Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8281,2,Mod(1,8281)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8281.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8281 = 7^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8281.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: | \(66.1241179138\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 11x^{6} + 36x^{4} - 31x^{2} + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.332375\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8281.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.332375 | 0.235025 | 0.117512 | − | 0.993071i | \(-0.462508\pi\) | ||||
0.117512 | + | 0.993071i | \(0.462508\pi\) | |||||||
\(3\) | −1.45984 | −0.842837 | −0.421419 | − | 0.906866i | \(-0.638468\pi\) | ||||
−0.421419 | + | 0.906866i | \(0.638468\pi\) | |||||||
\(4\) | −1.88953 | −0.944763 | ||||||||
\(5\) | −1.44562 | −0.646502 | −0.323251 | − | 0.946313i | \(-0.604776\pi\) | ||||
−0.323251 | + | 0.946313i | \(0.604776\pi\) | |||||||
\(6\) | −0.485214 | −0.198088 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.29278 | −0.457068 | ||||||||
\(9\) | −0.868875 | −0.289625 | ||||||||
\(10\) | −0.480489 | −0.151944 | ||||||||
\(11\) | −5.95516 | −1.79555 | −0.897774 | − | 0.440456i | \(-0.854817\pi\) | ||||
−0.897774 | + | 0.440456i | \(0.854817\pi\) | |||||||
\(12\) | 2.75840 | 0.796282 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.11037 | 0.544896 | ||||||||
\(16\) | 3.34936 | 0.837341 | ||||||||
\(17\) | −4.32871 | −1.04987 | −0.524933 | − | 0.851143i | \(-0.675910\pi\) | ||||
−0.524933 | + | 0.851143i | \(0.675910\pi\) | |||||||
\(18\) | −0.288793 | −0.0680691 | ||||||||
\(19\) | −1.95753 | −0.449089 | −0.224545 | − | 0.974464i | \(-0.572089\pi\) | ||||
−0.224545 | + | 0.974464i | \(0.572089\pi\) | |||||||
\(20\) | 2.73154 | 0.610791 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.97935 | −0.421998 | ||||||||
\(23\) | −0.540163 | −0.112632 | −0.0563158 | − | 0.998413i | \(-0.517935\pi\) | ||||
−0.0563158 | + | 0.998413i | \(0.517935\pi\) | |||||||
\(24\) | 1.88725 | 0.385234 | ||||||||
\(25\) | −2.91018 | −0.582036 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64793 | 1.08694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.15857 | 1.32931 | 0.664656 | − | 0.747149i | \(-0.268578\pi\) | ||||
0.664656 | + | 0.747149i | \(0.268578\pi\) | |||||||
\(30\) | 0.701436 | 0.128064 | ||||||||
\(31\) | 6.10800 | 1.09703 | 0.548514 | − | 0.836141i | \(-0.315194\pi\) | ||||
0.548514 | + | 0.836141i | \(0.315194\pi\) | |||||||
\(32\) | 3.69881 | 0.653864 | ||||||||
\(33\) | 8.69356 | 1.51336 | ||||||||
\(34\) | −1.43876 | −0.246745 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.64176 | 0.273627 | ||||||||
\(37\) | 8.02881 | 1.31993 | 0.659964 | − | 0.751297i | \(-0.270571\pi\) | ||||
0.659964 | + | 0.751297i | \(0.270571\pi\) | |||||||
\(38\) | −0.650636 | −0.105547 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.86887 | 0.295495 | ||||||||
\(41\) | 7.55362 | 1.17968 | 0.589839 | − | 0.807521i | \(-0.299191\pi\) | ||||
0.589839 | + | 0.807521i | \(0.299191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24839 | 0.647873 | 0.323936 | − | 0.946079i | \(-0.394994\pi\) | ||||
0.323936 | + | 0.946079i | \(0.394994\pi\) | |||||||
\(44\) | 11.2524 | 1.69637 | ||||||||
\(45\) | 1.25606 | 0.187243 | ||||||||
\(46\) | −0.179537 | −0.0264713 | ||||||||
\(47\) | −6.26084 | −0.913237 | −0.456618 | − | 0.889663i | \(-0.650940\pi\) | ||||
−0.456618 | + | 0.889663i | \(0.650940\pi\) | |||||||
\(48\) | −4.88953 | −0.705742 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.967272 | −0.136793 | ||||||||
\(51\) | 6.31922 | 0.884867 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.77905 | −0.381732 | −0.190866 | − | 0.981616i | \(-0.561130\pi\) | ||||
−0.190866 | + | 0.981616i | \(0.561130\pi\) | |||||||
\(54\) | 1.87723 | 0.255459 | ||||||||
\(55\) | 8.60891 | 1.16082 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.85768 | 0.378509 | ||||||||
\(58\) | 2.37933 | 0.312421 | ||||||||
\(59\) | 0.851152 | 0.110811 | 0.0554053 | − | 0.998464i | \(-0.482355\pi\) | ||||
0.0554053 | + | 0.998464i | \(0.482355\pi\) | |||||||
\(60\) | −3.98760 | −0.514798 | ||||||||
\(61\) | −6.77905 | −0.867969 | −0.433984 | − | 0.900920i | \(-0.642893\pi\) | ||||
−0.433984 | + | 0.900920i | \(0.642893\pi\) | |||||||
\(62\) | 2.03015 | 0.257829 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.46933 | −0.683667 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.88953 | 0.355676 | ||||||||
\(67\) | −0.987106 | −0.120594 | −0.0602971 | − | 0.998180i | \(-0.519205\pi\) | ||||
−0.0602971 | + | 0.998180i | \(0.519205\pi\) | |||||||
\(68\) | 8.17922 | 0.991876 | ||||||||
\(69\) | 0.788550 | 0.0949302 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.76223 | 0.446494 | 0.223247 | − | 0.974762i | \(-0.428334\pi\) | ||||
0.223247 | + | 0.974762i | \(0.428334\pi\) | |||||||
\(72\) | 1.12327 | 0.132378 | ||||||||
\(73\) | 9.13519 | 1.06919 | 0.534597 | − | 0.845107i | \(-0.320463\pi\) | ||||
0.534597 | + | 0.845107i | \(0.320463\pi\) | |||||||
\(74\) | 2.66858 | 0.310216 | ||||||||
\(75\) | 4.24839 | 0.490561 | ||||||||
\(76\) | 3.69881 | 0.424283 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.131125 | −0.0147527 | −0.00737636 | − | 0.999973i | \(-0.502348\pi\) | ||||
−0.00737636 | + | 0.999973i | \(0.502348\pi\) | |||||||
\(80\) | −4.84191 | −0.541342 | ||||||||
\(81\) | −5.63843 | −0.626492 | ||||||||
\(82\) | 2.51064 | 0.277253 | ||||||||
\(83\) | −2.66812 | −0.292865 | −0.146432 | − | 0.989221i | \(-0.546779\pi\) | ||||
−0.146432 | + | 0.989221i | \(0.546779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.25768 | 0.678741 | ||||||||
\(86\) | 1.41206 | 0.152266 | ||||||||
\(87\) | −10.4503 | −1.12039 | ||||||||
\(88\) | 7.69873 | 0.820687 | ||||||||
\(89\) | −9.71739 | −1.03004 | −0.515021 | − | 0.857178i | \(-0.672216\pi\) | ||||
−0.515021 | + | 0.857178i | \(0.672216\pi\) | |||||||
\(90\) | 0.417485 | 0.0440068 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.02065 | 0.106410 | ||||||||
\(93\) | −8.91668 | −0.924617 | ||||||||
\(94\) | −2.08095 | −0.214633 | ||||||||
\(95\) | 2.82985 | 0.290337 | ||||||||
\(96\) | −5.39966 | −0.551101 | ||||||||
\(97\) | −6.58319 | −0.668422 | −0.334211 | − | 0.942498i | \(-0.608470\pi\) | ||||
−0.334211 | + | 0.942498i | \(0.608470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.17429 | 0.520036 | ||||||||
\(100\) | 5.49886 | 0.549886 | ||||||||
\(101\) | 0.0708289 | 0.00704774 | 0.00352387 | − | 0.999994i | \(-0.498878\pi\) | ||||
0.00352387 | + | 0.999994i | \(0.498878\pi\) | |||||||
\(102\) | 2.10035 | 0.207966 | ||||||||
\(103\) | −6.33821 | −0.624522 | −0.312261 | − | 0.949996i | \(-0.601086\pi\) | ||||
−0.312261 | + | 0.949996i | \(0.601086\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.923689 | −0.0897166 | ||||||||
\(107\) | 7.74953 | 0.749175 | 0.374588 | − | 0.927192i | \(-0.377784\pi\) | ||||
0.374588 | + | 0.927192i | \(0.377784\pi\) | |||||||
\(108\) | −10.6719 | −1.02691 | ||||||||
