Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 17x^{8} + 36x^{7} + 75x^{6} - 174x^{5} - 69x^{4} + 260x^{3} - 104x^{2} - 24x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(3.06975\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.539617 | 0.311548 | 0.155774 | − | 0.987793i | \(-0.450213\pi\) | ||||
0.155774 | + | 0.987793i | \(0.450213\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.38661 | −1.51454 | −0.757269 | − | 0.653104i | \(-0.773467\pi\) | ||||
−0.757269 | + | 0.653104i | \(0.773467\pi\) | |||||||
\(6\) | −0.539617 | −0.220298 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.70881 | −0.902938 | ||||||||
\(10\) | 3.38661 | 1.07094 | ||||||||
\(11\) | 2.98763 | 0.900806 | 0.450403 | − | 0.892825i | \(-0.351280\pi\) | ||||
0.450403 | + | 0.892825i | \(0.351280\pi\) | |||||||
\(12\) | 0.539617 | 0.155774 | ||||||||
\(13\) | 0.00964170 | 0.00267413 | 0.00133706 | − | 0.999999i | \(-0.499574\pi\) | ||||
0.00133706 | + | 0.999999i | \(0.499574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.82747 | −0.471851 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.0684206 | 0.0165944 | 0.00829721 | − | 0.999966i | \(-0.497359\pi\) | ||||
0.00829721 | + | 0.999966i | \(0.497359\pi\) | |||||||
\(18\) | 2.70881 | 0.638473 | ||||||||
\(19\) | −0.966028 | −0.221622 | −0.110811 | − | 0.993841i | \(-0.535345\pi\) | ||||
−0.110811 | + | 0.993841i | \(0.535345\pi\) | |||||||
\(20\) | −3.38661 | −0.757269 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.98763 | −0.636966 | ||||||||
\(23\) | 1.61711 | 0.337190 | 0.168595 | − | 0.985685i | \(-0.446077\pi\) | ||||
0.168595 | + | 0.985685i | \(0.446077\pi\) | |||||||
\(24\) | −0.539617 | −0.110149 | ||||||||
\(25\) | 6.46911 | 1.29382 | ||||||||
\(26\) | −0.00964170 | −0.00189089 | ||||||||
\(27\) | −3.08057 | −0.592857 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.701234 | 0.130216 | 0.0651080 | − | 0.997878i | \(-0.479261\pi\) | ||||
0.0651080 | + | 0.997878i | \(0.479261\pi\) | |||||||
\(30\) | 1.82747 | 0.333649 | ||||||||
\(31\) | 7.29196 | 1.30967 | 0.654837 | − | 0.755770i | \(-0.272737\pi\) | ||||
0.654837 | + | 0.755770i | \(0.272737\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.61218 | 0.280644 | ||||||||
\(34\) | −0.0684206 | −0.0117340 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.70881 | −0.451469 | ||||||||
\(37\) | 4.88899 | 0.803745 | 0.401873 | − | 0.915696i | \(-0.368359\pi\) | ||||
0.401873 | + | 0.915696i | \(0.368359\pi\) | |||||||
\(38\) | 0.966028 | 0.156710 | ||||||||
\(39\) | 0.00520283 | 0.000833119 0 | ||||||||
\(40\) | 3.38661 | 0.535470 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.84951 | 0.282047 | 0.141023 | − | 0.990006i | \(-0.454961\pi\) | ||||
0.141023 | + | 0.990006i | \(0.454961\pi\) | |||||||
\(44\) | 2.98763 | 0.450403 | ||||||||
\(45\) | 9.17369 | 1.36753 | ||||||||
\(46\) | −1.61711 | −0.238429 | ||||||||
\(47\) | −3.16995 | −0.462385 | −0.231193 | − | 0.972908i | \(-0.574263\pi\) | ||||
−0.231193 | + | 0.972908i | \(0.574263\pi\) | |||||||
\(48\) | 0.539617 | 0.0778870 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.46911 | −0.914871 | ||||||||
\(51\) | 0.0369209 | 0.00516996 | ||||||||
\(52\) | 0.00964170 | 0.00133706 | ||||||||
\(53\) | −6.61947 | −0.909254 | −0.454627 | − | 0.890682i | \(-0.650227\pi\) | ||||
−0.454627 | + | 0.890682i | \(0.650227\pi\) | |||||||
\(54\) | 3.08057 | 0.419213 | ||||||||
\(55\) | −10.1179 | −1.36430 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.521285 | −0.0690459 | ||||||||
\(58\) | −0.701234 | −0.0920766 | ||||||||
\(59\) | −3.16550 | −0.412113 | −0.206057 | − | 0.978540i | \(-0.566063\pi\) | ||||
−0.206057 | + | 0.978540i | \(0.566063\pi\) | |||||||
\(60\) | −1.82747 | −0.235926 | ||||||||
\(61\) | −8.67612 | −1.11086 | −0.555432 | − | 0.831562i | \(-0.687447\pi\) | ||||
−0.555432 | + | 0.831562i | \(0.687447\pi\) | |||||||
\(62\) | −7.29196 | −0.926080 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0326527 | −0.00405007 | ||||||||
\(66\) | −1.61218 | −0.198446 | ||||||||
\(67\) | 8.55509 | 1.04517 | 0.522585 | − | 0.852587i | \(-0.324968\pi\) | ||||
0.522585 | + | 0.852587i | \(0.324968\pi\) | |||||||
\(68\) | 0.0684206 | 0.00829721 | ||||||||
\(69\) | 0.872619 | 0.105051 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.64077 | −0.432080 | −0.216040 | − | 0.976384i | \(-0.569314\pi\) | ||||
−0.216040 | + | 0.976384i | \(0.569314\pi\) | |||||||
\(72\) | 2.70881 | 0.319237 | ||||||||
\(73\) | −3.52157 | −0.412168 | −0.206084 | − | 0.978534i | \(-0.566072\pi\) | ||||
−0.206084 | + | 0.978534i | \(0.566072\pi\) | |||||||
\(74\) | −4.88899 | −0.568334 | ||||||||
\(75\) | 3.49085 | 0.403088 | ||||||||
\(76\) | −0.966028 | −0.110811 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.00520283 | −0.000589104 0 | ||||||||
\(79\) | 13.6955 | 1.54087 | 0.770434 | − | 0.637520i | \(-0.220040\pi\) | ||||
0.770434 | + | 0.637520i | \(0.220040\pi\) | |||||||
\(80\) | −3.38661 | −0.378634 | ||||||||
\(81\) | 6.46411 | 0.718234 | ||||||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | 6.62566 | 0.727261 | 0.363631 | − | 0.931543i | \(-0.381537\pi\) | ||||
0.363631 | + | 0.931543i | \(0.381537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.231714 | −0.0251329 | ||||||||
\(86\) | −1.84951 | −0.199437 | ||||||||
\(87\) | 0.378398 | 0.0405685 | ||||||||
\(88\) | −2.98763 | −0.318483 | ||||||||
\(89\) | −9.28595 | −0.984309 | −0.492154 | − | 0.870508i | \(-0.663790\pi\) | ||||
−0.492154 | + | 0.870508i | \(0.663790\pi\) | |||||||
\(90\) | −9.17369 | −0.966992 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.61711 | 0.168595 | ||||||||
\(93\) | 3.93487 | 0.408027 | ||||||||
\(94\) | 3.16995 | 0.326956 | ||||||||
\(95\) | 3.27156 | 0.335655 | ||||||||
\(96\) | −0.539617 | −0.0550744 | ||||||||
\(97\) | 4.17000 | 0.423399 | 0.211699 | − | 0.977335i | \(-0.432100\pi\) | ||||
0.211699 | + | 0.977335i | \(0.432100\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.09294 | −0.813372 | ||||||||
\(100\) | 6.46911 | 0.646911 | ||||||||
\(101\) | −5.41052 | −0.538367 | −0.269183 | − | 0.963089i | \(-0.586754\pi\) | ||||
−0.269183 | + | 0.963089i | \(0.586754\pi\) | |||||||
\(102\) | −0.0369209 | −0.00365571 | ||||||||
\(103\) | −13.4966 | −1.32986 | −0.664929 | − | 0.746906i | \(-0.731538\pi\) | ||||
−0.664929 | + | 0.746906i | \(0.731538\pi\) | |||||||
\(104\) | −0.00964170 | −0.000945447 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.61947 | 0.642940 | ||||||||
\(107\) | 9.54211 | 0.922470 | 0.461235 | − | 0.887278i | \(-0.347406\pi\) | ||||
0.461235 | + | 0.887278i | \(0.347406\pi\) | |||||||
\(108\) | −3.08057 | −0.296428 | ||||||||
\(109\) | −2.65081 | −0.253902 | −0.126951 | − | 0.991909i | \(-0.540519\pi\) | ||||
−0.126951 | + | 0.991909i | \(0.540519\pi\) | |||||||
\(110\) | 10.1179 | 0.964708 | ||||||||
\(111\) | 2.63818 | 0.250405 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.77537 | −0.731445 | −0.365723 | − | 0.930724i | \(-0.619178\pi\) | ||||
