Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5025,2,Mod(1,5025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5025, 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("5025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5025 = 3 \cdot 5^{2} \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5025.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: | \(40.1248270157\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 15x^{4} + 14x^{3} - 15x^{2} - 6x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1005) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.42013\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.42013 | 1.00419 | 0.502093 | − | 0.864814i | \(-0.332564\pi\) | ||||
0.502093 | + | 0.864814i | \(0.332564\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.0167760 | 0.00838802 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.42013 | −0.579767 | ||||||||
\(7\) | −3.66225 | −1.38420 | −0.692100 | − | 0.721802i | \(-0.743314\pi\) | ||||
−0.692100 | + | 0.721802i | \(0.743314\pi\) | |||||||
\(8\) | −2.81644 | −0.995762 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.26380 | 0.984072 | 0.492036 | − | 0.870575i | \(-0.336253\pi\) | ||||
0.492036 | + | 0.870575i | \(0.336253\pi\) | |||||||
\(12\) | −0.0167760 | −0.00484282 | ||||||||
\(13\) | 2.79966 | 0.776487 | 0.388244 | − | 0.921557i | \(-0.373082\pi\) | ||||
0.388244 | + | 0.921557i | \(0.373082\pi\) | |||||||
\(14\) | −5.20088 | −1.38999 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.03327 | −1.00832 | ||||||||
\(17\) | −2.12064 | −0.514331 | −0.257165 | − | 0.966367i | \(-0.582789\pi\) | ||||
−0.257165 | + | 0.966367i | \(0.582789\pi\) | |||||||
\(18\) | 1.42013 | 0.334728 | ||||||||
\(19\) | 6.67086 | 1.53040 | 0.765200 | − | 0.643793i | \(-0.222640\pi\) | ||||
0.765200 | + | 0.643793i | \(0.222640\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.66225 | 0.799168 | ||||||||
\(22\) | 4.63502 | 0.988190 | ||||||||
\(23\) | 1.64333 | 0.342658 | 0.171329 | − | 0.985214i | \(-0.445194\pi\) | ||||
0.171329 | + | 0.985214i | \(0.445194\pi\) | |||||||
\(24\) | 2.81644 | 0.574904 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.97589 | 0.779737 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.0614380 | −0.0116107 | ||||||||
\(29\) | 0.0189191 | 0.00351319 | 0.00175660 | − | 0.999998i | \(-0.499441\pi\) | ||||
0.00175660 | + | 0.999998i | \(0.499441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.5995 | −1.90373 | −0.951866 | − | 0.306516i | \(-0.900837\pi\) | ||||
−0.951866 | + | 0.306516i | \(0.900837\pi\) | |||||||
\(32\) | −0.0948971 | −0.0167756 | ||||||||
\(33\) | −3.26380 | −0.568154 | ||||||||
\(34\) | −3.01159 | −0.516483 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0167760 | 0.00279601 | ||||||||
\(37\) | 1.71472 | 0.281898 | 0.140949 | − | 0.990017i | \(-0.454985\pi\) | ||||
0.140949 | + | 0.990017i | \(0.454985\pi\) | |||||||
\(38\) | 9.47350 | 1.53681 | ||||||||
\(39\) | −2.79966 | −0.448305 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.81274 | 0.283102 | 0.141551 | − | 0.989931i | \(-0.454791\pi\) | ||||
0.141551 | + | 0.989931i | \(0.454791\pi\) | |||||||
\(42\) | 5.20088 | 0.802513 | ||||||||
\(43\) | 9.11183 | 1.38954 | 0.694770 | − | 0.719232i | \(-0.255506\pi\) | ||||
0.694770 | + | 0.719232i | \(0.255506\pi\) | |||||||
\(44\) | 0.0547536 | 0.00825441 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.33375 | 0.344092 | ||||||||
\(47\) | −3.76947 | −0.549834 | −0.274917 | − | 0.961468i | \(-0.588650\pi\) | ||||
−0.274917 | + | 0.961468i | \(0.588650\pi\) | |||||||
\(48\) | 4.03327 | 0.582152 | ||||||||
\(49\) | 6.41206 | 0.916009 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12064 | 0.296949 | ||||||||
\(52\) | 0.0469673 | 0.00651319 | ||||||||
\(53\) | −11.3124 | −1.55387 | −0.776936 | − | 0.629579i | \(-0.783227\pi\) | ||||
−0.776936 | + | 0.629579i | \(0.783227\pi\) | |||||||
\(54\) | −1.42013 | −0.193256 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.3145 | 1.37833 | ||||||||
\(57\) | −6.67086 | −0.883577 | ||||||||
\(58\) | 0.0268676 | 0.00352789 | ||||||||
\(59\) | 6.08164 | 0.791762 | 0.395881 | − | 0.918302i | \(-0.370439\pi\) | ||||
0.395881 | + | 0.918302i | \(0.370439\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.18949 | −0.920519 | −0.460260 | − | 0.887784i | \(-0.652244\pi\) | ||||
−0.460260 | + | 0.887784i | \(0.652244\pi\) | |||||||
\(62\) | −15.0527 | −1.91170 | ||||||||
\(63\) | −3.66225 | −0.461400 | ||||||||
\(64\) | 7.93177 | 0.991472 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.63502 | −0.570532 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | −0.0355759 | −0.00431422 | ||||||||
\(69\) | −1.64333 | −0.197834 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.11351 | −0.962896 | −0.481448 | − | 0.876475i | \(-0.659889\pi\) | ||||
−0.481448 | + | 0.876475i | \(0.659889\pi\) | |||||||
\(72\) | −2.81644 | −0.331921 | ||||||||
\(73\) | −5.96747 | −0.698440 | −0.349220 | − | 0.937041i | \(-0.613553\pi\) | ||||
−0.349220 | + | 0.937041i | \(0.613553\pi\) | |||||||
\(74\) | 2.43513 | 0.283078 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.111911 | 0.0128370 | ||||||||
\(77\) | −11.9528 | −1.36215 | ||||||||
\(78\) | −3.97589 | −0.450181 | ||||||||
\(79\) | −6.08780 | −0.684932 | −0.342466 | − | 0.939530i | \(-0.611262\pi\) | ||||
−0.342466 | + | 0.939530i | \(0.611262\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.57432 | 0.284287 | ||||||||
\(83\) | 1.95253 | 0.214318 | 0.107159 | − | 0.994242i | \(-0.465825\pi\) | ||||
0.107159 | + | 0.994242i | \(0.465825\pi\) | |||||||
\(84\) | 0.0614380 | 0.00670344 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.9400 | 1.39536 | ||||||||
\(87\) | −0.0189191 | −0.00202834 | ||||||||
\(88\) | −9.19229 | −0.979902 | ||||||||
\(89\) | 16.2631 | 1.72388 | 0.861942 | − | 0.507007i | \(-0.169248\pi\) | ||||
0.861942 | + | 0.507007i | \(0.169248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2531 | −1.07481 | ||||||||
\(92\) | 0.0275686 | 0.00287422 | ||||||||
\(93\) | 10.5995 | 1.09912 | ||||||||
\(94\) | −5.35315 | −0.552135 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0948971 | 0.00968539 | ||||||||
\(97\) | −4.43089 | −0.449888 | −0.224944 | − | 0.974372i | \(-0.572220\pi\) | ||||
−0.224944 | + | 0.974372i | \(0.572220\pi\) | |||||||
\(98\) | 9.10598 | 0.919843 | ||||||||
\(99\) | 3.26380 | 0.328024 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.6077 | −1.55302 | −0.776510 | − | 0.630105i | \(-0.783012\pi\) | ||||
−0.776510 | + | 0.630105i | \(0.783012\pi\) | |||||||
\(102\) | 3.01159 | 0.298192 | ||||||||
\(103\) | 1.97784 | 0.194882 | 0.0974411 | − | 0.995241i | \(-0.468934\pi\) | ||||
0.0974411 | + | 0.995241i | \(0.468934\pi\) | |||||||
\(104\) | −7.88509 | −0.773197 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.0651 | −1.56038 | ||||||||
\(107\) | −14.1608 | −1.36898 | −0.684488 | − | 0.729024i | \(-0.739974\pi\) | ||||
