Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.24217.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 5x^{3} - x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 671) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.369680\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33536 | −0.944241 | −0.472121 | − | 0.881534i | \(-0.656511\pi\) | ||||
−0.472121 | + | 0.881534i | \(0.656511\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.216816 | −0.108408 | ||||||||
\(5\) | −1.70504 | −0.762517 | −0.381258 | − | 0.924469i | \(-0.624509\pi\) | ||||
−0.381258 | + | 0.924469i | \(0.624509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.82358 | −1.44518 | −0.722589 | − | 0.691278i | \(-0.757048\pi\) | ||||
−0.722589 | + | 0.691278i | \(0.757048\pi\) | |||||||
\(8\) | 2.96025 | 1.04660 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.27684 | 0.720000 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41350 | −0.392035 | −0.196018 | − | 0.980600i | \(-0.562801\pi\) | ||||
−0.196018 | + | 0.980600i | \(0.562801\pi\) | |||||||
\(14\) | 5.10585 | 1.36460 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.51936 | −0.879840 | ||||||||
\(17\) | 2.70504 | 0.656068 | 0.328034 | − | 0.944666i | \(-0.393614\pi\) | ||||
0.328034 | + | 0.944666i | \(0.393614\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.25521 | −0.517380 | −0.258690 | − | 0.965960i | \(-0.583291\pi\) | ||||
−0.258690 | + | 0.965960i | \(0.583291\pi\) | |||||||
\(20\) | 0.369680 | 0.0826630 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.33536 | 0.284699 | ||||||||
\(23\) | −2.60270 | −0.542700 | −0.271350 | − | 0.962481i | \(-0.587470\pi\) | ||||
−0.271350 | + | 0.962481i | \(0.587470\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.09284 | −0.418568 | ||||||||
\(26\) | 1.88753 | 0.370176 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.829015 | 0.156669 | ||||||||
\(29\) | 5.40314 | 1.00334 | 0.501669 | − | 0.865060i | \(-0.332720\pi\) | ||||
0.501669 | + | 0.865060i | \(0.332720\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.94062 | 0.348546 | 0.174273 | − | 0.984697i | \(-0.444243\pi\) | ||||
0.174273 | + | 0.984697i | \(0.444243\pi\) | |||||||
\(32\) | −1.22088 | −0.215824 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.61220 | −0.619487 | ||||||||
\(35\) | 6.51936 | 1.10197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.07879 | 0.341751 | 0.170875 | − | 0.985293i | \(-0.445340\pi\) | ||||
0.170875 | + | 0.985293i | \(0.445340\pi\) | |||||||
\(38\) | 3.01151 | 0.488531 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.04734 | −0.798054 | ||||||||
\(41\) | 1.68627 | 0.263352 | 0.131676 | − | 0.991293i | \(-0.457964\pi\) | ||||
0.131676 | + | 0.991293i | \(0.457964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.50699 | 0.687309 | 0.343655 | − | 0.939096i | \(-0.388335\pi\) | ||||
0.343655 | + | 0.939096i | \(0.388335\pi\) | |||||||
\(44\) | 0.216816 | 0.0326863 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.47554 | 0.512440 | ||||||||
\(47\) | 2.55218 | 0.372273 | 0.186137 | − | 0.982524i | \(-0.440403\pi\) | ||||
0.186137 | + | 0.982524i | \(0.440403\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.61978 | 1.08854 | ||||||||
\(50\) | 2.79469 | 0.395229 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.306471 | 0.0424998 | ||||||||
\(53\) | 5.43865 | 0.747056 | 0.373528 | − | 0.927619i | \(-0.378148\pi\) | ||||
0.373528 | + | 0.927619i | \(0.378148\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.70504 | 0.229907 | ||||||||
\(56\) | −11.3187 | −1.51253 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.21513 | −0.947394 | ||||||||
\(59\) | −4.50124 | −0.586011 | −0.293006 | − | 0.956111i | \(-0.594655\pi\) | ||||
−0.293006 | + | 0.956111i | \(0.594655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | −2.59143 | −0.329111 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.66904 | 1.08363 | ||||||||
\(65\) | 2.41008 | 0.298933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34599 | 0.164438 | 0.0822192 | − | 0.996614i | \(-0.473799\pi\) | ||||
0.0822192 | + | 0.996614i | \(0.473799\pi\) | |||||||
\(68\) | −0.586497 | −0.0711232 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.70568 | −1.04053 | ||||||||
\(71\) | 2.13067 | 0.252865 | 0.126432 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126432 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.4393 | −1.45591 | −0.727955 | − | 0.685625i | \(-0.759529\pi\) | ||||
−0.727955 | + | 0.685625i | \(0.759529\pi\) | |||||||
\(74\) | −2.77593 | −0.322695 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.488966 | 0.0560882 | ||||||||
\(77\) | 3.82358 | 0.435738 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.83244 | −0.431183 | −0.215592 | − | 0.976484i | \(-0.569168\pi\) | ||||
−0.215592 | + | 0.976484i | \(0.569168\pi\) | |||||||
\(80\) | 6.00064 | 0.670892 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.25178 | −0.248668 | ||||||||
\(83\) | 7.05810 | 0.774727 | 0.387364 | − | 0.921927i | \(-0.373386\pi\) | ||||
0.387364 | + | 0.921927i | \(0.373386\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.61220 | −0.500263 | ||||||||
\(86\) | −6.01845 | −0.648986 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.96025 | −0.315563 | ||||||||
\(89\) | 13.7435 | 1.45681 | 0.728405 | − | 0.685147i | \(-0.240262\pi\) | ||||
0.728405 | + | 0.685147i | \(0.240262\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.40465 | 0.566561 | ||||||||
\(92\) | 0.564307 | 0.0588331 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.40807 | −0.351516 | ||||||||
\(95\) | 3.84522 | 0.394511 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.63215 | 0.774927 | 0.387464 | − | 0.921885i | \(-0.373351\pi\) | ||||
0.387464 | + | 0.921885i | \(0.373351\pi\) | |||||||
\(98\) | −10.1751 | −1.02784 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.453762 | 0.0453762 | ||||||||
\(101\) | −0.540109 | −0.0537429 | −0.0268714 | − | 0.999639i | \(-0.508554\pi\) | ||||
−0.0268714 | + | 0.999639i | \(0.508554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.3630 | 1.41523 | 0.707613 | − | 0.706600i | \(-0.249772\pi\) | ||||
0.707613 | + | 0.706600i | \(0.249772\pi\) | |||||||
\(104\) | −4.18432 | −0.410306 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.26255 | −0.705401 | ||||||||
\(107\) | 2.64826 | 0.256017 | 0.128009 | − | 0.991773i | \(-0.459141\pi\) | ||||
0.128009 | + | 0.991773i | \(0.459141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8191 | −1.22785 | −0.613923 | − | 0.789366i | \(-0.710410\pi\) | ||||
−0.613923 | + | 0.789366i | \(0.710410\pi\) | |||||||