−0.365723 | + | 0.930724i | \(0.619178\pi\) | |||||||
\(114\) | 0.521285 | 0.0488228 | ||||||||
\(115\) | −5.47651 | −0.510687 | ||||||||
\(116\) | 0.701234 | 0.0651080 | ||||||||
\(117\) | −0.0261176 | −0.00241457 | ||||||||
\(118\) | 3.16550 | 0.291408 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.82747 | 0.166825 | ||||||||
\(121\) | −2.07404 | −0.188549 | ||||||||
\(122\) | 8.67612 | 0.785499 | ||||||||
\(123\) | −0.539617 | −0.0486556 | ||||||||
\(124\) | 7.29196 | 0.654837 | ||||||||
\(125\) | −4.97531 | −0.445006 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.741046 | −0.0657572 | −0.0328786 | − | 0.999459i | \(-0.510467\pi\) | ||||
−0.0328786 | + | 0.999459i | \(0.510467\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.998025 | 0.0878712 | ||||||||
\(130\) | 0.0326527 | 0.00286383 | ||||||||
\(131\) | −6.45083 | −0.563612 | −0.281806 | − | 0.959471i | \(-0.590933\pi\) | ||||
−0.281806 | + | 0.959471i | \(0.590933\pi\) | |||||||
\(132\) | 1.61218 | 0.140322 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.55509 | −0.739047 | ||||||||
\(135\) | 10.4327 | 0.897903 | ||||||||
\(136\) | −0.0684206 | −0.00586701 | ||||||||
\(137\) | −15.7049 | −1.34176 | −0.670881 | − | 0.741565i | \(-0.734084\pi\) | ||||
−0.670881 | + | 0.741565i | \(0.734084\pi\) | |||||||
\(138\) | −0.872619 | −0.0742823 | ||||||||
\(139\) | −7.14333 | −0.605890 | −0.302945 | − | 0.953008i | \(-0.597970\pi\) | ||||
−0.302945 | + | 0.953008i | \(0.597970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.71056 | −0.144055 | ||||||||
\(142\) | 3.64077 | 0.305527 | ||||||||
\(143\) | 0.0288059 | 0.00240887 | ||||||||
\(144\) | −2.70881 | −0.225734 | ||||||||
\(145\) | −2.37481 | −0.197217 | ||||||||
\(146\) | 3.52157 | 0.291447 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.88899 | 0.401873 | ||||||||
\(149\) | −11.1088 | −0.910069 | −0.455035 | − | 0.890474i | \(-0.650373\pi\) | ||||
−0.455035 | + | 0.890474i | \(0.650373\pi\) | |||||||
\(150\) | −3.49085 | −0.285026 | ||||||||
\(151\) | −18.1410 | −1.47629 | −0.738147 | − | 0.674640i | \(-0.764299\pi\) | ||||
−0.738147 | + | 0.674640i | \(0.764299\pi\) | |||||||
\(152\) | 0.966028 | 0.0783552 | ||||||||
\(153\) | −0.185339 | −0.0149837 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.6950 | −1.98355 | ||||||||
\(156\) | 0.00520283 | 0.000416560 0 | ||||||||
\(157\) | −16.4130 | −1.30990 | −0.654952 | − | 0.755671i | \(-0.727311\pi\) | ||||
−0.654952 | + | 0.755671i | \(0.727311\pi\) | |||||||
\(158\) | −13.6955 | −1.08956 | ||||||||
\(159\) | −3.57198 | −0.283276 | ||||||||
\(160\) | 3.38661 | 0.267735 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.46411 | −0.507868 | ||||||||
\(163\) | −1.58395 | −0.124064 | −0.0620321 | − | 0.998074i | \(-0.519758\pi\) | ||||
−0.0620321 | + | 0.998074i | \(0.519758\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | −5.45982 | −0.425046 | ||||||||
\(166\) | −6.62566 | −0.514251 | ||||||||
\(167\) | −8.09972 | −0.626775 | −0.313388 | − | 0.949625i | \(-0.601464\pi\) | ||||
−0.313388 | + | 0.949625i | \(0.601464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9999 | −0.999993 | ||||||||
\(170\) | 0.231714 | 0.0177716 | ||||||||
\(171\) | 2.61679 | 0.200111 | ||||||||
\(172\) | 1.84951 | 0.141023 | ||||||||
\(173\) | −15.1576 | −1.15241 | −0.576207 | − | 0.817304i | \(-0.695468\pi\) | ||||
−0.576207 | + | 0.817304i | \(0.695468\pi\) | |||||||
\(174\) | −0.378398 | −0.0286863 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.98763 | 0.225201 | ||||||||
\(177\) | −1.70816 | −0.128393 | ||||||||
\(178\) | 9.28595 | 0.696011 | ||||||||
\(179\) | 17.0248 | 1.27249 | 0.636245 | − | 0.771487i | \(-0.280487\pi\) | ||||
0.636245 | + | 0.771487i | \(0.280487\pi\) | |||||||
\(180\) | 9.17369 | 0.683766 | ||||||||
\(181\) | 11.2271 | 0.834505 | 0.417253 | − | 0.908790i | \(-0.362993\pi\) | ||||
0.417253 | + | 0.908790i | \(0.362993\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.68178 | −0.346087 | ||||||||
\(184\) | −1.61711 | −0.119215 | ||||||||
\(185\) | −16.5571 | −1.21730 | ||||||||
\(186\) | −3.93487 | −0.288518 | ||||||||
\(187\) | 0.204416 | 0.0149484 | ||||||||
\(188\) | −3.16995 | −0.231193 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.27156 | −0.237344 | ||||||||
\(191\) | 23.6031 | 1.70786 | 0.853929 | − | 0.520389i | \(-0.174213\pi\) | ||||
0.853929 | + | 0.520389i | \(0.174213\pi\) | |||||||
\(192\) | 0.539617 | 0.0389435 | ||||||||
\(193\) | −8.41165 | −0.605484 | −0.302742 | − | 0.953073i | \(-0.597902\pi\) | ||||
−0.302742 | + | 0.953073i | \(0.597902\pi\) | |||||||
\(194\) | −4.17000 | −0.299388 | ||||||||
\(195\) | −0.0176199 | −0.00126179 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.93787 | −0.636797 | −0.318399 | − | 0.947957i | \(-0.603145\pi\) | ||||
−0.318399 | + | 0.947957i | \(0.603145\pi\) | |||||||
\(198\) | 8.09294 | 0.575141 | ||||||||
\(199\) | 20.9193 | 1.48293 | 0.741466 | − | 0.670990i | \(-0.234131\pi\) | ||||
0.741466 | + | 0.670990i | \(0.234131\pi\) | |||||||
\(200\) | −6.46911 | −0.457435 | ||||||||
\(201\) | 4.61647 | 0.325621 | ||||||||
\(202\) | 5.41052 | 0.380683 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.0369209 | 0.00258498 | ||||||||
\(205\) | 3.38661 | 0.236531 | ||||||||
\(206\) | 13.4966 | 0.940352 | ||||||||
\(207\) | −4.38044 | −0.304462 | ||||||||
\(208\) | 0.00964170 | 0.000668532 0 | ||||||||
\(209\) | −2.88614 | −0.199638 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5708 | 0.727722 | 0.363861 | − | 0.931453i | \(-0.381458\pi\) | ||||
0.363861 | + | 0.931453i | \(0.381458\pi\) | |||||||
\(212\) | −6.61947 | −0.454627 | ||||||||
\(213\) | −1.96462 | −0.134614 | ||||||||
\(214\) | −9.54211 | −0.652285 | ||||||||
\(215\) | −6.26355 | −0.427171 | ||||||||
\(216\) | 3.08057 | 0.209606 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.65081 | 0.179536 | ||||||||
\(219\) | −1.90030 | −0.128410 | ||||||||
\(220\) | −10.1179 | −0.682152 | ||||||||
\(221\) | 0.000659691 0 | 4.43756e−5 0 | ||||||||
\(222\) | −2.63818 | −0.177063 | ||||||||
\(223\) | −15.5890 | −1.04392 | −0.521959 | − | 0.852971i | \(-0.674798\pi\) | ||||
−0.521959 | + | 0.852971i | \(0.674798\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.5236 | −1.16824 | ||||||||
\(226\) | 7.77537 | 0.517210 | ||||||||
\(227\) | 2.96125 | 0.196545 | 0.0982726 | − | 0.995160i | \(-0.468668\pi\) | ||||
0.0982726 | + | 0.995160i | \(0.468668\pi\) | |||||||
\(228\) | −0.521285 | −0.0345230 | ||||||||
\(229\) | −24.3188 | −1.60703 | −0.803515 | − | 0.595284i | \(-0.797039\pi\) | ||||
−0.803515 | + | 0.595284i | \(0.797039\pi\) | |||||||
\(230\) | 5.47651 | 0.361110 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.701234 | −0.0460383 | ||||||||
\(233\) | −1.72516 | −0.113019 | −0.0565096 | − | 0.998402i | \(-0.517997\pi\) | ||||
−0.0565096 | + | 0.998402i | \(0.517997\pi\) | |||||||
\(234\) | 0.0261176 | 0.00170736 | ||||||||
\(235\) | 10.7354 | 0.700300 | ||||||||
