Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5577,2,Mod(1,5577)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5577, 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("5577.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5577 = 3 \cdot 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5577.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: | \(44.5325692073\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.36814\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5577.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36814 | −0.967420 | −0.483710 | − | 0.875228i | \(-0.660711\pi\) | ||||
−0.483710 | + | 0.875228i | \(0.660711\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.128197 | −0.0640985 | ||||||||
\(5\) | 2.18365 | 0.976558 | 0.488279 | − | 0.872688i | \(-0.337625\pi\) | ||||
0.488279 | + | 0.872688i | \(0.337625\pi\) | |||||||
\(6\) | −1.36814 | −0.558540 | ||||||||
\(7\) | −4.27070 | −1.61417 | −0.807087 | − | 0.590433i | \(-0.798957\pi\) | ||||
−0.807087 | + | 0.590433i | \(0.798957\pi\) | |||||||
\(8\) | 2.91167 | 1.02943 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.98753 | −0.944741 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.128197 | −0.0370073 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 5.84291 | 1.56158 | ||||||||
\(15\) | 2.18365 | 0.563816 | ||||||||
\(16\) | −3.72717 | −0.931793 | ||||||||
\(17\) | −3.79173 | −0.919629 | −0.459815 | − | 0.888015i | \(-0.652084\pi\) | ||||
−0.459815 | + | 0.888015i | \(0.652084\pi\) | |||||||
\(18\) | −1.36814 | −0.322473 | ||||||||
\(19\) | −3.17118 | −0.727519 | −0.363760 | − | 0.931493i | \(-0.618507\pi\) | ||||
−0.363760 | + | 0.931493i | \(0.618507\pi\) | |||||||
\(20\) | −0.279937 | −0.0625959 | ||||||||
\(21\) | −4.27070 | −0.931943 | ||||||||
\(22\) | −1.36814 | −0.291688 | ||||||||
\(23\) | −4.94243 | −1.03057 | −0.515284 | − | 0.857020i | \(-0.672313\pi\) | ||||
−0.515284 | + | 0.857020i | \(0.672313\pi\) | |||||||
\(24\) | 2.91167 | 0.594342 | ||||||||
\(25\) | −0.231676 | −0.0463352 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.547491 | 0.103466 | ||||||||
\(29\) | −7.35483 | −1.36576 | −0.682879 | − | 0.730531i | \(-0.739272\pi\) | ||||
−0.682879 | + | 0.730531i | \(0.739272\pi\) | |||||||
\(30\) | −2.98753 | −0.545447 | ||||||||
\(31\) | 0.0727448 | 0.0130654 | 0.00653268 | − | 0.999979i | \(-0.497921\pi\) | ||||
0.00653268 | + | 0.999979i | \(0.497921\pi\) | |||||||
\(32\) | −0.724050 | −0.127995 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 5.18761 | 0.889668 | ||||||||
\(35\) | −9.32571 | −1.57633 | ||||||||
\(36\) | −0.128197 | −0.0213662 | ||||||||
\(37\) | 3.66658 | 0.602782 | 0.301391 | − | 0.953501i | \(-0.402549\pi\) | ||||
0.301391 | + | 0.953501i | \(0.402549\pi\) | |||||||
\(38\) | 4.33862 | 0.703817 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.35806 | 1.00530 | ||||||||
\(41\) | −4.16722 | −0.650811 | −0.325405 | − | 0.945575i | \(-0.605501\pi\) | ||||
−0.325405 | + | 0.945575i | \(0.605501\pi\) | |||||||
\(42\) | 5.84291 | 0.901581 | ||||||||
\(43\) | 7.11697 | 1.08533 | 0.542664 | − | 0.839950i | \(-0.317416\pi\) | ||||
0.542664 | + | 0.839950i | \(0.317416\pi\) | |||||||
\(44\) | −0.128197 | −0.0193264 | ||||||||
\(45\) | 2.18365 | 0.325519 | ||||||||
\(46\) | 6.76193 | 0.996992 | ||||||||
\(47\) | 11.6337 | 1.69695 | 0.848477 | − | 0.529232i | \(-0.177520\pi\) | ||||
0.848477 | + | 0.529232i | \(0.177520\pi\) | |||||||
\(48\) | −3.72717 | −0.537971 | ||||||||
\(49\) | 11.2389 | 1.60556 | ||||||||
\(50\) | 0.316965 | 0.0448256 | ||||||||
\(51\) | −3.79173 | −0.530948 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.11268 | 0.702281 | 0.351140 | − | 0.936323i | \(-0.385794\pi\) | ||||
0.351140 | + | 0.936323i | \(0.385794\pi\) | |||||||
\(54\) | −1.36814 | −0.186180 | ||||||||
\(55\) | 2.18365 | 0.294443 | ||||||||
\(56\) | −12.4349 | −1.66168 | ||||||||
\(57\) | −3.17118 | −0.420034 | ||||||||
\(58\) | 10.0624 | 1.32126 | ||||||||
\(59\) | 5.62765 | 0.732658 | 0.366329 | − | 0.930485i | \(-0.380614\pi\) | ||||
0.366329 | + | 0.930485i | \(0.380614\pi\) | |||||||
\(60\) | −0.279937 | −0.0361398 | ||||||||
\(61\) | −5.40800 | −0.692424 | −0.346212 | − | 0.938156i | \(-0.612532\pi\) | ||||
−0.346212 | + | 0.938156i | \(0.612532\pi\) | |||||||
\(62\) | −0.0995250 | −0.0126397 | ||||||||
\(63\) | −4.27070 | −0.538058 | ||||||||
\(64\) | 8.44494 | 1.05562 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.36814 | −0.168406 | ||||||||
\(67\) | 10.1145 | 1.23569 | 0.617843 | − | 0.786302i | \(-0.288007\pi\) | ||||
0.617843 | + | 0.786302i | \(0.288007\pi\) | |||||||
\(68\) | 0.486088 | 0.0589469 | ||||||||
\(69\) | −4.94243 | −0.594998 | ||||||||
\(70\) | 12.7589 | 1.52498 | ||||||||
\(71\) | 9.62239 | 1.14197 | 0.570984 | − | 0.820961i | \(-0.306562\pi\) | ||||
0.570984 | + | 0.820961i | \(0.306562\pi\) | |||||||
\(72\) | 2.91167 | 0.343143 | ||||||||
\(73\) | 6.44736 | 0.754607 | 0.377303 | − | 0.926090i | \(-0.376851\pi\) | ||||
0.377303 | + | 0.926090i | \(0.376851\pi\) | |||||||
\(74\) | −5.01639 | −0.583144 | ||||||||
\(75\) | −0.231676 | −0.0267516 | ||||||||
\(76\) | 0.406536 | 0.0466329 | ||||||||
\(77\) | −4.27070 | −0.486692 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1209 | 1.13869 | 0.569347 | − | 0.822097i | \(-0.307196\pi\) | ||||
0.569347 | + | 0.822097i | \(0.307196\pi\) | |||||||
\(80\) | −8.13884 | −0.909949 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.70134 | 0.629607 | ||||||||
\(83\) | −7.80918 | −0.857169 | −0.428585 | − | 0.903502i | \(-0.640988\pi\) | ||||
−0.428585 | + | 0.903502i | \(0.640988\pi\) | |||||||
\(84\) | 0.547491 | 0.0597362 | ||||||||
\(85\) | −8.27981 | −0.898071 | ||||||||
\(86\) | −9.73700 | −1.04997 | ||||||||
\(87\) | −7.35483 | −0.788521 | ||||||||
\(88\) | 2.91167 | 0.310385 | ||||||||
\(89\) | 2.87912 | 0.305187 | 0.152593 | − | 0.988289i | \(-0.451238\pi\) | ||||
0.152593 | + | 0.988289i | \(0.451238\pi\) | |||||||
\(90\) | −2.98753 | −0.314914 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.633605 | 0.0660579 | ||||||||
\(93\) | 0.0727448 | 0.00754329 | ||||||||
\(94\) | −15.9166 | −1.64167 | ||||||||
\(95\) | −6.92475 | −0.710465 | ||||||||
\(96\) | −0.724050 | −0.0738980 | ||||||||
\(97\) | 3.79281 | 0.385101 | 0.192551 | − | 0.981287i | \(-0.438324\pi\) | ||||
0.192551 | + | 0.981287i | \(0.438324\pi\) | |||||||
\(98\) | −15.3764 | −1.55325 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0.0297002 | 0.00297002 | ||||||||
\(101\) | 12.8641 | 1.28003 | 0.640014 | − | 0.768363i | \(-0.278928\pi\) | ||||
0.640014 | + | 0.768363i | \(0.278928\pi\) | |||||||
\(102\) | 5.18761 | 0.513650 | ||||||||
\(103\) | −16.9975 | −1.67482 | −0.837409 | − | 0.546577i | \(-0.815930\pi\) | ||||
−0.837409 | + | 0.546577i | \(0.815930\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.32571 | −0.910096 | ||||||||
\(106\) | −6.99486 | −0.679400 | ||||||||
\(107\) | −12.6819 | −1.22600 | −0.613001 | − | 0.790082i | \(-0.710038\pi\) | ||||
−0.613001 | + | 0.790082i | \(0.710038\pi\) | |||||||
\(108\) | −0.128197 | −0.0123358 | ||||||||
