344 | −0.0392672 | − | 0.999229i | \(-0.512502\pi\) | ||||
−0.0392672 | + | 0.999229i | \(0.512502\pi\) | |||||||
\(264\) | 4.62336 | 0.284548 | ||||||||
\(265\) | 0.240627 | 0.0147816 | ||||||||
\(266\) | −4.28156 | −0.262519 | ||||||||
\(267\) | −12.4983 | −0.764886 | ||||||||
\(268\) | 10.1292 | 0.618738 | ||||||||
\(269\) | 17.6740 | 1.07760 | 0.538802 | − | 0.842432i | \(-0.318877\pi\) | ||||
0.538802 | + | 0.842432i | \(0.318877\pi\) | |||||||
\(270\) | 0.102561 | 0.00624165 | ||||||||
\(271\) | 1.59875 | 0.0971172 | 0.0485586 | − | 0.998820i | \(-0.484537\pi\) | ||||
0.0485586 | + | 0.998820i | \(0.484537\pi\) | |||||||
\(272\) | −4.98650 | −0.302351 | ||||||||
\(273\) | −28.5694 | −1.72910 | ||||||||
\(274\) | −1.46424 | −0.0884579 | ||||||||
\(275\) | −14.9781 | −0.903213 | ||||||||
\(276\) | −5.17941 | −0.311764 | ||||||||
\(277\) | −7.10665 | −0.426997 | −0.213498 | − | 0.976943i | \(-0.568486\pi\) | ||||
−0.213498 | + | 0.976943i | \(0.568486\pi\) | |||||||
\(278\) | −18.8318 | −1.12946 | ||||||||
\(279\) | 4.63623 | 0.277564 | ||||||||
\(280\) | 0.0786384 | 0.00469954 | ||||||||
\(281\) | 10.6124 | 0.633081 | 0.316540 | − | 0.948579i | \(-0.397479\pi\) | ||||
0.316540 | + | 0.948579i | \(0.397479\pi\) | |||||||
\(282\) | −1.79958 | −0.107163 | ||||||||
\(283\) | −25.6020 | −1.52188 | −0.760941 | − | 0.648821i | \(-0.775262\pi\) | ||||
−0.760941 | + | 0.648821i | \(0.775262\pi\) | |||||||
\(284\) | 4.96060 | 0.294357 | ||||||||
\(285\) | −0.0283449 | −0.00167901 | ||||||||
\(286\) | 12.9531 | 0.765932 | ||||||||
\(287\) | −48.7955 | −2.88031 | ||||||||
\(288\) | −0.618317 | −0.0364347 | ||||||||
\(289\) | 7.86516 | 0.462656 | ||||||||
\(290\) | −0.0635282 | −0.00373051 | ||||||||
\(291\) | 4.09789 | 0.240222 | ||||||||
\(292\) | −16.4077 | −0.960190 | ||||||||
\(293\) | −25.4146 | −1.48474 | −0.742368 | − | 0.669992i | \(-0.766297\pi\) | ||||
−0.742368 | + | 0.669992i | \(0.766297\pi\) | |||||||
\(294\) | 17.4879 | 1.01992 | ||||||||
\(295\) | 0.155706 | 0.00906556 | ||||||||
\(296\) | 0.329578 | 0.0191563 | ||||||||
\(297\) | −16.7288 | −0.970703 | ||||||||
\(298\) | −23.1725 | −1.34235 | ||||||||
\(299\) | −14.5110 | −0.839190 | ||||||||
\(300\) | −7.71583 | −0.445474 | ||||||||
\(301\) | 41.9467 | 2.41777 | ||||||||
\(302\) | 7.66353 | 0.440987 | ||||||||
\(303\) | −10.8220 | −0.621710 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −0.0296002 | −0.00169490 | ||||||||
\(306\) | 3.08324 | 0.176257 | ||||||||
\(307\) | 24.5408 | 1.40062 | 0.700310 | − | 0.713839i | \(-0.253045\pi\) | ||||
0.700310 | + | 0.713839i | \(0.253045\pi\) | |||||||
\(308\) | −12.8268 | −0.730874 | ||||||||
\(309\) | 9.32936 | 0.530729 | ||||||||
\(310\) | 0.137717 | 0.00782179 | ||||||||
\(311\) | 12.3101 | 0.698042 | 0.349021 | − | 0.937115i | \(-0.386514\pi\) | ||||
0.349021 | + | 0.937115i | \(0.386514\pi\) | |||||||
\(312\) | 6.67267 | 0.377765 | ||||||||
\(313\) | 0.609964 | 0.0344772 | 0.0172386 | − | 0.999851i | \(-0.494513\pi\) | ||||
0.0172386 | + | 0.999851i | \(0.494513\pi\) | |||||||
\(314\) | 9.09348 | 0.513175 | ||||||||
\(315\) | −0.0486235 | −0.00273962 | ||||||||
\(316\) | 8.25238 | 0.464233 | ||||||||
\(317\) | −25.1406 | −1.41203 | −0.706017 | − | 0.708194i | \(-0.749510\pi\) | ||||
−0.706017 | + | 0.708194i | \(0.749510\pi\) | |||||||
\(318\) | −20.2187 | −1.13381 | ||||||||
\(319\) | 10.3621 | 0.580169 | ||||||||
\(320\) | −0.0183668 | −0.00102673 | ||||||||
\(321\) | 10.3275 | 0.576424 | ||||||||
\(322\) | 14.3695 | 0.800778 | ||||||||
\(323\) | −4.98650 | −0.277456 | ||||||||
\(324\) | −6.76273 | −0.375707 | ||||||||
\(325\) | −21.6171 | −1.19910 | ||||||||
\(326\) | 10.6542 | 0.590080 | ||||||||
\(327\) | −9.69368 | −0.536062 | ||||||||
\(328\) | 11.3967 | 0.629275 | ||||||||
\(329\) | 4.99265 | 0.275254 | ||||||||
\(330\) | −0.0849163 | −0.00467449 | ||||||||
\(331\) | −20.7309 | −1.13947 | −0.569737 | − | 0.821827i | \(-0.692955\pi\) | ||||
−0.569737 | + | 0.821827i | \(0.692955\pi\) | |||||||
\(332\) | −3.64838 | −0.200231 | ||||||||
\(333\) | −0.203784 | −0.0111673 | ||||||||
\(334\) | −11.4669 | −0.627442 | ||||||||
\(335\) | −0.186040 | −0.0101645 | ||||||||
\(336\) | −6.60760 | −0.360474 | ||||||||
\(337\) | −16.8322 | −0.916910 | −0.458455 | − | 0.888718i | \(-0.651597\pi\) | ||||
−0.458455 | + | 0.888718i | \(0.651597\pi\) | |||||||
\(338\) | 5.69456 | 0.309743 | ||||||||
\(339\) | −13.5201 | −0.734313 | ||||||||
\(340\) | 0.0915859 | 0.00496694 | ||||||||
\(341\) | −22.4631 | −1.21644 | ||||||||
\(342\) | −0.618317 | −0.0334347 | ||||||||
\(343\) | −18.5466 | −1.00142 | ||||||||
\(344\) | −9.79706 | −0.528222 | ||||||||
\(345\) | 0.0951291 | 0.00512158 | ||||||||
\(346\) | −1.51469 | −0.0814303 | ||||||||
\(347\) | −34.3472 | −1.84385 | −0.921927 | − | 0.387363i | \(-0.873386\pi\) | ||||
−0.921927 | + | 0.387363i | \(0.873386\pi\) | |||||||
\(348\) | 5.33796 | 0.286145 | ||||||||
\(349\) | 4.32477 | 0.231500 | 0.115750 | − | 0.993278i | \(-0.463073\pi\) | ||||
0.115750 | + | 0.993278i | \(0.463073\pi\) | |||||||
\(350\) | 21.4063 | 1.14422 | ||||||||
\(351\) | −24.1438 | −1.28870 | ||||||||
\(352\) | 2.99582 | 0.159678 | ||||||||
