Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.249798 | −0.176634 | −0.0883168 | − | 0.996092i | \(-0.528149\pi\) | ||||
−0.0883168 | + | 0.996092i | \(0.528149\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.93760 | −0.968801 | ||||||||
\(5\) | 0.601573 | 0.269032 | 0.134516 | − | 0.990911i | \(-0.457052\pi\) | ||||
0.134516 | + | 0.990911i | \(0.457052\pi\) | |||||||
\(6\) | 0.249798 | 0.101980 | ||||||||
\(7\) | −2.69175 | −1.01738 | −0.508692 | − | 0.860949i | \(-0.669871\pi\) | ||||
−0.508692 | + | 0.860949i | \(0.669871\pi\) | |||||||
\(8\) | 0.983604 | 0.347756 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.150272 | −0.0475201 | ||||||||
\(11\) | −4.01000 | −1.20906 | −0.604530 | − | 0.796582i | \(-0.706639\pi\) | ||||
−0.604530 | + | 0.796582i | \(0.706639\pi\) | |||||||
\(12\) | 1.93760 | 0.559337 | ||||||||
\(13\) | 6.29531 | 1.74600 | 0.873002 | − | 0.487716i | \(-0.162170\pi\) | ||||
0.873002 | + | 0.487716i | \(0.162170\pi\) | |||||||
\(14\) | 0.672392 | 0.179704 | ||||||||
\(15\) | −0.601573 | −0.155326 | ||||||||
\(16\) | 3.62950 | 0.907375 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.249798 | −0.0588779 | ||||||||
\(19\) | 7.87938 | 1.80765 | 0.903827 | − | 0.427897i | \(-0.140745\pi\) | ||||
0.903827 | + | 0.427897i | \(0.140745\pi\) | |||||||
\(20\) | −1.16561 | −0.260638 | ||||||||
\(21\) | 2.69175 | 0.587387 | ||||||||
\(22\) | 1.00169 | 0.213561 | ||||||||
\(23\) | −0.0277886 | −0.00579432 | −0.00289716 | − | 0.999996i | \(-0.500922\pi\) | ||||
−0.00289716 | + | 0.999996i | \(0.500922\pi\) | |||||||
\(24\) | −0.983604 | −0.200777 | ||||||||
\(25\) | −4.63811 | −0.927622 | ||||||||
\(26\) | −1.57255 | −0.308403 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 5.21553 | 0.985642 | ||||||||
\(29\) | −7.65335 | −1.42119 | −0.710595 | − | 0.703601i | \(-0.751574\pi\) | ||||
−0.710595 | + | 0.703601i | \(0.751574\pi\) | |||||||
\(30\) | 0.150272 | 0.0274357 | ||||||||
\(31\) | 3.60362 | 0.647230 | 0.323615 | − | 0.946189i | \(-0.395102\pi\) | ||||
0.323615 | + | 0.946189i | \(0.395102\pi\) | |||||||
\(32\) | −2.87385 | −0.508029 | ||||||||
\(33\) | 4.01000 | 0.698051 | ||||||||
\(34\) | 0.249798 | 0.0428400 | ||||||||
\(35\) | −1.61928 | −0.273709 | ||||||||
\(36\) | −1.93760 | −0.322934 | ||||||||
\(37\) | −3.13719 | −0.515751 | −0.257876 | − | 0.966178i | \(-0.583022\pi\) | ||||
−0.257876 | + | 0.966178i | \(0.583022\pi\) | |||||||
\(38\) | −1.96825 | −0.319293 | ||||||||
\(39\) | −6.29531 | −1.00806 | ||||||||
\(40\) | 0.591710 | 0.0935576 | ||||||||
\(41\) | −8.77814 | −1.37092 | −0.685458 | − | 0.728112i | \(-0.740398\pi\) | ||||
−0.685458 | + | 0.728112i | \(0.740398\pi\) | |||||||
\(42\) | −0.672392 | −0.103752 | ||||||||
\(43\) | −5.84403 | −0.891206 | −0.445603 | − | 0.895231i | \(-0.647011\pi\) | ||||
−0.445603 | + | 0.895231i | \(0.647011\pi\) | |||||||
\(44\) | 7.76978 | 1.17134 | ||||||||
\(45\) | 0.601573 | 0.0896773 | ||||||||
\(46\) | 0.00694153 | 0.00102347 | ||||||||
\(47\) | −6.01959 | −0.878047 | −0.439023 | − | 0.898476i | \(-0.644675\pi\) | ||||
−0.439023 | + | 0.898476i | \(0.644675\pi\) | |||||||
\(48\) | −3.62950 | −0.523873 | ||||||||
\(49\) | 0.245493 | 0.0350704 | ||||||||
\(50\) | 1.15859 | 0.163849 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −12.1978 | −1.69153 | ||||||||
\(53\) | −10.8237 | −1.48674 | −0.743372 | − | 0.668878i | \(-0.766775\pi\) | ||||
−0.743372 | + | 0.668878i | \(0.766775\pi\) | |||||||
\(54\) | 0.249798 | 0.0339932 | ||||||||
\(55\) | −2.41231 | −0.325276 | ||||||||
\(56\) | −2.64761 | −0.353802 | ||||||||
\(57\) | −7.87938 | −1.04365 | ||||||||
\(58\) | 1.91179 | 0.251030 | ||||||||
\(59\) | 11.2876 | 1.46953 | 0.734763 | − | 0.678324i | \(-0.237293\pi\) | ||||
0.734763 | + | 0.678324i | \(0.237293\pi\) | |||||||
\(60\) | 1.16561 | 0.150480 | ||||||||
\(61\) | −0.767879 | −0.0983169 | −0.0491584 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491584 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(62\) | −0.900177 | −0.114323 | ||||||||
\(63\) | −2.69175 | −0.339128 | ||||||||
\(64\) | −6.54112 | −0.817640 | ||||||||
\(65\) | 3.78709 | 0.469731 | ||||||||
\(66\) | −1.00169 | −0.123299 | ||||||||
\(67\) | 11.3518 | 1.38685 | 0.693424 | − | 0.720530i | \(-0.256102\pi\) | ||||
0.693424 | + | 0.720530i | \(0.256102\pi\) | |||||||
\(68\) | 1.93760 | 0.234969 | ||||||||
\(69\) | 0.0277886 | 0.00334535 | ||||||||
\(70\) | 0.404493 | 0.0483462 | ||||||||
\(71\) | 3.73870 | 0.443702 | 0.221851 | − | 0.975081i | \(-0.428790\pi\) | ||||
0.221851 | + | 0.975081i | \(0.428790\pi\) | |||||||
\(72\) | 0.983604 | 0.115919 | ||||||||
\(73\) | 3.98797 | 0.466756 | 0.233378 | − | 0.972386i | \(-0.425022\pi\) | ||||
0.233378 | + | 0.972386i | \(0.425022\pi\) | |||||||
\(74\) | 0.783663 | 0.0910990 | ||||||||
\(75\) | 4.63811 | 0.535563 | ||||||||
\(76\) | −15.2671 | −1.75126 | ||||||||
\(77\) | 10.7939 | 1.23008 | ||||||||
\(78\) | 1.57255 | 0.178057 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 2.18341 | 0.244113 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.19276 | 0.242150 | ||||||||
\(83\) | 6.87292 | 0.754401 | 0.377201 | − | 0.926132i | \(-0.376887\pi\) | ||||
0.377201 | + | 0.926132i | \(0.376887\pi\) | |||||||
\(84\) | −5.21553 | −0.569061 | ||||||||
\(85\) | −0.601573 | −0.0652498 | ||||||||
\(86\) | 1.45983 | 0.157417 | ||||||||
\(87\) | 7.65335 | 0.820525 | ||||||||
\(88\) | −3.94425 | −0.420459 | ||||||||
\(89\) | −1.23369 | −0.130771 | −0.0653854 | − | 0.997860i | \(-0.520828\pi\) | ||||
−0.0653854 | + | 0.997860i | \(0.520828\pi\) | |||||||
\(90\) | −0.150272 | −0.0158400 | ||||||||
\(91\) | −16.9454 | −1.77636 | ||||||||
\(92\) | 0.0538432 | 0.00561354 | ||||||||
\(93\) | −3.60362 | −0.373678 | ||||||||
\(94\) | 1.50368 | 0.155093 | ||||||||
\(95\) | 4.74003 | 0.486317 | ||||||||
\(96\) | 2.87385 | 0.293311 | ||||||||
\(97\) | 12.6730 | 1.28675 | 0.643376 | − | 0.765550i | \(-0.277533\pi\) | ||||
0.643376 | + | 0.765550i | \(0.277533\pi\) | |||||||
\(98\) | −0.0613236 | −0.00619462 | ||||||||
\(99\) | −4.01000 | −0.403020 | ||||||||
\(100\) | 8.98681 | 0.898681 | ||||||||
\(101\) | −4.22605 | −0.420508 | −0.210254 | − | 0.977647i | \(-0.567429\pi\) | ||||
−0.210254 | + | 0.977647i | \(0.567429\pi\) | |||||||
\(102\) | −0.249798 | −0.0247337 | ||||||||
\(103\) | −2.21463 | −0.218214 | −0.109107 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109107 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(104\) | 6.19209 | 0.607184 | ||||||||
\(105\) | 1.61928 | 0.158026 | ||||||||
\(106\) | 2.70373 | 0.262609 | ||||||||
\(107\) | 3.48114 | 0.336534 | 0.168267 | − | 0.985741i | \(-0.446183\pi\) | ||||
0.168267 | + | 0.985741i | \(0.446183\pi\) | |||||||
\(108\) | 1.93760 | 0.186446 | ||||||||
\(109\) | 9.80627 | 0.939270 | 0.469635 | − | 0.882861i | \(-0.344385\pi\) | ||||
0.469635 | + | 0.882861i | \(0.344385\pi\) | |||||||
\(110\) | 0.602589 | 0.0574547 | ||||||||
\(111\) | 3.13719 | 0.297769 | ||||||||
\(112\) | −9.76969 | −0.923149 | ||||||||
\(113\) | 13.8424 | 1.30218 | 0.651091 | − | 0.759000i | \(-0.274312\pi\) | ||||
0.651091 | + | 0.759000i | \(0.274312\pi\) | |||||||
