Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3750,2,Mod(1,3750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3750, 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("3750.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3750 = 2 \cdot 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3750.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: | \(29.9439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.71684000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 18x^{6} + 10x^{5} + 101x^{4} + 40x^{3} - 132x^{2} - 96x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 150) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.74919\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3750.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.533559 | 0.201666 | 0.100833 | − | 0.994903i | \(-0.467849\pi\) | ||||
0.100833 | + | 0.994903i | \(0.467849\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.43425 | −0.432444 | −0.216222 | − | 0.976344i | \(-0.569373\pi\) | ||||
−0.216222 | + | 0.976344i | \(0.569373\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −6.57392 | −1.82328 | −0.911639 | − | 0.410991i | \(-0.865183\pi\) | ||||
−0.911639 | + | 0.410991i | \(0.865183\pi\) | |||||||
\(14\) | −0.533559 | −0.142600 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.958413 | 0.232449 | 0.116225 | − | 0.993223i | \(-0.462921\pi\) | ||||
0.116225 | + | 0.993223i | \(0.462921\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 0.212889 | 0.0488401 | 0.0244201 | − | 0.999702i | \(-0.492226\pi\) | ||||
0.0244201 | + | 0.999702i | \(0.492226\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.533559 | −0.116432 | ||||||||
\(22\) | 1.43425 | 0.305784 | ||||||||
\(23\) | −3.76401 | −0.784850 | −0.392425 | − | 0.919784i | \(-0.628364\pi\) | ||||
−0.392425 | + | 0.919784i | \(0.628364\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.57392 | 1.28925 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.533559 | 0.100833 | ||||||||
\(29\) | 6.19448 | 1.15029 | 0.575143 | − | 0.818053i | \(-0.304946\pi\) | ||||
0.575143 | + | 0.818053i | \(0.304946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.33773 | −0.419869 | −0.209934 | − | 0.977716i | \(-0.567325\pi\) | ||||
−0.209934 | + | 0.977716i | \(0.567325\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.43425 | 0.249671 | ||||||||
\(34\) | −0.958413 | −0.164367 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.06291 | −0.667938 | −0.333969 | − | 0.942584i | \(-0.608388\pi\) | ||||
−0.333969 | + | 0.942584i | \(0.608388\pi\) | |||||||
\(38\) | −0.212889 | −0.0345352 | ||||||||
\(39\) | 6.57392 | 1.05267 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.94156 | −1.24026 | −0.620132 | − | 0.784497i | \(-0.712921\pi\) | ||||
−0.620132 | + | 0.784497i | \(0.712921\pi\) | |||||||
\(42\) | 0.533559 | 0.0823300 | ||||||||
\(43\) | 11.3607 | 1.73250 | 0.866248 | − | 0.499614i | \(-0.166525\pi\) | ||||
0.866248 | + | 0.499614i | \(0.166525\pi\) | |||||||
\(44\) | −1.43425 | −0.216222 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.76401 | 0.554973 | ||||||||
\(47\) | −10.1489 | −1.48037 | −0.740186 | − | 0.672402i | \(-0.765263\pi\) | ||||
−0.740186 | + | 0.672402i | \(0.765263\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.71531 | −0.959331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.958413 | −0.134205 | ||||||||