\(109\) | 8.89607 | 0.852089 | 0.426045 | − | 0.904702i | \(-0.359907\pi\) | ||||
0.426045 | + | 0.904702i | \(0.359907\pi\) | |||||||
\(110\) | −2.98753 | −0.284850 | ||||||||
\(111\) | 3.66658 | 0.348017 | ||||||||
\(112\) | 15.9176 | 1.50408 | ||||||||
\(113\) | 1.36552 | 0.128457 | 0.0642287 | − | 0.997935i | \(-0.479541\pi\) | ||||
0.0642287 | + | 0.997935i | \(0.479541\pi\) | |||||||
\(114\) | 4.33862 | 0.406349 | ||||||||
\(115\) | −10.7925 | −1.00641 | ||||||||
\(116\) | 0.942868 | 0.0875431 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.69941 | −0.708788 | ||||||||
\(119\) | 16.1933 | 1.48444 | ||||||||
\(120\) | 6.35806 | 0.580409 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 7.39890 | 0.669865 | ||||||||
\(123\) | −4.16722 | −0.375746 | ||||||||
\(124\) | −0.00932567 | −0.000837470 0 | ||||||||
\(125\) | −11.4241 | −1.02181 | ||||||||
\(126\) | 5.84291 | 0.520528 | ||||||||
\(127\) | 10.4027 | 0.923093 | 0.461546 | − | 0.887116i | \(-0.347295\pi\) | ||||
0.461546 | + | 0.887116i | \(0.347295\pi\) | |||||||
\(128\) | −10.1058 | −0.893231 | ||||||||
\(129\) | 7.11697 | 0.626614 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0678 | −1.05437 | −0.527183 | − | 0.849752i | \(-0.676752\pi\) | ||||
−0.527183 | + | 0.849752i | \(0.676752\pi\) | |||||||
\(132\) | −0.128197 | −0.0111581 | ||||||||
\(133\) | 13.5432 | 1.17434 | ||||||||
\(134\) | −13.8381 | −1.19543 | ||||||||
\(135\) | 2.18365 | 0.187939 | ||||||||
\(136\) | −11.0403 | −0.946694 | ||||||||
\(137\) | 3.96114 | 0.338423 | 0.169211 | − | 0.985580i | \(-0.445878\pi\) | ||||
0.169211 | + | 0.985580i | \(0.445878\pi\) | |||||||
\(138\) | 6.76193 | 0.575613 | ||||||||
\(139\) | 18.2437 | 1.54741 | 0.773703 | − | 0.633548i | \(-0.218402\pi\) | ||||
0.773703 | + | 0.633548i | \(0.218402\pi\) | |||||||
\(140\) | 1.19553 | 0.101041 | ||||||||
\(141\) | 11.6337 | 0.979737 | ||||||||
\(142\) | −13.1648 | −1.10476 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.72717 | −0.310598 | ||||||||
\(145\) | −16.0604 | −1.33374 | ||||||||
\(146\) | −8.82089 | −0.730022 | ||||||||
\(147\) | 11.2389 | 0.926968 | ||||||||
\(148\) | −0.470045 | −0.0386375 | ||||||||
\(149\) | 13.8984 | 1.13860 | 0.569299 | − | 0.822131i | \(-0.307215\pi\) | ||||
0.569299 | + | 0.822131i | \(0.307215\pi\) | |||||||
\(150\) | 0.316965 | 0.0258801 | ||||||||
\(151\) | −2.29739 | −0.186959 | −0.0934795 | − | 0.995621i | \(-0.529799\pi\) | ||||
−0.0934795 | + | 0.995621i | \(0.529799\pi\) | |||||||
\(152\) | −9.23344 | −0.748931 | ||||||||
\(153\) | −3.79173 | −0.306543 | ||||||||
\(154\) | 5.84291 | 0.470835 | ||||||||
\(155\) | 0.158849 | 0.0127591 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.6293 | −1.24736 | −0.623678 | − | 0.781682i | \(-0.714362\pi\) | ||||
−0.623678 | + | 0.781682i | \(0.714362\pi\) | |||||||
\(158\) | −13.8468 | −1.10160 | ||||||||
\(159\) | 5.11268 | 0.405462 | ||||||||
\(160\) | −1.58107 | −0.124995 | ||||||||
\(161\) | 21.1076 | 1.66351 | ||||||||
\(162\) | −1.36814 | −0.107491 | ||||||||
\(163\) | 1.25583 | 0.0983643 | 0.0491822 | − | 0.998790i | \(-0.484339\pi\) | ||||
0.0491822 | + | 0.998790i | \(0.484339\pi\) | |||||||
\(164\) | 0.534226 | 0.0417160 | ||||||||
\(165\) | 2.18365 | 0.169997 | ||||||||
\(166\) | 10.6840 | 0.829243 | ||||||||
\(167\) | 17.3823 | 1.34509 | 0.672543 | − | 0.740058i | \(-0.265202\pi\) | ||||
0.672543 | + | 0.740058i | \(0.265202\pi\) | |||||||
\(168\) | −12.4349 | −0.959371 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 11.3279 | 0.868812 | ||||||||
\(171\) | −3.17118 | −0.242506 | ||||||||
\(172\) | −0.912375 | −0.0695679 | ||||||||
\(173\) | −12.0899 | −0.919178 | −0.459589 | − | 0.888132i | \(-0.652003\pi\) | ||||
−0.459589 | + | 0.888132i | \(0.652003\pi\) | |||||||
\(174\) | 10.0624 | 0.762831 | ||||||||
\(175\) | 0.989418 | 0.0747930 | ||||||||
\(176\) | −3.72717 | −0.280946 | ||||||||
\(177\) | 5.62765 | 0.423000 | ||||||||
\(178\) | −3.93904 | −0.295244 | ||||||||
\(179\) | −5.13094 | −0.383504 | −0.191752 | − | 0.981443i | \(-0.561417\pi\) | ||||
−0.191752 | + | 0.981443i | \(0.561417\pi\) | |||||||
\(180\) | −0.279937 | −0.0208653 | ||||||||
\(181\) | −23.3170 | −1.73314 | −0.866568 | − | 0.499059i | \(-0.833679\pi\) | ||||
−0.866568 | + | 0.499059i | \(0.833679\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.40800 | −0.399771 | ||||||||
\(184\) | −14.3907 | −1.06090 | ||||||||
\(185\) | 8.00653 | 0.588652 | ||||||||
\(186\) | −0.0995250 | −0.00729753 | ||||||||
\(187\) | −3.79173 | −0.277279 | ||||||||
\(188\) | −1.49141 | −0.108772 | ||||||||
\(189\) | −4.27070 | −0.310648 | ||||||||
\(190\) | 9.47402 | 0.687318 | ||||||||
\(191\) | 11.1231 | 0.804838 | 0.402419 | − | 0.915456i | \(-0.368169\pi\) | ||||
0.402419 | + | 0.915456i | \(0.368169\pi\) | |||||||
\(192\) | 8.44494 | 0.609461 | ||||||||
\(193\) | 23.1664 | 1.66756 | 0.833778 | − | 0.552099i | \(-0.186173\pi\) | ||||
0.833778 | + | 0.552099i | \(0.186173\pi\) | |||||||
\(194\) | −5.18909 | −0.372555 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.44079 | −0.102914 | ||||||||
\(197\) | 9.18435 | 0.654358 | 0.327179 | − | 0.944962i | \(-0.393902\pi\) | ||||
0.327179 | + | 0.944962i | \(0.393902\pi\) | |||||||
\(198\) | −1.36814 | −0.0972294 | ||||||||
\(199\) | 6.38937 | 0.452930 | 0.226465 | − | 0.974019i | \(-0.427283\pi\) | ||||
0.226465 | + | 0.974019i | \(0.427283\pi\) | |||||||
\(200\) | −0.674563 | −0.0476988 | ||||||||
\(201\) | 10.1145 | 0.713423 | ||||||||
\(202\) | −17.5999 | −1.23833 | ||||||||
\(203\) | 31.4103 | 2.20457 | ||||||||
\(204\) | 0.486088 | 0.0340330 | ||||||||
\(205\) | −9.09975 | −0.635554 | ||||||||
\(206\) | 23.2550 | 1.62025 | ||||||||
\(207\) | −4.94243 | −0.343522 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.17118 | −0.219355 | ||||||||
\(210\) | 12.7589 | 0.880446 | ||||||||
\(211\) | 22.4436 | 1.54508 | 0.772541 | − | 0.634965i | \(-0.218985\pi\) | ||||
0.772541 | + | 0.634965i | \(0.218985\pi\) | |||||||
\(212\) | −0.655431 | −0.0450152 | ||||||||
\(213\) | 9.62239 | 0.659315 | ||||||||
\(214\) | 17.3505 | 1.18606 | ||||||||
\(215\) | 15.5410 | 1.05989 | ||||||||
\(216\) | 2.91167 | 0.198114 | ||||||||
\(217\) | −0.310671 | −0.0210897 | ||||||||
\(218\) | −12.1711 | −0.824328 | ||||||||
\(219\) | 6.44736 | 0.435673 | ||||||||
\(220\) | −0.279937 | −0.0188734 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.01639 | −0.336678 | ||||||||
\(223\) | −16.5344 | −1.10722 | −0.553611 | − | 0.832775i | \(-0.686751\pi\) | ||||
−0.553611 | + | 0.832775i | \(0.686751\pi\) | |||||||
\(224\) | 3.09220 | 0.206606 | ||||||||
\(225\) | −0.231676 | −0.0154451 | ||||||||
\(226\) | −1.86822 | −0.124272 | ||||||||
\(227\) | −19.9826 | −1.32630 | −0.663148 | − | 0.748489i | \(-0.730780\pi\) | ||||
−0.663148 | + | 0.748489i | \(0.730780\pi\) | |||||||
\(228\) | 0.406536 | 0.0269235 | ||||||||
\(229\) | 15.8459 | 1.04713 | 0.523564 | − | 0.851986i | \(-0.324602\pi\) | ||||
0.523564 | + | 0.851986i | \(0.324602\pi\) | |||||||
\(230\) | 14.7657 | 0.973620 | ||||||||
\(231\) | −4.27070 | −0.280992 | ||||||||
\(232\) | −21.4148 | −1.40595 | ||||||||