\(110\) | −2.27684 | −0.217088 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.4566 | 1.27152 | ||||||||
\(113\) | −11.2624 | −1.05947 | −0.529737 | − | 0.848162i | \(-0.677710\pi\) | ||||
−0.529737 | + | 0.848162i | \(0.677710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.43770 | 0.413818 | ||||||||
\(116\) | −1.17149 | −0.108770 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.01077 | 0.553336 | ||||||||
\(119\) | −10.3429 | −0.948136 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.33536 | −0.120898 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.420758 | −0.0377852 | ||||||||
\(125\) | 12.0936 | 1.08168 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.5844 | 1.91531 | 0.957654 | − | 0.287922i | \(-0.0929645\pi\) | ||||
0.957654 | + | 0.287922i | \(0.0929645\pi\) | |||||||
\(128\) | −9.13451 | −0.807384 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.21832 | −0.282265 | ||||||||
\(131\) | 0.639961 | 0.0559136 | 0.0279568 | − | 0.999609i | \(-0.491100\pi\) | ||||
0.0279568 | + | 0.999609i | \(0.491100\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.62297 | 0.747706 | ||||||||
\(134\) | −1.79738 | −0.155270 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.00758 | 0.686644 | ||||||||
\(137\) | −12.9479 | −1.10621 | −0.553106 | − | 0.833111i | \(-0.686558\pi\) | ||||
−0.553106 | + | 0.833111i | \(0.686558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.69742 | 0.568068 | 0.284034 | − | 0.958814i | \(-0.408327\pi\) | ||||
0.284034 | + | 0.958814i | \(0.408327\pi\) | |||||||
\(140\) | −1.41350 | −0.119463 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.84522 | −0.238765 | ||||||||
\(143\) | 1.41350 | 0.118203 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.21257 | −0.765062 | ||||||||
\(146\) | 16.6109 | 1.37473 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.450715 | −0.0370486 | ||||||||
\(149\) | 9.11935 | 0.747086 | 0.373543 | − | 0.927613i | \(-0.378143\pi\) | ||||
0.373543 | + | 0.927613i | \(0.378143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.89341 | 0.154084 | 0.0770418 | − | 0.997028i | \(-0.475453\pi\) | ||||
0.0770418 | + | 0.997028i | \(0.475453\pi\) | |||||||
\(152\) | −6.67596 | −0.541492 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.10585 | −0.411441 | ||||||||
\(155\) | −3.30883 | −0.265772 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.5119 | −1.47741 | −0.738705 | − | 0.674029i | \(-0.764562\pi\) | ||||
−0.738705 | + | 0.674029i | \(0.764562\pi\) | |||||||
\(158\) | 5.11768 | 0.407141 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.08166 | 0.164569 | ||||||||
\(161\) | 9.95163 | 0.784298 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4961 | 1.13542 | 0.567712 | − | 0.823227i | \(-0.307829\pi\) | ||||
0.567712 | + | 0.823227i | \(0.307829\pi\) | |||||||
\(164\) | −0.365612 | −0.0285495 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.42510 | −0.731530 | ||||||||
\(167\) | 11.4744 | 0.887919 | 0.443959 | − | 0.896047i | \(-0.353573\pi\) | ||||
0.443959 | + | 0.896047i | \(0.353573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0020 | −0.846308 | ||||||||
\(170\) | 6.15894 | 0.472369 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.977189 | −0.0745099 | ||||||||
\(173\) | −21.0366 | −1.59938 | −0.799690 | − | 0.600413i | \(-0.795003\pi\) | ||||
−0.799690 | + | 0.600413i | \(0.795003\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00215 | 0.604906 | ||||||||
\(176\) | 3.51936 | 0.265282 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.3525 | −1.37558 | ||||||||
\(179\) | 15.9191 | 1.18985 | 0.594924 | − | 0.803782i | \(-0.297182\pi\) | ||||
0.594924 | + | 0.803782i | \(0.297182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.154850 | −0.0115099 | −0.00575497 | − | 0.999983i | \(-0.501832\pi\) | ||||
−0.00575497 | + | 0.999983i | \(0.501832\pi\) | |||||||
\(182\) | −7.21714 | −0.534970 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.70462 | −0.567992 | ||||||||
\(185\) | −3.54442 | −0.260591 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.70504 | −0.197812 | ||||||||
\(188\) | −0.553353 | −0.0403574 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.13474 | −0.372513 | ||||||||
\(191\) | 12.4405 | 0.900165 | 0.450083 | − | 0.892987i | \(-0.351395\pi\) | ||||
0.450083 | + | 0.892987i | \(0.351395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.9260 | −0.786470 | −0.393235 | − | 0.919438i | \(-0.628644\pi\) | ||||
−0.393235 | + | 0.919438i | \(0.628644\pi\) | |||||||
\(194\) | −10.1917 | −0.731719 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.65209 | −0.118007 | ||||||||
\(197\) | 13.4945 | 0.961441 | 0.480720 | − | 0.876874i | \(-0.340375\pi\) | ||||
0.480720 | + | 0.876874i | \(0.340375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3413 | −0.733074 | −0.366537 | − | 0.930403i | \(-0.619457\pi\) | ||||
−0.366537 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(200\) | −6.19532 | −0.438075 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.721240 | 0.0507463 | ||||||||
\(203\) | −20.6594 | −1.45000 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.87516 | −0.200810 | ||||||||
\(206\) | −19.1797 | −1.33631 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.97462 | 0.344928 | ||||||||
\(209\) | 2.25521 | 0.155996 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.4268 | −1.33739 | −0.668697 | − | 0.743535i | \(-0.733148\pi\) | ||||
−0.668697 | + | 0.743535i | \(0.733148\pi\) | |||||||
\(212\) | −1.17919 | −0.0809870 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.53638 | −0.241742 | ||||||||
\(215\) | −7.68459 | −0.524085 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.42012 | −0.503711 | ||||||||
\(218\) | 17.1181 | 1.15938 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.369680 | −0.0249238 | ||||||||
\(221\) | −3.82358 | −0.257202 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3560 | −1.22921 | −0.614603 | − | 0.788837i | \(-0.710684\pi\) | ||||
−0.614603 | + | 0.788837i | \(0.710684\pi\) | |||||||
\(224\) | 4.66815 | 0.311904 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.0393 | 1.00040 | ||||||||
\(227\) | 7.69300 | 0.510602 | 0.255301 | − | 0.966862i | \(-0.417825\pi\) | ||||
0.255301 | + | 0.966862i | \(0.417825\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.2490 | −1.53634 | −0.768169 | − | 0.640247i | \(-0.778832\pi\) | ||||
−0.768169 | + | 0.640247i | \(0.778832\pi\) | |||||||
\(230\) | −5.92592 | −0.390744 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.9946 | 1.05010 | ||||||||
\(233\) | 14.1638 | 0.927898 | 0.463949 | − | 0.885862i | \(-0.346432\pi\) | ||||