\(52\) | −6.57392 | −0.911639 | ||||||||
\(53\) | 3.23354 | 0.444162 | 0.222081 | − | 0.975028i | \(-0.428715\pi\) | ||||
0.222081 | + | 0.975028i | \(0.428715\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.533559 | −0.0712998 | ||||||||
\(57\) | −0.212889 | −0.0281978 | ||||||||
\(58\) | −6.19448 | −0.813375 | ||||||||
\(59\) | 7.52455 | 0.979613 | 0.489806 | − | 0.871831i | \(-0.337067\pi\) | ||||
0.489806 | + | 0.871831i | \(0.337067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5721 | 1.60969 | 0.804844 | − | 0.593486i | \(-0.202249\pi\) | ||||
0.804844 | + | 0.593486i | \(0.202249\pi\) | |||||||
\(62\) | 2.33773 | 0.296892 | ||||||||
\(63\) | 0.533559 | 0.0672221 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.43425 | −0.176544 | ||||||||
\(67\) | 6.91285 | 0.844539 | 0.422269 | − | 0.906470i | \(-0.361234\pi\) | ||||
0.422269 | + | 0.906470i | \(0.361234\pi\) | |||||||
\(68\) | 0.958413 | 0.116225 | ||||||||
\(69\) | 3.76401 | 0.453134 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1247 | 1.20158 | 0.600789 | − | 0.799408i | \(-0.294853\pi\) | ||||
0.600789 | + | 0.799408i | \(0.294853\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 13.9771 | 1.63589 | 0.817947 | − | 0.575294i | \(-0.195112\pi\) | ||||
0.817947 | + | 0.575294i | \(0.195112\pi\) | |||||||
\(74\) | 4.06291 | 0.472304 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.212889 | 0.0244201 | ||||||||
\(77\) | −0.765259 | −0.0872093 | ||||||||
\(78\) | −6.57392 | −0.744350 | ||||||||
\(79\) | 15.5279 | 1.74703 | 0.873515 | − | 0.486798i | \(-0.161835\pi\) | ||||
0.873515 | + | 0.486798i | \(0.161835\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.94156 | 0.876999 | ||||||||
\(83\) | −16.3308 | −1.79254 | −0.896270 | − | 0.443508i | \(-0.853734\pi\) | ||||
−0.896270 | + | 0.443508i | \(0.853734\pi\) | |||||||
\(84\) | −0.533559 | −0.0582161 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.3607 | −1.22506 | ||||||||
\(87\) | −6.19448 | −0.664118 | ||||||||
\(88\) | 1.43425 | 0.152892 | ||||||||
\(89\) | 5.62220 | 0.595951 | 0.297976 | − | 0.954573i | \(-0.403689\pi\) | ||||
0.297976 | + | 0.954573i | \(0.403689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50758 | −0.367694 | ||||||||
\(92\) | −3.76401 | −0.392425 | ||||||||
\(93\) | 2.33773 | 0.242411 | ||||||||
\(94\) | 10.1489 | 1.04678 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 5.56558 | 0.565099 | 0.282549 | − | 0.959253i | \(-0.408820\pi\) | ||||
0.282549 | + | 0.959253i | \(0.408820\pi\) | |||||||
\(98\) | 6.71531 | 0.678349 | ||||||||
\(99\) | −1.43425 | −0.144148 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.42708 | −0.938029 | −0.469015 | − | 0.883190i | \(-0.655391\pi\) | ||||
−0.469015 | + | 0.883190i | \(0.655391\pi\) | |||||||
\(102\) | 0.958413 | 0.0948971 | ||||||||
\(103\) | −7.99871 | −0.788137 | −0.394068 | − | 0.919081i | \(-0.628933\pi\) | ||||
−0.394068 | + | 0.919081i | \(0.628933\pi\) | |||||||
\(104\) | 6.57392 | 0.644626 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.23354 | −0.314070 | ||||||||
\(107\) | −18.9260 | −1.82964 | −0.914822 | − | 0.403857i | \(-0.867669\pi\) | ||||
−0.914822 | + | 0.403857i | \(0.867669\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.65524 | −0.254326 | −0.127163 | − | 0.991882i | \(-0.540587\pi\) | ||||
