Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, 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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(0\) |
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: | \( x^{12} - x^{11} - 25 x^{10} + 20 x^{9} + 224 x^{8} - 135 x^{7} - 865 x^{6} + 330 x^{5} + 1341 x^{4} - 127 x^{3} - 652 x^{2} - 48 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.49668\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.49668 | 1.44146 | 0.720730 | − | 0.693216i | \(-0.243807\pi\) | ||||
0.720730 | + | 0.693216i | \(0.243807\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.494819 | 0.221290 | 0.110645 | − | 0.993860i | \(-0.464708\pi\) | ||||
0.110645 | + | 0.993860i | \(0.464708\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18883 | 0.827299 | 0.413650 | − | 0.910436i | \(-0.364254\pi\) | ||||
0.413650 | + | 0.910436i | \(0.364254\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.23342 | 1.07781 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.30196 | 0.995579 | 0.497790 | − | 0.867298i | \(-0.334145\pi\) | ||||
0.497790 | + | 0.867298i | \(0.334145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.85717 | 1.06979 | 0.534893 | − | 0.844920i | \(-0.320352\pi\) | ||||
0.534893 | + | 0.844920i | \(0.320352\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.23541 | 0.318980 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.84942 | −0.691086 | −0.345543 | − | 0.938403i | \(-0.612305\pi\) | ||||
−0.345543 | + | 0.938403i | \(0.612305\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.107129 | −0.0245772 | −0.0122886 | − | 0.999924i | \(-0.503912\pi\) | ||||
−0.0122886 | + | 0.999924i | \(0.503912\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.46481 | 1.19252 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.225506 | −0.0470213 | −0.0235107 | − | 0.999724i | \(-0.507484\pi\) | ||||
−0.0235107 | + | 0.999724i | \(0.507484\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.75515 | −0.951031 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.582788 | 0.112158 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.21858 | −1.34046 | −0.670229 | − | 0.742155i | \(-0.733804\pi\) | ||||
−0.670229 | + | 0.742155i | \(0.733804\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.87493 | −0.336747 | −0.168374 | − | 0.985723i | \(-0.553852\pi\) | ||||
−0.168374 | + | 0.985723i | \(0.553852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.24395 | 1.43509 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.08307 | 0.183073 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.20486 | −0.855674 | −0.427837 | − | 0.903856i | \(-0.640724\pi\) | ||||
−0.427837 | + | 0.903856i | \(0.640724\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.63013 | 1.54206 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.59154 | 1.02943 | 0.514713 | − | 0.857363i | \(-0.327898\pi\) | ||||
0.514713 | + | 0.857363i | \(0.327898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.49233 | −0.990071 | −0.495036 | − | 0.868873i | \(-0.664845\pi\) | ||||
−0.495036 | + | 0.868873i | \(0.664845\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.59996 | 0.238508 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.83971 | 1.43527 | 0.717635 | − | 0.696419i | \(-0.245225\pi\) | ||||
0.717635 | + | 0.696419i | \(0.245225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.20903 | −0.315576 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.11410 | −0.996173 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.68672 | 0.506409 | 0.253205 | − | 0.967413i | \(-0.418515\pi\) | ||||
0.253205 | + | 0.967413i | \(0.418515\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.63387 | 0.220311 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.267468 | −0.0354270 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.17220 | 0.673364 | 0.336682 | − | 0.941618i | \(-0.390695\pi\) | ||||
0.336682 | + | 0.941618i | \(0.390695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.59021 | 0.715753 | 0.357877 | − | 0.933769i | \(-0.383501\pi\) | ||||
0.357877 | + | 0.933769i | \(0.383501\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.07741 | 0.891670 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.90860 | 0.236733 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.59776 | −0.561705 | −0.280853 | − | 0.959751i | \(-0.590617\pi\) | ||||
−0.280853 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.563018 | −0.0677794 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.33280 | 0.632887 | 0.316444 | − | 0.948611i | \(-0.397511\pi\) | ||||
0.316444 | + | 0.948611i | \(0.397511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.39626 | 0.280461 | 0.140230 | − | 0.990119i | \(-0.455216\pi\) | ||||
0.140230 | + | 0.990119i | \(0.455216\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.8721 | −1.37087 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.22743 | 0.823642 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.02964 | −0.678388 | −0.339194 | − | 0.940717i | \(-0.610154\pi\) | ||||
−0.339194 | + | 0.940717i | \(0.610154\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.24524 | −0.916138 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.72036 | 0.518127 | 0.259064 | − | 0.965860i | \(-0.416586\pi\) | ||||
0.259064 | + | 0.965860i | \(0.416586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.40995 | −0.152930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.0225 | −1.93222 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.842438 | 0.0892982 | 0.0446491 | − | 0.999003i | \(-0.485783\pi\) | ||||
0.0446491 | + | 0.999003i | \(0.485783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.44268 | 0.885034 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.68111 | −0.485408 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0530097 | −0.00543868 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3558 | 1.45761 | 0.728806 | − | 0.684720i | \(-0.240076\pi\) | ||||
0.728806 | + | 0.684720i | \(0.240076\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.6766 | 1.07304 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0608 | 1.39911 | 0.699553 | − | 0.714581i | \(-0.253383\pi\) | ||||
0.699553 | + | 0.714581i | \(0.253383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.48486 | 0.638972 | 0.319486 | − | 0.947591i | \(-0.396490\pi\) | ||||
