Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} - 2790 x^{3} - 352 x^{2} + 1768 x + 768 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.38143\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.60911 | −0.719616 | −0.359808 | − | 0.933026i | \(-0.617158\pi\) | ||||
−0.359808 | + | 0.933026i | \(0.617158\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.84255 | 1.07438 | 0.537192 | − | 0.843460i | \(-0.319485\pi\) | ||||
0.537192 | + | 0.843460i | \(0.319485\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.60911 | 0.508846 | ||||||||
\(11\) | −4.57260 | −1.37869 | −0.689345 | − | 0.724433i | \(-0.742102\pi\) | ||||
−0.689345 | + | 0.724433i | \(0.742102\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.84255 | −0.759704 | ||||||||
\(15\) | −1.60911 | −0.415471 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.96515 | 1.68930 | 0.844648 | − | 0.535322i | \(-0.179810\pi\) | ||||
0.844648 | + | 0.535322i | \(0.179810\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.10639 | 1.17149 | 0.585743 | − | 0.810497i | \(-0.300803\pi\) | ||||
0.585743 | + | 0.810497i | \(0.300803\pi\) | |||||||
\(20\) | −1.60911 | −0.359808 | ||||||||
\(21\) | 2.84255 | 0.620295 | ||||||||
\(22\) | 4.57260 | 0.974881 | ||||||||
\(23\) | −7.39805 | −1.54260 | −0.771300 | − | 0.636471i | \(-0.780393\pi\) | ||||
−0.771300 | + | 0.636471i | \(0.780393\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.41076 | −0.482152 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.84255 | 0.537192 | ||||||||
\(29\) | −7.17077 | −1.33158 | −0.665789 | − | 0.746140i | \(-0.731905\pi\) | ||||
−0.665789 | + | 0.746140i | \(0.731905\pi\) | |||||||
\(30\) | 1.60911 | 0.293782 | ||||||||
\(31\) | 4.44063 | 0.797560 | 0.398780 | − | 0.917047i | \(-0.369434\pi\) | ||||
0.398780 | + | 0.917047i | \(0.369434\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.57260 | −0.795987 | ||||||||
\(34\) | −6.96515 | −1.19451 | ||||||||
\(35\) | −4.57398 | −0.773144 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.817018 | −0.134317 | −0.0671584 | − | 0.997742i | \(-0.521393\pi\) | ||||
−0.0671584 | + | 0.997742i | \(0.521393\pi\) | |||||||
\(38\) | −5.10639 | −0.828366 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 1.60911 | 0.254423 | ||||||||
\(41\) | −11.4476 | −1.78782 | −0.893911 | − | 0.448244i | \(-0.852050\pi\) | ||||
−0.893911 | + | 0.448244i | \(0.852050\pi\) | |||||||
\(42\) | −2.84255 | −0.438615 | ||||||||
\(43\) | 4.69111 | 0.715387 | 0.357693 | − | 0.933839i | \(-0.383563\pi\) | ||||
0.357693 | + | 0.933839i | \(0.383563\pi\) | |||||||
\(44\) | −4.57260 | −0.689345 | ||||||||
\(45\) | −1.60911 | −0.239872 | ||||||||
\(46\) | 7.39805 | 1.09078 | ||||||||
\(47\) | −6.40573 | −0.934372 | −0.467186 | − | 0.884159i | \(-0.654732\pi\) | ||||
−0.467186 | + | 0.884159i | \(0.654732\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.08009 | 0.154299 | ||||||||
\(50\) | 2.41076 | 0.340933 | ||||||||
\(51\) | 6.96515 | 0.975315 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −8.74627 | −1.20139 | −0.600696 | − | 0.799477i | \(-0.705110\pi\) | ||||
−0.600696 | + | 0.799477i | \(0.705110\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 7.35782 | 0.992128 | ||||||||
\(56\) | −2.84255 | −0.379852 | ||||||||
\(57\) | 5.10639 | 0.676358 | ||||||||
\(58\) | 7.17077 | 0.941568 | ||||||||
\(59\) | 0.862231 | 0.112253 | 0.0561265 | − | 0.998424i | \(-0.482125\pi\) | ||||
0.0561265 | + | 0.998424i | \(0.482125\pi\) | |||||||
\(60\) | −1.60911 | −0.207735 | ||||||||
\(61\) | −5.94901 | −0.761693 | −0.380847 | − | 0.924638i | \(-0.624367\pi\) | ||||
−0.380847 | + | 0.924638i | \(0.624367\pi\) | |||||||
\(62\) | −4.44063 | −0.563960 | ||||||||
\(63\) | 2.84255 | 0.358128 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.60911 | −0.199586 | ||||||||
\(66\) | 4.57260 | 0.562848 | ||||||||
\(67\) | −5.12966 | −0.626687 | −0.313344 | − | 0.949640i | \(-0.601449\pi\) | ||||
−0.313344 | + | 0.949640i | \(0.601449\pi\) | |||||||
\(68\) | 6.96515 | 0.844648 | ||||||||
\(69\) | −7.39805 | −0.890621 | ||||||||
\(70\) | 4.57398 | 0.546695 | ||||||||
\(71\) | 5.91999 | 0.702574 | 0.351287 | − | 0.936268i | \(-0.385744\pi\) | ||||
0.351287 | + | 0.936268i | \(0.385744\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.48512 | −0.173821 | −0.0869103 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869103 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(74\) | 0.817018 | 0.0949764 | ||||||||
\(75\) | −2.41076 | −0.278371 | ||||||||
\(76\) | 5.10639 | 0.585743 | ||||||||
\(77\) | −12.9978 | −1.48124 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −16.1372 | −1.81557 | −0.907786 | − | 0.419433i | \(-0.862229\pi\) | ||||
−0.907786 | + | 0.419433i | \(0.862229\pi\) | |||||||
\(80\) | −1.60911 | −0.179904 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.4476 | 1.26418 | ||||||||
\(83\) | 7.18794 | 0.788979 | 0.394489 | − | 0.918900i | \(-0.370921\pi\) | ||||
0.394489 | + | 0.918900i | \(0.370921\pi\) | |||||||
\(84\) | 2.84255 | 0.310148 | ||||||||
\(85\) | −11.2077 | −1.21564 | ||||||||
\(86\) | −4.69111 | −0.505855 | ||||||||
\(87\) | −7.17077 | −0.768787 | ||||||||
\(88\) | 4.57260 | 0.487441 | ||||||||
\(89\) | 13.9273 | 1.47629 | 0.738143 | − | 0.674645i | \(-0.235703\pi\) | ||||
0.738143 | + | 0.674645i | \(0.235703\pi\) | |||||||
\(90\) | 1.60911 | 0.169615 | ||||||||
\(91\) | 2.84255 | 0.297980 | ||||||||
\(92\) | −7.39805 | −0.771300 | ||||||||
\(93\) | 4.44063 | 0.460472 | ||||||||
\(94\) | 6.40573 | 0.660701 | ||||||||
\(95\) | −8.21675 | −0.843021 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.58490 | −0.262457 | −0.131228 | − | 0.991352i | \(-0.541892\pi\) | ||||
−0.131228 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(98\) | −1.08009 | −0.109106 | ||||||||
\(99\) | −4.57260 | −0.459564 | ||||||||
\(100\) | −2.41076 | −0.241076 | ||||||||
\(101\) | 2.68909 | 0.267574 | 0.133787 | − | 0.991010i | \(-0.457286\pi\) | ||||
0.133787 | + | 0.991010i | \(0.457286\pi\) | |||||||
\(102\) | −6.96515 | −0.689652 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −4.57398 | −0.446375 | ||||||||
\(106\) | 8.74627 | 0.849513 | ||||||||
\(107\) | 15.4507 | 1.49367 | 0.746837 | − | 0.665008i | \(-0.231572\pi\) | ||||
0.746837 | + | 0.665008i | \(0.231572\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.02806 | −0.290036 | −0.145018 | − | 0.989429i | \(-0.546324\pi\) | ||||
−0.145018 | + | 0.989429i | \(0.546324\pi\) | |||||||
\(110\) | −7.35782 | −0.701541 | ||||||||
\(111\) | −0.817018 | −0.0775479 | ||||||||
\(112\) | 2.84255 | 0.268596 | ||||||||
\(113\) | −4.47739 | −0.421198 | −0.210599 | − | 0.977573i | \(-0.567541\pi\) | ||||
−0.210599 | + | 0.977573i | \(0.567541\pi\) | |||||||
\(114\) | −5.10639 | −0.478257 | ||||||||
\(115\) | 11.9043 | 1.11008 | ||||||||
\(116\) | −7.17077 | −0.665789 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −0.862231 | −0.0793748 | ||||||||
\(119\) | 19.7988 | 1.81495 | ||||||||
\(120\) | 1.60911 | 0.146891 | ||||||||