−0.127163 | + | 0.991882i | \(0.540587\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.06291 | 0.385634 | ||||||||
\(112\) | 0.533559 | 0.0504166 | ||||||||
\(113\) | −3.06283 | −0.288127 | −0.144063 | − | 0.989568i | \(-0.546017\pi\) | ||||
−0.144063 | + | 0.989568i | \(0.546017\pi\) | |||||||
\(114\) | 0.212889 | 0.0199389 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.19448 | 0.575143 | ||||||||
\(117\) | −6.57392 | −0.607759 | ||||||||
\(118\) | −7.52455 | −0.692691 | ||||||||
\(119\) | 0.511370 | 0.0468772 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.94292 | −0.812993 | ||||||||
\(122\) | −12.5721 | −1.13822 | ||||||||
\(123\) | 7.94156 | 0.716067 | ||||||||
\(124\) | −2.33773 | −0.209934 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.533559 | −0.0475332 | ||||||||
\(127\) | 6.48257 | 0.575235 | 0.287618 | − | 0.957745i | \(-0.407137\pi\) | ||||
0.287618 | + | 0.957745i | \(0.407137\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.3607 | −1.00026 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.45794 | −0.826344 | −0.413172 | − | 0.910653i | \(-0.635579\pi\) | ||||
−0.413172 | + | 0.910653i | \(0.635579\pi\) | |||||||
\(132\) | 1.43425 | 0.124836 | ||||||||
\(133\) | 0.113589 | 0.00984941 | ||||||||
\(134\) | −6.91285 | −0.597179 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.958413 | −0.0821833 | ||||||||
\(137\) | 12.3361 | 1.05394 | 0.526971 | − | 0.849883i | \(-0.323328\pi\) | ||||
0.526971 | + | 0.849883i | \(0.323328\pi\) | |||||||
\(138\) | −3.76401 | −0.320414 | ||||||||
\(139\) | 4.53918 | 0.385008 | 0.192504 | − | 0.981296i | \(-0.438339\pi\) | ||||
0.192504 | + | 0.981296i | \(0.438339\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.1489 | 0.854693 | ||||||||
\(142\) | −10.1247 | −0.849643 | ||||||||
\(143\) | 9.42867 | 0.788465 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.9771 | −1.15675 | ||||||||
\(147\) | 6.71531 | 0.553870 | ||||||||
\(148\) | −4.06291 | −0.333969 | ||||||||
\(149\) | 11.0750 | 0.907303 | 0.453651 | − | 0.891179i | \(-0.350121\pi\) | ||||
0.453651 | + | 0.891179i | \(0.350121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.63387 | −0.132962 | −0.0664812 | − | 0.997788i | \(-0.521177\pi\) | ||||
−0.0664812 | + | 0.997788i | \(0.521177\pi\) | |||||||
\(152\) | −0.212889 | −0.0172676 | ||||||||
\(153\) | 0.958413 | 0.0774831 | ||||||||
\(154\) | 0.765259 | 0.0616663 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.57392 | 0.526335 | ||||||||
\(157\) | −6.64544 | −0.530364 | −0.265182 | − | 0.964198i | \(-0.585432\pi\) | ||||
−0.265182 | + | 0.964198i | \(0.585432\pi\) | |||||||
\(158\) | −15.5279 | −1.23534 | ||||||||
\(159\) | −3.23354 | −0.256437 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00832 | −0.158278 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.1134 | 0.792142 | 0.396071 | − | 0.918220i | \(-0.370373\pi\) | ||||
0.396071 | + | 0.918220i | \(0.370373\pi\) | |||||||
\(164\) | −7.94156 | −0.620132 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.3308 | 1.26752 | ||||||||
\(167\) | −12.7885 | −0.989600 | −0.494800 | − | 0.869007i | \(-0.664759\pi\) | ||||
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(168\) | 0.533559 | 0.0411650 | ||||||||
\(169\) | 30.2165 | 2.32434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.212889 | 0.0162800 | ||||||||
\(172\) | 11.3607 | 0.866248 | ||||||||