−0.684488 | + | 0.729024i | \(0.739974\pi\) | |||||||
\(108\) | −0.0167760 | −0.00161427 | ||||||||
\(109\) | 7.47058 | 0.715552 | 0.357776 | − | 0.933807i | \(-0.383535\pi\) | ||||
0.357776 | + | 0.933807i | \(0.383535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.71472 | −0.162754 | ||||||||
\(112\) | 14.7708 | 1.39571 | ||||||||
\(113\) | −9.85628 | −0.927200 | −0.463600 | − | 0.886044i | \(-0.653443\pi\) | ||||
−0.463600 | + | 0.886044i | \(0.653443\pi\) | |||||||
\(114\) | −9.47350 | −0.887275 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.000317388 0 | 2.94687e−5 0 | ||||||||
\(117\) | 2.79966 | 0.258829 | ||||||||
\(118\) | 8.63674 | 0.795076 | ||||||||
\(119\) | 7.76631 | 0.711937 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.347627 | −0.0316025 | ||||||||
\(122\) | −10.2100 | −0.924372 | ||||||||
\(123\) | −1.81274 | −0.163449 | ||||||||
\(124\) | −0.177818 | −0.0159685 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.20088 | −0.463331 | ||||||||
\(127\) | −2.58185 | −0.229102 | −0.114551 | − | 0.993417i | \(-0.536543\pi\) | ||||
−0.114551 | + | 0.993417i | \(0.536543\pi\) | |||||||
\(128\) | 11.4540 | 1.01240 | ||||||||
\(129\) | −9.11183 | −0.802252 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.97007 | −0.608978 | −0.304489 | − | 0.952516i | \(-0.598486\pi\) | ||||
−0.304489 | + | 0.952516i | \(0.598486\pi\) | |||||||
\(132\) | −0.0547536 | −0.00476569 | ||||||||
\(133\) | −24.4303 | −2.11838 | ||||||||
\(134\) | −1.42013 | −0.122681 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.97266 | 0.512151 | ||||||||
\(137\) | −11.0644 | −0.945295 | −0.472648 | − | 0.881251i | \(-0.656702\pi\) | ||||
−0.472648 | + | 0.881251i | \(0.656702\pi\) | |||||||
\(138\) | −2.33375 | −0.198662 | ||||||||
\(139\) | −3.51297 | −0.297966 | −0.148983 | − | 0.988840i | \(-0.547600\pi\) | ||||
−0.148983 | + | 0.988840i | \(0.547600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.76947 | 0.317447 | ||||||||
\(142\) | −11.5223 | −0.966926 | ||||||||
\(143\) | 9.13754 | 0.764119 | ||||||||
\(144\) | −4.03327 | −0.336106 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.47460 | −0.701363 | ||||||||
\(147\) | −6.41206 | −0.528858 | ||||||||
\(148\) | 0.0287662 | 0.00236457 | ||||||||
\(149\) | −7.82118 | −0.640736 | −0.320368 | − | 0.947293i | \(-0.603807\pi\) | ||||
−0.320368 | + | 0.947293i | \(0.603807\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.04607 | −0.654780 | −0.327390 | − | 0.944889i | \(-0.606169\pi\) | ||||
−0.327390 | + | 0.944889i | \(0.606169\pi\) | |||||||
\(152\) | −18.7881 | −1.52391 | ||||||||
\(153\) | −2.12064 | −0.171444 | ||||||||
\(154\) | −16.9746 | −1.36785 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0469673 | −0.00376039 | ||||||||
\(157\) | 2.78927 | 0.222608 | 0.111304 | − | 0.993786i | \(-0.464497\pi\) | ||||
0.111304 | + | 0.993786i | \(0.464497\pi\) | |||||||
\(158\) | −8.64549 | −0.687798 | ||||||||
\(159\) | 11.3124 | 0.897129 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.01828 | −0.474307 | ||||||||
\(162\) | 1.42013 | 0.111576 | ||||||||
\(163\) | −21.6024 | −1.69203 | −0.846016 | − | 0.533158i | \(-0.821005\pi\) | ||||
−0.846016 | + | 0.533158i | \(0.821005\pi\) | |||||||
\(164\) | 0.0304105 | 0.00237466 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.77285 | 0.215215 | ||||||||
\(167\) | −18.3413 | −1.41930 | −0.709648 | − | 0.704557i | \(-0.751146\pi\) | ||||
−0.709648 | + | 0.704557i | \(0.751146\pi\) | |||||||
\(168\) | −10.3145 | −0.795781 | ||||||||
\(169\) | −5.16188 | −0.397068 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.67086 | 0.510133 | ||||||||
\(172\) | 0.152860 | 0.0116555 | ||||||||
\(173\) | 21.7221 | 1.65150 | 0.825751 | − | 0.564035i | \(-0.190752\pi\) | ||||
0.825751 | + | 0.564035i | \(0.190752\pi\) | |||||||
\(174\) | −0.0268676 | −0.00203683 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.1638 | −0.992257 | ||||||||
\(177\) | −6.08164 | −0.457124 | ||||||||
\(178\) | 23.0957 | 1.73110 | ||||||||
\(179\) | −16.1880 | −1.20995 | −0.604973 | − | 0.796246i | \(-0.706816\pi\) | ||||
−0.604973 | + | 0.796246i | \(0.706816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.670680 | −0.0498513 | −0.0249256 | − | 0.999689i | \(-0.507935\pi\) | ||||
−0.0249256 | + | 0.999689i | \(0.507935\pi\) | |||||||
\(182\) | −14.5607 | −1.07931 | ||||||||
\(183\) | 7.18949 | 0.531462 | ||||||||
\(184\) | −4.62834 | −0.341206 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.0527 | 1.10372 | ||||||||
\(187\) | −6.92134 | −0.506138 | ||||||||
\(188\) | −0.0632368 | −0.00461202 | ||||||||
\(189\) | 3.66225 | 0.266389 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.6974 | 0.774036 | 0.387018 | − | 0.922072i | \(-0.373505\pi\) | ||||
0.387018 | + | 0.922072i | \(0.373505\pi\) | |||||||
\(192\) | −7.93177 | −0.572427 | ||||||||
\(193\) | 7.09859 | 0.510968 | 0.255484 | − | 0.966813i | \(-0.417765\pi\) | ||||
0.255484 | + | 0.966813i | \(0.417765\pi\) | |||||||
\(194\) | −6.29244 | −0.451771 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.107569 | 0.00768350 | ||||||||
\(197\) | 13.9254 | 0.992147 | 0.496074 | − | 0.868281i | \(-0.334775\pi\) | ||||
0.496074 | + | 0.868281i | \(0.334775\pi\) | |||||||
\(198\) | 4.63502 | 0.329397 | ||||||||
\(199\) | −23.9299 | −1.69635 | −0.848173 | − | 0.529719i | \(-0.822297\pi\) | ||||
−0.848173 | + | 0.529719i | \(0.822297\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | −22.1649 | −1.55952 | ||||||||
\(203\) | −0.0692865 | −0.00486296 | ||||||||
\(204\) | 0.0355759 | 0.00249081 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.80879 | 0.195698 | ||||||||
\(207\) | 1.64333 | 0.114219 | ||||||||
\(208\) | −11.2918 | −0.782946 | ||||||||
\(209\) | 21.7723 | 1.50602 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.8988 | −1.30105 | −0.650524 | − | 0.759485i | \(-0.725451\pi\) | ||||
−0.650524 | + | 0.759485i | \(0.725451\pi\) | |||||||
\(212\) | −0.189777 | −0.0130339 | ||||||||
\(213\) | 8.11351 | 0.555928 | ||||||||
\(214\) | −20.1102 | −1.37471 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.81644 | 0.191635 | ||||||||
\(217\) | 38.8181 | 2.63514 | ||||||||
\(218\) | 10.6092 | 0.718547 | ||||||||
\(219\) | 5.96747 | 0.403244 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.93708 | −0.399371 | ||||||||
\(222\) | −2.43513 | −0.163435 | ||||||||
\(223\) | −3.78003 | −0.253129 | −0.126565 | − | 0.991958i | \(-0.540395\pi\) | ||||
−0.126565 | + | 0.991958i | \(0.540395\pi\) | |||||||
\(224\) | 0.347537 | 0.0232208 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.9972 | −0.931081 | ||||||||
\(227\) | −4.02424 | −0.267098 | −0.133549 | − | 0.991042i | \(-0.542637\pi\) | ||||
−0.133549 | + | 0.991042i | \(0.542637\pi\) | |||||||
\(228\) | −0.111911 | −0.00741146 | ||||||||
\(229\) | −15.3718 | −1.01580 | −0.507899 | − | 0.861416i | \(-0.669578\pi\) | ||||