\(121\) | 9.90866 | 0.900788 | ||||||||
\(122\) | 5.94901 | 0.538598 | ||||||||
\(123\) | −11.4476 | −1.03220 | ||||||||
\(124\) | 4.44063 | 0.398780 | ||||||||
\(125\) | 11.9247 | 1.06658 | ||||||||
\(126\) | −2.84255 | −0.253235 | ||||||||
\(127\) | 1.94343 | 0.172452 | 0.0862260 | − | 0.996276i | \(-0.472519\pi\) | ||||
0.0862260 | + | 0.996276i | \(0.472519\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.69111 | 0.413029 | ||||||||
\(130\) | 1.60911 | 0.141128 | ||||||||
\(131\) | 5.44624 | 0.475841 | 0.237920 | − | 0.971285i | \(-0.423534\pi\) | ||||
0.237920 | + | 0.971285i | \(0.423534\pi\) | |||||||
\(132\) | −4.57260 | −0.397994 | ||||||||
\(133\) | 14.5152 | 1.25862 | ||||||||
\(134\) | 5.12966 | 0.443135 | ||||||||
\(135\) | −1.60911 | −0.138490 | ||||||||
\(136\) | −6.96515 | −0.597256 | ||||||||
\(137\) | −5.97882 | −0.510805 | −0.255403 | − | 0.966835i | \(-0.582208\pi\) | ||||
−0.255403 | + | 0.966835i | \(0.582208\pi\) | |||||||
\(138\) | 7.39805 | 0.629764 | ||||||||
\(139\) | 0.970755 | 0.0823384 | 0.0411692 | − | 0.999152i | \(-0.486892\pi\) | ||||
0.0411692 | + | 0.999152i | \(0.486892\pi\) | |||||||
\(140\) | −4.57398 | −0.386572 | ||||||||
\(141\) | −6.40573 | −0.539460 | ||||||||
\(142\) | −5.91999 | −0.496795 | ||||||||
\(143\) | −4.57260 | −0.382380 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 11.5386 | 0.958225 | ||||||||
\(146\) | 1.48512 | 0.122910 | ||||||||
\(147\) | 1.08009 | 0.0890846 | ||||||||
\(148\) | −0.817018 | −0.0671584 | ||||||||
\(149\) | 3.63472 | 0.297768 | 0.148884 | − | 0.988855i | \(-0.452432\pi\) | ||||
0.148884 | + | 0.988855i | \(0.452432\pi\) | |||||||
\(150\) | 2.41076 | 0.196838 | ||||||||
\(151\) | −8.48578 | −0.690563 | −0.345281 | − | 0.938499i | \(-0.612217\pi\) | ||||
−0.345281 | + | 0.938499i | \(0.612217\pi\) | |||||||
\(152\) | −5.10639 | −0.414183 | ||||||||
\(153\) | 6.96515 | 0.563099 | ||||||||
\(154\) | 12.9978 | 1.04740 | ||||||||
\(155\) | −7.14546 | −0.573937 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 1.63370 | 0.130383 | 0.0651917 | − | 0.997873i | \(-0.479234\pi\) | ||||
0.0651917 | + | 0.997873i | \(0.479234\pi\) | |||||||
\(158\) | 16.1372 | 1.28380 | ||||||||
\(159\) | −8.74627 | −0.693624 | ||||||||
\(160\) | 1.60911 | 0.127211 | ||||||||
\(161\) | −21.0293 | −1.65734 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.6549 | −0.912881 | −0.456441 | − | 0.889754i | \(-0.650876\pi\) | ||||
−0.456441 | + | 0.889754i | \(0.650876\pi\) | |||||||
\(164\) | −11.4476 | −0.893911 | ||||||||
\(165\) | 7.35782 | 0.572806 | ||||||||
\(166\) | −7.18794 | −0.557892 | ||||||||
\(167\) | −10.1875 | −0.788333 | −0.394167 | − | 0.919039i | \(-0.628967\pi\) | ||||
−0.394167 | + | 0.919039i | \(0.628967\pi\) | |||||||
\(168\) | −2.84255 | −0.219308 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 11.2077 | 0.859591 | ||||||||
\(171\) | 5.10639 | 0.390495 | ||||||||
\(172\) | 4.69111 | 0.357693 | ||||||||
\(173\) | −4.35726 | −0.331276 | −0.165638 | − | 0.986187i | \(-0.552968\pi\) | ||||
−0.165638 | + | 0.986187i | \(0.552968\pi\) | |||||||
\(174\) | 7.17077 | 0.543614 | ||||||||
\(175\) | −6.85271 | −0.518016 | ||||||||
\(176\) | −4.57260 | −0.344673 | ||||||||
\(177\) | 0.862231 | 0.0648093 | ||||||||
\(178\) | −13.9273 | −1.04389 | ||||||||
\(179\) | 14.7457 | 1.10215 | 0.551074 | − | 0.834456i | \(-0.314218\pi\) | ||||
0.551074 | + | 0.834456i | \(0.314218\pi\) | |||||||
\(180\) | −1.60911 | −0.119936 | ||||||||
\(181\) | −20.1298 | −1.49624 | −0.748118 | − | 0.663566i | \(-0.769042\pi\) | ||||
−0.748118 | + | 0.663566i | \(0.769042\pi\) | |||||||
\(182\) | −2.84255 | −0.210704 | ||||||||
\(183\) | −5.94901 | −0.439764 | ||||||||
\(184\) | 7.39805 | 0.545392 | ||||||||
\(185\) | 1.31467 | 0.0966566 | ||||||||
\(186\) | −4.44063 | −0.325603 | ||||||||
\(187\) | −31.8488 | −2.32902 | ||||||||
\(188\) | −6.40573 | −0.467186 | ||||||||
\(189\) | 2.84255 | 0.206765 | ||||||||
\(190\) | 8.21675 | 0.596106 | ||||||||
\(191\) | −18.6504 | −1.34949 | −0.674747 | − | 0.738049i | \(-0.735747\pi\) | ||||
−0.674747 | + | 0.738049i | \(0.735747\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 3.50650 | 0.252403 | 0.126202 | − | 0.992005i | \(-0.459721\pi\) | ||||
0.126202 | + | 0.992005i | \(0.459721\pi\) | |||||||
\(194\) | 2.58490 | 0.185585 | ||||||||
\(195\) | −1.60911 | −0.115231 | ||||||||
\(196\) | 1.08009 | 0.0771496 | ||||||||
\(197\) | −2.08818 | −0.148776 | −0.0743882 | − | 0.997229i | \(-0.523700\pi\) | ||||
−0.0743882 | + | 0.997229i | \(0.523700\pi\) | |||||||
\(198\) | 4.57260 | 0.324960 | ||||||||
\(199\) | −4.31102 | −0.305600 | −0.152800 | − | 0.988257i | \(-0.548829\pi\) | ||||
−0.152800 | + | 0.988257i | \(0.548829\pi\) | |||||||
\(200\) | 2.41076 | 0.170467 | ||||||||
\(201\) | −5.12966 | −0.361818 | ||||||||
\(202\) | −2.68909 | −0.189204 | ||||||||
\(203\) | −20.3833 | −1.43062 | ||||||||
\(204\) | 6.96515 | 0.487658 | ||||||||
\(205\) | 18.4205 | 1.28655 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | −7.39805 | −0.514200 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −23.3495 | −1.61512 | ||||||||
\(210\) | 4.57398 | 0.315635 | ||||||||
\(211\) | −14.1685 | −0.975401 | −0.487701 | − | 0.873011i | \(-0.662164\pi\) | ||||
−0.487701 | + | 0.873011i | \(0.662164\pi\) | |||||||
\(212\) | −8.74627 | −0.600696 | ||||||||
\(213\) | 5.91999 | 0.405631 | ||||||||
\(214\) | −15.4507 | −1.05619 | ||||||||
\(215\) | −7.54851 | −0.514804 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 12.6227 | 0.856885 | ||||||||
\(218\) | 3.02806 | 0.205086 | ||||||||
\(219\) | −1.48512 | −0.100355 | ||||||||
\(220\) | 7.35782 | 0.496064 | ||||||||
\(221\) | 6.96515 | 0.468526 | ||||||||
\(222\) | 0.817018 | 0.0548346 | ||||||||
\(223\) | −6.11406 | −0.409428 | −0.204714 | − | 0.978822i | \(-0.565626\pi\) | ||||
−0.204714 | + | 0.978822i | \(0.565626\pi\) | |||||||
\(224\) | −2.84255 | −0.189926 | ||||||||
\(225\) | −2.41076 | −0.160717 | ||||||||
\(226\) | 4.47739 | 0.297832 | ||||||||
\(227\) | 11.5741 | 0.768202 | 0.384101 | − | 0.923291i | \(-0.374511\pi\) | ||||
0.384101 | + | 0.923291i | \(0.374511\pi\) | |||||||
\(228\) | 5.10639 | 0.338179 | ||||||||
\(229\) | −3.87756 | −0.256237 | −0.128118 | − | 0.991759i | \(-0.540894\pi\) | ||||
−0.128118 | + | 0.991759i | \(0.540894\pi\) | |||||||
\(230\) | −11.9043 | −0.784946 | ||||||||
\(231\) | −12.9978 | −0.855195 | ||||||||
\(232\) | 7.17077 | 0.470784 | ||||||||
\(233\) | −0.0308552 | −0.00202139 | −0.00101069 | − | 0.999999i | \(-0.500322\pi\) | ||||
−0.00101069 | + | 0.999999i | \(0.500322\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 10.3075 | 0.672389 | ||||||||
\(236\) | 0.862231 | 0.0561265 | ||||||||
\(237\) | −16.1372 | −1.04822 | ||||||||
\(238\) | −19.7988 | −1.28336 | ||||||||
\(239\) | 0.243671 | 0.0157618 | 0.00788089 | − | 0.999969i | \(-0.497491\pi\) | ||||
0.00788089 | + | 0.999969i | \(0.497491\pi\) | |||||||
\(240\) | −1.60911 | −0.103868 | ||||||||
\(241\) | 4.60369 | 0.296550 | 0.148275 | − | 0.988946i | \(-0.452628\pi\) | ||||
