Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7267,2,Mod(1,7267)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7267, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7267.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7267 = 13^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7267.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: | \(58.0272871489\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7267.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.585786 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | 0.585786 | 0.221406 | 0.110703 | − | 0.993854i | \(-0.464690\pi\) | ||||
0.110703 | + | 0.993854i | \(0.464690\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.828427 | 0.261972 | ||||||||
\(11\) | −1.82843 | −0.551292 | −0.275646 | − | 0.961259i | \(-0.588892\pi\) | ||||
−0.275646 | + | 0.961259i | \(0.588892\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.828427 | −0.221406 | ||||||||
\(15\) | 0.828427 | 0.213899 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 7.82843 | 1.89867 | 0.949336 | − | 0.314262i | \(-0.101757\pi\) | ||||
0.949336 | + | 0.314262i | \(0.101757\pi\) | |||||||
\(18\) | 1.41421 | 0.333333 | ||||||||
\(19\) | 4.82843 | 1.10772 | 0.553859 | − | 0.832611i | \(-0.313155\pi\) | ||||
0.553859 | + | 0.832611i | \(0.313155\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.828427 | −0.180778 | ||||||||
\(22\) | 2.58579 | 0.551292 | ||||||||
\(23\) | −4.65685 | −0.971021 | −0.485511 | − | 0.874231i | \(-0.661366\pi\) | ||||
−0.485511 | + | 0.874231i | \(0.661366\pi\) | |||||||
\(24\) | −4.00000 | −0.816497 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24264 | 0.787839 | 0.393919 | − | 0.919145i | \(-0.371119\pi\) | ||||
0.393919 | + | 0.919145i | \(0.371119\pi\) | |||||||
\(30\) | −1.17157 | −0.213899 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.58579 | 0.450128 | ||||||||
\(34\) | −11.0711 | −1.89867 | ||||||||
\(35\) | −0.343146 | −0.0580022 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.48528 | 1.39497 | 0.697486 | − | 0.716599i | \(-0.254302\pi\) | ||||
0.697486 | + | 0.716599i | \(0.254302\pi\) | |||||||
\(38\) | −6.82843 | −1.10772 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.65685 | −0.261972 | ||||||||
\(41\) | 3.82843 | 0.597900 | 0.298950 | − | 0.954269i | \(-0.403364\pi\) | ||||
0.298950 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(42\) | 1.17157 | 0.180778 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.585786 | 0.0873239 | ||||||||
\(46\) | 6.58579 | 0.971021 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 5.65685 | 0.816497 | ||||||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | 6.58579 | 0.931371 | ||||||||
\(51\) | −11.0711 | −1.55026 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.17157 | 1.12245 | 0.561226 | − | 0.827663i | \(-0.310330\pi\) | ||||
0.561226 | + | 0.827663i | \(0.310330\pi\) | |||||||
\(54\) | −8.00000 | −1.08866 | ||||||||
\(55\) | 1.07107 | 0.144423 | ||||||||
\(56\) | 1.65685 | 0.221406 | ||||||||
\(57\) | −6.82843 | −0.904447 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | −0.828427 | −0.107852 | −0.0539260 | − | 0.998545i | \(-0.517174\pi\) | ||||
−0.0539260 | + | 0.998545i | \(0.517174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.24264 | 1.05536 | 0.527681 | − | 0.849443i | \(-0.323062\pi\) | ||||
0.527681 | + | 0.849443i | \(0.323062\pi\) | |||||||
\(62\) | −4.24264 | −0.538816 | ||||||||
\(63\) | −0.585786 | −0.0738022 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.65685 | −0.450128 | ||||||||
\(67\) | −9.48528 | −1.15881 | −0.579406 | − | 0.815039i | \(-0.696715\pi\) | ||||
−0.579406 | + | 0.815039i | \(0.696715\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.58579 | 0.792836 | ||||||||
\(70\) | 0.485281 | 0.0580022 | ||||||||
\(71\) | 8.82843 | 1.04774 | 0.523871 | − | 0.851798i | \(-0.324487\pi\) | ||||
0.523871 | + | 0.851798i | \(0.324487\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | 7.75736 | 0.907930 | 0.453965 | − | 0.891019i | \(-0.350009\pi\) | ||||
0.453965 | + | 0.891019i | \(0.350009\pi\) | |||||||
\(74\) | −12.0000 | −1.39497 | ||||||||
\(75\) | 6.58579 | 0.760461 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.07107 | −0.122060 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.828427 | −0.0932053 | −0.0466027 | − | 0.998914i | \(-0.514839\pi\) | ||||
−0.0466027 | + | 0.998914i | \(0.514839\pi\) | |||||||
\(80\) | 2.34315 | 0.261972 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −5.41421 | −0.597900 | ||||||||
\(83\) | −14.6569 | −1.60880 | −0.804399 | − | 0.594089i | \(-0.797513\pi\) | ||||
−0.804399 | + | 0.594089i | \(0.797513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.58579 | −0.497398 | ||||||||
\(86\) | −1.41421 | −0.152499 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | −5.17157 | −0.551292 | ||||||||
\(89\) | 10.2426 | 1.08572 | 0.542859 | − | 0.839824i | \(-0.317342\pi\) | ||||
0.542859 | + | 0.839824i | \(0.317342\pi\) | |||||||
\(90\) | −0.828427 | −0.0873239 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.24264 | −0.439941 | ||||||||
\(94\) | 8.48528 | 0.875190 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.82843 | 0.388718 | 0.194359 | − | 0.980930i | \(-0.437737\pi\) | ||||
0.194359 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(98\) | 9.41421 | 0.950979 | ||||||||
\(99\) | 1.82843 | 0.183764 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.171573 | 0.0170721 | 0.00853607 | − | 0.999964i | \(-0.497283\pi\) | ||||
0.00853607 | + | 0.999964i | \(0.497283\pi\) | |||||||
\(102\) | 15.6569 | 1.55026 | ||||||||
\(103\) | 17.4853 | 1.72288 | 0.861438 | − | 0.507863i | \(-0.169564\pi\) | ||||
0.861438 | + | 0.507863i | \(0.169564\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.485281 | 0.0473586 | ||||||||
\(106\) | −11.5563 | −1.12245 | ||||||||
\(107\) | −11.6569 | −1.12691 | −0.563455 | − | 0.826147i | \(-0.690528\pi\) | ||||
−0.563455 | + | 0.826147i | \(0.690528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.9706 | −1.33814 | −0.669069 | − | 0.743201i | \(-0.733307\pi\) | ||||
−0.669069 | + | 0.743201i | \(0.733307\pi\) | |||||||
\(110\) | −1.51472 | −0.144423 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | −2.34315 | −0.221406 | ||||||||
\(113\) | −1.17157 | −0.110212 | −0.0551062 | − | 0.998481i | \(-0.517550\pi\) | ||||
−0.0551062 | + | 0.998481i | \(0.517550\pi\) | |||||||
\(114\) | 9.65685 | 0.904447 | ||||||||
\(115\) | 2.72792 | 0.254380 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.17157 | 0.107852 | ||||||||
\(119\) | 4.58579 | 0.420378 | ||||||||
\(120\) | 2.34315 | 0.213899 | ||||||||
\(121\) | −7.65685 | −0.696078 | ||||||||
\(122\) | −11.6569 | −1.05536 | ||||||||