−0.507899 | + | 0.861416i | \(0.669578\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.9528 | 0.786439 | ||||||||
\(232\) | −0.0532845 | −0.00349830 | ||||||||
\(233\) | 16.8263 | 1.10233 | 0.551164 | − | 0.834397i | \(-0.314184\pi\) | ||||
0.551164 | + | 0.834397i | \(0.314184\pi\) | |||||||
\(234\) | 3.97589 | 0.259912 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.102026 | 0.00664132 | ||||||||
\(237\) | 6.08780 | 0.395445 | ||||||||
\(238\) | 11.0292 | 0.714916 | ||||||||
\(239\) | 18.1984 | 1.17715 | 0.588577 | − | 0.808441i | \(-0.299688\pi\) | ||||
0.588577 | + | 0.808441i | \(0.299688\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.42628 | 0.607200 | 0.303600 | − | 0.952800i | \(-0.401811\pi\) | ||||
0.303600 | + | 0.952800i | \(0.401811\pi\) | |||||||
\(242\) | −0.493677 | −0.0317347 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.120611 | −0.00772133 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.57432 | −0.164133 | ||||||||
\(247\) | 18.6762 | 1.18834 | ||||||||
\(248\) | 29.8529 | 1.89566 | ||||||||
\(249\) | −1.95253 | −0.123737 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.65618 | 0.357015 | 0.178507 | − | 0.983939i | \(-0.442873\pi\) | ||||
0.178507 | + | 0.983939i | \(0.442873\pi\) | |||||||
\(252\) | −0.0614380 | −0.00387023 | ||||||||
\(253\) | 5.36349 | 0.337200 | ||||||||
\(254\) | −3.66657 | −0.230061 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.402597 | 0.0251623 | ||||||||
\(257\) | 19.5519 | 1.21961 | 0.609806 | − | 0.792551i | \(-0.291247\pi\) | ||||
0.609806 | + | 0.792551i | \(0.291247\pi\) | |||||||
\(258\) | −12.9400 | −0.805609 | ||||||||
\(259\) | −6.27973 | −0.390203 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0189191 | 0.00117106 | ||||||||
\(262\) | −9.89842 | −0.611526 | ||||||||
\(263\) | 2.84131 | 0.175203 | 0.0876013 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876013 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(264\) | 9.19229 | 0.565746 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −34.6943 | −2.12725 | ||||||||
\(267\) | −16.2631 | −0.995284 | ||||||||
\(268\) | −0.0167760 | −0.00102476 | ||||||||
\(269\) | −18.4970 | −1.12778 | −0.563890 | − | 0.825850i | \(-0.690696\pi\) | ||||
−0.563890 | + | 0.825850i | \(0.690696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.41652 | 0.329030 | 0.164515 | − | 0.986375i | \(-0.447394\pi\) | ||||
0.164515 | + | 0.986375i | \(0.447394\pi\) | |||||||
\(272\) | 8.55311 | 0.518609 | ||||||||
\(273\) | 10.2531 | 0.620544 | ||||||||
\(274\) | −15.7129 | −0.949252 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.0275686 | −0.00165943 | ||||||||
\(277\) | −31.1357 | −1.87076 | −0.935381 | − | 0.353643i | \(-0.884943\pi\) | ||||
−0.935381 | + | 0.353643i | \(0.884943\pi\) | |||||||
\(278\) | −4.98888 | −0.299213 | ||||||||
\(279\) | −10.5995 | −0.634577 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.812247 | 0.0484546 | 0.0242273 | − | 0.999706i | \(-0.492287\pi\) | ||||
0.0242273 | + | 0.999706i | \(0.492287\pi\) | |||||||
\(282\) | 5.35315 | 0.318776 | ||||||||
\(283\) | 7.04330 | 0.418681 | 0.209340 | − | 0.977843i | \(-0.432868\pi\) | ||||
0.209340 | + | 0.977843i | \(0.432868\pi\) | |||||||
\(284\) | −0.136113 | −0.00807679 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.9765 | 0.767317 | ||||||||
\(287\) | −6.63869 | −0.391869 | ||||||||
\(288\) | −0.0948971 | −0.00559186 | ||||||||
\(289\) | −12.5029 | −0.735464 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.43089 | 0.259743 | ||||||||
\(292\) | −0.100110 | −0.00585852 | ||||||||
\(293\) | −13.0361 | −0.761578 | −0.380789 | − | 0.924662i | \(-0.624348\pi\) | ||||
−0.380789 | + | 0.924662i | \(0.624348\pi\) | |||||||
\(294\) | −9.10598 | −0.531072 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.82941 | −0.280704 | ||||||||
\(297\) | −3.26380 | −0.189385 | ||||||||
\(298\) | −11.1071 | −0.643418 | ||||||||
\(299\) | 4.60077 | 0.266069 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.3698 | −1.92340 | ||||||||
\(302\) | −11.4265 | −0.657520 | ||||||||
\(303\) | 15.6077 | 0.896637 | ||||||||
\(304\) | −26.9054 | −1.54313 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.01159 | −0.172161 | ||||||||
\(307\) | −18.9833 | −1.08343 | −0.541716 | − | 0.840562i | \(-0.682225\pi\) | ||||
−0.541716 | + | 0.840562i | \(0.682225\pi\) | |||||||
\(308\) | −0.200521 | −0.0114258 | ||||||||
\(309\) | −1.97784 | −0.112515 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.11836 | −0.0634166 | −0.0317083 | − | 0.999497i | \(-0.510095\pi\) | ||||
−0.0317083 | + | 0.999497i | \(0.510095\pi\) | |||||||
\(312\) | 7.88509 | 0.446405 | ||||||||
\(313\) | 26.5721 | 1.50194 | 0.750972 | − | 0.660334i | \(-0.229585\pi\) | ||||
0.750972 | + | 0.660334i | \(0.229585\pi\) | |||||||
\(314\) | 3.96113 | 0.223540 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.102129 | −0.00574522 | ||||||||
\(317\) | 10.2185 | 0.573930 | 0.286965 | − | 0.957941i | \(-0.407354\pi\) | ||||
0.286965 | + | 0.957941i | \(0.407354\pi\) | |||||||
\(318\) | 16.0651 | 0.900883 | ||||||||
\(319\) | 0.0617481 | 0.00345723 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.1608 | 0.790379 | ||||||||
\(322\) | −8.54676 | −0.476292 | ||||||||
\(323\) | −14.1465 | −0.787132 | ||||||||
\(324\) | 0.0167760 | 0.000932002 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.6783 | −1.69911 | ||||||||
\(327\) | −7.47058 | −0.413124 | ||||||||
\(328\) | −5.10546 | −0.281902 | ||||||||
\(329\) | 13.8047 | 0.761080 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.73565 | −0.205330 | −0.102665 | − | 0.994716i | \(-0.532737\pi\) | ||||
−0.102665 | + | 0.994716i | \(0.532737\pi\) | |||||||
\(332\) | 0.0327557 | 0.00179771 | ||||||||
\(333\) | 1.71472 | 0.0939661 | ||||||||
\(334\) | −26.0471 | −1.42524 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −14.7708 | −0.805815 | ||||||||
\(337\) | 34.0269 | 1.85356 | 0.926782 | − | 0.375599i | \(-0.122563\pi\) | ||||
0.926782 | + | 0.375599i | \(0.122563\pi\) | |||||||
\(338\) | −7.33055 | −0.398729 | ||||||||
\(339\) | 9.85628 | 0.535319 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −34.5947 | −1.87341 | ||||||||
\(342\) | 9.47350 | 0.512268 | ||||||||
\(343\) | 2.15317 | 0.116260 | ||||||||
\(344\) | −25.6629 | −1.38365 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.8483 | 1.65841 | ||||||||
\(347\) | 29.2097 | 1.56806 | 0.784031 | − | 0.620722i | \(-0.213160\pi\) | ||||
0.784031 | + | 0.620722i | \(0.213160\pi\) | |||||||
\(348\) | −0.000317388 0 | −1.70138e−5 0 | ||||||||
\(349\) | 21.3114 | 1.14077 | 0.570386 | − | 0.821377i | \(-0.306794\pi\) | ||||
0.570386 | + | 0.821377i | \(0.306794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.79966 | −0.149435 | ||||||||
\(352\) | −0.309725 | −0.0165084 | ||||||||
\(353\) | 6.32580 | 0.336688 | 0.168344 | − | 0.985728i | \(-0.446158\pi\) | ||||
0.168344 | + | 0.985728i | \(0.446158\pi\) | |||||||
\(354\) | −8.63674 | −0.459037 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.272830 | 0.0144600 | ||||||||