\(114\) | 1.96825 | 0.184344 | ||||||||
\(115\) | −0.0167169 | −0.00155886 | ||||||||
\(116\) | 14.8291 | 1.37685 | ||||||||
\(117\) | 6.29531 | 0.582001 | ||||||||
\(118\) | −2.81963 | −0.259568 | ||||||||
\(119\) | 2.69175 | 0.246752 | ||||||||
\(120\) | −0.591710 | −0.0540155 | ||||||||
\(121\) | 5.08010 | 0.461827 | ||||||||
\(122\) | 0.191815 | 0.0173661 | ||||||||
\(123\) | 8.77814 | 0.791498 | ||||||||
\(124\) | −6.98239 | −0.627037 | ||||||||
\(125\) | −5.79803 | −0.518592 | ||||||||
\(126\) | 0.672392 | 0.0599014 | ||||||||
\(127\) | −3.04605 | −0.270293 | −0.135147 | − | 0.990826i | \(-0.543151\pi\) | ||||
−0.135147 | + | 0.990826i | \(0.543151\pi\) | |||||||
\(128\) | 7.38165 | 0.652452 | ||||||||
\(129\) | 5.84403 | 0.514538 | ||||||||
\(130\) | −0.946007 | −0.0829703 | ||||||||
\(131\) | 3.57711 | 0.312533 | 0.156267 | − | 0.987715i | \(-0.450054\pi\) | ||||
0.156267 | + | 0.987715i | \(0.450054\pi\) | |||||||
\(132\) | −7.76978 | −0.676273 | ||||||||
\(133\) | −21.2093 | −1.83908 | ||||||||
\(134\) | −2.83566 | −0.244964 | ||||||||
\(135\) | −0.601573 | −0.0517752 | ||||||||
\(136\) | −0.983604 | −0.0843433 | ||||||||
\(137\) | 3.12447 | 0.266941 | 0.133471 | − | 0.991053i | \(-0.457388\pi\) | ||||
0.133471 | + | 0.991053i | \(0.457388\pi\) | |||||||
\(138\) | −0.00694153 | −0.000590902 0 | ||||||||
\(139\) | 2.85097 | 0.241816 | 0.120908 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120908 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(140\) | 3.13752 | 0.265169 | ||||||||
\(141\) | 6.01959 | 0.506941 | ||||||||
\(142\) | −0.933919 | −0.0783727 | ||||||||
\(143\) | −25.2442 | −2.11102 | ||||||||
\(144\) | 3.62950 | 0.302458 | ||||||||
\(145\) | −4.60405 | −0.382346 | ||||||||
\(146\) | −0.996185 | −0.0824449 | ||||||||
\(147\) | −0.245493 | −0.0202479 | ||||||||
\(148\) | 6.07862 | 0.499660 | ||||||||
\(149\) | 13.0077 | 1.06563 | 0.532816 | − | 0.846231i | \(-0.321134\pi\) | ||||
0.532816 | + | 0.846231i | \(0.321134\pi\) | |||||||
\(150\) | −1.15859 | −0.0945984 | ||||||||
\(151\) | 4.01752 | 0.326941 | 0.163470 | − | 0.986548i | \(-0.447731\pi\) | ||||
0.163470 | + | 0.986548i | \(0.447731\pi\) | |||||||
\(152\) | 7.75019 | 0.628624 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −2.69629 | −0.217273 | ||||||||
\(155\) | 2.16784 | 0.174125 | ||||||||
\(156\) | 12.1978 | 0.976605 | ||||||||
\(157\) | 16.2233 | 1.29476 | 0.647380 | − | 0.762167i | \(-0.275865\pi\) | ||||
0.647380 | + | 0.762167i | \(0.275865\pi\) | |||||||
\(158\) | −0.249798 | −0.0198728 | ||||||||
\(159\) | 10.8237 | 0.858372 | ||||||||
\(160\) | −1.72883 | −0.136676 | ||||||||
\(161\) | 0.0747998 | 0.00589505 | ||||||||
\(162\) | −0.249798 | −0.0196260 | ||||||||
\(163\) | −15.2873 | −1.19740 | −0.598698 | − | 0.800975i | \(-0.704315\pi\) | ||||
−0.598698 | + | 0.800975i | \(0.704315\pi\) | |||||||
\(164\) | 17.0085 | 1.32814 | ||||||||
\(165\) | 2.41231 | 0.187798 | ||||||||
\(166\) | −1.71684 | −0.133253 | ||||||||
\(167\) | 11.8122 | 0.914059 | 0.457030 | − | 0.889452i | \(-0.348913\pi\) | ||||
0.457030 | + | 0.889452i | \(0.348913\pi\) | |||||||
\(168\) | 2.64761 | 0.204268 | ||||||||
\(169\) | 26.6309 | 2.04853 | ||||||||
\(170\) | 0.150272 | 0.0115253 | ||||||||
\(171\) | 7.87938 | 0.602552 | ||||||||
\(172\) | 11.3234 | 0.863401 | ||||||||
\(173\) | −11.4073 | −0.867283 | −0.433641 | − | 0.901086i | \(-0.642772\pi\) | ||||
−0.433641 | + | 0.901086i | \(0.642772\pi\) | |||||||
\(174\) | −1.91179 | −0.144932 | ||||||||
\(175\) | 12.4846 | 0.943748 | ||||||||
\(176\) | −14.5543 | −1.09707 | ||||||||
\(177\) | −11.2876 | −0.848431 | ||||||||
\(178\) | 0.308173 | 0.0230985 | ||||||||
\(179\) | 18.2483 | 1.36394 | 0.681972 | − | 0.731378i | \(-0.261122\pi\) | ||||
0.681972 | + | 0.731378i | \(0.261122\pi\) | |||||||
\(180\) | −1.16561 | −0.0868794 | ||||||||
\(181\) | −20.9086 | −1.55412 | −0.777060 | − | 0.629426i | \(-0.783290\pi\) | ||||
−0.777060 | + | 0.629426i | \(0.783290\pi\) | |||||||
\(182\) | 4.23291 | 0.313764 | ||||||||
\(183\) | 0.767879 | 0.0567633 | ||||||||
\(184\) | −0.0273330 | −0.00201501 | ||||||||
\(185\) | −1.88725 | −0.138753 | ||||||||
\(186\) | 0.900177 | 0.0660042 | ||||||||
\(187\) | 4.01000 | 0.293240 | ||||||||
\(188\) | 11.6636 | 0.850652 | ||||||||
\(189\) | 2.69175 | 0.195796 | ||||||||
\(190\) | −1.18405 | −0.0858999 | ||||||||
\(191\) | 11.5276 | 0.834107 | 0.417053 | − | 0.908882i | \(-0.363063\pi\) | ||||
0.417053 | + | 0.908882i | \(0.363063\pi\) | |||||||
\(192\) | 6.54112 | 0.472065 | ||||||||
\(193\) | 12.3391 | 0.888188 | 0.444094 | − | 0.895980i | \(-0.353526\pi\) | ||||
0.444094 | + | 0.895980i | \(0.353526\pi\) | |||||||
\(194\) | −3.16570 | −0.227284 | ||||||||
\(195\) | −3.78709 | −0.271199 | ||||||||
\(196\) | −0.475668 | −0.0339763 | ||||||||
\(197\) | −18.5801 | −1.32378 | −0.661888 | − | 0.749602i | \(-0.730245\pi\) | ||||
−0.661888 | + | 0.749602i | \(0.730245\pi\) | |||||||
\(198\) | 1.00169 | 0.0711869 | ||||||||
\(199\) | 8.55614 | 0.606529 | 0.303264 | − | 0.952906i | \(-0.401923\pi\) | ||||
0.303264 | + | 0.952906i | \(0.401923\pi\) | |||||||
\(200\) | −4.56206 | −0.322587 | ||||||||
\(201\) | −11.3518 | −0.800697 | ||||||||
\(202\) | 1.05566 | 0.0742758 | ||||||||
\(203\) | 20.6009 | 1.44590 | ||||||||
\(204\) | −1.93760 | −0.135659 | ||||||||
\(205\) | −5.28070 | −0.368820 | ||||||||
\(206\) | 0.553210 | 0.0385440 | ||||||||
\(207\) | −0.0277886 | −0.00193144 | ||||||||
\(208\) | 22.8488 | 1.58428 | ||||||||
\(209\) | −31.5963 | −2.18556 | ||||||||
\(210\) | −0.404493 | −0.0279127 | ||||||||
\(211\) | −2.28730 | −0.157464 | −0.0787321 | − | 0.996896i | \(-0.525087\pi\) | ||||
−0.0787321 | + | 0.996896i | \(0.525087\pi\) | |||||||
\(212\) | 20.9719 | 1.44036 | ||||||||
\(213\) | −3.73870 | −0.256171 | ||||||||
\(214\) | −0.869580 | −0.0594433 | ||||||||
\(215\) | −3.51561 | −0.239763 | ||||||||
\(216\) | −0.983604 | −0.0669258 | ||||||||
\(217\) | −9.70004 | −0.658482 | ||||||||
\(218\) | −2.44958 | −0.165907 | ||||||||
\(219\) | −3.98797 | −0.269482 | ||||||||
\(220\) | 4.67409 | 0.315127 | ||||||||
\(221\) | −6.29531 | −0.423468 | ||||||||
\(222\) | −0.783663 | −0.0525960 | ||||||||
\(223\) | −17.4110 | −1.16593 | −0.582964 | − | 0.812498i | \(-0.698107\pi\) | ||||
−0.582964 | + | 0.812498i | \(0.698107\pi\) | |||||||
\(224\) | 7.73567 | 0.516861 | ||||||||
\(225\) | −4.63811 | −0.309207 | ||||||||
\(226\) | −3.45780 | −0.230009 | ||||||||
\(227\) | −14.3574 | −0.952934 | −0.476467 | − | 0.879192i | \(-0.658083\pi\) | ||||
−0.476467 | + | 0.879192i | \(0.658083\pi\) | |||||||
\(228\) | 15.2671 | 1.01109 | ||||||||
\(229\) | −19.8645 | −1.31268 | −0.656340 | − | 0.754465i | \(-0.727896\pi\) | ||||
−0.656340 | + | 0.754465i | \(0.727896\pi\) | |||||||
\(230\) | 0.00417584 | 0.000275347 0 | ||||||||
\(231\) | −10.7939 | −0.710186 | ||||||||
\(232\) | −7.52786 | −0.494228 | ||||||||
\(233\) | −1.19241 | −0.0781175 | −0.0390587 | − | 0.999237i | \(-0.512436\pi\) | ||||
−0.0390587 | + | 0.999237i | \(0.512436\pi\) | |||||||
\(234\) | −1.57255 | −0.102801 | ||||||||
\(235\) | −3.62122 | −0.236223 | ||||||||