0.148275 | + | 0.988946i | \(0.452628\pi\) | |||||||
\(242\) | −9.90866 | −0.636953 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.94901 | −0.380847 | ||||||||
\(245\) | −1.73799 | −0.111036 | ||||||||
\(246\) | 11.4476 | 0.729875 | ||||||||
\(247\) | 5.10639 | 0.324912 | ||||||||
\(248\) | −4.44063 | −0.281980 | ||||||||
\(249\) | 7.18794 | 0.455517 | ||||||||
\(250\) | −11.9247 | −0.754187 | ||||||||
\(251\) | −18.3295 | −1.15695 | −0.578475 | − | 0.815700i | \(-0.696352\pi\) | ||||
−0.578475 | + | 0.815700i | \(0.696352\pi\) | |||||||
\(252\) | 2.84255 | 0.179064 | ||||||||
\(253\) | 33.8283 | 2.12677 | ||||||||
\(254\) | −1.94343 | −0.121942 | ||||||||
\(255\) | −11.2077 | −0.701853 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.93770 | −0.495140 | −0.247570 | − | 0.968870i | \(-0.579632\pi\) | ||||
−0.247570 | + | 0.968870i | \(0.579632\pi\) | |||||||
\(258\) | −4.69111 | −0.292055 | ||||||||
\(259\) | −2.32241 | −0.144308 | ||||||||
\(260\) | −1.60911 | −0.0997928 | ||||||||
\(261\) | −7.17077 | −0.443859 | ||||||||
\(262\) | −5.44624 | −0.336470 | ||||||||
\(263\) | 0.633427 | 0.0390588 | 0.0195294 | − | 0.999809i | \(-0.493783\pi\) | ||||
0.0195294 | + | 0.999809i | \(0.493783\pi\) | |||||||
\(264\) | 4.57260 | 0.281424 | ||||||||
\(265\) | 14.0737 | 0.864542 | ||||||||
\(266\) | −14.5152 | −0.889982 | ||||||||
\(267\) | 13.9273 | 0.852334 | ||||||||
\(268\) | −5.12966 | −0.313344 | ||||||||
\(269\) | 1.06226 | 0.0647672 | 0.0323836 | − | 0.999476i | \(-0.489690\pi\) | ||||
0.0323836 | + | 0.999476i | \(0.489690\pi\) | |||||||
\(270\) | 1.60911 | 0.0979274 | ||||||||
\(271\) | 25.8546 | 1.57056 | 0.785279 | − | 0.619142i | \(-0.212520\pi\) | ||||
0.785279 | + | 0.619142i | \(0.212520\pi\) | |||||||
\(272\) | 6.96515 | 0.422324 | ||||||||
\(273\) | 2.84255 | 0.172039 | ||||||||
\(274\) | 5.97882 | 0.361194 | ||||||||
\(275\) | 11.0234 | 0.664739 | ||||||||
\(276\) | −7.39805 | −0.445310 | ||||||||
\(277\) | −24.9779 | −1.50077 | −0.750387 | − | 0.660998i | \(-0.770133\pi\) | ||||
−0.750387 | + | 0.660998i | \(0.770133\pi\) | |||||||
\(278\) | −0.970755 | −0.0582220 | ||||||||
\(279\) | 4.44063 | 0.265853 | ||||||||
\(280\) | 4.57398 | 0.273348 | ||||||||
\(281\) | 6.09885 | 0.363827 | 0.181913 | − | 0.983315i | \(-0.441771\pi\) | ||||
0.181913 | + | 0.983315i | \(0.441771\pi\) | |||||||
\(282\) | 6.40573 | 0.381456 | ||||||||
\(283\) | 12.1903 | 0.724636 | 0.362318 | − | 0.932055i | \(-0.381985\pi\) | ||||
0.362318 | + | 0.932055i | \(0.381985\pi\) | |||||||
\(284\) | 5.91999 | 0.351287 | ||||||||
\(285\) | −8.21675 | −0.486718 | ||||||||
\(286\) | 4.57260 | 0.270383 | ||||||||
\(287\) | −32.5405 | −1.92081 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 31.5133 | 1.85372 | ||||||||
\(290\) | −11.5386 | −0.677568 | ||||||||
\(291\) | −2.58490 | −0.151530 | ||||||||
\(292\) | −1.48512 | −0.0869103 | ||||||||
\(293\) | −15.6402 | −0.913711 | −0.456855 | − | 0.889541i | \(-0.651024\pi\) | ||||
−0.456855 | + | 0.889541i | \(0.651024\pi\) | |||||||
\(294\) | −1.08009 | −0.0629923 | ||||||||
\(295\) | −1.38743 | −0.0807790 | ||||||||
\(296\) | 0.817018 | 0.0474882 | ||||||||
\(297\) | −4.57260 | −0.265329 | ||||||||
\(298\) | −3.63472 | −0.210554 | ||||||||
\(299\) | −7.39805 | −0.427840 | ||||||||
\(300\) | −2.41076 | −0.139185 | ||||||||
\(301\) | 13.3347 | 0.768600 | ||||||||
\(302\) | 8.48578 | 0.488302 | ||||||||
\(303\) | 2.68909 | 0.154484 | ||||||||
\(304\) | 5.10639 | 0.292872 | ||||||||
\(305\) | 9.57262 | 0.548127 | ||||||||
\(306\) | −6.96515 | −0.398171 | ||||||||
\(307\) | −3.23081 | −0.184392 | −0.0921960 | − | 0.995741i | \(-0.529389\pi\) | ||||
−0.0921960 | + | 0.995741i | \(0.529389\pi\) | |||||||
\(308\) | −12.9978 | −0.740621 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 7.14546 | 0.405835 | ||||||||
\(311\) | −21.8255 | −1.23761 | −0.618807 | − | 0.785543i | \(-0.712384\pi\) | ||||
−0.618807 | + | 0.785543i | \(0.712384\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −15.6711 | −0.885781 | −0.442890 | − | 0.896576i | \(-0.646047\pi\) | ||||
−0.442890 | + | 0.896576i | \(0.646047\pi\) | |||||||
\(314\) | −1.63370 | −0.0921950 | ||||||||
\(315\) | −4.57398 | −0.257715 | ||||||||
\(316\) | −16.1372 | −0.907786 | ||||||||
\(317\) | 4.78367 | 0.268677 | 0.134339 | − | 0.990935i | \(-0.457109\pi\) | ||||
0.134339 | + | 0.990935i | \(0.457109\pi\) | |||||||
\(318\) | 8.74627 | 0.490466 | ||||||||
\(319\) | 32.7890 | 1.83583 | ||||||||
\(320\) | −1.60911 | −0.0899520 | ||||||||
\(321\) | 15.4507 | 0.862373 | ||||||||
\(322\) | 21.0293 | 1.17192 | ||||||||
\(323\) | 35.5667 | 1.97899 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.41076 | −0.133725 | ||||||||
\(326\) | 11.6549 | 0.645505 | ||||||||
\(327\) | −3.02806 | −0.167452 | ||||||||
\(328\) | 11.4476 | 0.632091 | ||||||||
\(329\) | −18.2086 | −1.00387 | ||||||||
\(330\) | −7.35782 | −0.405035 | ||||||||
\(331\) | −5.01013 | −0.275382 | −0.137691 | − | 0.990475i | \(-0.543968\pi\) | ||||
−0.137691 | + | 0.990475i | \(0.543968\pi\) | |||||||
\(332\) | 7.18794 | 0.394489 | ||||||||
\(333\) | −0.817018 | −0.0447723 | ||||||||
\(334\) | 10.1875 | 0.557436 | ||||||||
\(335\) | 8.25419 | 0.450974 | ||||||||
\(336\) | 2.84255 | 0.155074 | ||||||||
\(337\) | −11.2909 | −0.615055 | −0.307528 | − | 0.951539i | \(-0.599502\pi\) | ||||
−0.307528 | + | 0.951539i | \(0.599502\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −4.47739 | −0.243179 | ||||||||
\(340\) | −11.2077 | −0.607822 | ||||||||
\(341\) | −20.3052 | −1.09959 | ||||||||
\(342\) | −5.10639 | −0.276122 | ||||||||
\(343\) | −16.8276 | −0.908607 | ||||||||
\(344\) | −4.69111 | −0.252927 | ||||||||
\(345\) | 11.9043 | 0.640905 | ||||||||
\(346\) | 4.35726 | 0.234247 | ||||||||
\(347\) | 0.556221 | 0.0298595 | 0.0149297 | − | 0.999889i | \(-0.495248\pi\) | ||||
0.0149297 | + | 0.999889i | \(0.495248\pi\) | |||||||
\(348\) | −7.17077 | −0.384393 | ||||||||
\(349\) | 20.7543 | 1.11095 | 0.555475 | − | 0.831533i | \(-0.312536\pi\) | ||||
0.555475 | + | 0.831533i | \(0.312536\pi\) | |||||||
\(350\) | 6.85271 | 0.366293 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 4.57260 | 0.243720 | ||||||||
\(353\) | −16.4735 | −0.876795 | −0.438398 | − | 0.898781i | \(-0.644454\pi\) | ||||
−0.438398 | + | 0.898781i | \(0.644454\pi\) | |||||||
\(354\) | −0.862231 | −0.0458271 | ||||||||
\(355\) | −9.52592 | −0.505583 | ||||||||
\(356\) | 13.9273 | 0.738143 | ||||||||
\(357\) | 19.7988 | 1.04786 | ||||||||
\(358\) | −14.7457 | −0.779337 | ||||||||
\(359\) | 27.2326 | 1.43728 | 0.718640 | − | 0.695382i | \(-0.244765\pi\) | ||||
0.718640 | + | 0.695382i | \(0.244765\pi\) | |||||||
\(360\) | 1.60911 | 0.0848076 | ||||||||
\(361\) | 7.07521 | 0.372380 | ||||||||
\(362\) | 20.1298 | 1.05800 | ||||||||
\(363\) | 9.90866 | 0.520070 | ||||||||
\(364\) | 2.84255 | 0.148990 | ||||||||
\(365\) | 2.38973 | 0.125084 | ||||||||
\(366\) | 5.94901 | 0.310960 | ||||||||
\(367\) | −23.2016 | −1.21111 | −0.605556 | − | 0.795803i | \(-0.707049\pi\) | ||||