0.319486 | + | 0.947591i | \(0.396490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.70409 | 0.263892 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −20.2063 | −1.95342 | −0.976709 | − | 0.214570i | \(-0.931165\pi\) | ||||
−0.976709 | + | 0.214570i | \(0.931165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.396911 | −0.0380172 | −0.0190086 | − | 0.999819i | \(-0.506051\pi\) | ||||
−0.0190086 | + | 0.999819i | \(0.506051\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.9949 | −1.23342 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.7683 | −1.57743 | −0.788716 | − | 0.614757i | \(-0.789254\pi\) | ||||
−0.788716 | + | 0.614757i | \(0.789254\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.111585 | −0.0104053 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.4719 | 1.15302 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.23689 | −0.571735 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0970461 | −0.00882237 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.4570 | 1.48388 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.82703 | −0.431743 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.0545 | −1.15840 | −0.579199 | − | 0.815186i | \(-0.696635\pi\) | ||||
−0.579199 | + | 0.815186i | \(0.696635\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.2093 | −1.42715 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6292 | −1.54027 | −0.770136 | − | 0.637879i | \(-0.779812\pi\) | ||||
−0.770136 | + | 0.637879i | \(0.779812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.234488 | −0.0203327 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.288374 | 0.0248193 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.36166 | −0.287206 | −0.143603 | − | 0.989635i | \(-0.545869\pi\) | ||||
−0.143603 | + | 0.989635i | \(0.545869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3887 | −1.30525 | −0.652627 | − | 0.757679i | \(-0.726333\pi\) | ||||
−0.652627 | + | 0.757679i | \(0.726333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.5666 | 2.06888 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.7362 | 1.06506 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.57189 | −0.296629 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.51526 | −0.454891 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.19953 | 0.753655 | 0.376827 | − | 0.926284i | \(-0.377015\pi\) | ||||
0.376827 | + | 0.926284i | \(0.377015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.85480 | −0.232320 | −0.116160 | − | 0.993231i | \(-0.537059\pi\) | ||||
−0.116160 | + | 0.993231i | \(0.537059\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.21338 | −0.744858 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.927751 | −0.0745188 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.468866 | −0.0374196 | −0.0187098 | − | 0.999825i | \(-0.505956\pi\) | ||||
−0.0187098 | + | 0.999825i | \(0.505956\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.20456 | 0.729969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.493594 | −0.0389007 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.65346 | −0.521139 | −0.260570 | − | 0.965455i | \(-0.583910\pi\) | ||||
−0.260570 | + | 0.965455i | \(0.583910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.07926 | 0.317570 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.87777 | 0.144444 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.346395 | −0.0264895 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.4806 | 1.10094 | 0.550470 | − | 0.834855i | \(-0.314448\pi\) | ||||
0.550470 | + | 0.834855i | \(0.314448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.4082 | −0.786787 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.9134 | 0.970627 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.70746 | −0.576083 | −0.288041 | − | 0.957618i | \(-0.593004\pi\) | ||||
−0.288041 | + | 0.957618i | \(0.593004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.84835 | 0.732022 | 0.366011 | − | 0.930610i | \(-0.380723\pi\) | ||||
0.366011 | + | 0.930610i | \(0.380723\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.9570 | 1.03173 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.57546 | −0.189352 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.40868 | −0.688031 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.27562 | 0.0927878 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.36643 | 0.388301 | 0.194151 | − | 0.980972i | \(-0.437805\pi\) | ||||
0.194151 | + | 0.980972i | \(0.437805\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.36645 | 0.458267 | 0.229134 | − | 0.973395i | \(-0.426411\pi\) | ||||
0.229134 | + | 0.973395i | \(0.426411\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.76517 | 0.341241 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.4195 | 1.09860 | 0.549298 | − | 0.835626i | \(-0.314895\pi\) | ||||
0.549298 | + | 0.835626i | \(0.314895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.2605 | 0.727346 | 0.363673 | − | 0.931527i | \(-0.381523\pi\) | ||||
0.363673 | + | 0.931527i | \(0.381523\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.4791 | −0.809676 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.8002 | −1.10896 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.26162 | 0.227801 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.729158 | −0.0506800 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.353737 | −0.0244685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.55220 | −0.451072 | −0.225536 | − | 0.974235i | \(-0.572413\pi\) | ||||
−0.225536 | + | 0.974235i | \(0.572413\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.3143 | 0.912282 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.21253 | −0.219093 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.10390 | −0.278591 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.98270 | 0.404273 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.9907 | −0.739314 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.7596 | −1.59106 | −0.795529 | − | 0.605916i | \(-0.792807\pi\) | ||||
−0.795529 | + | 0.605916i | \(0.792807\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.3754 | −1.02503 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.95489 | −0.395240 | −0.197620 | − | 0.980279i | \(-0.563321\pi\) | ||||
−0.197620 | + | 0.980279i | \(0.563321\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9016 | −0.852563 | −0.426282 | − | 0.904590i | \(-0.640177\pi\) | ||||