\(123\) | −5.41421 | −0.488183 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0.828427 | 0.0738022 | ||||||||
\(127\) | −1.82843 | −0.162247 | −0.0811233 | − | 0.996704i | \(-0.525851\pi\) | ||||
−0.0811233 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | −1.41421 | −0.124515 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.65685 | −0.144760 | −0.0723800 | − | 0.997377i | \(-0.523059\pi\) | ||||
−0.0723800 | + | 0.997377i | \(0.523059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 13.4142 | 1.15881 | ||||||||
\(135\) | −3.31371 | −0.285199 | ||||||||
\(136\) | 22.1421 | 1.89867 | ||||||||
\(137\) | −2.48528 | −0.212332 | −0.106166 | − | 0.994348i | \(-0.533857\pi\) | ||||
−0.106166 | + | 0.994348i | \(0.533857\pi\) | |||||||
\(138\) | −9.31371 | −0.792836 | ||||||||
\(139\) | −11.4853 | −0.974169 | −0.487084 | − | 0.873355i | \(-0.661940\pi\) | ||||
−0.487084 | + | 0.873355i | \(0.661940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.48528 | 0.714590 | ||||||||
\(142\) | −12.4853 | −1.04774 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | −2.48528 | −0.206391 | ||||||||
\(146\) | −10.9706 | −0.907930 | ||||||||
\(147\) | 9.41421 | 0.776471 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.48528 | 0.695141 | 0.347571 | − | 0.937654i | \(-0.387007\pi\) | ||||
0.347571 | + | 0.937654i | \(0.387007\pi\) | |||||||
\(150\) | −9.31371 | −0.760461 | ||||||||
\(151\) | −9.75736 | −0.794043 | −0.397021 | − | 0.917809i | \(-0.629956\pi\) | ||||
−0.397021 | + | 0.917809i | \(0.629956\pi\) | |||||||
\(152\) | 13.6569 | 1.10772 | ||||||||
\(153\) | −7.82843 | −0.632891 | ||||||||
\(154\) | 1.51472 | 0.122060 | ||||||||
\(155\) | −1.75736 | −0.141154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0000 | −0.798087 | −0.399043 | − | 0.916932i | \(-0.630658\pi\) | ||||
−0.399043 | + | 0.916932i | \(0.630658\pi\) | |||||||
\(158\) | 1.17157 | 0.0932053 | ||||||||
\(159\) | −11.5563 | −0.916478 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.72792 | −0.214990 | ||||||||
\(162\) | 7.07107 | 0.555556 | ||||||||
\(163\) | 20.2426 | 1.58553 | 0.792763 | − | 0.609530i | \(-0.208642\pi\) | ||||
0.792763 | + | 0.609530i | \(0.208642\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.51472 | −0.117921 | ||||||||
\(166\) | 20.7279 | 1.60880 | ||||||||
\(167\) | −8.31371 | −0.643334 | −0.321667 | − | 0.946853i | \(-0.604243\pi\) | ||||
−0.321667 | + | 0.946853i | \(0.604243\pi\) | |||||||
\(168\) | −2.34315 | −0.180778 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.48528 | 0.497398 | ||||||||
\(171\) | −4.82843 | −0.369239 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3431 | 0.938432 | 0.469216 | − | 0.883083i | \(-0.344537\pi\) | ||||
0.469216 | + | 0.883083i | \(0.344537\pi\) | |||||||
\(174\) | 8.48528 | 0.643268 | ||||||||
\(175\) | −2.72792 | −0.206212 | ||||||||
\(176\) | 7.31371 | 0.551292 | ||||||||
\(177\) | 1.17157 | 0.0880608 | ||||||||
\(178\) | −14.4853 | −1.08572 | ||||||||
\(179\) | −7.41421 | −0.554164 | −0.277082 | − | 0.960846i | \(-0.589367\pi\) | ||||
−0.277082 | + | 0.960846i | \(0.589367\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3137 | −1.13826 | −0.569129 | − | 0.822248i | \(-0.692720\pi\) | ||||
−0.569129 | + | 0.822248i | \(0.692720\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.6569 | −0.861699 | ||||||||
\(184\) | −13.1716 | −0.971021 | ||||||||
\(185\) | −4.97056 | −0.365443 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | −14.3137 | −1.04672 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.31371 | 0.241037 | ||||||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 22.1421 | 1.60215 | 0.801074 | − | 0.598565i | \(-0.204262\pi\) | ||||
0.801074 | + | 0.598565i | \(0.204262\pi\) | |||||||
\(192\) | −11.3137 | −0.816497 | ||||||||
\(193\) | 17.9706 | 1.29355 | 0.646775 | − | 0.762681i | \(-0.276117\pi\) | ||||
0.646775 | + | 0.762681i | \(0.276117\pi\) | |||||||
\(194\) | −5.41421 | −0.388718 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.1421 | −1.00759 | −0.503793 | − | 0.863825i | \(-0.668062\pi\) | ||||
−0.503793 | + | 0.863825i | \(0.668062\pi\) | |||||||
\(198\) | −2.58579 | −0.183764 | ||||||||
\(199\) | −3.65685 | −0.259228 | −0.129614 | − | 0.991565i | \(-0.541374\pi\) | ||||
−0.129614 | + | 0.991565i | \(0.541374\pi\) | |||||||
\(200\) | −13.1716 | −0.931371 | ||||||||
\(201\) | 13.4142 | 0.946166 | ||||||||
\(202\) | −0.242641 | −0.0170721 | ||||||||
\(203\) | 2.48528 | 0.174433 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.24264 | −0.156633 | ||||||||
\(206\) | −24.7279 | −1.72288 | ||||||||
\(207\) | 4.65685 | 0.323674 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.82843 | −0.610675 | ||||||||
\(210\) | −0.686292 | −0.0473586 | ||||||||
\(211\) | 28.1421 | 1.93738 | 0.968692 | − | 0.248265i | \(-0.0798602\pi\) | ||||
0.968692 | + | 0.248265i | \(0.0798602\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.4853 | −0.855477 | ||||||||
\(214\) | 16.4853 | 1.12691 | ||||||||
\(215\) | −0.585786 | −0.0399503 | ||||||||
\(216\) | 16.0000 | 1.08866 | ||||||||
\(217\) | 1.75736 | 0.119297 | ||||||||
\(218\) | 19.7574 | 1.33814 | ||||||||
\(219\) | −10.9706 | −0.741322 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 16.9706 | 1.13899 | ||||||||
\(223\) | −23.8995 | −1.60043 | −0.800214 | − | 0.599714i | \(-0.795281\pi\) | ||||
−0.800214 | + | 0.599714i | \(0.795281\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.65685 | 0.310457 | ||||||||
\(226\) | 1.65685 | 0.110212 | ||||||||
\(227\) | 17.6569 | 1.17193 | 0.585963 | − | 0.810338i | \(-0.300716\pi\) | ||||
0.585963 | + | 0.810338i | \(0.300716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.97056 | −0.526710 | −0.263355 | − | 0.964699i | \(-0.584829\pi\) | ||||
−0.263355 | + | 0.964699i | \(0.584829\pi\) | |||||||
\(230\) | −3.85786 | −0.254380 | ||||||||
\(231\) | 1.51472 | 0.0996612 | ||||||||
\(232\) | 12.0000 | 0.787839 | ||||||||
\(233\) | −0.828427 | −0.0542721 | −0.0271360 | − | 0.999632i | \(-0.508639\pi\) | ||||
−0.0271360 | + | 0.999632i | \(0.508639\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.51472 | 0.229275 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.17157 | 0.0761018 | ||||||||
\(238\) | −6.48528 | −0.420378 | ||||||||
\(239\) | 2.48528 | 0.160759 | 0.0803797 | − | 0.996764i | \(-0.474387\pi\) | ||||
0.0803797 | + | 0.996764i | \(0.474387\pi\) | |||||||
\(240\) | −3.31371 | −0.213899 | ||||||||
\(241\) | −4.00000 | −0.257663 | −0.128831 | − | 0.991667i | \(-0.541123\pi\) | ||||
−0.128831 | + | 0.991667i | \(0.541123\pi\) | |||||||
\(242\) | 10.8284 | 0.696078 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.89949 | 0.249130 | ||||||||