−0.605556 | + | 0.795803i | \(0.707049\pi\) | |||||||
\(368\) | −7.39805 | −0.385650 | ||||||||
\(369\) | −11.4476 | −0.595941 | ||||||||
\(370\) | −1.31467 | −0.0683465 | ||||||||
\(371\) | −24.8617 | −1.29076 | ||||||||
\(372\) | 4.44063 | 0.230236 | ||||||||
\(373\) | 8.85675 | 0.458585 | 0.229293 | − | 0.973358i | \(-0.426359\pi\) | ||||
0.229293 | + | 0.973358i | \(0.426359\pi\) | |||||||
\(374\) | 31.8488 | 1.64686 | ||||||||
\(375\) | 11.9247 | 0.615791 | ||||||||
\(376\) | 6.40573 | 0.330350 | ||||||||
\(377\) | −7.17077 | −0.369313 | ||||||||
\(378\) | −2.84255 | −0.146205 | ||||||||
\(379\) | −16.6386 | −0.854668 | −0.427334 | − | 0.904094i | \(-0.640547\pi\) | ||||
−0.427334 | + | 0.904094i | \(0.640547\pi\) | |||||||
\(380\) | −8.21675 | −0.421510 | ||||||||
\(381\) | 1.94343 | 0.0995652 | ||||||||
\(382\) | 18.6504 | 0.954236 | ||||||||
\(383\) | −11.0662 | −0.565459 | −0.282729 | − | 0.959200i | \(-0.591240\pi\) | ||||
−0.282729 | + | 0.959200i | \(0.591240\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 20.9150 | 1.06593 | ||||||||
\(386\) | −3.50650 | −0.178476 | ||||||||
\(387\) | 4.69111 | 0.238462 | ||||||||
\(388\) | −2.58490 | −0.131228 | ||||||||
\(389\) | −7.44643 | −0.377549 | −0.188775 | − | 0.982020i | \(-0.560452\pi\) | ||||
−0.188775 | + | 0.982020i | \(0.560452\pi\) | |||||||
\(390\) | 1.60911 | 0.0814805 | ||||||||
\(391\) | −51.5285 | −2.60591 | ||||||||
\(392\) | −1.08009 | −0.0545530 | ||||||||
\(393\) | 5.44624 | 0.274727 | ||||||||
\(394\) | 2.08818 | 0.105201 | ||||||||
\(395\) | 25.9665 | 1.30652 | ||||||||
\(396\) | −4.57260 | −0.229782 | ||||||||
\(397\) | −8.13122 | −0.408094 | −0.204047 | − | 0.978961i | \(-0.565410\pi\) | ||||
−0.204047 | + | 0.978961i | \(0.565410\pi\) | |||||||
\(398\) | 4.31102 | 0.216092 | ||||||||
\(399\) | 14.5152 | 0.726667 | ||||||||
\(400\) | −2.41076 | −0.120538 | ||||||||
\(401\) | −30.5947 | −1.52782 | −0.763912 | − | 0.645320i | \(-0.776724\pi\) | ||||
−0.763912 | + | 0.645320i | \(0.776724\pi\) | |||||||
\(402\) | 5.12966 | 0.255844 | ||||||||
\(403\) | 4.44063 | 0.221203 | ||||||||
\(404\) | 2.68909 | 0.133787 | ||||||||
\(405\) | −1.60911 | −0.0799574 | ||||||||
\(406\) | 20.3833 | 1.01160 | ||||||||
\(407\) | 3.73589 | 0.185181 | ||||||||
\(408\) | −6.96515 | −0.344826 | ||||||||
\(409\) | 15.2968 | 0.756376 | 0.378188 | − | 0.925729i | \(-0.376547\pi\) | ||||
0.378188 | + | 0.925729i | \(0.376547\pi\) | |||||||
\(410\) | −18.4205 | −0.909726 | ||||||||
\(411\) | −5.97882 | −0.294913 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 2.45094 | 0.120603 | ||||||||
\(414\) | 7.39805 | 0.363594 | ||||||||
\(415\) | −11.5662 | −0.567762 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 0.970755 | 0.0475381 | ||||||||
\(418\) | 23.3495 | 1.14206 | ||||||||
\(419\) | −18.8495 | −0.920857 | −0.460428 | − | 0.887697i | \(-0.652304\pi\) | ||||
−0.460428 | + | 0.887697i | \(0.652304\pi\) | |||||||
\(420\) | −4.57398 | −0.223187 | ||||||||
\(421\) | 39.5238 | 1.92627 | 0.963137 | − | 0.269011i | \(-0.0866968\pi\) | ||||
0.963137 | + | 0.269011i | \(0.0866968\pi\) | |||||||
\(422\) | 14.1685 | 0.689713 | ||||||||
\(423\) | −6.40573 | −0.311457 | ||||||||
\(424\) | 8.74627 | 0.424756 | ||||||||
\(425\) | −16.7913 | −0.814498 | ||||||||
\(426\) | −5.91999 | −0.286824 | ||||||||
\(427\) | −16.9104 | −0.818350 | ||||||||
\(428\) | 15.4507 | 0.746837 | ||||||||
\(429\) | −4.57260 | −0.220767 | ||||||||
\(430\) | 7.54851 | 0.364021 | ||||||||
\(431\) | −9.74194 | −0.469253 | −0.234626 | − | 0.972086i | \(-0.575387\pi\) | ||||
−0.234626 | + | 0.972086i | \(0.575387\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −26.0803 | −1.25334 | −0.626670 | − | 0.779285i | \(-0.715582\pi\) | ||||
−0.626670 | + | 0.779285i | \(0.715582\pi\) | |||||||
\(434\) | −12.6227 | −0.605909 | ||||||||
\(435\) | 11.5386 | 0.553232 | ||||||||
\(436\) | −3.02806 | −0.145018 | ||||||||
\(437\) | −37.7773 | −1.80714 | ||||||||
\(438\) | 1.48512 | 0.0709619 | ||||||||
\(439\) | −28.2846 | −1.34995 | −0.674975 | − | 0.737840i | \(-0.735846\pi\) | ||||
−0.674975 | + | 0.737840i | \(0.735846\pi\) | |||||||
\(440\) | −7.35782 | −0.350770 | ||||||||
\(441\) | 1.08009 | 0.0514330 | ||||||||
\(442\) | −6.96515 | −0.331298 | ||||||||
\(443\) | −1.32483 | −0.0629448 | −0.0314724 | − | 0.999505i | \(-0.510020\pi\) | ||||
−0.0314724 | + | 0.999505i | \(0.510020\pi\) | |||||||
\(444\) | −0.817018 | −0.0387739 | ||||||||
\(445\) | −22.4105 | −1.06236 | ||||||||
\(446\) | 6.11406 | 0.289509 | ||||||||
\(447\) | 3.63472 | 0.171916 | ||||||||
\(448\) | 2.84255 | 0.134298 | ||||||||
\(449\) | 36.8887 | 1.74088 | 0.870442 | − | 0.492271i | \(-0.163833\pi\) | ||||
0.870442 | + | 0.492271i | \(0.163833\pi\) | |||||||
\(450\) | 2.41076 | 0.113644 | ||||||||
\(451\) | 52.3455 | 2.46485 | ||||||||
\(452\) | −4.47739 | −0.210599 | ||||||||
\(453\) | −8.48578 | −0.398697 | ||||||||
\(454\) | −11.5741 | −0.543201 | ||||||||
\(455\) | −4.57398 | −0.214431 | ||||||||
\(456\) | −5.10639 | −0.239129 | ||||||||
\(457\) | −24.7797 | −1.15914 | −0.579572 | − | 0.814921i | \(-0.696780\pi\) | ||||
−0.579572 | + | 0.814921i | \(0.696780\pi\) | |||||||
\(458\) | 3.87756 | 0.181187 | ||||||||
\(459\) | 6.96515 | 0.325105 | ||||||||
\(460\) | 11.9043 | 0.555040 | ||||||||
\(461\) | 17.9360 | 0.835365 | 0.417682 | − | 0.908593i | \(-0.362842\pi\) | ||||
0.417682 | + | 0.908593i | \(0.362842\pi\) | |||||||
\(462\) | 12.9978 | 0.604714 | ||||||||
\(463\) | −6.09532 | −0.283273 | −0.141637 | − | 0.989919i | \(-0.545236\pi\) | ||||
−0.141637 | + | 0.989919i | \(0.545236\pi\) | |||||||
\(464\) | −7.17077 | −0.332894 | ||||||||
\(465\) | −7.14546 | −0.331363 | ||||||||
\(466\) | 0.0308552 | 0.00142934 | ||||||||
\(467\) | 32.7750 | 1.51664 | 0.758322 | − | 0.651880i | \(-0.226019\pi\) | ||||
0.758322 | + | 0.651880i | \(0.226019\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −14.5813 | −0.673302 | ||||||||
\(470\) | −10.3075 | −0.475451 | ||||||||
\(471\) | 1.63370 | 0.0752769 | ||||||||
\(472\) | −0.862231 | −0.0396874 | ||||||||
\(473\) | −21.4505 | −0.986297 | ||||||||
\(474\) | 16.1372 | 0.741205 | ||||||||
\(475\) | −12.3103 | −0.564835 | ||||||||
\(476\) | 19.7988 | 0.907476 | ||||||||
\(477\) | −8.74627 | −0.400464 | ||||||||
\(478\) | −0.243671 | −0.0111453 | ||||||||
\(479\) | 27.7395 | 1.26745 | 0.633725 | − | 0.773558i | \(-0.281525\pi\) | ||||
0.633725 | + | 0.773558i | \(0.281525\pi\) | |||||||
\(480\) | 1.60911 | 0.0734455 | ||||||||
\(481\) | −0.817018 | −0.0372528 | ||||||||
\(482\) | −4.60369 | −0.209692 | ||||||||
\(483\) | −21.0293 | −0.956868 | ||||||||
\(484\) | 9.90866 | 0.450394 | ||||||||
\(485\) | 4.15939 | 0.188868 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −35.9493 | −1.62902 | −0.814510 | − | 0.580150i | \(-0.802994\pi\) | ||||
−0.814510 | + | 0.580150i | \(0.802994\pi\) | |||||||
\(488\) | 5.94901 | 0.269299 | ||||||||
\(489\) | −11.6549 | −0.527052 | ||||||||
\(490\) | 1.73799 | 0.0785144 | ||||||||
\(491\) | −29.2751 | −1.32117 | −0.660583 | − | 0.750753i | \(-0.729691\pi\) | ||||