−0.426282 | + | 0.904590i | \(0.640177\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0446 | 1.18725 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.3615 | 0.744314 | 0.372157 | − | 0.928170i | \(-0.378618\pi\) | ||||
0.372157 | + | 0.928170i | \(0.378618\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.86888 | 0.317610 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.0541 | −0.977869 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.86306 | 0.637989 | 0.318994 | − | 0.947757i | \(-0.396655\pi\) | ||||
0.318994 | + | 0.947757i | \(0.396655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.9764 | 1.35121 | 0.675604 | − | 0.737265i | \(-0.263883\pi\) | ||||
0.675604 | + | 0.737265i | \(0.263883\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3341 | −1.43273 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.09307 | −0.0698338 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.413216 | −0.0262923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.7853 | 0.746860 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.9866 | 0.882826 | 0.441413 | − | 0.897304i | \(-0.354477\pi\) | ||||
0.441413 | + | 0.897304i | \(0.354477\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.744613 | −0.0468134 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.52019 | −0.220443 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.8077 | 0.674167 | 0.337083 | − | 0.941475i | \(-0.390560\pi\) | ||||
0.337083 | + | 0.941475i | \(0.390560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3926 | −0.707899 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.3407 | −1.44476 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.3432 | −1.06943 | −0.534713 | − | 0.845034i | \(-0.679580\pi\) | ||||
−0.534713 | + | 0.845034i | \(0.679580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82426 | 0.112063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.10330 | 0.128720 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.6873 | −1.20036 | −0.600179 | − | 0.799865i | \(-0.704904\pi\) | ||||
−0.600179 | + | 0.799865i | \(0.704904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.06608 | −0.246997 | −0.123499 | − | 0.992345i | \(-0.539411\pi\) | ||||
−0.123499 | + | 0.992345i | \(0.539411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.0787 | 1.27574 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.7013 | −0.946826 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.61121 | −0.457313 | −0.228657 | − | 0.973507i | \(-0.573433\pi\) | ||||
−0.228657 | + | 0.973507i | \(0.573433\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.06245 | −0.362949 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.85439 | −0.587864 | −0.293932 | − | 0.955826i | \(-0.594964\pi\) | ||||
−0.293932 | + | 0.955826i | \(0.594964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7241 | −0.815815 | −0.407907 | − | 0.913023i | \(-0.633741\pi\) | ||||
−0.407907 | + | 0.913023i | \(0.633741\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.132348 | −0.00783964 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.4277 | 0.851643 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.88081 | −0.522400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 35.8419 | 2.10109 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.5483 | 1.14203 | 0.571013 | − | 0.820941i | \(-0.306551\pi\) | ||||
0.571013 | + | 0.820941i | \(0.306551\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.55930 | 0.149008 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.92434 | 0.111662 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.869816 | −0.0503028 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.2106 | −0.819085 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.1054 | 2.01675 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.76614 | 0.158389 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0316 | 0.914970 | 0.457485 | − | 0.889217i | \(-0.348750\pi\) | ||||
0.457485 | + | 0.889217i | \(0.348750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.1906 | 0.921054 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.8931 | 0.674398 | 0.337199 | − | 0.941433i | \(-0.390521\pi\) | ||||
0.337199 | + | 0.941433i | \(0.390521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.4125 | −0.588551 | −0.294276 | − | 0.955721i | \(-0.595078\pi\) | ||||
−0.294276 | + | 0.955721i | \(0.595078\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.50204 | 0.197317 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.2739 | 1.25103 | 0.625514 | − | 0.780213i | \(-0.284889\pi\) | ||||
0.625514 | + | 0.780213i | \(0.284889\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.8355 | −1.33453 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −50.4487 | −2.81577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.305257 | 0.0169849 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.3414 | −1.01740 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.990961 | −0.0548003 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.5374 | 1.18740 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.31964 | −0.237429 | −0.118714 | − | 0.992928i | \(-0.537877\pi\) | ||||
−0.118714 | + | 0.992928i | \(0.537877\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.8295 | −0.922253 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.27506 | −0.124300 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.451358 | 0.0245870 | 0.0122935 | − | 0.999924i | \(-0.496087\pi\) | ||||
0.0122935 | + | 0.999924i | \(0.496087\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −41.8652 | −2.27381 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.19095 | −0.335259 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1570 | −1.08838 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.278592 | −0.0149989 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.11053 | 0.0596163 | 0.0298081 | − | 0.999556i | \(-0.490510\pi\) | ||||
0.0298081 | + | 0.999556i | \(0.490510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.44374 | −0.130810 | −0.0654052 | − | 0.997859i | \(-0.520834\pi\) | ||||
−0.0654052 | + | 0.997859i | \(0.520834\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.24791 | 0.119985 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9606 | 0.689825 | 0.344912 | − | 0.938635i | \(-0.387909\pi\) | ||||