\(246\) | 7.65685 | 0.488183 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.48528 | 0.538816 | ||||||||
\(249\) | 20.7279 | 1.31358 | ||||||||
\(250\) | −8.00000 | −0.505964 | ||||||||
\(251\) | −5.14214 | −0.324569 | −0.162284 | − | 0.986744i | \(-0.551886\pi\) | ||||
−0.162284 | + | 0.986744i | \(0.551886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.51472 | 0.535316 | ||||||||
\(254\) | 2.58579 | 0.162247 | ||||||||
\(255\) | 6.48528 | 0.406124 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.2426 | −0.638918 | −0.319459 | − | 0.947600i | \(-0.603501\pi\) | ||||
−0.319459 | + | 0.947600i | \(0.603501\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | 4.97056 | 0.308856 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.24264 | −0.262613 | ||||||||
\(262\) | 2.34315 | 0.144760 | ||||||||
\(263\) | −28.1421 | −1.73532 | −0.867659 | − | 0.497159i | \(-0.834376\pi\) | ||||
−0.867659 | + | 0.497159i | \(0.834376\pi\) | |||||||
\(264\) | 7.31371 | 0.450128 | ||||||||
\(265\) | −4.78680 | −0.294051 | ||||||||
\(266\) | −4.00000 | −0.245256 | ||||||||
\(267\) | −14.4853 | −0.886485 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00000 | −0.182913 | −0.0914566 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914566 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(270\) | 4.68629 | 0.285199 | ||||||||
\(271\) | −7.97056 | −0.484177 | −0.242089 | − | 0.970254i | \(-0.577832\pi\) | ||||
−0.242089 | + | 0.970254i | \(0.577832\pi\) | |||||||
\(272\) | −31.3137 | −1.89867 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.51472 | 0.212332 | ||||||||
\(275\) | 8.51472 | 0.513457 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8995 | −0.714971 | −0.357486 | − | 0.933919i | \(-0.616366\pi\) | ||||
−0.357486 | + | 0.933919i | \(0.616366\pi\) | |||||||
\(278\) | 16.2426 | 0.974169 | ||||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | −0.970563 | −0.0580022 | ||||||||
\(281\) | −2.65685 | −0.158495 | −0.0792473 | − | 0.996855i | \(-0.525252\pi\) | ||||
−0.0792473 | + | 0.996855i | \(0.525252\pi\) | |||||||
\(282\) | −12.0000 | −0.714590 | ||||||||
\(283\) | −4.31371 | −0.256423 | −0.128212 | − | 0.991747i | \(-0.540924\pi\) | ||||
−0.128212 | + | 0.991747i | \(0.540924\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.24264 | 0.132379 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.2843 | 2.60496 | ||||||||
\(290\) | 3.51472 | 0.206391 | ||||||||
\(291\) | −5.41421 | −0.317387 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.6569 | −1.26521 | −0.632603 | − | 0.774476i | \(-0.718014\pi\) | ||||
−0.632603 | + | 0.774476i | \(0.718014\pi\) | |||||||
\(294\) | −13.3137 | −0.776471 | ||||||||
\(295\) | 0.485281 | 0.0282542 | ||||||||
\(296\) | 24.0000 | 1.39497 | ||||||||
\(297\) | −10.3431 | −0.600170 | ||||||||
\(298\) | −12.0000 | −0.695141 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.585786 | 0.0337642 | ||||||||
\(302\) | 13.7990 | 0.794043 | ||||||||
\(303\) | −0.242641 | −0.0139393 | ||||||||
\(304\) | −19.3137 | −1.10772 | ||||||||
\(305\) | −4.82843 | −0.276475 | ||||||||
\(306\) | 11.0711 | 0.632891 | ||||||||
\(307\) | 12.7990 | 0.730477 | 0.365238 | − | 0.930914i | \(-0.380987\pi\) | ||||
0.365238 | + | 0.930914i | \(0.380987\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −24.7279 | −1.40672 | ||||||||
\(310\) | 2.48528 | 0.141154 | ||||||||
\(311\) | 19.9706 | 1.13243 | 0.566213 | − | 0.824259i | \(-0.308408\pi\) | ||||
0.566213 | + | 0.824259i | \(0.308408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.2132 | 0.972948 | 0.486474 | − | 0.873695i | \(-0.338283\pi\) | ||||
0.486474 | + | 0.873695i | \(0.338283\pi\) | |||||||
\(314\) | 14.1421 | 0.798087 | ||||||||
\(315\) | 0.343146 | 0.0193341 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.1716 | −1.13295 | −0.566474 | − | 0.824079i | \(-0.691693\pi\) | ||||
−0.566474 | + | 0.824079i | \(0.691693\pi\) | |||||||
\(318\) | 16.3431 | 0.916478 | ||||||||
\(319\) | −7.75736 | −0.434329 | ||||||||
\(320\) | −4.68629 | −0.261972 | ||||||||
\(321\) | 16.4853 | 0.920119 | ||||||||
\(322\) | 3.85786 | 0.214990 | ||||||||
\(323\) | 37.7990 | 2.10319 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −28.6274 | −1.58553 | ||||||||
\(327\) | 19.7574 | 1.09258 | ||||||||
\(328\) | 10.8284 | 0.597900 | ||||||||
\(329\) | −3.51472 | −0.193773 | ||||||||
\(330\) | 2.14214 | 0.117921 | ||||||||
\(331\) | −18.5858 | −1.02157 | −0.510784 | − | 0.859709i | \(-0.670645\pi\) | ||||
−0.510784 | + | 0.859709i | \(0.670645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.48528 | −0.464991 | ||||||||
\(334\) | 11.7574 | 0.643334 | ||||||||
\(335\) | 5.55635 | 0.303576 | ||||||||
\(336\) | 3.31371 | 0.180778 | ||||||||
\(337\) | −5.00000 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.65685 | 0.0899880 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.48528 | −0.297045 | ||||||||
\(342\) | 6.82843 | 0.369239 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 2.82843 | 0.152499 | ||||||||
\(345\) | −3.85786 | −0.207700 | ||||||||
\(346\) | −17.4558 | −0.938432 | ||||||||
\(347\) | −7.41421 | −0.398016 | −0.199008 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199008 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7574 | 0.629357 | 0.314679 | − | 0.949198i | \(-0.398103\pi\) | ||||
0.314679 | + | 0.949198i | \(0.398103\pi\) | |||||||
\(350\) | 3.85786 | 0.206212 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.171573 | −0.00913190 | −0.00456595 | − | 0.999990i | \(-0.501453\pi\) | ||||
−0.00456595 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(354\) | −1.65685 | −0.0880608 | ||||||||
\(355\) | −5.17157 | −0.274479 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.48528 | −0.343237 | ||||||||
\(358\) | 10.4853 | 0.554164 | ||||||||
\(359\) | 32.6569 | 1.72356 | 0.861781 | − | 0.507280i | \(-0.169349\pi\) | ||||
0.861781 | + | 0.507280i | \(0.169349\pi\) | |||||||
\(360\) | 1.65685 | 0.0873239 | ||||||||
\(361\) | 4.31371 | 0.227037 | ||||||||
\(362\) | 21.6569 | 1.13826 | ||||||||
\(363\) | 10.8284 | 0.568345 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.54416 | −0.237852 | ||||||||
\(366\) | 16.4853 | 0.861699 | ||||||||
\(367\) | −29.7990 | −1.55549 | −0.777747 | − | 0.628577i | \(-0.783638\pi\) | ||||
−0.777747 | + | 0.628577i | \(0.783638\pi\) | |||||||
\(368\) | 18.6274 | 0.971021 | ||||||||
\(369\) | −3.82843 | −0.199300 | ||||||||
\(370\) | 7.02944 | 0.365443 | ||||||||
\(371\) | 4.78680 | 0.248518 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.48528 | −0.439351 | −0.219676 | − | 0.975573i | \(-0.570500\pi\) | ||||
−0.219676 | + | 0.975573i | \(0.570500\pi\) | |||||||
\(374\) | 20.2426 | 1.04672 | ||||||||
\(375\) | −8.00000 | −0.413118 | ||||||||