\(353\) | −35.6842 | −1.89928 | −0.949638 | − | 0.313349i | \(-0.898549\pi\) | ||||
−0.949638 | + | 0.313349i | \(0.898549\pi\) | |||||||
\(354\) | −13.0832 | −0.695365 | ||||||||
\(355\) | −0.0911102 | −0.00483563 | ||||||||
\(356\) | −8.09860 | −0.429225 | ||||||||
\(357\) | 32.9488 | 1.74383 | ||||||||
\(358\) | 11.9286 | 0.630447 | ||||||||
\(359\) | 7.05580 | 0.372391 | 0.186195 | − | 0.982513i | \(-0.440384\pi\) | ||||
0.186195 | + | 0.982513i | \(0.440384\pi\) | |||||||
\(360\) | 0.0113565 | 0.000598540 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −10.4087 | −0.547071 | ||||||||
\(363\) | −3.12521 | −0.164031 | ||||||||
\(364\) | −18.5123 | −0.970306 | ||||||||
\(365\) | 0.301357 | 0.0157738 | ||||||||
\(366\) | 2.48716 | 0.130006 | ||||||||
\(367\) | −27.3530 | −1.42782 | −0.713908 | − | 0.700240i | \(-0.753076\pi\) | ||||
−0.713908 | + | 0.700240i | \(0.753076\pi\) | |||||||
\(368\) | −3.35613 | −0.174950 | ||||||||
\(369\) | −7.04675 | −0.366839 | ||||||||
\(370\) | −0.00605328 | −0.000314695 0 | ||||||||
\(371\) | 56.0935 | 2.91223 | ||||||||
\(372\) | −11.5717 | −0.599963 | ||||||||
\(373\) | 25.0734 | 1.29825 | 0.649126 | − | 0.760681i | \(-0.275135\pi\) | ||||
0.649126 | + | 0.760681i | \(0.275135\pi\) | |||||||
\(374\) | −14.9387 | −0.772459 | ||||||||
\(375\) | 0.283439 | 0.0146368 | ||||||||
\(376\) | −1.16608 | −0.0601361 | ||||||||
\(377\) | 14.9552 | 0.770230 | ||||||||
\(378\) | 23.9084 | 1.22972 | ||||||||
\(379\) | −24.1253 | −1.23923 | −0.619616 | − | 0.784905i | \(-0.712712\pi\) | ||||
−0.619616 | + | 0.784905i | \(0.712712\pi\) | |||||||
\(380\) | −0.0183668 | −0.000942196 0 | ||||||||
\(381\) | −10.9241 | −0.559659 | ||||||||
\(382\) | −6.81941 | −0.348911 | ||||||||
\(383\) | 12.0159 | 0.613982 | 0.306991 | − | 0.951712i | \(-0.400678\pi\) | ||||
0.306991 | + | 0.951712i | \(0.400678\pi\) | |||||||
\(384\) | 1.54327 | 0.0787547 | ||||||||
\(385\) | 0.235587 | 0.0120066 | ||||||||
\(386\) | −0.388352 | −0.0197666 | ||||||||
\(387\) | 6.05769 | 0.307930 | ||||||||
\(388\) | 2.65533 | 0.134804 | ||||||||
\(389\) | 26.8420 | 1.36095 | 0.680473 | − | 0.732774i | \(-0.261775\pi\) | ||||
0.680473 | + | 0.732774i | \(0.261775\pi\) | |||||||
\(390\) | −0.122555 | −0.00620584 | ||||||||
\(391\) | 16.7353 | 0.846341 | ||||||||
\(392\) | 11.3317 | 0.572339 | ||||||||
\(393\) | 17.3713 | 0.876268 | ||||||||
\(394\) | −7.14947 | −0.360185 | ||||||||
\(395\) | −0.151570 | −0.00762630 | ||||||||
\(396\) | −1.85237 | −0.0930849 | ||||||||
\(397\) | 13.3275 | 0.668890 | 0.334445 | − | 0.942415i | \(-0.391451\pi\) | ||||
0.334445 | + | 0.942415i | \(0.391451\pi\) | |||||||
\(398\) | 15.4828 | 0.776084 | ||||||||
\(399\) | −6.60760 | −0.330794 | ||||||||
\(400\) | −4.99966 | −0.249983 | ||||||||
\(401\) | 10.0490 | 0.501824 | 0.250912 | − | 0.968010i | \(-0.419269\pi\) | ||||
0.250912 | + | 0.968010i | \(0.419269\pi\) | |||||||
\(402\) | 15.6320 | 0.779656 | ||||||||
\(403\) | −32.4199 | −1.61495 | ||||||||
\(404\) | −7.01241 | −0.348880 | ||||||||
\(405\) | 0.124210 | 0.00617203 | ||||||||
\(406\) | −14.8093 | −0.734975 | ||||||||
\(407\) | 0.987356 | 0.0489414 | ||||||||
\(408\) | −7.69551 | −0.380985 | ||||||||
\(409\) | −26.9528 | −1.33273 | −0.666365 | − | 0.745625i | \(-0.732151\pi\) | ||||
−0.666365 | + | 0.745625i | \(0.732151\pi\) | |||||||
\(410\) | −0.209320 | −0.0103376 | ||||||||
\(411\) | −2.25972 | −0.111464 | ||||||||
\(412\) | 6.04519 | 0.297825 | ||||||||
\(413\) | 36.2973 | 1.78607 | ||||||||
\(414\) | 2.07515 | 0.101988 | ||||||||
\(415\) | 0.0670091 | 0.00328935 | ||||||||
\(416\) | 4.32372 | 0.211988 | ||||||||
\(417\) | −29.0626 | −1.42320 | ||||||||
\(418\) | 2.99582 | 0.146530 | ||||||||
\(419\) | 13.2440 | 0.647013 | 0.323507 | − | 0.946226i | \(-0.395138\pi\) | ||||
0.323507 | + | 0.946226i | \(0.395138\pi\) | |||||||
\(420\) | 0.121360 | 0.00592178 | ||||||||
\(421\) | 1.92237 | 0.0936908 | 0.0468454 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468454 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 0.721008 | 0.0350566 | ||||||||
\(424\) | −13.1012 | −0.636250 | ||||||||
\(425\) | 24.9308 | 1.20932 | ||||||||
\(426\) | 7.65555 | 0.370912 | ||||||||
\(427\) | −6.90024 | −0.333926 | ||||||||
\(428\) | 6.69195 | 0.323468 | ||||||||
\(429\) | 19.9901 | 0.965132 | ||||||||
\(430\) | 0.179940 | 0.00867750 | ||||||||
\(431\) | 19.3188 | 0.930556 | 0.465278 | − | 0.885165i | \(-0.345954\pi\) | ||||
0.465278 | + | 0.885165i | \(0.345954\pi\) | |||||||
\(432\) | −5.58404 | −0.268662 | ||||||||
\(433\) | 6.94110 | 0.333568 | 0.166784 | − | 0.985993i | \(-0.446662\pi\) | ||||
0.166784 | + | 0.985993i | \(0.446662\pi\) | |||||||
\(434\) | 32.1037 | 1.54103 | ||||||||
\(435\) | −0.0980412 | −0.00470072 | ||||||||
\(436\) | −6.28126 | −0.300818 | ||||||||
\(437\) | −3.35613 | −0.160545 | ||||||||
\(438\) | −25.3216 | −1.20991 | ||||||||
\(439\) | 15.0788 | 0.719670 | 0.359835 | − | 0.933016i | \(-0.382833\pi\) | ||||
0.359835 | + | 0.933016i | \(0.382833\pi\) | |||||||
\(440\) | −0.0550236 | −0.00262315 | ||||||||
\(441\) | −7.00660 | −0.333648 | ||||||||
\(442\) | −21.5602 | −1.02552 | ||||||||
\(443\) | −23.4720 | −1.11519 | −0.557594 | − | 0.830114i | \(-0.688275\pi\) | ||||