\(173\) | 13.6575 | 1.03836 | 0.519182 | − | 0.854664i | \(-0.326237\pi\) | ||||
0.519182 | + | 0.854664i | \(0.326237\pi\) | |||||||
\(174\) | 6.19448 | 0.469602 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.43425 | −0.108111 | ||||||||
\(177\) | −7.52455 | −0.565580 | ||||||||
\(178\) | −5.62220 | −0.421401 | ||||||||
\(179\) | 2.99142 | 0.223589 | 0.111795 | − | 0.993731i | \(-0.464340\pi\) | ||||
0.111795 | + | 0.993731i | \(0.464340\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.62285 | 0.566602 | 0.283301 | − | 0.959031i | \(-0.408570\pi\) | ||||
0.283301 | + | 0.959031i | \(0.408570\pi\) | |||||||
\(182\) | 3.50758 | 0.259999 | ||||||||
\(183\) | −12.5721 | −0.929354 | ||||||||
\(184\) | 3.76401 | 0.277487 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.33773 | −0.171411 | ||||||||
\(187\) | −1.37461 | −0.100521 | ||||||||
\(188\) | −10.1489 | −0.740186 | ||||||||
\(189\) | −0.533559 | −0.0388107 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.40045 | −0.607835 | −0.303917 | − | 0.952698i | \(-0.598295\pi\) | ||||
−0.303917 | + | 0.952698i | \(0.598295\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 10.5266 | 0.757723 | 0.378861 | − | 0.925453i | \(-0.376316\pi\) | ||||
0.378861 | + | 0.925453i | \(0.376316\pi\) | |||||||
\(194\) | −5.56558 | −0.399585 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.71531 | −0.479665 | ||||||||
\(197\) | 10.2080 | 0.727293 | 0.363647 | − | 0.931537i | \(-0.381532\pi\) | ||||
0.363647 | + | 0.931537i | \(0.381532\pi\) | |||||||
\(198\) | 1.43425 | 0.101928 | ||||||||
\(199\) | 3.84318 | 0.272436 | 0.136218 | − | 0.990679i | \(-0.456505\pi\) | ||||
0.136218 | + | 0.990679i | \(0.456505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.91285 | −0.487595 | ||||||||
\(202\) | 9.42708 | 0.663287 | ||||||||
\(203\) | 3.30512 | 0.231974 | ||||||||
\(204\) | −0.958413 | −0.0671023 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.99871 | 0.557297 | ||||||||
\(207\) | −3.76401 | −0.261617 | ||||||||
\(208\) | −6.57392 | −0.455820 | ||||||||
\(209\) | −0.305337 | −0.0211206 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.24920 | 0.361370 | 0.180685 | − | 0.983541i | \(-0.442169\pi\) | ||||
0.180685 | + | 0.983541i | \(0.442169\pi\) | |||||||
\(212\) | 3.23354 | 0.222081 | ||||||||
\(213\) | −10.1247 | −0.693731 | ||||||||
\(214\) | 18.9260 | 1.29375 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.24732 | −0.0846734 | ||||||||
\(218\) | 2.65524 | 0.179836 | ||||||||
\(219\) | −13.9771 | −0.944484 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.30054 | −0.423820 | ||||||||
\(222\) | −4.06291 | −0.272685 | ||||||||
\(223\) | 19.2782 | 1.29097 | 0.645483 | − | 0.763774i | \(-0.276656\pi\) | ||||
0.645483 | + | 0.763774i | \(0.276656\pi\) | |||||||
\(224\) | −0.533559 | −0.0356499 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.06283 | 0.203736 | ||||||||
\(227\) | −8.43957 | −0.560154 | −0.280077 | − | 0.959978i | \(-0.590360\pi\) | ||||
−0.280077 | + | 0.959978i | \(0.590360\pi\) | |||||||
\(228\) | −0.212889 | −0.0140989 | ||||||||
\(229\) | 5.95568 | 0.393563 | 0.196781 | − | 0.980447i | \(-0.436951\pi\) | ||||
0.196781 | + | 0.980447i | \(0.436951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.765259 | 0.0503503 | ||||||||
\(232\) | −6.19448 | −0.406688 | ||||||||
\(233\) | 2.09293 | 0.137112 | 0.0685561 | − | 0.997647i | \(-0.478161\pi\) | ||||