\(376\) | −16.9706 | −0.875190 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.68629 | −0.241037 | ||||||||
\(379\) | −7.68629 | −0.394818 | −0.197409 | − | 0.980321i | \(-0.563253\pi\) | ||||
−0.197409 | + | 0.980321i | \(0.563253\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.58579 | 0.132474 | ||||||||
\(382\) | −31.3137 | −1.60215 | ||||||||
\(383\) | 3.51472 | 0.179594 | 0.0897969 | − | 0.995960i | \(-0.471378\pi\) | ||||
0.0897969 | + | 0.995960i | \(0.471378\pi\) | |||||||
\(384\) | 16.0000 | 0.816497 | ||||||||
\(385\) | 0.627417 | 0.0319761 | ||||||||
\(386\) | −25.4142 | −1.29355 | ||||||||
\(387\) | −1.00000 | −0.0508329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.6274 | 1.45147 | 0.725734 | − | 0.687976i | \(-0.241500\pi\) | ||||
0.725734 | + | 0.687976i | \(0.241500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.4558 | −1.84365 | ||||||||
\(392\) | −18.8284 | −0.950979 | ||||||||
\(393\) | 2.34315 | 0.118196 | ||||||||
\(394\) | 20.0000 | 1.00759 | ||||||||
\(395\) | 0.485281 | 0.0244172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.4558 | 1.07684 | 0.538419 | − | 0.842677i | \(-0.319022\pi\) | ||||
0.538419 | + | 0.842677i | \(0.319022\pi\) | |||||||
\(398\) | 5.17157 | 0.259228 | ||||||||
\(399\) | −4.00000 | −0.200250 | ||||||||
\(400\) | 18.6274 | 0.931371 | ||||||||
\(401\) | 29.4853 | 1.47242 | 0.736212 | − | 0.676751i | \(-0.236612\pi\) | ||||
0.736212 | + | 0.676751i | \(0.236612\pi\) | |||||||
\(402\) | −18.9706 | −0.946166 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.92893 | 0.145540 | ||||||||
\(406\) | −3.51472 | −0.174433 | ||||||||
\(407\) | −15.5147 | −0.769036 | ||||||||
\(408\) | −31.3137 | −1.55026 | ||||||||
\(409\) | −36.8701 | −1.82311 | −0.911554 | − | 0.411181i | \(-0.865116\pi\) | ||||
−0.911554 | + | 0.411181i | \(0.865116\pi\) | |||||||
\(410\) | 3.17157 | 0.156633 | ||||||||
\(411\) | 3.51472 | 0.173368 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.485281 | −0.0238791 | ||||||||
\(414\) | −6.58579 | −0.323674 | ||||||||
\(415\) | 8.58579 | 0.421460 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.2426 | 0.795406 | ||||||||
\(418\) | 12.4853 | 0.610675 | ||||||||
\(419\) | −4.10051 | −0.200323 | −0.100161 | − | 0.994971i | \(-0.531936\pi\) | ||||
−0.100161 | + | 0.994971i | \(0.531936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.34315 | 0.211672 | 0.105836 | − | 0.994384i | \(-0.466248\pi\) | ||||
0.105836 | + | 0.994384i | \(0.466248\pi\) | |||||||
\(422\) | −39.7990 | −1.93738 | ||||||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 23.1127 | 1.12245 | ||||||||
\(425\) | −36.4558 | −1.76837 | ||||||||
\(426\) | 17.6569 | 0.855477 | ||||||||
\(427\) | 4.82843 | 0.233664 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.828427 | 0.0399503 | ||||||||
\(431\) | 33.2843 | 1.60325 | 0.801623 | − | 0.597829i | \(-0.203970\pi\) | ||||
0.801623 | + | 0.597829i | \(0.203970\pi\) | |||||||
\(432\) | −22.6274 | −1.08866 | ||||||||
\(433\) | 30.2426 | 1.45337 | 0.726684 | − | 0.686972i | \(-0.241060\pi\) | ||||
0.726684 | + | 0.686972i | \(0.241060\pi\) | |||||||
\(434\) | −2.48528 | −0.119297 | ||||||||
\(435\) | 3.51472 | 0.168518 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.4853 | −1.07562 | ||||||||
\(438\) | 15.5147 | 0.741322 | ||||||||
\(439\) | −5.48528 | −0.261798 | −0.130899 | − | 0.991396i | \(-0.541786\pi\) | ||||
−0.130899 | + | 0.991396i | \(0.541786\pi\) | |||||||
\(440\) | 3.02944 | 0.144423 | ||||||||
\(441\) | 6.65685 | 0.316993 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.1421 | 1.71716 | 0.858582 | − | 0.512676i | \(-0.171346\pi\) | ||||
0.858582 | + | 0.512676i | \(0.171346\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | 33.7990 | 1.60043 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 4.68629 | 0.221406 | ||||||||
\(449\) | 9.21320 | 0.434798 | 0.217399 | − | 0.976083i | \(-0.430243\pi\) | ||||
0.217399 | + | 0.976083i | \(0.430243\pi\) | |||||||
\(450\) | −6.58579 | −0.310457 | ||||||||
\(451\) | −7.00000 | −0.329617 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.7990 | 0.648333 | ||||||||
\(454\) | −24.9706 | −1.17193 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −19.3137 | −0.904447 | ||||||||
\(457\) | 24.7279 | 1.15672 | 0.578362 | − | 0.815780i | \(-0.303692\pi\) | ||||
0.578362 | + | 0.815780i | \(0.303692\pi\) | |||||||
\(458\) | 11.2721 | 0.526710 | ||||||||
\(459\) | 44.2843 | 2.06701 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.62742 | 0.122371 | 0.0611855 | − | 0.998126i | \(-0.480512\pi\) | ||||
0.0611855 | + | 0.998126i | \(0.480512\pi\) | |||||||
\(462\) | −2.14214 | −0.0996612 | ||||||||
\(463\) | 5.27208 | 0.245014 | 0.122507 | − | 0.992468i | \(-0.460907\pi\) | ||||
0.122507 | + | 0.992468i | \(0.460907\pi\) | |||||||
\(464\) | −16.9706 | −0.787839 | ||||||||
\(465\) | 2.48528 | 0.115252 | ||||||||
\(466\) | 1.17157 | 0.0542721 | ||||||||
\(467\) | 12.3431 | 0.571173 | 0.285586 | − | 0.958353i | \(-0.407812\pi\) | ||||
0.285586 | + | 0.958353i | \(0.407812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.55635 | −0.256568 | ||||||||
\(470\) | −4.97056 | −0.229275 | ||||||||
\(471\) | 14.1421 | 0.651635 | ||||||||
\(472\) | −2.34315 | −0.107852 | ||||||||
\(473\) | −1.82843 | −0.0840712 | ||||||||
\(474\) | −1.65685 | −0.0761018 | ||||||||
\(475\) | −22.4853 | −1.03170 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.17157 | −0.374151 | ||||||||
\(478\) | −3.51472 | −0.160759 | ||||||||
\(479\) | −4.65685 | −0.212777 | −0.106389 | − | 0.994325i | \(-0.533929\pi\) | ||||
−0.106389 | + | 0.994325i | \(0.533929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.65685 | 0.257663 | ||||||||
\(483\) | 3.85786 | 0.175539 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.24264 | −0.101833 | ||||||||
\(486\) | 14.0000 | 0.635053 | ||||||||
\(487\) | −33.6569 | −1.52514 | −0.762569 | − | 0.646907i | \(-0.776062\pi\) | ||||
−0.762569 | + | 0.646907i | \(0.776062\pi\) | |||||||
\(488\) | 23.3137 | 1.05536 | ||||||||
\(489\) | −28.6274 | −1.29458 | ||||||||
\(490\) | −5.51472 | −0.249130 | ||||||||
\(491\) | 10.5858 | 0.477730 | 0.238865 | − | 0.971053i | \(-0.423225\pi\) | ||||
0.238865 | + | 0.971053i | \(0.423225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.2132 | 1.49585 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.07107 | −0.0481409 | ||||||||
\(496\) | −12.0000 | −0.538816 | ||||||||
\(497\) | 5.17157 | 0.231977 | ||||||||
\(498\) | −29.3137 | −1.31358 | ||||||||
\(499\) | 34.2426 | 1.53291 | 0.766456 | − | 0.642297i | \(-0.222019\pi\) | ||||
0.766456 | + | 0.642297i | \(0.222019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.7574 | 0.525280 | ||||||||
\(502\) | 7.27208 | 0.324569 | ||||||||