−0.660583 | + | 0.750753i | \(0.729691\pi\) | |||||||
\(492\) | −11.4476 | −0.516100 | ||||||||
\(493\) | −49.9454 | −2.24943 | ||||||||
\(494\) | −5.10639 | −0.229747 | ||||||||
\(495\) | 7.35782 | 0.330709 | ||||||||
\(496\) | 4.44063 | 0.199390 | ||||||||
\(497\) | 16.8279 | 0.754833 | ||||||||
\(498\) | −7.18794 | −0.322099 | ||||||||
\(499\) | −2.29770 | −0.102859 | −0.0514297 | − | 0.998677i | \(-0.516378\pi\) | ||||
−0.0514297 | + | 0.998677i | \(0.516378\pi\) | |||||||
\(500\) | 11.9247 | 0.533291 | ||||||||
\(501\) | −10.1875 | −0.455145 | ||||||||
\(502\) | 18.3295 | 0.818087 | ||||||||
\(503\) | −12.8249 | −0.571835 | −0.285917 | − | 0.958254i | \(-0.592298\pi\) | ||||
−0.285917 | + | 0.958254i | \(0.592298\pi\) | |||||||
\(504\) | −2.84255 | −0.126617 | ||||||||
\(505\) | −4.32704 | −0.192551 | ||||||||
\(506\) | −33.8283 | −1.50385 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 1.94343 | 0.0862260 | ||||||||
\(509\) | −18.0905 | −0.801849 | −0.400924 | − | 0.916111i | \(-0.631311\pi\) | ||||
−0.400924 | + | 0.916111i | \(0.631311\pi\) | |||||||
\(510\) | 11.2077 | 0.496285 | ||||||||
\(511\) | −4.22154 | −0.186750 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.10639 | 0.225453 | ||||||||
\(514\) | 7.93770 | 0.350117 | ||||||||
\(515\) | 1.60911 | 0.0709059 | ||||||||
\(516\) | 4.69111 | 0.206514 | ||||||||
\(517\) | 29.2908 | 1.28821 | ||||||||
\(518\) | 2.32241 | 0.102041 | ||||||||
\(519\) | −4.35726 | −0.191262 | ||||||||
\(520\) | 1.60911 | 0.0705642 | ||||||||
\(521\) | 20.9542 | 0.918019 | 0.459010 | − | 0.888431i | \(-0.348204\pi\) | ||||
0.459010 | + | 0.888431i | \(0.348204\pi\) | |||||||
\(522\) | 7.17077 | 0.313856 | ||||||||
\(523\) | −5.27308 | −0.230576 | −0.115288 | − | 0.993332i | \(-0.536779\pi\) | ||||
−0.115288 | + | 0.993332i | \(0.536779\pi\) | |||||||
\(524\) | 5.44624 | 0.237920 | ||||||||
\(525\) | −6.85271 | −0.299077 | ||||||||
\(526\) | −0.633427 | −0.0276187 | ||||||||
\(527\) | 30.9296 | 1.34732 | ||||||||
\(528\) | −4.57260 | −0.198997 | ||||||||
\(529\) | 31.7312 | 1.37962 | ||||||||
\(530\) | −14.0737 | −0.611323 | ||||||||
\(531\) | 0.862231 | 0.0374176 | ||||||||
\(532\) | 14.5152 | 0.629312 | ||||||||
\(533\) | −11.4476 | −0.495853 | ||||||||
\(534\) | −13.9273 | −0.602691 | ||||||||
\(535\) | −24.8619 | −1.07487 | ||||||||
\(536\) | 5.12966 | 0.221567 | ||||||||
\(537\) | 14.7457 | 0.636326 | ||||||||
\(538\) | −1.06226 | −0.0457973 | ||||||||
\(539\) | −4.93884 | −0.212731 | ||||||||
\(540\) | −1.60911 | −0.0692451 | ||||||||
\(541\) | 11.2091 | 0.481919 | 0.240959 | − | 0.970535i | \(-0.422538\pi\) | ||||
0.240959 | + | 0.970535i | \(0.422538\pi\) | |||||||
\(542\) | −25.8546 | −1.11055 | ||||||||
\(543\) | −20.1298 | −0.863852 | ||||||||
\(544\) | −6.96515 | −0.298628 | ||||||||
\(545\) | 4.87249 | 0.208715 | ||||||||
\(546\) | −2.84255 | −0.121650 | ||||||||
\(547\) | 18.3150 | 0.783095 | 0.391547 | − | 0.920158i | \(-0.371940\pi\) | ||||
0.391547 | + | 0.920158i | \(0.371940\pi\) | |||||||
\(548\) | −5.97882 | −0.255403 | ||||||||
\(549\) | −5.94901 | −0.253898 | ||||||||
\(550\) | −11.0234 | −0.470041 | ||||||||
\(551\) | −36.6167 | −1.55993 | ||||||||
\(552\) | 7.39805 | 0.314882 | ||||||||
\(553\) | −45.8707 | −1.95062 | ||||||||
\(554\) | 24.9779 | 1.06121 | ||||||||
\(555\) | 1.31467 | 0.0558047 | ||||||||
\(556\) | 0.970755 | 0.0411692 | ||||||||
\(557\) | 19.5113 | 0.826719 | 0.413360 | − | 0.910568i | \(-0.364355\pi\) | ||||
0.413360 | + | 0.910568i | \(0.364355\pi\) | |||||||
\(558\) | −4.44063 | −0.187987 | ||||||||
\(559\) | 4.69111 | 0.198413 | ||||||||
\(560\) | −4.57398 | −0.193286 | ||||||||
\(561\) | −31.8488 | −1.34466 | ||||||||
\(562\) | −6.09885 | −0.257264 | ||||||||
\(563\) | 30.4444 | 1.28308 | 0.641540 | − | 0.767090i | \(-0.278296\pi\) | ||||
0.641540 | + | 0.767090i | \(0.278296\pi\) | |||||||
\(564\) | −6.40573 | −0.269730 | ||||||||
\(565\) | 7.20463 | 0.303101 | ||||||||
\(566\) | −12.1903 | −0.512395 | ||||||||
\(567\) | 2.84255 | 0.119376 | ||||||||
\(568\) | −5.91999 | −0.248397 | ||||||||
\(569\) | 44.5917 | 1.86938 | 0.934690 | − | 0.355463i | \(-0.115677\pi\) | ||||
0.934690 | + | 0.355463i | \(0.115677\pi\) | |||||||
\(570\) | 8.21675 | 0.344162 | ||||||||
\(571\) | −37.2634 | −1.55942 | −0.779712 | − | 0.626139i | \(-0.784634\pi\) | ||||
−0.779712 | + | 0.626139i | \(0.784634\pi\) | |||||||
\(572\) | −4.57260 | −0.191190 | ||||||||
\(573\) | −18.6504 | −0.779131 | ||||||||
\(574\) | 32.5405 | 1.35822 | ||||||||
\(575\) | 17.8349 | 0.743768 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −4.87519 | −0.202957 | −0.101479 | − | 0.994838i | \(-0.532357\pi\) | ||||
−0.101479 | + | 0.994838i | \(0.532357\pi\) | |||||||
\(578\) | −31.5133 | −1.31078 | ||||||||
\(579\) | 3.50650 | 0.145725 | ||||||||
\(580\) | 11.5386 | 0.479113 | ||||||||
\(581\) | 20.4321 | 0.847666 | ||||||||
\(582\) | 2.58490 | 0.107148 | ||||||||
\(583\) | 39.9932 | 1.65635 | ||||||||
\(584\) | 1.48512 | 0.0614548 | ||||||||
\(585\) | −1.60911 | −0.0665286 | ||||||||
\(586\) | 15.6402 | 0.646091 | ||||||||
\(587\) | −3.09476 | −0.127735 | −0.0638673 | − | 0.997958i | \(-0.520343\pi\) | ||||
−0.0638673 | + | 0.997958i | \(0.520343\pi\) | |||||||
\(588\) | 1.08009 | 0.0445423 | ||||||||
\(589\) | 22.6756 | 0.934331 | ||||||||
\(590\) | 1.38743 | 0.0571194 | ||||||||
\(591\) | −2.08818 | −0.0858961 | ||||||||
\(592\) | −0.817018 | −0.0335792 | ||||||||
\(593\) | −17.1003 | −0.702227 | −0.351114 | − | 0.936333i | \(-0.614197\pi\) | ||||
−0.351114 | + | 0.936333i | \(0.614197\pi\) | |||||||
\(594\) | 4.57260 | 0.187616 | ||||||||
\(595\) | −31.8584 | −1.30607 | ||||||||
\(596\) | 3.63472 | 0.148884 | ||||||||
\(597\) | −4.31102 | −0.176438 | ||||||||
\(598\) | 7.39805 | 0.302529 | ||||||||
\(599\) | 20.3018 | 0.829510 | 0.414755 | − | 0.909933i | \(-0.363867\pi\) | ||||
0.414755 | + | 0.909933i | \(0.363867\pi\) | |||||||
\(600\) | 2.41076 | 0.0984189 | ||||||||
\(601\) | −42.8024 | −1.74595 | −0.872973 | − | 0.487769i | \(-0.837811\pi\) | ||||
−0.872973 | + | 0.487769i | \(0.837811\pi\) | |||||||
\(602\) | −13.3347 | −0.543482 | ||||||||
\(603\) | −5.12966 | −0.208896 | ||||||||
\(604\) | −8.48578 | −0.345281 | ||||||||
\(605\) | −15.9441 | −0.648221 | ||||||||
\(606\) | −2.68909 | −0.109237 | ||||||||
\(607\) | 28.4394 | 1.15432 | 0.577161 | − | 0.816631i | \(-0.304161\pi\) | ||||
0.577161 | + | 0.816631i | \(0.304161\pi\) | |||||||
\(608\) | −5.10639 | −0.207091 | ||||||||
\(609\) | −20.3833 | −0.825972 | ||||||||
\(610\) | −9.57262 | −0.387584 | ||||||||
\(611\) | −6.40573 | −0.259148 | ||||||||
\(612\) | 6.96515 | 0.281549 | ||||||||
\(613\) | 42.3147 | 1.70907 | 0.854537 | − | 0.519391i | \(-0.173841\pi\) | ||||
0.854537 | + | 0.519391i | \(0.173841\pi\) | |||||||
\(614\) | 3.23081 | 0.130385 | ||||||||
\(615\) | 18.4205 | 0.742788 | ||||||||
\(616\) | 12.9978 | 0.523698 | ||||||||
\(617\) | 5.20542 | 0.209562 | 0.104781 | − | 0.994495i | \(-0.466586\pi\) | ||||