\(236\) | −21.8710 | −1.42368 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −0.672392 | −0.0435847 | ||||||||
\(239\) | 9.86106 | 0.637859 | 0.318930 | − | 0.947778i | \(-0.396677\pi\) | ||||
0.318930 | + | 0.947778i | \(0.396677\pi\) | |||||||
\(240\) | −2.18341 | −0.140939 | ||||||||
\(241\) | 11.7090 | 0.754246 | 0.377123 | − | 0.926163i | \(-0.376913\pi\) | ||||
0.377123 | + | 0.926163i | \(0.376913\pi\) | |||||||
\(242\) | −1.26900 | −0.0815742 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.48784 | 0.0952494 | ||||||||
\(245\) | 0.147682 | 0.00943506 | ||||||||
\(246\) | −2.19276 | −0.139805 | ||||||||
\(247\) | 49.6032 | 3.15617 | ||||||||
\(248\) | 3.54454 | 0.225078 | ||||||||
\(249\) | −6.87292 | −0.435554 | ||||||||
\(250\) | 1.44834 | 0.0916008 | ||||||||
\(251\) | −10.6286 | −0.670869 | −0.335435 | − | 0.942064i | \(-0.608883\pi\) | ||||
−0.335435 | + | 0.942064i | \(0.608883\pi\) | |||||||
\(252\) | 5.21553 | 0.328547 | ||||||||
\(253\) | 0.111432 | 0.00700569 | ||||||||
\(254\) | 0.760897 | 0.0477429 | ||||||||
\(255\) | 0.601573 | 0.0376720 | ||||||||
\(256\) | 11.2383 | 0.702395 | ||||||||
\(257\) | 14.1092 | 0.880107 | 0.440053 | − | 0.897972i | \(-0.354960\pi\) | ||||
0.440053 | + | 0.897972i | \(0.354960\pi\) | |||||||
\(258\) | −1.45983 | −0.0908848 | ||||||||
\(259\) | 8.44452 | 0.524717 | ||||||||
\(260\) | −7.33787 | −0.455075 | ||||||||
\(261\) | −7.65335 | −0.473730 | ||||||||
\(262\) | −0.893553 | −0.0552039 | ||||||||
\(263\) | 8.07927 | 0.498189 | 0.249095 | − | 0.968479i | \(-0.419867\pi\) | ||||
0.249095 | + | 0.968479i | \(0.419867\pi\) | |||||||
\(264\) | 3.94425 | 0.242752 | ||||||||
\(265\) | −6.51123 | −0.399982 | ||||||||
\(266\) | 5.29803 | 0.324843 | ||||||||
\(267\) | 1.23369 | 0.0755005 | ||||||||
\(268\) | −21.9953 | −1.34358 | ||||||||
\(269\) | 20.5467 | 1.25275 | 0.626377 | − | 0.779520i | \(-0.284537\pi\) | ||||
0.626377 | + | 0.779520i | \(0.284537\pi\) | |||||||
\(270\) | 0.150272 | 0.00914524 | ||||||||
\(271\) | 21.9411 | 1.33283 | 0.666415 | − | 0.745581i | \(-0.267828\pi\) | ||||
0.666415 | + | 0.745581i | \(0.267828\pi\) | |||||||
\(272\) | −3.62950 | −0.220071 | ||||||||
\(273\) | 16.9454 | 1.02558 | ||||||||
\(274\) | −0.780485 | −0.0471508 | ||||||||
\(275\) | 18.5988 | 1.12155 | ||||||||
\(276\) | −0.0538432 | −0.00324098 | ||||||||
\(277\) | −22.0171 | −1.32288 | −0.661438 | − | 0.750000i | \(-0.730054\pi\) | ||||
−0.661438 | + | 0.750000i | \(0.730054\pi\) | |||||||
\(278\) | −0.712165 | −0.0427128 | ||||||||
\(279\) | 3.60362 | 0.215743 | ||||||||
\(280\) | −1.59273 | −0.0951840 | ||||||||
\(281\) | −12.9901 | −0.774924 | −0.387462 | − | 0.921886i | \(-0.626648\pi\) | ||||
−0.387462 | + | 0.921886i | \(0.626648\pi\) | |||||||
\(282\) | −1.50368 | −0.0895428 | ||||||||
\(283\) | 25.5826 | 1.52073 | 0.760365 | − | 0.649496i | \(-0.225020\pi\) | ||||
0.760365 | + | 0.649496i | \(0.225020\pi\) | |||||||
\(284\) | −7.24411 | −0.429859 | ||||||||
\(285\) | −4.74003 | −0.280775 | ||||||||
\(286\) | 6.30594 | 0.372878 | ||||||||
\(287\) | 23.6285 | 1.39475 | ||||||||
\(288\) | −2.87385 | −0.169343 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.15008 | 0.0675351 | ||||||||
\(291\) | −12.6730 | −0.742907 | ||||||||
\(292\) | −7.72709 | −0.452194 | ||||||||
\(293\) | −4.43391 | −0.259032 | −0.129516 | − | 0.991577i | \(-0.541342\pi\) | ||||
−0.129516 | + | 0.991577i | \(0.541342\pi\) | |||||||
\(294\) | 0.0613236 | 0.00357647 | ||||||||
\(295\) | 6.79035 | 0.395349 | ||||||||
\(296\) | −3.08575 | −0.179356 | ||||||||
\(297\) | 4.01000 | 0.232684 | ||||||||
\(298\) | −3.24929 | −0.188226 | ||||||||
\(299\) | −0.174938 | −0.0101169 | ||||||||
\(300\) | −8.98681 | −0.518853 | ||||||||
\(301\) | 15.7306 | 0.906699 | ||||||||
\(302\) | −1.00357 | −0.0577488 | ||||||||
\(303\) | 4.22605 | 0.242780 | ||||||||
\(304\) | 28.5982 | 1.64022 | ||||||||
\(305\) | −0.461936 | −0.0264504 | ||||||||
\(306\) | 0.249798 | 0.0142800 | ||||||||
\(307\) | 16.4764 | 0.940358 | 0.470179 | − | 0.882571i | \(-0.344189\pi\) | ||||
0.470179 | + | 0.882571i | \(0.344189\pi\) | |||||||
\(308\) | −20.9143 | −1.19170 | ||||||||
\(309\) | 2.21463 | 0.125986 | ||||||||
\(310\) | −0.541523 | −0.0307564 | ||||||||
\(311\) | −23.7040 | −1.34413 | −0.672066 | − | 0.740491i | \(-0.734593\pi\) | ||||
−0.672066 | + | 0.740491i | \(0.734593\pi\) | |||||||
\(312\) | −6.19209 | −0.350558 | ||||||||
\(313\) | −14.7103 | −0.831473 | −0.415736 | − | 0.909485i | \(-0.636476\pi\) | ||||
−0.415736 | + | 0.909485i | \(0.636476\pi\) | |||||||
\(314\) | −4.05254 | −0.228698 | ||||||||
\(315\) | −1.61928 | −0.0912362 | ||||||||
\(316\) | −1.93760 | −0.108999 | ||||||||
\(317\) | 13.4989 | 0.758174 | 0.379087 | − | 0.925361i | \(-0.376238\pi\) | ||||
0.379087 | + | 0.925361i | \(0.376238\pi\) | |||||||
\(318\) | −2.70373 | −0.151617 | ||||||||
\(319\) | 30.6899 | 1.71831 | ||||||||
\(320\) | −3.93496 | −0.219971 | ||||||||
\(321\) | −3.48114 | −0.194298 | ||||||||
\(322\) | −0.0186848 | −0.00104126 | ||||||||
\(323\) | −7.87938 | −0.438421 | ||||||||
\(324\) | −1.93760 | −0.107645 | ||||||||
\(325\) | −29.1983 | −1.61963 | ||||||||
\(326\) | 3.81874 | 0.211500 | ||||||||
\(327\) | −9.80627 | −0.542288 | ||||||||
\(328\) | −8.63421 | −0.476745 | ||||||||
\(329\) | 16.2032 | 0.893311 | ||||||||
\(330\) | −0.602589 | −0.0331715 | ||||||||
\(331\) | 32.2146 | 1.77068 | 0.885338 | − | 0.464948i | \(-0.153927\pi\) | ||||
0.885338 | + | 0.464948i | \(0.153927\pi\) | |||||||
\(332\) | −13.3170 | −0.730864 | ||||||||
\(333\) | −3.13719 | −0.171917 | ||||||||
\(334\) | −2.95067 | −0.161454 | ||||||||
\(335\) | 6.82896 | 0.373106 | ||||||||
\(336\) | 9.76969 | 0.532980 | ||||||||
\(337\) | −6.53365 | −0.355911 | −0.177955 | − | 0.984039i | \(-0.556948\pi\) | ||||
−0.177955 | + | 0.984039i | \(0.556948\pi\) | |||||||
\(338\) | −6.65234 | −0.361840 | ||||||||
\(339\) | −13.8424 | −0.751815 | ||||||||
\(340\) | 1.16561 | 0.0632140 | ||||||||
\(341\) | −14.4505 | −0.782540 | ||||||||
\(342\) | −1.96825 | −0.106431 | ||||||||
\(343\) | 18.1814 | 0.981704 | ||||||||
\(344\) | −5.74821 | −0.309923 | ||||||||
\(345\) | 0.0167169 | 0.000900007 0 | ||||||||
\(346\) | 2.84952 | 0.153191 | ||||||||
\(347\) | 27.4956 | 1.47604 | 0.738021 | − | 0.674778i | \(-0.235761\pi\) | ||||
0.738021 | + | 0.674778i | \(0.235761\pi\) | |||||||
\(348\) | −14.8291 | −0.794925 | ||||||||
\(349\) | 1.02891 | 0.0550765 | 0.0275383 | − | 0.999621i | \(-0.491233\pi\) | ||||
0.0275383 | + | 0.999621i | \(0.491233\pi\) | |||||||
\(350\) | −3.11863 | −0.166698 | ||||||||
\(351\) | −6.29531 | −0.336019 | ||||||||
\(352\) | 11.5241 | 0.614238 | ||||||||
\(353\) | 22.5864 | 1.20215 | 0.601076 | − | 0.799192i | \(-0.294739\pi\) | ||||
0.601076 | + | 0.799192i | \(0.294739\pi\) | |||||||
\(354\) | 2.81963 | 0.149862 | ||||||||
\(355\) | 2.24910 | 0.119370 | ||||||||
\(356\) | 2.39040 | 0.126691 | ||||||||
\(357\) | −2.69175 | −0.142462 | ||||||||
\(358\) | −4.55839 | −0.240919 | ||||||||
\(359\) | 7.69373 | 0.406059 | 0.203030 | − | 0.979173i | \(-0.434921\pi\) | ||||
0.203030 | + | 0.979173i | \(0.434921\pi\) | |||||||
\(360\) | 0.591710 | 0.0311859 | ||||||||
\(361\) | 43.0847 | 2.26762 | ||||||||