\(109\) | −0.0335623 | −0.00321468 | −0.00160734 | − | 0.999999i | \(-0.500512\pi\) | ||||
−0.00160734 | + | 0.999999i | \(0.500512\pi\) | |||||||
\(110\) | 2.86139 | 0.272823 | ||||||||
\(111\) | −11.7208 | −1.11249 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.19987 | −0.865451 | −0.432725 | − | 0.901526i | \(-0.642448\pi\) | ||||
−0.432725 | + | 0.901526i | \(0.642448\pi\) | |||||||
\(114\) | 0.949823 | 0.0889591 | ||||||||
\(115\) | 0.780871 | 0.0728166 | ||||||||
\(116\) | −13.5263 | −1.25589 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.282902 | 0.0260432 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.72825 | −0.249054 | ||||||||
\(121\) | 24.4639 | 2.22399 | ||||||||
\(122\) | −2.25319 | −0.203994 | ||||||||
\(123\) | −11.0271 | −0.994276 | ||||||||
\(124\) | −11.5412 | −1.03643 | ||||||||
\(125\) | 11.4351 | 1.02279 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3952 | 1.27737 | 0.638683 | − | 0.769470i | \(-0.279480\pi\) | ||||
0.638683 | + | 0.769470i | \(0.279480\pi\) | |||||||
\(128\) | −9.21550 | −0.814542 | ||||||||
\(129\) | −6.20195 | −0.546052 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.46828 | 0.827248 | 0.413624 | − | 0.910448i | \(-0.364263\pi\) | ||||
0.413624 | + | 0.910448i | \(0.364263\pi\) | |||||||
\(132\) | −16.4267 | −1.42976 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.328090 | −0.0283426 | ||||||||
\(135\) | −8.16477 | −0.702711 | ||||||||
\(136\) | 5.59609 | 0.479860 | ||||||||
\(137\) | 16.6063 | 1.41877 | 0.709384 | − | 0.704822i | \(-0.248973\pi\) | ||||
0.709384 | + | 0.704822i | \(0.248973\pi\) | |||||||
\(138\) | 0.262094 | 0.0223110 | ||||||||
\(139\) | −18.4778 | −1.56726 | −0.783632 | − | 0.621225i | \(-0.786635\pi\) | ||||
−0.783632 | + | 0.621225i | \(0.786635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.13980 | 0.769710 | ||||||||
\(142\) | 1.25047 | 0.104937 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.91018 | −0.242515 | ||||||||
\(145\) | −10.3486 | −0.859402 | ||||||||
\(146\) | 3.03631 | 0.251287 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.1707 | −1.24702 | ||||||||
\(149\) | −3.08080 | −0.252389 | −0.126195 | − | 0.992006i | \(-0.540276\pi\) | ||||
−0.126195 | + | 0.992006i | \(0.540276\pi\) | |||||||
\(150\) | 1.41206 | 0.115294 | ||||||||
\(151\) | 2.54885 | 0.207422 | 0.103711 | − | 0.994607i | \(-0.466928\pi\) | ||||
0.103711 | + | 0.994607i | \(0.466928\pi\) | |||||||
\(152\) | 2.53067 | 0.205264 | ||||||||
\(153\) | 3.76111 | 0.304068 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.82985 | −0.709231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.40904 | 0.750923 | 0.375461 | − | 0.926838i | \(-0.377484\pi\) | ||||
0.375461 | + | 0.926838i | \(0.377484\pi\) | |||||||
\(158\) | −0.0435828 | −0.00346726 | ||||||||
\(159\) | 4.05697 | 0.321738 | ||||||||
\(160\) | −5.34708 | −0.422724 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.87408 | −0.147241 | ||||||||
\(163\) | 0.695157 | 0.0544489 | 0.0272244 | − | 0.999629i | \(-0.491333\pi\) | ||||
0.0272244 | + | 0.999629i | \(0.491333\pi\) | |||||||
\(164\) | −14.2728 | −1.11452 | ||||||||
\(165\) | −12.5676 | −0.978387 | ||||||||
\(166\) | −0.886819 | −0.0688305 | ||||||||
\(167\) | −13.9840 | −1.08211 | −0.541056 | − | 0.840986i | \(-0.681975\pi\) | ||||
−0.541056 | + | 0.840986i | \(0.681975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.07990 | 0.159521 | ||||||||
\(171\) | 1.70085 | 0.130067 | ||||||||
\(172\) | −8.02744 | −0.612087 | ||||||||
\(173\) | 5.43648 | 0.413328 | 0.206664 | − | 0.978412i | \(-0.433739\pi\) | ||||
0.206664 | + | 0.978412i | \(0.433739\pi\) | |||||||
\(174\) | −3.47344 | −0.263321 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −19.9460 | −1.50349 | ||||||||
\(177\) | −1.24254 | −0.0933953 | ||||||||
\(178\) | −3.22982 | −0.242085 | ||||||||
\(179\) | 5.35824 | 0.400493 | 0.200247 | − | 0.979745i | \(-0.435826\pi\) | ||||
0.200247 | + | 0.979745i | \(0.435826\pi\) | |||||||
\(180\) | −2.37337 | −0.176900 | ||||||||
\(181\) | −7.54016 | −0.560456 | −0.280228 | − | 0.959933i | \(-0.590410\pi\) | ||||
−0.280228 | + | 0.959933i | \(0.590410\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.89632 | 0.731557 | ||||||||
\(184\) | 0.698313 | 0.0514803 | ||||||||
\(185\) | −11.6066 | −0.853336 | ||||||||
\(186\) | −2.96369 | −0.217308 | ||||||||
\(187\) | 25.7782 | 1.88509 | ||||||||
\(188\) | 11.8300 | 0.862793 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.940574 | 0.0682364 | ||||||||
\(191\) | 13.5463 | 0.980178 | 0.490089 | − | 0.871672i | \(-0.336964\pi\) | ||||
0.490089 | + | 0.871672i | \(0.336964\pi\) | |||||||
\(192\) | 7.98434 | 0.576220 | ||||||||
\(193\) | 18.5562 | 1.33571 | 0.667853 | − | 0.744293i | \(-0.267213\pi\) | ||||
0.667853 | + | 0.744293i | \(0.267213\pi\) | |||||||
\(194\) | −2.18809 | −0.157096 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.66812 | −0.190096 | −0.0950480 | − | 0.995473i | \(-0.530300\pi\) | ||||
−0.0950480 | + | 0.995473i | \(0.530300\pi\) | |||||||
\(198\) | 1.71981 | 0.122221 | ||||||||
\(199\) | −20.1999 | −1.43193 | −0.715965 | − | 0.698136i | \(-0.754013\pi\) | ||||
−0.715965 | + | 0.698136i | \(0.754013\pi\) | |||||||
\(200\) | 3.76223 | 0.266030 | ||||||||
\(201\) | 1.44101 | 0.101641 | ||||||||
\(202\) | 0.0235418 | 0.00165639 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −11.9403 | −0.835990 | ||||||||
\(205\) | −10.9197 | −0.762663 | ||||||||
\(206\) | −2.10666 | −0.146778 | ||||||||
\(207\) | 0.469334 | 0.0326210 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.6574 | 0.806361 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1268 | 0.903683 | 0.451842 | − | 0.892098i | \(-0.350767\pi\) | ||||
0.451842 | + | 0.892098i | \(0.350767\pi\) | |||||||
\(212\) | 5.25109 | 0.360647 | ||||||||
\(213\) | −5.49224 | −0.376322 | ||||||||
\(214\) | 2.57575 | 0.176075 | ||||||||
\(215\) | −6.14156 | −0.418851 | ||||||||
\(216\) | −7.30155 | −0.496807 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.0111553 | −0.000755530 0 | ||||||||
\(219\) | −13.3359 | −0.901157 | ||||||||
\(220\) | −16.2668 | −1.09670 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.89569 | −0.261462 | ||||||||
\(223\) | 2.22334 | 0.148886 | 0.0744428 | − | 0.997225i | \(-0.476282\pi\) | ||||
0.0744428 | + | 0.997225i | \(0.476282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.52858 | 0.168572 | ||||||||
\(226\) | −3.05781 | −0.203402 | ||||||||
\(227\) | −27.1045 | −1.79899 | −0.899495 | − | 0.436931i | \(-0.856065\pi\) | ||||
−0.899495 | + | 0.436931i | \(0.856065\pi\) | |||||||
\(228\) | −5.39966 | −0.357601 | ||||||||
\(229\) | 18.9887 | 1.25481 | 0.627406 | − | 0.778693i | \(-0.284117\pi\) | ||||
0.627406 | + | 0.778693i | \(0.284117\pi\) | |||||||
\(230\) | 0.259542 | 0.0171137 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.25447 | −0.607586 | ||||||||
\(233\) | 21.7400 | 1.42424 | 0.712118 | − | 0.702059i | \(-0.247736\pi\) | ||||
0.712118 | + | 0.702059i | \(0.247736\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.05080 | 0.590409 | ||||||||
\(236\) | −1.60827 | −0.104690 | ||||||||