0.463949 | + | 0.885862i | \(0.346432\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.35156 | −0.283864 | ||||||||
\(236\) | 0.975942 | 0.0635284 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.8115 | 0.895269 | ||||||||
\(239\) | −18.0080 | −1.16484 | −0.582422 | − | 0.812887i | \(-0.697895\pi\) | ||||
−0.582422 | + | 0.812887i | \(0.697895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1562 | 1.16955 | 0.584773 | − | 0.811197i | \(-0.301183\pi\) | ||||
0.584773 | + | 0.811197i | \(0.301183\pi\) | |||||||
\(242\) | −1.33536 | −0.0858401 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.216816 | −0.0138802 | ||||||||
\(245\) | −12.9920 | −0.830030 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.18774 | 0.202831 | ||||||||
\(248\) | 5.74471 | 0.364790 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16.1493 | −1.02137 | ||||||||
\(251\) | −2.13114 | −0.134517 | −0.0672583 | − | 0.997736i | \(-0.521425\pi\) | ||||
−0.0672583 | + | 0.997736i | \(0.521425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.60270 | 0.163630 | ||||||||
\(254\) | −28.8229 | −1.80851 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.14023 | −0.321264 | ||||||||
\(257\) | −5.50360 | −0.343305 | −0.171653 | − | 0.985158i | \(-0.554911\pi\) | ||||
−0.171653 | + | 0.985158i | \(0.554911\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.94842 | −0.493891 | ||||||||
\(260\) | −0.522544 | −0.0324068 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.854577 | −0.0527960 | ||||||||
\(263\) | 8.52076 | 0.525413 | 0.262706 | − | 0.964876i | \(-0.415385\pi\) | ||||
0.262706 | + | 0.964876i | \(0.415385\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.27311 | −0.569643 | ||||||||
\(266\) | −11.5148 | −0.706015 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.291832 | −0.0178265 | ||||||||
\(269\) | 6.75644 | 0.411948 | 0.205974 | − | 0.978558i | \(-0.433964\pi\) | ||||
0.205974 | + | 0.978558i | \(0.433964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.8835 | 1.08635 | 0.543174 | − | 0.839620i | \(-0.317223\pi\) | ||||
0.543174 | + | 0.839620i | \(0.317223\pi\) | |||||||
\(272\) | −9.52000 | −0.577235 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.2901 | 1.04453 | ||||||||
\(275\) | 2.09284 | 0.126203 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.4528 | −1.16881 | −0.584403 | − | 0.811464i | \(-0.698671\pi\) | ||||
−0.584403 | + | 0.811464i | \(0.698671\pi\) | |||||||
\(278\) | −8.94346 | −0.536393 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.2989 | 1.15333 | ||||||||
\(281\) | −4.87363 | −0.290736 | −0.145368 | − | 0.989378i | \(-0.546437\pi\) | ||||
−0.145368 | + | 0.989378i | \(0.546437\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.7696 | −0.699631 | −0.349815 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349815 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(284\) | −0.461965 | −0.0274126 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.88753 | −0.111612 | ||||||||
\(287\) | −6.44761 | −0.380590 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.68276 | −0.569574 | ||||||||
\(290\) | 12.3021 | 0.722403 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.69704 | 0.157832 | ||||||||
\(293\) | −6.94596 | −0.405787 | −0.202894 | − | 0.979201i | \(-0.565035\pi\) | ||||
−0.202894 | + | 0.979201i | \(0.565035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.67479 | 0.446843 | ||||||||
\(296\) | 6.15372 | 0.357678 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.1776 | −0.705430 | ||||||||
\(299\) | 3.67892 | 0.212757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.2328 | −0.993284 | ||||||||
\(302\) | −2.52838 | −0.145492 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.93688 | 0.455211 | ||||||||
\(305\) | −1.70504 | −0.0976303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6737 | −0.666256 | −0.333128 | − | 0.942882i | \(-0.608104\pi\) | ||||
−0.333128 | + | 0.942882i | \(0.608104\pi\) | |||||||
\(308\) | −0.829015 | −0.0472375 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.41848 | 0.250953 | ||||||||
\(311\) | 1.00838 | 0.0571797 | 0.0285899 | − | 0.999591i | \(-0.490898\pi\) | ||||
0.0285899 | + | 0.999591i | \(0.490898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.72938 | 0.154274 | 0.0771369 | − | 0.997021i | \(-0.475422\pi\) | ||||
0.0771369 | + | 0.997021i | \(0.475422\pi\) | |||||||
\(314\) | 24.7200 | 1.39503 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.830935 | 0.0467438 | ||||||||
\(317\) | 16.6058 | 0.932676 | 0.466338 | − | 0.884607i | \(-0.345573\pi\) | ||||
0.466338 | + | 0.884607i | \(0.345573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.40314 | −0.302518 | ||||||||
\(320\) | −14.7810 | −0.826286 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.2890 | −0.740567 | ||||||||
\(323\) | −6.10042 | −0.339437 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.95824 | 0.164093 | ||||||||
\(326\) | −19.3575 | −1.07211 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.99179 | 0.275625 | ||||||||
\(329\) | −9.75845 | −0.538001 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.5759 | −1.13095 | −0.565476 | − | 0.824765i | \(-0.691307\pi\) | ||||
−0.565476 | + | 0.824765i | \(0.691307\pi\) | |||||||
\(332\) | −1.53031 | −0.0839868 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.3225 | −0.838410 | ||||||||
\(335\) | −2.29496 | −0.125387 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.6890 | −1.01806 | −0.509028 | − | 0.860750i | \(-0.669995\pi\) | ||||
−0.509028 | + | 0.860750i | \(0.669995\pi\) | |||||||
\(338\) | 14.6916 | 0.799119 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | −1.94062 | −0.105091 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.36978 | −0.127956 | ||||||||
\(344\) | 13.3418 | 0.719341 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 28.0914 | 1.51020 | ||||||||
\(347\) | 2.11153 | 0.113353 | 0.0566765 | − | 0.998393i | \(-0.481950\pi\) | ||||
0.0566765 | + | 0.998393i | \(0.481950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3375 | −1.14217 | −0.571084 | − | 0.820891i | \(-0.693477\pi\) | ||||
−0.571084 | + | 0.820891i | \(0.693477\pi\) | |||||||
\(350\) | −10.6857 | −0.571177 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.22088 | 0.0650734 | ||||||||
\(353\) | −23.1273 | −1.23094 | −0.615471 | − | 0.788159i | \(-0.711034\pi\) | ||||
−0.615471 | + | 0.788159i | \(0.711034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.63288 | −0.192813 | ||||||||
\(356\) | −2.97982 | −0.157930 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.2577 | −1.12350 | ||||||||
\(359\) | −5.99727 | −0.316524 | −0.158262 | − | 0.987397i | \(-0.550589\pi\) | ||||