−0.557594 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(444\) | 0.508628 | 0.0241384 | ||||||||
\(445\) | 0.148745 | 0.00705120 | ||||||||
\(446\) | −8.09141 | −0.383140 | ||||||||
\(447\) | −35.7614 | −1.69146 | ||||||||
\(448\) | −4.28156 | −0.202285 | ||||||||
\(449\) | 30.7862 | 1.45289 | 0.726445 | − | 0.687225i | \(-0.241171\pi\) | ||||
0.726445 | + | 0.687225i | \(0.241171\pi\) | |||||||
\(450\) | 3.09138 | 0.145729 | ||||||||
\(451\) | 34.1424 | 1.60770 | ||||||||
\(452\) | −8.76071 | −0.412069 | ||||||||
\(453\) | 11.8269 | 0.555676 | ||||||||
\(454\) | 5.20647 | 0.244352 | ||||||||
\(455\) | 0.340011 | 0.0159399 | ||||||||
\(456\) | 1.54327 | 0.0722703 | ||||||||
\(457\) | 29.0387 | 1.35837 | 0.679185 | − | 0.733967i | \(-0.262333\pi\) | ||||
0.679185 | + | 0.733967i | \(0.262333\pi\) | |||||||
\(458\) | 17.2283 | 0.805023 | ||||||||
\(459\) | 27.8448 | 1.29968 | ||||||||
\(460\) | 0.0616412 | 0.00287404 | ||||||||
\(461\) | −31.6706 | −1.47505 | −0.737524 | − | 0.675321i | \(-0.764005\pi\) | ||||
−0.737524 | + | 0.675321i | \(0.764005\pi\) | |||||||
\(462\) | −19.7952 | −0.920955 | ||||||||
\(463\) | 9.65031 | 0.448488 | 0.224244 | − | 0.974533i | \(-0.428009\pi\) | ||||
0.224244 | + | 0.974533i | \(0.428009\pi\) | |||||||
\(464\) | 3.45887 | 0.160574 | ||||||||
\(465\) | 0.212534 | 0.00985604 | ||||||||
\(466\) | −2.72435 | −0.126203 | ||||||||
\(467\) | 22.4722 | 1.03989 | 0.519946 | − | 0.854199i | \(-0.325952\pi\) | ||||
0.519946 | + | 0.854199i | \(0.325952\pi\) | |||||||
\(468\) | −2.67343 | −0.123579 | ||||||||
\(469\) | −43.3686 | −2.00258 | ||||||||
\(470\) | 0.0214172 | 0.000987900 0 | ||||||||
\(471\) | 14.0337 | 0.646639 | ||||||||
\(472\) | −8.47759 | −0.390213 | ||||||||
\(473\) | −29.3502 | −1.34953 | ||||||||
\(474\) | 12.7357 | 0.584968 | ||||||||
\(475\) | −4.99966 | −0.229400 | ||||||||
\(476\) | 21.3500 | 0.978575 | ||||||||
\(477\) | 8.10068 | 0.370905 | ||||||||
\(478\) | −19.9630 | −0.913087 | ||||||||
\(479\) | 28.5859 | 1.30612 | 0.653062 | − | 0.757305i | \(-0.273484\pi\) | ||||
0.653062 | + | 0.757305i | \(0.273484\pi\) | |||||||
\(480\) | −0.0283449 | −0.00129376 | ||||||||
\(481\) | 1.42500 | 0.0649745 | ||||||||
\(482\) | −11.8516 | −0.539826 | ||||||||
\(483\) | 22.1759 | 1.00904 | ||||||||
\(484\) | −2.02506 | −0.0920481 | ||||||||
\(485\) | −0.0487698 | −0.00221452 | ||||||||
\(486\) | 6.31540 | 0.286472 | ||||||||
\(487\) | −18.7107 | −0.847863 | −0.423931 | − | 0.905694i | \(-0.639350\pi\) | ||||
−0.423931 | + | 0.905694i | \(0.639350\pi\) | |||||||
\(488\) | 1.61162 | 0.0729545 | ||||||||
\(489\) | 16.4423 | 0.743545 | ||||||||
\(490\) | −0.208128 | −0.00940224 | ||||||||
\(491\) | 42.0521 | 1.89778 | 0.948892 | − | 0.315602i | \(-0.102206\pi\) | ||||
0.948892 | + | 0.315602i | \(0.102206\pi\) | |||||||
\(492\) | 17.5881 | 0.792934 | ||||||||
\(493\) | −17.2476 | −0.776794 | ||||||||
\(494\) | 4.32372 | 0.194533 | ||||||||
\(495\) | 0.0340220 | 0.00152918 | ||||||||
\(496\) | −7.49814 | −0.336677 | ||||||||
\(497\) | −21.2391 | −0.952704 | ||||||||
\(498\) | −5.63044 | −0.252306 | ||||||||
\(499\) | −28.9174 | −1.29452 | −0.647261 | − | 0.762268i | \(-0.724086\pi\) | ||||
−0.647261 | + | 0.762268i | \(0.724086\pi\) | |||||||
\(500\) | 0.183662 | 0.00821360 | ||||||||
\(501\) | −17.6966 | −0.790624 | ||||||||
\(502\) | 14.8904 | 0.664591 | ||||||||
\(503\) | −11.7612 | −0.524407 | −0.262203 | − | 0.965013i | \(-0.584449\pi\) | ||||
−0.262203 | + | 0.965013i | \(0.584449\pi\) | |||||||
\(504\) | 2.64736 | 0.117923 | ||||||||
\(505\) | 0.128795 | 0.00573132 | ||||||||
\(506\) | −10.0544 | −0.446971 | ||||||||
\(507\) | 8.78824 | 0.390299 | ||||||||
\(508\) | −7.07855 | −0.314060 | ||||||||
\(509\) | −13.7154 | −0.607924 | −0.303962 | − | 0.952684i | \(-0.598310\pi\) | ||||
−0.303962 | + | 0.952684i | \(0.598310\pi\) | |||||||
\(510\) | 0.141342 | 0.00625872 | ||||||||
\(511\) | 70.2507 | 3.10771 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.58404 | −0.246541 | ||||||||
\(514\) | 22.5355 | 0.993997 | ||||||||
\(515\) | −0.111031 | −0.00489259 | ||||||||
\(516\) | −15.1195 | −0.665599 | ||||||||
\(517\) | −3.49337 | −0.153638 | ||||||||
\(518\) | −1.41111 | −0.0620005 | ||||||||
\(519\) | −2.33758 | −0.102608 | ||||||||
\(520\) | −0.0794128 | −0.00348248 | ||||||||
\(521\) | −40.7620 | −1.78581 | −0.892907 | − | 0.450240i | \(-0.851338\pi\) | ||||
−0.892907 | + | 0.450240i | \(0.851338\pi\) | |||||||
\(522\) | −2.13868 | −0.0936073 | ||||||||
\(523\) | 4.58595 | 0.200530 | 0.100265 | − | 0.994961i | \(-0.468031\pi\) | ||||
0.100265 | + | 0.994961i | \(0.468031\pi\) | |||||||
\(524\) | 11.2562 | 0.491729 | ||||||||
\(525\) | 33.0358 | 1.44180 | ||||||||
\(526\) | −1.27361 | −0.0555322 | ||||||||
\(527\) | 37.3895 | 1.62871 | ||||||||
\(528\) | 4.62336 | 0.201206 | ||||||||
\(529\) | −11.7364 | −0.510279 | ||||||||
\(530\) | 0.240627 | 0.0104522 | ||||||||
\(531\) | 5.24184 | 0.227476 | ||||||||
\(532\) | −4.28156 | −0.185629 | ||||||||
\(533\) | 49.2760 | 2.13438 | ||||||||
\(534\) | −12.4983 | −0.540856 | ||||||||
\(535\) | −0.122910 | −0.00531385 | ||||||||
\(536\) | 10.1292 | 0.437514 | ||||||||
\(537\) | 18.4091 | 0.794410 | ||||||||