\(237\) | 0.191421 | 0.0124342 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.9695 | 1.29172 | 0.645861 | − | 0.763455i | \(-0.276499\pi\) | ||||
0.645861 | + | 0.763455i | \(0.276499\pi\) | |||||||
\(240\) | 7.06841 | 0.456264 | ||||||||
\(241\) | −3.23048 | −0.208094 | −0.104047 | − | 0.994572i | \(-0.533179\pi\) | ||||
−0.104047 | + | 0.994572i | \(0.533179\pi\) | |||||||
\(242\) | 8.13120 | 0.522694 | ||||||||
\(243\) | −8.71259 | −0.558913 | ||||||||
\(244\) | 12.8092 | 0.820025 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.66512 | −0.233680 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.89632 | −0.501417 | ||||||||
\(249\) | 3.89503 | 0.246837 | ||||||||
\(250\) | 3.80075 | 0.240381 | ||||||||
\(251\) | −12.4916 | −0.788466 | −0.394233 | − | 0.919011i | \(-0.628990\pi\) | ||||
−0.394233 | + | 0.919011i | \(0.628990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.21675 | 0.202236 | ||||||||
\(254\) | 4.78460 | 0.300213 | ||||||||
\(255\) | −9.13519 | −0.572068 | ||||||||
\(256\) | 7.87566 | 0.492229 | ||||||||
\(257\) | −5.82757 | −0.363514 | −0.181757 | − | 0.983343i | \(-0.558178\pi\) | ||||
−0.181757 | + | 0.983343i | \(0.558178\pi\) | |||||||
\(258\) | −2.06138 | −0.128336 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.21990 | −0.385002 | ||||||||
\(262\) | 3.14702 | 0.194424 | ||||||||
\(263\) | 17.5147 | 1.08000 | 0.540002 | − | 0.841664i | \(-0.318424\pi\) | ||||
0.540002 | + | 0.841664i | \(0.318424\pi\) | |||||||
\(264\) | −11.2389 | −0.691706 | ||||||||
\(265\) | 4.01746 | 0.246791 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.1858 | 0.868157 | ||||||||
\(268\) | 1.86516 | 0.113933 | ||||||||
\(269\) | −22.3287 | −1.36141 | −0.680703 | − | 0.732560i | \(-0.738325\pi\) | ||||
−0.680703 | + | 0.732560i | \(0.738325\pi\) | |||||||
\(270\) | −2.71377 | −0.165155 | ||||||||
\(271\) | 26.3695 | 1.60183 | 0.800916 | − | 0.598777i | \(-0.204346\pi\) | ||||
0.800916 | + | 0.598777i | \(0.204346\pi\) | |||||||
\(272\) | −14.4984 | −0.879097 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.51951 | 0.333446 | ||||||||
\(275\) | 17.3306 | 1.04507 | ||||||||
\(276\) | −1.48999 | −0.0896866 | ||||||||
\(277\) | −9.37618 | −0.563360 | −0.281680 | − | 0.959508i | \(-0.590892\pi\) | ||||
−0.281680 | + | 0.959508i | \(0.590892\pi\) | |||||||
\(278\) | −6.14156 | −0.368346 | ||||||||
\(279\) | −5.30709 | −0.317727 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.7754 | −1.06039 | −0.530195 | − | 0.847876i | \(-0.677881\pi\) | ||||
−0.530195 | + | 0.847876i | \(0.677881\pi\) | |||||||
\(282\) | 3.03785 | 0.180901 | ||||||||
\(283\) | 9.60662 | 0.571055 | 0.285527 | − | 0.958371i | \(-0.407831\pi\) | ||||
0.285527 | + | 0.958371i | \(0.407831\pi\) | |||||||
\(284\) | −7.10883 | −0.421832 | ||||||||
\(285\) | −4.13113 | −0.244707 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.21380 | −0.189375 | ||||||||
\(289\) | 1.73775 | 0.102221 | ||||||||
\(290\) | −3.43961 | −0.201981 | ||||||||
\(291\) | 9.61039 | 0.563371 | ||||||||
\(292\) | −17.2612 | −1.01013 | ||||||||
\(293\) | 11.6338 | 0.679654 | 0.339827 | − | 0.940488i | \(-0.389631\pi\) | ||||
0.339827 | + | 0.940488i | \(0.389631\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.23044 | −0.0716392 | ||||||||
\(296\) | −10.3795 | −0.603297 | ||||||||
\(297\) | −33.6343 | −1.95166 | ||||||||
\(298\) | −1.02398 | −0.0593177 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −8.02744 | −0.463464 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.847174 | 0.0487494 | ||||||||
\(303\) | −0.103399 | −0.00594010 | ||||||||
\(304\) | −6.55649 | −0.376041 | ||||||||
\(305\) | 9.79995 | 0.561143 | ||||||||
\(306\) | 1.25010 | 0.0714635 | ||||||||
\(307\) | −13.8280 | −0.789204 | −0.394602 | − | 0.918852i | \(-0.629118\pi\) | ||||
−0.394602 | + | 0.918852i | \(0.629118\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.25275 | 0.526371 | ||||||||
\(310\) | −2.93483 | −0.166687 | ||||||||
\(311\) | −30.7144 | −1.74165 | −0.870827 | − | 0.491590i | \(-0.836416\pi\) | ||||
−0.870827 | + | 0.491590i | \(0.836416\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.0867 | −0.626657 | −0.313328 | − | 0.949645i | \(-0.601444\pi\) | ||||
−0.313328 | + | 0.949645i | \(0.601444\pi\) | |||||||
\(314\) | 3.12733 | 0.176486 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.247764 | 0.0139378 | ||||||||
\(317\) | −23.8834 | −1.34142 | −0.670712 | − | 0.741718i | \(-0.734011\pi\) | ||||
−0.670712 | + | 0.741718i | \(0.734011\pi\) | |||||||
\(318\) | 1.34844 | 0.0756165 | ||||||||
\(319\) | −42.6304 | −2.38684 | ||||||||
\(320\) | 7.90659 | 0.441992 | ||||||||
\(321\) | −11.3130 | −0.631433 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.47360 | 0.471484 | ||||||||
\(324\) | 10.6540 | 0.591887 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.231053 | 0.0127968 | ||||||||
\(327\) | 0.0489954 | 0.00270945 | ||||||||
\(328\) | −9.76519 | −0.539192 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.17716 | −0.229945 | ||||||||
\(331\) | −18.3240 | −1.00718 | −0.503589 | − | 0.863943i | \(-0.667987\pi\) | ||||
−0.503589 | + | 0.863943i | \(0.667987\pi\) | |||||||
\(332\) | 5.04149 | 0.276688 | ||||||||
\(333\) | −6.97603 | −0.382284 | ||||||||
\(334\) | −4.64793 | −0.254323 | ||||||||
\(335\) | 1.42698 | 0.0779643 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.21762 | −0.393169 | −0.196584 | − | 0.980487i | \(-0.562985\pi\) | ||||
−0.196584 | + | 0.980487i | \(0.562985\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.4303 | 0.729434 | ||||||||
\(340\) | −11.8241 | −0.641249 | ||||||||
\(341\) | −36.3741 | −1.96977 | ||||||||
\(342\) | 0.565321 | 0.0305691 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.49224 | −0.296122 | ||||||||
\(345\) | −1.13994 | −0.0613725 | ||||||||
\(346\) | 1.80695 | 0.0971423 | ||||||||
\(347\) | −21.0782 | −1.13154 | −0.565770 | − | 0.824563i | \(-0.691421\pi\) | ||||
−0.565770 | + | 0.824563i | \(0.691421\pi\) | |||||||
\(348\) | 19.7462 | 1.05851 | ||||||||
\(349\) | 30.7629 | 1.64670 | 0.823350 | − | 0.567534i | \(-0.192102\pi\) | ||||
0.823350 | + | 0.567534i | \(0.192102\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −22.0270 | −1.17404 | ||||||||
\(353\) | −6.12173 | −0.325827 | −0.162913 | − | 0.986640i | \(-0.552089\pi\) | ||||
−0.162913 | + | 0.986640i | \(0.552089\pi\) | |||||||
\(354\) | −0.412991 | −0.0219502 | ||||||||
\(355\) | −5.43876 | −0.288659 | ||||||||
\(356\) | 18.3613 | 0.973145 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.78095 | 0.0941259 | ||||||||
\(359\) | −19.4287 | −1.02541 | −0.512703 | − | 0.858566i | \(-0.671356\pi\) | ||||
−0.512703 | + | 0.858566i | \(0.671356\pi\) | |||||||
\(360\) | −1.62382 | −0.0855827 | ||||||||
\(361\) | −15.1681 | −0.798319 | ||||||||
\(362\) | −2.50616 | −0.131721 | ||||||||
\(363\) | −35.7133 | −1.87446 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.2060 | −0.691235 | ||||||||
\(366\) | 3.28929 | 0.171934 | ||||||||
\(367\) | 5.40467 | 0.282122 | 0.141061 | − | 0.990001i | \(-0.454949\pi\) | ||||
0.141061 | + | 0.990001i | \(0.454949\pi\) | |||||||