\(357\) | −7.76631 | −0.411037 | ||||||||
\(358\) | −22.9891 | −1.21501 | ||||||||
\(359\) | −14.7835 | −0.780245 | −0.390123 | − | 0.920763i | \(-0.627567\pi\) | ||||
−0.390123 | + | 0.920763i | \(0.627567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.5004 | 1.34212 | ||||||||
\(362\) | −0.952454 | −0.0500599 | ||||||||
\(363\) | 0.347627 | 0.0182457 | ||||||||
\(364\) | −0.172006 | −0.00901555 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.2100 | 0.533686 | ||||||||
\(367\) | −22.8315 | −1.19180 | −0.595898 | − | 0.803060i | \(-0.703204\pi\) | ||||
−0.595898 | + | 0.803060i | \(0.703204\pi\) | |||||||
\(368\) | −6.62799 | −0.345508 | ||||||||
\(369\) | 1.81274 | 0.0943672 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 41.4287 | 2.15087 | ||||||||
\(372\) | 0.177818 | 0.00921944 | ||||||||
\(373\) | −29.0985 | −1.50666 | −0.753332 | − | 0.657640i | \(-0.771555\pi\) | ||||
−0.753332 | + | 0.657640i | \(0.771555\pi\) | |||||||
\(374\) | −9.82922 | −0.508257 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6165 | 0.547504 | ||||||||
\(377\) | 0.0529672 | 0.00272795 | ||||||||
\(378\) | 5.20088 | 0.267504 | ||||||||
\(379\) | 16.6978 | 0.857708 | 0.428854 | − | 0.903374i | \(-0.358917\pi\) | ||||
0.428854 | + | 0.903374i | \(0.358917\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.58185 | 0.132272 | ||||||||
\(382\) | 15.1917 | 0.777275 | ||||||||
\(383\) | −24.5499 | −1.25444 | −0.627220 | − | 0.778842i | \(-0.715807\pi\) | ||||
−0.627220 | + | 0.778842i | \(0.715807\pi\) | |||||||
\(384\) | −11.4540 | −0.584508 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0809 | 0.513106 | ||||||||
\(387\) | 9.11183 | 0.463180 | ||||||||
\(388\) | −0.0743327 | −0.00377367 | ||||||||
\(389\) | −35.1081 | −1.78005 | −0.890025 | − | 0.455912i | \(-0.849313\pi\) | ||||
−0.890025 | + | 0.455912i | \(0.849313\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.48491 | −0.176239 | ||||||||
\(392\) | −18.0592 | −0.912127 | ||||||||
\(393\) | 6.97007 | 0.351593 | ||||||||
\(394\) | 19.7760 | 0.996299 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0547536 | 0.00275147 | ||||||||
\(397\) | 17.8265 | 0.894686 | 0.447343 | − | 0.894363i | \(-0.352370\pi\) | ||||
0.447343 | + | 0.894363i | \(0.352370\pi\) | |||||||
\(398\) | −33.9836 | −1.70345 | ||||||||
\(399\) | 24.4303 | 1.22305 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.97752 | 0.198628 | 0.0993140 | − | 0.995056i | \(-0.468335\pi\) | ||||
0.0993140 | + | 0.995056i | \(0.468335\pi\) | |||||||
\(402\) | 1.42013 | 0.0708298 | ||||||||
\(403\) | −29.6751 | −1.47822 | ||||||||
\(404\) | −0.261835 | −0.0130268 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0983960 | −0.00488331 | ||||||||
\(407\) | 5.59650 | 0.277408 | ||||||||
\(408\) | −5.97266 | −0.295691 | ||||||||
\(409\) | 35.9212 | 1.77619 | 0.888094 | − | 0.459661i | \(-0.152029\pi\) | ||||
0.888094 | + | 0.459661i | \(0.152029\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0644 | 0.545767 | ||||||||
\(412\) | 0.0331803 | 0.00163468 | ||||||||
\(413\) | −22.2725 | −1.09596 | ||||||||
\(414\) | 2.33375 | 0.114697 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.265680 | −0.0130260 | ||||||||
\(417\) | 3.51297 | 0.172031 | ||||||||
\(418\) | 30.9196 | 1.51233 | ||||||||
\(419\) | −13.8740 | −0.677789 | −0.338895 | − | 0.940824i | \(-0.610053\pi\) | ||||
−0.338895 | + | 0.940824i | \(0.610053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.5473 | 1.97616 | 0.988078 | − | 0.153952i | \(-0.0492000\pi\) | ||||
0.988078 | + | 0.153952i | \(0.0492000\pi\) | |||||||
\(422\) | −26.8388 | −1.30649 | ||||||||
\(423\) | −3.76947 | −0.183278 | ||||||||
\(424\) | 31.8606 | 1.54729 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11.5223 | 0.558255 | ||||||||
\(427\) | 26.3297 | 1.27418 | ||||||||
\(428\) | −0.237562 | −0.0114830 | ||||||||
\(429\) | −9.13754 | −0.441164 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.79550 | −0.471833 | −0.235916 | − | 0.971773i | \(-0.575809\pi\) | ||||
−0.235916 | + | 0.971773i | \(0.575809\pi\) | |||||||
\(432\) | 4.03327 | 0.194051 | ||||||||
\(433\) | 19.1370 | 0.919667 | 0.459833 | − | 0.888005i | \(-0.347909\pi\) | ||||
0.459833 | + | 0.888005i | \(0.347909\pi\) | |||||||
\(434\) | 55.1268 | 2.64617 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.125327 | 0.00600206 | ||||||||
\(437\) | 10.9624 | 0.524404 | ||||||||
\(438\) | 8.47460 | 0.404932 | ||||||||
\(439\) | 8.03843 | 0.383653 | 0.191827 | − | 0.981429i | \(-0.438559\pi\) | ||||
0.191827 | + | 0.981429i | \(0.438559\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.41206 | 0.305336 | ||||||||
\(442\) | −8.43144 | −0.401043 | ||||||||
\(443\) | 13.0740 | 0.621162 | 0.310581 | − | 0.950547i | \(-0.399476\pi\) | ||||
0.310581 | + | 0.950547i | \(0.399476\pi\) | |||||||
\(444\) | −0.0287662 | −0.00136518 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.36814 | −0.254189 | ||||||||
\(447\) | 7.82118 | 0.369929 | ||||||||
\(448\) | −29.0481 | −1.37240 | ||||||||
\(449\) | −25.1929 | −1.18892 | −0.594462 | − | 0.804124i | \(-0.702635\pi\) | ||||
−0.594462 | + | 0.804124i | \(0.702635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.91640 | 0.278592 | ||||||||
\(452\) | −0.165349 | −0.00777737 | ||||||||
\(453\) | 8.04607 | 0.378037 | ||||||||
\(454\) | −5.71495 | −0.268216 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 18.7881 | 0.879832 | ||||||||
\(457\) | −4.80210 | −0.224633 | −0.112316 | − | 0.993672i | \(-0.535827\pi\) | ||||
−0.112316 | + | 0.993672i | \(0.535827\pi\) | |||||||
\(458\) | −21.8300 | −1.02005 | ||||||||
\(459\) | 2.12064 | 0.0989830 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.82376 | −0.317814 | −0.158907 | − | 0.987294i | \(-0.550797\pi\) | ||||
−0.158907 | + | 0.987294i | \(0.550797\pi\) | |||||||
\(462\) | 16.9746 | 0.789730 | ||||||||
\(463\) | 6.34009 | 0.294649 | 0.147324 | − | 0.989088i | \(-0.452934\pi\) | ||||
0.147324 | + | 0.989088i | \(0.452934\pi\) | |||||||
\(464\) | −0.0763059 | −0.00354241 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.8956 | 1.10694 | ||||||||
\(467\) | 13.1557 | 0.608774 | 0.304387 | − | 0.952549i | \(-0.401548\pi\) | ||||
0.304387 | + | 0.952549i | \(0.401548\pi\) | |||||||
\(468\) | 0.0469673 | 0.00217106 | ||||||||
\(469\) | 3.66225 | 0.169107 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.78927 | −0.128523 | ||||||||
\(472\) | −17.1286 | −0.788407 | ||||||||
\(473\) | 29.7392 | 1.36741 | ||||||||
\(474\) | 8.64549 | 0.397100 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.130288 | 0.00597174 | ||||||||
\(477\) | −11.3124 | −0.517957 | ||||||||
\(478\) | 25.8441 | 1.18208 | ||||||||
\(479\) | −34.9990 | −1.59915 | −0.799574 | − | 0.600568i | \(-0.794941\pi\) | ||||
−0.799574 | + | 0.600568i | \(0.794941\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.80064 | 0.218890 | ||||||||
\(482\) | 13.3866 | 0.609741 | ||||||||