−0.158262 | + | 0.987397i | \(0.550589\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9140 | −0.732318 | ||||||||
\(362\) | 0.206781 | 0.0108682 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.17182 | −0.0614198 | ||||||||
\(365\) | 21.2095 | 1.11016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5421 | 0.811292 | 0.405646 | − | 0.914030i | \(-0.367047\pi\) | ||||
0.405646 | + | 0.914030i | \(0.367047\pi\) | |||||||
\(368\) | 9.15982 | 0.477489 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.73307 | 0.246060 | ||||||||
\(371\) | −20.7951 | −1.07963 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.9020 | 1.70360 | 0.851800 | − | 0.523868i | \(-0.175511\pi\) | ||||
0.851800 | + | 0.523868i | \(0.175511\pi\) | |||||||
\(374\) | 3.61220 | 0.186782 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.55507 | 0.389623 | ||||||||
\(377\) | −7.63736 | −0.393344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.2472 | −0.834561 | −0.417281 | − | 0.908778i | \(-0.637017\pi\) | ||||
−0.417281 | + | 0.908778i | \(0.637017\pi\) | |||||||
\(380\) | −0.833706 | −0.0427682 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.6126 | −0.849973 | ||||||||
\(383\) | −31.4959 | −1.60936 | −0.804682 | − | 0.593706i | \(-0.797664\pi\) | ||||
−0.804682 | + | 0.593706i | \(0.797664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.51936 | −0.332257 | ||||||||
\(386\) | 14.5901 | 0.742618 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.65477 | −0.0840085 | ||||||||
\(389\) | −39.1814 | −1.98658 | −0.993289 | − | 0.115662i | \(-0.963101\pi\) | ||||
−0.993289 | + | 0.115662i | \(0.963101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.04040 | −0.356048 | ||||||||
\(392\) | 22.5564 | 1.13927 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.0200 | −0.907832 | ||||||||
\(395\) | 6.53446 | 0.328784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2329 | 1.11584 | 0.557920 | − | 0.829895i | \(-0.311600\pi\) | ||||
0.557920 | + | 0.829895i | \(0.311600\pi\) | |||||||
\(398\) | 13.8093 | 0.692199 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.36546 | 0.368273 | ||||||||
\(401\) | 21.6821 | 1.08275 | 0.541377 | − | 0.840780i | \(-0.317903\pi\) | ||||
0.541377 | + | 0.840780i | \(0.317903\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.74307 | −0.136642 | ||||||||
\(404\) | 0.117105 | 0.00582617 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 27.5877 | 1.36915 | ||||||||
\(407\) | −2.07879 | −0.103042 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4770 | −1.55644 | −0.778218 | − | 0.627994i | \(-0.783876\pi\) | ||||
−0.778218 | + | 0.627994i | \(0.783876\pi\) | |||||||
\(410\) | 3.83938 | 0.189613 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.11413 | −0.153422 | ||||||||
\(413\) | 17.2108 | 0.846891 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0343 | −0.590743 | ||||||||
\(416\) | 1.72572 | 0.0846106 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.01151 | −0.147298 | ||||||||
\(419\) | −10.2586 | −0.501167 | −0.250583 | − | 0.968095i | \(-0.580622\pi\) | ||||
−0.250583 | + | 0.968095i | \(0.580622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1615 | 0.738928 | 0.369464 | − | 0.929245i | \(-0.379541\pi\) | ||||
0.369464 | + | 0.929245i | \(0.379541\pi\) | |||||||
\(422\) | 25.9417 | 1.26282 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 16.0997 | 0.781872 | ||||||||
\(425\) | −5.66122 | −0.274609 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.82358 | −0.185036 | ||||||||
\(428\) | −0.574187 | −0.0277544 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.2617 | 0.494863 | ||||||||
\(431\) | −11.3162 | −0.545081 | −0.272541 | − | 0.962144i | \(-0.587864\pi\) | ||||
−0.272541 | + | 0.962144i | \(0.587864\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.5749 | 1.13294 | 0.566469 | − | 0.824083i | \(-0.308309\pi\) | ||||
0.566469 | + | 0.824083i | \(0.308309\pi\) | |||||||
\(434\) | 9.90853 | 0.475625 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.77939 | 0.133109 | ||||||||
\(437\) | 5.86962 | 0.280782 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.4939 | 0.548572 | 0.274286 | − | 0.961648i | \(-0.411559\pi\) | ||||
0.274286 | + | 0.961648i | \(0.411559\pi\) | |||||||
\(440\) | 5.04734 | 0.240622 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.10585 | 0.242861 | ||||||||
\(443\) | 3.89812 | 0.185205 | 0.0926027 | − | 0.995703i | \(-0.470481\pi\) | ||||
0.0926027 | + | 0.995703i | \(0.470481\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.4332 | −1.11084 | ||||||||
\(446\) | 24.5118 | 1.16067 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.1468 | −1.56604 | ||||||||
\(449\) | −9.64992 | −0.455408 | −0.227704 | − | 0.973730i | \(-0.573122\pi\) | ||||
−0.227704 | + | 0.973730i | \(0.573122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.68627 | −0.0794036 | ||||||||
\(452\) | 2.44187 | 0.114856 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.2729 | −0.482132 | ||||||||
\(455\) | −9.21513 | −0.432012 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.14484 | 0.287443 | 0.143722 | − | 0.989618i | \(-0.454093\pi\) | ||||
0.143722 | + | 0.989618i | \(0.454093\pi\) | |||||||
\(458\) | 31.0458 | 1.45067 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.962166 | −0.0448612 | ||||||||
\(461\) | −29.4655 | −1.37235 | −0.686173 | − | 0.727438i | \(-0.740711\pi\) | ||||
−0.686173 | + | 0.727438i | \(0.740711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0053 | −0.929727 | −0.464864 | − | 0.885382i | \(-0.653897\pi\) | ||||
−0.464864 | + | 0.885382i | \(0.653897\pi\) | |||||||
\(464\) | −19.0156 | −0.882777 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.9137 | −0.876160 | ||||||||
\(467\) | −9.14972 | −0.423399 | −0.211699 | − | 0.977335i | \(-0.567900\pi\) | ||||
−0.211699 | + | 0.977335i | \(0.567900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.14649 | −0.237643 | ||||||||
\(470\) | 5.81089 | 0.268037 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.3248 | −0.613322 | ||||||||
\(473\) | −4.50699 | −0.207232 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.71979 | 0.216559 | ||||||||
\(476\) | 2.24252 | 0.102786 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.0472 | 1.09989 | ||||||||
\(479\) | 32.8073 | 1.49900 | 0.749501 | − | 0.662003i | \(-0.230293\pi\) | ||||
0.749501 | + | 0.662003i | \(0.230293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.93837 | −0.133978 | ||||||||
\(482\) | −24.2451 | −1.10433 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.216816 | −0.00985529 | ||||||||