\(368\) | −1.80920 | −0.0943111 | ||||||||
\(369\) | −6.56315 | −0.341664 | ||||||||
\(370\) | −3.85776 | −0.200555 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 16.8483 | 0.873544 | ||||||||
\(373\) | 16.2507 | 0.841428 | 0.420714 | − | 0.907193i | \(-0.361780\pi\) | ||||
0.420714 | + | 0.907193i | \(0.361780\pi\) | |||||||
\(374\) | 8.56803 | 0.443042 | ||||||||
\(375\) | −16.6934 | −0.862045 | ||||||||
\(376\) | 8.09390 | 0.417411 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1730 | 1.29305 | 0.646525 | − | 0.762893i | \(-0.276222\pi\) | ||||
0.646525 | + | 0.762893i | \(0.276222\pi\) | |||||||
\(380\) | −5.34708 | −0.274300 | ||||||||
\(381\) | −21.0146 | −1.07661 | ||||||||
\(382\) | 4.50247 | 0.230366 | ||||||||
\(383\) | −3.81438 | −0.194906 | −0.0974529 | − | 0.995240i | \(-0.531070\pi\) | ||||
−0.0974529 | + | 0.995240i | \(0.531070\pi\) | |||||||
\(384\) | 13.4531 | 0.686527 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.16764 | 0.313924 | ||||||||
\(387\) | −3.69132 | −0.187640 | ||||||||
\(388\) | 12.4391 | 0.631500 | ||||||||
\(389\) | −2.87096 | −0.145563 | −0.0727817 | − | 0.997348i | \(-0.523188\pi\) | ||||
−0.0727817 | + | 0.997348i | \(0.523188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.33821 | 0.118248 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8222 | −0.697236 | ||||||||
\(394\) | −0.886819 | −0.0446773 | ||||||||
\(395\) | 0.189557 | 0.00953766 | ||||||||
\(396\) | −9.77696 | −0.491310 | ||||||||
\(397\) | 19.1184 | 0.959524 | 0.479762 | − | 0.877399i | \(-0.340723\pi\) | ||||
0.479762 | + | 0.877399i | \(0.340723\pi\) | |||||||
\(398\) | −6.71394 | −0.336539 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.74725 | −0.487362 | ||||||||
\(401\) | 2.99824 | 0.149725 | 0.0748625 | − | 0.997194i | \(-0.476148\pi\) | ||||
0.0748625 | + | 0.997194i | \(0.476148\pi\) | |||||||
\(402\) | 0.478958 | 0.0238882 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.133833 | −0.00665844 | ||||||||
\(405\) | 8.15104 | 0.405028 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −47.8129 | −2.37000 | ||||||||
\(408\) | −8.16937 | −0.404444 | ||||||||
\(409\) | 34.0805 | 1.68517 | 0.842587 | − | 0.538560i | \(-0.181031\pi\) | ||||
0.842587 | + | 0.538560i | \(0.181031\pi\) | |||||||
\(410\) | −3.62943 | −0.179245 | ||||||||
\(411\) | −24.2424 | −1.19579 | ||||||||
\(412\) | 11.9762 | 0.590026 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.155995 | 0.00766674 | ||||||||
\(415\) | 3.85710 | 0.189337 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 26.9746 | 1.32095 | ||||||||
\(418\) | 3.87464 | 0.189515 | ||||||||
\(419\) | −34.7759 | −1.69891 | −0.849457 | − | 0.527657i | \(-0.823071\pi\) | ||||
−0.849457 | + | 0.527657i | \(0.823071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.1400 | −1.17651 | −0.588257 | − | 0.808674i | \(-0.700186\pi\) | ||||
−0.588257 | + | 0.808674i | \(0.700186\pi\) | |||||||
\(422\) | 4.36301 | 0.212388 | ||||||||
\(423\) | 5.43988 | 0.264496 | ||||||||
\(424\) | 3.59271 | 0.174478 | ||||||||
\(425\) | 12.5973 | 0.611060 | ||||||||
\(426\) | −1.82549 | −0.0884451 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.6429 | −0.707793 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.04130 | −0.0984404 | ||||||||
\(431\) | −4.76477 | −0.229511 | −0.114755 | − | 0.993394i | \(-0.536608\pi\) | ||||
−0.114755 | + | 0.993394i | \(0.536608\pi\) | |||||||
\(432\) | 18.9170 | 0.910143 | ||||||||
\(433\) | −22.0231 | −1.05836 | −0.529181 | − | 0.848509i | \(-0.677501\pi\) | ||||
−0.529181 | + | 0.848509i | \(0.677501\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 15.1072 | 0.724337 | ||||||||
\(436\) | 0.0634168 | 0.00303711 | ||||||||
\(437\) | 1.05739 | 0.0505817 | ||||||||
\(438\) | −4.43252 | −0.211794 | ||||||||
\(439\) | −3.43240 | −0.163819 | −0.0819097 | − | 0.996640i | \(-0.526102\pi\) | ||||
−0.0819097 | + | 0.996640i | \(0.526102\pi\) | |||||||
\(440\) | −11.1294 | −0.530576 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.70594 | −0.413632 | −0.206816 | − | 0.978380i | \(-0.566310\pi\) | ||||
−0.206816 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(444\) | 22.1467 | 1.05104 | ||||||||
\(445\) | 14.0477 | 0.665923 | ||||||||
\(446\) | 0.738982 | 0.0349918 | ||||||||
\(447\) | 4.49747 | 0.212723 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.6120 | −0.831159 | −0.415580 | − | 0.909557i | \(-0.636421\pi\) | ||||
−0.415580 | + | 0.909557i | \(0.636421\pi\) | |||||||
\(450\) | 0.840438 | 0.0396186 | ||||||||
\(451\) | −44.9830 | −2.11817 | ||||||||
\(452\) | 17.3834 | 0.817646 | ||||||||
\(453\) | −3.72090 | −0.174823 | ||||||||
\(454\) | −9.00887 | −0.422807 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.69436 | −0.173004 | ||||||||
\(457\) | 9.07268 | 0.424402 | 0.212201 | − | 0.977226i | \(-0.431937\pi\) | ||||
0.212201 | + | 0.977226i | \(0.431937\pi\) | |||||||
\(458\) | 6.31139 | 0.294912 | ||||||||
\(459\) | −24.4483 | −1.14115 | ||||||||
\(460\) | −1.47548 | −0.0687944 | ||||||||
\(461\) | 6.58319 | 0.306610 | 0.153305 | − | 0.988179i | \(-0.451008\pi\) | ||||
0.153305 | + | 0.988179i | \(0.451008\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.47344 | −0.161424 | −0.0807121 | − | 0.996737i | \(-0.525719\pi\) | ||||
−0.0807121 | + | 0.996737i | \(0.525719\pi\) | |||||||
\(464\) | 23.9766 | 1.11309 | ||||||||
\(465\) | 12.8901 | 0.597766 | ||||||||
\(466\) | 7.22585 | 0.334731 | ||||||||
\(467\) | −29.7854 | −1.37830 | −0.689152 | − | 0.724617i | \(-0.742017\pi\) | ||||
−0.689152 | + | 0.724617i | \(0.742017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.00826 | 0.138761 | ||||||||
\(471\) | −13.7357 | −0.632906 | ||||||||
\(472\) | −1.10035 | −0.0506479 | ||||||||
\(473\) | −25.2998 | −1.16329 | ||||||||
\(474\) | 0.0636237 | 0.00292233 | ||||||||
\(475\) | 5.69677 | 0.261386 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.41465 | 0.110559 | ||||||||
\(478\) | 6.63738 | 0.303587 | ||||||||
\(479\) | 35.1855 | 1.60767 | 0.803833 | − | 0.594855i | \(-0.202791\pi\) | ||||
0.803833 | + | 0.594855i | \(0.202791\pi\) | |||||||
\(480\) | 7.80587 | 0.356288 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.07373 | −0.0489072 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −46.2252 | −2.10115 | ||||||||
\(485\) | 9.51680 | 0.432136 | ||||||||
\(486\) | −2.89585 | −0.131358 | ||||||||
\(487\) | 1.80154 | 0.0816355 | 0.0408178 | − | 0.999167i | \(-0.487004\pi\) | ||||
0.0408178 | + | 0.999167i | \(0.487004\pi\) | |||||||
\(488\) | 8.76384 | 0.396721 | ||||||||
\(489\) | −1.01482 | −0.0458916 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.19322 | −0.369755 | −0.184877 | − | 0.982762i | \(-0.559189\pi\) | ||||
−0.184877 | + | 0.982762i | \(0.559189\pi\) | |||||||
\(492\) | 20.8359 | 0.939356 | ||||||||
\(493\) | −30.9874 | −1.39560 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.48006 | −0.336204 | ||||||||
\(496\) | 20.4579 | 0.918587 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.29461 | 0.0580129 | ||||||||
\(499\) | 36.5164 | 1.63470 | 0.817350 | − | 0.576141i | \(-0.195442\pi\) | ||||