\(483\) | 6.01828 | 0.273841 | ||||||||
\(484\) | −0.00583181 | −0.000265082 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.42013 | −0.0644185 | ||||||||
\(487\) | 35.5178 | 1.60946 | 0.804732 | − | 0.593639i | \(-0.202309\pi\) | ||||
0.804732 | + | 0.593639i | \(0.202309\pi\) | |||||||
\(488\) | 20.2488 | 0.916618 | ||||||||
\(489\) | 21.6024 | 0.976895 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.2985 | 1.14171 | 0.570853 | − | 0.821052i | \(-0.306613\pi\) | ||||
0.570853 | + | 0.821052i | \(0.306613\pi\) | |||||||
\(492\) | −0.0304105 | −0.00137101 | ||||||||
\(493\) | −0.0401206 | −0.00180694 | ||||||||
\(494\) | 26.5226 | 1.19331 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 42.7508 | 1.91957 | ||||||||
\(497\) | 29.7137 | 1.33284 | ||||||||
\(498\) | −2.77285 | −0.124255 | ||||||||
\(499\) | −6.05417 | −0.271022 | −0.135511 | − | 0.990776i | \(-0.543268\pi\) | ||||
−0.135511 | + | 0.990776i | \(0.543268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.3413 | 0.819430 | ||||||||
\(502\) | 8.03252 | 0.358509 | ||||||||
\(503\) | −17.6401 | −0.786533 | −0.393266 | − | 0.919425i | \(-0.628655\pi\) | ||||
−0.393266 | + | 0.919425i | \(0.628655\pi\) | |||||||
\(504\) | 10.3145 | 0.459445 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.61687 | 0.338611 | ||||||||
\(507\) | 5.16188 | 0.229247 | ||||||||
\(508\) | −0.0433132 | −0.00192171 | ||||||||
\(509\) | 38.6106 | 1.71138 | 0.855692 | − | 0.517486i | \(-0.173132\pi\) | ||||
0.855692 | + | 0.517486i | \(0.173132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.8544 | 0.966780 | ||||||||
\(512\) | −22.3362 | −0.987129 | ||||||||
\(513\) | −6.67086 | −0.294526 | ||||||||
\(514\) | 27.7662 | 1.22472 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.152860 | −0.00672930 | ||||||||
\(517\) | −12.3028 | −0.541076 | ||||||||
\(518\) | −8.91805 | −0.391837 | ||||||||
\(519\) | −21.7221 | −0.953495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.934016 | 0.0409200 | 0.0204600 | − | 0.999791i | \(-0.493487\pi\) | ||||
0.0204600 | + | 0.999791i | \(0.493487\pi\) | |||||||
\(522\) | 0.0268676 | 0.00117596 | ||||||||
\(523\) | −44.0708 | −1.92708 | −0.963542 | − | 0.267558i | \(-0.913783\pi\) | ||||
−0.963542 | + | 0.267558i | \(0.913783\pi\) | |||||||
\(524\) | −0.116930 | −0.00510812 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.03503 | 0.175936 | ||||||||
\(527\) | 22.4778 | 0.979148 | ||||||||
\(528\) | 13.1638 | 0.572880 | ||||||||
\(529\) | −20.2995 | −0.882586 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.08164 | 0.263921 | ||||||||
\(532\) | −0.409844 | −0.0177690 | ||||||||
\(533\) | 5.07505 | 0.219825 | ||||||||
\(534\) | −23.0957 | −0.999450 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.81644 | 0.121652 | ||||||||
\(537\) | 16.1880 | 0.698562 | ||||||||
\(538\) | −26.2681 | −1.13250 | ||||||||
\(539\) | 20.9277 | 0.901419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.5988 | −1.01459 | −0.507295 | − | 0.861772i | \(-0.669355\pi\) | ||||
−0.507295 | + | 0.861772i | \(0.669355\pi\) | |||||||
\(542\) | 7.69218 | 0.330407 | ||||||||
\(543\) | 0.670680 | 0.0287816 | ||||||||
\(544\) | 0.201243 | 0.00862820 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.5607 | 0.623141 | ||||||||
\(547\) | −25.0627 | −1.07160 | −0.535801 | − | 0.844344i | \(-0.679990\pi\) | ||||
−0.535801 | + | 0.844344i | \(0.679990\pi\) | |||||||
\(548\) | −0.185617 | −0.00792915 | ||||||||
\(549\) | −7.18949 | −0.306840 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.126207 | 0.00537659 | ||||||||
\(552\) | 4.62834 | 0.196995 | ||||||||
\(553\) | 22.2951 | 0.948082 | ||||||||
\(554\) | −44.2168 | −1.87859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0589337 | −0.00249934 | ||||||||
\(557\) | −34.0542 | −1.44292 | −0.721461 | − | 0.692456i | \(-0.756529\pi\) | ||||
−0.721461 | + | 0.692456i | \(0.756529\pi\) | |||||||
\(558\) | −15.0527 | −0.637233 | ||||||||
\(559\) | 25.5101 | 1.07896 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.92134 | 0.292219 | ||||||||
\(562\) | 1.15350 | 0.0486574 | ||||||||
\(563\) | 12.2856 | 0.517777 | 0.258889 | − | 0.965907i | \(-0.416644\pi\) | ||||
0.258889 | + | 0.965907i | \(0.416644\pi\) | |||||||
\(564\) | 0.0632368 | 0.00266275 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.0024 | 0.420433 | ||||||||
\(567\) | −3.66225 | −0.153800 | ||||||||
\(568\) | 22.8512 | 0.958816 | ||||||||
\(569\) | 28.8290 | 1.20858 | 0.604288 | − | 0.796766i | \(-0.293458\pi\) | ||||
0.604288 | + | 0.796766i | \(0.293458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.57238 | −0.107651 | −0.0538253 | − | 0.998550i | \(-0.517141\pi\) | ||||
−0.0538253 | + | 0.998550i | \(0.517141\pi\) | |||||||
\(572\) | 0.153292 | 0.00640945 | ||||||||
\(573\) | −10.6974 | −0.446890 | ||||||||
\(574\) | −9.42782 | −0.393509 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.93177 | 0.330491 | ||||||||
\(577\) | 22.9339 | 0.954752 | 0.477376 | − | 0.878699i | \(-0.341588\pi\) | ||||
0.477376 | + | 0.878699i | \(0.341588\pi\) | |||||||
\(578\) | −17.7558 | −0.738542 | ||||||||
\(579\) | −7.09859 | −0.295007 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.15066 | −0.296659 | ||||||||
\(582\) | 6.29244 | 0.260830 | ||||||||
\(583\) | −36.9213 | −1.52912 | ||||||||
\(584\) | 16.8070 | 0.695480 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.5130 | −0.764765 | ||||||||
\(587\) | −28.1157 | −1.16046 | −0.580229 | − | 0.814453i | \(-0.697037\pi\) | ||||
−0.580229 | + | 0.814453i | \(0.697037\pi\) | |||||||
\(588\) | −0.107569 | −0.00443607 | ||||||||
\(589\) | −70.7079 | −2.91347 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.9254 | −0.572816 | ||||||||
\(592\) | −6.91593 | −0.284243 | ||||||||
\(593\) | 17.2239 | 0.707301 | 0.353650 | − | 0.935378i | \(-0.384940\pi\) | ||||
0.353650 | + | 0.935378i | \(0.384940\pi\) | |||||||
\(594\) | −4.63502 | −0.190177 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.131208 | −0.00537451 | ||||||||
\(597\) | 23.9299 | 0.979386 | ||||||||
\(598\) | 6.53370 | 0.267183 | ||||||||
\(599\) | −27.8806 | −1.13917 | −0.569585 | − | 0.821933i | \(-0.692896\pi\) | ||||
−0.569585 | + | 0.821933i | \(0.692896\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.48766 | −0.346219 | −0.173109 | − | 0.984903i | \(-0.555381\pi\) | ||||
−0.173109 | + | 0.984903i | \(0.555381\pi\) | |||||||
\(602\) | −47.3895 | −1.93145 | ||||||||
\(603\) | −1.00000 | −0.0407231 | ||||||||
\(604\) | −0.134981 | −0.00549230 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 22.1649 | 0.900389 | ||||||||
\(607\) | −44.8744 | −1.82140 | −0.910698 | − | 0.413074i | \(-0.864455\pi\) | ||||
−0.910698 | + | 0.413074i | \(0.864455\pi\) | |||||||
\(608\) | −0.633045 | −0.0256734 | ||||||||
\(609\) | 0.0692865 | 0.00280763 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.5533 | −0.426939 | ||||||||
\(612\) | −0.0355759 | −0.00143807 | ||||||||