0.104781 | + | 0.994495i | \(0.466586\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −40.1514 | −1.61382 | −0.806910 | − | 0.590674i | \(-0.798862\pi\) | ||||
−0.806910 | + | 0.590674i | \(0.798862\pi\) | |||||||
\(620\) | −7.14546 | −0.286969 | ||||||||
\(621\) | −7.39805 | −0.296874 | ||||||||
\(622\) | 21.8255 | 0.875125 | ||||||||
\(623\) | 39.5889 | 1.58610 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −7.13442 | −0.285377 | ||||||||
\(626\) | 15.6711 | 0.626341 | ||||||||
\(627\) | −23.3495 | −0.932488 | ||||||||
\(628\) | 1.63370 | 0.0651917 | ||||||||
\(629\) | −5.69065 | −0.226901 | ||||||||
\(630\) | 4.57398 | 0.182232 | ||||||||
\(631\) | 33.9516 | 1.35159 | 0.675795 | − | 0.737090i | \(-0.263800\pi\) | ||||
0.675795 | + | 0.737090i | \(0.263800\pi\) | |||||||
\(632\) | 16.1372 | 0.641902 | ||||||||
\(633\) | −14.1685 | −0.563148 | ||||||||
\(634\) | −4.78367 | −0.189984 | ||||||||
\(635\) | −3.12720 | −0.124099 | ||||||||
\(636\) | −8.74627 | −0.346812 | ||||||||
\(637\) | 1.08009 | 0.0427949 | ||||||||
\(638\) | −32.7890 | −1.29813 | ||||||||
\(639\) | 5.91999 | 0.234191 | ||||||||
\(640\) | 1.60911 | 0.0636057 | ||||||||
\(641\) | −25.8159 | −1.01967 | −0.509834 | − | 0.860273i | \(-0.670293\pi\) | ||||
−0.509834 | + | 0.860273i | \(0.670293\pi\) | |||||||
\(642\) | −15.4507 | −0.609790 | ||||||||
\(643\) | −18.0616 | −0.712279 | −0.356140 | − | 0.934433i | \(-0.615907\pi\) | ||||
−0.356140 | + | 0.934433i | \(0.615907\pi\) | |||||||
\(644\) | −21.0293 | −0.828672 | ||||||||
\(645\) | −7.54851 | −0.297222 | ||||||||
\(646\) | −35.5667 | −1.39935 | ||||||||
\(647\) | −34.2875 | −1.34798 | −0.673991 | − | 0.738739i | \(-0.735421\pi\) | ||||
−0.673991 | + | 0.738739i | \(0.735421\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −3.94264 | −0.154762 | ||||||||
\(650\) | 2.41076 | 0.0945578 | ||||||||
\(651\) | 12.6227 | 0.494723 | ||||||||
\(652\) | −11.6549 | −0.456441 | ||||||||
\(653\) | −19.3922 | −0.758876 | −0.379438 | − | 0.925217i | \(-0.623883\pi\) | ||||
−0.379438 | + | 0.925217i | \(0.623883\pi\) | |||||||
\(654\) | 3.02806 | 0.118407 | ||||||||
\(655\) | −8.76361 | −0.342423 | ||||||||
\(656\) | −11.4476 | −0.446956 | ||||||||
\(657\) | −1.48512 | −0.0579402 | ||||||||
\(658\) | 18.2086 | 0.709846 | ||||||||
\(659\) | −8.93576 | −0.348088 | −0.174044 | − | 0.984738i | \(-0.555683\pi\) | ||||
−0.174044 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(660\) | 7.35782 | 0.286403 | ||||||||
\(661\) | 26.2423 | 1.02071 | 0.510354 | − | 0.859965i | \(-0.329515\pi\) | ||||
0.510354 | + | 0.859965i | \(0.329515\pi\) | |||||||
\(662\) | 5.01013 | 0.194724 | ||||||||
\(663\) | 6.96515 | 0.270504 | ||||||||
\(664\) | −7.18794 | −0.278946 | ||||||||
\(665\) | −23.3565 | −0.905727 | ||||||||
\(666\) | 0.817018 | 0.0316588 | ||||||||
\(667\) | 53.0497 | 2.05409 | ||||||||
\(668\) | −10.1875 | −0.394167 | ||||||||
\(669\) | −6.11406 | −0.236383 | ||||||||
\(670\) | −8.25419 | −0.318887 | ||||||||
\(671\) | 27.2025 | 1.05014 | ||||||||
\(672\) | −2.84255 | −0.109654 | ||||||||
\(673\) | −25.8503 | −0.996456 | −0.498228 | − | 0.867046i | \(-0.666016\pi\) | ||||
−0.498228 | + | 0.867046i | \(0.666016\pi\) | |||||||
\(674\) | 11.2909 | 0.434910 | ||||||||
\(675\) | −2.41076 | −0.0927903 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −8.54439 | −0.328387 | −0.164194 | − | 0.986428i | \(-0.552502\pi\) | ||||
−0.164194 | + | 0.986428i | \(0.552502\pi\) | |||||||
\(678\) | 4.47739 | 0.171953 | ||||||||
\(679\) | −7.34771 | −0.281979 | ||||||||
\(680\) | 11.2077 | 0.429795 | ||||||||
\(681\) | 11.5741 | 0.443522 | ||||||||
\(682\) | 20.3052 | 0.777527 | ||||||||
\(683\) | −4.47036 | −0.171053 | −0.0855267 | − | 0.996336i | \(-0.527257\pi\) | ||||
−0.0855267 | + | 0.996336i | \(0.527257\pi\) | |||||||
\(684\) | 5.10639 | 0.195248 | ||||||||
\(685\) | 9.62059 | 0.367584 | ||||||||
\(686\) | 16.8276 | 0.642482 | ||||||||
\(687\) | −3.87756 | −0.147938 | ||||||||
\(688\) | 4.69111 | 0.178847 | ||||||||
\(689\) | −8.74627 | −0.333206 | ||||||||
\(690\) | −11.9043 | −0.453189 | ||||||||
\(691\) | 4.28713 | 0.163090 | 0.0815451 | − | 0.996670i | \(-0.474015\pi\) | ||||
0.0815451 | + | 0.996670i | \(0.474015\pi\) | |||||||
\(692\) | −4.35726 | −0.165638 | ||||||||
\(693\) | −12.9978 | −0.493747 | ||||||||
\(694\) | −0.556221 | −0.0211138 | ||||||||
\(695\) | −1.56205 | −0.0592521 | ||||||||
\(696\) | 7.17077 | 0.271807 | ||||||||
\(697\) | −79.7345 | −3.02016 | ||||||||
\(698\) | −20.7543 | −0.785560 | ||||||||
\(699\) | −0.0308552 | −0.00116705 | ||||||||
\(700\) | −6.85271 | −0.259008 | ||||||||
\(701\) | −42.7745 | −1.61557 | −0.807786 | − | 0.589476i | \(-0.799334\pi\) | ||||
−0.807786 | + | 0.589476i | \(0.799334\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −4.17201 | −0.157350 | ||||||||
\(704\) | −4.57260 | −0.172336 | ||||||||
\(705\) | 10.3075 | 0.388204 | ||||||||
\(706\) | 16.4735 | 0.619988 | ||||||||
\(707\) | 7.64387 | 0.287477 | ||||||||
\(708\) | 0.862231 | 0.0324046 | ||||||||
\(709\) | −35.9901 | −1.35164 | −0.675819 | − | 0.737067i | \(-0.736210\pi\) | ||||
−0.675819 | + | 0.737067i | \(0.736210\pi\) | |||||||
\(710\) | 9.52592 | 0.357501 | ||||||||
\(711\) | −16.1372 | −0.605191 | ||||||||
\(712\) | −13.9273 | −0.521946 | ||||||||
\(713\) | −32.8520 | −1.23032 | ||||||||
\(714\) | −19.7988 | −0.740951 | ||||||||
\(715\) | 7.35782 | 0.275167 | ||||||||
\(716\) | 14.7457 | 0.551074 | ||||||||
\(717\) | 0.243671 | 0.00910007 | ||||||||
\(718\) | −27.2326 | −1.01631 | ||||||||
\(719\) | 35.1165 | 1.30962 | 0.654812 | − | 0.755791i | \(-0.272748\pi\) | ||||
0.654812 | + | 0.755791i | \(0.272748\pi\) | |||||||
\(720\) | −1.60911 | −0.0599680 | ||||||||
\(721\) | −2.84255 | −0.105862 | ||||||||
\(722\) | −7.07521 | −0.263312 | ||||||||
\(723\) | 4.60369 | 0.171213 | ||||||||
\(724\) | −20.1298 | −0.748118 | ||||||||
\(725\) | 17.2870 | 0.642023 | ||||||||
\(726\) | −9.90866 | −0.367745 | ||||||||
\(727\) | 25.7215 | 0.953959 | 0.476980 | − | 0.878914i | \(-0.341732\pi\) | ||||
0.476980 | + | 0.878914i | \(0.341732\pi\) | |||||||
\(728\) | −2.84255 | −0.105352 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.38973 | −0.0884478 | ||||||||
\(731\) | 32.6742 | 1.20850 | ||||||||
\(732\) | −5.94901 | −0.219882 | ||||||||
\(733\) | 9.22246 | 0.340639 | 0.170320 | − | 0.985389i | \(-0.445520\pi\) | ||||
0.170320 | + | 0.985389i | \(0.445520\pi\) | |||||||
\(734\) | 23.2016 | 0.856386 | ||||||||
\(735\) | −1.73799 | −0.0641068 | ||||||||
\(736\) | 7.39805 | 0.272696 | ||||||||
\(737\) | 23.4559 | 0.864008 | ||||||||
\(738\) | 11.4476 | 0.421394 | ||||||||
\(739\) | 25.3614 | 0.932934 | 0.466467 | − | 0.884539i | \(-0.345527\pi\) | ||||
0.466467 | + | 0.884539i | \(0.345527\pi\) | |||||||
\(740\) | 1.31467 | 0.0483283 | ||||||||
\(741\) | 5.10639 | 0.187588 | ||||||||
\(742\) | 24.8617 | 0.912702 | ||||||||
\(743\) | −0.554445 | −0.0203406 | −0.0101703 | − | 0.999948i | \(-0.503237\pi\) | ||||
−0.0101703 | + | 0.999948i | \(0.503237\pi\) | |||||||
\(744\) | −4.44063 | −0.162801 | ||||||||