0.817350 | + | 0.576141i | \(0.195442\pi\) | |||||||
\(500\) | −21.6070 | −0.966293 | ||||||||
\(501\) | 20.4143 | 0.912045 | ||||||||
\(502\) | −4.15192 | −0.185309 | ||||||||
\(503\) | 3.02972 | 0.135089 | 0.0675443 | − | 0.997716i | \(-0.478484\pi\) | ||||
0.0675443 | + | 0.997716i | \(0.478484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.102392 | −0.00455637 | ||||||||
\(506\) | 1.06917 | 0.0475304 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −27.2001 | −1.20681 | ||||||||
\(509\) | 29.3447 | 1.30068 | 0.650341 | − | 0.759642i | \(-0.274626\pi\) | ||||
0.650341 | + | 0.759642i | \(0.274626\pi\) | |||||||
\(510\) | −3.03631 | −0.134450 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 21.0487 | 0.930229 | ||||||||
\(513\) | −11.0560 | −0.488135 | ||||||||
\(514\) | −1.93694 | −0.0854348 | ||||||||
\(515\) | 9.16265 | 0.403755 | ||||||||
\(516\) | 11.7188 | 0.515890 | ||||||||
\(517\) | 37.2843 | 1.63976 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.93637 | −0.348368 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.6838 | 1.30047 | 0.650236 | − | 0.759732i | \(-0.274670\pi\) | ||||
0.650236 | + | 0.759732i | \(0.274670\pi\) | |||||||
\(522\) | −2.06734 | −0.0904851 | ||||||||
\(523\) | −20.5727 | −0.899583 | −0.449791 | − | 0.893134i | \(-0.648502\pi\) | ||||
−0.449791 | + | 0.893134i | \(0.648502\pi\) | |||||||
\(524\) | −17.8906 | −0.781553 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.82146 | 0.253828 | ||||||||
\(527\) | −26.4398 | −1.15173 | ||||||||
\(528\) | 29.1179 | 1.26719 | ||||||||
\(529\) | −22.7082 | −0.987314 | ||||||||
\(530\) | 1.33530 | 0.0580019 | ||||||||
\(531\) | −0.739544 | −0.0320935 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.71501 | 0.204039 | ||||||||
\(535\) | −11.2029 | −0.484343 | ||||||||
\(536\) | 1.27611 | 0.0551197 | ||||||||
\(537\) | −7.82216 | −0.337551 | ||||||||
\(538\) | −7.42151 | −0.319964 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 15.4275 | 0.663896 | ||||||||
\(541\) | 34.0668 | 1.46465 | 0.732324 | − | 0.680957i | \(-0.238436\pi\) | ||||
0.732324 | + | 0.680957i | \(0.238436\pi\) | |||||||
\(542\) | 8.76457 | 0.376470 | ||||||||
\(543\) | 11.0074 | 0.472373 | ||||||||
\(544\) | −16.0111 | −0.686470 | ||||||||
\(545\) | 0.0485183 | 0.00207830 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.850931 | −0.0363832 | −0.0181916 | − | 0.999835i | \(-0.505791\pi\) | ||||
−0.0181916 | + | 0.999835i | \(0.505791\pi\) | |||||||
\(548\) | −31.3780 | −1.34040 | ||||||||
\(549\) | 5.89015 | 0.251385 | ||||||||
\(550\) | 5.76026 | 0.245618 | ||||||||
\(551\) | −14.0131 | −0.596980 | ||||||||
\(552\) | −1.01942 | −0.0433895 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.11641 | −0.132404 | ||||||||
\(555\) | 16.9438 | 0.719224 | ||||||||
\(556\) | 34.9143 | 1.48069 | ||||||||
\(557\) | −17.7281 | −0.751162 | −0.375581 | − | 0.926789i | \(-0.622557\pi\) | ||||
−0.375581 | + | 0.926789i | \(0.622557\pi\) | |||||||
\(558\) | −1.76394 | −0.0746737 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.6319 | −1.58882 | ||||||||
\(562\) | −5.90809 | −0.249218 | ||||||||
\(563\) | 24.1806 | 1.01909 | 0.509545 | − | 0.860444i | \(-0.329814\pi\) | ||||
0.509545 | + | 0.860444i | \(0.329814\pi\) | |||||||
\(564\) | −17.2699 | −0.727194 | ||||||||
\(565\) | 13.2995 | 0.559515 | ||||||||
\(566\) | 3.19301 | 0.134212 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.86375 | −0.204078 | ||||||||
\(569\) | −42.7749 | −1.79322 | −0.896608 | − | 0.442825i | \(-0.853976\pi\) | ||||
−0.896608 | + | 0.442825i | \(0.853976\pi\) | |||||||
\(570\) | −1.37308 | −0.0575122 | ||||||||
\(571\) | 7.36280 | 0.308124 | 0.154062 | − | 0.988061i | \(-0.450765\pi\) | ||||
0.154062 | + | 0.988061i | \(0.450765\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.7754 | −0.826131 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.57197 | 0.0655557 | ||||||||
\(576\) | 4.75217 | 0.198007 | ||||||||
\(577\) | 8.19393 | 0.341118 | 0.170559 | − | 0.985347i | \(-0.445443\pi\) | ||||
0.170559 | + | 0.985347i | \(0.445443\pi\) | |||||||
\(578\) | 0.577585 | 0.0240244 | ||||||||
\(579\) | −27.0891 | −1.12578 | ||||||||
\(580\) | 19.5539 | 0.811932 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.19426 | 0.132406 | ||||||||
\(583\) | 16.5497 | 0.685419 | ||||||||
\(584\) | −11.8098 | −0.488694 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.86679 | 0.159736 | ||||||||
\(587\) | −39.1141 | −1.61441 | −0.807205 | − | 0.590271i | \(-0.799021\pi\) | ||||
−0.807205 | + | 0.590271i | \(0.799021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.9566 | −0.492664 | ||||||||
\(590\) | −0.408969 | −0.0168370 | ||||||||
\(591\) | 3.89503 | 0.160220 | ||||||||
\(592\) | 26.8914 | 1.10523 | ||||||||
\(593\) | 1.21338 | 0.0498276 | 0.0249138 | − | 0.999690i | \(-0.492069\pi\) | ||||
0.0249138 | + | 0.999690i | \(0.492069\pi\) | |||||||
\(594\) | −11.1792 | −0.458689 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.82125 | 0.238448 | ||||||||
\(597\) | 29.4885 | 1.20688 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.6638 | 1.33461 | 0.667303 | − | 0.744786i | \(-0.267449\pi\) | ||||
0.667303 | + | 0.744786i | \(0.267449\pi\) | |||||||
\(600\) | −5.49224 | −0.224220 | ||||||||
\(601\) | −2.50114 | −0.102024 | −0.0510118 | − | 0.998698i | \(-0.516245\pi\) | ||||
−0.0510118 | + | 0.998698i | \(0.516245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.857671 | 0.0349271 | ||||||||
\(604\) | −4.81611 | −0.195965 | ||||||||
\(605\) | −35.3656 | −1.43781 | ||||||||
\(606\) | −0.0343672 | −0.00139607 | ||||||||
\(607\) | −12.6456 | −0.513271 | −0.256635 | − | 0.966508i | \(-0.582614\pi\) | ||||
−0.256635 | + | 0.966508i | \(0.582614\pi\) | |||||||
\(608\) | −7.24055 | −0.293643 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.25726 | 0.131883 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7.10672 | −0.287272 | ||||||||
\(613\) | 20.0280 | 0.808923 | 0.404462 | − | 0.914555i | \(-0.367459\pi\) | ||||
0.404462 | + | 0.914555i | \(0.367459\pi\) | |||||||
\(614\) | −4.59608 | −0.185483 | ||||||||
\(615\) | 15.9409 | 0.642801 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.2926 | −1.82341 | −0.911705 | − | 0.410846i | \(-0.865233\pi\) | ||||
−0.911705 | + | 0.410846i | \(0.865233\pi\) | |||||||
\(618\) | 3.07539 | 0.123710 | ||||||||
\(619\) | 4.43315 | 0.178183 | 0.0890917 | − | 0.996023i | \(-0.471604\pi\) | ||||
0.0890917 | + | 0.996023i | \(0.471604\pi\) | |||||||
\(620\) | 16.6842 | 0.670055 | ||||||||
\(621\) | −3.05080 | −0.122424 | ||||||||
\(622\) | −10.2087 | −0.409332 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.97997 | −0.0791988 | ||||||||
\(626\) | −3.68494 | −0.147280 | ||||||||
\(627\) | −17.0179 | −0.679631 | ||||||||
\(628\) | −17.7786 | −0.709444 | ||||||||
\(629\) | −34.7544 | −1.38575 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.7358 | 0.785672 | 0.392836 | − | 0.919609i | \(-0.371494\pi\) | ||||
0.392836 | + | 0.919609i | \(0.371494\pi\) | |||||||
\(632\) | 0.169516 | 0.00674300 | ||||||||
\(633\) | −19.1629 | −0.761658 | ||||||||