\(362\) | 5.22291 | 0.274510 | ||||||||
\(363\) | −5.08010 | −0.266636 | ||||||||
\(364\) | 32.8334 | 1.72094 | ||||||||
\(365\) | 2.39906 | 0.125572 | ||||||||
\(366\) | −0.191815 | −0.0100263 | ||||||||
\(367\) | 18.2696 | 0.953665 | 0.476832 | − | 0.878994i | \(-0.341785\pi\) | ||||
0.476832 | + | 0.878994i | \(0.341785\pi\) | |||||||
\(368\) | −0.100859 | −0.00525762 | ||||||||
\(369\) | −8.77814 | −0.456972 | ||||||||
\(370\) | 0.471431 | 0.0245085 | ||||||||
\(371\) | 29.1345 | 1.51259 | ||||||||
\(372\) | 6.98239 | 0.362020 | ||||||||
\(373\) | 9.68397 | 0.501417 | 0.250709 | − | 0.968063i | \(-0.419336\pi\) | ||||
0.250709 | + | 0.968063i | \(0.419336\pi\) | |||||||
\(374\) | −1.00169 | −0.0517961 | ||||||||
\(375\) | 5.79803 | 0.299409 | ||||||||
\(376\) | −5.92089 | −0.305346 | ||||||||
\(377\) | −48.1802 | −2.48140 | ||||||||
\(378\) | −0.672392 | −0.0345841 | ||||||||
\(379\) | −2.60077 | −0.133593 | −0.0667964 | − | 0.997767i | \(-0.521278\pi\) | ||||
−0.0667964 | + | 0.997767i | \(0.521278\pi\) | |||||||
\(380\) | −9.18428 | −0.471144 | ||||||||
\(381\) | 3.04605 | 0.156054 | ||||||||
\(382\) | −2.87957 | −0.147331 | ||||||||
\(383\) | −22.3068 | −1.13982 | −0.569912 | − | 0.821706i | \(-0.693023\pi\) | ||||
−0.569912 | + | 0.821706i | \(0.693023\pi\) | |||||||
\(384\) | −7.38165 | −0.376693 | ||||||||
\(385\) | 6.49332 | 0.330930 | ||||||||
\(386\) | −3.08228 | −0.156884 | ||||||||
\(387\) | −5.84403 | −0.297069 | ||||||||
\(388\) | −24.5553 | −1.24661 | ||||||||
\(389\) | −14.7227 | −0.746472 | −0.373236 | − | 0.927736i | \(-0.621752\pi\) | ||||
−0.373236 | + | 0.927736i | \(0.621752\pi\) | |||||||
\(390\) | 0.946007 | 0.0479029 | ||||||||
\(391\) | 0.0277886 | 0.00140533 | ||||||||
\(392\) | 0.241468 | 0.0121960 | ||||||||
\(393\) | −3.57711 | −0.180441 | ||||||||
\(394\) | 4.64127 | 0.233824 | ||||||||
\(395\) | 0.601573 | 0.0302684 | ||||||||
\(396\) | 7.76978 | 0.390446 | ||||||||
\(397\) | 22.2911 | 1.11876 | 0.559378 | − | 0.828913i | \(-0.311040\pi\) | ||||
0.559378 | + | 0.828913i | \(0.311040\pi\) | |||||||
\(398\) | −2.13731 | −0.107133 | ||||||||
\(399\) | 21.2093 | 1.06179 | ||||||||
\(400\) | −16.8340 | −0.841701 | ||||||||
\(401\) | −19.8299 | −0.990259 | −0.495129 | − | 0.868819i | \(-0.664879\pi\) | ||||
−0.495129 | + | 0.868819i | \(0.664879\pi\) | |||||||
\(402\) | 2.83566 | 0.141430 | ||||||||
\(403\) | 22.6859 | 1.13007 | ||||||||
\(404\) | 8.18840 | 0.407388 | ||||||||
\(405\) | 0.601573 | 0.0298924 | ||||||||
\(406\) | −5.14605 | −0.255394 | ||||||||
\(407\) | 12.5801 | 0.623574 | ||||||||
\(408\) | 0.983604 | 0.0486956 | ||||||||
\(409\) | −16.4773 | −0.814749 | −0.407375 | − | 0.913261i | \(-0.633556\pi\) | ||||
−0.407375 | + | 0.913261i | \(0.633556\pi\) | |||||||
\(410\) | 1.31911 | 0.0651460 | ||||||||
\(411\) | −3.12447 | −0.154119 | ||||||||
\(412\) | 4.29107 | 0.211406 | ||||||||
\(413\) | −30.3835 | −1.49507 | ||||||||
\(414\) | 0.00694153 | 0.000341158 0 | ||||||||
\(415\) | 4.13457 | 0.202958 | ||||||||
\(416\) | −18.0918 | −0.887022 | ||||||||
\(417\) | −2.85097 | −0.139613 | ||||||||
\(418\) | 7.89269 | 0.386044 | ||||||||
\(419\) | −19.9343 | −0.973856 | −0.486928 | − | 0.873442i | \(-0.661883\pi\) | ||||
−0.486928 | + | 0.873442i | \(0.661883\pi\) | |||||||
\(420\) | −3.13752 | −0.153095 | ||||||||
\(421\) | 27.9251 | 1.36099 | 0.680494 | − | 0.732754i | \(-0.261765\pi\) | ||||
0.680494 | + | 0.732754i | \(0.261765\pi\) | |||||||
\(422\) | 0.571362 | 0.0278135 | ||||||||
\(423\) | −6.01959 | −0.292682 | ||||||||
\(424\) | −10.6462 | −0.517025 | ||||||||
\(425\) | 4.63811 | 0.224981 | ||||||||
\(426\) | 0.933919 | 0.0452485 | ||||||||
\(427\) | 2.06694 | 0.100026 | ||||||||
\(428\) | −6.74506 | −0.326035 | ||||||||
\(429\) | 25.2442 | 1.21880 | ||||||||
\(430\) | 0.878192 | 0.0423502 | ||||||||
\(431\) | 37.9667 | 1.82879 | 0.914397 | − | 0.404819i | \(-0.132666\pi\) | ||||
0.914397 | + | 0.404819i | \(0.132666\pi\) | |||||||
\(432\) | −3.62950 | −0.174624 | ||||||||
\(433\) | −2.28993 | −0.110047 | −0.0550234 | − | 0.998485i | \(-0.517523\pi\) | ||||
−0.0550234 | + | 0.998485i | \(0.517523\pi\) | |||||||
\(434\) | 2.42305 | 0.116310 | ||||||||
\(435\) | 4.60405 | 0.220747 | ||||||||
\(436\) | −19.0006 | −0.909966 | ||||||||
\(437\) | −0.218957 | −0.0104741 | ||||||||
\(438\) | 0.996185 | 0.0475996 | ||||||||
\(439\) | −2.44673 | −0.116776 | −0.0583880 | − | 0.998294i | \(-0.518596\pi\) | ||||
−0.0583880 | + | 0.998294i | \(0.518596\pi\) | |||||||
\(440\) | −2.37276 | −0.113117 | ||||||||
\(441\) | 0.245493 | 0.0116901 | ||||||||
\(442\) | 1.57255 | 0.0747988 | ||||||||
\(443\) | 8.23273 | 0.391149 | 0.195574 | − | 0.980689i | \(-0.437343\pi\) | ||||
0.195574 | + | 0.980689i | \(0.437343\pi\) | |||||||
\(444\) | −6.07862 | −0.288479 | ||||||||
\(445\) | −0.742154 | −0.0351815 | ||||||||
\(446\) | 4.34924 | 0.205942 | ||||||||
\(447\) | −13.0077 | −0.615243 | ||||||||
\(448\) | 17.6070 | 0.831854 | ||||||||
\(449\) | −0.490723 | −0.0231587 | −0.0115793 | − | 0.999933i | \(-0.503686\pi\) | ||||
−0.0115793 | + | 0.999933i | \(0.503686\pi\) | |||||||
\(450\) | 1.15859 | 0.0546164 | ||||||||
\(451\) | 35.2003 | 1.65752 | ||||||||
\(452\) | −26.8210 | −1.26155 | ||||||||
\(453\) | −4.01752 | −0.188759 | ||||||||
\(454\) | 3.58645 | 0.168320 | ||||||||
\(455\) | −10.1939 | −0.477897 | ||||||||
\(456\) | −7.75019 | −0.362936 | ||||||||
\(457\) | 30.1693 | 1.41126 | 0.705631 | − | 0.708580i | \(-0.250664\pi\) | ||||
0.705631 | + | 0.708580i | \(0.250664\pi\) | |||||||
\(458\) | 4.96210 | 0.231864 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 0.0323906 | 0.00151022 | ||||||||
\(461\) | 32.9453 | 1.53442 | 0.767208 | − | 0.641399i | \(-0.221646\pi\) | ||||
0.767208 | + | 0.641399i | \(0.221646\pi\) | |||||||
\(462\) | 2.69629 | 0.125443 | ||||||||
\(463\) | 1.25815 | 0.0584712 | 0.0292356 | − | 0.999573i | \(-0.490693\pi\) | ||||
0.0292356 | + | 0.999573i | \(0.490693\pi\) | |||||||
\(464\) | −27.7778 | −1.28955 | ||||||||
\(465\) | −2.16784 | −0.100531 | ||||||||
\(466\) | 0.297862 | 0.0137982 | ||||||||
\(467\) | −30.5249 | −1.41252 | −0.706261 | − | 0.707951i | \(-0.749620\pi\) | ||||
−0.706261 | + | 0.707951i | \(0.749620\pi\) | |||||||
\(468\) | −12.1978 | −0.563843 | ||||||||
\(469\) | −30.5562 | −1.41096 | ||||||||
\(470\) | 0.904573 | 0.0417249 | ||||||||
\(471\) | −16.2233 | −0.747530 | ||||||||
\(472\) | 11.1026 | 0.511037 | ||||||||
\(473\) | 23.4346 | 1.07752 | ||||||||
\(474\) | 0.249798 | 0.0114736 | ||||||||
\(475\) | −36.5454 | −1.67682 | ||||||||
\(476\) | −5.21553 | −0.239053 | ||||||||
\(477\) | −10.8237 | −0.495582 | ||||||||
\(478\) | −2.46327 | −0.112667 | ||||||||
\(479\) | 22.4564 | 1.02606 | 0.513030 | − | 0.858371i | \(-0.328523\pi\) | ||||
0.513030 | + | 0.858371i | \(0.328523\pi\) | |||||||
\(480\) | 1.72883 | 0.0789100 | ||||||||
\(481\) | −19.7496 | −0.900503 | ||||||||
\(482\) | −2.92489 | −0.133225 | ||||||||
\(483\) | −0.0747998 | −0.00340351 | ||||||||
\(484\) | −9.84320 | −0.447418 | ||||||||
\(485\) | 7.62377 | 0.346177 | ||||||||
\(486\) | 0.249798 | 0.0113311 | ||||||||
\(487\) | 28.4735 | 1.29026 | 0.645129 | − | 0.764074i | \(-0.276804\pi\) | ||||