0.0685561 | + | 0.997647i | \(0.478161\pi\) | |||||||
\(234\) | 6.57392 | 0.429751 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.52455 | 0.489806 | ||||||||
\(237\) | −15.5279 | −1.00865 | ||||||||
\(238\) | −0.511370 | −0.0331472 | ||||||||
\(239\) | 9.89840 | 0.640274 | 0.320137 | − | 0.947371i | \(-0.396271\pi\) | ||||
0.320137 | + | 0.947371i | \(0.396271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4567 | −1.38215 | −0.691074 | − | 0.722784i | \(-0.742862\pi\) | ||||
−0.691074 | + | 0.722784i | \(0.742862\pi\) | |||||||
\(242\) | 8.94292 | 0.574873 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.5721 | 0.804844 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.94156 | −0.506336 | ||||||||
\(247\) | −1.39952 | −0.0890491 | ||||||||
\(248\) | 2.33773 | 0.148446 | ||||||||
\(249\) | 16.3308 | 1.03492 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.10753 | −0.259265 | −0.129632 | − | 0.991562i | \(-0.541380\pi\) | ||||
−0.129632 | + | 0.991562i | \(0.541380\pi\) | |||||||
\(252\) | 0.533559 | 0.0336111 | ||||||||
\(253\) | 5.39854 | 0.339404 | ||||||||
\(254\) | −6.48257 | −0.406753 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 30.7748 | 1.91968 | 0.959839 | − | 0.280552i | \(-0.0905176\pi\) | ||||
0.959839 | + | 0.280552i | \(0.0905176\pi\) | |||||||
\(258\) | 11.3607 | 0.707289 | ||||||||
\(259\) | −2.16780 | −0.134701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.19448 | 0.383429 | ||||||||
\(262\) | 9.45794 | 0.584313 | ||||||||
\(263\) | 28.3729 | 1.74955 | 0.874773 | − | 0.484533i | \(-0.161011\pi\) | ||||
0.874773 | + | 0.484533i | \(0.161011\pi\) | |||||||
\(264\) | −1.43425 | −0.0882722 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.113589 | −0.00696458 | ||||||||
\(267\) | −5.62220 | −0.344073 | ||||||||
\(268\) | 6.91285 | 0.422269 | ||||||||
\(269\) | 10.6668 | 0.650364 | 0.325182 | − | 0.945651i | \(-0.394574\pi\) | ||||
0.325182 | + | 0.945651i | \(0.394574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.8439 | 1.38767 | 0.693835 | − | 0.720134i | \(-0.255920\pi\) | ||||
0.693835 | + | 0.720134i | \(0.255920\pi\) | |||||||
\(272\) | 0.958413 | 0.0581123 | ||||||||
\(273\) | 3.50758 | 0.212288 | ||||||||
\(274\) | −12.3361 | −0.745250 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.76401 | 0.226567 | ||||||||
\(277\) | 31.4592 | 1.89020 | 0.945099 | − | 0.326784i | \(-0.105965\pi\) | ||||
0.945099 | + | 0.326784i | \(0.105965\pi\) | |||||||
\(278\) | −4.53918 | −0.272242 | ||||||||
\(279\) | −2.33773 | −0.139956 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.7785 | −0.642992 | −0.321496 | − | 0.946911i | \(-0.604186\pi\) | ||||
−0.321496 | + | 0.946911i | \(0.604186\pi\) | |||||||
\(282\) | −10.1489 | −0.604359 | ||||||||
\(283\) | 4.16428 | 0.247541 | 0.123770 | − | 0.992311i | \(-0.460501\pi\) | ||||
0.123770 | + | 0.992311i | \(0.460501\pi\) | |||||||
\(284\) | 10.1247 | 0.600789 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.42867 | −0.557529 | ||||||||
\(287\) | −4.23729 | −0.250120 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.0814 | −0.945967 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.56558 | −0.326260 | ||||||||
\(292\) | 13.9771 | 0.817947 | ||||||||
\(293\) | 17.9603 | 1.04925 | 0.524626 | − | 0.851333i | \(-0.324205\pi\) | ||||
0.524626 | + | 0.851333i | \(0.324205\pi\) | |||||||