\(503\) | 42.7696 | 1.90700 | 0.953500 | − | 0.301393i | \(-0.0974516\pi\) | ||||
0.953500 | + | 0.301393i | \(0.0974516\pi\) | |||||||
\(504\) | −1.65685 | −0.0738022 | ||||||||
\(505\) | −0.100505 | −0.00447242 | ||||||||
\(506\) | −12.0416 | −0.535316 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.4853 | −0.775021 | −0.387511 | − | 0.921865i | \(-0.626665\pi\) | ||||
−0.387511 | + | 0.921865i | \(0.626665\pi\) | |||||||
\(510\) | −9.17157 | −0.406124 | ||||||||
\(511\) | 4.54416 | 0.201022 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | 27.3137 | 1.20593 | ||||||||
\(514\) | 14.4853 | 0.638918 | ||||||||
\(515\) | −10.2426 | −0.451345 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.9706 | 0.482485 | ||||||||
\(518\) | −7.02944 | −0.308856 | ||||||||
\(519\) | −17.4558 | −0.766227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.0711 | 1.36125 | 0.680624 | − | 0.732633i | \(-0.261709\pi\) | ||||
0.680624 | + | 0.732633i | \(0.261709\pi\) | |||||||
\(522\) | 6.00000 | 0.262613 | ||||||||
\(523\) | 3.21320 | 0.140504 | 0.0702518 | − | 0.997529i | \(-0.477620\pi\) | ||||
0.0702518 | + | 0.997529i | \(0.477620\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.85786 | 0.168371 | ||||||||
\(526\) | 39.7990 | 1.73532 | ||||||||
\(527\) | 23.4853 | 1.02303 | ||||||||
\(528\) | −10.3431 | −0.450128 | ||||||||
\(529\) | −1.31371 | −0.0571178 | ||||||||
\(530\) | 6.76955 | 0.294051 | ||||||||
\(531\) | 0.828427 | 0.0359507 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 20.4853 | 0.886485 | ||||||||
\(535\) | 6.82843 | 0.295219 | ||||||||
\(536\) | −26.8284 | −1.15881 | ||||||||
\(537\) | 10.4853 | 0.452473 | ||||||||
\(538\) | 4.24264 | 0.182913 | ||||||||
\(539\) | 12.1716 | 0.524267 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.7990 | 1.32415 | 0.662076 | − | 0.749437i | \(-0.269676\pi\) | ||||
0.662076 | + | 0.749437i | \(0.269676\pi\) | |||||||
\(542\) | 11.2721 | 0.484177 | ||||||||
\(543\) | 21.6569 | 0.929385 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.18377 | 0.350554 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.00000 | 0.384812 | 0.192406 | − | 0.981315i | \(-0.438371\pi\) | ||||
0.192406 | + | 0.981315i | \(0.438371\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.24264 | −0.351787 | ||||||||
\(550\) | −12.0416 | −0.513457 | ||||||||
\(551\) | 20.4853 | 0.872702 | ||||||||
\(552\) | 18.6274 | 0.792836 | ||||||||
\(553\) | −0.485281 | −0.0206363 | ||||||||
\(554\) | 16.8284 | 0.714971 | ||||||||
\(555\) | 7.02944 | 0.298383 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.00000 | 0.381342 | 0.190671 | − | 0.981654i | \(-0.438934\pi\) | ||||
0.190671 | + | 0.981654i | \(0.438934\pi\) | |||||||
\(558\) | 4.24264 | 0.179605 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.37258 | 0.0580022 | ||||||||
\(561\) | 20.2426 | 0.854645 | ||||||||
\(562\) | 3.75736 | 0.158495 | ||||||||
\(563\) | −5.62742 | −0.237167 | −0.118584 | − | 0.992944i | \(-0.537835\pi\) | ||||
−0.118584 | + | 0.992944i | \(0.537835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.686292 | 0.0288725 | ||||||||
\(566\) | 6.10051 | 0.256423 | ||||||||
\(567\) | −2.92893 | −0.123004 | ||||||||
\(568\) | 24.9706 | 1.04774 | ||||||||
\(569\) | 24.6569 | 1.03367 | 0.516835 | − | 0.856085i | \(-0.327110\pi\) | ||||
0.516835 | + | 0.856085i | \(0.327110\pi\) | |||||||
\(570\) | −5.65685 | −0.236940 | ||||||||
\(571\) | 11.0711 | 0.463310 | 0.231655 | − | 0.972798i | \(-0.425586\pi\) | ||||
0.231655 | + | 0.972798i | \(0.425586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.3137 | −1.30815 | ||||||||
\(574\) | −3.17157 | −0.132379 | ||||||||
\(575\) | 21.6863 | 0.904381 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | −18.9289 | −0.788022 | −0.394011 | − | 0.919106i | \(-0.628913\pi\) | ||||
−0.394011 | + | 0.919106i | \(0.628913\pi\) | |||||||
\(578\) | −62.6274 | −2.60496 | ||||||||
\(579\) | −25.4142 | −1.05618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.58579 | −0.356198 | ||||||||
\(582\) | 7.65685 | 0.317387 | ||||||||
\(583\) | −14.9411 | −0.618798 | ||||||||
\(584\) | 21.9411 | 0.907930 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.6274 | 1.26521 | ||||||||
\(587\) | 5.79899 | 0.239350 | 0.119675 | − | 0.992813i | \(-0.461815\pi\) | ||||
0.119675 | + | 0.992813i | \(0.461815\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.4853 | 0.596856 | ||||||||
\(590\) | −0.686292 | −0.0282542 | ||||||||
\(591\) | 20.0000 | 0.822690 | ||||||||
\(592\) | −33.9411 | −1.39497 | ||||||||
\(593\) | −5.07107 | −0.208244 | −0.104122 | − | 0.994565i | \(-0.533203\pi\) | ||||
−0.104122 | + | 0.994565i | \(0.533203\pi\) | |||||||
\(594\) | 14.6274 | 0.600170 | ||||||||
\(595\) | −2.68629 | −0.110127 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.17157 | 0.211658 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.3431 | 1.03549 | 0.517746 | − | 0.855534i | \(-0.326771\pi\) | ||||
0.517746 | + | 0.855534i | \(0.326771\pi\) | |||||||
\(600\) | 18.6274 | 0.760461 | ||||||||
\(601\) | 8.97056 | 0.365917 | 0.182958 | − | 0.983121i | \(-0.441433\pi\) | ||||
0.182958 | + | 0.983121i | \(0.441433\pi\) | |||||||
\(602\) | −0.828427 | −0.0337642 | ||||||||
\(603\) | 9.48528 | 0.386271 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.48528 | 0.182353 | ||||||||
\(606\) | 0.343146 | 0.0139393 | ||||||||
\(607\) | 0.970563 | 0.0393939 | 0.0196970 | − | 0.999806i | \(-0.493730\pi\) | ||||
0.0196970 | + | 0.999806i | \(0.493730\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.51472 | −0.142424 | ||||||||
\(610\) | 6.82843 | 0.276475 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.17157 | −0.0473194 | −0.0236597 | − | 0.999720i | \(-0.507532\pi\) | ||||
−0.0236597 | + | 0.999720i | \(0.507532\pi\) | |||||||
\(614\) | −18.1005 | −0.730477 | ||||||||
\(615\) | 3.17157 | 0.127890 | ||||||||
\(616\) | −3.02944 | −0.122060 | ||||||||
\(617\) | 13.9706 | 0.562434 | 0.281217 | − | 0.959644i | \(-0.409262\pi\) | ||||
0.281217 | + | 0.959644i | \(0.409262\pi\) | |||||||
\(618\) | 34.9706 | 1.40672 | ||||||||
\(619\) | 4.97056 | 0.199784 | 0.0998919 | − | 0.994998i | \(-0.468150\pi\) | ||||
0.0998919 | + | 0.994998i | \(0.468150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.3431 | −1.05711 | ||||||||
\(622\) | −28.2426 | −1.13243 | ||||||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | −24.3431 | −0.972948 | ||||||||
\(627\) | 12.4853 | 0.498614 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 66.4264 | 2.64859 | ||||||||
\(630\) | −0.485281 | −0.0193341 | ||||||||
\(631\) | 26.7696 | 1.06568 | 0.532840 | − | 0.846216i | \(-0.321125\pi\) | ||||
0.532840 | + | 0.846216i | \(0.321125\pi\) | |||||||
\(632\) | −2.34315 | −0.0932053 | ||||||||