\(745\) | −5.84867 | −0.214279 | ||||||||
\(746\) | −8.85675 | −0.324269 | ||||||||
\(747\) | 7.18794 | 0.262993 | ||||||||
\(748\) | −31.8488 | −1.16451 | ||||||||
\(749\) | 43.9193 | 1.60478 | ||||||||
\(750\) | −11.9247 | −0.435430 | ||||||||
\(751\) | −5.17316 | −0.188771 | −0.0943856 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943856 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(752\) | −6.40573 | −0.233593 | ||||||||
\(753\) | −18.3295 | −0.667965 | ||||||||
\(754\) | 7.17077 | 0.261144 | ||||||||
\(755\) | 13.6546 | 0.496940 | ||||||||
\(756\) | 2.84255 | 0.103383 | ||||||||
\(757\) | 24.3558 | 0.885228 | 0.442614 | − | 0.896712i | \(-0.354051\pi\) | ||||
0.442614 | + | 0.896712i | \(0.354051\pi\) | |||||||
\(758\) | 16.6386 | 0.604342 | ||||||||
\(759\) | 33.8283 | 1.22789 | ||||||||
\(760\) | 8.21675 | 0.298053 | ||||||||
\(761\) | −14.6861 | −0.532372 | −0.266186 | − | 0.963922i | \(-0.585764\pi\) | ||||
−0.266186 | + | 0.963922i | \(0.585764\pi\) | |||||||
\(762\) | −1.94343 | −0.0704032 | ||||||||
\(763\) | −8.60743 | −0.311610 | ||||||||
\(764\) | −18.6504 | −0.674747 | ||||||||
\(765\) | −11.2077 | −0.405215 | ||||||||
\(766\) | 11.0662 | 0.399840 | ||||||||
\(767\) | 0.862231 | 0.0311334 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 39.7035 | 1.43174 | 0.715872 | − | 0.698231i | \(-0.246029\pi\) | ||||
0.715872 | + | 0.698231i | \(0.246029\pi\) | |||||||
\(770\) | −20.9150 | −0.753723 | ||||||||
\(771\) | −7.93770 | −0.285869 | ||||||||
\(772\) | 3.50650 | 0.126202 | ||||||||
\(773\) | −40.0586 | −1.44081 | −0.720403 | − | 0.693555i | \(-0.756043\pi\) | ||||
−0.720403 | + | 0.693555i | \(0.756043\pi\) | |||||||
\(774\) | −4.69111 | −0.168618 | ||||||||
\(775\) | −10.7053 | −0.384546 | ||||||||
\(776\) | 2.58490 | 0.0927925 | ||||||||
\(777\) | −2.32241 | −0.0833161 | ||||||||
\(778\) | 7.44643 | 0.266968 | ||||||||
\(779\) | −58.4562 | −2.09441 | ||||||||
\(780\) | −1.60911 | −0.0576154 | ||||||||
\(781\) | −27.0697 | −0.968632 | ||||||||
\(782\) | 51.5285 | 1.84266 | ||||||||
\(783\) | −7.17077 | −0.256262 | ||||||||
\(784\) | 1.08009 | 0.0385748 | ||||||||
\(785\) | −2.62880 | −0.0938260 | ||||||||
\(786\) | −5.44624 | −0.194261 | ||||||||
\(787\) | 55.0910 | 1.96378 | 0.981891 | − | 0.189446i | \(-0.0606692\pi\) | ||||
0.981891 | + | 0.189446i | \(0.0606692\pi\) | |||||||
\(788\) | −2.08818 | −0.0743882 | ||||||||
\(789\) | 0.633427 | 0.0225506 | ||||||||
\(790\) | −25.9665 | −0.923846 | ||||||||
\(791\) | −12.7272 | −0.452528 | ||||||||
\(792\) | 4.57260 | 0.162480 | ||||||||
\(793\) | −5.94901 | −0.211256 | ||||||||
\(794\) | 8.13122 | 0.288566 | ||||||||
\(795\) | 14.0737 | 0.499143 | ||||||||
\(796\) | −4.31102 | −0.152800 | ||||||||
\(797\) | −54.7705 | −1.94007 | −0.970035 | − | 0.242964i | \(-0.921880\pi\) | ||||
−0.970035 | + | 0.242964i | \(0.921880\pi\) | |||||||
\(798\) | −14.5152 | −0.513831 | ||||||||
\(799\) | −44.6168 | −1.57843 | ||||||||
\(800\) | 2.41076 | 0.0852333 | ||||||||
\(801\) | 13.9273 | 0.492095 | ||||||||
\(802\) | 30.5947 | 1.08034 | ||||||||
\(803\) | 6.79087 | 0.239645 | ||||||||
\(804\) | −5.12966 | −0.180909 | ||||||||
\(805\) | 33.8385 | 1.19265 | ||||||||
\(806\) | −4.44063 | −0.156414 | ||||||||
\(807\) | 1.06226 | 0.0373933 | ||||||||
\(808\) | −2.68909 | −0.0946018 | ||||||||
\(809\) | −23.2987 | −0.819139 | −0.409569 | − | 0.912279i | \(-0.634321\pi\) | ||||
−0.409569 | + | 0.912279i | \(0.634321\pi\) | |||||||
\(810\) | 1.60911 | 0.0565384 | ||||||||
\(811\) | 28.6759 | 1.00695 | 0.503474 | − | 0.864010i | \(-0.332055\pi\) | ||||
0.503474 | + | 0.864010i | \(0.332055\pi\) | |||||||
\(812\) | −20.3833 | −0.715312 | ||||||||
\(813\) | 25.8546 | 0.906762 | ||||||||
\(814\) | −3.73589 | −0.130943 | ||||||||
\(815\) | 18.7540 | 0.656924 | ||||||||
\(816\) | 6.96515 | 0.243829 | ||||||||
\(817\) | 23.9546 | 0.838066 | ||||||||
\(818\) | −15.2968 | −0.534839 | ||||||||
\(819\) | 2.84255 | 0.0993268 | ||||||||
\(820\) | 18.4205 | 0.643273 | ||||||||
\(821\) | 2.70362 | 0.0943568 | 0.0471784 | − | 0.998886i | \(-0.484977\pi\) | ||||
0.0471784 | + | 0.998886i | \(0.484977\pi\) | |||||||
\(822\) | 5.97882 | 0.208535 | ||||||||
\(823\) | −17.3732 | −0.605592 | −0.302796 | − | 0.953055i | \(-0.597920\pi\) | ||||
−0.302796 | + | 0.953055i | \(0.597920\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | 11.0234 | 0.383787 | ||||||||
\(826\) | −2.45094 | −0.0852789 | ||||||||
\(827\) | −44.1877 | −1.53656 | −0.768279 | − | 0.640115i | \(-0.778887\pi\) | ||||
−0.768279 | + | 0.640115i | \(0.778887\pi\) | |||||||
\(828\) | −7.39805 | −0.257100 | ||||||||
\(829\) | −37.5709 | −1.30489 | −0.652446 | − | 0.757835i | \(-0.726257\pi\) | ||||
−0.652446 | + | 0.757835i | \(0.726257\pi\) | |||||||
\(830\) | 11.5662 | 0.401468 | ||||||||
\(831\) | −24.9779 | −0.866473 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 7.52301 | 0.260657 | ||||||||
\(834\) | −0.970755 | −0.0336145 | ||||||||
\(835\) | 16.3928 | 0.567298 | ||||||||
\(836\) | −23.3495 | −0.807558 | ||||||||
\(837\) | 4.44063 | 0.153491 | ||||||||
\(838\) | 18.8495 | 0.651144 | ||||||||
\(839\) | −28.3089 | −0.977333 | −0.488667 | − | 0.872471i | \(-0.662517\pi\) | ||||
−0.488667 | + | 0.872471i | \(0.662517\pi\) | |||||||
\(840\) | 4.57398 | 0.157817 | ||||||||
\(841\) | 22.4199 | 0.773100 | ||||||||
\(842\) | −39.5238 | −1.36208 | ||||||||
\(843\) | 6.09885 | 0.210055 | ||||||||
\(844\) | −14.1685 | −0.487701 | ||||||||
\(845\) | −1.60911 | −0.0553551 | ||||||||
\(846\) | 6.40573 | 0.220234 | ||||||||
\(847\) | 28.1659 | 0.967791 | ||||||||
\(848\) | −8.74627 | −0.300348 | ||||||||
\(849\) | 12.1903 | 0.418369 | ||||||||
\(850\) | 16.7913 | 0.575937 | ||||||||
\(851\) | 6.04434 | 0.207197 | ||||||||
\(852\) | 5.91999 | 0.202816 | ||||||||
\(853\) | 2.80830 | 0.0961544 | 0.0480772 | − | 0.998844i | \(-0.484691\pi\) | ||||
0.0480772 | + | 0.998844i | \(0.484691\pi\) | |||||||
\(854\) | 16.9104 | 0.578661 | ||||||||
\(855\) | −8.21675 | −0.281007 | ||||||||
\(856\) | −15.4507 | −0.528093 | ||||||||
\(857\) | 52.8361 | 1.80485 | 0.902424 | − | 0.430849i | \(-0.141786\pi\) | ||||
0.902424 | + | 0.430849i | \(0.141786\pi\) | |||||||
\(858\) | 4.57260 | 0.156106 | ||||||||
\(859\) | 22.0375 | 0.751908 | 0.375954 | − | 0.926638i | \(-0.377315\pi\) | ||||
0.375954 | + | 0.926638i | \(0.377315\pi\) | |||||||
\(860\) | −7.54851 | −0.257402 | ||||||||
\(861\) | −32.5405 | −1.10898 | ||||||||
\(862\) | 9.74194 | 0.331812 | ||||||||
\(863\) | −43.1974 | −1.47046 | −0.735229 | − | 0.677819i | \(-0.762925\pi\) | ||||
−0.735229 | + | 0.677819i | \(0.762925\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 7.01131 | 0.238392 | ||||||||
\(866\) | 26.0803 | 0.886245 | ||||||||
\(867\) | 31.5133 | 1.07025 | ||||||||
\(868\) | 12.6227 | 0.428443 | ||||||||
\(869\) | 73.7888 | 2.50311 | ||||||||
\(870\) | −11.5386 | −0.391194 | ||||||||
\(871\) | −5.12966 | −0.173812 | ||||||||
\(872\) | 3.02806 | 0.102543 | ||||||||
\(873\) | −2.58490 | −0.0874856 | ||||||||