0.645129 | + | 0.764074i | \(0.276804\pi\) | |||||||
\(488\) | −0.755289 | −0.0341903 | ||||||||
\(489\) | 15.2873 | 0.691317 | ||||||||
\(490\) | −0.0368907 | −0.00166655 | ||||||||
\(491\) | −22.3317 | −1.00782 | −0.503909 | − | 0.863757i | \(-0.668105\pi\) | ||||
−0.503909 | + | 0.863757i | \(0.668105\pi\) | |||||||
\(492\) | −17.0085 | −0.766804 | ||||||||
\(493\) | 7.65335 | 0.344689 | ||||||||
\(494\) | −12.3908 | −0.557486 | ||||||||
\(495\) | −2.41231 | −0.108425 | ||||||||
\(496\) | 13.0794 | 0.587280 | ||||||||
\(497\) | −10.0636 | −0.451415 | ||||||||
\(498\) | 1.71684 | 0.0769335 | ||||||||
\(499\) | −14.2687 | −0.638753 | −0.319377 | − | 0.947628i | \(-0.603474\pi\) | ||||
−0.319377 | + | 0.947628i | \(0.603474\pi\) | |||||||
\(500\) | 11.2343 | 0.502412 | ||||||||
\(501\) | −11.8122 | −0.527732 | ||||||||
\(502\) | 2.65499 | 0.118498 | ||||||||
\(503\) | −2.91169 | −0.129826 | −0.0649129 | − | 0.997891i | \(-0.520677\pi\) | ||||
−0.0649129 | + | 0.997891i | \(0.520677\pi\) | |||||||
\(504\) | −2.64761 | −0.117934 | ||||||||
\(505\) | −2.54228 | −0.113130 | ||||||||
\(506\) | −0.0278355 | −0.00123744 | ||||||||
\(507\) | −26.6309 | −1.18272 | ||||||||
\(508\) | 5.90203 | 0.261860 | ||||||||
\(509\) | −24.1866 | −1.07205 | −0.536026 | − | 0.844201i | \(-0.680075\pi\) | ||||
−0.536026 | + | 0.844201i | \(0.680075\pi\) | |||||||
\(510\) | −0.150272 | −0.00665414 | ||||||||
\(511\) | −10.7346 | −0.474871 | ||||||||
\(512\) | −17.5706 | −0.776519 | ||||||||
\(513\) | −7.87938 | −0.347883 | ||||||||
\(514\) | −3.52444 | −0.155456 | ||||||||
\(515\) | −1.33226 | −0.0587066 | ||||||||
\(516\) | −11.3234 | −0.498485 | ||||||||
\(517\) | 24.1385 | 1.06161 | ||||||||
\(518\) | −2.10942 | −0.0926827 | ||||||||
\(519\) | 11.4073 | 0.500726 | ||||||||
\(520\) | 3.72500 | 0.163352 | ||||||||
\(521\) | 16.3236 | 0.715151 | 0.357576 | − | 0.933884i | \(-0.383603\pi\) | ||||
0.357576 | + | 0.933884i | \(0.383603\pi\) | |||||||
\(522\) | 1.91179 | 0.0836767 | ||||||||
\(523\) | 40.2601 | 1.76045 | 0.880225 | − | 0.474556i | \(-0.157391\pi\) | ||||
0.880225 | + | 0.474556i | \(0.157391\pi\) | |||||||
\(524\) | −6.93101 | −0.302782 | ||||||||
\(525\) | −12.4846 | −0.544873 | ||||||||
\(526\) | −2.01818 | −0.0879970 | ||||||||
\(527\) | −3.60362 | −0.156976 | ||||||||
\(528\) | 14.5543 | 0.633394 | ||||||||
\(529\) | −22.9992 | −0.999966 | ||||||||
\(530\) | 1.62649 | 0.0706502 | ||||||||
\(531\) | 11.2876 | 0.489842 | ||||||||
\(532\) | 41.0952 | 1.78170 | ||||||||
\(533\) | −55.2611 | −2.39362 | ||||||||
\(534\) | −0.308173 | −0.0133359 | ||||||||
\(535\) | 2.09416 | 0.0905384 | ||||||||
\(536\) | 11.1657 | 0.482285 | ||||||||
\(537\) | −18.2483 | −0.787474 | ||||||||
\(538\) | −5.13252 | −0.221279 | ||||||||
\(539\) | −0.984427 | −0.0424023 | ||||||||
\(540\) | 1.16561 | 0.0501598 | ||||||||
\(541\) | 8.33378 | 0.358297 | 0.179149 | − | 0.983822i | \(-0.442666\pi\) | ||||
0.179149 | + | 0.983822i | \(0.442666\pi\) | |||||||
\(542\) | −5.48085 | −0.235423 | ||||||||
\(543\) | 20.9086 | 0.897272 | ||||||||
\(544\) | 2.87385 | 0.123215 | ||||||||
\(545\) | 5.89919 | 0.252694 | ||||||||
\(546\) | −4.23291 | −0.181152 | ||||||||
\(547\) | 4.12593 | 0.176412 | 0.0882060 | − | 0.996102i | \(-0.471887\pi\) | ||||
0.0882060 | + | 0.996102i | \(0.471887\pi\) | |||||||
\(548\) | −6.05398 | −0.258613 | ||||||||
\(549\) | −0.767879 | −0.0327723 | ||||||||
\(550\) | −4.64594 | −0.198104 | ||||||||
\(551\) | −60.3037 | −2.56902 | ||||||||
\(552\) | 0.0273330 | 0.00116337 | ||||||||
\(553\) | −2.69175 | −0.114465 | ||||||||
\(554\) | 5.49981 | 0.233665 | ||||||||
\(555\) | 1.88725 | 0.0801093 | ||||||||
\(556\) | −5.52404 | −0.234271 | ||||||||
\(557\) | −35.2923 | −1.49538 | −0.747691 | − | 0.664047i | \(-0.768838\pi\) | ||||
−0.747691 | + | 0.664047i | \(0.768838\pi\) | |||||||
\(558\) | −0.900177 | −0.0381075 | ||||||||
\(559\) | −36.7900 | −1.55605 | ||||||||
\(560\) | −5.87719 | −0.248356 | ||||||||
\(561\) | −4.01000 | −0.169302 | ||||||||
\(562\) | 3.24490 | 0.136878 | ||||||||
\(563\) | −20.9611 | −0.883404 | −0.441702 | − | 0.897162i | \(-0.645625\pi\) | ||||
−0.441702 | + | 0.897162i | \(0.645625\pi\) | |||||||
\(564\) | −11.6636 | −0.491124 | ||||||||
\(565\) | 8.32721 | 0.350328 | ||||||||
\(566\) | −6.39049 | −0.268612 | ||||||||
\(567\) | −2.69175 | −0.113043 | ||||||||
\(568\) | 3.67740 | 0.154300 | ||||||||
\(569\) | 39.8443 | 1.67036 | 0.835179 | − | 0.549978i | \(-0.185364\pi\) | ||||
0.835179 | + | 0.549978i | \(0.185364\pi\) | |||||||
\(570\) | 1.18405 | 0.0495943 | ||||||||
\(571\) | −25.0859 | −1.04981 | −0.524907 | − | 0.851160i | \(-0.675900\pi\) | ||||
−0.524907 | + | 0.851160i | \(0.675900\pi\) | |||||||
\(572\) | 48.9132 | 2.04516 | ||||||||
\(573\) | −11.5276 | −0.481572 | ||||||||
\(574\) | −5.90235 | −0.246359 | ||||||||
\(575\) | 0.128887 | 0.00537494 | ||||||||
\(576\) | −6.54112 | −0.272547 | ||||||||
\(577\) | 21.3996 | 0.890877 | 0.445438 | − | 0.895313i | \(-0.353048\pi\) | ||||
0.445438 | + | 0.895313i | \(0.353048\pi\) | |||||||
\(578\) | −0.249798 | −0.0103902 | ||||||||
\(579\) | −12.3391 | −0.512796 | ||||||||
\(580\) | 8.92081 | 0.370417 | ||||||||
\(581\) | −18.5002 | −0.767516 | ||||||||
\(582\) | 3.16570 | 0.131222 | ||||||||
\(583\) | 43.4029 | 1.79756 | ||||||||
\(584\) | 3.92258 | 0.162318 | ||||||||
\(585\) | 3.78709 | 0.156577 | ||||||||
\(586\) | 1.10758 | 0.0457538 | ||||||||
\(587\) | −1.65094 | −0.0681417 | −0.0340708 | − | 0.999419i | \(-0.510847\pi\) | ||||
−0.0340708 | + | 0.999419i | \(0.510847\pi\) | |||||||
\(588\) | 0.475668 | 0.0196162 | ||||||||
\(589\) | 28.3943 | 1.16997 | ||||||||
\(590\) | −1.69621 | −0.0698320 | ||||||||
\(591\) | 18.5801 | 0.764283 | ||||||||
\(592\) | −11.3864 | −0.467980 | ||||||||
\(593\) | −16.2107 | −0.665695 | −0.332848 | − | 0.942981i | \(-0.608010\pi\) | ||||
−0.332848 | + | 0.942981i | \(0.608010\pi\) | |||||||
\(594\) | −1.00169 | −0.0410998 | ||||||||
\(595\) | 1.61928 | 0.0663841 | ||||||||
\(596\) | −25.2037 | −1.03238 | ||||||||
\(597\) | −8.55614 | −0.350180 | ||||||||
\(598\) | 0.0436991 | 0.00178699 | ||||||||
\(599\) | 42.1829 | 1.72355 | 0.861774 | − | 0.507293i | \(-0.169354\pi\) | ||||
0.861774 | + | 0.507293i | \(0.169354\pi\) | |||||||
\(600\) | 4.56206 | 0.186245 | ||||||||
\(601\) | −32.4009 | −1.32166 | −0.660830 | − | 0.750536i | \(-0.729795\pi\) | ||||
−0.660830 | + | 0.750536i | \(0.729795\pi\) | |||||||
\(602\) | −3.92948 | −0.160154 | ||||||||
\(603\) | 11.3518 | 0.462282 | ||||||||
\(604\) | −7.78434 | −0.316740 | ||||||||
\(605\) | 3.05605 | 0.124246 | ||||||||
\(606\) | −1.05566 | −0.0428832 | ||||||||
\(607\) | 26.4988 | 1.07555 | 0.537776 | − | 0.843087i | \(-0.319264\pi\) | ||||
0.537776 | + | 0.843087i | \(0.319264\pi\) | |||||||
\(608\) | −22.6442 | −0.918342 | ||||||||
\(609\) | −20.6009 | −0.834789 | ||||||||
\(610\) | 0.115391 | 0.00467203 | ||||||||
\(611\) | −37.8951 | −1.53307 | ||||||||
\(612\) | 1.93760 | 0.0783229 | ||||||||
\(613\) | 26.9517 | 1.08857 | 0.544284 | − | 0.838901i | \(-0.316801\pi\) | ||||
0.544284 | + | 0.838901i | \(0.316801\pi\) | |||||||
\(614\) | −4.11577 | −0.166099 | ||||||||