\(633\) | −39.7990 | −1.58187 | ||||||||
\(634\) | 28.5269 | 1.13295 | ||||||||
\(635\) | 1.07107 | 0.0425040 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.9706 | 0.434329 | ||||||||
\(639\) | −8.82843 | −0.349247 | ||||||||
\(640\) | 6.62742 | 0.261972 | ||||||||
\(641\) | 1.55635 | 0.0614721 | 0.0307360 | − | 0.999528i | \(-0.490215\pi\) | ||||
0.0307360 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(642\) | −23.3137 | −0.920119 | ||||||||
\(643\) | 9.51472 | 0.375224 | 0.187612 | − | 0.982243i | \(-0.439925\pi\) | ||||
0.187612 | + | 0.982243i | \(0.439925\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.828427 | 0.0326193 | ||||||||
\(646\) | −53.4558 | −2.10319 | ||||||||
\(647\) | −6.82843 | −0.268453 | −0.134227 | − | 0.990951i | \(-0.542855\pi\) | ||||
−0.134227 | + | 0.990951i | \(0.542855\pi\) | |||||||
\(648\) | −14.1421 | −0.555556 | ||||||||
\(649\) | 1.51472 | 0.0594579 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.48528 | −0.0974059 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.8284 | 0.815079 | 0.407540 | − | 0.913188i | \(-0.366387\pi\) | ||||
0.407540 | + | 0.913188i | \(0.366387\pi\) | |||||||
\(654\) | −27.9411 | −1.09258 | ||||||||
\(655\) | 0.970563 | 0.0379230 | ||||||||
\(656\) | −15.3137 | −0.597900 | ||||||||
\(657\) | −7.75736 | −0.302643 | ||||||||
\(658\) | 4.97056 | 0.193773 | ||||||||
\(659\) | −6.31371 | −0.245947 | −0.122974 | − | 0.992410i | \(-0.539243\pi\) | ||||
−0.122974 | + | 0.992410i | \(0.539243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.0000 | 0.661223 | 0.330612 | − | 0.943767i | \(-0.392745\pi\) | ||||
0.330612 | + | 0.943767i | \(0.392745\pi\) | |||||||
\(662\) | 26.2843 | 1.02157 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −41.4558 | −1.60880 | ||||||||
\(665\) | −1.65685 | −0.0642501 | ||||||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | −19.7574 | −0.765008 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.7990 | 1.30674 | ||||||||
\(670\) | −7.85786 | −0.303576 | ||||||||
\(671\) | −15.0711 | −0.581812 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.72792 | 0.336437 | 0.168218 | − | 0.985750i | \(-0.446199\pi\) | ||||
0.168218 | + | 0.985750i | \(0.446199\pi\) | |||||||
\(674\) | 7.07107 | 0.272367 | ||||||||
\(675\) | −26.3431 | −1.01395 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.8284 | 0.646769 | 0.323384 | − | 0.946268i | \(-0.395179\pi\) | ||||
0.323384 | + | 0.946268i | \(0.395179\pi\) | |||||||
\(678\) | −2.34315 | −0.0899880 | ||||||||
\(679\) | 2.24264 | 0.0860647 | ||||||||
\(680\) | −12.9706 | −0.497398 | ||||||||
\(681\) | −24.9706 | −0.956874 | ||||||||
\(682\) | 7.75736 | 0.297045 | ||||||||
\(683\) | −4.45584 | −0.170498 | −0.0852491 | − | 0.996360i | \(-0.527169\pi\) | ||||
−0.0852491 | + | 0.996360i | \(0.527169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.45584 | 0.0556249 | ||||||||
\(686\) | 11.3137 | 0.431959 | ||||||||
\(687\) | 11.2721 | 0.430057 | ||||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5.45584 | 0.207700 | ||||||||
\(691\) | 1.27208 | 0.0483921 | 0.0241961 | − | 0.999707i | \(-0.492297\pi\) | ||||
0.0241961 | + | 0.999707i | \(0.492297\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.07107 | 0.0406865 | ||||||||
\(694\) | 10.4853 | 0.398016 | ||||||||
\(695\) | 6.72792 | 0.255205 | ||||||||
\(696\) | −16.9706 | −0.643268 | ||||||||
\(697\) | 29.9706 | 1.13522 | ||||||||
\(698\) | −16.6274 | −0.629357 | ||||||||
\(699\) | 1.17157 | 0.0443130 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3431 | −0.692811 | −0.346406 | − | 0.938085i | \(-0.612598\pi\) | ||||
−0.346406 | + | 0.938085i | \(0.612598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.9706 | 1.54523 | ||||||||
\(704\) | −14.6274 | −0.551292 | ||||||||
\(705\) | −4.97056 | −0.187202 | ||||||||
\(706\) | 0.242641 | 0.00913190 | ||||||||
\(707\) | 0.100505 | 0.00377988 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1127 | −0.905571 | −0.452786 | − | 0.891619i | \(-0.649570\pi\) | ||||
−0.452786 | + | 0.891619i | \(0.649570\pi\) | |||||||
\(710\) | 7.31371 | 0.274479 | ||||||||
\(711\) | 0.828427 | 0.0310684 | ||||||||
\(712\) | 28.9706 | 1.08572 | ||||||||
\(713\) | −13.9706 | −0.523202 | ||||||||
\(714\) | 9.17157 | 0.343237 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.51472 | −0.131260 | ||||||||
\(718\) | −46.1838 | −1.72356 | ||||||||
\(719\) | 22.6274 | 0.843860 | 0.421930 | − | 0.906628i | \(-0.361353\pi\) | ||||
0.421930 | + | 0.906628i | \(0.361353\pi\) | |||||||
\(720\) | −2.34315 | −0.0873239 | ||||||||
\(721\) | 10.2426 | 0.381456 | ||||||||
\(722\) | −6.10051 | −0.227037 | ||||||||
\(723\) | 5.65685 | 0.210381 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.7574 | −0.733770 | ||||||||
\(726\) | −15.3137 | −0.568345 | ||||||||
\(727\) | 8.97056 | 0.332700 | 0.166350 | − | 0.986067i | \(-0.446802\pi\) | ||||
0.166350 | + | 0.986067i | \(0.446802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 6.42641 | 0.237852 | ||||||||
\(731\) | 7.82843 | 0.289545 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.9706 | 0.626822 | 0.313411 | − | 0.949618i | \(-0.398528\pi\) | ||||
0.313411 | + | 0.949618i | \(0.398528\pi\) | |||||||
\(734\) | 42.1421 | 1.55549 | ||||||||
\(735\) | −5.51472 | −0.203413 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.3431 | 0.638843 | ||||||||
\(738\) | 5.41421 | 0.199300 | ||||||||
\(739\) | −11.4558 | −0.421410 | −0.210705 | − | 0.977550i | \(-0.567576\pi\) | ||||
−0.210705 | + | 0.977550i | \(0.567576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.76955 | −0.248518 | ||||||||
\(743\) | 47.1127 | 1.72840 | 0.864199 | − | 0.503151i | \(-0.167826\pi\) | ||||
0.864199 | + | 0.503151i | \(0.167826\pi\) | |||||||
\(744\) | −12.0000 | −0.439941 | ||||||||
\(745\) | −4.97056 | −0.182107 | ||||||||
\(746\) | 12.0000 | 0.439351 | ||||||||
\(747\) | 14.6569 | 0.536266 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.82843 | −0.249505 | ||||||||
\(750\) | 11.3137 | 0.413118 | ||||||||
\(751\) | −20.2426 | −0.738664 | −0.369332 | − | 0.929297i | \(-0.620414\pi\) | ||||
−0.369332 | + | 0.929297i | \(0.620414\pi\) | |||||||
\(752\) | 24.0000 | 0.875190 | ||||||||
\(753\) | 7.27208 | 0.265009 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.71573 | 0.208017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.4853 | 0.744550 | 0.372275 | − | 0.928122i | \(-0.378578\pi\) | ||||
0.372275 | + | 0.928122i | \(0.378578\pi\) | |||||||
\(758\) | 10.8701 | 0.394818 | ||||||||
\(759\) | −12.0416 | −0.437083 | ||||||||
\(760\) | −8.00000 | −0.290191 | ||||||||
\(761\) | 43.1127 | 1.56283 | 0.781417 | − | 0.624009i | \(-0.214497\pi\) | ||||
0.781417 | + | 0.624009i | \(0.214497\pi\) | |||||||
\(762\) | −3.65685 | −0.132474 | ||||||||