\(233\) | 15.9195 | 1.04292 | 0.521460 | − | 0.853276i | \(-0.325388\pi\) | ||||
0.521460 | + | 0.853276i | \(0.325388\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.4040 | 1.65717 | ||||||||
\(236\) | −0.721449 | −0.0469623 | ||||||||
\(237\) | 10.1209 | 0.657425 | ||||||||
\(238\) | −22.1547 | −1.43608 | ||||||||
\(239\) | 16.9898 | 1.09898 | 0.549491 | − | 0.835500i | \(-0.314822\pi\) | ||||
0.549491 | + | 0.835500i | \(0.314822\pi\) | |||||||
\(240\) | −8.13884 | −0.525360 | ||||||||
\(241\) | −21.9883 | −1.41639 | −0.708197 | − | 0.706015i | \(-0.750491\pi\) | ||||
−0.708197 | + | 0.706015i | \(0.750491\pi\) | |||||||
\(242\) | −1.36814 | −0.0879473 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.693290 | 0.0443834 | ||||||||
\(245\) | 24.5418 | 1.56792 | ||||||||
\(246\) | 5.70134 | 0.363504 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.211809 | 0.0134499 | ||||||||
\(249\) | −7.80918 | −0.494887 | ||||||||
\(250\) | 15.6298 | 0.988516 | ||||||||
\(251\) | 11.9461 | 0.754029 | 0.377015 | − | 0.926207i | \(-0.376951\pi\) | ||||
0.377015 | + | 0.926207i | \(0.376951\pi\) | |||||||
\(252\) | 0.547491 | 0.0344887 | ||||||||
\(253\) | −4.94243 | −0.310728 | ||||||||
\(254\) | −14.2324 | −0.893019 | ||||||||
\(255\) | −8.27981 | −0.518502 | ||||||||
\(256\) | −3.06382 | −0.191489 | ||||||||
\(257\) | 28.3671 | 1.76949 | 0.884746 | − | 0.466074i | \(-0.154332\pi\) | ||||
0.884746 | + | 0.466074i | \(0.154332\pi\) | |||||||
\(258\) | −9.73700 | −0.606199 | ||||||||
\(259\) | −15.6589 | −0.972995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.35483 | −0.455253 | ||||||||
\(262\) | 16.5104 | 1.02001 | ||||||||
\(263\) | −1.37798 | −0.0849699 | −0.0424849 | − | 0.999097i | \(-0.513527\pi\) | ||||
−0.0424849 | + | 0.999097i | \(0.513527\pi\) | |||||||
\(264\) | 2.91167 | 0.179201 | ||||||||
\(265\) | 11.1643 | 0.685818 | ||||||||
\(266\) | −18.5289 | −1.13608 | ||||||||
\(267\) | 2.87912 | 0.176200 | ||||||||
\(268\) | −1.29665 | −0.0792056 | ||||||||
\(269\) | −14.6274 | −0.891847 | −0.445923 | − | 0.895071i | \(-0.647125\pi\) | ||||
−0.445923 | + | 0.895071i | \(0.647125\pi\) | |||||||
\(270\) | −2.98753 | −0.181816 | ||||||||
\(271\) | 13.3040 | 0.808158 | 0.404079 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404079 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(272\) | 14.1324 | 0.856904 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.41938 | −0.327397 | ||||||||
\(275\) | −0.231676 | −0.0139706 | ||||||||
\(276\) | 0.633605 | 0.0381385 | ||||||||
\(277\) | 22.1581 | 1.33135 | 0.665676 | − | 0.746241i | \(-0.268143\pi\) | ||||
0.665676 | + | 0.746241i | \(0.268143\pi\) | |||||||
\(278\) | −24.9598 | −1.49699 | ||||||||
\(279\) | 0.0727448 | 0.00435512 | ||||||||
\(280\) | −27.1534 | −1.62273 | ||||||||
\(281\) | −2.12589 | −0.126820 | −0.0634100 | − | 0.997988i | \(-0.520198\pi\) | ||||
−0.0634100 | + | 0.997988i | \(0.520198\pi\) | |||||||
\(282\) | −15.9166 | −0.947817 | ||||||||
\(283\) | −31.1036 | −1.84892 | −0.924458 | − | 0.381283i | \(-0.875482\pi\) | ||||
−0.924458 | + | 0.381283i | \(0.875482\pi\) | |||||||
\(284\) | −1.23356 | −0.0731984 | ||||||||
\(285\) | −6.92475 | −0.410187 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.7970 | 1.05052 | ||||||||
\(288\) | −0.724050 | −0.0426650 | ||||||||
\(289\) | −2.62279 | −0.154282 | ||||||||
\(290\) | 21.9728 | 1.29029 | ||||||||
\(291\) | 3.79281 | 0.222338 | ||||||||
\(292\) | −0.826533 | −0.0483692 | ||||||||
\(293\) | 16.9009 | 0.987363 | 0.493682 | − | 0.869643i | \(-0.335651\pi\) | ||||
0.493682 | + | 0.869643i | \(0.335651\pi\) | |||||||
\(294\) | −15.3764 | −0.896767 | ||||||||
\(295\) | 12.2888 | 0.715483 | ||||||||
\(296\) | 10.6759 | 0.620523 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −19.0149 | −1.10150 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.0297002 | 0.00171474 | ||||||||
\(301\) | −30.3945 | −1.75191 | ||||||||
\(302\) | 3.14315 | 0.180868 | ||||||||
\(303\) | 12.8641 | 0.739025 | ||||||||
\(304\) | 11.8195 | 0.677897 | ||||||||
\(305\) | −11.8092 | −0.676192 | ||||||||
\(306\) | 5.18761 | 0.296556 | ||||||||
\(307\) | −24.6110 | −1.40462 | −0.702312 | − | 0.711869i | \(-0.747849\pi\) | ||||
−0.702312 | + | 0.711869i | \(0.747849\pi\) | |||||||
\(308\) | 0.547491 | 0.0311962 | ||||||||
\(309\) | −16.9975 | −0.966956 | ||||||||
\(310\) | −0.217328 | −0.0123434 | ||||||||
\(311\) | −1.00504 | −0.0569904 | −0.0284952 | − | 0.999594i | \(-0.509072\pi\) | ||||
−0.0284952 | + | 0.999594i | \(0.509072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.8744 | −0.784227 | −0.392114 | − | 0.919917i | \(-0.628256\pi\) | ||||
−0.392114 | + | 0.919917i | \(0.628256\pi\) | |||||||
\(314\) | 21.3831 | 1.20672 | ||||||||
\(315\) | −9.32571 | −0.525444 | ||||||||
\(316\) | −1.29747 | −0.0729886 | ||||||||
\(317\) | 15.6405 | 0.878460 | 0.439230 | − | 0.898375i | \(-0.355251\pi\) | ||||
0.439230 | + | 0.898375i | \(0.355251\pi\) | |||||||
\(318\) | −6.99486 | −0.392252 | ||||||||
\(319\) | −7.35483 | −0.411792 | ||||||||
\(320\) | 18.4408 | 1.03087 | ||||||||
\(321\) | −12.6819 | −0.707832 | ||||||||
\(322\) | −28.8782 | −1.60932 | ||||||||
\(323\) | 12.0243 | 0.669048 | ||||||||
\(324\) | −0.128197 | −0.00712206 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.71815 | −0.0951596 | ||||||||
\(327\) | 8.89607 | 0.491954 | ||||||||
\(328\) | −12.1336 | −0.669964 | ||||||||
\(329\) | −49.6842 | −2.73918 | ||||||||
\(330\) | −2.98753 | −0.164458 | ||||||||
\(331\) | 23.1426 | 1.27203 | 0.636017 | − | 0.771675i | \(-0.280581\pi\) | ||||
0.636017 | + | 0.771675i | \(0.280581\pi\) | |||||||
\(332\) | 1.00111 | 0.0549433 | ||||||||
\(333\) | 3.66658 | 0.200927 | ||||||||
\(334\) | −23.7814 | −1.30126 | ||||||||
\(335\) | 22.0866 | 1.20672 | ||||||||
\(336\) | 15.9176 | 0.868378 | ||||||||
\(337\) | 15.1946 | 0.827705 | 0.413853 | − | 0.910344i | \(-0.364183\pi\) | ||||
0.413853 | + | 0.910344i | \(0.364183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.36552 | 0.0741650 | ||||||||
\(340\) | 1.06145 | 0.0575650 | ||||||||
\(341\) | 0.0727448 | 0.00393935 | ||||||||
\(342\) | 4.33862 | 0.234606 | ||||||||
\(343\) | −18.1030 | −0.977472 | ||||||||
\(344\) | 20.7223 | 1.11727 | ||||||||
\(345\) | −10.7925 | −0.581050 | ||||||||
\(346\) | 16.5407 | 0.889231 | ||||||||
\(347\) | 16.6545 | 0.894061 | 0.447030 | − | 0.894519i | \(-0.352482\pi\) | ||||
0.447030 | + | 0.894519i | \(0.352482\pi\) | |||||||
\(348\) | 0.942868 | 0.0505430 | ||||||||
\(349\) | −29.1080 | −1.55812 | −0.779058 | − | 0.626952i | \(-0.784302\pi\) | ||||
−0.779058 | + | 0.626952i | \(0.784302\pi\) | |||||||
\(350\) | −1.35366 | −0.0723562 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.724050 | −0.0385920 | ||||||||
\(353\) | 29.1723 | 1.55268 | 0.776342 | − | 0.630312i | \(-0.217073\pi\) | ||||
0.776342 | + | 0.630312i | \(0.217073\pi\) | |||||||
\(354\) | −7.69941 | −0.409219 | ||||||||
\(355\) | 21.0119 | 1.11520 | ||||||||
\(356\) | −0.369095 | −0.0195620 | ||||||||
\(357\) | 16.1933 | 0.857043 | ||||||||
\(358\) | 7.01983 | 0.371010 | ||||||||
\(359\) | −18.0809 | −0.954271 | −0.477136 | − | 0.878830i | \(-0.658325\pi\) | ||||