\(613\) | 10.6398 | 0.429738 | 0.214869 | − | 0.976643i | \(-0.431068\pi\) | ||||
0.214869 | + | 0.976643i | \(0.431068\pi\) | |||||||
\(614\) | −26.9587 | −1.08797 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 33.6645 | 1.35638 | ||||||||
\(617\) | −36.3155 | −1.46201 | −0.731003 | − | 0.682374i | \(-0.760948\pi\) | ||||
−0.731003 | + | 0.682374i | \(0.760948\pi\) | |||||||
\(618\) | −2.80879 | −0.112986 | ||||||||
\(619\) | −26.4333 | −1.06244 | −0.531221 | − | 0.847233i | \(-0.678267\pi\) | ||||
−0.531221 | + | 0.847233i | \(0.678267\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.64333 | −0.0659445 | ||||||||
\(622\) | −1.58823 | −0.0636821 | ||||||||
\(623\) | −59.5595 | −2.38620 | ||||||||
\(624\) | 11.2918 | 0.452034 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 37.7359 | 1.50823 | ||||||||
\(627\) | −21.7723 | −0.869503 | ||||||||
\(628\) | 0.0467929 | 0.00186724 | ||||||||
\(629\) | −3.63630 | −0.144989 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0074 | 0.995529 | 0.497765 | − | 0.867312i | \(-0.334154\pi\) | ||||
0.497765 | + | 0.867312i | \(0.334154\pi\) | |||||||
\(632\) | 17.1459 | 0.682029 | ||||||||
\(633\) | 18.8988 | 0.751161 | ||||||||
\(634\) | 14.5117 | 0.576332 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.189777 | 0.00752513 | ||||||||
\(637\) | 17.9516 | 0.711269 | ||||||||
\(638\) | 0.0876905 | 0.00347170 | ||||||||
\(639\) | −8.11351 | −0.320965 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.6060 | −1.68283 | −0.841417 | − | 0.540386i | \(-0.818278\pi\) | ||||
−0.841417 | + | 0.540386i | \(0.818278\pi\) | |||||||
\(642\) | 20.1102 | 0.793687 | ||||||||
\(643\) | 20.6664 | 0.815003 | 0.407502 | − | 0.913205i | \(-0.366400\pi\) | ||||
0.407502 | + | 0.913205i | \(0.366400\pi\) | |||||||
\(644\) | −0.100963 | −0.00397850 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.0899 | −0.790426 | ||||||||
\(647\) | −39.4826 | −1.55222 | −0.776111 | − | 0.630596i | \(-0.782810\pi\) | ||||
−0.776111 | + | 0.630596i | \(0.782810\pi\) | |||||||
\(648\) | −2.81644 | −0.110640 | ||||||||
\(649\) | 19.8492 | 0.779151 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38.8181 | −1.52140 | ||||||||
\(652\) | −0.362403 | −0.0141928 | ||||||||
\(653\) | 9.79998 | 0.383503 | 0.191751 | − | 0.981444i | \(-0.438583\pi\) | ||||
0.191751 | + | 0.981444i | \(0.438583\pi\) | |||||||
\(654\) | −10.6092 | −0.414853 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.31125 | −0.285456 | ||||||||
\(657\) | −5.96747 | −0.232813 | ||||||||
\(658\) | 19.6046 | 0.764266 | ||||||||
\(659\) | 2.40593 | 0.0937218 | 0.0468609 | − | 0.998901i | \(-0.485078\pi\) | ||||
0.0468609 | + | 0.998901i | \(0.485078\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.3264 | 0.712813 | 0.356407 | − | 0.934331i | \(-0.384002\pi\) | ||||
0.356407 | + | 0.934331i | \(0.384002\pi\) | |||||||
\(662\) | −5.30511 | −0.206189 | ||||||||
\(663\) | 5.93708 | 0.230577 | ||||||||
\(664\) | −5.49919 | −0.213410 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.43513 | 0.0943593 | ||||||||
\(667\) | 0.0310903 | 0.00120382 | ||||||||
\(668\) | −0.307695 | −0.0119051 | ||||||||
\(669\) | 3.78003 | 0.146144 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.4650 | −0.905857 | ||||||||
\(672\) | −0.347537 | −0.0134065 | ||||||||
\(673\) | 18.7300 | 0.721988 | 0.360994 | − | 0.932568i | \(-0.382437\pi\) | ||||
0.360994 | + | 0.932568i | \(0.382437\pi\) | |||||||
\(674\) | 48.3227 | 1.86132 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.0865959 | −0.00333061 | ||||||||
\(677\) | −38.8504 | −1.49314 | −0.746570 | − | 0.665307i | \(-0.768301\pi\) | ||||
−0.746570 | + | 0.665307i | \(0.768301\pi\) | |||||||
\(678\) | 13.9972 | 0.537560 | ||||||||
\(679\) | 16.2270 | 0.622735 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.02424 | 0.154209 | ||||||||
\(682\) | −49.1291 | −1.88125 | ||||||||
\(683\) | −21.5365 | −0.824070 | −0.412035 | − | 0.911168i | \(-0.635182\pi\) | ||||
−0.412035 | + | 0.911168i | \(0.635182\pi\) | |||||||
\(684\) | 0.111911 | 0.00427901 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.05778 | 0.116747 | ||||||||
\(687\) | 15.3718 | 0.586472 | ||||||||
\(688\) | −36.7505 | −1.40110 | ||||||||
\(689\) | −31.6708 | −1.20656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.4334 | −1.34795 | −0.673974 | − | 0.738755i | \(-0.735414\pi\) | ||||
−0.673974 | + | 0.738755i | \(0.735414\pi\) | |||||||
\(692\) | 0.364411 | 0.0138528 | ||||||||
\(693\) | −11.9528 | −0.454051 | ||||||||
\(694\) | 41.4817 | 1.57462 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0532845 | 0.00201975 | ||||||||
\(697\) | −3.84416 | −0.145608 | ||||||||
\(698\) | 30.2650 | 1.14555 | ||||||||
\(699\) | −16.8263 | −0.636429 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.8588 | 1.84537 | 0.922686 | − | 0.385551i | \(-0.125989\pi\) | ||||
0.922686 | + | 0.385551i | \(0.125989\pi\) | |||||||
\(702\) | −3.97589 | −0.150060 | ||||||||
\(703\) | 11.4387 | 0.431417 | ||||||||
\(704\) | 25.8877 | 0.975680 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.98348 | 0.338098 | ||||||||
\(707\) | 57.1591 | 2.14969 | ||||||||
\(708\) | −0.102026 | −0.00383437 | ||||||||
\(709\) | −24.4737 | −0.919128 | −0.459564 | − | 0.888145i | \(-0.651994\pi\) | ||||
−0.459564 | + | 0.888145i | \(0.651994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.08780 | −0.228311 | ||||||||
\(712\) | −45.8040 | −1.71658 | ||||||||
\(713\) | −17.4185 | −0.652329 | ||||||||
\(714\) | −11.0292 | −0.412757 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.271570 | −0.0101490 | ||||||||
\(717\) | −18.1984 | −0.679630 | ||||||||
\(718\) | −20.9946 | −0.783511 | ||||||||
\(719\) | −6.98045 | −0.260327 | −0.130163 | − | 0.991493i | \(-0.541550\pi\) | ||||
−0.130163 | + | 0.991493i | \(0.541550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.24334 | −0.269756 | ||||||||
\(722\) | 36.2139 | 1.34774 | ||||||||
\(723\) | −9.42628 | −0.350567 | ||||||||
\(724\) | −0.0112514 | −0.000418153 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.493677 | 0.0183221 | ||||||||
\(727\) | 23.9628 | 0.888731 | 0.444366 | − | 0.895846i | \(-0.353429\pi\) | ||||
0.444366 | + | 0.895846i | \(0.353429\pi\) | |||||||
\(728\) | 28.8772 | 1.07026 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.3229 | −0.714684 | ||||||||
\(732\) | 0.120611 | 0.00445791 | ||||||||
\(733\) | 23.1099 | 0.853582 | 0.426791 | − | 0.904350i | \(-0.359644\pi\) | ||||
0.426791 | + | 0.904350i | \(0.359644\pi\) | |||||||
\(734\) | −32.4238 | −1.19678 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.155947 | −0.00574829 | ||||||||
\(737\) | −3.26380 | −0.120224 | ||||||||
\(738\) | 2.57432 | 0.0947622 | ||||||||
\(739\) | 33.9813 | 1.25002 | 0.625011 | − | 0.780616i | \(-0.285095\pi\) | ||||
0.625011 | + | 0.780616i | \(0.285095\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.6762 | −0.686086 | ||||||||
\(742\) | 58.8342 | 2.15987 | ||||||||