\(294\) | −6.71531 | −0.391645 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.06291 | 0.236152 | ||||||||
\(297\) | 1.43425 | 0.0832238 | ||||||||
\(298\) | −11.0750 | −0.641560 | ||||||||
\(299\) | 24.7443 | 1.43100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.06163 | 0.349386 | ||||||||
\(302\) | 1.63387 | 0.0940187 | ||||||||
\(303\) | 9.42708 | 0.541571 | ||||||||
\(304\) | 0.212889 | 0.0122100 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.958413 | −0.0547888 | ||||||||
\(307\) | 20.8174 | 1.18811 | 0.594056 | − | 0.804423i | \(-0.297526\pi\) | ||||
0.594056 | + | 0.804423i | \(0.297526\pi\) | |||||||
\(308\) | −0.765259 | −0.0436047 | ||||||||
\(309\) | 7.99871 | 0.455031 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4526 | −1.10305 | −0.551527 | − | 0.834157i | \(-0.685955\pi\) | ||||
−0.551527 | + | 0.834157i | \(0.685955\pi\) | |||||||
\(312\) | −6.57392 | −0.372175 | ||||||||
\(313\) | −5.88310 | −0.332532 | −0.166266 | − | 0.986081i | \(-0.553171\pi\) | ||||
−0.166266 | + | 0.986081i | \(0.553171\pi\) | |||||||
\(314\) | 6.64544 | 0.375024 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.5279 | 0.873515 | ||||||||
\(317\) | 10.7610 | 0.604400 | 0.302200 | − | 0.953245i | \(-0.402279\pi\) | ||||
0.302200 | + | 0.953245i | \(0.402279\pi\) | |||||||
\(318\) | 3.23354 | 0.181328 | ||||||||
\(319\) | −8.88445 | −0.497434 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.9260 | 1.05635 | ||||||||
\(322\) | 2.00832 | 0.111919 | ||||||||
\(323\) | 0.204036 | 0.0113528 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.1134 | −0.560129 | ||||||||
\(327\) | 2.65524 | 0.146835 | ||||||||
\(328\) | 7.94156 | 0.438500 | ||||||||
\(329\) | −5.41505 | −0.298541 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.617092 | −0.0339184 | −0.0169592 | − | 0.999856i | \(-0.505399\pi\) | ||||
−0.0169592 | + | 0.999856i | \(0.505399\pi\) | |||||||
\(332\) | −16.3308 | −0.896270 | ||||||||
\(333\) | −4.06291 | −0.222646 | ||||||||
\(334\) | 12.7885 | 0.699753 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.533559 | −0.0291080 | ||||||||
\(337\) | 15.4106 | 0.839471 | 0.419735 | − | 0.907647i | \(-0.362123\pi\) | ||||
0.419735 | + | 0.907647i | \(0.362123\pi\) | |||||||
\(338\) | −30.2165 | −1.64356 | ||||||||
\(339\) | 3.06283 | 0.166350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.35289 | 0.181569 | ||||||||
\(342\) | −0.212889 | −0.0115117 | ||||||||
\(343\) | −7.31793 | −0.395131 | ||||||||
\(344\) | −11.3607 | −0.612530 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.6575 | −0.734234 | ||||||||
\(347\) | −22.6565 | −1.21627 | −0.608133 | − | 0.793835i | \(-0.708081\pi\) | ||||
−0.608133 | + | 0.793835i | \(0.708081\pi\) | |||||||
\(348\) | −6.19448 | −0.332059 | ||||||||
\(349\) | −16.9543 | −0.907544 | −0.453772 | − | 0.891118i | \(-0.649922\pi\) | ||||
−0.453772 | + | 0.891118i | \(0.649922\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.57392 | 0.350890 | ||||||||
\(352\) | 1.43425 | 0.0764459 | ||||||||
\(353\) | −6.06255 | −0.322677 | −0.161339 | − | 0.986899i | \(-0.551581\pi\) | ||||
−0.161339 | + | 0.986899i | \(0.551581\pi\) | |||||||
\(354\) | 7.52455 | 0.399925 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.62220 | 0.297976 | ||||||||
\(357\) | −0.511370 | −0.0270646 | ||||||||
\(358\) | −2.99142 | −0.158101 | ||||||||