−0.477136 | + | 0.878830i | \(0.658325\pi\) | |||||||
\(360\) | 6.35806 | 0.335099 | ||||||||
\(361\) | −8.94359 | −0.470715 | ||||||||
\(362\) | 31.9008 | 1.67667 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0788 | 0.736917 | ||||||||
\(366\) | 7.39890 | 0.386747 | ||||||||
\(367\) | 18.1338 | 0.946578 | 0.473289 | − | 0.880907i | \(-0.343067\pi\) | ||||
0.473289 | + | 0.880907i | \(0.343067\pi\) | |||||||
\(368\) | 18.4213 | 0.960275 | ||||||||
\(369\) | −4.16722 | −0.216937 | ||||||||
\(370\) | −10.9540 | −0.569474 | ||||||||
\(371\) | −21.8347 | −1.13360 | ||||||||
\(372\) | −0.00932567 | −0.000483513 0 | ||||||||
\(373\) | −15.8564 | −0.821012 | −0.410506 | − | 0.911858i | \(-0.634648\pi\) | ||||
−0.410506 | + | 0.911858i | \(0.634648\pi\) | |||||||
\(374\) | 5.18761 | 0.268245 | ||||||||
\(375\) | −11.4241 | −0.589940 | ||||||||
\(376\) | 33.8736 | 1.74690 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.84291 | 0.300527 | ||||||||
\(379\) | −18.3431 | −0.942224 | −0.471112 | − | 0.882073i | \(-0.656147\pi\) | ||||
−0.471112 | + | 0.882073i | \(0.656147\pi\) | |||||||
\(380\) | 0.887733 | 0.0455397 | ||||||||
\(381\) | 10.4027 | 0.532948 | ||||||||
\(382\) | −15.2179 | −0.778617 | ||||||||
\(383\) | 16.1019 | 0.822768 | 0.411384 | − | 0.911462i | \(-0.365046\pi\) | ||||
0.411384 | + | 0.911462i | \(0.365046\pi\) | |||||||
\(384\) | −10.1058 | −0.515707 | ||||||||
\(385\) | −9.32571 | −0.475282 | ||||||||
\(386\) | −31.6949 | −1.61323 | ||||||||
\(387\) | 7.11697 | 0.361776 | ||||||||
\(388\) | −0.486227 | −0.0246844 | ||||||||
\(389\) | 32.7166 | 1.65880 | 0.829400 | − | 0.558655i | \(-0.188683\pi\) | ||||
0.829400 | + | 0.558655i | \(0.188683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.7403 | 0.947740 | ||||||||
\(392\) | 32.7239 | 1.65281 | ||||||||
\(393\) | −12.0678 | −0.608738 | ||||||||
\(394\) | −12.5655 | −0.633039 | ||||||||
\(395\) | 22.1006 | 1.11200 | ||||||||
\(396\) | −0.128197 | −0.00644214 | ||||||||
\(397\) | 3.51685 | 0.176506 | 0.0882529 | − | 0.996098i | \(-0.471872\pi\) | ||||
0.0882529 | + | 0.996098i | \(0.471872\pi\) | |||||||
\(398\) | −8.74154 | −0.438174 | ||||||||
\(399\) | 13.5432 | 0.678007 | ||||||||
\(400\) | 0.863496 | 0.0431748 | ||||||||
\(401\) | −18.6231 | −0.929992 | −0.464996 | − | 0.885313i | \(-0.653944\pi\) | ||||
−0.464996 | + | 0.885313i | \(0.653944\pi\) | |||||||
\(402\) | −13.8381 | −0.690180 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.64914 | −0.0820480 | ||||||||
\(405\) | 2.18365 | 0.108506 | ||||||||
\(406\) | −42.9736 | −2.13275 | ||||||||
\(407\) | 3.66658 | 0.181746 | ||||||||
\(408\) | −11.0403 | −0.546574 | ||||||||
\(409\) | 17.6809 | 0.874262 | 0.437131 | − | 0.899398i | \(-0.355995\pi\) | ||||
0.437131 | + | 0.899398i | \(0.355995\pi\) | |||||||
\(410\) | 12.4497 | 0.614848 | ||||||||
\(411\) | 3.96114 | 0.195388 | ||||||||
\(412\) | 2.17903 | 0.107353 | ||||||||
\(413\) | −24.0340 | −1.18264 | ||||||||
\(414\) | 6.76193 | 0.332331 | ||||||||
\(415\) | −17.0525 | −0.837075 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.2437 | 0.893395 | ||||||||
\(418\) | 4.33862 | 0.212209 | ||||||||
\(419\) | −1.93036 | −0.0943044 | −0.0471522 | − | 0.998888i | \(-0.515015\pi\) | ||||
−0.0471522 | + | 0.998888i | \(0.515015\pi\) | |||||||
\(420\) | 1.19553 | 0.0583358 | ||||||||
\(421\) | −7.21742 | −0.351756 | −0.175878 | − | 0.984412i | \(-0.556276\pi\) | ||||
−0.175878 | + | 0.984412i | \(0.556276\pi\) | |||||||
\(422\) | −30.7060 | −1.49474 | ||||||||
\(423\) | 11.6337 | 0.565651 | ||||||||
\(424\) | 14.8864 | 0.722949 | ||||||||
\(425\) | 0.878452 | 0.0426112 | ||||||||
\(426\) | −13.1648 | −0.637835 | ||||||||
\(427\) | 23.0960 | 1.11769 | ||||||||
\(428\) | 1.62578 | 0.0785849 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.2622 | −1.02535 | ||||||||
\(431\) | −29.7876 | −1.43482 | −0.717408 | − | 0.696653i | \(-0.754672\pi\) | ||||
−0.717408 | + | 0.696653i | \(0.754672\pi\) | |||||||
\(432\) | −3.72717 | −0.179324 | ||||||||
\(433\) | −25.2468 | −1.21329 | −0.606643 | − | 0.794975i | \(-0.707484\pi\) | ||||
−0.606643 | + | 0.794975i | \(0.707484\pi\) | |||||||
\(434\) | 0.425041 | 0.0204026 | ||||||||
\(435\) | −16.0604 | −0.770036 | ||||||||
\(436\) | −1.14045 | −0.0546177 | ||||||||
\(437\) | 15.6733 | 0.749758 | ||||||||
\(438\) | −8.82089 | −0.421478 | ||||||||
\(439\) | −9.07110 | −0.432940 | −0.216470 | − | 0.976289i | \(-0.569454\pi\) | ||||
−0.216470 | + | 0.976289i | \(0.569454\pi\) | |||||||
\(440\) | 6.35806 | 0.303109 | ||||||||
\(441\) | 11.2389 | 0.535185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0753 | −0.573715 | −0.286858 | − | 0.957973i | \(-0.592611\pi\) | ||||
−0.286858 | + | 0.957973i | \(0.592611\pi\) | |||||||
\(444\) | −0.470045 | −0.0223074 | ||||||||
\(445\) | 6.28700 | 0.298032 | ||||||||
\(446\) | 22.6213 | 1.07115 | ||||||||
\(447\) | 13.8984 | 0.657370 | ||||||||
\(448\) | −36.0658 | −1.70395 | ||||||||
\(449\) | 8.94438 | 0.422111 | 0.211056 | − | 0.977474i | \(-0.432310\pi\) | ||||
0.211056 | + | 0.977474i | \(0.432310\pi\) | |||||||
\(450\) | 0.316965 | 0.0149419 | ||||||||
\(451\) | −4.16722 | −0.196227 | ||||||||
\(452\) | −0.175056 | −0.00823394 | ||||||||
\(453\) | −2.29739 | −0.107941 | ||||||||
\(454\) | 27.3390 | 1.28308 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.23344 | −0.432395 | ||||||||
\(457\) | −28.4975 | −1.33305 | −0.666527 | − | 0.745481i | \(-0.732220\pi\) | ||||
−0.666527 | + | 0.745481i | \(0.732220\pi\) | |||||||
\(458\) | −21.6794 | −1.01301 | ||||||||
\(459\) | −3.79173 | −0.176983 | ||||||||
\(460\) | 1.38357 | 0.0645093 | ||||||||
\(461\) | −19.2580 | −0.896932 | −0.448466 | − | 0.893800i | \(-0.648030\pi\) | ||||
−0.448466 | + | 0.893800i | \(0.648030\pi\) | |||||||
\(462\) | 5.84291 | 0.271837 | ||||||||
\(463\) | 36.3639 | 1.68997 | 0.844987 | − | 0.534787i | \(-0.179608\pi\) | ||||
0.844987 | + | 0.534787i | \(0.179608\pi\) | |||||||
\(464\) | 27.4127 | 1.27260 | ||||||||
\(465\) | 0.158849 | 0.00736645 | ||||||||
\(466\) | −21.7801 | −1.00894 | ||||||||
\(467\) | 1.70345 | 0.0788264 | 0.0394132 | − | 0.999223i | \(-0.487451\pi\) | ||||
0.0394132 | + | 0.999223i | \(0.487451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.1961 | −1.99461 | ||||||||
\(470\) | −34.7562 | −1.60318 | ||||||||
\(471\) | −15.6293 | −0.720161 | ||||||||
\(472\) | 16.3859 | 0.754220 | ||||||||
\(473\) | 7.11697 | 0.327239 | ||||||||
\(474\) | −13.8468 | −0.636006 | ||||||||
\(475\) | 0.734687 | 0.0337097 | ||||||||
\(476\) | −2.07594 | −0.0951505 | ||||||||
\(477\) | 5.11268 | 0.234094 | ||||||||
\(478\) | −23.2444 | −1.06318 | ||||||||
\(479\) | −24.5812 | −1.12314 | −0.561571 | − | 0.827429i | \(-0.689803\pi\) | ||||
−0.561571 | + | 0.827429i | \(0.689803\pi\) | |||||||
\(480\) | −1.58107 | −0.0721657 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 30.0831 | 1.37025 | ||||||||
\(483\) | 21.1076 | 0.960431 | ||||||||
\(484\) | −0.128197 | −0.00582714 | ||||||||
\(485\) | 8.28216 | 0.376074 | ||||||||
\(486\) | −1.36814 | −0.0620600 | ||||||||
\(487\) | 40.5270 | 1.83646 | 0.918228 | − | 0.396053i | \(-0.129620\pi\) | ||||