\(485\) | −13.0131 | −0.590895 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.6056 | −1.06967 | −0.534835 | − | 0.844956i | \(-0.679626\pi\) | ||||
−0.534835 | + | 0.844956i | \(0.679626\pi\) | |||||||
\(488\) | 2.96025 | 0.134004 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.3490 | 0.783749 | ||||||||
\(491\) | 12.5762 | 0.567556 | 0.283778 | − | 0.958890i | \(-0.408412\pi\) | ||||
0.283778 | + | 0.958890i | \(0.408412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.6157 | 0.658259 | ||||||||
\(494\) | −4.25678 | −0.191522 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.82974 | −0.306664 | ||||||||
\(497\) | −8.14681 | −0.365434 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.9798 | 1.16301 | 0.581507 | − | 0.813542i | \(-0.302463\pi\) | ||||
0.581507 | + | 0.813542i | \(0.302463\pi\) | |||||||
\(500\) | −2.62208 | −0.117263 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.84584 | 0.127016 | ||||||||
\(503\) | 22.2224 | 0.990846 | 0.495423 | − | 0.868652i | \(-0.335013\pi\) | ||||
0.495423 | + | 0.868652i | \(0.335013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.920908 | 0.0409799 | ||||||||
\(506\) | −3.47554 | −0.154506 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.67985 | −0.207635 | ||||||||
\(509\) | −13.1445 | −0.582620 | −0.291310 | − | 0.956629i | \(-0.594091\pi\) | ||||
−0.291310 | + | 0.956629i | \(0.594091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.5627 | 2.10405 | ||||||||
\(512\) | 25.1331 | 1.11073 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.34928 | 0.324163 | ||||||||
\(515\) | −24.4894 | −1.07913 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.55218 | −0.112245 | ||||||||
\(518\) | 10.6140 | 0.466352 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.13443 | 0.312865 | ||||||||
\(521\) | −28.1051 | −1.23131 | −0.615653 | − | 0.788017i | \(-0.711108\pi\) | ||||
−0.615653 | + | 0.788017i | \(0.711108\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.7361 | 1.30027 | 0.650134 | − | 0.759820i | \(-0.274713\pi\) | ||||
0.650134 | + | 0.759820i | \(0.274713\pi\) | |||||||
\(524\) | −0.138754 | −0.00606149 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3783 | −0.496117 | ||||||||
\(527\) | 5.24946 | 0.228670 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2260 | −0.705477 | ||||||||
\(530\) | 12.3829 | 0.537880 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.86960 | −0.0810574 | ||||||||
\(533\) | −2.38355 | −0.103243 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.51539 | −0.195217 | ||||||||
\(536\) | 3.98445 | 0.172102 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.02228 | −0.388978 | ||||||||
\(539\) | −7.61978 | −0.328207 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.77397 | 0.162256 | 0.0811278 | − | 0.996704i | \(-0.474148\pi\) | ||||
0.0811278 | + | 0.996704i | \(0.474148\pi\) | |||||||
\(542\) | −23.8809 | −1.02577 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.30254 | −0.141595 | ||||||||
\(545\) | 21.8571 | 0.936254 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.3850 | −1.04263 | −0.521315 | − | 0.853365i | \(-0.674558\pi\) | ||||
−0.521315 | + | 0.853365i | \(0.674558\pi\) | |||||||
\(548\) | 2.80731 | 0.119922 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.79469 | −0.119166 | ||||||||
\(551\) | −12.1852 | −0.519107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6536 | 0.623136 | ||||||||
\(554\) | 25.9765 | 1.10363 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.45211 | −0.0615832 | ||||||||
\(557\) | −40.2900 | −1.70714 | −0.853571 | − | 0.520977i | \(-0.825568\pi\) | ||||
−0.853571 | + | 0.520977i | \(0.825568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.37064 | −0.269449 | ||||||||
\(560\) | −22.9440 | −0.969559 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.50804 | 0.274525 | ||||||||
\(563\) | 18.6626 | 0.786534 | 0.393267 | − | 0.919424i | \(-0.371345\pi\) | ||||
0.393267 | + | 0.919424i | \(0.371345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2028 | 0.807867 | ||||||||
\(566\) | 15.7167 | 0.660620 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.30732 | 0.264649 | ||||||||
\(569\) | 24.0420 | 1.00789 | 0.503946 | − | 0.863735i | \(-0.331881\pi\) | ||||
0.503946 | + | 0.863735i | \(0.331881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.78884 | −0.116710 | −0.0583548 | − | 0.998296i | \(-0.518585\pi\) | ||||
−0.0583548 | + | 0.998296i | \(0.518585\pi\) | |||||||
\(572\) | −0.306471 | −0.0128142 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.60987 | 0.359369 | ||||||||
\(575\) | 5.44703 | 0.227157 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3226 | 0.846040 | 0.423020 | − | 0.906120i | \(-0.360970\pi\) | ||||
0.423020 | + | 0.906120i | \(0.360970\pi\) | |||||||
\(578\) | 12.9300 | 0.537816 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.99744 | 0.0829390 | ||||||||
\(581\) | −26.9872 | −1.11962 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.43865 | −0.225246 | ||||||||
\(584\) | −36.8234 | −1.52376 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.27534 | 0.383161 | ||||||||
\(587\) | −45.0937 | −1.86122 | −0.930608 | − | 0.366017i | \(-0.880721\pi\) | ||||
−0.930608 | + | 0.366017i | \(0.880721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.37650 | −0.180331 | ||||||||
\(590\) | −10.2486 | −0.421928 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.31600 | −0.300686 | ||||||||
\(593\) | 15.7514 | 0.646833 | 0.323417 | − | 0.946257i | \(-0.395168\pi\) | ||||
0.323417 | + | 0.946257i | \(0.395168\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.6351 | 0.722969 | ||||||||
\(596\) | −1.97722 | −0.0809903 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.91268 | −0.200894 | ||||||||
\(599\) | 6.67520 | 0.272741 | 0.136371 | − | 0.990658i | \(-0.456456\pi\) | ||||
0.136371 | + | 0.990658i | \(0.456456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.63719 | −0.229946 | −0.114973 | − | 0.993369i | \(-0.536678\pi\) | ||||
−0.114973 | + | 0.993369i | \(0.536678\pi\) | |||||||
\(602\) | 23.0120 | 0.937900 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.410522 | −0.0167039 | ||||||||
\(605\) | −1.70504 | −0.0693197 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1058 | 0.978423 | 0.489212 | − | 0.872165i | \(-0.337285\pi\) | ||||
0.489212 | + | 0.872165i | \(0.337285\pi\) | |||||||
\(608\) | 2.75335 | 0.111663 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.27684 | 0.0921865 | ||||||||
\(611\) | −3.60751 | −0.145944 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.8312 | −1.32604 | −0.663019 | − | 0.748603i | \(-0.730725\pi\) | ||||
−0.663019 | + | 0.748603i | \(0.730725\pi\) | |||||||