0.344912 | + | 0.938635i | \(0.387909\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.63877 | 0.140051 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.5715 | −0.824133 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.9552 | −1.00042 | −0.500209 | − | 0.865905i | \(-0.666743\pi\) | ||||
−0.500209 | + | 0.865905i | \(0.666743\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9885 | −0.999396 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.242293 | −0.0127171 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.18571 | 0.0620631 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2063 | 0.793763 | 0.396882 | − | 0.917870i | \(-0.370092\pi\) | ||||
0.396882 | + | 0.917870i | \(0.370092\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.3133 | 1.10952 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.06959 | 0.418952 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.6863 | 1.32999 | 0.664993 | − | 0.746849i | \(-0.268434\pi\) | ||||
0.664993 | + | 0.746849i | \(0.268434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0516 | −0.622341 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.8433 | −1.43400 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.5271 | 0.900308 | 0.450154 | − | 0.892951i | \(-0.351369\pi\) | ||||
0.450154 | + | 0.892951i | \(0.351369\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.5929 | −1.66979 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.7028 | −0.546886 | −0.273443 | − | 0.961888i | \(-0.588162\pi\) | ||||
−0.273443 | + | 0.961888i | \(0.588162\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.57627 | 0.182263 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.9925 | −1.06711 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.9576 | −0.961188 | −0.480594 | − | 0.876943i | \(-0.659579\pi\) | ||||
−0.480594 | + | 0.876943i | \(0.659579\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.642562 | 0.0324958 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.0146 | −2.22024 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.98358 | −0.150120 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.52120 | −0.226912 | −0.113456 | − | 0.993543i | \(-0.536192\pi\) | ||||
−0.113456 | + | 0.993543i | \(0.536192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.585442 | −0.0293087 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9485 | 0.846365 | 0.423183 | − | 0.906044i | \(-0.360913\pi\) | ||||
0.423183 | + | 0.906044i | \(0.360913\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.23193 | −0.360248 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.07990 | −0.202732 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.1863 | −0.851892 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.0728 | −0.596964 | −0.298482 | − | 0.954415i | \(-0.596480\pi\) | ||||
−0.298482 | + | 0.954415i | \(0.596480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.39300 | −0.413996 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3211 | 0.557073 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.33573 | 0.114656 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.4208 | −1.88147 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.78051 | −0.135837 | −0.0679183 | − | 0.997691i | \(-0.521636\pi\) | ||||
−0.0679183 | + | 0.997691i | \(0.521636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.6855 | 1.59299 | 0.796496 | − | 0.604644i | \(-0.206685\pi\) | ||||
0.796496 | + | 0.604644i | \(0.206685\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.8160 | 1.54695 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.5494 | 0.657244 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.2360 | 0.592142 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.7983 | 1.53524 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.02096 | −0.193683 | −0.0968415 | − | 0.995300i | \(-0.530874\pi\) | ||||
−0.0968415 | + | 0.995300i | \(0.530874\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.1701 | −1.44988 | −0.724942 | − | 0.688810i | \(-0.758133\pi\) | ||||
−0.724942 | + | 0.688810i | \(0.758133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.91788 | −0.427580 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0241584 | 0.00115565 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.1555 | −0.580150 | −0.290075 | − | 0.957004i | \(-0.593680\pi\) | ||||
−0.290075 | + | 0.957004i | \(0.593680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.14275 | −0.340131 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.4039 | 0.684350 | 0.342175 | − | 0.939636i | \(-0.388836\pi\) | ||||
0.342175 | + | 0.939636i | \(0.388836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.416854 | 0.0197608 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.9683 | 1.08636 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.7784 | −1.35814 | −0.679069 | − | 0.734074i | \(-0.737616\pi\) | ||||
−0.679069 | + | 0.734074i | \(0.737616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.7650 | 1.02487 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.12753 | −0.334880 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.17760 | 0.195849 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.06627 | −0.283768 | −0.141884 | − | 0.989883i | \(-0.545316\pi\) | ||||
−0.141884 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.66061 | −0.0775105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.3042 | −0.945660 | −0.472830 | − | 0.881154i | \(-0.656768\pi\) | ||||
−0.472830 | + | 0.881154i | \(0.656768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.6608 | −0.495451 | −0.247725 | − | 0.968830i | \(-0.579683\pi\) | ||||
−0.247725 | + | 0.968830i | \(0.579683\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.31630 | −0.107416 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.1698 | 0.887072 | 0.443536 | − | 0.896257i | \(-0.353724\pi\) | ||||
0.443536 | + | 0.896257i | \(0.353724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0637 | −0.464698 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.17061 | −0.0539389 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.4374 | −0.985694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.509417 | 0.0233737 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.9207 | 0.545812 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.8451 | 1.27228 | 0.636138 | − | 0.771575i | \(-0.280531\pi\) | ||||