\(763\) | −8.18377 | −0.296272 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.58579 | 0.165799 | ||||||||
\(766\) | −4.97056 | −0.179594 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.7696 | 1.03746 | 0.518728 | − | 0.854939i | \(-0.326406\pi\) | ||||
0.518728 | + | 0.854939i | \(0.326406\pi\) | |||||||
\(770\) | −0.887302 | −0.0319761 | ||||||||
\(771\) | 14.4853 | 0.521675 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.8995 | −1.00348 | −0.501738 | − | 0.865020i | \(-0.667306\pi\) | ||||
−0.501738 | + | 0.865020i | \(0.667306\pi\) | |||||||
\(774\) | 1.41421 | 0.0508329 | ||||||||
\(775\) | −13.9706 | −0.501837 | ||||||||
\(776\) | 10.8284 | 0.388718 | ||||||||
\(777\) | −7.02944 | −0.252180 | ||||||||
\(778\) | −40.4853 | −1.45147 | ||||||||
\(779\) | 18.4853 | 0.662304 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.1421 | −0.577611 | ||||||||
\(782\) | 51.5563 | 1.84365 | ||||||||
\(783\) | 24.0000 | 0.857690 | ||||||||
\(784\) | 26.6274 | 0.950979 | ||||||||
\(785\) | 5.85786 | 0.209076 | ||||||||
\(786\) | −3.31371 | −0.118196 | ||||||||
\(787\) | 29.7990 | 1.06222 | 0.531110 | − | 0.847303i | \(-0.321775\pi\) | ||||
0.531110 | + | 0.847303i | \(0.321775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 39.7990 | 1.41688 | ||||||||
\(790\) | −0.686292 | −0.0244172 | ||||||||
\(791\) | −0.686292 | −0.0244017 | ||||||||
\(792\) | 5.17157 | 0.183764 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −30.3431 | −1.07684 | ||||||||
\(795\) | 6.76955 | 0.240091 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6863 | 0.449372 | 0.224686 | − | 0.974431i | \(-0.427864\pi\) | ||||
0.224686 | + | 0.974431i | \(0.427864\pi\) | |||||||
\(798\) | 5.65685 | 0.200250 | ||||||||
\(799\) | −46.9706 | −1.66170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.2426 | −0.361906 | ||||||||
\(802\) | −41.6985 | −1.47242 | ||||||||
\(803\) | −14.1838 | −0.500534 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.59798 | 0.0563214 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.24264 | 0.149348 | ||||||||
\(808\) | 0.485281 | 0.0170721 | ||||||||
\(809\) | 5.65685 | 0.198884 | 0.0994422 | − | 0.995043i | \(-0.468294\pi\) | ||||
0.0994422 | + | 0.995043i | \(0.468294\pi\) | |||||||
\(810\) | −4.14214 | −0.145540 | ||||||||
\(811\) | −48.7279 | −1.71107 | −0.855534 | − | 0.517746i | \(-0.826771\pi\) | ||||
−0.855534 | + | 0.517746i | \(0.826771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.2721 | 0.395329 | ||||||||
\(814\) | 21.9411 | 0.769036 | ||||||||
\(815\) | −11.8579 | −0.415363 | ||||||||
\(816\) | 44.2843 | 1.55026 | ||||||||
\(817\) | 4.82843 | 0.168925 | ||||||||
\(818\) | 52.1421 | 1.82311 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.1127 | −0.352936 | −0.176468 | − | 0.984306i | \(-0.556467\pi\) | ||||
−0.176468 | + | 0.984306i | \(0.556467\pi\) | |||||||
\(822\) | −4.97056 | −0.173368 | ||||||||
\(823\) | −43.3431 | −1.51085 | −0.755424 | − | 0.655237i | \(-0.772569\pi\) | ||||
−0.755424 | + | 0.655237i | \(0.772569\pi\) | |||||||
\(824\) | 49.4558 | 1.72288 | ||||||||
\(825\) | −12.0416 | −0.419236 | ||||||||
\(826\) | 0.686292 | 0.0238791 | ||||||||
\(827\) | −9.65685 | −0.335802 | −0.167901 | − | 0.985804i | \(-0.553699\pi\) | ||||
−0.167901 | + | 0.985804i | \(0.553699\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.7990 | −0.548722 | −0.274361 | − | 0.961627i | \(-0.588466\pi\) | ||||
−0.274361 | + | 0.961627i | \(0.588466\pi\) | |||||||
\(830\) | −12.1421 | −0.421460 | ||||||||
\(831\) | 16.8284 | 0.583772 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −52.1127 | −1.80560 | ||||||||
\(834\) | −22.9706 | −0.795406 | ||||||||
\(835\) | 4.87006 | 0.168535 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.9706 | 0.586588 | ||||||||
\(838\) | 5.79899 | 0.200323 | ||||||||
\(839\) | −4.87006 | −0.168133 | −0.0840665 | − | 0.996460i | \(-0.526791\pi\) | ||||
−0.0840665 | + | 0.996460i | \(0.526791\pi\) | |||||||
\(840\) | 1.37258 | 0.0473586 | ||||||||
\(841\) | −11.0000 | −0.379310 | ||||||||
\(842\) | −6.14214 | −0.211672 | ||||||||
\(843\) | 3.75736 | 0.129410 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.48528 | −0.291730 | ||||||||
\(847\) | −4.48528 | −0.154116 | ||||||||
\(848\) | −32.6863 | −1.12245 | ||||||||
\(849\) | 6.10051 | 0.209369 | ||||||||
\(850\) | 51.5563 | 1.76837 | ||||||||
\(851\) | −39.5147 | −1.35455 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.5980 | 1.11613 | 0.558067 | − | 0.829796i | \(-0.311543\pi\) | ||||
0.558067 | + | 0.829796i | \(0.311543\pi\) | |||||||
\(854\) | −6.82843 | −0.233664 | ||||||||
\(855\) | 2.82843 | 0.0967302 | ||||||||
\(856\) | −32.9706 | −1.12691 | ||||||||
\(857\) | −3.65685 | −0.124916 | −0.0624579 | − | 0.998048i | \(-0.519894\pi\) | ||||
−0.0624579 | + | 0.998048i | \(0.519894\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9706 | −0.579028 | −0.289514 | − | 0.957174i | \(-0.593494\pi\) | ||||
−0.289514 | + | 0.957174i | \(0.593494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.17157 | −0.108087 | ||||||||
\(862\) | −47.0711 | −1.60325 | ||||||||
\(863\) | −43.2548 | −1.47241 | −0.736206 | − | 0.676758i | \(-0.763384\pi\) | ||||
−0.736206 | + | 0.676758i | \(0.763384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.23045 | −0.245843 | ||||||||
\(866\) | −42.7696 | −1.45337 | ||||||||
\(867\) | −62.6274 | −2.12694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.51472 | 0.0513833 | ||||||||
\(870\) | −4.97056 | −0.168518 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −39.5147 | −1.33814 | ||||||||
\(873\) | −3.82843 | −0.129573 | ||||||||
\(874\) | 31.7990 | 1.07562 | ||||||||
\(875\) | 3.31371 | 0.112024 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.79899 | 0.0945152 | 0.0472576 | − | 0.998883i | \(-0.484952\pi\) | ||||
0.0472576 | + | 0.998883i | \(0.484952\pi\) | |||||||
\(878\) | 7.75736 | 0.261798 | ||||||||
\(879\) | 30.6274 | 1.03304 | ||||||||
\(880\) | −4.28427 | −0.144423 | ||||||||
\(881\) | −54.2548 | −1.82789 | −0.913946 | − | 0.405836i | \(-0.866980\pi\) | ||||
−0.913946 | + | 0.405836i | \(0.866980\pi\) | |||||||
\(882\) | −9.41421 | −0.316993 | ||||||||
\(883\) | −41.9706 | −1.41242 | −0.706211 | − | 0.708001i | \(-0.749597\pi\) | ||||
−0.706211 | + | 0.708001i | \(0.749597\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.686292 | −0.0230694 | ||||||||
\(886\) | −51.1127 | −1.71716 | ||||||||
\(887\) | 25.0294 | 0.840406 | 0.420203 | − | 0.907430i | \(-0.361959\pi\) | ||||
0.420203 | + | 0.907430i | \(0.361959\pi\) | |||||||
\(888\) | −33.9411 | −1.13899 | ||||||||
\(889\) | −1.07107 | −0.0359225 | ||||||||
\(890\) | 8.48528 | 0.284427 | ||||||||