\(236\) | −3.16550 | −0.206057 | ||||||||
\(237\) | 7.39034 | 0.480054 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.61482 | −0.621931 | −0.310965 | − | 0.950421i | \(-0.600652\pi\) | ||||
−0.310965 | + | 0.950421i | \(0.600652\pi\) | |||||||
\(240\) | −1.82747 | −0.117963 | ||||||||
\(241\) | 14.4222 | 0.929014 | 0.464507 | − | 0.885570i | \(-0.346232\pi\) | ||||
0.464507 | + | 0.885570i | \(0.346232\pi\) | |||||||
\(242\) | 2.07404 | 0.133324 | ||||||||
\(243\) | 12.7299 | 0.816621 | ||||||||
\(244\) | −8.67612 | −0.555432 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.539617 | 0.0344047 | ||||||||
\(247\) | −0.00931416 | −0.000592646 0 | ||||||||
\(248\) | −7.29196 | −0.463040 | ||||||||
\(249\) | 3.57532 | 0.226577 | ||||||||
\(250\) | 4.97531 | 0.314666 | ||||||||
\(251\) | 1.02742 | 0.0648503 | 0.0324251 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324251 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.83133 | 0.303743 | ||||||||
\(254\) | 0.741046 | 0.0464974 | ||||||||
\(255\) | −0.125037 | −0.00783010 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.56650 | −0.347229 | −0.173614 | − | 0.984814i | \(-0.555545\pi\) | ||||
−0.173614 | + | 0.984814i | \(0.555545\pi\) | |||||||
\(258\) | −0.998025 | −0.0621343 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0326527 | −0.00202503 | ||||||||
\(261\) | −1.89951 | −0.117577 | ||||||||
\(262\) | 6.45083 | 0.398534 | ||||||||
\(263\) | −10.5040 | −0.647705 | −0.323853 | − | 0.946108i | \(-0.604978\pi\) | ||||
−0.323853 | + | 0.946108i | \(0.604978\pi\) | |||||||
\(264\) | −1.61218 | −0.0992228 | ||||||||
\(265\) | 22.4175 | 1.37710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.01086 | −0.306660 | ||||||||
\(268\) | 8.55509 | 0.522585 | ||||||||
\(269\) | −27.8900 | −1.70049 | −0.850243 | − | 0.526391i | \(-0.823545\pi\) | ||||
−0.850243 | + | 0.526391i | \(0.823545\pi\) | |||||||
\(270\) | −10.4327 | −0.634914 | ||||||||
\(271\) | 11.8811 | 0.721725 | 0.360863 | − | 0.932619i | \(-0.382482\pi\) | ||||
0.360863 | + | 0.932619i | \(0.382482\pi\) | |||||||
\(272\) | 0.0684206 | 0.00414861 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7049 | 0.948768 | ||||||||
\(275\) | 19.3273 | 1.16548 | ||||||||
\(276\) | 0.872619 | 0.0525255 | ||||||||
\(277\) | −5.89117 | −0.353966 | −0.176983 | − | 0.984214i | \(-0.556634\pi\) | ||||
−0.176983 | + | 0.984214i | \(0.556634\pi\) | |||||||
\(278\) | 7.14333 | 0.428429 | ||||||||
\(279\) | −19.7526 | −1.18255 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3163 | −0.734726 | −0.367363 | − | 0.930078i | \(-0.619739\pi\) | ||||
−0.367363 | + | 0.930078i | \(0.619739\pi\) | |||||||
\(282\) | 1.71056 | 0.101862 | ||||||||
\(283\) | −7.63451 | −0.453824 | −0.226912 | − | 0.973915i | \(-0.572863\pi\) | ||||
−0.226912 | + | 0.973915i | \(0.572863\pi\) | |||||||
\(284\) | −3.64077 | −0.216040 | ||||||||
\(285\) | 1.76539 | 0.104573 | ||||||||
\(286\) | −0.0288059 | −0.00170333 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.70881 | 0.159618 | ||||||||
\(289\) | −16.9953 | −0.999725 | ||||||||
\(290\) | 2.37481 | 0.139453 | ||||||||
\(291\) | 2.25020 | 0.131909 | ||||||||
\(292\) | −3.52157 | −0.206084 | ||||||||
\(293\) | −26.4456 | −1.54497 | −0.772485 | − | 0.635034i | \(-0.780986\pi\) | ||||
−0.772485 | + | 0.635034i | \(0.780986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7203 | 0.624161 | ||||||||
\(296\) | −4.88899 | −0.284167 | ||||||||
\(297\) | −9.20363 | −0.534049 | ||||||||
\(298\) | 11.1088 | 0.643516 | ||||||||
\(299\) | 0.0155917 | 0.000901690 0 | ||||||||
\(300\) | 3.49085 | 0.201544 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.1410 | 1.04390 | ||||||||
\(303\) | −2.91961 | −0.167727 | ||||||||
\(304\) | −0.966028 | −0.0554055 | ||||||||
\(305\) | 29.3826 | 1.68244 | ||||||||
\(306\) | 0.185339 | 0.0105951 | ||||||||
\(307\) | −11.1342 | −0.635462 | −0.317731 | − | 0.948181i | \(-0.602921\pi\) | ||||
−0.317731 | + | 0.948181i | \(0.602921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.28299 | −0.414315 | ||||||||
\(310\) | 24.6950 | 1.40258 | ||||||||
\(311\) | 5.52223 | 0.313137 | 0.156569 | − | 0.987667i | \(-0.449957\pi\) | ||||
0.156569 | + | 0.987667i | \(0.449957\pi\) | |||||||
\(312\) | −0.00520283 | −0.000294552 0 | ||||||||
\(313\) | −11.1544 | −0.630486 | −0.315243 | − | 0.949011i | \(-0.602086\pi\) | ||||
−0.315243 | + | 0.949011i | \(0.602086\pi\) | |||||||
\(314\) | 16.4130 | 0.926242 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.6955 | 0.770434 | ||||||||
\(317\) | 3.17686 | 0.178430 | 0.0892151 | − | 0.996012i | \(-0.471564\pi\) | ||||
0.0892151 | + | 0.996012i | \(0.471564\pi\) | |||||||
\(318\) | 3.57198 | 0.200307 | ||||||||
\(319\) | 2.09503 | 0.117299 | ||||||||
\(320\) | −3.38661 | −0.189317 | ||||||||
\(321\) | 5.14909 | 0.287394 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0660962 | −0.00367769 | ||||||||
\(324\) | 6.46411 | 0.359117 | ||||||||
\(325\) | 0.0623733 | 0.00345985 | ||||||||
\(326\) | 1.58395 | 0.0877266 | ||||||||
\(327\) | −1.43042 | −0.0791027 | ||||||||
\(328\) | 1.00000 | 0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.45982 | 0.300553 | ||||||||
\(331\) | 13.3594 | 0.734298 | 0.367149 | − | 0.930162i | \(-0.380334\pi\) | ||||
0.367149 | + | 0.930162i | \(0.380334\pi\) | |||||||
\(332\) | 6.62566 | 0.363631 | ||||||||
\(333\) | −13.2434 | −0.725732 | ||||||||
\(334\) | 8.09972 | 0.443197 | ||||||||
\(335\) | −28.9727 | −1.58295 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.0885 | 1.80245 | 0.901224 | − | 0.433354i | \(-0.142670\pi\) | ||||
0.901224 | + | 0.433354i | \(0.142670\pi\) | |||||||
\(338\) | 12.9999 | 0.707102 | ||||||||
\(339\) | −4.19572 | −0.227880 | ||||||||
\(340\) | −0.231714 | −0.0125664 | ||||||||
\(341\) | 21.7857 | 1.17976 | ||||||||
\(342\) | −2.61679 | −0.141500 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.84951 | −0.0997187 | ||||||||
\(345\) | −2.95522 | −0.159104 | ||||||||
\(346\) | 15.1576 | 0.814880 | ||||||||
\(347\) | 3.93552 | 0.211270 | 0.105635 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105635 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(348\) | 0.378398 | 0.0202843 | ||||||||
\(349\) | 6.95104 | 0.372080 | 0.186040 | − | 0.982542i | \(-0.440435\pi\) | ||||
0.186040 | + | 0.982542i | \(0.440435\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0297020 | −0.00158537 | ||||||||
\(352\) | −2.98763 | −0.159241 | ||||||||
\(353\) | −20.8201 | −1.10814 | −0.554072 | − | 0.832469i | \(-0.686927\pi\) | ||||
−0.554072 | + | 0.832469i | \(0.686927\pi\) | |||||||
\(354\) | 1.70816 | 0.0907876 | ||||||||
\(355\) | 12.3299 | 0.654402 | ||||||||
\(356\) | −9.28595 | −0.492154 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −17.0248 | −0.899786 | ||||||||
\(359\) | −21.1534 | −1.11643 | −0.558217 | − | 0.829695i | \(-0.688514\pi\) | ||||
−0.558217 | + | 0.829695i | \(0.688514\pi\) | |||||||
\(360\) | −9.17369 | −0.483496 | ||||||||
\(361\) | −18.0668 | −0.950884 | ||||||||