0.918228 | + | 0.396053i | \(0.129620\pi\) | |||||||
\(488\) | −15.7463 | −0.712802 | ||||||||
\(489\) | 1.25583 | 0.0567907 | ||||||||
\(490\) | −33.5766 | −1.51683 | ||||||||
\(491\) | 16.8245 | 0.759277 | 0.379639 | − | 0.925135i | \(-0.376048\pi\) | ||||
0.379639 | + | 0.925135i | \(0.376048\pi\) | |||||||
\(492\) | 0.534226 | 0.0240848 | ||||||||
\(493\) | 27.8875 | 1.25599 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.18365 | 0.0981477 | ||||||||
\(496\) | −0.271132 | −0.0121742 | ||||||||
\(497\) | −41.0943 | −1.84333 | ||||||||
\(498\) | 10.6840 | 0.478764 | ||||||||
\(499\) | 28.5150 | 1.27651 | 0.638254 | − | 0.769826i | \(-0.279657\pi\) | ||||
0.638254 | + | 0.769826i | \(0.279657\pi\) | |||||||
\(500\) | 1.46454 | 0.0654963 | ||||||||
\(501\) | 17.3823 | 0.776586 | ||||||||
\(502\) | −16.3439 | −0.729463 | ||||||||
\(503\) | 27.4200 | 1.22260 | 0.611299 | − | 0.791400i | \(-0.290647\pi\) | ||||
0.611299 | + | 0.791400i | \(0.290647\pi\) | |||||||
\(504\) | −12.4349 | −0.553893 | ||||||||
\(505\) | 28.0908 | 1.25002 | ||||||||
\(506\) | 6.76193 | 0.300604 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.33360 | −0.0591689 | ||||||||
\(509\) | −25.4659 | −1.12876 | −0.564378 | − | 0.825516i | \(-0.690884\pi\) | ||||
−0.564378 | + | 0.825516i | \(0.690884\pi\) | |||||||
\(510\) | 11.3279 | 0.501609 | ||||||||
\(511\) | −27.5348 | −1.21807 | ||||||||
\(512\) | 24.4032 | 1.07848 | ||||||||
\(513\) | −3.17118 | −0.140011 | ||||||||
\(514\) | −38.8101 | −1.71184 | ||||||||
\(515\) | −37.1167 | −1.63556 | ||||||||
\(516\) | −0.912375 | −0.0401651 | ||||||||
\(517\) | 11.6337 | 0.511651 | ||||||||
\(518\) | 21.4235 | 0.941295 | ||||||||
\(519\) | −12.0899 | −0.530688 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.38806 | 0.104623 | 0.0523113 | − | 0.998631i | \(-0.483341\pi\) | ||||
0.0523113 | + | 0.998631i | \(0.483341\pi\) | |||||||
\(522\) | 10.0624 | 0.440421 | ||||||||
\(523\) | 45.6041 | 1.99413 | 0.997064 | − | 0.0765769i | \(-0.0243991\pi\) | ||||
0.997064 | + | 0.0765769i | \(0.0243991\pi\) | |||||||
\(524\) | 1.54705 | 0.0675833 | ||||||||
\(525\) | 0.989418 | 0.0431818 | ||||||||
\(526\) | 1.88527 | 0.0822015 | ||||||||
\(527\) | −0.275829 | −0.0120153 | ||||||||
\(528\) | −3.72717 | −0.162204 | ||||||||
\(529\) | 1.42760 | 0.0620694 | ||||||||
\(530\) | −15.2743 | −0.663474 | ||||||||
\(531\) | 5.62765 | 0.244219 | ||||||||
\(532\) | −1.73620 | −0.0752736 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.93904 | −0.170459 | ||||||||
\(535\) | −27.6927 | −1.19726 | ||||||||
\(536\) | 29.4501 | 1.27205 | ||||||||
\(537\) | −5.13094 | −0.221416 | ||||||||
\(538\) | 20.0123 | 0.862791 | ||||||||
\(539\) | 11.2389 | 0.484093 | ||||||||
\(540\) | −0.279937 | −0.0120466 | ||||||||
\(541\) | −29.4997 | −1.26829 | −0.634145 | − | 0.773214i | \(-0.718648\pi\) | ||||
−0.634145 | + | 0.773214i | \(0.718648\pi\) | |||||||
\(542\) | −18.2017 | −0.781828 | ||||||||
\(543\) | −23.3170 | −1.00063 | ||||||||
\(544\) | 2.74540 | 0.117708 | ||||||||
\(545\) | 19.4259 | 0.832114 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.75142 | 0.331427 | 0.165713 | − | 0.986174i | \(-0.447007\pi\) | ||||
0.165713 | + | 0.986174i | \(0.447007\pi\) | |||||||
\(548\) | −0.507806 | −0.0216924 | ||||||||
\(549\) | −5.40800 | −0.230808 | ||||||||
\(550\) | 0.316965 | 0.0135154 | ||||||||
\(551\) | 23.3235 | 0.993616 | ||||||||
\(552\) | −14.3907 | −0.612509 | ||||||||
\(553\) | −43.2235 | −1.83805 | ||||||||
\(554\) | −30.3153 | −1.28798 | ||||||||
\(555\) | 8.00653 | 0.339858 | ||||||||
\(556\) | −2.33878 | −0.0991865 | ||||||||
\(557\) | −20.2857 | −0.859534 | −0.429767 | − | 0.902940i | \(-0.641404\pi\) | ||||
−0.429767 | + | 0.902940i | \(0.641404\pi\) | |||||||
\(558\) | −0.0995250 | −0.00421323 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 34.7585 | 1.46882 | ||||||||
\(561\) | −3.79173 | −0.160087 | ||||||||
\(562\) | 2.90851 | 0.122688 | ||||||||
\(563\) | −32.7633 | −1.38081 | −0.690403 | − | 0.723425i | \(-0.742567\pi\) | ||||
−0.690403 | + | 0.723425i | \(0.742567\pi\) | |||||||
\(564\) | −1.49141 | −0.0627997 | ||||||||
\(565\) | 2.98182 | 0.125446 | ||||||||
\(566\) | 42.5540 | 1.78868 | ||||||||
\(567\) | −4.27070 | −0.179353 | ||||||||
\(568\) | 28.0172 | 1.17558 | ||||||||
\(569\) | 27.8002 | 1.16545 | 0.582723 | − | 0.812671i | \(-0.301987\pi\) | ||||
0.582723 | + | 0.812671i | \(0.301987\pi\) | |||||||
\(570\) | 9.47402 | 0.396823 | ||||||||
\(571\) | 43.4425 | 1.81801 | 0.909007 | − | 0.416782i | \(-0.136842\pi\) | ||||
0.909007 | + | 0.416782i | \(0.136842\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.1231 | 0.464674 | ||||||||
\(574\) | −24.3487 | −1.01630 | ||||||||
\(575\) | 1.14504 | 0.0477515 | ||||||||
\(576\) | 8.44494 | 0.351873 | ||||||||
\(577\) | 25.7084 | 1.07025 | 0.535127 | − | 0.844772i | \(-0.320264\pi\) | ||||
0.535127 | + | 0.844772i | \(0.320264\pi\) | |||||||
\(578\) | 3.58834 | 0.149255 | ||||||||
\(579\) | 23.1664 | 0.962764 | ||||||||
\(580\) | 2.05889 | 0.0854909 | ||||||||
\(581\) | 33.3507 | 1.38362 | ||||||||
\(582\) | −5.18909 | −0.215095 | ||||||||
\(583\) | 5.11268 | 0.211746 | ||||||||
\(584\) | 18.7726 | 0.776815 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.1228 | −0.955195 | ||||||||
\(587\) | 1.44805 | 0.0597673 | 0.0298837 | − | 0.999553i | \(-0.490486\pi\) | ||||
0.0298837 | + | 0.999553i | \(0.490486\pi\) | |||||||
\(588\) | −1.44079 | −0.0594173 | ||||||||
\(589\) | −0.230687 | −0.00950530 | ||||||||
\(590\) | −16.8128 | −0.692173 | ||||||||
\(591\) | 9.18435 | 0.377794 | ||||||||
\(592\) | −13.6660 | −0.561668 | ||||||||
\(593\) | 4.27539 | 0.175569 | 0.0877845 | − | 0.996139i | \(-0.472021\pi\) | ||||
0.0877845 | + | 0.996139i | \(0.472021\pi\) | |||||||
\(594\) | −1.36814 | −0.0561354 | ||||||||
\(595\) | 35.3606 | 1.44964 | ||||||||
\(596\) | −1.78173 | −0.0729824 | ||||||||
\(597\) | 6.38937 | 0.261499 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.9807 | 0.652953 | 0.326476 | − | 0.945205i | \(-0.394139\pi\) | ||||
0.326476 | + | 0.945205i | \(0.394139\pi\) | |||||||
\(600\) | −0.674563 | −0.0275389 | ||||||||
\(601\) | −25.2647 | −1.03057 | −0.515283 | − | 0.857020i | \(-0.672313\pi\) | ||||
−0.515283 | + | 0.857020i | \(0.672313\pi\) | |||||||
\(602\) | 41.5838 | 1.69483 | ||||||||
\(603\) | 10.1145 | 0.411895 | ||||||||
\(604\) | 0.294519 | 0.0119838 | ||||||||
\(605\) | 2.18365 | 0.0887780 | ||||||||
\(606\) | −17.5999 | −0.714948 | ||||||||
\(607\) | 41.6506 | 1.69055 | 0.845273 | − | 0.534334i | \(-0.179437\pi\) | ||||
0.845273 | + | 0.534334i | \(0.179437\pi\) | |||||||
\(608\) | 2.29610 | 0.0931190 | ||||||||
\(609\) | 31.4103 | 1.27281 | ||||||||
\(610\) | 16.1566 | 0.654162 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.486088 | 0.0196490 | ||||||||
\(613\) | 16.1620 | 0.652777 | 0.326388 | − | 0.945236i | \(-0.394168\pi\) | ||||
0.326388 | + | 0.945236i | \(0.394168\pi\) | |||||||
\(614\) | 33.6713 | 1.35886 | ||||||||
\(615\) | −9.09975 | −0.366937 | ||||||||
\(616\) | −12.4349 | −0.501015 | ||||||||
\(617\) | 8.12561 | 0.327125 | 0.163562 | − | 0.986533i | \(-0.447701\pi\) | ||||