\(538\) | 17.6740 | 0.761981 | ||||||||
\(539\) | 33.9479 | 1.46224 | ||||||||
\(540\) | 0.102561 | 0.00441352 | ||||||||
\(541\) | 26.9915 | 1.16046 | 0.580228 | − | 0.814454i | \(-0.302963\pi\) | ||||
0.580228 | + | 0.814454i | \(0.302963\pi\) | |||||||
\(542\) | 1.59875 | 0.0686723 | ||||||||
\(543\) | −16.0635 | −0.689351 | ||||||||
\(544\) | −4.98650 | −0.213794 | ||||||||
\(545\) | 0.115367 | 0.00494176 | ||||||||
\(546\) | −28.5694 | −1.22266 | ||||||||
\(547\) | 11.9950 | 0.512871 | 0.256435 | − | 0.966561i | \(-0.417452\pi\) | ||||
0.256435 | + | 0.966561i | \(0.417452\pi\) | |||||||
\(548\) | −1.46424 | −0.0625492 | ||||||||
\(549\) | −0.996491 | −0.0425292 | ||||||||
\(550\) | −14.9781 | −0.638668 | ||||||||
\(551\) | 3.45887 | 0.147353 | ||||||||
\(552\) | −5.17941 | −0.220450 | ||||||||
\(553\) | −35.3331 | −1.50251 | ||||||||
\(554\) | −7.10665 | −0.301932 | ||||||||
\(555\) | −0.00934185 | −0.000396540 0 | ||||||||
\(556\) | −18.8318 | −0.798647 | ||||||||
\(557\) | 26.8346 | 1.13702 | 0.568510 | − | 0.822676i | \(-0.307520\pi\) | ||||
0.568510 | + | 0.822676i | \(0.307520\pi\) | |||||||
\(558\) | 4.63623 | 0.196267 | ||||||||
\(559\) | −42.3597 | −1.79163 | ||||||||
\(560\) | 0.0786384 | 0.00332308 | ||||||||
\(561\) | −23.0544 | −0.973357 | ||||||||
\(562\) | 10.6124 | 0.447656 | ||||||||
\(563\) | −15.0988 | −0.636338 | −0.318169 | − | 0.948034i | \(-0.603068\pi\) | ||||
−0.318169 | + | 0.948034i | \(0.603068\pi\) | |||||||
\(564\) | −1.79958 | −0.0757760 | ||||||||
\(565\) | 0.160906 | 0.00676937 | ||||||||
\(566\) | −25.6020 | −1.07613 | ||||||||
\(567\) | 28.9550 | 1.21600 | ||||||||
\(568\) | 4.96060 | 0.208142 | ||||||||
\(569\) | −10.4562 | −0.438345 | −0.219173 | − | 0.975686i | \(-0.570336\pi\) | ||||
−0.219173 | + | 0.975686i | \(0.570336\pi\) | |||||||
\(570\) | −0.0283449 | −0.00118724 | ||||||||
\(571\) | 9.63933 | 0.403393 | 0.201697 | − | 0.979448i | \(-0.435354\pi\) | ||||
0.201697 | + | 0.979448i | \(0.435354\pi\) | |||||||
\(572\) | 12.9531 | 0.541596 | ||||||||
\(573\) | −10.5242 | −0.439654 | ||||||||
\(574\) | −48.7955 | −2.03668 | ||||||||
\(575\) | 16.7795 | 0.699754 | ||||||||
\(576\) | −0.618317 | −0.0257632 | ||||||||
\(577\) | −5.67312 | −0.236175 | −0.118088 | − | 0.993003i | \(-0.537676\pi\) | ||||
−0.118088 | + | 0.993003i | \(0.537676\pi\) | |||||||
\(578\) | 7.86516 | 0.327147 | ||||||||
\(579\) | −0.599333 | −0.0249074 | ||||||||
\(580\) | −0.0635282 | −0.00263787 | ||||||||
\(581\) | 15.6208 | 0.648059 | ||||||||
\(582\) | 4.09789 | 0.169863 | ||||||||
\(583\) | −39.2488 | −1.62552 | ||||||||
\(584\) | −16.4077 | −0.678957 | ||||||||
\(585\) | 0.0491023 | 0.00203013 | ||||||||
\(586\) | −25.4146 | −1.04987 | ||||||||
\(587\) | 14.4963 | 0.598326 | 0.299163 | − | 0.954202i | \(-0.403293\pi\) | ||||
0.299163 | + | 0.954202i | \(0.403293\pi\) | |||||||
\(588\) | 17.4879 | 0.721190 | ||||||||
\(589\) | −7.49814 | −0.308956 | ||||||||
\(590\) | 0.155706 | 0.00641032 | ||||||||
\(591\) | −11.0336 | −0.453860 | ||||||||
\(592\) | 0.329578 | 0.0135456 | ||||||||
\(593\) | 2.22876 | 0.0915241 | 0.0457620 | − | 0.998952i | \(-0.485428\pi\) | ||||
0.0457620 | + | 0.998952i | \(0.485428\pi\) | |||||||
\(594\) | −16.7288 | −0.686390 | ||||||||
\(595\) | −0.392130 | −0.0160758 | ||||||||
\(596\) | −23.1725 | −0.949183 | ||||||||
\(597\) | 23.8942 | 0.977924 | ||||||||
\(598\) | −14.5110 | −0.593397 | ||||||||
\(599\) | −7.07178 | −0.288945 | −0.144473 | − | 0.989509i | \(-0.546149\pi\) | ||||
−0.144473 | + | 0.989509i | \(0.546149\pi\) | |||||||
\(600\) | −7.71583 | −0.314997 | ||||||||
\(601\) | 38.4735 | 1.56937 | 0.784683 | − | 0.619897i | \(-0.212826\pi\) | ||||
0.784683 | + | 0.619897i | \(0.212826\pi\) | |||||||
\(602\) | 41.9467 | 1.70962 | ||||||||
\(603\) | −6.26304 | −0.255051 | ||||||||
\(604\) | 7.66353 | 0.311825 | ||||||||
\(605\) | 0.0371938 | 0.00151214 | ||||||||
\(606\) | −10.8220 | −0.439615 | ||||||||
\(607\) | 40.3893 | 1.63935 | 0.819676 | − | 0.572828i | \(-0.194154\pi\) | ||||
0.819676 | + | 0.572828i | \(0.194154\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −22.8548 | −0.926123 | ||||||||
\(610\) | −0.0296002 | −0.00119848 | ||||||||
\(611\) | −5.04181 | −0.203970 | ||||||||
\(612\) | 3.08324 | 0.124632 | ||||||||
\(613\) | 38.8530 | 1.56926 | 0.784628 | − | 0.619967i | \(-0.212854\pi\) | ||||
0.784628 | + | 0.619967i | \(0.212854\pi\) | |||||||
\(614\) | 24.5408 | 0.990388 | ||||||||
\(615\) | −0.323037 | −0.0130261 | ||||||||
\(616\) | −12.8268 | −0.516806 | ||||||||
\(617\) | 18.0179 | 0.725372 | 0.362686 | − | 0.931911i | \(-0.381860\pi\) | ||||
0.362686 | + | 0.931911i | \(0.381860\pi\) | |||||||
\(618\) | 9.32936 | 0.375282 | ||||||||
\(619\) | −7.60231 | −0.305562 | −0.152781 | − | 0.988260i | \(-0.548823\pi\) | ||||
−0.152781 | + | 0.988260i | \(0.548823\pi\) | |||||||
\(620\) | 0.137717 | 0.00553084 | ||||||||
\(621\) | 18.7408 | 0.752040 | ||||||||
\(622\) | 12.3101 | 0.493590 | ||||||||
\(623\) | 34.6746 | 1.38921 | ||||||||
\(624\) | 6.67267 | 0.267121 | ||||||||
\(625\) | 24.9949 | 0.999798 | ||||||||
\(626\) | 0.609964 | 0.0243791 | ||||||||
\(627\) | 4.62336 | 0.184639 | ||||||||
\(628\) | 9.09348 | 0.362869 | ||||||||