\(362\) | −11.2271 | −0.590084 | ||||||||
\(363\) | −1.11919 | −0.0587421 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9262 | 0.624244 | ||||||||
\(366\) | 4.68178 | 0.244721 | ||||||||
\(367\) | 8.46679 | 0.441963 | 0.220981 | − | 0.975278i | \(-0.429074\pi\) | ||||
0.220981 | + | 0.975278i | \(0.429074\pi\) | |||||||
\(368\) | 1.61711 | 0.0842976 | ||||||||
\(369\) | 2.70881 | 0.141015 | ||||||||
\(370\) | 16.5571 | 0.860762 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.93487 | 0.204013 | ||||||||
\(373\) | 20.6334 | 1.06836 | 0.534179 | − | 0.845371i | \(-0.320621\pi\) | ||||
0.534179 | + | 0.845371i | \(0.320621\pi\) | |||||||
\(374\) | −0.204416 | −0.0105701 | ||||||||
\(375\) | −2.68476 | −0.138641 | ||||||||
\(376\) | 3.16995 | 0.163478 | ||||||||
\(377\) | 0.00676109 | 0.000348214 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.0545 | 1.38970 | 0.694848 | − | 0.719156i | \(-0.255472\pi\) | ||||
0.694848 | + | 0.719156i | \(0.255472\pi\) | |||||||
\(380\) | 3.27156 | 0.167827 | ||||||||
\(381\) | −0.399881 | −0.0204865 | ||||||||
\(382\) | −23.6031 | −1.20764 | ||||||||
\(383\) | 9.98846 | 0.510387 | 0.255193 | − | 0.966890i | \(-0.417861\pi\) | ||||
0.255193 | + | 0.966890i | \(0.417861\pi\) | |||||||
\(384\) | −0.539617 | −0.0275372 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.41165 | 0.428142 | ||||||||
\(387\) | −5.00997 | −0.254671 | ||||||||
\(388\) | 4.17000 | 0.211699 | ||||||||
\(389\) | 31.1899 | 1.58139 | 0.790696 | − | 0.612209i | \(-0.209719\pi\) | ||||
0.790696 | + | 0.612209i | \(0.209719\pi\) | |||||||
\(390\) | 0.0176199 | 0.000892221 0 | ||||||||
\(391\) | 0.110643 | 0.00559548 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.48098 | −0.175592 | ||||||||
\(394\) | 8.93787 | 0.450284 | ||||||||
\(395\) | −46.3814 | −2.33370 | ||||||||
\(396\) | −8.09294 | −0.406686 | ||||||||
\(397\) | 19.7434 | 0.990891 | 0.495445 | − | 0.868639i | \(-0.335005\pi\) | ||||
0.495445 | + | 0.868639i | \(0.335005\pi\) | |||||||
\(398\) | −20.9193 | −1.04859 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.46911 | 0.323456 | ||||||||
\(401\) | −11.2580 | −0.562196 | −0.281098 | − | 0.959679i | \(-0.590699\pi\) | ||||
−0.281098 | + | 0.959679i | \(0.590699\pi\) | |||||||
\(402\) | −4.61647 | −0.230249 | ||||||||
\(403\) | 0.0703069 | 0.00350224 | ||||||||
\(404\) | −5.41052 | −0.269183 | ||||||||
\(405\) | −21.8914 | −1.08779 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.6065 | 0.724018 | ||||||||
\(408\) | −0.0369209 | −0.00182786 | ||||||||
\(409\) | 7.27124 | 0.359540 | 0.179770 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179770 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(410\) | −3.38661 | −0.167253 | ||||||||
\(411\) | −8.47464 | −0.418023 | ||||||||
\(412\) | −13.4966 | −0.664929 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.38044 | 0.215287 | ||||||||
\(415\) | −22.4385 | −1.10146 | ||||||||
\(416\) | −0.00964170 | −0.000472723 0 | ||||||||
\(417\) | −3.85467 | −0.188764 | ||||||||
\(418\) | 2.88614 | 0.141166 | ||||||||
\(419\) | −24.3697 | −1.19054 | −0.595268 | − | 0.803527i | \(-0.702954\pi\) | ||||
−0.595268 | + | 0.803527i | \(0.702954\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.6797 | −0.569236 | −0.284618 | − | 0.958641i | \(-0.591867\pi\) | ||||
−0.284618 | + | 0.958641i | \(0.591867\pi\) | |||||||
\(422\) | −10.5708 | −0.514577 | ||||||||
\(423\) | 8.58681 | 0.417505 | ||||||||
\(424\) | 6.61947 | 0.321470 | ||||||||
\(425\) | 0.442620 | 0.0214702 | ||||||||
\(426\) | 1.96462 | 0.0951863 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.54211 | 0.461235 | ||||||||
\(429\) | 0.0155442 | 0.000750479 0 | ||||||||
\(430\) | 6.26355 | 0.302055 | ||||||||
\(431\) | 14.2910 | 0.688374 | 0.344187 | − | 0.938901i | \(-0.388155\pi\) | ||||
0.344187 | + | 0.938901i | \(0.388155\pi\) | |||||||
\(432\) | −3.08057 | −0.148214 | ||||||||
\(433\) | −4.06751 | −0.195472 | −0.0977360 | − | 0.995212i | \(-0.531160\pi\) | ||||
−0.0977360 | + | 0.995212i | \(0.531160\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.28149 | −0.0614425 | ||||||||
\(436\) | −2.65081 | −0.126951 | ||||||||
\(437\) | −1.56217 | −0.0747288 | ||||||||
\(438\) | 1.90030 | 0.0907997 | ||||||||
\(439\) | −17.6381 | −0.841820 | −0.420910 | − | 0.907102i | \(-0.638289\pi\) | ||||
−0.420910 | + | 0.907102i | \(0.638289\pi\) | |||||||
\(440\) | 10.1179 | 0.482354 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.000659691 0 | −3.13783e−5 0 | ||||||||
\(443\) | 2.09016 | 0.0993066 | 0.0496533 | − | 0.998767i | \(-0.484188\pi\) | ||||
0.0496533 | + | 0.998767i | \(0.484188\pi\) | |||||||
\(444\) | 2.63818 | 0.125203 | ||||||||
\(445\) | 31.4479 | 1.49077 | ||||||||
\(446\) | 15.5890 | 0.738161 | ||||||||
\(447\) | −5.99451 | −0.283530 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.1404 | −0.525746 | −0.262873 | − | 0.964830i | \(-0.584670\pi\) | ||||
−0.262873 | + | 0.964830i | \(0.584670\pi\) | |||||||
\(450\) | 17.5236 | 0.826071 | ||||||||
\(451\) | −2.98763 | −0.140682 | ||||||||
\(452\) | −7.77537 | −0.365723 | ||||||||
\(453\) | −9.78920 | −0.459937 | ||||||||
\(454\) | −2.96125 | −0.138978 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.521285 | 0.0244114 | ||||||||
\(457\) | −26.4289 | −1.23629 | −0.618147 | − | 0.786063i | \(-0.712116\pi\) | ||||
−0.618147 | + | 0.786063i | \(0.712116\pi\) | |||||||
\(458\) | 24.3188 | 1.13634 | ||||||||
\(459\) | −0.210775 | −0.00983811 | ||||||||
\(460\) | −5.47651 | −0.255344 | ||||||||
\(461\) | −2.37152 | −0.110453 | −0.0552263 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552263 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.8802 | 0.923912 | 0.461956 | − | 0.886903i | \(-0.347148\pi\) | ||||
0.461956 | + | 0.886903i | \(0.347148\pi\) | |||||||
\(464\) | 0.701234 | 0.0325540 | ||||||||
\(465\) | −13.3258 | −0.617971 | ||||||||
\(466\) | 1.72516 | 0.0799166 | ||||||||
\(467\) | −20.1463 | −0.932262 | −0.466131 | − | 0.884716i | \(-0.654352\pi\) | ||||
−0.466131 | + | 0.884716i | \(0.654352\pi\) | |||||||
\(468\) | −0.0261176 | −0.00120729 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10.7354 | −0.495187 | ||||||||
\(471\) | −8.85676 | −0.408098 | ||||||||
\(472\) | 3.16550 | 0.145704 | ||||||||
\(473\) | 5.52565 | 0.254070 | ||||||||
\(474\) | −7.39034 | −0.339450 | ||||||||
\(475\) | −6.24934 | −0.286740 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.9309 | 0.821000 | ||||||||
\(478\) | 9.61482 | 0.439771 | ||||||||
\(479\) | −42.0146 | −1.91970 | −0.959848 | − | 0.280521i | \(-0.909493\pi\) | ||||
−0.959848 | + | 0.280521i | \(0.909493\pi\) | |||||||
\(480\) | 1.82747 | 0.0834123 | ||||||||
\(481\) | 0.0471382 | 0.00214932 | ||||||||
\(482\) | −14.4222 | −0.656912 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.07404 | −0.0942745 | ||||||||
\(485\) | −14.1221 | −0.641253 | ||||||||
\(486\) | −12.7299 | −0.577438 | ||||||||
\(487\) | 11.7506 | 0.532472 | 0.266236 | − | 0.963908i | \(-0.414220\pi\) | ||||