0.163562 | + | 0.986533i | \(0.447701\pi\) | |||||||
\(618\) | 23.2550 | 0.935453 | ||||||||
\(619\) | 7.09593 | 0.285209 | 0.142605 | − | 0.989780i | \(-0.454452\pi\) | ||||
0.142605 | + | 0.989780i | \(0.454452\pi\) | |||||||
\(620\) | −0.0203640 | −0.000817838 0 | ||||||||
\(621\) | −4.94243 | −0.198333 | ||||||||
\(622\) | 1.37503 | 0.0551337 | ||||||||
\(623\) | −12.2959 | −0.492624 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.7879 | −0.951518 | ||||||||
\(626\) | 18.9821 | 0.758677 | ||||||||
\(627\) | −3.17118 | −0.126645 | ||||||||
\(628\) | 2.00363 | 0.0799536 | ||||||||
\(629\) | −13.9027 | −0.554337 | ||||||||
\(630\) | 12.7589 | 0.508325 | ||||||||
\(631\) | 3.62153 | 0.144171 | 0.0720854 | − | 0.997398i | \(-0.477035\pi\) | ||||
0.0720854 | + | 0.997398i | \(0.477035\pi\) | |||||||
\(632\) | 29.4688 | 1.17221 | ||||||||
\(633\) | 22.4436 | 0.892053 | ||||||||
\(634\) | −21.3984 | −0.849840 | ||||||||
\(635\) | 22.7159 | 0.901453 | ||||||||
\(636\) | −0.655431 | −0.0259895 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.0624 | 0.398375 | ||||||||
\(639\) | 9.62239 | 0.380656 | ||||||||
\(640\) | −22.0674 | −0.872291 | ||||||||
\(641\) | −8.81244 | −0.348070 | −0.174035 | − | 0.984739i | \(-0.555681\pi\) | ||||
−0.174035 | + | 0.984739i | \(0.555681\pi\) | |||||||
\(642\) | 17.3505 | 0.684771 | ||||||||
\(643\) | −47.2262 | −1.86242 | −0.931210 | − | 0.364484i | \(-0.881245\pi\) | ||||
−0.931210 | + | 0.364484i | \(0.881245\pi\) | |||||||
\(644\) | −2.70594 | −0.106629 | ||||||||
\(645\) | 15.5410 | 0.611925 | ||||||||
\(646\) | −16.4509 | −0.647251 | ||||||||
\(647\) | 41.0552 | 1.61405 | 0.807023 | − | 0.590520i | \(-0.201077\pi\) | ||||
0.807023 | + | 0.590520i | \(0.201077\pi\) | |||||||
\(648\) | 2.91167 | 0.114381 | ||||||||
\(649\) | 5.62765 | 0.220905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.310671 | −0.0121762 | ||||||||
\(652\) | −0.160994 | −0.00630501 | ||||||||
\(653\) | 36.9362 | 1.44542 | 0.722712 | − | 0.691149i | \(-0.242895\pi\) | ||||
0.722712 | + | 0.691149i | \(0.242895\pi\) | |||||||
\(654\) | −12.1711 | −0.475926 | ||||||||
\(655\) | −26.3518 | −1.02965 | ||||||||
\(656\) | 15.5320 | 0.606421 | ||||||||
\(657\) | 6.44736 | 0.251536 | ||||||||
\(658\) | 67.9748 | 2.64994 | ||||||||
\(659\) | 39.7980 | 1.55031 | 0.775154 | − | 0.631772i | \(-0.217672\pi\) | ||||
0.775154 | + | 0.631772i | \(0.217672\pi\) | |||||||
\(660\) | −0.279937 | −0.0108965 | ||||||||
\(661\) | −21.8622 | −0.850342 | −0.425171 | − | 0.905113i | \(-0.639786\pi\) | ||||
−0.425171 | + | 0.905113i | \(0.639786\pi\) | |||||||
\(662\) | −31.6623 | −1.23059 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.7378 | −0.882396 | ||||||||
\(665\) | 29.5736 | 1.14681 | ||||||||
\(666\) | −5.01639 | −0.194381 | ||||||||
\(667\) | 36.3507 | 1.40751 | ||||||||
\(668\) | −2.22836 | −0.0862180 | ||||||||
\(669\) | −16.5344 | −0.639255 | ||||||||
\(670\) | −30.2175 | −1.16740 | ||||||||
\(671\) | −5.40800 | −0.208774 | ||||||||
\(672\) | 3.09220 | 0.119284 | ||||||||
\(673\) | −32.3152 | −1.24566 | −0.622830 | − | 0.782357i | \(-0.714017\pi\) | ||||
−0.622830 | + | 0.782357i | \(0.714017\pi\) | |||||||
\(674\) | −20.7884 | −0.800739 | ||||||||
\(675\) | −0.231676 | −0.00891721 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.1472 | −0.812753 | −0.406376 | − | 0.913706i | \(-0.633208\pi\) | ||||
−0.406376 | + | 0.913706i | \(0.633208\pi\) | |||||||
\(678\) | −1.86822 | −0.0717487 | ||||||||
\(679\) | −16.1979 | −0.621620 | ||||||||
\(680\) | −24.1081 | −0.924502 | ||||||||
\(681\) | −19.9826 | −0.765737 | ||||||||
\(682\) | −0.0995250 | −0.00381101 | ||||||||
\(683\) | −24.7401 | −0.946654 | −0.473327 | − | 0.880887i | \(-0.656947\pi\) | ||||
−0.473327 | + | 0.880887i | \(0.656947\pi\) | |||||||
\(684\) | 0.406536 | 0.0155443 | ||||||||
\(685\) | 8.64973 | 0.330489 | ||||||||
\(686\) | 24.7675 | 0.945626 | ||||||||
\(687\) | 15.8459 | 0.604560 | ||||||||
\(688\) | −26.5262 | −1.01130 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 14.7657 | 0.562120 | ||||||||
\(691\) | 22.7394 | 0.865047 | 0.432523 | − | 0.901623i | \(-0.357623\pi\) | ||||
0.432523 | + | 0.901623i | \(0.357623\pi\) | |||||||
\(692\) | 1.54989 | 0.0589180 | ||||||||
\(693\) | −4.27070 | −0.162231 | ||||||||
\(694\) | −22.7857 | −0.864932 | ||||||||
\(695\) | 39.8377 | 1.51113 | ||||||||
\(696\) | −21.4148 | −0.811727 | ||||||||
\(697\) | 15.8010 | 0.598505 | ||||||||
\(698\) | 39.8238 | 1.50735 | ||||||||
\(699\) | 15.9195 | 0.602130 | ||||||||
\(700\) | −0.126840 | −0.00479412 | ||||||||
\(701\) | −23.8173 | −0.899567 | −0.449783 | − | 0.893138i | \(-0.648499\pi\) | ||||
−0.449783 | + | 0.893138i | \(0.648499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.6274 | −0.438536 | ||||||||
\(704\) | 8.44494 | 0.318281 | ||||||||
\(705\) | 25.4040 | 0.956769 | ||||||||
\(706\) | −39.9117 | −1.50210 | ||||||||
\(707\) | −54.9389 | −2.06619 | ||||||||
\(708\) | −0.721449 | −0.0271137 | ||||||||
\(709\) | 15.8902 | 0.596770 | 0.298385 | − | 0.954446i | \(-0.403552\pi\) | ||||
0.298385 | + | 0.954446i | \(0.403552\pi\) | |||||||
\(710\) | −28.7472 | −1.07886 | ||||||||
\(711\) | 10.1209 | 0.379565 | ||||||||
\(712\) | 8.38305 | 0.314168 | ||||||||
\(713\) | −0.359536 | −0.0134647 | ||||||||
\(714\) | −22.1547 | −0.829120 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.657771 | 0.0245821 | ||||||||
\(717\) | 16.9898 | 0.634497 | ||||||||
\(718\) | 24.7371 | 0.923181 | ||||||||
\(719\) | 4.64051 | 0.173062 | 0.0865309 | − | 0.996249i | \(-0.472422\pi\) | ||||
0.0865309 | + | 0.996249i | \(0.472422\pi\) | |||||||
\(720\) | −8.13884 | −0.303316 | ||||||||
\(721\) | 72.5914 | 2.70345 | ||||||||
\(722\) | 12.2361 | 0.455379 | ||||||||
\(723\) | −21.9883 | −0.817755 | ||||||||
\(724\) | 2.98917 | 0.111091 | ||||||||
\(725\) | 1.70394 | 0.0632826 | ||||||||
\(726\) | −1.36814 | −0.0507764 | ||||||||
\(727\) | −14.5583 | −0.539938 | −0.269969 | − | 0.962869i | \(-0.587013\pi\) | ||||
−0.269969 | + | 0.962869i | \(0.587013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.2617 | −0.712908 | ||||||||
\(731\) | −26.9856 | −0.998100 | ||||||||
\(732\) | 0.693290 | 0.0256247 | ||||||||
\(733\) | 34.2475 | 1.26496 | 0.632480 | − | 0.774576i | \(-0.282037\pi\) | ||||
0.632480 | + | 0.774576i | \(0.282037\pi\) | |||||||
\(734\) | −24.8096 | −0.915738 | ||||||||
\(735\) | 24.5418 | 0.905238 | ||||||||
\(736\) | 3.57856 | 0.131908 | ||||||||
\(737\) | 10.1145 | 0.372573 | ||||||||
\(738\) | 5.70134 | 0.209869 | ||||||||
\(739\) | −30.5325 | −1.12316 | −0.561578 | − | 0.827424i | \(-0.689806\pi\) | ||||
−0.561578 | + | 0.827424i | \(0.689806\pi\) | |||||||
\(740\) | −1.02641 | −0.0377317 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 29.8729 | 1.09667 | ||||||||
\(743\) | 2.86476 | 0.105098 | 0.0525490 | − | 0.998618i | \(-0.483265\pi\) | ||||
0.0525490 | + | 0.998618i | \(0.483265\pi\) | |||||||
\(744\) | 0.211809 | 0.00776529 | ||||||||
\(745\) | 30.3491 | 1.11191 | ||||||||
\(746\) | 21.6937 | 0.794263 | ||||||||
\(747\) | −7.80918 | −0.285723 | ||||||||