\(634\) | −7.93824 | −0.315268 | ||||||||
\(635\) | −20.8100 | −0.825819 | ||||||||
\(636\) | −7.66574 | −0.303967 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.1693 | −0.560968 | ||||||||
\(639\) | −3.26891 | −0.129316 | ||||||||
\(640\) | 13.3221 | 0.526603 | ||||||||
\(641\) | 39.6425 | 1.56579 | 0.782893 | − | 0.622157i | \(-0.213743\pi\) | ||||
0.782893 | + | 0.622157i | \(0.213743\pi\) | |||||||
\(642\) | −3.76018 | −0.148402 | ||||||||
\(643\) | 20.8300 | 0.821453 | 0.410727 | − | 0.911759i | \(-0.365275\pi\) | ||||
0.410727 | + | 0.911759i | \(0.365275\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.96568 | 0.353023 | ||||||||
\(646\) | 2.81642 | 0.110810 | ||||||||
\(647\) | 15.7441 | 0.618965 | 0.309482 | − | 0.950905i | \(-0.399844\pi\) | ||||
0.309482 | + | 0.950905i | \(0.399844\pi\) | |||||||
\(648\) | 7.28927 | 0.286350 | ||||||||
\(649\) | −5.06874 | −0.198966 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.31352 | −0.0514413 | ||||||||
\(653\) | −27.0264 | −1.05762 | −0.528812 | − | 0.848739i | \(-0.677362\pi\) | ||||
−0.528812 | + | 0.848739i | \(0.677362\pi\) | |||||||
\(654\) | 0.0162849 | 0.000636789 0 | ||||||||
\(655\) | −13.6876 | −0.534817 | ||||||||
\(656\) | 25.2998 | 0.987792 | ||||||||
\(657\) | −7.93734 | −0.309665 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.79491 | −0.264692 | −0.132346 | − | 0.991204i | \(-0.542251\pi\) | ||||
−0.132346 | + | 0.991204i | \(0.542251\pi\) | |||||||
\(660\) | 23.7468 | 0.924344 | ||||||||
\(661\) | 7.20526 | 0.280252 | 0.140126 | − | 0.990134i | \(-0.455249\pi\) | ||||
0.140126 | + | 0.990134i | \(0.455249\pi\) | |||||||
\(662\) | −6.09044 | −0.236712 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.44930 | 0.133859 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.31866 | −0.0898463 | ||||||||
\(667\) | −3.86679 | −0.149723 | ||||||||
\(668\) | 26.4231 | 1.02234 | ||||||||
\(669\) | −3.24571 | −0.125486 | ||||||||
\(670\) | 0.474293 | 0.0183236 | ||||||||
\(671\) | 40.3703 | 1.55848 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.32130 | 0.320763 | 0.160381 | − | 0.987055i | \(-0.448728\pi\) | ||||
0.160381 | + | 0.987055i | \(0.448728\pi\) | |||||||
\(674\) | −2.39896 | −0.0924044 | ||||||||
\(675\) | −16.4365 | −0.632640 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.9956 | 1.15283 | 0.576413 | − | 0.817159i | \(-0.304452\pi\) | ||||
0.576413 | + | 0.817159i | \(0.304452\pi\) | |||||||
\(678\) | 4.46391 | 0.171435 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.08982 | −0.310231 | ||||||||
\(681\) | 39.5682 | 1.51626 | ||||||||
\(682\) | −12.0899 | −0.462944 | ||||||||
\(683\) | 36.0839 | 1.38071 | 0.690356 | − | 0.723469i | \(-0.257454\pi\) | ||||
0.690356 | + | 0.723469i | \(0.257454\pi\) | |||||||
\(684\) | −3.21380 | −0.122883 | ||||||||
\(685\) | −24.0064 | −0.917236 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.7205 | −1.05760 | ||||||||
\(688\) | 14.2294 | 0.542491 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.378889 | −0.0144241 | ||||||||
\(691\) | −25.7677 | −0.980248 | −0.490124 | − | 0.871653i | \(-0.663049\pi\) | ||||
−0.490124 | + | 0.871653i | \(0.663049\pi\) | |||||||
\(692\) | −10.2724 | −0.390497 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.00589 | −0.265940 | ||||||||
\(695\) | 26.7119 | 1.01324 | ||||||||
\(696\) | 13.5100 | 0.512096 | ||||||||
\(697\) | −32.6974 | −1.23850 | ||||||||
\(698\) | 10.2248 | 0.387016 | ||||||||
\(699\) | −31.7369 | −1.20040 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.7872 | 1.57828 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.7167 | −0.592765 | ||||||||
\(704\) | 32.5708 | 1.22756 | ||||||||
\(705\) | −13.2127 | −0.497619 | ||||||||
\(706\) | −2.03471 | −0.0765774 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.34782 | 0.0882364 | ||||||||
\(709\) | −0.343847 | −0.0129135 | −0.00645673 | − | 0.999979i | \(-0.502055\pi\) | ||||
−0.00645673 | + | 0.999979i | \(0.502055\pi\) | |||||||
\(710\) | −1.80771 | −0.0678421 | ||||||||
\(711\) | 0.113931 | 0.00427276 | ||||||||
\(712\) | 12.5625 | 0.470799 | ||||||||
\(713\) | −3.29931 | −0.123560 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.1245 | −0.378372 | ||||||||
\(717\) | −29.1523 | −1.08871 | ||||||||
\(718\) | −6.45761 | −0.240996 | ||||||||
\(719\) | −8.78010 | −0.327443 | −0.163721 | − | 0.986507i | \(-0.552350\pi\) | ||||
−0.163721 | + | 0.986507i | \(0.552350\pi\) | |||||||
\(720\) | 4.20702 | 0.156786 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.04149 | −0.187625 | ||||||||
\(723\) | 4.71598 | 0.175389 | ||||||||
\(724\) | 14.2473 | 0.529498 | ||||||||
\(725\) | −20.8327 | −0.773707 | ||||||||
\(726\) | −11.8702 | −0.440546 | ||||||||
\(727\) | 17.3658 | 0.644064 | 0.322032 | − | 0.946729i | \(-0.395634\pi\) | ||||
0.322032 | + | 0.946729i | \(0.395634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.6343 | 1.09757 | ||||||||
\(730\) | −4.38936 | −0.162458 | ||||||||
\(731\) | −18.3900 | −0.680180 | ||||||||
\(732\) | −18.6994 | −0.691148 | ||||||||
\(733\) | −9.05895 | −0.334600 | −0.167300 | − | 0.985906i | \(-0.553505\pi\) | ||||
−0.167300 | + | 0.985906i | \(0.553505\pi\) | |||||||
\(734\) | 1.79638 | 0.0663056 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.99796 | −0.0736458 | ||||||||
\(737\) | 5.87837 | 0.216533 | ||||||||
\(738\) | −2.18143 | −0.0802995 | ||||||||
\(739\) | 7.07843 | 0.260384 | 0.130192 | − | 0.991489i | \(-0.458441\pi\) | ||||
0.130192 | + | 0.991489i | \(0.458441\pi\) | |||||||
\(740\) | 21.9310 | 0.806201 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.6779 | 0.538479 | 0.269240 | − | 0.963073i | \(-0.413228\pi\) | ||||
0.269240 | + | 0.963073i | \(0.413228\pi\) | |||||||
\(744\) | 11.5273 | 0.422613 | ||||||||
\(745\) | 4.45367 | 0.163170 | ||||||||
\(746\) | 5.40132 | 0.197756 | ||||||||
\(747\) | 2.31827 | 0.0848209 | ||||||||
\(748\) | −48.7085 | −1.78096 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.54848 | −0.202602 | ||||||||
\(751\) | −31.7113 | −1.15716 | −0.578580 | − | 0.815626i | \(-0.696393\pi\) | ||||
−0.578580 | + | 0.815626i | \(0.696393\pi\) | |||||||
\(752\) | −20.9698 | −0.764691 | ||||||||
\(753\) | 18.2358 | 0.664548 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.68467 | −0.134099 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5317 | 0.564510 | 0.282255 | − | 0.959339i | \(-0.408918\pi\) | ||||
0.282255 | + | 0.959339i | \(0.408918\pi\) | |||||||
\(758\) | 8.36688 | 0.303899 | ||||||||
\(759\) | −4.69594 | −0.170452 | ||||||||
\(760\) | −3.65839 | −0.132704 | ||||||||
\(761\) | 0.250369 | 0.00907587 | 0.00453794 | − | 0.999990i | \(-0.498556\pi\) | ||||
0.00453794 | + | 0.999990i | \(0.498556\pi\) | |||||||
\(762\) | −6.98474 | −0.253030 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −25.5961 | −0.926036 | ||||||||
\(765\) | −5.43714 | −0.196580 | ||||||||
\(766\) | −1.26781 | −0.0458077 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −11.4972 | −0.414869 | ||||||||
\(769\) | −24.0146 | −0.865988 | −0.432994 | − | 0.901397i | \(-0.642543\pi\) | ||||