0.266236 | + | 0.963908i | \(0.414220\pi\) | |||||||
\(488\) | 8.67612 | 0.392750 | ||||||||
\(489\) | −0.854724 | −0.0386520 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.2530 | −0.868875 | −0.434438 | − | 0.900702i | \(-0.643053\pi\) | ||||
−0.434438 | + | 0.900702i | \(0.643053\pi\) | |||||||
\(492\) | −0.539617 | −0.0243278 | ||||||||
\(493\) | 0.0479788 | 0.00216086 | ||||||||
\(494\) | 0.00931416 | 0.000419064 0 | ||||||||
\(495\) | 27.4076 | 1.23188 | ||||||||
\(496\) | 7.29196 | 0.327419 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.57532 | −0.160214 | ||||||||
\(499\) | 17.7083 | 0.792730 | 0.396365 | − | 0.918093i | \(-0.370271\pi\) | ||||
0.396365 | + | 0.918093i | \(0.370271\pi\) | |||||||
\(500\) | −4.97531 | −0.222503 | ||||||||
\(501\) | −4.37075 | −0.195271 | ||||||||
\(502\) | −1.02742 | −0.0458561 | ||||||||
\(503\) | −2.66677 | −0.118906 | −0.0594528 | − | 0.998231i | \(-0.518936\pi\) | ||||
−0.0594528 | + | 0.998231i | \(0.518936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.3233 | 0.815377 | ||||||||
\(506\) | −4.83133 | −0.214779 | ||||||||
\(507\) | −7.01497 | −0.311546 | ||||||||
\(508\) | −0.741046 | −0.0328786 | ||||||||
\(509\) | −13.2720 | −0.588270 | −0.294135 | − | 0.955764i | \(-0.595031\pi\) | ||||
−0.294135 | + | 0.955764i | \(0.595031\pi\) | |||||||
\(510\) | 0.125037 | 0.00553672 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.97592 | 0.131390 | ||||||||
\(514\) | 5.56650 | 0.245528 | ||||||||
\(515\) | 45.7077 | 2.01412 | ||||||||
\(516\) | 0.998025 | 0.0439356 | ||||||||
\(517\) | −9.47066 | −0.416519 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.17932 | −0.359032 | ||||||||
\(520\) | 0.0326527 | 0.00143191 | ||||||||
\(521\) | 15.8768 | 0.695575 | 0.347788 | − | 0.937573i | \(-0.386933\pi\) | ||||
0.347788 | + | 0.937573i | \(0.386933\pi\) | |||||||
\(522\) | 1.89951 | 0.0831394 | ||||||||
\(523\) | −30.0813 | −1.31537 | −0.657683 | − | 0.753295i | \(-0.728463\pi\) | ||||
−0.657683 | + | 0.753295i | \(0.728463\pi\) | |||||||
\(524\) | −6.45083 | −0.281806 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.5040 | 0.457997 | ||||||||
\(527\) | 0.498920 | 0.0217333 | ||||||||
\(528\) | 1.61218 | 0.0701611 | ||||||||
\(529\) | −20.3850 | −0.886303 | ||||||||
\(530\) | −22.4175 | −0.973756 | ||||||||
\(531\) | 8.57475 | 0.372112 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.00964170 | −0.000417629 0 | ||||||||
\(534\) | 5.01086 | 0.216841 | ||||||||
\(535\) | −32.3154 | −1.39712 | ||||||||
\(536\) | −8.55509 | −0.369524 | ||||||||
\(537\) | 9.18685 | 0.396442 | ||||||||
\(538\) | 27.8900 | 1.20243 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 10.4327 | 0.448952 | ||||||||
\(541\) | −45.8018 | −1.96917 | −0.984587 | − | 0.174893i | \(-0.944042\pi\) | ||||
−0.984587 | + | 0.174893i | \(0.944042\pi\) | |||||||
\(542\) | −11.8811 | −0.510337 | ||||||||
\(543\) | 6.05835 | 0.259989 | ||||||||
\(544\) | −0.0684206 | −0.00293351 | ||||||||
\(545\) | 8.97727 | 0.384544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7657 | 0.674091 | 0.337045 | − | 0.941488i | \(-0.390572\pi\) | ||||
0.337045 | + | 0.941488i | \(0.390572\pi\) | |||||||
\(548\) | −15.7049 | −0.670881 | ||||||||
\(549\) | 23.5020 | 1.00304 | ||||||||
\(550\) | −19.3273 | −0.824121 | ||||||||
\(551\) | −0.677412 | −0.0288587 | ||||||||
\(552\) | −0.872619 | −0.0371411 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.89117 | 0.250292 | ||||||||
\(555\) | −8.93449 | −0.379248 | ||||||||
\(556\) | −7.14333 | −0.302945 | ||||||||
\(557\) | −31.7121 | −1.34369 | −0.671843 | − | 0.740694i | \(-0.734497\pi\) | ||||
−0.671843 | + | 0.740694i | \(0.734497\pi\) | |||||||
\(558\) | 19.7526 | 0.836192 | ||||||||
\(559\) | 0.0178324 | 0.000754230 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.110306 | 0.00465713 | ||||||||
\(562\) | 12.3163 | 0.519530 | ||||||||
\(563\) | 1.89988 | 0.0800705 | 0.0400353 | − | 0.999198i | \(-0.487253\pi\) | ||||
0.0400353 | + | 0.999198i | \(0.487253\pi\) | |||||||
\(564\) | −1.71056 | −0.0720276 | ||||||||
\(565\) | 26.3321 | 1.10780 | ||||||||
\(566\) | 7.63451 | 0.320902 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.64077 | 0.152763 | ||||||||
\(569\) | −21.2474 | −0.890736 | −0.445368 | − | 0.895348i | \(-0.646927\pi\) | ||||
−0.445368 | + | 0.895348i | \(0.646927\pi\) | |||||||
\(570\) | −1.76539 | −0.0739440 | ||||||||
\(571\) | 28.9274 | 1.21057 | 0.605287 | − | 0.796008i | \(-0.293059\pi\) | ||||
0.605287 | + | 0.796008i | \(0.293059\pi\) | |||||||
\(572\) | 0.0288059 | 0.00120443 | ||||||||
\(573\) | 12.7366 | 0.532080 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.4613 | 0.436264 | ||||||||
\(576\) | −2.70881 | −0.112867 | ||||||||
\(577\) | 27.6536 | 1.15123 | 0.575617 | − | 0.817719i | \(-0.304762\pi\) | ||||
0.575617 | + | 0.817719i | \(0.304762\pi\) | |||||||
\(578\) | 16.9953 | 0.706912 | ||||||||
\(579\) | −4.53907 | −0.188637 | ||||||||
\(580\) | −2.37481 | −0.0986084 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.25020 | −0.0932739 | ||||||||
\(583\) | −19.7766 | −0.819061 | ||||||||
\(584\) | 3.52157 | 0.145723 | ||||||||
\(585\) | 0.0884500 | 0.00365696 | ||||||||
\(586\) | 26.4456 | 1.09246 | ||||||||
\(587\) | −4.41980 | −0.182425 | −0.0912123 | − | 0.995831i | \(-0.529074\pi\) | ||||
−0.0912123 | + | 0.995831i | \(0.529074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.04423 | −0.290253 | ||||||||
\(590\) | −10.7203 | −0.441348 | ||||||||
\(591\) | −4.82303 | −0.198393 | ||||||||
\(592\) | 4.88899 | 0.200936 | ||||||||
\(593\) | −11.6028 | −0.476468 | −0.238234 | − | 0.971208i | \(-0.576569\pi\) | ||||
−0.238234 | + | 0.971208i | \(0.576569\pi\) | |||||||
\(594\) | 9.20363 | 0.377629 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.1088 | −0.455035 | ||||||||
\(597\) | 11.2884 | 0.462005 | ||||||||
\(598\) | −0.0155917 | −0.000637591 0 | ||||||||
\(599\) | −15.2032 | −0.621187 | −0.310593 | − | 0.950543i | \(-0.600528\pi\) | ||||
−0.310593 | + | 0.950543i | \(0.600528\pi\) | |||||||
\(600\) | −3.49085 | −0.142513 | ||||||||
\(601\) | 33.4852 | 1.36589 | 0.682944 | − | 0.730470i | \(-0.260699\pi\) | ||||
0.682944 | + | 0.730470i | \(0.260699\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −23.1741 | −0.943724 | ||||||||
\(604\) | −18.1410 | −0.738147 | ||||||||
\(605\) | 7.02396 | 0.285565 | ||||||||
\(606\) | 2.91961 | 0.118601 | ||||||||
\(607\) | −39.4996 | −1.60324 | −0.801620 | − | 0.597834i | \(-0.796028\pi\) | ||||
−0.801620 | + | 0.597834i | \(0.796028\pi\) | |||||||
\(608\) | 0.966028 | 0.0391776 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.3826 | −1.18967 | ||||||||
\(611\) | −0.0305638 | −0.00123648 | ||||||||
\(612\) | −0.185339 | −0.00749187 | ||||||||
\(613\) | 21.6181 | 0.873146 | 0.436573 | − | 0.899669i | \(-0.356192\pi\) | ||||
0.436573 | + | 0.899669i | \(0.356192\pi\) | |||||||
\(614\) | 11.1342 | 0.449339 | ||||||||