\(629\) | −1.64344 | −0.0655282 | ||||||||
\(630\) | −0.0486235 | −0.00193721 | ||||||||
\(631\) | 19.4370 | 0.773775 | 0.386888 | − | 0.922127i | \(-0.373550\pi\) | ||||
0.386888 | + | 0.922127i | \(0.373550\pi\) | |||||||
\(632\) | 8.25238 | 0.328262 | ||||||||
\(633\) | −1.54327 | −0.0613395 | ||||||||
\(634\) | −25.1406 | −0.998459 | ||||||||
\(635\) | 0.130010 | 0.00515929 | ||||||||
\(636\) | −20.2187 | −0.801722 | ||||||||
\(637\) | 48.9953 | 1.94126 | ||||||||
\(638\) | 10.3621 | 0.410241 | ||||||||
\(639\) | −3.06722 | −0.121337 | ||||||||
\(640\) | −0.0183668 | −0.000726011 0 | ||||||||
\(641\) | 27.0542 | 1.06858 | 0.534288 | − | 0.845302i | \(-0.320580\pi\) | ||||
0.534288 | + | 0.845302i | \(0.320580\pi\) | |||||||
\(642\) | 10.3275 | 0.407594 | ||||||||
\(643\) | −14.8373 | −0.585124 | −0.292562 | − | 0.956247i | \(-0.594508\pi\) | ||||
−0.292562 | + | 0.956247i | \(0.594508\pi\) | |||||||
\(644\) | 14.3695 | 0.566236 | ||||||||
\(645\) | 0.277697 | 0.0109343 | ||||||||
\(646\) | −4.98650 | −0.196191 | ||||||||
\(647\) | −6.15956 | −0.242157 | −0.121079 | − | 0.992643i | \(-0.538635\pi\) | ||||
−0.121079 | + | 0.992643i | \(0.538635\pi\) | |||||||
\(648\) | −6.76273 | −0.265665 | ||||||||
\(649\) | −25.3973 | −0.996933 | ||||||||
\(650\) | −21.6171 | −0.847894 | ||||||||
\(651\) | 49.5447 | 1.94181 | ||||||||
\(652\) | 10.6542 | 0.417250 | ||||||||
\(653\) | −14.7092 | −0.575615 | −0.287808 | − | 0.957688i | \(-0.592926\pi\) | ||||
−0.287808 | + | 0.957688i | \(0.592926\pi\) | |||||||
\(654\) | −9.69368 | −0.379053 | ||||||||
\(655\) | −0.206740 | −0.00807799 | ||||||||
\(656\) | 11.3967 | 0.444965 | ||||||||
\(657\) | 10.1452 | 0.395801 | ||||||||
\(658\) | 4.99265 | 0.194634 | ||||||||
\(659\) | 11.4941 | 0.447747 | 0.223874 | − | 0.974618i | \(-0.428130\pi\) | ||||
0.223874 | + | 0.974618i | \(0.428130\pi\) | |||||||
\(660\) | −0.0849163 | −0.00330536 | ||||||||
\(661\) | 48.8731 | 1.90094 | 0.950471 | − | 0.310813i | \(-0.100601\pi\) | ||||
0.950471 | + | 0.310813i | \(0.100601\pi\) | |||||||
\(662\) | −20.7309 | −0.805729 | ||||||||
\(663\) | −33.2732 | −1.29223 | ||||||||
\(664\) | −3.64838 | −0.141585 | ||||||||
\(665\) | 0.0786384 | 0.00304947 | ||||||||
\(666\) | −0.203784 | −0.00789645 | ||||||||
\(667\) | −11.6084 | −0.449479 | ||||||||
\(668\) | −11.4669 | −0.443669 | ||||||||
\(669\) | −12.4872 | −0.482785 | ||||||||
\(670\) | −0.186040 | −0.00718736 | ||||||||
\(671\) | 4.82812 | 0.186387 | ||||||||
\(672\) | −6.60760 | −0.254894 | ||||||||
\(673\) | −17.6053 | −0.678635 | −0.339318 | − | 0.940672i | \(-0.610196\pi\) | ||||
−0.339318 | + | 0.940672i | \(0.610196\pi\) | |||||||
\(674\) | −16.8322 | −0.648353 | ||||||||
\(675\) | 27.9183 | 1.07458 | ||||||||
\(676\) | 5.69456 | 0.219021 | ||||||||
\(677\) | −9.65642 | −0.371126 | −0.185563 | − | 0.982632i | \(-0.559411\pi\) | ||||
−0.185563 | + | 0.982632i | \(0.559411\pi\) | |||||||
\(678\) | −13.5201 | −0.519238 | ||||||||
\(679\) | −11.3689 | −0.436300 | ||||||||
\(680\) | 0.0915859 | 0.00351216 | ||||||||
\(681\) | 8.03499 | 0.307902 | ||||||||
\(682\) | −22.4631 | −0.860156 | ||||||||
\(683\) | 21.3129 | 0.815516 | 0.407758 | − | 0.913090i | \(-0.366311\pi\) | ||||
0.407758 | + | 0.913090i | \(0.366311\pi\) | |||||||
\(684\) | −0.618317 | −0.0236419 | ||||||||
\(685\) | 0.0268934 | 0.00102754 | ||||||||
\(686\) | −18.5466 | −0.708112 | ||||||||
\(687\) | 26.5879 | 1.01439 | ||||||||
\(688\) | −9.79706 | −0.373509 | ||||||||
\(689\) | −56.6459 | −2.15804 | ||||||||
\(690\) | 0.0951291 | 0.00362150 | ||||||||
\(691\) | −14.3588 | −0.546235 | −0.273117 | − | 0.961981i | \(-0.588055\pi\) | ||||
−0.273117 | + | 0.961981i | \(0.588055\pi\) | |||||||
\(692\) | −1.51469 | −0.0575799 | ||||||||
\(693\) | 7.93101 | 0.301274 | ||||||||
\(694\) | −34.3472 | −1.30380 | ||||||||
\(695\) | 0.345880 | 0.0131200 | ||||||||
\(696\) | 5.33796 | 0.202335 | ||||||||
\(697\) | −56.8294 | −2.15257 | ||||||||
\(698\) | 4.32477 | 0.163695 | ||||||||
\(699\) | −4.20440 | −0.159025 | ||||||||
\(700\) | 21.4063 | 0.809084 | ||||||||
\(701\) | 46.7020 | 1.76391 | 0.881956 | − | 0.471332i | \(-0.156227\pi\) | ||||
0.881956 | + | 0.471332i | \(0.156227\pi\) | |||||||
\(702\) | −24.1438 | −0.911250 | ||||||||
\(703\) | 0.329578 | 0.0124303 | ||||||||
\(704\) | 2.99582 | 0.112909 | ||||||||
\(705\) | 0.0330525 | 0.00124483 | ||||||||
\(706\) | −35.6842 | −1.34299 | ||||||||
\(707\) | 30.0240 | 1.12917 | ||||||||
\(708\) | −13.0832 | −0.491697 | ||||||||
\(709\) | 46.8548 | 1.75967 | 0.879835 | − | 0.475279i | \(-0.157653\pi\) | ||||
0.879835 | + | 0.475279i | \(0.157653\pi\) | |||||||
\(710\) | −0.0911102 | −0.00341931 | ||||||||
\(711\) | −5.10259 | −0.191362 | ||||||||
\(712\) | −8.09860 | −0.303508 | ||||||||
\(713\) | 25.1647 | 0.942426 | ||||||||
\(714\) | 32.9488 | 1.23308 | ||||||||
\(715\) | −0.237907 | −0.00889720 | ||||||||
\(716\) | 11.9286 | 0.445793 | ||||||||
\(717\) | −30.8083 | −1.15056 | ||||||||
\(718\) | 7.05580 | 0.263320 | ||||||||
\(719\) | 41.6234 | 1.55229 | 0.776145 | − | 0.630555i | \(-0.217173\pi\) | ||||
0.776145 | + | 0.630555i | \(0.217173\pi\) | |||||||
\(720\) | 0.0113565 | 0.000423231 0 | ||||||||