\(891\) | 9.14214 | 0.306273 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.9706 | −0.969463 | ||||||||
\(894\) | 16.9706 | 0.567581 | ||||||||
\(895\) | 4.34315 | 0.145175 | ||||||||
\(896\) | −6.62742 | −0.221406 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.0294 | −0.434798 | ||||||||
\(899\) | 12.7279 | 0.424500 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.9706 | 2.13117 | ||||||||
\(902\) | 9.89949 | 0.329617 | ||||||||
\(903\) | −0.828427 | −0.0275683 | ||||||||
\(904\) | −3.31371 | −0.110212 | ||||||||
\(905\) | 8.97056 | 0.298192 | ||||||||
\(906\) | −19.5147 | −0.648333 | ||||||||
\(907\) | 13.9706 | 0.463885 | 0.231942 | − | 0.972730i | \(-0.425492\pi\) | ||||
0.231942 | + | 0.972730i | \(0.425492\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.171573 | −0.00569071 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.24264 | 0.140565 | 0.0702825 | − | 0.997527i | \(-0.477610\pi\) | ||||
0.0702825 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(912\) | 27.3137 | 0.904447 | ||||||||
\(913\) | 26.7990 | 0.886917 | ||||||||
\(914\) | −34.9706 | −1.15672 | ||||||||
\(915\) | 6.82843 | 0.225741 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.970563 | −0.0320508 | ||||||||
\(918\) | −62.6274 | −2.06701 | ||||||||
\(919\) | −29.4853 | −0.972630 | −0.486315 | − | 0.873784i | \(-0.661659\pi\) | ||||
−0.486315 | + | 0.873784i | \(0.661659\pi\) | |||||||
\(920\) | 7.71573 | 0.254380 | ||||||||
\(921\) | −18.1005 | −0.596432 | ||||||||
\(922\) | −3.71573 | −0.122371 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.5147 | −1.29924 | ||||||||
\(926\) | −7.45584 | −0.245014 | ||||||||
\(927\) | −17.4853 | −0.574292 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.8284 | −1.47077 | −0.735386 | − | 0.677648i | \(-0.762999\pi\) | ||||
−0.735386 | + | 0.677648i | \(0.762999\pi\) | |||||||
\(930\) | −3.51472 | −0.115252 | ||||||||
\(931\) | −32.1421 | −1.05342 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.2426 | −0.924623 | ||||||||
\(934\) | −17.4558 | −0.571173 | ||||||||
\(935\) | 8.38478 | 0.274212 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0122 | 1.01312 | 0.506562 | − | 0.862203i | \(-0.330916\pi\) | ||||
0.506562 | + | 0.862203i | \(0.330916\pi\) | |||||||
\(938\) | 7.85786 | 0.256568 | ||||||||
\(939\) | −24.3431 | −0.794409 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.6274 | −0.444241 | −0.222121 | − | 0.975019i | \(-0.571298\pi\) | ||||
−0.222121 | + | 0.975019i | \(0.571298\pi\) | |||||||
\(942\) | −20.0000 | −0.651635 | ||||||||
\(943\) | −17.8284 | −0.580573 | ||||||||
\(944\) | 3.31371 | 0.107852 | ||||||||
\(945\) | −1.94113 | −0.0631448 | ||||||||
\(946\) | 2.58579 | 0.0840712 | ||||||||
\(947\) | 0.171573 | 0.00557537 | 0.00278768 | − | 0.999996i | \(-0.499113\pi\) | ||||
0.00278768 | + | 0.999996i | \(0.499113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 31.7990 | 1.03170 | ||||||||
\(951\) | 28.5269 | 0.925048 | ||||||||
\(952\) | 12.9706 | 0.420378 | ||||||||
\(953\) | 24.0416 | 0.778785 | 0.389392 | − | 0.921072i | \(-0.372685\pi\) | ||||
0.389392 | + | 0.921072i | \(0.372685\pi\) | |||||||
\(954\) | 11.5563 | 0.374151 | ||||||||
\(955\) | −12.9706 | −0.419718 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.9706 | 0.354628 | ||||||||
\(958\) | 6.58579 | 0.212777 | ||||||||
\(959\) | −1.45584 | −0.0470117 | ||||||||
\(960\) | 6.62742 | 0.213899 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.6569 | 0.375637 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.5269 | −0.338873 | ||||||||
\(966\) | −5.45584 | −0.175539 | ||||||||
\(967\) | −26.9411 | −0.866368 | −0.433184 | − | 0.901305i | \(-0.642610\pi\) | ||||
−0.433184 | + | 0.901305i | \(0.642610\pi\) | |||||||
\(968\) | −21.6569 | −0.696078 | ||||||||
\(969\) | −53.4558 | −1.71725 | ||||||||
\(970\) | 3.17157 | 0.101833 | ||||||||
\(971\) | 25.1421 | 0.806850 | 0.403425 | − | 0.915013i | \(-0.367820\pi\) | ||||
0.403425 | + | 0.915013i | \(0.367820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.72792 | −0.215687 | ||||||||
\(974\) | 47.5980 | 1.52514 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32.9706 | −1.05536 | ||||||||
\(977\) | 0.686292 | 0.0219564 | 0.0109782 | − | 0.999940i | \(-0.496505\pi\) | ||||
0.0109782 | + | 0.999940i | \(0.496505\pi\) | |||||||
\(978\) | 40.4853 | 1.29458 | ||||||||
\(979\) | −18.7279 | −0.598547 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.9706 | 0.446046 | ||||||||
\(982\) | −14.9706 | −0.477730 | ||||||||
\(983\) | −2.52691 | −0.0805960 | −0.0402980 | − | 0.999188i | \(-0.512831\pi\) | ||||
−0.0402980 | + | 0.999188i | \(0.512831\pi\) | |||||||
\(984\) | −15.3137 | −0.488183 | ||||||||
\(985\) | 8.28427 | 0.263959 | ||||||||
\(986\) | −46.9706 | −1.49585 | ||||||||
\(987\) | 4.97056 | 0.158215 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.65685 | −0.148079 | ||||||||
\(990\) | 1.51472 | 0.0481409 | ||||||||
\(991\) | −19.5563 | −0.621228 | −0.310614 | − | 0.950536i | \(-0.600535\pi\) | ||||
−0.310614 | + | 0.950536i | \(0.600535\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.2843 | 0.834106 | ||||||||
\(994\) | −7.31371 | −0.231977 | ||||||||
\(995\) | 2.14214 | 0.0679103 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.0711 | 0.540646 | 0.270323 | − | 0.962770i | \(-0.412869\pi\) | ||||
0.270323 | + | 0.962770i | \(0.412869\pi\) | |||||||
\(998\) | −48.4264 | −1.53291 | ||||||||
\(999\) | 48.0000 | 1.51865 |
(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 | 7267.2.a.b.1.1 | 2 | ||
13.12 | even | 2 | 43.2.a.b.1.2 | ✓ | 2 | ||
39.38 | odd | 2 | 387.2.a.h.1.1 | 2 | |||
52.51 | odd | 2 | 688.2.a.f.1.2 | 2 | |||
65.12 | odd | 4 | 1075.2.b.f.474.3 | 4 | |||
65.38 | odd | 4 | 1075.2.b.f.474.2 | 4 | |||
65.64 | even | 2 | 1075.2.a.i.1.1 | 2 | |||
91.90 | odd | 2 | 2107.2.a.b.1.2 | 2 | |||
104.51 | odd | 2 | 2752.2.a.m.1.1 | 2 | |||
104.77 | even | 2 | 2752.2.a.l.1.2 | 2 | |||
143.142 | odd | 2 | 5203.2.a.f.1.1 | 2 | |||
156.155 | even | 2 | 6192.2.a.bd.1.2 | 2 | |||
195.194 | odd | 2 | 9675.2.a.bf.1.2 | 2 | |||
559.558 | odd | 2 | 1849.2.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.a.b.1.2 | ✓ | 2 | 13.12 | even | 2 | ||
387.2.a.h.1.1 | 2 | 39.38 | odd | 2 | |||
688.2.a.f.1.2 | 2 | 52.51 | odd | 2 | |||
1075.2.a.i.1.1 | 2 | 65.64 | even | 2 | |||
1075.2.b.f.474.2 | 4 | 65.38 | odd | 4 | |||
1075.2.b.f.474.3 | 4 | 65.12 | odd | 4 | |||
1849.2.a.f.1.1 | 2 | 559.558 | odd | 2 | |||
2107.2.a.b.1.2 | 2 | 91.90 | odd | 2 | |||
2752.2.a.l.1.2 | 2 | 104.77 | even | 2 | |||
2752.2.a.m.1.1 | 2 | 104.51 | odd | 2 | |||
5203.2.a.f.1.1 | 2 | 143.142 | odd | 2 | |||
6192.2.a.bd.1.2 | 2 | 156.155 | even | 2 | |||
7267.2.a.b.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9675.2.a.bf.1.2 | 2 | 195.194 | odd | 2 |