\(874\) | 37.7773 | 1.27784 | ||||||||
\(875\) | 33.8967 | 1.14592 | ||||||||
\(876\) | −1.48512 | −0.0501777 | ||||||||
\(877\) | −2.44950 | −0.0827137 | −0.0413569 | − | 0.999144i | \(-0.513168\pi\) | ||||
−0.0413569 | + | 0.999144i | \(0.513168\pi\) | |||||||
\(878\) | 28.2846 | 0.954559 | ||||||||
\(879\) | −15.6402 | −0.527531 | ||||||||
\(880\) | 7.35782 | 0.248032 | ||||||||
\(881\) | −3.04447 | −0.102571 | −0.0512855 | − | 0.998684i | \(-0.516332\pi\) | ||||
−0.0512855 | + | 0.998684i | \(0.516332\pi\) | |||||||
\(882\) | −1.08009 | −0.0363686 | ||||||||
\(883\) | −18.2491 | −0.614131 | −0.307066 | − | 0.951688i | \(-0.599347\pi\) | ||||
−0.307066 | + | 0.951688i | \(0.599347\pi\) | |||||||
\(884\) | 6.96515 | 0.234263 | ||||||||
\(885\) | −1.38743 | −0.0466378 | ||||||||
\(886\) | 1.32483 | 0.0445087 | ||||||||
\(887\) | 20.3594 | 0.683602 | 0.341801 | − | 0.939772i | \(-0.388963\pi\) | ||||
0.341801 | + | 0.939772i | \(0.388963\pi\) | |||||||
\(888\) | 0.817018 | 0.0274173 | ||||||||
\(889\) | 5.52431 | 0.185279 | ||||||||
\(890\) | 22.4105 | 0.751201 | ||||||||
\(891\) | −4.57260 | −0.153188 | ||||||||
\(892\) | −6.11406 | −0.204714 | ||||||||
\(893\) | −32.7102 | −1.09460 | ||||||||
\(894\) | −3.63472 | −0.121563 | ||||||||
\(895\) | −23.7275 | −0.793124 | ||||||||
\(896\) | −2.84255 | −0.0949629 | ||||||||
\(897\) | −7.39805 | −0.247014 | ||||||||
\(898\) | −36.8887 | −1.23099 | ||||||||
\(899\) | −31.8427 | −1.06201 | ||||||||
\(900\) | −2.41076 | −0.0803587 | ||||||||
\(901\) | −60.9190 | −2.02951 | ||||||||
\(902\) | −52.3455 | −1.74291 | ||||||||
\(903\) | 13.3347 | 0.443751 | ||||||||
\(904\) | 4.47739 | 0.148916 | ||||||||
\(905\) | 32.3911 | 1.07672 | ||||||||
\(906\) | 8.48578 | 0.281921 | ||||||||
\(907\) | −42.0999 | −1.39790 | −0.698952 | − | 0.715168i | \(-0.746350\pi\) | ||||
−0.698952 | + | 0.715168i | \(0.746350\pi\) | |||||||
\(908\) | 11.5741 | 0.384101 | ||||||||
\(909\) | 2.68909 | 0.0891914 | ||||||||
\(910\) | 4.57398 | 0.151626 | ||||||||
\(911\) | 31.7160 | 1.05080 | 0.525400 | − | 0.850856i | \(-0.323916\pi\) | ||||
0.525400 | + | 0.850856i | \(0.323916\pi\) | |||||||
\(912\) | 5.10639 | 0.169089 | ||||||||
\(913\) | −32.8676 | −1.08776 | ||||||||
\(914\) | 24.7797 | 0.819639 | ||||||||
\(915\) | 9.57262 | 0.316461 | ||||||||
\(916\) | −3.87756 | −0.128118 | ||||||||
\(917\) | 15.4812 | 0.511235 | ||||||||
\(918\) | −6.96515 | −0.229884 | ||||||||
\(919\) | 47.6436 | 1.57162 | 0.785808 | − | 0.618470i | \(-0.212247\pi\) | ||||
0.785808 | + | 0.618470i | \(0.212247\pi\) | |||||||
\(920\) | −11.9043 | −0.392473 | ||||||||
\(921\) | −3.23081 | −0.106459 | ||||||||
\(922\) | −17.9360 | −0.590692 | ||||||||
\(923\) | 5.91999 | 0.194859 | ||||||||
\(924\) | −12.9978 | −0.427598 | ||||||||
\(925\) | 1.96963 | 0.0647612 | ||||||||
\(926\) | 6.09532 | 0.200305 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 7.17077 | 0.235392 | ||||||||
\(929\) | −26.1267 | −0.857190 | −0.428595 | − | 0.903497i | \(-0.640991\pi\) | ||||
−0.428595 | + | 0.903497i | \(0.640991\pi\) | |||||||
\(930\) | 7.14546 | 0.234309 | ||||||||
\(931\) | 5.51538 | 0.180759 | ||||||||
\(932\) | −0.0308552 | −0.00101069 | ||||||||
\(933\) | −21.8255 | −0.714536 | ||||||||
\(934\) | −32.7750 | −1.07243 | ||||||||
\(935\) | 51.2483 | 1.67600 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −15.1510 | −0.494962 | −0.247481 | − | 0.968893i | \(-0.579603\pi\) | ||||
−0.247481 | + | 0.968893i | \(0.579603\pi\) | |||||||
\(938\) | 14.5813 | 0.476097 | ||||||||
\(939\) | −15.6711 | −0.511406 | ||||||||
\(940\) | 10.3075 | 0.336195 | ||||||||
\(941\) | −37.7111 | −1.22935 | −0.614674 | − | 0.788781i | \(-0.710712\pi\) | ||||
−0.614674 | + | 0.788781i | \(0.710712\pi\) | |||||||
\(942\) | −1.63370 | −0.0532288 | ||||||||
\(943\) | 84.6903 | 2.75790 | ||||||||
\(944\) | 0.862231 | 0.0280632 | ||||||||
\(945\) | −4.57398 | −0.148792 | ||||||||
\(946\) | 21.4505 | 0.697417 | ||||||||
\(947\) | 32.6297 | 1.06032 | 0.530162 | − | 0.847896i | \(-0.322131\pi\) | ||||
0.530162 | + | 0.847896i | \(0.322131\pi\) | |||||||
\(948\) | −16.1372 | −0.524111 | ||||||||
\(949\) | −1.48512 | −0.0482091 | ||||||||
\(950\) | 12.3103 | 0.399398 | ||||||||
\(951\) | 4.78367 | 0.155121 | ||||||||
\(952\) | −19.7988 | −0.641682 | ||||||||
\(953\) | 14.2906 | 0.462918 | 0.231459 | − | 0.972845i | \(-0.425650\pi\) | ||||
0.231459 | + | 0.972845i | \(0.425650\pi\) | |||||||
\(954\) | 8.74627 | 0.283171 | ||||||||
\(955\) | 30.0105 | 0.971118 | ||||||||
\(956\) | 0.243671 | 0.00788089 | ||||||||
\(957\) | 32.7890 | 1.05992 | ||||||||
\(958\) | −27.7395 | −0.896223 | ||||||||
\(959\) | −16.9951 | −0.548800 | ||||||||
\(960\) | −1.60911 | −0.0519338 | ||||||||
\(961\) | −11.2808 | −0.363898 | ||||||||
\(962\) | 0.817018 | 0.0263417 | ||||||||
\(963\) | 15.4507 | 0.497891 | ||||||||
\(964\) | 4.60369 | 0.148275 | ||||||||
\(965\) | −5.64234 | −0.181633 | ||||||||
\(966\) | 21.0293 | 0.676608 | ||||||||
\(967\) | 5.69742 | 0.183217 | 0.0916084 | − | 0.995795i | \(-0.470799\pi\) | ||||
0.0916084 | + | 0.995795i | \(0.470799\pi\) | |||||||
\(968\) | −9.90866 | −0.318477 | ||||||||
\(969\) | 35.5667 | 1.14257 | ||||||||
\(970\) | −4.15939 | −0.133550 | ||||||||
\(971\) | −5.23681 | −0.168057 | −0.0840287 | − | 0.996463i | \(-0.526779\pi\) | ||||
−0.0840287 | + | 0.996463i | \(0.526779\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 2.75942 | 0.0884630 | ||||||||
\(974\) | 35.9493 | 1.15189 | ||||||||
\(975\) | −2.41076 | −0.0772062 | ||||||||
\(976\) | −5.94901 | −0.190423 | ||||||||
\(977\) | −32.9126 | −1.05297 | −0.526483 | − | 0.850185i | \(-0.676490\pi\) | ||||
−0.526483 | + | 0.850185i | \(0.676490\pi\) | |||||||
\(978\) | 11.6549 | 0.372682 | ||||||||
\(979\) | −63.6837 | −2.03534 | ||||||||
\(980\) | −1.73799 | −0.0555181 | ||||||||
\(981\) | −3.02806 | −0.0966787 | ||||||||
\(982\) | 29.2751 | 0.934206 | ||||||||
\(983\) | 25.3432 | 0.808322 | 0.404161 | − | 0.914688i | \(-0.367564\pi\) | ||||
0.404161 | + | 0.914688i | \(0.367564\pi\) | |||||||
\(984\) | 11.4476 | 0.364938 | ||||||||
\(985\) | 3.36011 | 0.107062 | ||||||||
\(986\) | 49.9454 | 1.59059 | ||||||||
\(987\) | −18.2086 | −0.579587 | ||||||||
\(988\) | 5.10639 | 0.162456 | ||||||||
\(989\) | −34.7050 | −1.10356 | ||||||||
\(990\) | −7.35782 | −0.233847 | ||||||||
\(991\) | −32.4714 | −1.03149 | −0.515744 | − | 0.856743i | \(-0.672485\pi\) | ||||
−0.515744 | + | 0.856743i | \(0.672485\pi\) | |||||||
\(992\) | −4.44063 | −0.140990 | ||||||||
\(993\) | −5.01013 | −0.158992 | ||||||||
\(994\) | −16.8279 | −0.533748 | ||||||||
\(995\) | 6.93691 | 0.219915 | ||||||||
\(996\) | 7.18794 | 0.227759 | ||||||||
\(997\) | 51.4453 | 1.62929 | 0.814645 | − | 0.579961i | \(-0.196932\pi\) | ||||
0.814645 | + | 0.579961i | \(0.196932\pi\) | |||||||
\(998\) | 2.29770 | 0.0727326 | ||||||||
\(999\) | −0.817018 | −0.0258493 |
(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 | 8034.2.a.w.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.w.1.5 | ✓ | 12 | 1.1 | even | 1 | trivial |