\(721\) | −25.8828 | −0.963927 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −18.2902 | −0.680221 | ||||||||
\(724\) | −10.4087 | −0.386838 | ||||||||
\(725\) | −17.2932 | −0.642252 | ||||||||
\(726\) | −3.12521 | −0.115988 | ||||||||
\(727\) | 25.8166 | 0.957486 | 0.478743 | − | 0.877955i | \(-0.341092\pi\) | ||||
0.478743 | + | 0.877955i | \(0.341092\pi\) | |||||||
\(728\) | −18.5123 | −0.686110 | ||||||||
\(729\) | 30.0346 | 1.11239 | ||||||||
\(730\) | 0.301357 | 0.0111537 | ||||||||
\(731\) | 48.8530 | 1.80689 | ||||||||
\(732\) | 2.48716 | 0.0919282 | ||||||||
\(733\) | 19.5479 | 0.722018 | 0.361009 | − | 0.932562i | \(-0.382432\pi\) | ||||
0.361009 | + | 0.932562i | \(0.382432\pi\) | |||||||
\(734\) | −27.3530 | −1.00962 | ||||||||
\(735\) | −0.321197 | −0.0118475 | ||||||||
\(736\) | −3.35613 | −0.123708 | ||||||||
\(737\) | 30.3452 | 1.11778 | ||||||||
\(738\) | −7.04675 | −0.259394 | ||||||||
\(739\) | 50.7120 | 1.86547 | 0.932735 | − | 0.360563i | \(-0.117415\pi\) | ||||
0.932735 | + | 0.360563i | \(0.117415\pi\) | |||||||
\(740\) | −0.00605328 | −0.000222523 0 | ||||||||
\(741\) | 6.67267 | 0.245127 | ||||||||
\(742\) | 56.0935 | 2.05926 | ||||||||
\(743\) | −6.50281 | −0.238565 | −0.119283 | − | 0.992860i | \(-0.538059\pi\) | ||||
−0.119283 | + | 0.992860i | \(0.538059\pi\) | |||||||
\(744\) | −11.5717 | −0.424238 | ||||||||
\(745\) | 0.425604 | 0.0155929 | ||||||||
\(746\) | 25.0734 | 0.918002 | ||||||||
\(747\) | 2.25586 | 0.0825375 | ||||||||
\(748\) | −14.9387 | −0.546211 | ||||||||
\(749\) | −28.6520 | −1.04692 | ||||||||
\(750\) | 0.283439 | 0.0103497 | ||||||||
\(751\) | 40.6645 | 1.48387 | 0.741933 | − | 0.670474i | \(-0.233909\pi\) | ||||
0.741933 | + | 0.670474i | \(0.233909\pi\) | |||||||
\(752\) | −1.16608 | −0.0425226 | ||||||||
\(753\) | 22.9799 | 0.837434 | ||||||||
\(754\) | 14.9552 | 0.544635 | ||||||||
\(755\) | −0.140754 | −0.00512258 | ||||||||
\(756\) | 23.9084 | 0.869540 | ||||||||
\(757\) | −18.5282 | −0.673421 | −0.336710 | − | 0.941608i | \(-0.609314\pi\) | ||||
−0.336710 | + | 0.941608i | \(0.609314\pi\) | |||||||
\(758\) | −24.1253 | −0.876269 | ||||||||
\(759\) | −15.5166 | −0.563216 | ||||||||
\(760\) | −0.0183668 | −0.000666233 0 | ||||||||
\(761\) | −30.0134 | −1.08799 | −0.543993 | − | 0.839090i | \(-0.683088\pi\) | ||||
−0.543993 | + | 0.839090i | \(0.683088\pi\) | |||||||
\(762\) | −10.9241 | −0.395739 | ||||||||
\(763\) | 26.8936 | 0.973613 | ||||||||
\(764\) | −6.81941 | −0.246718 | ||||||||
\(765\) | −0.0566291 | −0.00204743 | ||||||||
\(766\) | 12.0159 | 0.434151 | ||||||||
\(767\) | −36.6547 | −1.32353 | ||||||||
\(768\) | 1.54327 | 0.0556880 | ||||||||
\(769\) | −32.2840 | −1.16419 | −0.582096 | − | 0.813120i | \(-0.697767\pi\) | ||||
−0.582096 | + | 0.813120i | \(0.697767\pi\) | |||||||
\(770\) | 0.235587 | 0.00848995 | ||||||||
\(771\) | 34.7783 | 1.25251 | ||||||||
\(772\) | −0.388352 | −0.0139771 | ||||||||
\(773\) | −13.9236 | −0.500798 | −0.250399 | − | 0.968143i | \(-0.580562\pi\) | ||||
−0.250399 | + | 0.968143i | \(0.580562\pi\) | |||||||
\(774\) | 6.05769 | 0.217739 | ||||||||
\(775\) | 37.4882 | 1.34662 | ||||||||
\(776\) | 2.65533 | 0.0953207 | ||||||||
\(777\) | −2.17772 | −0.0781252 | ||||||||
\(778\) | 26.8420 | 0.962333 | ||||||||
\(779\) | 11.3967 | 0.408328 | ||||||||
\(780\) | −0.122555 | −0.00438819 | ||||||||
\(781\) | 14.8611 | 0.531771 | ||||||||
\(782\) | 16.7353 | 0.598454 | ||||||||
\(783\) | −19.3144 | −0.690242 | ||||||||
\(784\) | 11.3317 | 0.404705 | ||||||||
\(785\) | −0.167018 | −0.00596113 | ||||||||
\(786\) | 17.3713 | 0.619615 | ||||||||
\(787\) | 11.6370 | 0.414814 | 0.207407 | − | 0.978255i | \(-0.433498\pi\) | ||||
0.207407 | + | 0.978255i | \(0.433498\pi\) | |||||||
\(788\) | −7.14947 | −0.254689 | ||||||||
\(789\) | −1.96553 | −0.0699748 | ||||||||
\(790\) | −0.151570 | −0.00539261 | ||||||||
\(791\) | 37.5095 | 1.33368 | ||||||||
\(792\) | −1.85237 | −0.0658210 | ||||||||
\(793\) | 6.96819 | 0.247448 | ||||||||
\(794\) | 13.3275 | 0.472977 | ||||||||
\(795\) | 0.371352 | 0.0131705 | ||||||||
\(796\) | 15.4828 | 0.548774 | ||||||||
\(797\) | 52.4829 | 1.85904 | 0.929521 | − | 0.368770i | \(-0.120221\pi\) | ||||
0.929521 | + | 0.368770i | \(0.120221\pi\) | |||||||
\(798\) | −6.60760 | −0.233907 | ||||||||
\(799\) | 5.81467 | 0.205708 | ||||||||
\(800\) | −4.99966 | −0.176765 | ||||||||
\(801\) | 5.00750 | 0.176931 | ||||||||
\(802\) | 10.0490 | 0.354843 | ||||||||
\(803\) | −49.1546 | −1.73463 | ||||||||
\(804\) | 15.6320 | 0.551300 | ||||||||
\(805\) | −0.263921 | −0.00930198 | ||||||||
\(806\) | −32.4199 | −1.14194 | ||||||||
\(807\) | 27.2758 | 0.960153 | ||||||||
\(808\) | −7.01241 | −0.246696 | ||||||||
\(809\) | −11.5027 | −0.404413 | −0.202206 | − | 0.979343i | \(-0.564811\pi\) | ||||
−0.202206 | + | 0.979343i | \(0.564811\pi\) | |||||||
\(810\) | 0.124210 | 0.00436428 | ||||||||
\(811\) | 30.5401 | 1.07241 | 0.536203 | − | 0.844089i | \(-0.319858\pi\) | ||||
0.536203 | + | 0.844089i | \(0.319858\pi\) | |||||||
\(812\) | −14.8093 | −0.519706 | ||||||||
\(813\) | 2.46731 | 0.0865322 | ||||||||
\(814\) | 0.987356 | 0.0346068 | ||||||||
\(815\) | −0.195683 | −0.00685447 | ||||||||