\(615\) | 5.28070 | 0.212938 | ||||||||
\(616\) | 10.6169 | 0.427768 | ||||||||
\(617\) | −12.1534 | −0.489276 | −0.244638 | − | 0.969615i | \(-0.578669\pi\) | ||||
−0.244638 | + | 0.969615i | \(0.578669\pi\) | |||||||
\(618\) | −0.553210 | −0.0222534 | ||||||||
\(619\) | −48.8721 | −1.96434 | −0.982168 | − | 0.188005i | \(-0.939798\pi\) | ||||
−0.982168 | + | 0.188005i | \(0.939798\pi\) | |||||||
\(620\) | −4.20042 | −0.168693 | ||||||||
\(621\) | 0.0277886 | 0.00111512 | ||||||||
\(622\) | 5.92122 | 0.237419 | ||||||||
\(623\) | 3.32078 | 0.133044 | ||||||||
\(624\) | −22.8488 | −0.914685 | ||||||||
\(625\) | 19.7026 | 0.788104 | ||||||||
\(626\) | 3.67459 | 0.146866 | ||||||||
\(627\) | 31.5963 | 1.26184 | ||||||||
\(628\) | −31.4343 | −1.25436 | ||||||||
\(629\) | 3.13719 | 0.125088 | ||||||||
\(630\) | 0.404493 | 0.0161154 | ||||||||
\(631\) | 0.205425 | 0.00817784 | 0.00408892 | − | 0.999992i | \(-0.498698\pi\) | ||||
0.00408892 | + | 0.999992i | \(0.498698\pi\) | |||||||
\(632\) | 0.983604 | 0.0391257 | ||||||||
\(633\) | 2.28730 | 0.0909120 | ||||||||
\(634\) | −3.37199 | −0.133919 | ||||||||
\(635\) | −1.83242 | −0.0727175 | ||||||||
\(636\) | −20.9719 | −0.831592 | ||||||||
\(637\) | 1.54545 | 0.0612331 | ||||||||
\(638\) | −7.66627 | −0.303511 | ||||||||
\(639\) | 3.73870 | 0.147901 | ||||||||
\(640\) | 4.44061 | 0.175530 | ||||||||
\(641\) | 26.9007 | 1.06251 | 0.531257 | − | 0.847211i | \(-0.321720\pi\) | ||||
0.531257 | + | 0.847211i | \(0.321720\pi\) | |||||||
\(642\) | 0.869580 | 0.0343196 | ||||||||
\(643\) | 43.9322 | 1.73252 | 0.866259 | − | 0.499596i | \(-0.166518\pi\) | ||||
0.866259 | + | 0.499596i | \(0.166518\pi\) | |||||||
\(644\) | −0.144932 | −0.00571113 | ||||||||
\(645\) | 3.51561 | 0.138427 | ||||||||
\(646\) | 1.96825 | 0.0774399 | ||||||||
\(647\) | −11.9167 | −0.468493 | −0.234247 | − | 0.972177i | \(-0.575262\pi\) | ||||
−0.234247 | + | 0.972177i | \(0.575262\pi\) | |||||||
\(648\) | 0.983604 | 0.0386396 | ||||||||
\(649\) | −45.2635 | −1.77675 | ||||||||
\(650\) | 7.29368 | 0.286082 | ||||||||
\(651\) | 9.70004 | 0.380175 | ||||||||
\(652\) | 29.6207 | 1.16004 | ||||||||
\(653\) | −0.908436 | −0.0355499 | −0.0177749 | − | 0.999842i | \(-0.505658\pi\) | ||||
−0.0177749 | + | 0.999842i | \(0.505658\pi\) | |||||||
\(654\) | 2.44958 | 0.0957863 | ||||||||
\(655\) | 2.15189 | 0.0840814 | ||||||||
\(656\) | −31.8603 | −1.24393 | ||||||||
\(657\) | 3.98797 | 0.155585 | ||||||||
\(658\) | −4.04752 | −0.157789 | ||||||||
\(659\) | 50.3795 | 1.96251 | 0.981253 | − | 0.192724i | \(-0.0617323\pi\) | ||||
0.981253 | + | 0.192724i | \(0.0617323\pi\) | |||||||
\(660\) | −4.67409 | −0.181939 | ||||||||
\(661\) | 27.3573 | 1.06408 | 0.532039 | − | 0.846720i | \(-0.321426\pi\) | ||||
0.532039 | + | 0.846720i | \(0.321426\pi\) | |||||||
\(662\) | −8.04714 | −0.312761 | ||||||||
\(663\) | 6.29531 | 0.244489 | ||||||||
\(664\) | 6.76023 | 0.262348 | ||||||||
\(665\) | −12.7590 | −0.494771 | ||||||||
\(666\) | 0.783663 | 0.0303663 | ||||||||
\(667\) | 0.212676 | 0.00823484 | ||||||||
\(668\) | −22.8874 | −0.885541 | ||||||||
\(669\) | 17.4110 | 0.673149 | ||||||||
\(670\) | −1.70586 | −0.0659031 | ||||||||
\(671\) | 3.07920 | 0.118871 | ||||||||
\(672\) | −7.73567 | −0.298410 | ||||||||
\(673\) | −17.0332 | −0.656582 | −0.328291 | − | 0.944577i | \(-0.606473\pi\) | ||||
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(674\) | 1.63209 | 0.0628658 | ||||||||
\(675\) | 4.63811 | 0.178521 | ||||||||
\(676\) | −51.6001 | −1.98462 | ||||||||
\(677\) | 5.34461 | 0.205410 | 0.102705 | − | 0.994712i | \(-0.467250\pi\) | ||||
0.102705 | + | 0.994712i | \(0.467250\pi\) | |||||||
\(678\) | 3.45780 | 0.132796 | ||||||||
\(679\) | −34.1126 | −1.30912 | ||||||||
\(680\) | −0.591710 | −0.0226910 | ||||||||
\(681\) | 14.3574 | 0.550177 | ||||||||
\(682\) | 3.60971 | 0.138223 | ||||||||
\(683\) | 1.88682 | 0.0721971 | 0.0360985 | − | 0.999348i | \(-0.488507\pi\) | ||||
0.0360985 | + | 0.999348i | \(0.488507\pi\) | |||||||
\(684\) | −15.2671 | −0.583752 | ||||||||
\(685\) | 1.87960 | 0.0718157 | ||||||||
\(686\) | −4.54168 | −0.173402 | ||||||||
\(687\) | 19.8645 | 0.757876 | ||||||||
\(688\) | −21.2109 | −0.808658 | ||||||||
\(689\) | −68.1383 | −2.59586 | ||||||||
\(690\) | −0.00417584 | −0.000158971 0 | ||||||||
\(691\) | 49.8882 | 1.89784 | 0.948918 | − | 0.315522i | \(-0.102179\pi\) | ||||
0.948918 | + | 0.315522i | \(0.102179\pi\) | |||||||
\(692\) | 22.1028 | 0.840224 | ||||||||
\(693\) | 10.7939 | 0.410026 | ||||||||
\(694\) | −6.86834 | −0.260719 | ||||||||
\(695\) | 1.71507 | 0.0650562 | ||||||||
\(696\) | 7.52786 | 0.285343 | ||||||||
\(697\) | 8.77814 | 0.332496 | ||||||||
\(698\) | −0.257020 | −0.00972837 | ||||||||
\(699\) | 1.19241 | 0.0451011 | ||||||||
\(700\) | −24.1902 | −0.914303 | ||||||||
\(701\) | −14.5824 | −0.550769 | −0.275385 | − | 0.961334i | \(-0.588805\pi\) | ||||
−0.275385 | + | 0.961334i | \(0.588805\pi\) | |||||||
\(702\) | 1.57255 | 0.0593522 | ||||||||
\(703\) | −24.7191 | −0.932300 | ||||||||
\(704\) | 26.2299 | 0.988576 | ||||||||
\(705\) | 3.62122 | 0.136383 | ||||||||
\(706\) | −5.64203 | −0.212341 | ||||||||
\(707\) | 11.3754 | 0.427818 | ||||||||
\(708\) | 21.8710 | 0.821961 | ||||||||
\(709\) | −36.9391 | −1.38728 | −0.693639 | − | 0.720323i | \(-0.743994\pi\) | ||||
−0.693639 | + | 0.720323i | \(0.743994\pi\) | |||||||
\(710\) | −0.561821 | −0.0210848 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −1.21346 | −0.0454764 | ||||||||
\(713\) | −0.100140 | −0.00375026 | ||||||||
\(714\) | 0.672392 | 0.0251636 | ||||||||
\(715\) | −15.1862 | −0.567933 | ||||||||
\(716\) | −35.3580 | −1.32139 | ||||||||
\(717\) | −9.86106 | −0.368268 | ||||||||
\(718\) | −1.92188 | −0.0717238 | ||||||||
\(719\) | 11.9176 | 0.444451 | 0.222225 | − | 0.974995i | \(-0.428668\pi\) | ||||
0.222225 | + | 0.974995i | \(0.428668\pi\) | |||||||
\(720\) | 2.18341 | 0.0813709 | ||||||||
\(721\) | 5.96123 | 0.222008 | ||||||||
\(722\) | −10.7625 | −0.400537 | ||||||||
\(723\) | −11.7090 | −0.435464 | ||||||||
\(724\) | 40.5124 | 1.50563 | ||||||||
\(725\) | 35.4971 | 1.31833 | ||||||||
\(726\) | 1.26900 | 0.0470969 | ||||||||
\(727\) | −23.1710 | −0.859363 | −0.429682 | − | 0.902980i | \(-0.641374\pi\) | ||||
−0.429682 | + | 0.902980i | \(0.641374\pi\) | |||||||
\(728\) | −16.6675 | −0.617740 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.599279 | −0.0221803 | ||||||||
\(731\) | 5.84403 | 0.216149 | ||||||||
\(732\) | −1.48784 | −0.0549923 | ||||||||
\(733\) | −19.0576 | −0.703910 | −0.351955 | − | 0.936017i | \(-0.614483\pi\) | ||||
−0.351955 | + | 0.936017i | \(0.614483\pi\) | |||||||
\(734\) | −4.56370 | −0.168449 | ||||||||
\(735\) | −0.147682 | −0.00544734 | ||||||||
\(736\) | 0.0798602 | 0.00294369 | ||||||||
\(737\) | −45.5208 | −1.67678 | ||||||||
\(738\) | 2.19276 | 0.0807166 | ||||||||
\(739\) | 10.0997 | 0.371525 | 0.185763 | − | 0.982595i | \(-0.440524\pi\) | ||||
0.185763 | + | 0.982595i | \(0.440524\pi\) | |||||||
\(740\) | 3.65674 | 0.134424 | ||||||||
\(741\) | −49.6032 | −1.82222 | ||||||||
\(742\) | −7.27774 | −0.267174 | ||||||||