\(614\) | 15.5886 | 0.629107 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3187 | 0.456045 | ||||||||
\(617\) | 25.0263 | 1.00752 | 0.503760 | − | 0.863844i | \(-0.331950\pi\) | ||||
0.503760 | + | 0.863844i | \(0.331950\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.4385 | −0.741106 | −0.370553 | − | 0.928811i | \(-0.620832\pi\) | ||||
−0.370553 | + | 0.928811i | \(0.620832\pi\) | |||||||
\(620\) | 0.717409 | 0.0288119 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.34654 | −0.0539915 | ||||||||
\(623\) | −52.5495 | −2.10535 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.1558 | −0.406233 | ||||||||
\(626\) | −3.64471 | −0.145672 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.01368 | 0.160163 | ||||||||
\(629\) | 5.62320 | 0.224212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0576 | 0.480004 | 0.240002 | − | 0.970772i | \(-0.422852\pi\) | ||||
0.240002 | + | 0.970772i | \(0.422852\pi\) | |||||||
\(632\) | −11.3450 | −0.451278 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.1747 | −0.880671 | ||||||||
\(635\) | −36.8023 | −1.46045 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.7706 | −0.426746 | ||||||||
\(638\) | 7.21513 | 0.285650 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.5747 | 0.615644 | ||||||||
\(641\) | −32.4028 | −1.27983 | −0.639917 | − | 0.768444i | \(-0.721031\pi\) | ||||
−0.639917 | + | 0.768444i | \(0.721031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.25921 | 0.0496584 | 0.0248292 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248292 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(644\) | −2.15768 | −0.0850243 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.14625 | 0.320510 | ||||||||
\(647\) | 9.53579 | 0.374890 | 0.187445 | − | 0.982275i | \(-0.439979\pi\) | ||||
0.187445 | + | 0.982275i | \(0.439979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.50124 | 0.176689 | ||||||||
\(650\) | −3.95031 | −0.154944 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.14300 | −0.123089 | ||||||||
\(653\) | −23.6093 | −0.923904 | −0.461952 | − | 0.886905i | \(-0.652851\pi\) | ||||
−0.461952 | + | 0.886905i | \(0.652851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.09116 | −0.0426351 | ||||||||
\(656\) | −5.93460 | −0.231707 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.0310 | 0.508003 | ||||||||
\(659\) | 32.2394 | 1.25587 | 0.627934 | − | 0.778267i | \(-0.283901\pi\) | ||||
0.627934 | + | 0.778267i | \(0.283901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.2262 | 1.17566 | 0.587831 | − | 0.808984i | \(-0.299982\pi\) | ||||
0.587831 | + | 0.808984i | \(0.299982\pi\) | |||||||
\(662\) | 27.4762 | 1.06789 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.8937 | 0.810834 | ||||||||
\(665\) | −14.7025 | −0.570138 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.0627 | −0.544512 | ||||||||
\(668\) | −2.48785 | −0.0962576 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.06460 | 0.118396 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.0579 | −1.58267 | −0.791333 | − | 0.611385i | \(-0.790613\pi\) | ||||
−0.791333 | + | 0.611385i | \(0.790613\pi\) | |||||||
\(674\) | 24.9566 | 0.961291 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.38542 | 0.0917467 | ||||||||
\(677\) | −23.1892 | −0.891232 | −0.445616 | − | 0.895224i | \(-0.647015\pi\) | ||||
−0.445616 | + | 0.895224i | \(0.647015\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1822 | −1.11991 | ||||||||
\(680\) | −13.6532 | −0.523578 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.59143 | 0.0992308 | ||||||||
\(683\) | −33.4783 | −1.28101 | −0.640506 | − | 0.767953i | \(-0.721276\pi\) | ||||
−0.640506 | + | 0.767953i | \(0.721276\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.0767 | 0.843506 | ||||||||
\(686\) | 3.16451 | 0.120821 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.8617 | −0.604722 | ||||||||
\(689\) | −7.68755 | −0.292872 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4751 | 0.398493 | 0.199247 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199247 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(692\) | 4.56107 | 0.173386 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.81965 | −0.107033 | ||||||||
\(695\) | −11.4194 | −0.433161 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.56144 | 0.172777 | ||||||||
\(698\) | 28.4932 | 1.07848 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.73500 | −0.0655767 | ||||||||
\(701\) | 6.90150 | 0.260666 | 0.130333 | − | 0.991470i | \(-0.458395\pi\) | ||||
0.130333 | + | 0.991470i | \(0.458395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.68810 | −0.176815 | ||||||||
\(704\) | −8.66904 | −0.326727 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.8833 | 1.16231 | ||||||||
\(707\) | 2.06515 | 0.0776680 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.7827 | −0.968290 | −0.484145 | − | 0.874988i | \(-0.660869\pi\) | ||||
−0.484145 | + | 0.874988i | \(0.660869\pi\) | |||||||
\(710\) | 4.85120 | 0.182062 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 40.6842 | 1.52470 | ||||||||
\(713\) | −5.05085 | −0.189156 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.41008 | −0.0901318 | ||||||||
\(716\) | −3.45152 | −0.128989 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.00851 | 0.298875 | ||||||||
\(719\) | −22.4484 | −0.837182 | −0.418591 | − | 0.908175i | \(-0.637476\pi\) | ||||
−0.418591 | + | 0.908175i | \(0.637476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.9180 | −2.04525 | ||||||||
\(722\) | 18.5802 | 0.691485 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.0335741 | 0.00124777 | ||||||||
\(725\) | −11.3079 | −0.419965 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.2835 | 0.641011 | 0.320505 | − | 0.947247i | \(-0.396147\pi\) | ||||
0.320505 | + | 0.947247i | \(0.396147\pi\) | |||||||
\(728\) | 15.9991 | 0.592965 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28.3223 | −1.04825 | ||||||||
\(731\) | 12.1916 | 0.450922 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.8357 | −0.547969 | −0.273984 | − | 0.961734i | \(-0.588342\pi\) | ||||
−0.273984 | + | 0.961734i | \(0.588342\pi\) | |||||||
\(734\) | −20.7543 | −0.766055 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.17759 | 0.117128 | ||||||||
\(737\) | −1.34599 | −0.0495801 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.5903 | 1.64028 | 0.820141 | − | 0.572162i | \(-0.193895\pi\) | ||||
0.820141 | + | 0.572162i | \(0.193895\pi\) | |||||||
\(740\) | 0.768487 | 0.0282502 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27.7690 | 1.01943 | ||||||||
\(743\) | 7.79582 | 0.286001 | 0.143000 | − | 0.989723i | \(-0.454325\pi\) | ||||