\(816\) | −7.69551 | −0.269397 | ||||||||
\(817\) | −9.79706 | −0.342756 | ||||||||
\(818\) | −26.9528 | −0.942383 | ||||||||
\(819\) | 11.4464 | 0.399971 | ||||||||
\(820\) | −0.209320 | −0.00730977 | ||||||||
\(821\) | −13.4060 | −0.467873 | −0.233936 | − | 0.972252i | \(-0.575161\pi\) | ||||
−0.233936 | + | 0.972252i | \(0.575161\pi\) | |||||||
\(822\) | −2.25972 | −0.0788167 | ||||||||
\(823\) | 10.4822 | 0.365385 | 0.182692 | − | 0.983170i | \(-0.441519\pi\) | ||||
0.182692 | + | 0.983170i | \(0.441519\pi\) | |||||||
\(824\) | 6.04519 | 0.210594 | ||||||||
\(825\) | −23.1152 | −0.804770 | ||||||||
\(826\) | 36.2973 | 1.26294 | ||||||||
\(827\) | −1.51148 | −0.0525593 | −0.0262796 | − | 0.999655i | \(-0.508366\pi\) | ||||
−0.0262796 | + | 0.999655i | \(0.508366\pi\) | |||||||
\(828\) | 2.07515 | 0.0721165 | ||||||||
\(829\) | −40.3604 | −1.40177 | −0.700887 | − | 0.713272i | \(-0.747212\pi\) | ||||
−0.700887 | + | 0.713272i | \(0.747212\pi\) | |||||||
\(830\) | 0.0670091 | 0.00232592 | ||||||||
\(831\) | −10.9675 | −0.380458 | ||||||||
\(832\) | 4.32372 | 0.149898 | ||||||||
\(833\) | −56.5057 | −1.95781 | ||||||||
\(834\) | −29.0626 | −1.00636 | ||||||||
\(835\) | 0.210610 | 0.00728848 | ||||||||
\(836\) | 2.99582 | 0.103613 | ||||||||
\(837\) | 41.8699 | 1.44724 | ||||||||
\(838\) | 13.2440 | 0.457508 | ||||||||
\(839\) | 5.09661 | 0.175955 | 0.0879773 | − | 0.996122i | \(-0.471960\pi\) | ||||
0.0879773 | + | 0.996122i | \(0.471960\pi\) | |||||||
\(840\) | 0.121360 | 0.00418733 | ||||||||
\(841\) | −17.0362 | −0.587457 | ||||||||
\(842\) | 1.92237 | 0.0662494 | ||||||||
\(843\) | 16.3777 | 0.564080 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −0.104591 | −0.00359803 | ||||||||
\(846\) | 0.721008 | 0.0247888 | ||||||||
\(847\) | 8.67040 | 0.297919 | ||||||||
\(848\) | −13.1012 | −0.449897 | ||||||||
\(849\) | −39.5108 | −1.35601 | ||||||||
\(850\) | 24.9308 | 0.855120 | ||||||||
\(851\) | −1.10611 | −0.0379168 | ||||||||
\(852\) | 7.65555 | 0.262275 | ||||||||
\(853\) | −12.5382 | −0.429301 | −0.214651 | − | 0.976691i | \(-0.568861\pi\) | ||||
−0.214651 | + | 0.976691i | \(0.568861\pi\) | |||||||
\(854\) | −6.90024 | −0.236121 | ||||||||
\(855\) | 0.0113565 | 0.000388384 0 | ||||||||
\(856\) | 6.69195 | 0.228726 | ||||||||
\(857\) | −41.7933 | −1.42763 | −0.713816 | − | 0.700333i | \(-0.753035\pi\) | ||||
−0.713816 | + | 0.700333i | \(0.753035\pi\) | |||||||
\(858\) | 19.9901 | 0.682451 | ||||||||
\(859\) | −6.59686 | −0.225082 | −0.112541 | − | 0.993647i | \(-0.535899\pi\) | ||||
−0.112541 | + | 0.993647i | \(0.535899\pi\) | |||||||
\(860\) | 0.179940 | 0.00613592 | ||||||||
\(861\) | −75.3046 | −2.56637 | ||||||||
\(862\) | 19.3188 | 0.658002 | ||||||||
\(863\) | −36.9702 | −1.25848 | −0.629241 | − | 0.777210i | \(-0.716634\pi\) | ||||
−0.629241 | + | 0.777210i | \(0.716634\pi\) | |||||||
\(864\) | −5.58404 | −0.189973 | ||||||||
\(865\) | 0.0278200 | 0.000945908 0 | ||||||||
\(866\) | 6.94110 | 0.235868 | ||||||||
\(867\) | 12.1381 | 0.412230 | ||||||||
\(868\) | 32.1037 | 1.08967 | ||||||||
\(869\) | 24.7227 | 0.838659 | ||||||||
\(870\) | −0.0980412 | −0.00332391 | ||||||||
\(871\) | 43.7957 | 1.48396 | ||||||||
\(872\) | −6.28126 | −0.212710 | ||||||||
\(873\) | −1.64183 | −0.0555677 | ||||||||
\(874\) | −3.35613 | −0.113523 | ||||||||
\(875\) | −0.786358 | −0.0265837 | ||||||||
\(876\) | −25.3216 | −0.855536 | ||||||||
\(877\) | −22.7670 | −0.768787 | −0.384393 | − | 0.923169i | \(-0.625589\pi\) | ||||
−0.384393 | + | 0.923169i | \(0.625589\pi\) | |||||||
\(878\) | 15.0788 | 0.508883 | ||||||||
\(879\) | −39.2216 | −1.32291 | ||||||||
\(880\) | −0.0550236 | −0.00185484 | ||||||||
\(881\) | −2.98165 | −0.100454 | −0.0502271 | − | 0.998738i | \(-0.515995\pi\) | ||||
−0.0502271 | + | 0.998738i | \(0.515995\pi\) | |||||||
\(882\) | −7.00660 | −0.235925 | ||||||||
\(883\) | −57.4053 | −1.93184 | −0.965920 | − | 0.258839i | \(-0.916660\pi\) | ||||
−0.965920 | + | 0.258839i | \(0.916660\pi\) | |||||||
\(884\) | −21.5602 | −0.725149 | ||||||||
\(885\) | 0.240297 | 0.00807748 | ||||||||
\(886\) | −23.4720 | −0.788556 | ||||||||
\(887\) | −47.4645 | −1.59370 | −0.796852 | − | 0.604175i | \(-0.793503\pi\) | ||||
−0.796852 | + | 0.604175i | \(0.793503\pi\) | |||||||
\(888\) | 0.508628 | 0.0170684 | ||||||||
\(889\) | 30.3072 | 1.01647 | ||||||||
\(890\) | 0.148745 | 0.00498595 | ||||||||
\(891\) | −20.2599 | −0.678733 | ||||||||
\(892\) | −8.09141 | −0.270921 | ||||||||
\(893\) | −1.16608 | −0.0390214 | ||||||||
\(894\) | −35.7614 | −1.19604 | ||||||||
\(895\) | −0.219090 | −0.00732338 | ||||||||
\(896\) | −4.28156 | −0.143037 | ||||||||
\(897\) | −22.3943 | −0.747725 | ||||||||
\(898\) | 30.7862 | 1.02735 | ||||||||
\(899\) | −25.9351 | −0.864983 | ||||||||
\(900\) | 3.09138 | 0.103046 | ||||||||
\(901\) | 65.3290 | 2.17643 | ||||||||
\(902\) | 34.1424 | 1.13682 | ||||||||
\(903\) | 64.7351 | 2.15425 | ||||||||
\(904\) | −8.76071 | −0.291377 | ||||||||
\(905\) | 0.191175 | 0.00635487 | ||||||||
\(906\) | 11.8269 | 0.392923 | ||||||||
\(907\) | 33.3822 | 1.10844 | 0.554220 | − | 0.832370i | \(-0.313017\pi\) | ||||
0.554220 | + | 0.832370i | \(0.313017\pi\) | |||||||
\(908\) | 5.20647 | 0.172783 | ||||||||