\(743\) | 36.1643 | 1.32674 | 0.663369 | − | 0.748292i | \(-0.269126\pi\) | ||||
0.663369 | + | 0.748292i | \(0.269126\pi\) | |||||||
\(744\) | −3.54454 | −0.129949 | ||||||||
\(745\) | 7.82508 | 0.286689 | ||||||||
\(746\) | −2.41904 | −0.0885672 | ||||||||
\(747\) | 6.87292 | 0.251467 | ||||||||
\(748\) | −7.76978 | −0.284091 | ||||||||
\(749\) | −9.37034 | −0.342385 | ||||||||
\(750\) | −1.44834 | −0.0528857 | ||||||||
\(751\) | −38.1877 | −1.39349 | −0.696745 | − | 0.717319i | \(-0.745369\pi\) | ||||
−0.696745 | + | 0.717319i | \(0.745369\pi\) | |||||||
\(752\) | −21.8481 | −0.796718 | ||||||||
\(753\) | 10.6286 | 0.387326 | ||||||||
\(754\) | 12.0353 | 0.438300 | ||||||||
\(755\) | 2.41683 | 0.0879575 | ||||||||
\(756\) | −5.21553 | −0.189687 | ||||||||
\(757\) | −5.71912 | −0.207865 | −0.103932 | − | 0.994584i | \(-0.533143\pi\) | ||||
−0.103932 | + | 0.994584i | \(0.533143\pi\) | |||||||
\(758\) | 0.649667 | 0.0235970 | ||||||||
\(759\) | −0.111432 | −0.00404474 | ||||||||
\(760\) | 4.66231 | 0.169120 | ||||||||
\(761\) | 12.2142 | 0.442766 | 0.221383 | − | 0.975187i | \(-0.428943\pi\) | ||||
0.221383 | + | 0.975187i | \(0.428943\pi\) | |||||||
\(762\) | −0.760897 | −0.0275644 | ||||||||
\(763\) | −26.3960 | −0.955599 | ||||||||
\(764\) | −22.3359 | −0.808083 | ||||||||
\(765\) | −0.601573 | −0.0217499 | ||||||||
\(766\) | 5.57219 | 0.201331 | ||||||||
\(767\) | 71.0592 | 2.56580 | ||||||||
\(768\) | −11.2383 | −0.405528 | ||||||||
\(769\) | −48.5415 | −1.75045 | −0.875226 | − | 0.483714i | \(-0.839288\pi\) | ||||
−0.875226 | + | 0.483714i | \(0.839288\pi\) | |||||||
\(770\) | −1.62202 | −0.0584535 | ||||||||
\(771\) | −14.1092 | −0.508130 | ||||||||
\(772\) | −23.9083 | −0.860477 | ||||||||
\(773\) | 35.5001 | 1.27685 | 0.638425 | − | 0.769684i | \(-0.279586\pi\) | ||||
0.638425 | + | 0.769684i | \(0.279586\pi\) | |||||||
\(774\) | 1.45983 | 0.0524723 | ||||||||
\(775\) | −16.7140 | −0.600385 | ||||||||
\(776\) | 12.4653 | 0.447477 | ||||||||
\(777\) | −8.44452 | −0.302945 | ||||||||
\(778\) | 3.67770 | 0.131852 | ||||||||
\(779\) | −69.1664 | −2.47814 | ||||||||
\(780\) | 7.33787 | 0.262738 | ||||||||
\(781\) | −14.9922 | −0.536463 | ||||||||
\(782\) | −0.00694153 | −0.000248229 0 | ||||||||
\(783\) | 7.65335 | 0.273508 | ||||||||
\(784\) | 0.891017 | 0.0318220 | ||||||||
\(785\) | 9.75951 | 0.348332 | ||||||||
\(786\) | 0.893553 | 0.0318720 | ||||||||
\(787\) | −38.3312 | −1.36636 | −0.683180 | − | 0.730250i | \(-0.739403\pi\) | ||||
−0.683180 | + | 0.730250i | \(0.739403\pi\) | |||||||
\(788\) | 36.0008 | 1.28248 | ||||||||
\(789\) | −8.07927 | −0.287630 | ||||||||
\(790\) | −0.150272 | −0.00534643 | ||||||||
\(791\) | −37.2602 | −1.32482 | ||||||||
\(792\) | −3.94425 | −0.140153 | ||||||||
\(793\) | −4.83404 | −0.171662 | ||||||||
\(794\) | −5.56826 | −0.197610 | ||||||||
\(795\) | 6.51123 | 0.230930 | ||||||||
\(796\) | −16.5784 | −0.587606 | ||||||||
\(797\) | 12.9802 | 0.459782 | 0.229891 | − | 0.973216i | \(-0.426163\pi\) | ||||
0.229891 | + | 0.973216i | \(0.426163\pi\) | |||||||
\(798\) | −5.29803 | −0.187548 | ||||||||
\(799\) | 6.01959 | 0.212958 | ||||||||
\(800\) | 13.3292 | 0.471259 | ||||||||
\(801\) | −1.23369 | −0.0435902 | ||||||||
\(802\) | 4.95347 | 0.174913 | ||||||||
\(803\) | −15.9918 | −0.564337 | ||||||||
\(804\) | 21.9953 | 0.775715 | ||||||||
\(805\) | 0.0449976 | 0.00158596 | ||||||||
\(806\) | −5.66689 | −0.199608 | ||||||||
\(807\) | −20.5467 | −0.723278 | ||||||||
\(808\) | −4.15676 | −0.146234 | ||||||||
\(809\) | 13.6188 | 0.478811 | 0.239405 | − | 0.970920i | \(-0.423047\pi\) | ||||
0.239405 | + | 0.970920i | \(0.423047\pi\) | |||||||
\(810\) | −0.150272 | −0.00528001 | ||||||||
\(811\) | 29.2445 | 1.02691 | 0.513457 | − | 0.858115i | \(-0.328365\pi\) | ||||
0.513457 | + | 0.858115i | \(0.328365\pi\) | |||||||
\(812\) | −39.9162 | −1.40079 | ||||||||
\(813\) | −21.9411 | −0.769509 | ||||||||
\(814\) | −3.14249 | −0.110144 | ||||||||
\(815\) | −9.19645 | −0.322138 | ||||||||
\(816\) | 3.62950 | 0.127058 | ||||||||
\(817\) | −46.0474 | −1.61099 | ||||||||
\(818\) | 4.11599 | 0.143912 | ||||||||
\(819\) | −16.9454 | −0.592119 | ||||||||
\(820\) | 10.2319 | 0.357313 | ||||||||
\(821\) | −31.0045 | −1.08207 | −0.541033 | − | 0.841002i | \(-0.681966\pi\) | ||||
−0.541033 | + | 0.841002i | \(0.681966\pi\) | |||||||
\(822\) | 0.780485 | 0.0272226 | ||||||||
\(823\) | −47.6571 | −1.66122 | −0.830610 | − | 0.556854i | \(-0.812008\pi\) | ||||
−0.830610 | + | 0.556854i | \(0.812008\pi\) | |||||||
\(824\) | −2.17832 | −0.0758854 | ||||||||
\(825\) | −18.5988 | −0.647528 | ||||||||
\(826\) | 7.58972 | 0.264080 | ||||||||
\(827\) | 19.9323 | 0.693113 | 0.346557 | − | 0.938029i | \(-0.387351\pi\) | ||||
0.346557 | + | 0.938029i | \(0.387351\pi\) | |||||||
\(828\) | 0.0538432 | 0.00187118 | ||||||||
\(829\) | 13.9548 | 0.484670 | 0.242335 | − | 0.970193i | \(-0.422087\pi\) | ||||
0.242335 | + | 0.970193i | \(0.422087\pi\) | |||||||
\(830\) | −1.03281 | −0.0358492 | ||||||||
\(831\) | 22.0171 | 0.763763 | ||||||||
\(832\) | −41.1784 | −1.42760 | ||||||||
\(833\) | −0.245493 | −0.00850583 | ||||||||
\(834\) | 0.712165 | 0.0246603 | ||||||||
\(835\) | 7.10593 | 0.245911 | ||||||||
\(836\) | 61.2211 | 2.11738 | ||||||||
\(837\) | −3.60362 | −0.124559 | ||||||||
\(838\) | 4.97955 | 0.172016 | ||||||||
\(839\) | 23.3920 | 0.807582 | 0.403791 | − | 0.914851i | \(-0.367692\pi\) | ||||
0.403791 | + | 0.914851i | \(0.367692\pi\) | |||||||
\(840\) | 1.59273 | 0.0549545 | ||||||||
\(841\) | 29.5737 | 1.01978 | ||||||||
\(842\) | −6.97564 | −0.240396 | ||||||||
\(843\) | 12.9901 | 0.447403 | ||||||||
\(844\) | 4.43187 | 0.152551 | ||||||||
\(845\) | 16.0204 | 0.551120 | ||||||||
\(846\) | 1.50368 | 0.0516975 | ||||||||
\(847\) | −13.6743 | −0.469856 | ||||||||
\(848\) | −39.2845 | −1.34903 | ||||||||
\(849\) | −25.5826 | −0.877994 | ||||||||
\(850\) | −1.15859 | −0.0397393 | ||||||||
\(851\) | 0.0871781 | 0.00298843 | ||||||||
\(852\) | 7.24411 | 0.248179 | ||||||||
\(853\) | 31.5811 | 1.08132 | 0.540659 | − | 0.841242i | \(-0.318175\pi\) | ||||
0.540659 | + | 0.841242i | \(0.318175\pi\) | |||||||
\(854\) | −0.516316 | −0.0176680 | ||||||||
\(855\) | 4.74003 | 0.162106 | ||||||||
\(856\) | 3.42406 | 0.117032 | ||||||||
\(857\) | −12.8744 | −0.439780 | −0.219890 | − | 0.975525i | \(-0.570570\pi\) | ||||
−0.219890 | + | 0.975525i | \(0.570570\pi\) | |||||||
\(858\) | −6.30594 | −0.215281 | ||||||||
\(859\) | 50.1112 | 1.70977 | 0.854886 | − | 0.518817i | \(-0.173627\pi\) | ||||
0.854886 | + | 0.518817i | \(0.173627\pi\) | |||||||
\(860\) | 6.81186 | 0.232282 | ||||||||
\(861\) | −23.6285 | −0.805258 | ||||||||
\(862\) | −9.48400 | −0.323026 | ||||||||
\(863\) | 3.75594 | 0.127854 | 0.0639269 | − | 0.997955i | \(-0.479638\pi\) | ||||
0.0639269 | + | 0.997955i | \(0.479638\pi\) | |||||||
\(864\) | 2.87385 | 0.0977703 | ||||||||
\(865\) | −6.86234 | −0.233327 | ||||||||
\(866\) | 0.572018 | 0.0194380 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 18.7948 | 0.637937 | ||||||||
\(869\) | −4.01000 | −0.136030 | ||||||||
\(870\) | −1.15008 | −0.0389914 | ||||||||
\(871\) | 71.4633 | 2.42144 | ||||||||
\(872\) | 9.64548 | 0.326637 | ||||||||