\(748\) | 0.486088 | 0.0177732 | ||||||||
\(749\) | 54.1604 | 1.97898 | ||||||||
\(750\) | 15.6298 | 0.570720 | ||||||||
\(751\) | 38.1810 | 1.39324 | 0.696621 | − | 0.717439i | \(-0.254686\pi\) | ||||
0.696621 | + | 0.717439i | \(0.254686\pi\) | |||||||
\(752\) | −43.3609 | −1.58121 | ||||||||
\(753\) | 11.9461 | 0.435339 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.01670 | −0.182576 | ||||||||
\(756\) | 0.547491 | 0.0199121 | ||||||||
\(757\) | −38.9456 | −1.41550 | −0.707750 | − | 0.706463i | \(-0.750290\pi\) | ||||
−0.707750 | + | 0.706463i | \(0.750290\pi\) | |||||||
\(758\) | 25.0960 | 0.911526 | ||||||||
\(759\) | −4.94243 | −0.179399 | ||||||||
\(760\) | −20.1626 | −0.731374 | ||||||||
\(761\) | −26.9359 | −0.976427 | −0.488214 | − | 0.872724i | \(-0.662351\pi\) | ||||
−0.488214 | + | 0.872724i | \(0.662351\pi\) | |||||||
\(762\) | −14.2324 | −0.515585 | ||||||||
\(763\) | −37.9925 | −1.37542 | ||||||||
\(764\) | −1.42595 | −0.0515889 | ||||||||
\(765\) | −8.27981 | −0.299357 | ||||||||
\(766\) | −22.0296 | −0.795962 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.06382 | −0.110556 | ||||||||
\(769\) | 3.83575 | 0.138321 | 0.0691603 | − | 0.997606i | \(-0.477968\pi\) | ||||
0.0691603 | + | 0.997606i | \(0.477968\pi\) | |||||||
\(770\) | 12.7589 | 0.459798 | ||||||||
\(771\) | 28.3671 | 1.02162 | ||||||||
\(772\) | −2.96987 | −0.106888 | ||||||||
\(773\) | 21.7215 | 0.781267 | 0.390633 | − | 0.920546i | \(-0.372256\pi\) | ||||
0.390633 | + | 0.920546i | \(0.372256\pi\) | |||||||
\(774\) | −9.73700 | −0.349989 | ||||||||
\(775\) | −0.0168532 | −0.000605385 0 | ||||||||
\(776\) | 11.0434 | 0.396435 | ||||||||
\(777\) | −15.6589 | −0.561759 | ||||||||
\(778\) | −44.7609 | −1.60476 | ||||||||
\(779\) | 13.2150 | 0.473478 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.62239 | 0.344316 | ||||||||
\(782\) | −25.6394 | −0.916863 | ||||||||
\(783\) | −7.35483 | −0.262840 | ||||||||
\(784\) | −41.8893 | −1.49605 | ||||||||
\(785\) | −34.1290 | −1.21811 | ||||||||
\(786\) | 16.5104 | 0.588905 | ||||||||
\(787\) | 32.8705 | 1.17171 | 0.585853 | − | 0.810417i | \(-0.300760\pi\) | ||||
0.585853 | + | 0.810417i | \(0.300760\pi\) | |||||||
\(788\) | −1.17741 | −0.0419434 | ||||||||
\(789\) | −1.37798 | −0.0490574 | ||||||||
\(790\) | −30.2366 | −1.07577 | ||||||||
\(791\) | −5.83174 | −0.207353 | ||||||||
\(792\) | 2.91167 | 0.103462 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4.81154 | −0.170755 | ||||||||
\(795\) | 11.1643 | 0.395957 | ||||||||
\(796\) | −0.819098 | −0.0290322 | ||||||||
\(797\) | −2.27867 | −0.0807147 | −0.0403573 | − | 0.999185i | \(-0.512850\pi\) | ||||
−0.0403573 | + | 0.999185i | \(0.512850\pi\) | |||||||
\(798\) | −18.5289 | −0.655918 | ||||||||
\(799\) | −44.1120 | −1.56057 | ||||||||
\(800\) | 0.167745 | 0.00593068 | ||||||||
\(801\) | 2.87912 | 0.101729 | ||||||||
\(802\) | 25.4789 | 0.899693 | ||||||||
\(803\) | 6.44736 | 0.227523 | ||||||||
\(804\) | −1.29665 | −0.0457294 | ||||||||
\(805\) | 46.0917 | 1.62452 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.6274 | −0.514908 | ||||||||
\(808\) | 37.4561 | 1.31770 | ||||||||
\(809\) | 25.3935 | 0.892786 | 0.446393 | − | 0.894837i | \(-0.352708\pi\) | ||||
0.446393 | + | 0.894837i | \(0.352708\pi\) | |||||||
\(810\) | −2.98753 | −0.104971 | ||||||||
\(811\) | −32.7178 | −1.14888 | −0.574439 | − | 0.818548i | \(-0.694780\pi\) | ||||
−0.574439 | + | 0.818548i | \(0.694780\pi\) | |||||||
\(812\) | −4.02671 | −0.141310 | ||||||||
\(813\) | 13.3040 | 0.466590 | ||||||||
\(814\) | −5.01639 | −0.175824 | ||||||||
\(815\) | 2.74230 | 0.0960584 | ||||||||
\(816\) | 14.1324 | 0.494734 | ||||||||
\(817\) | −22.5692 | −0.789597 | ||||||||
\(818\) | −24.1899 | −0.845779 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.16656 | 0.0407381 | ||||||||
\(821\) | −31.2361 | −1.09015 | −0.545073 | − | 0.838388i | \(-0.683498\pi\) | ||||
−0.545073 | + | 0.838388i | \(0.683498\pi\) | |||||||
\(822\) | −5.41938 | −0.189023 | ||||||||
\(823\) | 8.94424 | 0.311777 | 0.155888 | − | 0.987775i | \(-0.450176\pi\) | ||||
0.155888 | + | 0.987775i | \(0.450176\pi\) | |||||||
\(824\) | −49.4912 | −1.72411 | ||||||||
\(825\) | −0.231676 | −0.00806592 | ||||||||
\(826\) | 32.8819 | 1.14411 | ||||||||
\(827\) | −28.6667 | −0.996838 | −0.498419 | − | 0.866936i | \(-0.666086\pi\) | ||||
−0.498419 | + | 0.866936i | \(0.666086\pi\) | |||||||
\(828\) | 0.633605 | 0.0220193 | ||||||||
\(829\) | 39.5515 | 1.37368 | 0.686839 | − | 0.726809i | \(-0.258998\pi\) | ||||
0.686839 | + | 0.726809i | \(0.258998\pi\) | |||||||
\(830\) | 23.3302 | 0.809803 | ||||||||
\(831\) | 22.1581 | 0.768656 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −42.6148 | −1.47652 | ||||||||
\(834\) | −24.9598 | −0.864289 | ||||||||
\(835\) | 37.9569 | 1.31355 | ||||||||
\(836\) | 0.406536 | 0.0140604 | ||||||||
\(837\) | 0.0727448 | 0.00251443 | ||||||||
\(838\) | 2.64100 | 0.0912320 | ||||||||
\(839\) | 45.1833 | 1.55990 | 0.779951 | − | 0.625840i | \(-0.215244\pi\) | ||||
0.779951 | + | 0.625840i | \(0.215244\pi\) | |||||||
\(840\) | −27.1534 | −0.936881 | ||||||||
\(841\) | 25.0936 | 0.865296 | ||||||||
\(842\) | 9.87443 | 0.340295 | ||||||||
\(843\) | −2.12589 | −0.0732195 | ||||||||
\(844\) | −2.87720 | −0.0990375 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15.9166 | −0.547222 | ||||||||
\(847\) | −4.27070 | −0.146743 | ||||||||
\(848\) | −19.0558 | −0.654380 | ||||||||
\(849\) | −31.1036 | −1.06747 | ||||||||
\(850\) | −1.20184 | −0.0412229 | ||||||||
\(851\) | −18.1218 | −0.621208 | ||||||||
\(852\) | −1.23356 | −0.0422611 | ||||||||
\(853\) | −13.2579 | −0.453943 | −0.226972 | − | 0.973901i | \(-0.572882\pi\) | ||||
−0.226972 | + | 0.973901i | \(0.572882\pi\) | |||||||
\(854\) | −31.5985 | −1.08128 | ||||||||
\(855\) | −6.92475 | −0.236822 | ||||||||
\(856\) | −36.9254 | −1.26208 | ||||||||
\(857\) | 38.9268 | 1.32971 | 0.664857 | − | 0.746971i | \(-0.268493\pi\) | ||||
0.664857 | + | 0.746971i | \(0.268493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.2750 | −0.725893 | −0.362947 | − | 0.931810i | \(-0.618229\pi\) | ||||
−0.362947 | + | 0.931810i | \(0.618229\pi\) | |||||||
\(860\) | −1.99231 | −0.0679371 | ||||||||
\(861\) | 17.7970 | 0.606519 | ||||||||
\(862\) | 40.7535 | 1.38807 | ||||||||
\(863\) | −8.94497 | −0.304490 | −0.152245 | − | 0.988343i | \(-0.548650\pi\) | ||||
−0.152245 | + | 0.988343i | \(0.548650\pi\) | |||||||
\(864\) | −0.724050 | −0.0246327 | ||||||||
\(865\) | −26.4001 | −0.897630 | ||||||||
\(866\) | 34.5412 | 1.17376 | ||||||||
\(867\) | −2.62279 | −0.0890746 | ||||||||
\(868\) | 0.0398271 | 0.00135182 | ||||||||
\(869\) | 10.1209 | 0.343329 | ||||||||
\(870\) | 21.9728 | 0.744948 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 25.9024 | 0.877166 | ||||||||
\(873\) | 3.79281 | 0.128367 | ||||||||
\(874\) | −21.4433 | −0.725331 | ||||||||
\(875\) | 48.7891 | 1.64937 | ||||||||
\(876\) | −0.826533 | −0.0279260 | ||||||||
\(877\) | 11.5696 | 0.390679 | 0.195340 | − | 0.980736i | \(-0.437419\pi\) | ||||
0.195340 | + | 0.980736i | \(0.437419\pi\) | |||||||
\(878\) | 12.4105 | 0.418835 | ||||||||