\(909\) | 4.33589 | 0.143812 | ||||||||
\(910\) | 0.340011 | 0.0112712 | ||||||||
\(911\) | −21.2119 | −0.702783 | −0.351392 | − | 0.936229i | \(-0.614291\pi\) | ||||
−0.351392 | + | 0.936229i | \(0.614291\pi\) | |||||||
\(912\) | 1.54327 | 0.0511028 | ||||||||
\(913\) | −10.9299 | −0.361727 | ||||||||
\(914\) | 29.0387 | 0.960513 | ||||||||
\(915\) | −0.0456812 | −0.00151017 | ||||||||
\(916\) | 17.2283 | 0.569238 | ||||||||
\(917\) | −48.1940 | −1.59151 | ||||||||
\(918\) | 27.8448 | 0.919016 | ||||||||
\(919\) | −19.8236 | −0.653921 | −0.326960 | − | 0.945038i | \(-0.606024\pi\) | ||||
−0.326960 | + | 0.945038i | \(0.606024\pi\) | |||||||
\(920\) | 0.0616412 | 0.00203225 | ||||||||
\(921\) | 37.8731 | 1.24796 | ||||||||
\(922\) | −31.6706 | −1.04302 | ||||||||
\(923\) | 21.4482 | 0.705978 | ||||||||
\(924\) | −19.7952 | −0.651214 | ||||||||
\(925\) | −1.64778 | −0.0541786 | ||||||||
\(926\) | 9.65031 | 0.317129 | ||||||||
\(927\) | −3.73784 | −0.122767 | ||||||||
\(928\) | 3.45887 | 0.113543 | ||||||||
\(929\) | −21.4766 | −0.704624 | −0.352312 | − | 0.935883i | \(-0.614604\pi\) | ||||
−0.352312 | + | 0.935883i | \(0.614604\pi\) | |||||||
\(930\) | 0.212534 | 0.00696927 | ||||||||
\(931\) | 11.3317 | 0.371383 | ||||||||
\(932\) | −2.72435 | −0.0892389 | ||||||||
\(933\) | 18.9978 | 0.621961 | ||||||||
\(934\) | 22.4722 | 0.735314 | ||||||||
\(935\) | 0.274375 | 0.00897302 | ||||||||
\(936\) | −2.67343 | −0.0873838 | ||||||||
\(937\) | 12.9240 | 0.422210 | 0.211105 | − | 0.977463i | \(-0.432294\pi\) | ||||
0.211105 | + | 0.977463i | \(0.432294\pi\) | |||||||
\(938\) | −43.3686 | −1.41604 | ||||||||
\(939\) | 0.941339 | 0.0307194 | ||||||||
\(940\) | 0.0214172 | 0.000698551 0 | ||||||||
\(941\) | −37.3371 | −1.21715 | −0.608577 | − | 0.793495i | \(-0.708259\pi\) | ||||
−0.608577 | + | 0.793495i | \(0.708259\pi\) | |||||||
\(942\) | 14.0337 | 0.457243 | ||||||||
\(943\) | −38.2486 | −1.24555 | ||||||||
\(944\) | −8.47759 | −0.275922 | ||||||||
\(945\) | −0.439120 | −0.0142846 | ||||||||
\(946\) | −29.3502 | −0.954258 | ||||||||
\(947\) | −51.8654 | −1.68540 | −0.842700 | − | 0.538383i | \(-0.819035\pi\) | ||||
−0.842700 | + | 0.538383i | \(0.819035\pi\) | |||||||
\(948\) | 12.7357 | 0.413635 | ||||||||
\(949\) | −70.9424 | −2.30289 | ||||||||
\(950\) | −4.99966 | −0.162210 | ||||||||
\(951\) | −38.7987 | −1.25813 | ||||||||
\(952\) | 21.3500 | 0.691957 | ||||||||
\(953\) | −36.3691 | −1.17811 | −0.589055 | − | 0.808093i | \(-0.700500\pi\) | ||||
−0.589055 | + | 0.808093i | \(0.700500\pi\) | |||||||
\(954\) | 8.10068 | 0.262269 | ||||||||
\(955\) | 0.125251 | 0.00405301 | ||||||||
\(956\) | −19.9630 | −0.645650 | ||||||||
\(957\) | 15.9916 | 0.516934 | ||||||||
\(958\) | 28.5859 | 0.923569 | ||||||||
\(959\) | 6.26922 | 0.202444 | ||||||||
\(960\) | −0.0283449 | −0.000914828 0 | ||||||||
\(961\) | 25.2222 | 0.813619 | ||||||||
\(962\) | 1.42500 | 0.0459439 | ||||||||
\(963\) | −4.13775 | −0.133337 | ||||||||
\(964\) | −11.8516 | −0.381714 | ||||||||
\(965\) | 0.00713278 | 0.000229612 0 | ||||||||
\(966\) | 22.1759 | 0.713499 | ||||||||
\(967\) | 43.1048 | 1.38616 | 0.693078 | − | 0.720863i | \(-0.256254\pi\) | ||||
0.693078 | + | 0.720863i | \(0.256254\pi\) | |||||||
\(968\) | −2.02506 | −0.0650878 | ||||||||
\(969\) | −7.69551 | −0.247215 | ||||||||
\(970\) | −0.0487698 | −0.00156590 | ||||||||
\(971\) | 21.9570 | 0.704635 | 0.352318 | − | 0.935880i | \(-0.385394\pi\) | ||||
0.352318 | + | 0.935880i | \(0.385394\pi\) | |||||||
\(972\) | 6.31540 | 0.202566 | ||||||||
\(973\) | 80.6295 | 2.58486 | ||||||||
\(974\) | −18.7107 | −0.599530 | ||||||||
\(975\) | −33.3611 | −1.06841 | ||||||||
\(976\) | 1.61162 | 0.0515866 | ||||||||
\(977\) | −38.1719 | −1.22123 | −0.610614 | − | 0.791928i | \(-0.709077\pi\) | ||||
−0.610614 | + | 0.791928i | \(0.709077\pi\) | |||||||
\(978\) | 16.4423 | 0.525766 | ||||||||
\(979\) | −24.2620 | −0.775416 | ||||||||
\(980\) | −0.208128 | −0.00664839 | ||||||||
\(981\) | 3.88381 | 0.124001 | ||||||||
\(982\) | 42.0521 | 1.34194 | ||||||||
\(983\) | −5.48626 | −0.174984 | −0.0874922 | − | 0.996165i | \(-0.527885\pi\) | ||||
−0.0874922 | + | 0.996165i | \(0.527885\pi\) | |||||||
\(984\) | 17.5881 | 0.560689 | ||||||||
\(985\) | 0.131313 | 0.00418397 | ||||||||
\(986\) | −17.2476 | −0.549276 | ||||||||
\(987\) | 7.70500 | 0.245253 | ||||||||
\(988\) | 4.32372 | 0.137556 | ||||||||
\(989\) | 32.8802 | 1.04553 | ||||||||
\(990\) | 0.0340220 | 0.00108129 | ||||||||
\(991\) | 22.3505 | 0.709987 | 0.354994 | − | 0.934869i | \(-0.384483\pi\) | ||||
0.354994 | + | 0.934869i | \(0.384483\pi\) | |||||||
\(992\) | −7.49814 | −0.238066 | ||||||||
\(993\) | −31.9934 | −1.01528 | ||||||||
\(994\) | −21.2391 | −0.673663 | ||||||||
\(995\) | −0.284370 | −0.00901512 | ||||||||
\(996\) | −5.63044 | −0.178407 | ||||||||
\(997\) | 14.6811 | 0.464954 | 0.232477 | − | 0.972602i | \(-0.425317\pi\) | ||||
0.232477 | + | 0.972602i | \(0.425317\pi\) | |||||||
\(998\) | −28.9174 | −0.915365 | ||||||||
\(999\) | −1.84038 | −0.0582269 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8018.2.a.d.1.25 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.25 | ✓ | 30 | 1.1 | even | 1 | trivial |