0.636138 | + | 0.771575i | \(0.280531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.0761 | −0.915389 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.23235 | −0.0560738 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.10353 | 0.322555 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.32856 | −0.0602027 | −0.0301014 | − | 0.999547i | \(-0.509583\pi\) | ||||
−0.0301014 | + | 0.999547i | \(0.509583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.6116 | −0.751201 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1475 | 1.31541 | 0.657704 | − | 0.753277i | \(-0.271528\pi\) | ||||
0.657704 | + | 0.753277i | \(0.271528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.5688 | 0.926371 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.28301 | 0.237453 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.6726 | 0.523587 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.303970 | 0.0136076 | 0.00680379 | − | 0.999977i | \(-0.497834\pi\) | ||||
0.00680379 | + | 0.999977i | \(0.497834\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.49668 | −0.111544 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.9185 | 0.888121 | 0.444061 | − | 0.895997i | \(-0.353537\pi\) | ||||
0.444061 | + | 0.895997i | \(0.353537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.95756 | 0.309608 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.68819 | 0.208210 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.68611 | −0.296357 | −0.148178 | − | 0.988961i | \(-0.547341\pi\) | ||||
−0.148178 | + | 0.988961i | \(0.547341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.24500 | 0.232025 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0624337 | −0.00275652 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.20883 | 0.141398 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.4904 | 1.42892 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.1535 | 1.58696 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.2937 | −1.45862 | −0.729312 | − | 0.684181i | \(-0.760160\pi\) | ||||
−0.729312 | + | 0.684181i | \(0.760160\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.2397 | −0.535205 | −0.267602 | − | 0.963529i | \(-0.586231\pi\) | ||||
−0.267602 | + | 0.963529i | \(0.586231\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25.9860 | −1.13412 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.34246 | 0.232721 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9491 | −0.997789 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.7239 | 0.725757 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4247 | 1.10127 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.99846 | −0.432271 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.2431 | −0.830401 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.29415 | −0.314181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.88900 | −0.210195 | −0.105097 | − | 0.994462i | \(-0.533515\pi\) | ||||
−0.105097 | + | 0.994462i | \(0.533515\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.5882 | 1.05518 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.196399 | −0.00841281 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.59128 | 0.367337 | 0.183668 | − | 0.982988i | \(-0.441203\pi\) | ||||
0.183668 | + | 0.982988i | \(0.441203\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.0755 | 0.771445 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.773323 | 0.0329447 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.1978 | −0.561229 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.43012 | −0.272943 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.8867 | −0.927371 | −0.463686 | − | 0.886000i | \(-0.653473\pi\) | ||||
−0.463686 | + | 0.886000i | \(0.653473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.0420 | −1.05917 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23.4905 | −0.991769 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.5539 | 1.75129 | 0.875644 | − | 0.482958i | \(-0.160438\pi\) | ||||
0.875644 | + | 0.482958i | \(0.160438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.29729 | −0.349070 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0474 | −0.757920 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 45.4970 | 1.90733 | 0.953667 | − | 0.300865i | \(-0.0972754\pi\) | ||||
0.953667 | + | 0.300865i | \(0.0972754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8624 | 0.580124 | 0.290062 | − | 0.957008i | \(-0.406324\pi\) | ||||
0.290062 | + | 0.957008i | \(0.406324\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.3983 | 0.559721 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.07232 | 0.0447187 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.35521 | −0.139679 | −0.0698395 | − | 0.997558i | \(-0.522249\pi\) | ||||
−0.0698395 | + | 0.997558i | \(0.522249\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.8950 | 0.660574 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3321 | 0.428646 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.1734 | 0.504171 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.17132 | 0.255153 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.8863 | −1.19226 | −0.596132 | − | 0.802886i | \(-0.703297\pi\) | ||||
−0.596132 | + | 0.802886i | \(0.703297\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.200860 | 0.00827630 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.4977 | 1.58358 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.6015 | 1.21559 | 0.607795 | − | 0.794094i | \(-0.292054\pi\) | ||||
0.607795 | + | 0.794094i | \(0.292054\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.08613 | −0.126519 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.6172 | 1.04844 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.8865 | 0.975976 | 0.487988 | − | 0.872850i | \(-0.337731\pi\) | ||||
0.487988 | + | 0.872850i | \(0.337731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.08030 | −0.370393 | −0.185197 | − | 0.982701i | \(-0.559292\pi\) | ||||
−0.185197 | + | 0.982701i | \(0.559292\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.8665 | −0.605411 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.0480202 | −0.00195230 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.4683 | −0.911959 | −0.455979 | − | 0.889990i | \(-0.650711\pi\) | ||||
−0.455979 | + | 0.889990i | \(0.650711\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −39.4482 | −1.59852 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.9535 | 1.53543 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.3738 | 1.67107 | 0.835536 | − | 0.549435i | \(-0.185157\pi\) | ||||