\(879\) | 16.9009 | 0.570055 | ||||||||
\(880\) | −8.13884 | −0.274360 | ||||||||
\(881\) | −13.2958 | −0.447947 | −0.223974 | − | 0.974595i | \(-0.571903\pi\) | ||||
−0.223974 | + | 0.974595i | \(0.571903\pi\) | |||||||
\(882\) | −15.3764 | −0.517749 | ||||||||
\(883\) | −18.7422 | −0.630726 | −0.315363 | − | 0.948971i | \(-0.602126\pi\) | ||||
−0.315363 | + | 0.948971i | \(0.602126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.2888 | 0.413084 | ||||||||
\(886\) | 16.5207 | 0.555024 | ||||||||
\(887\) | 41.6306 | 1.39782 | 0.698910 | − | 0.715210i | \(-0.253669\pi\) | ||||
0.698910 | + | 0.715210i | \(0.253669\pi\) | |||||||
\(888\) | 10.6759 | 0.358259 | ||||||||
\(889\) | −44.4269 | −1.49003 | ||||||||
\(890\) | −8.60148 | −0.288322 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 2.11966 | 0.0709713 | ||||||||
\(893\) | −36.8927 | −1.23457 | ||||||||
\(894\) | −19.0149 | −0.635953 | ||||||||
\(895\) | −11.2042 | −0.374514 | ||||||||
\(896\) | 43.1586 | 1.44183 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.2372 | −0.408359 | ||||||||
\(899\) | −0.535026 | −0.0178441 | ||||||||
\(900\) | 0.0297002 | 0.000990005 0 | ||||||||
\(901\) | −19.3859 | −0.645838 | ||||||||
\(902\) | 5.70134 | 0.189834 | ||||||||
\(903\) | −30.3945 | −1.01146 | ||||||||
\(904\) | 3.97595 | 0.132238 | ||||||||
\(905\) | −50.9161 | −1.69251 | ||||||||
\(906\) | 3.14315 | 0.104424 | ||||||||
\(907\) | 37.0540 | 1.23036 | 0.615179 | − | 0.788387i | \(-0.289084\pi\) | ||||
0.615179 | + | 0.788387i | \(0.289084\pi\) | |||||||
\(908\) | 2.56172 | 0.0850136 | ||||||||
\(909\) | 12.8641 | 0.426676 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.8739 | −1.45361 | −0.726804 | − | 0.686845i | \(-0.758995\pi\) | ||||
−0.726804 | + | 0.686845i | \(0.758995\pi\) | |||||||
\(912\) | 11.8195 | 0.391384 | ||||||||
\(913\) | −7.80918 | −0.258446 | ||||||||
\(914\) | 38.9885 | 1.28962 | ||||||||
\(915\) | −11.8092 | −0.390400 | ||||||||
\(916\) | −2.03140 | −0.0671194 | ||||||||
\(917\) | 51.5378 | 1.70193 | ||||||||
\(918\) | 5.18761 | 0.171217 | ||||||||
\(919\) | −30.1561 | −0.994759 | −0.497380 | − | 0.867533i | \(-0.665704\pi\) | ||||
−0.497380 | + | 0.867533i | \(0.665704\pi\) | |||||||
\(920\) | −31.4243 | −1.03603 | ||||||||
\(921\) | −24.6110 | −0.810961 | ||||||||
\(922\) | 26.3475 | 0.867710 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.547491 | 0.0180111 | ||||||||
\(925\) | −0.849459 | −0.0279300 | ||||||||
\(926\) | −49.7508 | −1.63491 | ||||||||
\(927\) | −16.9975 | −0.558272 | ||||||||
\(928\) | 5.32527 | 0.174810 | ||||||||
\(929\) | −29.2684 | −0.960264 | −0.480132 | − | 0.877196i | \(-0.659411\pi\) | ||||
−0.480132 | + | 0.877196i | \(0.659411\pi\) | |||||||
\(930\) | −0.217328 | −0.00712645 | ||||||||
\(931\) | −35.6406 | −1.16807 | ||||||||
\(932\) | −2.04083 | −0.0668496 | ||||||||
\(933\) | −1.00504 | −0.0329034 | ||||||||
\(934\) | −2.33056 | −0.0762583 | ||||||||
\(935\) | −8.27981 | −0.270779 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.7979 | −0.483427 | −0.241713 | − | 0.970348i | \(-0.577709\pi\) | ||||
−0.241713 | + | 0.970348i | \(0.577709\pi\) | |||||||
\(938\) | 59.0983 | 1.92963 | ||||||||
\(939\) | −13.8744 | −0.452774 | ||||||||
\(940\) | −3.25672 | −0.106222 | ||||||||
\(941\) | 17.5021 | 0.570553 | 0.285276 | − | 0.958445i | \(-0.407915\pi\) | ||||
0.285276 | + | 0.958445i | \(0.407915\pi\) | |||||||
\(942\) | 21.3831 | 0.696698 | ||||||||
\(943\) | 20.5962 | 0.670704 | ||||||||
\(944\) | −20.9752 | −0.682686 | ||||||||
\(945\) | −9.32571 | −0.303365 | ||||||||
\(946\) | −9.73700 | −0.316577 | ||||||||
\(947\) | 32.5998 | 1.05935 | 0.529675 | − | 0.848201i | \(-0.322314\pi\) | ||||
0.529675 | + | 0.848201i | \(0.322314\pi\) | |||||||
\(948\) | −1.29747 | −0.0421400 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.00515 | −0.0326115 | ||||||||
\(951\) | 15.6405 | 0.507179 | ||||||||
\(952\) | 47.1496 | 1.52813 | ||||||||
\(953\) | −44.8368 | −1.45241 | −0.726204 | − | 0.687479i | \(-0.758717\pi\) | ||||
−0.726204 | + | 0.687479i | \(0.758717\pi\) | |||||||
\(954\) | −6.99486 | −0.226467 | ||||||||
\(955\) | 24.2889 | 0.785971 | ||||||||
\(956\) | −2.17805 | −0.0704431 | ||||||||
\(957\) | −7.35483 | −0.237748 | ||||||||
\(958\) | 33.6304 | 1.08655 | ||||||||
\(959\) | −16.9168 | −0.546273 | ||||||||
\(960\) | 18.4408 | 0.595174 | ||||||||
\(961\) | −30.9947 | −0.999829 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.6819 | −0.408667 | ||||||||
\(964\) | 2.81884 | 0.0907887 | ||||||||
\(965\) | 50.5874 | 1.62847 | ||||||||
\(966\) | −28.8782 | −0.929140 | ||||||||
\(967\) | 21.7225 | 0.698550 | 0.349275 | − | 0.937020i | \(-0.386428\pi\) | ||||
0.349275 | + | 0.937020i | \(0.386428\pi\) | |||||||
\(968\) | 2.91167 | 0.0935846 | ||||||||
\(969\) | 12.0243 | 0.386275 | ||||||||
\(970\) | −11.3311 | −0.363821 | ||||||||
\(971\) | −28.7521 | −0.922699 | −0.461349 | − | 0.887219i | \(-0.652635\pi\) | ||||
−0.461349 | + | 0.887219i | \(0.652635\pi\) | |||||||
\(972\) | −0.128197 | −0.00411192 | ||||||||
\(973\) | −77.9132 | −2.49778 | ||||||||
\(974\) | −55.4466 | −1.77662 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.1566 | 0.645196 | ||||||||
\(977\) | 13.7868 | 0.441077 | 0.220539 | − | 0.975378i | \(-0.429218\pi\) | ||||
0.220539 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(978\) | −1.71815 | −0.0549404 | ||||||||
\(979\) | 2.87912 | 0.0920172 | ||||||||
\(980\) | −3.14619 | −0.100501 | ||||||||
\(981\) | 8.89607 | 0.284030 | ||||||||
\(982\) | −23.0182 | −0.734540 | ||||||||
\(983\) | −32.5478 | −1.03811 | −0.519056 | − | 0.854740i | \(-0.673716\pi\) | ||||
−0.519056 | + | 0.854740i | \(0.673716\pi\) | |||||||
\(984\) | −12.1336 | −0.386804 | ||||||||
\(985\) | 20.0554 | 0.639018 | ||||||||
\(986\) | −38.1540 | −1.21507 | ||||||||
\(987\) | −49.6842 | −1.58146 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.1751 | −1.11850 | ||||||||
\(990\) | −2.98753 | −0.0949501 | ||||||||
\(991\) | −3.97937 | −0.126409 | −0.0632044 | − | 0.998001i | \(-0.520132\pi\) | ||||
−0.0632044 | + | 0.998001i | \(0.520132\pi\) | |||||||
\(992\) | −0.0526709 | −0.00167230 | ||||||||
\(993\) | 23.1426 | 0.734409 | ||||||||
\(994\) | 56.2227 | 1.78328 | ||||||||
\(995\) | 13.9521 | 0.442312 | ||||||||
\(996\) | 1.00111 | 0.0317215 | ||||||||
\(997\) | −24.9767 | −0.791021 | −0.395511 | − | 0.918461i | \(-0.629432\pi\) | ||||
−0.395511 | + | 0.918461i | \(0.629432\pi\) | |||||||
\(998\) | −39.0125 | −1.23492 | ||||||||
\(999\) | 3.66658 | 0.116006 |
(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 | 5577.2.a.y.1.2 | 7 | ||
13.5 | odd | 4 | 429.2.b.b.298.10 | yes | 14 | ||
13.8 | odd | 4 | 429.2.b.b.298.5 | ✓ | 14 | ||
13.12 | even | 2 | 5577.2.a.x.1.6 | 7 | |||
39.5 | even | 4 | 1287.2.b.c.298.5 | 14 | |||
39.8 | even | 4 | 1287.2.b.c.298.10 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.5 | ✓ | 14 | 13.8 | odd | 4 | ||
429.2.b.b.298.10 | yes | 14 | 13.5 | odd | 4 | ||
1287.2.b.c.298.5 | 14 | 39.5 | even | 4 | |||
1287.2.b.c.298.10 | 14 | 39.8 | even | 4 | |||
5577.2.a.x.1.6 | 7 | 13.12 | even | 2 | |||
5577.2.a.y.1.2 | 7 | 1.1 | even | 1 | trivial |