0.143000 | + | 0.989723i | \(0.454325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.5489 | −0.569666 | ||||||||
\(746\) | −43.9359 | −1.60861 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.586497 | 0.0214444 | ||||||||
\(749\) | −10.1258 | −0.369990 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4136 | 1.00034 | 0.500169 | − | 0.865928i | \(-0.333271\pi\) | ||||
0.500169 | + | 0.865928i | \(0.333271\pi\) | |||||||
\(752\) | −8.98202 | −0.327541 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.1986 | 0.371412 | ||||||||
\(755\) | −3.22834 | −0.117491 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.2330 | −0.626345 | −0.313172 | − | 0.949696i | \(-0.601392\pi\) | ||||
−0.313172 | + | 0.949696i | \(0.601392\pi\) | |||||||
\(758\) | 21.6958 | 0.788028 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.3828 | 0.412897 | ||||||||
\(761\) | −48.2896 | −1.75050 | −0.875248 | − | 0.483674i | \(-0.839302\pi\) | ||||
−0.875248 | + | 0.483674i | \(0.839302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 49.0149 | 1.77446 | ||||||||
\(764\) | −2.69731 | −0.0975853 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.0583 | 1.51963 | ||||||||
\(767\) | 6.36251 | 0.229737 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.13048 | −0.148949 | −0.0744745 | − | 0.997223i | \(-0.523728\pi\) | ||||
−0.0744745 | + | 0.997223i | \(0.523728\pi\) | |||||||
\(770\) | 8.70568 | 0.313731 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.36893 | 0.0852598 | ||||||||
\(773\) | 2.03774 | 0.0732926 | 0.0366463 | − | 0.999328i | \(-0.488333\pi\) | ||||
0.0366463 | + | 0.999328i | \(0.488333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.06141 | −0.145890 | ||||||||
\(776\) | 22.5930 | 0.811043 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 52.3213 | 1.87581 | ||||||||
\(779\) | −3.80290 | −0.136253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.13067 | −0.0762415 | ||||||||
\(782\) | 9.40146 | 0.336196 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.8167 | −0.957740 | ||||||||
\(785\) | 31.5635 | 1.12655 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.5037 | 1.12299 | 0.561494 | − | 0.827481i | \(-0.310227\pi\) | ||||
0.561494 | + | 0.827481i | \(0.310227\pi\) | |||||||
\(788\) | −2.92582 | −0.104228 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.72585 | −0.310452 | ||||||||
\(791\) | 43.0626 | 1.53113 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.41350 | −0.0501950 | ||||||||
\(794\) | −29.6890 | −1.05362 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.24216 | 0.0794712 | ||||||||
\(797\) | 40.5246 | 1.43545 | 0.717727 | − | 0.696325i | \(-0.245183\pi\) | ||||
0.717727 | + | 0.696325i | \(0.245183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.90373 | 0.244237 | ||||||||
\(800\) | 2.55512 | 0.0903370 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.9534 | −1.02238 | ||||||||
\(803\) | 12.4393 | 0.438973 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.9679 | −0.598040 | ||||||||
\(806\) | 3.66299 | 0.129023 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.59886 | −0.0562476 | ||||||||
\(809\) | −45.9846 | −1.61673 | −0.808367 | − | 0.588679i | \(-0.799648\pi\) | ||||
−0.808367 | + | 0.588679i | \(0.799648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5553 | −0.756909 | −0.378454 | − | 0.925620i | \(-0.623544\pi\) | ||||
−0.378454 | + | 0.925620i | \(0.623544\pi\) | |||||||
\(812\) | 4.47929 | 0.157192 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.77593 | 0.0972963 | ||||||||
\(815\) | −24.7165 | −0.865780 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.1642 | −0.355600 | ||||||||
\(818\) | 42.0331 | 1.46965 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.623383 | 0.0217695 | ||||||||
\(821\) | 31.9758 | 1.11596 | 0.557982 | − | 0.829853i | \(-0.311576\pi\) | ||||
0.557982 | + | 0.829853i | \(0.311576\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.65642 | 0.162313 | 0.0811563 | − | 0.996701i | \(-0.474139\pi\) | ||||
0.0811563 | + | 0.996701i | \(0.474139\pi\) | |||||||
\(824\) | 42.5179 | 1.48118 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.9827 | −0.799669 | ||||||||
\(827\) | −48.3361 | −1.68081 | −0.840405 | − | 0.541959i | \(-0.817683\pi\) | ||||
−0.840405 | + | 0.541959i | \(0.817683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.7090 | −0.788717 | −0.394358 | − | 0.918957i | \(-0.629033\pi\) | ||||
−0.394358 | + | 0.918957i | \(0.629033\pi\) | |||||||
\(830\) | 16.0702 | 0.557804 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.2537 | −0.424821 | ||||||||
\(833\) | 20.6118 | 0.714157 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.5644 | −0.677053 | ||||||||
\(836\) | −0.488966 | −0.0169112 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.6990 | 0.473222 | ||||||||
\(839\) | −7.55301 | −0.260759 | −0.130379 | − | 0.991464i | \(-0.541620\pi\) | ||||
−0.130379 | + | 0.991464i | \(0.541620\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.193941 | 0.00668761 | ||||||||
\(842\) | −20.2461 | −0.697727 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.21204 | 0.144985 | ||||||||
\(845\) | 18.7589 | 0.645324 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.82358 | −0.131380 | ||||||||
\(848\) | −19.1406 | −0.657289 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.55976 | 0.259298 | ||||||||
\(851\) | −5.41046 | −0.185468 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.3846 | −1.00611 | −0.503054 | − | 0.864255i | \(-0.667790\pi\) | ||||
−0.503054 | + | 0.864255i | \(0.667790\pi\) | |||||||
\(854\) | 5.10585 | 0.174719 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.83951 | 0.267949 | ||||||||
\(857\) | 7.21276 | 0.246383 | 0.123192 | − | 0.992383i | \(-0.460687\pi\) | ||||
0.123192 | + | 0.992383i | \(0.460687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9437 | 0.919308 | 0.459654 | − | 0.888098i | \(-0.347973\pi\) | ||||
0.459654 | + | 0.888098i | \(0.347973\pi\) | |||||||
\(860\) | 1.66615 | 0.0568151 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.1112 | 0.514689 | ||||||||
\(863\) | −0.507609 | −0.0172792 | −0.00863961 | − | 0.999963i | \(-0.502750\pi\) | ||||
−0.00863961 | + | 0.999963i | \(0.502750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.8682 | 1.21955 | ||||||||
\(866\) | −31.4810 | −1.06977 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.60880 | 0.0546064 | ||||||||
\(869\) | 3.83244 | 0.130007 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.90256 | −0.0644657 | ||||||||
\(872\) | −37.9477 | −1.28507 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.83805 | −0.265126 | ||||||||