\(615\) | 1.82747 | 0.0736908 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32602 | −0.0533835 | −0.0266918 | − | 0.999644i | \(-0.508497\pi\) | ||||
−0.0266918 | + | 0.999644i | \(0.508497\pi\) | |||||||
\(618\) | 7.28299 | 0.292965 | ||||||||
\(619\) | 39.2016 | 1.57564 | 0.787822 | − | 0.615903i | \(-0.211209\pi\) | ||||
0.787822 | + | 0.615903i | \(0.211209\pi\) | |||||||
\(620\) | −24.6950 | −0.991775 | ||||||||
\(621\) | −4.98162 | −0.199905 | ||||||||
\(622\) | −5.52223 | −0.221421 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.00520283 | 0.000208280 0 | ||||||||
\(625\) | −15.4961 | −0.619845 | ||||||||
\(626\) | 11.1544 | 0.445821 | ||||||||
\(627\) | −1.55741 | −0.0621970 | ||||||||
\(628\) | −16.4130 | −0.654952 | ||||||||
\(629\) | 0.334507 | 0.0133377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.0119 | −0.836469 | −0.418235 | − | 0.908339i | \(-0.637351\pi\) | ||||
−0.418235 | + | 0.908339i | \(0.637351\pi\) | |||||||
\(632\) | −13.6955 | −0.544779 | ||||||||
\(633\) | 5.70417 | 0.226721 | ||||||||
\(634\) | −3.17686 | −0.126169 | ||||||||
\(635\) | 2.50963 | 0.0995917 | ||||||||
\(636\) | −3.57198 | −0.141638 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.09503 | −0.0829431 | ||||||||
\(639\) | 9.86217 | 0.390142 | ||||||||
\(640\) | 3.38661 | 0.133867 | ||||||||
\(641\) | −9.17231 | −0.362284 | −0.181142 | − | 0.983457i | \(-0.557979\pi\) | ||||
−0.181142 | + | 0.983457i | \(0.557979\pi\) | |||||||
\(642\) | −5.14909 | −0.203218 | ||||||||
\(643\) | −18.2534 | −0.719845 | −0.359923 | − | 0.932982i | \(-0.617197\pi\) | ||||
−0.359923 | + | 0.932982i | \(0.617197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.37992 | −0.133084 | ||||||||
\(646\) | 0.0660962 | 0.00260052 | ||||||||
\(647\) | 21.6102 | 0.849583 | 0.424792 | − | 0.905291i | \(-0.360347\pi\) | ||||
0.424792 | + | 0.905291i | \(0.360347\pi\) | |||||||
\(648\) | −6.46411 | −0.253934 | ||||||||
\(649\) | −9.45736 | −0.371234 | ||||||||
\(650\) | −0.0623733 | −0.00244648 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.58395 | −0.0620321 | ||||||||
\(653\) | −37.3303 | −1.46085 | −0.730423 | − | 0.682995i | \(-0.760677\pi\) | ||||
−0.730423 | + | 0.682995i | \(0.760677\pi\) | |||||||
\(654\) | 1.43042 | 0.0559340 | ||||||||
\(655\) | 21.8464 | 0.853611 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | 9.53927 | 0.372162 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.38062 | 0.170645 | 0.0853224 | − | 0.996353i | \(-0.472808\pi\) | ||||
0.0853224 | + | 0.996353i | \(0.472808\pi\) | |||||||
\(660\) | −5.45982 | −0.212523 | ||||||||
\(661\) | 42.5771 | 1.65606 | 0.828029 | − | 0.560685i | \(-0.189462\pi\) | ||||
0.828029 | + | 0.560685i | \(0.189462\pi\) | |||||||
\(662\) | −13.3594 | −0.519227 | ||||||||
\(663\) | 0.000355980 0 | 1.38251e−5 0 | ||||||||
\(664\) | −6.62566 | −0.257126 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.2434 | 0.513170 | ||||||||
\(667\) | 1.13397 | 0.0439075 | ||||||||
\(668\) | −8.09972 | −0.313388 | ||||||||
\(669\) | −8.41210 | −0.325230 | ||||||||
\(670\) | 28.9727 | 1.11931 | ||||||||
\(671\) | −25.9211 | −1.00067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.4996 | 1.56115 | 0.780573 | − | 0.625065i | \(-0.214927\pi\) | ||||
0.780573 | + | 0.625065i | \(0.214927\pi\) | |||||||
\(674\) | −33.0885 | −1.27452 | ||||||||
\(675\) | −19.9286 | −0.767052 | ||||||||
\(676\) | −12.9999 | −0.499996 | ||||||||
\(677\) | 3.09659 | 0.119012 | 0.0595058 | − | 0.998228i | \(-0.481048\pi\) | ||||
0.0595058 | + | 0.998228i | \(0.481048\pi\) | |||||||
\(678\) | 4.19572 | 0.161136 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.231714 | 0.00888581 | ||||||||
\(681\) | 1.59794 | 0.0612333 | ||||||||
\(682\) | −21.7857 | −0.834218 | ||||||||
\(683\) | 24.4003 | 0.933650 | 0.466825 | − | 0.884350i | \(-0.345398\pi\) | ||||
0.466825 | + | 0.884350i | \(0.345398\pi\) | |||||||
\(684\) | 2.61679 | 0.100055 | ||||||||
\(685\) | 53.1864 | 2.03215 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.1228 | −0.500667 | ||||||||
\(688\) | 1.84951 | 0.0705117 | ||||||||
\(689\) | −0.0638230 | −0.00243146 | ||||||||
\(690\) | 2.95522 | 0.112503 | ||||||||
\(691\) | 0.130749 | 0.00497394 | 0.00248697 | − | 0.999997i | \(-0.499208\pi\) | ||||
0.00248697 | + | 0.999997i | \(0.499208\pi\) | |||||||
\(692\) | −15.1576 | −0.576207 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.93552 | −0.149390 | ||||||||
\(695\) | 24.1917 | 0.917643 | ||||||||
\(696\) | −0.378398 | −0.0143431 | ||||||||
\(697\) | −0.0684206 | −0.00259161 | ||||||||
\(698\) | −6.95104 | −0.263101 | ||||||||
\(699\) | −0.930927 | −0.0352109 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.9200 | −0.978985 | −0.489493 | − | 0.872007i | \(-0.662818\pi\) | ||||
−0.489493 | + | 0.872007i | \(0.662818\pi\) | |||||||
\(702\) | 0.0297020 | 0.00112103 | ||||||||
\(703\) | −4.72290 | −0.178128 | ||||||||
\(704\) | 2.98763 | 0.112601 | ||||||||
\(705\) | 5.79300 | 0.218177 | ||||||||
\(706\) | 20.8201 | 0.783576 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.70816 | −0.0641965 | ||||||||
\(709\) | −9.45952 | −0.355260 | −0.177630 | − | 0.984097i | \(-0.556843\pi\) | ||||
−0.177630 | + | 0.984097i | \(0.556843\pi\) | |||||||
\(710\) | −12.3299 | −0.462732 | ||||||||
\(711\) | −37.0986 | −1.39131 | ||||||||
\(712\) | 9.28595 | 0.348006 | ||||||||
\(713\) | 11.7919 | 0.441609 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0975543 | −0.00364832 | ||||||||
\(716\) | 17.0248 | 0.636245 | ||||||||
\(717\) | −5.18832 | −0.193761 | ||||||||
\(718\) | 21.1534 | 0.789438 | ||||||||
\(719\) | −15.2451 | −0.568547 | −0.284274 | − | 0.958743i | \(-0.591752\pi\) | ||||
−0.284274 | + | 0.958743i | \(0.591752\pi\) | |||||||
\(720\) | 9.17369 | 0.341883 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.0668 | 0.672376 | ||||||||
\(723\) | 7.78245 | 0.289432 | ||||||||
\(724\) | 11.2271 | 0.417253 | ||||||||
\(725\) | 4.53636 | 0.168476 | ||||||||
\(726\) | 1.11919 | 0.0415369 | ||||||||
\(727\) | 32.6402 | 1.21056 | 0.605279 | − | 0.796013i | \(-0.293061\pi\) | ||||
0.605279 | + | 0.796013i | \(0.293061\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.5231 | −0.463818 | ||||||||
\(730\) | −11.9262 | −0.441407 | ||||||||
\(731\) | 0.126544 | 0.00468041 | ||||||||
\(732\) | −4.68178 | −0.173044 | ||||||||
\(733\) | 10.7460 | 0.396912 | 0.198456 | − | 0.980110i | \(-0.436407\pi\) | ||||
0.198456 | + | 0.980110i | \(0.436407\pi\) | |||||||
\(734\) | −8.46679 | −0.312515 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.61711 | −0.0596074 | ||||||||
\(737\) | 25.5595 | 0.941496 | ||||||||
\(738\) | −2.70881 | −0.0997128 | ||||||||
\(739\) | −7.11218 | −0.261626 | −0.130813 | − | 0.991407i | \(-0.541759\pi\) | ||||
−0.130813 | + | 0.991407i | \(0.541759\pi\) | |||||||
\(740\) | −16.5571 | −0.608651 | ||||||||
\(741\) | −0.00502608 | −0.000184638 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.2345 | −1.07251 | −0.536255 | − | 0.844056i | \(-0.680162\pi\) | ||||