\(359\) | 18.8987 | 0.997437 | 0.498718 | − | 0.866764i | \(-0.333804\pi\) | ||||
0.498718 | + | 0.866764i | \(0.333804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9547 | −0.997615 | ||||||||
\(362\) | −7.62285 | −0.400648 | ||||||||
\(363\) | 8.94292 | 0.469381 | ||||||||
\(364\) | −3.50758 | −0.183847 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.5721 | 0.657152 | ||||||||
\(367\) | 25.0483 | 1.30751 | 0.653756 | − | 0.756705i | \(-0.273192\pi\) | ||||
0.653756 | + | 0.756705i | \(0.273192\pi\) | |||||||
\(368\) | −3.76401 | −0.196213 | ||||||||
\(369\) | −7.94156 | −0.413421 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.72529 | 0.0895725 | ||||||||
\(372\) | 2.33773 | 0.121206 | ||||||||
\(373\) | 11.8954 | 0.615922 | 0.307961 | − | 0.951399i | \(-0.400353\pi\) | ||||
0.307961 | + | 0.951399i | \(0.400353\pi\) | |||||||
\(374\) | 1.37461 | 0.0710792 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.1489 | 0.523390 | ||||||||
\(377\) | −40.7220 | −2.09729 | ||||||||
\(378\) | 0.533559 | 0.0274433 | ||||||||
\(379\) | 27.5184 | 1.41353 | 0.706763 | − | 0.707450i | \(-0.250155\pi\) | ||||
0.706763 | + | 0.707450i | \(0.250155\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.48257 | −0.332112 | ||||||||
\(382\) | 8.40045 | 0.429804 | ||||||||
\(383\) | 22.0314 | 1.12575 | 0.562877 | − | 0.826541i | \(-0.309695\pi\) | ||||
0.562877 | + | 0.826541i | \(0.309695\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.5266 | −0.535791 | ||||||||
\(387\) | 11.3607 | 0.577499 | ||||||||
\(388\) | 5.56558 | 0.282549 | ||||||||
\(389\) | 17.4892 | 0.886738 | 0.443369 | − | 0.896339i | \(-0.353783\pi\) | ||||
0.443369 | + | 0.896339i | \(0.353783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.60748 | −0.182438 | ||||||||
\(392\) | 6.71531 | 0.339175 | ||||||||
\(393\) | 9.45794 | 0.477090 | ||||||||
\(394\) | −10.2080 | −0.514274 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.43425 | −0.0720739 | ||||||||
\(397\) | 24.4990 | 1.22957 | 0.614786 | − | 0.788694i | \(-0.289242\pi\) | ||||
0.614786 | + | 0.788694i | \(0.289242\pi\) | |||||||
\(398\) | −3.84318 | −0.192641 | ||||||||
\(399\) | −0.113589 | −0.00568656 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.04105 | 0.0519875 | 0.0259937 | − | 0.999662i | \(-0.491725\pi\) | ||||
0.0259937 | + | 0.999662i | \(0.491725\pi\) | |||||||
\(402\) | 6.91285 | 0.344782 | ||||||||
\(403\) | 15.3681 | 0.765537 | ||||||||
\(404\) | −9.42708 | −0.469015 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.30512 | −0.164030 | ||||||||
\(407\) | 5.82724 | 0.288845 | ||||||||
\(408\) | 0.958413 | 0.0474485 | ||||||||
\(409\) | 22.2568 | 1.10053 | 0.550263 | − | 0.834991i | \(-0.314527\pi\) | ||||
0.550263 | + | 0.834991i | \(0.314527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.3361 | −0.608494 | ||||||||
\(412\) | −7.99871 | −0.394068 | ||||||||
\(413\) | 4.01479 | 0.197555 | ||||||||
\(414\) | 3.76401 | 0.184991 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.57392 | 0.322313 | ||||||||
\(417\) | −4.53918 | −0.222284 | ||||||||
\(418\) | 0.305337 | 0.0149345 | ||||||||
\(419\) | −23.1294 | −1.12994 | −0.564972 | − | 0.825110i | \(-0.691113\pi\) | ||||
−0.564972 | + | 0.825110i | \(0.691113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.76139 | 0.475741 | 0.237870 | − | 0.971297i | \(-0.423551\pi\) | ||||
0.237870 | + | 0.971297i | \(0.423551\pi\) | |||||||