0.835536 | + | 0.549435i | \(0.185157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.14323 | 0.328367 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.34719 | −0.215270 | −0.107635 | − | 0.994190i | \(-0.534328\pi\) | ||||
−0.107635 | + | 0.994190i | \(0.534328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.7477 | −1.23586 | −0.617928 | − | 0.786235i | \(-0.712028\pi\) | ||||
−0.617928 | + | 0.786235i | \(0.712028\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.131422 | −0.00527379 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.84395 | 0.0738763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.3873 | 0.855491 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.883170 | −0.0352704 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.8308 | 0.591344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.83570 | −0.152697 | −0.0763483 | − | 0.997081i | \(-0.524326\pi\) | ||||
−0.0763483 | + | 0.997081i | \(0.524326\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.3588 | −0.650202 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.45961 | −0.256342 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.52062 | −0.337599 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.2432 | 0.682131 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.3733 | 1.63415 | 0.817073 | − | 0.576534i | \(-0.195595\pi\) | ||||
0.817073 | + | 0.576534i | \(0.195595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.6923 | 1.44700 | 0.723501 | − | 0.690323i | \(-0.242532\pi\) | ||||
0.723501 | + | 0.690323i | \(0.242532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.02066 | −0.315813 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.32189 | 0.169911 | 0.0849554 | − | 0.996385i | \(-0.472925\pi\) | ||||
0.0849554 | + | 0.996385i | \(0.472925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.0784 | 0.670387 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.2461 | −0.401578 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.9208 | 0.466495 | 0.233248 | − | 0.972417i | \(-0.425065\pi\) | ||||
0.233248 | + | 0.972417i | \(0.425065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.72327 | −0.340846 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.74812 | 0.302283 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.12791 | 0.277664 | 0.138832 | − | 0.990316i | \(-0.455665\pi\) | ||||
0.138832 | + | 0.990316i | \(0.455665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.5190 | 1.61490 | 0.807450 | − | 0.589936i | \(-0.200847\pi\) | ||||
0.807450 | + | 0.589936i | \(0.200847\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.4403 | −1.06569 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.116029 | −0.00449941 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.62784 | 0.0630301 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −59.3201 | −2.29345 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4587 | 0.712589 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.2896 | 1.55305 | 0.776526 | − | 0.630086i | \(-0.216980\pi\) | ||||
0.776526 | + | 0.630086i | \(0.216980\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.77124 | −0.106665 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.1689 | 0.467690 | 0.233845 | − | 0.972274i | \(-0.424869\pi\) | ||||
0.233845 | + | 0.972274i | \(0.424869\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.4224 | 1.20588 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8675 | −0.569723 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.2454 | 0.965989 | 0.482995 | − | 0.875623i | \(-0.339549\pi\) | ||||
0.482995 | + | 0.875623i | \(0.339549\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.66341 | −0.0635557 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.2113 | −1.22894 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.2203 | 0.541750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.6993 | 0.939607 | 0.469803 | − | 0.882771i | \(-0.344325\pi\) | ||||
0.469803 | + | 0.882771i | \(0.344325\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.3693 | 0.887728 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.61463 | −0.288839 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.7821 | −0.711422 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.3660 | 1.07290 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.3982 | −1.75243 | −0.876217 | − | 0.481916i | \(-0.839941\pi\) | ||||
−0.876217 | + | 0.481916i | \(0.839941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.557594 | 0.0210301 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.1560 | 0.457823 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.7767 | 1.15748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.362206 | 0.0136029 | 0.00680146 | − | 0.999977i | \(-0.497835\pi\) | ||||
0.00680146 | + | 0.999977i | \(0.497835\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.4964 | −0.731172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.422809 | 0.0158343 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.30213 | 0.235686 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.6249 | 0.919635 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.0968 | 1.75641 | 0.878207 | − | 0.478280i | \(-0.158740\pi\) | ||||
0.878207 | + | 0.478280i | \(0.158740\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.1942 | 0.528621 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 52.3714 | 1.94771 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.3255 | 1.27482 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.9450 | −1.25895 | −0.629475 | − | 0.777021i | \(-0.716730\pi\) | ||||
−0.629475 | + | 0.777021i | \(0.716730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31.0255 | −1.14909 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.4994 | 0.684224 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.7995 | 0.915989 | 0.457994 | − | 0.888955i | \(-0.348568\pi\) | ||||
0.457994 | + | 0.888955i | \(0.348568\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.72905 | −0.100663 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.1816 | −0.559222 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.4197 | 1.85472 | 0.927360 | − | 0.374170i | \(-0.122073\pi\) | ||||
0.927360 | + | 0.374170i | \(0.122073\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.03167 | −0.0378994 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.4622 | −1.08086 | −0.540432 | − | 0.841387i | \(-0.681739\pi\) | ||||