−0.432994 | + | 0.901397i | \(0.642543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.50731 | 0.306383 | ||||||||
\(772\) | −35.0625 | −1.26193 | ||||||||
\(773\) | 30.5062 | 1.09723 | 0.548616 | − | 0.836074i | \(-0.315155\pi\) | ||||
0.548616 | + | 0.836074i | \(0.315155\pi\) | |||||||
\(774\) | −1.22690 | −0.0441001 | ||||||||
\(775\) | −17.7754 | −0.638510 | ||||||||
\(776\) | 8.51064 | 0.305514 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.954237 | −0.0342110 | ||||||||
\(779\) | −14.7865 | −0.529780 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.4047 | −0.801702 | ||||||||
\(782\) | 0.777163 | 0.0277913 | ||||||||
\(783\) | 40.4311 | 1.44489 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.6019 | −0.485473 | ||||||||
\(786\) | −4.59414 | −0.163868 | ||||||||
\(787\) | 19.8492 | 0.707548 | 0.353774 | − | 0.935331i | \(-0.384898\pi\) | ||||
0.353774 | + | 0.935331i | \(0.384898\pi\) | |||||||
\(788\) | 5.04149 | 0.179596 | ||||||||
\(789\) | −25.5686 | −0.910268 | ||||||||
\(790\) | 0.0630042 | 0.00224159 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.68923 | −0.237691 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6.35448 | 0.225512 | ||||||||
\(795\) | −5.86484 | −0.208004 | ||||||||
\(796\) | 38.1682 | 1.35284 | ||||||||
\(797\) | −52.2894 | −1.85219 | −0.926093 | − | 0.377296i | \(-0.876854\pi\) | ||||
−0.926093 | + | 0.377296i | \(0.876854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.1014 | 0.958777 | ||||||||
\(800\) | −10.7642 | −0.380572 | ||||||||
\(801\) | 8.44319 | 0.298326 | ||||||||
\(802\) | 0.996542 | 0.0351891 | ||||||||
\(803\) | −54.4015 | −1.91979 | ||||||||
\(804\) | −2.72283 | −0.0960269 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.5963 | 1.14744 | ||||||||
\(808\) | −0.0915664 | −0.00322129 | ||||||||
\(809\) | −2.36460 | −0.0831349 | −0.0415674 | − | 0.999136i | \(-0.513235\pi\) | ||||
−0.0415674 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(810\) | 2.70920 | 0.0951917 | ||||||||
\(811\) | 23.6646 | 0.830978 | 0.415489 | − | 0.909598i | \(-0.363610\pi\) | ||||
0.415489 | + | 0.909598i | \(0.363610\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38.4952 | −1.35008 | ||||||||
\(814\) | −15.8918 | −0.557008 | ||||||||
\(815\) | −1.00493 | −0.0352013 | ||||||||
\(816\) | 21.1654 | 0.740936 | ||||||||
\(817\) | −8.31636 | −0.290953 | ||||||||
\(818\) | 11.3275 | 0.396058 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.6330 | 0.720536 | ||||||||
\(821\) | 3.57753 | 0.124857 | 0.0624284 | − | 0.998049i | \(-0.480115\pi\) | ||||
0.0624284 | + | 0.998049i | \(0.480115\pi\) | |||||||
\(822\) | −8.05759 | −0.281041 | ||||||||
\(823\) | −29.9422 | −1.04372 | −0.521859 | − | 0.853032i | \(-0.674761\pi\) | ||||
−0.521859 | + | 0.853032i | \(0.674761\pi\) | |||||||
\(824\) | 8.19393 | 0.285449 | ||||||||
\(825\) | −25.2998 | −0.880827 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.32620 | 0.324304 | 0.162152 | − | 0.986766i | \(-0.448157\pi\) | ||||
0.162152 | + | 0.986766i | \(0.448157\pi\) | |||||||
\(828\) | −0.886819 | −0.0308191 | ||||||||
\(829\) | −38.2268 | −1.32767 | −0.663836 | − | 0.747878i | \(-0.731073\pi\) | ||||
−0.663836 | + | 0.747878i | \(0.731073\pi\) | |||||||
\(830\) | 1.28200 | 0.0444990 | ||||||||
\(831\) | 13.6877 | 0.474821 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.96568 | 0.310456 | ||||||||
\(835\) | 20.2155 | 0.699587 | ||||||||
\(836\) | −22.0270 | −0.761820 | ||||||||
\(837\) | 34.4975 | 1.19241 | ||||||||
\(838\) | −11.5587 | −0.399287 | ||||||||
\(839\) | −23.4981 | −0.811244 | −0.405622 | − | 0.914041i | \(-0.632945\pi\) | ||||
−0.405622 | + | 0.914041i | \(0.632945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2451 | 0.767071 | ||||||||
\(842\) | −8.02356 | −0.276510 | ||||||||
\(843\) | 25.9491 | 0.893736 | ||||||||
\(844\) | −24.8034 | −0.853767 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.80808 | 0.0621632 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.30806 | −0.319640 | ||||||||
\(849\) | −14.0241 | −0.481306 | ||||||||
\(850\) | 4.18704 | 0.143614 | ||||||||
\(851\) | −4.33686 | −0.148666 | ||||||||
\(852\) | 10.3777 | 0.355535 | ||||||||
\(853\) | −40.9295 | −1.40140 | −0.700700 | − | 0.713456i | \(-0.747129\pi\) | ||||
−0.700700 | + | 0.713456i | \(0.747129\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.45879 | −0.0840888 | ||||||||
\(856\) | −10.0185 | −0.342424 | ||||||||
\(857\) | 11.6620 | 0.398366 | 0.199183 | − | 0.979962i | \(-0.436171\pi\) | ||||
0.199183 | + | 0.979962i | \(0.436171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.2776 | −0.964820 | −0.482410 | − | 0.875945i | \(-0.660238\pi\) | ||||
−0.482410 | + | 0.875945i | \(0.660238\pi\) | |||||||
\(860\) | 11.6046 | 0.395715 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.58369 | −0.0539407 | ||||||||
\(863\) | 11.4442 | 0.389567 | 0.194783 | − | 0.980846i | \(-0.437600\pi\) | ||||
0.194783 | + | 0.980846i | \(0.437600\pi\) | |||||||
\(864\) | 20.8906 | 0.710713 | ||||||||
\(865\) | −7.85909 | −0.267217 | ||||||||
\(866\) | −7.31993 | −0.248741 | ||||||||
\(867\) | −2.53683 | −0.0861553 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.780871 | 0.0264892 | ||||||||
\(870\) | 5.02127 | 0.170237 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.0433887 | 0.00146933 | ||||||||
\(873\) | 5.71997 | 0.193592 | ||||||||
\(874\) | 0.351449 | 0.0118879 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 25.1985 | 0.851380 | ||||||||
\(877\) | 56.3486 | 1.90276 | 0.951378 | − | 0.308026i | \(-0.0996684\pi\) | ||||
0.951378 | + | 0.308026i | \(0.0996684\pi\) | |||||||
\(878\) | −1.14084 | −0.0385016 | ||||||||
\(879\) | −16.9835 | −0.572838 | ||||||||
\(880\) | 28.8344 | 0.972006 | ||||||||
\(881\) | 1.16418 | 0.0392221 | 0.0196111 | − | 0.999808i | \(-0.493757\pi\) | ||||
0.0196111 | + | 0.999808i | \(0.493757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.1881 | −0.410162 | −0.205081 | − | 0.978745i | \(-0.565746\pi\) | ||||
−0.205081 | + | 0.978745i | \(0.565746\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.79625 | 0.0603802 | ||||||||
\(886\) | −2.89364 | −0.0972138 | ||||||||
\(887\) | −30.6641 | −1.02960 | −0.514799 | − | 0.857311i | \(-0.672134\pi\) | ||||
−0.514799 | + | 0.857311i | \(0.672134\pi\) | |||||||
\(888\) | 15.1524 | 0.508481 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.66910 | 0.156509 | ||||||||
\(891\) | 33.5778 | 1.12490 | ||||||||
\(892\) | −4.20105 | −0.140662 | ||||||||
\(893\) | 12.2558 | 0.410125 | ||||||||
\(894\) | 1.49485 | 0.0499952 | ||||||||
\(895\) | −7.74598 | −0.258920 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.85378 | −0.195343 | ||||||||
\(899\) | 43.7245 | 1.45829 | ||||||||
\(900\) | −4.77782 | −0.159261 | ||||||||
\(901\) | 12.0297 | 0.400768 | ||||||||
\(902\) | −14.9512 | −0.497822 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.8934 | 0.395570 | ||||||||
\(905\) | 10.9002 | 0.362336 | ||||||||
\(906\) | −1.23674 | −0.0410878 | ||||||||
\(907\) | −11.6479 | −0.386763 | −0.193382 | − | 0.981124i | \(-0.561946\pi\) | ||||