\(743\) | 48.0961 | 1.76447 | 0.882237 | − | 0.470805i | \(-0.156036\pi\) | ||||
0.882237 | + | 0.470805i | \(0.156036\pi\) | |||||||
\(744\) | −29.8529 | −1.09446 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −41.3238 | −1.51297 | ||||||||
\(747\) | 1.95253 | 0.0714394 | ||||||||
\(748\) | −0.116113 | −0.00424550 | ||||||||
\(749\) | 51.8604 | 1.89494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −54.3642 | −1.98378 | −0.991888 | − | 0.127113i | \(-0.959429\pi\) | ||||
−0.991888 | + | 0.127113i | \(0.959429\pi\) | |||||||
\(752\) | 15.2033 | 0.554408 | ||||||||
\(753\) | −5.65618 | −0.206123 | ||||||||
\(754\) | 0.0752204 | 0.00273936 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.0614380 | 0.00223448 | ||||||||
\(757\) | 33.9263 | 1.23307 | 0.616537 | − | 0.787326i | \(-0.288535\pi\) | ||||
0.616537 | + | 0.787326i | \(0.288535\pi\) | |||||||
\(758\) | 23.7131 | 0.861298 | ||||||||
\(759\) | −5.36349 | −0.194683 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.4554 | −1.28526 | −0.642628 | − | 0.766178i | \(-0.722156\pi\) | ||||
−0.642628 | + | 0.766178i | \(0.722156\pi\) | |||||||
\(762\) | 3.66657 | 0.132826 | ||||||||
\(763\) | −27.3591 | −0.990467 | ||||||||
\(764\) | 0.179460 | 0.00649262 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.8641 | −1.25969 | ||||||||
\(767\) | 17.0266 | 0.614793 | ||||||||
\(768\) | −0.402597 | −0.0145275 | ||||||||
\(769\) | −31.2069 | −1.12535 | −0.562675 | − | 0.826678i | \(-0.690228\pi\) | ||||
−0.562675 | + | 0.826678i | \(0.690228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.5519 | −0.704143 | ||||||||
\(772\) | 0.119086 | 0.00428601 | ||||||||
\(773\) | −27.8700 | −1.00241 | −0.501207 | − | 0.865328i | \(-0.667110\pi\) | ||||
−0.501207 | + | 0.865328i | \(0.667110\pi\) | |||||||
\(774\) | 12.9400 | 0.465119 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.4793 | 0.447982 | ||||||||
\(777\) | 6.27973 | 0.225284 | ||||||||
\(778\) | −49.8581 | −1.78750 | ||||||||
\(779\) | 12.0925 | 0.433259 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.4808 | −0.947559 | ||||||||
\(782\) | −4.94903 | −0.176977 | ||||||||
\(783\) | −0.0189191 | −0.000676114 0 | ||||||||
\(784\) | −25.8616 | −0.923628 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.89842 | 0.353065 | ||||||||
\(787\) | 30.5100 | 1.08756 | 0.543782 | − | 0.839227i | \(-0.316992\pi\) | ||||
0.543782 | + | 0.839227i | \(0.316992\pi\) | |||||||
\(788\) | 0.233614 | 0.00832215 | ||||||||
\(789\) | −2.84131 | −0.101153 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.0961 | 1.28343 | ||||||||
\(792\) | −9.19229 | −0.326634 | ||||||||
\(793\) | −20.1282 | −0.714772 | ||||||||
\(794\) | 25.3160 | 0.898430 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.401449 | −0.0142290 | ||||||||
\(797\) | −5.47315 | −0.193869 | −0.0969345 | − | 0.995291i | \(-0.530904\pi\) | ||||
−0.0969345 | + | 0.995291i | \(0.530904\pi\) | |||||||
\(798\) | 34.6943 | 1.22817 | ||||||||
\(799\) | 7.99370 | 0.282797 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.2631 | 0.574628 | ||||||||
\(802\) | 5.64861 | 0.199459 | ||||||||
\(803\) | −19.4766 | −0.687315 | ||||||||
\(804\) | 0.0167760 | 0.000591645 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −42.1426 | −1.48441 | ||||||||
\(807\) | 18.4970 | 0.651124 | ||||||||
\(808\) | 43.9580 | 1.54644 | ||||||||
\(809\) | −2.36549 | −0.0831661 | −0.0415830 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415830 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.2573 | −0.746443 | −0.373222 | − | 0.927742i | \(-0.621747\pi\) | ||||
−0.373222 | + | 0.927742i | \(0.621747\pi\) | |||||||
\(812\) | −0.00116235 | −4.07906e−5 0 | ||||||||
\(813\) | −5.41652 | −0.189966 | ||||||||
\(814\) | 7.94777 | 0.278569 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.55311 | −0.299419 | ||||||||
\(817\) | 60.7837 | 2.12655 | ||||||||
\(818\) | 51.0129 | 1.78362 | ||||||||
\(819\) | −10.2531 | −0.358271 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.6538 | −0.965124 | −0.482562 | − | 0.875862i | \(-0.660294\pi\) | ||||
−0.482562 | + | 0.875862i | \(0.660294\pi\) | |||||||
\(822\) | 15.7129 | 0.548051 | ||||||||
\(823\) | 1.58378 | 0.0552070 | 0.0276035 | − | 0.999619i | \(-0.491212\pi\) | ||||
0.0276035 | + | 0.999619i | \(0.491212\pi\) | |||||||
\(824\) | −5.57047 | −0.194056 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.6299 | −1.10054 | ||||||||
\(827\) | −13.1210 | −0.456261 | −0.228130 | − | 0.973631i | \(-0.573261\pi\) | ||||
−0.228130 | + | 0.973631i | \(0.573261\pi\) | |||||||
\(828\) | 0.0275686 | 0.000958073 0 | ||||||||
\(829\) | 5.81240 | 0.201873 | 0.100937 | − | 0.994893i | \(-0.467816\pi\) | ||||
0.100937 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.1357 | 1.08008 | ||||||||
\(832\) | 22.2063 | 0.769865 | ||||||||
\(833\) | −13.5977 | −0.471132 | ||||||||
\(834\) | 4.98888 | 0.172751 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.365253 | 0.0126326 | ||||||||
\(837\) | 10.5995 | 0.366373 | ||||||||
\(838\) | −19.7029 | −0.680626 | ||||||||
\(839\) | 15.3259 | 0.529108 | 0.264554 | − | 0.964371i | \(-0.414775\pi\) | ||||
0.264554 | + | 0.964371i | \(0.414775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9996 | −0.999988 | ||||||||
\(842\) | 57.5826 | 1.98443 | ||||||||
\(843\) | −0.812247 | −0.0279753 | ||||||||
\(844\) | −0.317047 | −0.0109132 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.35315 | −0.184045 | ||||||||
\(847\) | 1.27310 | 0.0437441 | ||||||||
\(848\) | 45.6258 | 1.56680 | ||||||||
\(849\) | −7.04330 | −0.241725 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.81785 | 0.0965946 | ||||||||
\(852\) | 0.136113 | 0.00466314 | ||||||||
\(853\) | −5.98528 | −0.204932 | −0.102466 | − | 0.994737i | \(-0.532673\pi\) | ||||
−0.102466 | + | 0.994737i | \(0.532673\pi\) | |||||||
\(854\) | 37.3916 | 1.27952 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 39.8831 | 1.36318 | ||||||||
\(857\) | 31.0336 | 1.06009 | 0.530044 | − | 0.847970i | \(-0.322175\pi\) | ||||
0.530044 | + | 0.847970i | \(0.322175\pi\) | |||||||
\(858\) | −12.9765 | −0.443011 | ||||||||
\(859\) | 26.3730 | 0.899834 | 0.449917 | − | 0.893070i | \(-0.351454\pi\) | ||||
0.449917 | + | 0.893070i | \(0.351454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.63869 | 0.226246 | ||||||||
\(862\) | −13.9109 | −0.473807 | ||||||||
\(863\) | 20.2885 | 0.690630 | 0.345315 | − | 0.938487i | \(-0.387772\pi\) | ||||
0.345315 | + | 0.938487i | \(0.387772\pi\) | |||||||
\(864\) | 0.0948971 | 0.00322846 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 27.1771 | 0.923516 | ||||||||
\(867\) | 12.5029 | 0.424620 | ||||||||
\(868\) | 0.651214 | 0.0221036 | ||||||||
\(869\) | −19.8694 | −0.674022 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.79966 | −0.0948630 | ||||||||
\(872\) | −21.0405 | −0.712520 | ||||||||
\(873\) | −4.43089 | −0.149963 | ||||||||