−0.540432 | + | 0.841387i | \(0.681739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.55210 | 0.166776 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.2629 | 0.558442 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.2281 | −1.61606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.2575 | −1.35954 | −0.679772 | − | 0.733423i | \(-0.737921\pi\) | ||||
−0.679772 | + | 0.733423i | \(0.737921\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.9201 | 1.27256 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.41261 | −0.0514101 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.3744 | −1.06763 | −0.533815 | − | 0.845601i | \(-0.679242\pi\) | ||||
−0.533815 | + | 0.845601i | \(0.679242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.85906 | −0.0674797 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1050 | −0.511305 | −0.255652 | − | 0.966769i | \(-0.582290\pi\) | ||||
−0.255652 | + | 0.966769i | \(0.582290\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.868770 | −0.0314516 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.55896 | −0.164829 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.9501 | 0.720356 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.563122 | −0.0203067 | −0.0101534 | − | 0.999948i | \(-0.503232\pi\) | ||||
−0.0101534 | + | 0.999948i | \(0.503232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.9834 | 0.971785 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.4287 | 1.16638 | 0.583189 | − | 0.812336i | \(-0.301805\pi\) | ||||
0.583189 | + | 0.812336i | \(0.301805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.91558 | 0.320257 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.4436 | −1.02041 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.706148 | −0.0253004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.6087 | 0.630089 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.20690 | −0.150342 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.232004 | −0.00828057 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.3905 | 1.54671 | 0.773353 | − | 0.633976i | \(-0.218578\pi\) | ||||
0.773353 | + | 0.633976i | \(0.218578\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43.3004 | −1.54154 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.7030 | −1.30501 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.5624 | 0.765703 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.55459 | 0.161535 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.1876 | 0.608817 | 0.304408 | − | 0.952542i | \(-0.401541\pi\) | ||||
0.304408 | + | 0.952542i | \(0.401541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.0375 | −0.991895 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.72396 | 0.0962463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.91236 | 0.279221 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.244240 | −0.00860832 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −49.1531 | −1.73027 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.9798 | −0.456344 | −0.228172 | − | 0.973621i | \(-0.573275\pi\) | ||||
−0.228172 | + | 0.973621i | \(0.573275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0137 | −0.667660 | −0.333830 | − | 0.942633i | \(-0.608341\pi\) | ||||
−0.333830 | + | 0.942633i | \(0.608341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.1517 | −0.356036 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.29226 | −0.115323 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.695520 | 0.0243332 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.2988 | 0.953896 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.4281 | 1.34115 | 0.670574 | − | 0.741842i | \(-0.266048\pi\) | ||||
0.670574 | + | 0.741842i | \(0.266048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.1962 | −1.26172 | −0.630860 | − | 0.775897i | \(-0.717298\pi\) | ||||
−0.630860 | + | 0.775897i | \(0.717298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39.2013 | −1.36481 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.8350 | −1.17656 | −0.588279 | − | 0.808658i | \(-0.700194\pi\) | ||||
−0.588279 | + | 0.808658i | \(0.700194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.5410 | 1.13020 | 0.565099 | − | 0.825023i | \(-0.308838\pi\) | ||||
0.565099 | + | 0.825023i | \(0.308838\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.0028 | −0.659199 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.29447 | 0.218090 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.494819 | −0.0171239 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.09269 | −0.0377688 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.6028 | −0.987478 | −0.493739 | − | 0.869610i | \(-0.664370\pi\) | ||||
−0.493739 | + | 0.869610i | \(0.664370\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.1080 | 0.796826 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.6033 | −0.847382 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.929154 | 0.0319639 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.212417 | −0.00729874 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.2648 | −1.17596 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.17373 | 0.0402349 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.4616 | 1.00874 | 0.504372 | − | 0.863486i | \(-0.331724\pi\) | ||||
0.504372 | + | 0.863486i | \(0.331724\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.171403 | −0.00586185 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.23304 | −0.0762793 | −0.0381397 | − | 0.999272i | \(-0.512143\pi\) | ||||
−0.0381397 | + | 0.999272i | \(0.512143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.7098 | −1.01369 | −0.506843 | − | 0.862038i | \(-0.669188\pi\) | ||||
−0.506843 | + | 0.862038i | \(0.669188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.0215 | 1.22761 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.6497 | 1.65605 | 0.828027 | − | 0.560688i | \(-0.189463\pi\) | ||||
0.828027 | + | 0.560688i | \(0.189463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.16528 | 0.243627 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.1726 | −0.753020 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.9096 | −0.675389 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.7343 | −0.600905 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.4184 | 1.57103 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.5655 | −0.357181 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 55.2990 | 1.86732 | 0.933658 | − | 0.358167i | \(-0.116598\pi\) | ||||