−0.536255 | + | 0.844056i | \(0.680162\pi\) | |||||||
\(744\) | −3.93487 | −0.144259 | ||||||||
\(745\) | 37.6212 | 1.37833 | ||||||||
\(746\) | −20.6334 | −0.755444 | ||||||||
\(747\) | −17.9477 | −0.656671 | ||||||||
\(748\) | 0.204416 | 0.00747418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.68476 | 0.0980337 | ||||||||
\(751\) | −23.9539 | −0.874091 | −0.437046 | − | 0.899439i | \(-0.643975\pi\) | ||||
−0.437046 | + | 0.899439i | \(0.643975\pi\) | |||||||
\(752\) | −3.16995 | −0.115596 | ||||||||
\(753\) | 0.554414 | 0.0202040 | ||||||||
\(754\) | −0.00676109 | −0.000246225 0 | ||||||||
\(755\) | 61.4365 | 2.23590 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.9884 | −0.544761 | −0.272380 | − | 0.962190i | \(-0.587811\pi\) | ||||
−0.272380 | + | 0.962190i | \(0.587811\pi\) | |||||||
\(758\) | −27.0545 | −0.982664 | ||||||||
\(759\) | 2.60707 | 0.0946305 | ||||||||
\(760\) | −3.27156 | −0.118672 | ||||||||
\(761\) | 16.3237 | 0.591733 | 0.295867 | − | 0.955229i | \(-0.404392\pi\) | ||||
0.295867 | + | 0.955229i | \(0.404392\pi\) | |||||||
\(762\) | 0.399881 | 0.0144862 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 23.6031 | 0.853929 | ||||||||
\(765\) | 0.627669 | 0.0226934 | ||||||||
\(766\) | −9.98846 | −0.360898 | ||||||||
\(767\) | −0.0305208 | −0.00110204 | ||||||||
\(768\) | 0.539617 | 0.0194718 | ||||||||
\(769\) | 46.1029 | 1.66251 | 0.831256 | − | 0.555890i | \(-0.187622\pi\) | ||||
0.831256 | + | 0.555890i | \(0.187622\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.00378 | −0.108178 | ||||||||
\(772\) | −8.41165 | −0.302742 | ||||||||
\(773\) | −40.2629 | −1.44816 | −0.724078 | − | 0.689718i | \(-0.757734\pi\) | ||||
−0.724078 | + | 0.689718i | \(0.757734\pi\) | |||||||
\(774\) | 5.00997 | 0.180079 | ||||||||
\(775\) | 47.1725 | 1.69449 | ||||||||
\(776\) | −4.17000 | −0.149694 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.1899 | −1.11821 | ||||||||
\(779\) | 0.966028 | 0.0346115 | ||||||||
\(780\) | −0.0176199 | −0.000630895 0 | ||||||||
\(781\) | −10.8773 | −0.389220 | ||||||||
\(782\) | −0.110643 | −0.00395660 | ||||||||
\(783\) | −2.16020 | −0.0771994 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55.5845 | 1.98390 | ||||||||
\(786\) | 3.48098 | 0.124162 | ||||||||
\(787\) | −14.1353 | −0.503868 | −0.251934 | − | 0.967744i | \(-0.581067\pi\) | ||||
−0.251934 | + | 0.967744i | \(0.581067\pi\) | |||||||
\(788\) | −8.93787 | −0.318399 | ||||||||
\(789\) | −5.66814 | −0.201791 | ||||||||
\(790\) | 46.3814 | 1.65018 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.09294 | 0.287570 | ||||||||
\(793\) | −0.0836526 | −0.00297059 | ||||||||
\(794\) | −19.7434 | −0.700666 | ||||||||
\(795\) | 12.0969 | 0.429033 | ||||||||
\(796\) | 20.9193 | 0.741466 | ||||||||
\(797\) | −20.7201 | −0.733943 | −0.366972 | − | 0.930232i | \(-0.619605\pi\) | ||||
−0.366972 | + | 0.930232i | \(0.619605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.216890 | −0.00767301 | ||||||||
\(800\) | −6.46911 | −0.228718 | ||||||||
\(801\) | 25.1539 | 0.888769 | ||||||||
\(802\) | 11.2580 | 0.397533 | ||||||||
\(803\) | −10.5212 | −0.371283 | ||||||||
\(804\) | 4.61647 | 0.162810 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.0703069 | −0.00247646 | ||||||||
\(807\) | −15.0499 | −0.529783 | ||||||||
\(808\) | 5.41052 | 0.190341 | ||||||||
\(809\) | 33.2683 | 1.16965 | 0.584825 | − | 0.811159i | \(-0.301163\pi\) | ||||
0.584825 | + | 0.811159i | \(0.301163\pi\) | |||||||
\(810\) | 21.8914 | 0.769186 | ||||||||
\(811\) | 41.8531 | 1.46966 | 0.734831 | − | 0.678250i | \(-0.237261\pi\) | ||||
0.734831 | + | 0.678250i | \(0.237261\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.41124 | 0.224852 | ||||||||
\(814\) | −14.6065 | −0.511958 | ||||||||
\(815\) | 5.36420 | 0.187900 | ||||||||
\(816\) | 0.0369209 | 0.00129249 | ||||||||
\(817\) | −1.78667 | −0.0625078 | ||||||||
\(818\) | −7.27124 | −0.254233 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.38661 | 0.118265 | ||||||||
\(821\) | 16.8738 | 0.588900 | 0.294450 | − | 0.955667i | \(-0.404864\pi\) | ||||
0.294450 | + | 0.955667i | \(0.404864\pi\) | |||||||
\(822\) | 8.47464 | 0.295587 | ||||||||
\(823\) | −46.6603 | −1.62648 | −0.813238 | − | 0.581931i | \(-0.802298\pi\) | ||||
−0.813238 | + | 0.581931i | \(0.802298\pi\) | |||||||
\(824\) | 13.4966 | 0.470176 | ||||||||
\(825\) | 10.4294 | 0.363104 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.7692 | 1.41768 | 0.708841 | − | 0.705368i | \(-0.249218\pi\) | ||||
0.708841 | + | 0.705368i | \(0.249218\pi\) | |||||||
\(828\) | −4.38044 | −0.152231 | ||||||||
\(829\) | −20.5803 | −0.714783 | −0.357392 | − | 0.933955i | \(-0.616334\pi\) | ||||
−0.357392 | + | 0.933955i | \(0.616334\pi\) | |||||||
\(830\) | 22.4385 | 0.778853 | ||||||||
\(831\) | −3.17898 | −0.110278 | ||||||||
\(832\) | 0.00964170 | 0.000334266 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.85467 | 0.133476 | ||||||||
\(835\) | 27.4306 | 0.949275 | ||||||||
\(836\) | −2.88614 | −0.0998192 | ||||||||
\(837\) | −22.4634 | −0.776449 | ||||||||
\(838\) | 24.3697 | 0.841836 | ||||||||
\(839\) | 51.2811 | 1.77042 | 0.885210 | − | 0.465192i | \(-0.154015\pi\) | ||||
0.885210 | + | 0.465192i | \(0.154015\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5083 | −0.983044 | ||||||||
\(842\) | 11.6797 | 0.402511 | ||||||||
\(843\) | −6.64606 | −0.228903 | ||||||||
\(844\) | 10.5708 | 0.363861 | ||||||||
\(845\) | 44.0256 | 1.51453 | ||||||||
\(846\) | −8.58681 | −0.295221 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.61947 | −0.227313 | ||||||||
\(849\) | −4.11971 | −0.141388 | ||||||||
\(850\) | −0.442620 | −0.0151818 | ||||||||
\(851\) | 7.90602 | 0.271015 | ||||||||
\(852\) | −1.96462 | −0.0673069 | ||||||||
\(853\) | 41.1032 | 1.40735 | 0.703674 | − | 0.710523i | \(-0.251542\pi\) | ||||
0.703674 | + | 0.710523i | \(0.251542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.86204 | −0.303075 | ||||||||
\(856\) | −9.54211 | −0.326143 | ||||||||
\(857\) | −26.8788 | −0.918164 | −0.459082 | − | 0.888394i | \(-0.651822\pi\) | ||||
−0.459082 | + | 0.888394i | \(0.651822\pi\) | |||||||
\(858\) | −0.0155442 | −0.000530669 0 | ||||||||
\(859\) | 40.3148 | 1.37552 | 0.687761 | − | 0.725937i | \(-0.258594\pi\) | ||||
0.687761 | + | 0.725937i | \(0.258594\pi\) | |||||||
\(860\) | −6.26355 | −0.213585 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.2910 | −0.486754 | ||||||||
\(863\) | −49.3950 | −1.68143 | −0.840713 | − | 0.541480i | \(-0.817864\pi\) | ||||
−0.840713 | + | 0.541480i | \(0.817864\pi\) | |||||||
\(864\) | 3.08057 | 0.104803 | ||||||||
\(865\) | 51.3330 | 1.74537 | ||||||||
\(866\) | 4.06751 | 0.138220 | ||||||||
\(867\) | −9.17097 | −0.311462 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.9172 | 1.38802 | ||||||||
\(870\) | 1.28149 | 0.0434464 | ||||||||
\(871\) | 0.0824857 | 0.00279492 | ||||||||
\(872\) | 2.65081 | 0.0897679 | ||||||||
\(873\) | −11.2957 | −0.382303 | ||||||||