\(874\) | 15.5681 | 0.526598 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.100110 | 0.00338242 | ||||||||
\(877\) | 45.1636 | 1.52507 | 0.762533 | − | 0.646949i | \(-0.223955\pi\) | ||||
0.762533 | + | 0.646949i | \(0.223955\pi\) | |||||||
\(878\) | 11.4156 | 0.385259 | ||||||||
\(879\) | 13.0361 | 0.439697 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0663 | −0.406524 | −0.203262 | − | 0.979124i | \(-0.565154\pi\) | ||||
−0.203262 | + | 0.979124i | \(0.565154\pi\) | |||||||
\(882\) | 9.10598 | 0.306614 | ||||||||
\(883\) | 7.10948 | 0.239253 | 0.119627 | − | 0.992819i | \(-0.461830\pi\) | ||||
0.119627 | + | 0.992819i | \(0.461830\pi\) | |||||||
\(884\) | −0.0996007 | −0.00334993 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.5667 | 0.623762 | ||||||||
\(887\) | 14.8013 | 0.496980 | 0.248490 | − | 0.968634i | \(-0.420066\pi\) | ||||
0.248490 | + | 0.968634i | \(0.420066\pi\) | |||||||
\(888\) | 4.82941 | 0.162064 | ||||||||
\(889\) | 9.45538 | 0.317123 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.26380 | 0.109341 | ||||||||
\(892\) | −0.0634139 | −0.00212325 | ||||||||
\(893\) | −25.1456 | −0.841466 | ||||||||
\(894\) | 11.1071 | 0.371477 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −41.9473 | −1.40136 | ||||||||
\(897\) | −4.60077 | −0.153615 | ||||||||
\(898\) | −35.7772 | −1.19390 | ||||||||
\(899\) | −0.200534 | −0.00668817 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.9894 | 0.799204 | ||||||||
\(902\) | 8.40207 | 0.279758 | ||||||||
\(903\) | 33.3698 | 1.11048 | ||||||||
\(904\) | 27.7596 | 0.923271 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.4265 | 0.379619 | ||||||||
\(907\) | −37.2992 | −1.23850 | −0.619250 | − | 0.785194i | \(-0.712563\pi\) | ||||
−0.619250 | + | 0.785194i | \(0.712563\pi\) | |||||||
\(908\) | −0.0675108 | −0.00224042 | ||||||||
\(909\) | −15.6077 | −0.517673 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.6810 | 0.751455 | 0.375728 | − | 0.926730i | \(-0.377393\pi\) | ||||
0.375728 | + | 0.926730i | \(0.377393\pi\) | |||||||
\(912\) | 26.9054 | 0.890926 | ||||||||
\(913\) | 6.37267 | 0.210905 | ||||||||
\(914\) | −6.81962 | −0.225573 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.257878 | −0.00852054 | ||||||||
\(917\) | 25.5261 | 0.842947 | ||||||||
\(918\) | 3.01159 | 0.0993973 | ||||||||
\(919\) | −18.0709 | −0.596103 | −0.298052 | − | 0.954550i | \(-0.596337\pi\) | ||||
−0.298052 | + | 0.954550i | \(0.596337\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.9833 | 0.625520 | ||||||||
\(922\) | −9.69064 | −0.319144 | ||||||||
\(923\) | −22.7151 | −0.747677 | ||||||||
\(924\) | 0.200521 | 0.00659666 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.00376 | 0.295882 | ||||||||
\(927\) | 1.97784 | 0.0649608 | ||||||||
\(928\) | −0.00179537 | −5.89359e−5 0 | ||||||||
\(929\) | 7.79262 | 0.255667 | 0.127834 | − | 0.991796i | \(-0.459198\pi\) | ||||
0.127834 | + | 0.991796i | \(0.459198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.7740 | 1.40186 | ||||||||
\(932\) | 0.282279 | 0.00924635 | ||||||||
\(933\) | 1.11836 | 0.0366136 | ||||||||
\(934\) | 18.6828 | 0.611321 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.88509 | −0.257732 | ||||||||
\(937\) | 10.5694 | 0.345289 | 0.172644 | − | 0.984984i | \(-0.444769\pi\) | ||||
0.172644 | + | 0.984984i | \(0.444769\pi\) | |||||||
\(938\) | 5.20088 | 0.169815 | ||||||||
\(939\) | −26.5721 | −0.867148 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.2843 | −0.922040 | −0.461020 | − | 0.887390i | \(-0.652516\pi\) | ||||
−0.461020 | + | 0.887390i | \(0.652516\pi\) | |||||||
\(942\) | −3.96113 | −0.129061 | ||||||||
\(943\) | 2.97892 | 0.0970070 | ||||||||
\(944\) | −24.5289 | −0.798348 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 42.2335 | 1.37313 | ||||||||
\(947\) | −36.7152 | −1.19308 | −0.596541 | − | 0.802582i | \(-0.703459\pi\) | ||||
−0.596541 | + | 0.802582i | \(0.703459\pi\) | |||||||
\(948\) | 0.102129 | 0.00331700 | ||||||||
\(949\) | −16.7069 | −0.542329 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.2185 | −0.331359 | ||||||||
\(952\) | −21.8734 | −0.708919 | ||||||||
\(953\) | −1.66770 | −0.0540220 | −0.0270110 | − | 0.999635i | \(-0.508599\pi\) | ||||
−0.0270110 | + | 0.999635i | \(0.508599\pi\) | |||||||
\(954\) | −16.0651 | −0.520125 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.305296 | 0.00987398 | ||||||||
\(957\) | −0.0617481 | −0.00199603 | ||||||||
\(958\) | −49.7033 | −1.60584 | ||||||||
\(959\) | 40.5206 | 1.30848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81.3500 | 2.62419 | ||||||||
\(962\) | 6.81754 | 0.219806 | ||||||||
\(963\) | −14.1608 | −0.456326 | ||||||||
\(964\) | 0.158136 | 0.00509320 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.54676 | 0.274987 | ||||||||
\(967\) | 4.98539 | 0.160319 | 0.0801597 | − | 0.996782i | \(-0.474457\pi\) | ||||
0.0801597 | + | 0.996782i | \(0.474457\pi\) | |||||||
\(968\) | 0.979071 | 0.0314685 | ||||||||
\(969\) | 14.1465 | 0.454451 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.0306 | −1.28464 | −0.642321 | − | 0.766436i | \(-0.722028\pi\) | ||||
−0.642321 | + | 0.766436i | \(0.722028\pi\) | |||||||
\(972\) | −0.0167760 | −0.000538092 0 | ||||||||
\(973\) | 12.8654 | 0.412445 | ||||||||
\(974\) | 50.4399 | 1.61620 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.9971 | 0.928176 | ||||||||
\(977\) | −58.9565 | −1.88619 | −0.943094 | − | 0.332527i | \(-0.892099\pi\) | ||||
−0.943094 | + | 0.332527i | \(0.892099\pi\) | |||||||
\(978\) | 30.6783 | 0.980983 | ||||||||
\(979\) | 53.0794 | 1.69643 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.47058 | 0.238517 | ||||||||
\(982\) | 35.9272 | 1.14648 | ||||||||
\(983\) | 23.1568 | 0.738587 | 0.369293 | − | 0.929313i | \(-0.379600\pi\) | ||||
0.369293 | + | 0.929313i | \(0.379600\pi\) | |||||||
\(984\) | 5.10546 | 0.162756 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.0569766 | −0.00181450 | ||||||||
\(987\) | −13.8047 | −0.439410 | ||||||||
\(988\) | 0.313312 | 0.00996778 | ||||||||
\(989\) | 14.9737 | 0.476137 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.9504 | −0.760810 | −0.380405 | − | 0.924820i | \(-0.624215\pi\) | ||||
−0.380405 | + | 0.924820i | \(0.624215\pi\) | |||||||
\(992\) | 1.00586 | 0.0319362 | ||||||||
\(993\) | 3.73565 | 0.118547 | ||||||||
\(994\) | 42.1974 | 1.33842 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0327557 | −0.00103791 | ||||||||
\(997\) | 46.4764 | 1.47192 | 0.735961 | − | 0.677024i | \(-0.236731\pi\) | ||||
0.735961 | + | 0.677024i | \(0.236731\pi\) | |||||||
\(998\) | −8.59773 | −0.272156 | ||||||||
\(999\) | −1.71472 | −0.0542513 |
(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 | 5025.2.a.bb.1.6 | 7 | ||
5.4 | even | 2 | 1005.2.a.i.1.2 | ✓ | 7 | ||
15.14 | odd | 2 | 3015.2.a.l.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1005.2.a.i.1.2 | ✓ | 7 | 5.4 | even | 2 | ||
3015.2.a.l.1.6 | 7 | 15.14 | odd | 2 | |||
5025.2.a.bb.1.6 | 7 | 1.1 | even | 1 | trivial |