−0.193382 | + | 0.981124i | \(0.561946\pi\) | |||||||
\(908\) | 51.2147 | 1.69962 | ||||||||
\(909\) | −0.0615414 | −0.00204120 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5833 | −0.880743 | −0.440371 | − | 0.897816i | \(-0.645153\pi\) | ||||
−0.440371 | + | 0.897816i | \(0.645153\pi\) | |||||||
\(912\) | 9.57141 | 0.316941 | ||||||||
\(913\) | 15.8891 | 0.525852 | ||||||||
\(914\) | 3.01553 | 0.0997450 | ||||||||
\(915\) | −14.3063 | −0.472953 | ||||||||
\(916\) | −35.8797 | −1.18550 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −8.12600 | −0.268198 | ||||||||
\(919\) | −45.7079 | −1.50777 | −0.753883 | − | 0.657009i | \(-0.771821\pi\) | ||||
−0.753883 | + | 0.657009i | \(0.771821\pi\) | |||||||
\(920\) | −1.00950 | −0.0332821 | ||||||||
\(921\) | 20.1866 | 0.665171 | ||||||||
\(922\) | 2.18809 | 0.0720609 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.3653 | −0.768246 | ||||||||
\(926\) | −1.15448 | −0.0379387 | ||||||||
\(927\) | 5.50711 | 0.180877 | ||||||||
\(928\) | 26.4782 | 0.869189 | ||||||||
\(929\) | −11.0651 | −0.363035 | −0.181518 | − | 0.983388i | \(-0.558101\pi\) | ||||
−0.181518 | + | 0.983388i | \(0.558101\pi\) | |||||||
\(930\) | 4.28437 | 0.140490 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −41.0784 | −1.34557 | ||||||||
\(933\) | 44.8380 | 1.46793 | ||||||||
\(934\) | −9.89994 | −0.323936 | ||||||||
\(935\) | −37.2655 | −1.21871 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.6584 | 1.88362 | 0.941808 | − | 0.336150i | \(-0.109125\pi\) | ||||
0.941808 | + | 0.336150i | \(0.109125\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.1848 | 0.528170 | ||||||||
\(940\) | −17.1017 | −0.557797 | ||||||||
\(941\) | −16.9745 | −0.553351 | −0.276676 | − | 0.960963i | \(-0.589233\pi\) | ||||
−0.276676 | + | 0.960963i | \(0.589233\pi\) | |||||||
\(942\) | −4.56540 | −0.148749 | ||||||||
\(943\) | −4.08018 | −0.132869 | ||||||||
\(944\) | 2.85082 | 0.0927862 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.40904 | −0.273401 | ||||||||
\(947\) | 16.6962 | 0.542552 | 0.271276 | − | 0.962502i | \(-0.412554\pi\) | ||||
0.271276 | + | 0.962502i | \(0.412554\pi\) | |||||||
\(948\) | −0.361696 | −0.0117473 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.89347 | 0.0614322 | ||||||||
\(951\) | 34.8658 | 1.13060 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.2473 | −0.591089 | −0.295545 | − | 0.955329i | \(-0.595501\pi\) | ||||
−0.295545 | + | 0.955329i | \(0.595501\pi\) | |||||||
\(954\) | 0.802570 | 0.0259842 | ||||||||
\(955\) | −19.5829 | −0.633687 | ||||||||
\(956\) | −37.7330 | −1.22037 | ||||||||
\(957\) | 62.2334 | 2.01172 | ||||||||
\(958\) | 11.6948 | 0.377841 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −11.5423 | −0.372527 | ||||||||
\(961\) | 6.30763 | 0.203472 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.73337 | −0.216980 | ||||||||
\(964\) | 6.10408 | 0.196599 | ||||||||
\(965\) | −26.8253 | −0.863537 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.5845 | 0.951374 | 0.475687 | − | 0.879615i | \(-0.342199\pi\) | ||||
0.475687 | + | 0.879615i | \(0.342199\pi\) | |||||||
\(968\) | −31.6265 | −1.01652 | ||||||||
\(969\) | −12.3701 | −0.397384 | ||||||||
\(970\) | 3.16315 | 0.101563 | ||||||||
\(971\) | −15.1301 | −0.485548 | −0.242774 | − | 0.970083i | \(-0.578057\pi\) | ||||
−0.242774 | + | 0.970083i | \(0.578057\pi\) | |||||||
\(972\) | 16.4627 | 0.528040 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.598787 | 0.0191864 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.7055 | −0.726786 | ||||||||
\(977\) | −32.4636 | −1.03860 | −0.519301 | − | 0.854591i | \(-0.673808\pi\) | ||||
−0.519301 | + | 0.854591i | \(0.673808\pi\) | |||||||
\(978\) | −0.337300 | −0.0107857 | ||||||||
\(979\) | 57.8686 | 1.84949 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0291614 | 0.000931052 0 | ||||||||
\(982\) | −2.72322 | −0.0869016 | ||||||||
\(983\) | −44.2945 | −1.41278 | −0.706388 | − | 0.707825i | \(-0.749677\pi\) | ||||
−0.706388 | + | 0.707825i | \(0.749677\pi\) | |||||||
\(984\) | 14.2556 | 0.454452 | ||||||||
\(985\) | 3.85710 | 0.122897 | ||||||||
\(986\) | −10.2994 | −0.328001 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.29482 | −0.0729710 | ||||||||
\(990\) | −2.48619 | −0.0790163 | ||||||||
\(991\) | −8.52117 | −0.270684 | −0.135342 | − | 0.990799i | \(-0.543213\pi\) | ||||
−0.135342 | + | 0.990799i | \(0.543213\pi\) | |||||||
\(992\) | 22.5923 | 0.717307 | ||||||||
\(993\) | 26.7500 | 0.848887 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.2014 | 0.925746 | ||||||||
\(996\) | −7.35976 | −0.233203 | ||||||||
\(997\) | 6.77905 | 0.214695 | 0.107347 | − | 0.994222i | \(-0.465764\pi\) | ||||
0.107347 | + | 0.994222i | \(0.465764\pi\) | |||||||
\(998\) | 12.1372 | 0.384195 | ||||||||
\(999\) | 45.3462 | 1.43469 |
(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 | 8281.2.a.cj.1.5 | 8 | ||
7.3 | odd | 6 | 1183.2.e.i.170.4 | 16 | |||
7.5 | odd | 6 | 1183.2.e.i.508.4 | 16 | |||
7.6 | odd | 2 | 8281.2.a.ck.1.5 | 8 | |||
13.5 | odd | 4 | 637.2.c.e.246.4 | 8 | |||
13.8 | odd | 4 | 637.2.c.e.246.5 | 8 | |||
13.12 | even | 2 | inner | 8281.2.a.cj.1.4 | 8 | ||
91.5 | even | 12 | 91.2.r.a.25.4 | ✓ | 16 | ||
91.12 | odd | 6 | 1183.2.e.i.508.5 | 16 | |||
91.18 | odd | 12 | 637.2.r.f.324.5 | 16 | |||
91.31 | even | 12 | 91.2.r.a.51.5 | yes | 16 | ||
91.34 | even | 4 | 637.2.c.f.246.5 | 8 | |||
91.38 | odd | 6 | 1183.2.e.i.170.5 | 16 | |||
91.44 | odd | 12 | 637.2.r.f.116.4 | 16 | |||
91.47 | even | 12 | 91.2.r.a.25.5 | yes | 16 | ||
91.60 | odd | 12 | 637.2.r.f.324.4 | 16 | |||
91.73 | even | 12 | 91.2.r.a.51.4 | yes | 16 | ||
91.83 | even | 4 | 637.2.c.f.246.4 | 8 | |||
91.86 | odd | 12 | 637.2.r.f.116.5 | 16 | |||
91.90 | odd | 2 | 8281.2.a.ck.1.4 | 8 | |||
273.5 | odd | 12 | 819.2.dl.e.298.5 | 16 | |||
273.47 | odd | 12 | 819.2.dl.e.298.4 | 16 | |||
273.122 | odd | 12 | 819.2.dl.e.415.4 | 16 | |||
273.164 | odd | 12 | 819.2.dl.e.415.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.4 | ✓ | 16 | 91.5 | even | 12 | ||
91.2.r.a.25.5 | yes | 16 | 91.47 | even | 12 | ||
91.2.r.a.51.4 | yes | 16 | 91.73 | even | 12 | ||
91.2.r.a.51.5 | yes | 16 | 91.31 | even | 12 | ||
637.2.c.e.246.4 | 8 | 13.5 | odd | 4 | |||
637.2.c.e.246.5 | 8 | 13.8 | odd | 4 | |||
637.2.c.f.246.4 | 8 | 91.83 | even | 4 | |||
637.2.c.f.246.5 | 8 | 91.34 | even | 4 | |||
637.2.r.f.116.4 | 16 | 91.44 | odd | 12 | |||
637.2.r.f.116.5 | 16 | 91.86 | odd | 12 | |||
637.2.r.f.324.4 | 16 | 91.60 | odd | 12 | |||
637.2.r.f.324.5 | 16 | 91.18 | odd | 12 | |||
819.2.dl.e.298.4 | 16 | 273.47 | odd | 12 | |||
819.2.dl.e.298.5 | 16 | 273.5 | odd | 12 | |||
819.2.dl.e.415.4 | 16 | 273.122 | odd | 12 | |||
819.2.dl.e.415.5 | 16 | 273.164 | odd | 12 | |||
1183.2.e.i.170.4 | 16 | 7.3 | odd | 6 | |||
1183.2.e.i.170.5 | 16 | 91.38 | odd | 6 | |||
1183.2.e.i.508.4 | 16 | 7.5 | odd | 6 | |||
1183.2.e.i.508.5 | 16 | 91.12 | odd | 6 | |||
8281.2.a.cj.1.4 | 8 | 13.12 | even | 2 | inner | ||
8281.2.a.cj.1.5 | 8 | 1.1 | even | 1 | trivial | ||
8281.2.a.ck.1.4 | 8 | 91.90 | odd | 2 | |||
8281.2.a.ck.1.5 | 8 | 7.6 | odd | 2 |