\(874\) | 1.56217 | 0.0528412 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.90030 | −0.0642051 | ||||||||
\(877\) | −26.3155 | −0.888612 | −0.444306 | − | 0.895875i | \(-0.646550\pi\) | ||||
−0.444306 | + | 0.895875i | \(0.646550\pi\) | |||||||
\(878\) | 17.6381 | 0.595257 | ||||||||
\(879\) | −14.2705 | −0.481332 | ||||||||
\(880\) | −10.1179 | −0.341076 | ||||||||
\(881\) | 2.76108 | 0.0930231 | 0.0465116 | − | 0.998918i | \(-0.485190\pi\) | ||||
0.0465116 | + | 0.998918i | \(0.485190\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.8887 | −1.27506 | −0.637529 | − | 0.770427i | \(-0.720043\pi\) | ||||
−0.637529 | + | 0.770427i | \(0.720043\pi\) | |||||||
\(884\) | 0.000659691 0 | 2.21878e−5 0 | ||||||||
\(885\) | 5.78486 | 0.194456 | ||||||||
\(886\) | −2.09016 | −0.0702203 | ||||||||
\(887\) | −27.4974 | −0.923273 | −0.461637 | − | 0.887069i | \(-0.652738\pi\) | ||||
−0.461637 | + | 0.887069i | \(0.652738\pi\) | |||||||
\(888\) | −2.63818 | −0.0885316 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −31.4479 | −1.05414 | ||||||||
\(891\) | 19.3124 | 0.646990 | ||||||||
\(892\) | −15.5890 | −0.521959 | ||||||||
\(893\) | 3.06226 | 0.102475 | ||||||||
\(894\) | 5.99451 | 0.200486 | ||||||||
\(895\) | −57.6562 | −1.92723 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.00841353 | 0.000280920 0 | ||||||||
\(898\) | 11.1404 | 0.371758 | ||||||||
\(899\) | 5.11337 | 0.170540 | ||||||||
\(900\) | −17.5236 | −0.584121 | ||||||||
\(901\) | −0.452908 | −0.0150885 | ||||||||
\(902\) | 2.98763 | 0.0994774 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.77537 | 0.258605 | ||||||||
\(905\) | −38.0219 | −1.26389 | ||||||||
\(906\) | 9.78920 | 0.325224 | ||||||||
\(907\) | −41.3773 | −1.37391 | −0.686956 | − | 0.726699i | \(-0.741053\pi\) | ||||
−0.686956 | + | 0.726699i | \(0.741053\pi\) | |||||||
\(908\) | 2.96125 | 0.0982726 | ||||||||
\(909\) | 14.6561 | 0.486112 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.8447 | 1.65143 | 0.825715 | − | 0.564087i | \(-0.190772\pi\) | ||||
0.825715 | + | 0.564087i | \(0.190772\pi\) | |||||||
\(912\) | −0.521285 | −0.0172615 | ||||||||
\(913\) | 19.7951 | 0.655121 | ||||||||
\(914\) | 26.4289 | 0.874192 | ||||||||
\(915\) | 15.8554 | 0.524162 | ||||||||
\(916\) | −24.3188 | −0.803515 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.210775 | 0.00695660 | ||||||||
\(919\) | 4.40801 | 0.145407 | 0.0727035 | − | 0.997354i | \(-0.476837\pi\) | ||||
0.0727035 | + | 0.997354i | \(0.476837\pi\) | |||||||
\(920\) | 5.47651 | 0.180555 | ||||||||
\(921\) | −6.00820 | −0.197977 | ||||||||
\(922\) | 2.37152 | 0.0781017 | ||||||||
\(923\) | −0.0351033 | −0.00115544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31.6274 | 1.03990 | ||||||||
\(926\) | −19.8802 | −0.653304 | ||||||||
\(927\) | 36.5597 | 1.20078 | ||||||||
\(928\) | −0.701234 | −0.0230191 | ||||||||
\(929\) | 16.9983 | 0.557696 | 0.278848 | − | 0.960335i | \(-0.410047\pi\) | ||||
0.278848 | + | 0.960335i | \(0.410047\pi\) | |||||||
\(930\) | 13.3258 | 0.436972 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.72516 | −0.0565096 | ||||||||
\(933\) | 2.97989 | 0.0975573 | ||||||||
\(934\) | 20.1463 | 0.659209 | ||||||||
\(935\) | −0.692276 | −0.0226398 | ||||||||
\(936\) | 0.0261176 | 0.000853680 0 | ||||||||
\(937\) | 13.3600 | 0.436452 | 0.218226 | − | 0.975898i | \(-0.429973\pi\) | ||||
0.218226 | + | 0.975898i | \(0.429973\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.01912 | −0.196427 | ||||||||
\(940\) | 10.7354 | 0.350150 | ||||||||
\(941\) | 37.8940 | 1.23531 | 0.617654 | − | 0.786450i | \(-0.288083\pi\) | ||||
0.617654 | + | 0.786450i | \(0.288083\pi\) | |||||||
\(942\) | 8.85676 | 0.288569 | ||||||||
\(943\) | −1.61711 | −0.0526603 | ||||||||
\(944\) | −3.16550 | −0.103028 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.52565 | −0.179654 | ||||||||
\(947\) | 33.5264 | 1.08946 | 0.544731 | − | 0.838611i | \(-0.316632\pi\) | ||||
0.544731 | + | 0.838611i | \(0.316632\pi\) | |||||||
\(948\) | 7.39034 | 0.240027 | ||||||||
\(949\) | −0.0339539 | −0.00110219 | ||||||||
\(950\) | 6.24934 | 0.202756 | ||||||||
\(951\) | 1.71429 | 0.0555896 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.9263 | 1.19616 | 0.598079 | − | 0.801437i | \(-0.295931\pi\) | ||||
0.598079 | + | 0.801437i | \(0.295931\pi\) | |||||||
\(954\) | −17.9309 | −0.580534 | ||||||||
\(955\) | −79.9344 | −2.58662 | ||||||||
\(956\) | −9.61482 | −0.310965 | ||||||||
\(957\) | 1.13052 | 0.0365444 | ||||||||
\(958\) | 42.0146 | 1.35743 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.82747 | −0.0589814 | ||||||||
\(961\) | 22.1726 | 0.715247 | ||||||||
\(962\) | −0.0471382 | −0.00151980 | ||||||||
\(963\) | −25.8478 | −0.832933 | ||||||||
\(964\) | 14.4222 | 0.464507 | ||||||||
\(965\) | 28.4870 | 0.917028 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.3356 | 1.87595 | 0.937973 | − | 0.346708i | \(-0.112700\pi\) | ||||
0.937973 | + | 0.346708i | \(0.112700\pi\) | |||||||
\(968\) | 2.07404 | 0.0666622 | ||||||||
\(969\) | −0.0356666 | −0.00114578 | ||||||||
\(970\) | 14.1221 | 0.453435 | ||||||||
\(971\) | −26.4840 | −0.849911 | −0.424955 | − | 0.905214i | \(-0.639710\pi\) | ||||
−0.424955 | + | 0.905214i | \(0.639710\pi\) | |||||||
\(972\) | 12.7299 | 0.408311 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −11.7506 | −0.376514 | ||||||||
\(975\) | 0.0336577 | 0.00107791 | ||||||||
\(976\) | −8.67612 | −0.277716 | ||||||||
\(977\) | 24.6468 | 0.788522 | 0.394261 | − | 0.918999i | \(-0.371001\pi\) | ||||
0.394261 | + | 0.918999i | \(0.371001\pi\) | |||||||
\(978\) | 0.854724 | 0.0273311 | ||||||||
\(979\) | −27.7430 | −0.886671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.18056 | 0.229258 | ||||||||
\(982\) | 19.2530 | 0.614388 | ||||||||
\(983\) | 44.0018 | 1.40344 | 0.701720 | − | 0.712452i | \(-0.252416\pi\) | ||||
0.701720 | + | 0.712452i | \(0.252416\pi\) | |||||||
\(984\) | 0.539617 | 0.0172024 | ||||||||
\(985\) | 30.2691 | 0.964453 | ||||||||
\(986\) | −0.0479788 | −0.00152796 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.00931416 | −0.000296323 0 | ||||||||
\(989\) | 2.99085 | 0.0951035 | ||||||||
\(990\) | −27.4076 | −0.871072 | ||||||||
\(991\) | −33.7218 | −1.07121 | −0.535604 | − | 0.844470i | \(-0.679916\pi\) | ||||
−0.535604 | + | 0.844470i | \(0.679916\pi\) | |||||||
\(992\) | −7.29196 | −0.231520 | ||||||||
\(993\) | 7.20895 | 0.228769 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −70.8456 | −2.24596 | ||||||||
\(996\) | 3.57532 | 0.113288 | ||||||||
\(997\) | 34.3401 | 1.08756 | 0.543781 | − | 0.839227i | \(-0.316992\pi\) | ||||
0.543781 | + | 0.839227i | \(0.316992\pi\) | |||||||
\(998\) | −17.7083 | −0.560545 | ||||||||
\(999\) | −15.0609 | −0.476506 |
(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 | 4018.2.a.br.1.7 | ✓ | 10 | |
7.6 | odd | 2 | 4018.2.a.bs.1.4 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4018.2.a.br.1.7 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4018.2.a.bs.1.4 | yes | 10 | 7.6 | odd | 2 |