\(875\) | −46.2408 | −1.56322 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.3897 | 1.46517 | 0.732583 | − | 0.680677i | \(-0.238314\pi\) | ||||
0.732583 | + | 0.680677i | \(0.238314\pi\) | |||||||
\(878\) | −15.3484 | −0.517984 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.00064 | −0.202282 | ||||||||
\(881\) | 28.8083 | 0.970575 | 0.485288 | − | 0.874355i | \(-0.338715\pi\) | ||||
0.485288 | + | 0.874355i | \(0.338715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.4794 | −1.12667 | −0.563336 | − | 0.826228i | \(-0.690482\pi\) | ||||
−0.563336 | + | 0.826228i | \(0.690482\pi\) | |||||||
\(884\) | 0.829015 | 0.0278828 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.20539 | −0.174879 | ||||||||
\(887\) | −40.9969 | −1.37654 | −0.688271 | − | 0.725453i | \(-0.741630\pi\) | ||||
−0.688271 | + | 0.725453i | \(0.741630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −82.5298 | −2.76796 | ||||||||
\(890\) | 31.2918 | 1.04890 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.97987 | 0.133256 | ||||||||
\(893\) | −5.75568 | −0.192607 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.1427 | −0.907279 | ||||||||
\(896\) | 34.9265 | 1.16681 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.8861 | 0.430015 | ||||||||
\(899\) | 10.4854 | 0.349709 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7118 | 0.490120 | ||||||||
\(902\) | 2.25178 | 0.0749761 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.3394 | −1.10885 | ||||||||
\(905\) | 0.264026 | 0.00877652 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.25129 | −0.307184 | −0.153592 | − | 0.988134i | \(-0.549084\pi\) | ||||
−0.153592 | + | 0.988134i | \(0.549084\pi\) | |||||||
\(908\) | −1.66797 | −0.0553534 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.3055 | 0.407924 | ||||||||
\(911\) | 45.2640 | 1.49966 | 0.749831 | − | 0.661629i | \(-0.230135\pi\) | ||||
0.749831 | + | 0.661629i | \(0.230135\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.05810 | −0.233589 | ||||||||
\(914\) | −8.20556 | −0.271416 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.04077 | 0.166552 | ||||||||
\(917\) | −2.44694 | −0.0808052 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.4379 | −1.82873 | −0.914364 | − | 0.404892i | \(-0.867309\pi\) | ||||
−0.914364 | + | 0.404892i | \(0.867309\pi\) | |||||||
\(920\) | 13.1367 | 0.433104 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 39.3470 | 1.29583 | ||||||||
\(923\) | −3.01172 | −0.0991318 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.35057 | −0.143046 | ||||||||
\(926\) | 26.7143 | 0.877887 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.59661 | −0.216544 | ||||||||
\(929\) | 18.7740 | 0.615955 | 0.307977 | − | 0.951394i | \(-0.400348\pi\) | ||||
0.307977 | + | 0.951394i | \(0.400348\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.1842 | −0.563189 | ||||||||
\(932\) | −3.07093 | −0.100592 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12.2182 | 0.399791 | ||||||||
\(935\) | 4.61220 | 0.150835 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.9016 | −0.617488 | −0.308744 | − | 0.951145i | \(-0.599909\pi\) | ||||
−0.308744 | + | 0.951145i | \(0.599909\pi\) | |||||||
\(938\) | 6.87241 | 0.224392 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.943489 | 0.0307732 | ||||||||
\(941\) | 40.7528 | 1.32850 | 0.664252 | − | 0.747509i | \(-0.268750\pi\) | ||||
0.664252 | + | 0.747509i | \(0.268750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.38886 | −0.142921 | ||||||||
\(944\) | 15.8415 | 0.515596 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.01845 | 0.195677 | ||||||||
\(947\) | −45.2880 | −1.47166 | −0.735831 | − | 0.677166i | \(-0.763208\pi\) | ||||
−0.735831 | + | 0.677166i | \(0.763208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.5830 | 0.570768 | ||||||||
\(950\) | −6.30261 | −0.204484 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −30.6176 | −0.992324 | ||||||||
\(953\) | 28.1077 | 0.910498 | 0.455249 | − | 0.890364i | \(-0.349550\pi\) | ||||
0.455249 | + | 0.890364i | \(0.349550\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.2116 | −0.686391 | ||||||||
\(956\) | 3.90444 | 0.126279 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −43.8095 | −1.41542 | ||||||||
\(959\) | 49.5073 | 1.59867 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.2340 | −0.878516 | ||||||||
\(962\) | 3.92378 | 0.126508 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.93657 | −0.126788 | ||||||||
\(965\) | 18.6292 | 0.599697 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.7895 | −0.957966 | −0.478983 | − | 0.877824i | \(-0.658994\pi\) | ||||
−0.478983 | + | 0.877824i | \(0.658994\pi\) | |||||||
\(968\) | 2.96025 | 0.0951459 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.3772 | 0.557948 | ||||||||
\(971\) | −28.0668 | −0.900706 | −0.450353 | − | 0.892851i | \(-0.648702\pi\) | ||||
−0.450353 | + | 0.892851i | \(0.648702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.6081 | −0.820959 | ||||||||
\(974\) | 31.5219 | 1.01003 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.51936 | −0.112652 | ||||||||
\(977\) | 21.3268 | 0.682306 | 0.341153 | − | 0.940008i | \(-0.389183\pi\) | ||||
0.341153 | + | 0.940008i | \(0.389183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.7435 | −0.439245 | ||||||||
\(980\) | 2.81688 | 0.0899820 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.7938 | −0.535910 | ||||||||
\(983\) | −53.8387 | −1.71719 | −0.858594 | − | 0.512657i | \(-0.828661\pi\) | ||||
−0.858594 | + | 0.512657i | \(0.828661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.0086 | −0.733115 | ||||||||
\(986\) | −19.5172 | −0.621555 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.691154 | −0.0219886 | ||||||||
\(989\) | −11.7303 | −0.373003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.4123 | 0.775484 | 0.387742 | − | 0.921768i | \(-0.373255\pi\) | ||||
0.387742 | + | 0.921768i | \(0.373255\pi\) | |||||||
\(992\) | −2.36927 | −0.0752245 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.8789 | 0.345058 | ||||||||
\(995\) | 17.6323 | 0.558981 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.4541 | 1.40788 | 0.703938 | − | 0.710262i | \(-0.251423\pi\) | ||||
0.703938 | + | 0.710262i | \(0.251423\pi\) | |||||||
\(998\) | −34.6923 | −1.09817 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.a.1.1 | 5 | ||
3.2 | odd | 2 | 671.2.a.a.1.5 | ✓ | 5 | ||
33.32 | even | 2 | 7381.2.a.g.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.a.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
6039.2.a.a.1.1 | 5 | 1.1 | even | 1 | trivial | ||
7381.2.a.g.1.1 | 5 | 33.32 | even | 2 |