0.933658 | + | 0.358167i | \(0.116598\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 48.8060 | 1.64619 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.19113 | 0.174893 | 0.0874467 | − | 0.996169i | \(-0.472129\pi\) | ||||
0.0874467 | + | 0.996169i | \(0.472129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.0328 | −1.71739 | −0.858696 | − | 0.512486i | \(-0.828725\pi\) | ||||
−0.858696 | + | 0.512486i | \(0.828725\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.38977 | 0.214790 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.0401 | 0.605728 | 0.302864 | − | 0.953034i | \(-0.402057\pi\) | ||||
0.302864 | + | 0.953034i | \(0.402057\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.5740 | −0.958342 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −27.2255 | −0.912087 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.05412 | −0.0352749 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.81380 | −0.127481 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.17166 | −0.0725095 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.5343 | 0.451396 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.5050 | −0.349972 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.4793 | −1.18068 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.87315 | 0.161989 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.1331 | −1.56503 | −0.782515 | − | 0.622632i | \(-0.786063\pi\) | ||||
−0.782515 | + | 0.622632i | \(0.786063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.4646 | 1.50797 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.8008 | −1.51745 | −0.758724 | − | 0.651412i | \(-0.774177\pi\) | ||||
−0.758724 | + | 0.651412i | \(0.774177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5865 | 0.515837 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.90618 | 0.228311 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.5873 | −1.27427 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.37906 | 0.309387 | 0.154693 | − | 0.987963i | \(-0.450561\pi\) | ||||
0.154693 | + | 0.987963i | \(0.450561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.0257 | 1.31889 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.5695 | 0.677054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.7499 | 0.813773 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.9683 | 0.688690 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.8937 | 1.70258 | 0.851288 | − | 0.524699i | \(-0.175822\pi\) | ||||
0.851288 | + | 0.524699i | \(0.175822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.236653 | 0.00775597 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.6934 | 0.972118 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.65559 | −0.152254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.5263 | 0.376549 | 0.188274 | − | 0.982116i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982116i | \(0.439711\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.9968 | −0.848373 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.2254 | −0.757126 | −0.378563 | − | 0.925576i | \(-0.623582\pi\) | ||||
−0.378563 | + | 0.925576i | \(0.623582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.48643 | −0.0484050 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.631202 | 0.0205330 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.30372 | 0.0748610 | 0.0374305 | − | 0.999299i | \(-0.488083\pi\) | ||||
0.0374305 | + | 0.999299i | \(0.488083\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.24278 | 0.300033 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 55.6109 | 1.80331 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.0992 | −0.456718 | −0.228359 | − | 0.973577i | \(-0.573336\pi\) | ||||
−0.228359 | + | 0.973577i | \(0.573336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.65541 | 0.0859271 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −59.5097 | −1.92367 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.35809 | −0.237605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.4846 | −0.886601 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −65.3356 | −2.10541 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.15024 | 0.101410 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.5491 | −1.59339 | −0.796696 | − | 0.604380i | \(-0.793421\pi\) | ||||
−0.796696 | + | 0.604380i | \(0.793421\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.762129 | 0.0244831 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.32257 | 0.299175 | 0.149588 | − | 0.988748i | \(-0.452205\pi\) | ||||
0.149588 | + | 0.988748i | \(0.452205\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.6833 | −1.07984 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −45.7928 | −1.46654 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.7294 | −1.07910 | −0.539550 | − | 0.841954i | \(-0.681406\pi\) | ||||
−0.539550 | + | 0.841954i | \(0.681406\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.78170 | 0.0889034 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.28338 | −0.0409752 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.58538 | 0.273831 | 0.136915 | − | 0.990583i | \(-0.456281\pi\) | ||||
0.136915 | + | 0.990583i | \(0.456281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.62988 | 0.243108 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 53.7722 | 1.71159 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.46406 | 0.0465545 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.4087 | −1.63305 | −0.816525 | − | 0.577310i | \(-0.804102\pi\) | ||||
−0.816525 | + | 0.577310i | \(0.804102\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.7848 | −0.342244 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.07708 | 0.160954 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.24495 | −0.166109 | −0.0830546 | − | 0.996545i | \(-0.526468\pi\) | ||||
−0.0830546 | + | 0.996545i | \(0.526468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.03333 | −0.0959703 |
(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 | 1336.2.a.d.1.11 | ✓ | 12 | |
4.3 | odd | 2 | 2672.2.a.p.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.d.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2672.2.a.p.1.2 | 12 | 4.3 | odd | 2 |