\(873\) | 12.6730 | 0.428918 | ||||||||
\(874\) | 0.0546950 | 0.00185009 | ||||||||
\(875\) | 15.6068 | 0.527607 | ||||||||
\(876\) | 7.72709 | 0.261074 | ||||||||
\(877\) | 0.789518 | 0.0266601 | 0.0133301 | − | 0.999911i | \(-0.495757\pi\) | ||||
0.0133301 | + | 0.999911i | \(0.495757\pi\) | |||||||
\(878\) | 0.611187 | 0.0206266 | ||||||||
\(879\) | 4.43391 | 0.149552 | ||||||||
\(880\) | −8.75548 | −0.295147 | ||||||||
\(881\) | 28.0249 | 0.944182 | 0.472091 | − | 0.881550i | \(-0.343499\pi\) | ||||
0.472091 | + | 0.881550i | \(0.343499\pi\) | |||||||
\(882\) | −0.0613236 | −0.00206487 | ||||||||
\(883\) | 0.0211698 | 0.000712420 0 | 0.000356210 | − | 1.00000i | \(-0.499887\pi\) | ||||
0.000356210 | 1.00000i | \(0.499887\pi\) | ||||||||
\(884\) | 12.1978 | 0.410256 | ||||||||
\(885\) | −6.79035 | −0.228255 | ||||||||
\(886\) | −2.05652 | −0.0690900 | ||||||||
\(887\) | −32.9697 | −1.10701 | −0.553507 | − | 0.832845i | \(-0.686711\pi\) | ||||
−0.553507 | + | 0.832845i | \(0.686711\pi\) | |||||||
\(888\) | 3.08575 | 0.103551 | ||||||||
\(889\) | 8.19920 | 0.274992 | ||||||||
\(890\) | 0.185388 | 0.00621424 | ||||||||
\(891\) | −4.01000 | −0.134340 | ||||||||
\(892\) | 33.7356 | 1.12955 | ||||||||
\(893\) | −47.4306 | −1.58721 | ||||||||
\(894\) | 3.24929 | 0.108673 | ||||||||
\(895\) | 10.9777 | 0.366945 | ||||||||
\(896\) | −19.8695 | −0.663795 | ||||||||
\(897\) | 0.174938 | 0.00584100 | ||||||||
\(898\) | 0.122582 | 0.00409060 | ||||||||
\(899\) | −27.5798 | −0.919837 | ||||||||
\(900\) | 8.98681 | 0.299560 | ||||||||
\(901\) | 10.8237 | 0.360589 | ||||||||
\(902\) | −8.79297 | −0.292774 | ||||||||
\(903\) | −15.7306 | −0.523483 | ||||||||
\(904\) | 13.6154 | 0.452842 | ||||||||
\(905\) | −12.5780 | −0.418108 | ||||||||
\(906\) | 1.00357 | 0.0333413 | ||||||||
\(907\) | −45.0629 | −1.49629 | −0.748145 | − | 0.663536i | \(-0.769055\pi\) | ||||
−0.748145 | + | 0.663536i | \(0.769055\pi\) | |||||||
\(908\) | 27.8189 | 0.923203 | ||||||||
\(909\) | −4.22605 | −0.140169 | ||||||||
\(910\) | 2.54641 | 0.0844126 | ||||||||
\(911\) | 3.35577 | 0.111181 | 0.0555907 | − | 0.998454i | \(-0.482296\pi\) | ||||
0.0555907 | + | 0.998454i | \(0.482296\pi\) | |||||||
\(912\) | −28.5982 | −0.946982 | ||||||||
\(913\) | −27.5604 | −0.912117 | ||||||||
\(914\) | −7.53623 | −0.249276 | ||||||||
\(915\) | 0.461936 | 0.0152711 | ||||||||
\(916\) | 38.4894 | 1.27173 | ||||||||
\(917\) | −9.62866 | −0.317966 | ||||||||
\(918\) | −0.249798 | −0.00824455 | ||||||||
\(919\) | −29.8453 | −0.984507 | −0.492253 | − | 0.870452i | \(-0.663827\pi\) | ||||
−0.492253 | + | 0.870452i | \(0.663827\pi\) | |||||||
\(920\) | −0.0164428 | −0.000542103 0 | ||||||||
\(921\) | −16.4764 | −0.542916 | ||||||||
\(922\) | −8.22966 | −0.271029 | ||||||||
\(923\) | 23.5363 | 0.774706 | ||||||||
\(924\) | 20.9143 | 0.688029 | ||||||||
\(925\) | 14.5506 | 0.478422 | ||||||||
\(926\) | −0.314283 | −0.0103280 | ||||||||
\(927\) | −2.21463 | −0.0727381 | ||||||||
\(928\) | 21.9946 | 0.722007 | ||||||||
\(929\) | 58.6973 | 1.92580 | 0.962898 | − | 0.269865i | \(-0.0869792\pi\) | ||||
0.962898 | + | 0.269865i | \(0.0869792\pi\) | |||||||
\(930\) | 0.541523 | 0.0177572 | ||||||||
\(931\) | 1.93433 | 0.0633952 | ||||||||
\(932\) | 2.31042 | 0.0756802 | ||||||||
\(933\) | 23.7040 | 0.776035 | ||||||||
\(934\) | 7.62504 | 0.249499 | ||||||||
\(935\) | 2.41231 | 0.0788910 | ||||||||
\(936\) | 6.19209 | 0.202395 | ||||||||
\(937\) | −2.20885 | −0.0721599 | −0.0360799 | − | 0.999349i | \(-0.511487\pi\) | ||||
−0.0360799 | + | 0.999349i | \(0.511487\pi\) | |||||||
\(938\) | 7.63288 | 0.249222 | ||||||||
\(939\) | 14.7103 | 0.480051 | ||||||||
\(940\) | 7.01649 | 0.228853 | ||||||||
\(941\) | 57.5794 | 1.87704 | 0.938518 | − | 0.345230i | \(-0.112199\pi\) | ||||
0.938518 | + | 0.345230i | \(0.112199\pi\) | |||||||
\(942\) | 4.05254 | 0.132039 | ||||||||
\(943\) | 0.243932 | 0.00794353 | ||||||||
\(944\) | 40.9685 | 1.33341 | ||||||||
\(945\) | 1.61928 | 0.0526753 | ||||||||
\(946\) | −5.85390 | −0.190327 | ||||||||
\(947\) | 46.2003 | 1.50131 | 0.750654 | − | 0.660696i | \(-0.229739\pi\) | ||||
0.750654 | + | 0.660696i | \(0.229739\pi\) | |||||||
\(948\) | 1.93760 | 0.0629304 | ||||||||
\(949\) | 25.1055 | 0.814959 | ||||||||
\(950\) | 9.12897 | 0.296183 | ||||||||
\(951\) | −13.4989 | −0.437732 | ||||||||
\(952\) | 2.64761 | 0.0858096 | ||||||||
\(953\) | −30.7402 | −0.995772 | −0.497886 | − | 0.867242i | \(-0.665890\pi\) | ||||
−0.497886 | + | 0.867242i | \(0.665890\pi\) | |||||||
\(954\) | 2.70373 | 0.0875364 | ||||||||
\(955\) | 6.93469 | 0.224401 | ||||||||
\(956\) | −19.1068 | −0.617958 | ||||||||
\(957\) | −30.6899 | −0.992064 | ||||||||
\(958\) | −5.60956 | −0.181237 | ||||||||
\(959\) | −8.41028 | −0.271582 | ||||||||
\(960\) | 3.93496 | 0.127000 | ||||||||
\(961\) | −18.0139 | −0.581093 | ||||||||
\(962\) | 4.93340 | 0.159059 | ||||||||
\(963\) | 3.48114 | 0.112178 | ||||||||
\(964\) | −22.6875 | −0.730714 | ||||||||
\(965\) | 7.42288 | 0.238951 | ||||||||
\(966\) | 0.0186848 | 0.000601174 0 | ||||||||
\(967\) | 23.5600 | 0.757638 | 0.378819 | − | 0.925471i | \(-0.376330\pi\) | ||||
0.378819 | + | 0.925471i | \(0.376330\pi\) | |||||||
\(968\) | 4.99680 | 0.160603 | ||||||||
\(969\) | 7.87938 | 0.253122 | ||||||||
\(970\) | −1.90440 | −0.0611466 | ||||||||
\(971\) | −9.69426 | −0.311103 | −0.155552 | − | 0.987828i | \(-0.549716\pi\) | ||||
−0.155552 | + | 0.987828i | \(0.549716\pi\) | |||||||
\(972\) | 1.93760 | 0.0621486 | ||||||||
\(973\) | −7.67408 | −0.246020 | ||||||||
\(974\) | −7.11262 | −0.227903 | ||||||||
\(975\) | 29.1983 | 0.935095 | ||||||||
\(976\) | −2.78702 | −0.0892103 | ||||||||
\(977\) | 37.8674 | 1.21149 | 0.605743 | − | 0.795660i | \(-0.292876\pi\) | ||||
0.605743 | + | 0.795660i | \(0.292876\pi\) | |||||||
\(978\) | −3.81874 | −0.122110 | ||||||||
\(979\) | 4.94709 | 0.158110 | ||||||||
\(980\) | −0.286149 | −0.00914070 | ||||||||
\(981\) | 9.80627 | 0.313090 | ||||||||
\(982\) | 5.57842 | 0.178015 | ||||||||
\(983\) | 6.38505 | 0.203652 | 0.101826 | − | 0.994802i | \(-0.467532\pi\) | ||||
0.101826 | + | 0.994802i | \(0.467532\pi\) | |||||||
\(984\) | 8.63421 | 0.275249 | ||||||||
\(985\) | −11.1773 | −0.356138 | ||||||||
\(986\) | −1.91179 | −0.0608837 | ||||||||
\(987\) | −16.2032 | −0.515753 | ||||||||
\(988\) | −96.1111 | −3.05770 | ||||||||
\(989\) | 0.162397 | 0.00516394 | ||||||||
\(990\) | 0.602589 | 0.0191516 | ||||||||
\(991\) | 7.00641 | 0.222566 | 0.111283 | − | 0.993789i | \(-0.464504\pi\) | ||||
0.111283 | + | 0.993789i | \(0.464504\pi\) | |||||||
\(992\) | −10.3563 | −0.328812 | ||||||||
\(993\) | −32.2146 | −1.02230 | ||||||||
\(994\) | 2.51387 | 0.0797352 | ||||||||
\(995\) | 5.14715 | 0.163176 | ||||||||
\(996\) | 13.3170 | 0.421965 | ||||||||
\(997\) | −22.2470 | −0.704569 | −0.352284 | − | 0.935893i | \(-0.614595\pi\) | ||||
−0.352284 | + | 0.935893i | \(0.614595\pi\) | |||||||
\(998\) | 3.56428 | 0.112825 | ||||||||
\(999\) | 3.13719 | 0.0992563 |
(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 | 4029.2.a.l.1.15 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.15 | ✓ | 32 | 1.1 | even | 1 | trivial |