\(422\) | −5.24920 | −0.255527 | ||||||||
\(423\) | −10.1489 | −0.493457 | ||||||||
\(424\) | −3.23354 | −0.157035 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.1247 | 0.490542 | ||||||||
\(427\) | 6.70794 | 0.324620 | ||||||||
\(428\) | −18.9260 | −0.914822 | ||||||||
\(429\) | −9.42867 | −0.455220 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.49298 | 0.409093 | 0.204546 | − | 0.978857i | \(-0.434428\pi\) | ||||
0.204546 | + | 0.978857i | \(0.434428\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −22.0042 | −1.05745 | −0.528727 | − | 0.848792i | \(-0.677330\pi\) | ||||
−0.528727 | + | 0.848792i | \(0.677330\pi\) | |||||||
\(434\) | 1.24732 | 0.0598731 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.65524 | −0.127163 | ||||||||
\(437\) | −0.801317 | −0.0383322 | ||||||||
\(438\) | 13.9771 | 0.667851 | ||||||||
\(439\) | −38.3582 | −1.83074 | −0.915369 | − | 0.402615i | \(-0.868101\pi\) | ||||
−0.915369 | + | 0.402615i | \(0.868101\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.71531 | −0.319777 | ||||||||
\(442\) | 6.30054 | 0.299686 | ||||||||
\(443\) | −12.7478 | −0.605666 | −0.302833 | − | 0.953044i | \(-0.597932\pi\) | ||||
−0.302833 | + | 0.953044i | \(0.597932\pi\) | |||||||
\(444\) | 4.06291 | 0.192817 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.2782 | −0.912851 | ||||||||
\(447\) | −11.0750 | −0.523831 | ||||||||
\(448\) | 0.533559 | 0.0252083 | ||||||||
\(449\) | 18.0358 | 0.851161 | 0.425580 | − | 0.904921i | \(-0.360070\pi\) | ||||
0.425580 | + | 0.904921i | \(0.360070\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3902 | 0.536344 | ||||||||
\(452\) | −3.06283 | −0.144063 | ||||||||
\(453\) | 1.63387 | 0.0767659 | ||||||||
\(454\) | 8.43957 | 0.396089 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.212889 | 0.00996944 | ||||||||
\(457\) | 21.1495 | 0.989334 | 0.494667 | − | 0.869083i | \(-0.335290\pi\) | ||||
0.494667 | + | 0.869083i | \(0.335290\pi\) | |||||||
\(458\) | −5.95568 | −0.278291 | ||||||||
\(459\) | −0.958413 | −0.0447349 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.0085 | 1.49078 | 0.745391 | − | 0.666627i | \(-0.232263\pi\) | ||||
0.745391 | + | 0.666627i | \(0.232263\pi\) | |||||||
\(462\) | −0.765259 | −0.0356031 | ||||||||
\(463\) | −28.7776 | −1.33741 | −0.668703 | − | 0.743529i | \(-0.733150\pi\) | ||||
−0.668703 | + | 0.743529i | \(0.733150\pi\) | |||||||
\(464\) | 6.19448 | 0.287572 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.09293 | −0.0969529 | ||||||||
\(467\) | −5.20326 | −0.240778 | −0.120389 | − | 0.992727i | \(-0.538414\pi\) | ||||
−0.120389 | + | 0.992727i | \(0.538414\pi\) | |||||||
\(468\) | −6.57392 | −0.303880 | ||||||||
\(469\) | 3.68841 | 0.170315 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.64544 | 0.306206 | ||||||||
\(472\) | −7.52455 | −0.346345 | ||||||||
\(473\) | −16.2942 | −0.749207 | ||||||||
\(474\) | 15.5279 | 0.713222 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.511370 | 0.0234386 | ||||||||
\(477\) | 3.23354 | 0.148054 | ||||||||
\(478\) | −9.89840 | −0.452742 | ||||||||
\(479\) | −39.6385 | −1.81113 | −0.905565 | − | 0.424206i | \(-0.860553\pi\) | ||||
−0.905565 | + | 0.424206i | \(0.860553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.7093 | 1.21784 | ||||||||
\(482\) | 21.4567 | 0.977326 | ||||||||
\(483\) | 2.00832 | 0.0913818 | ||||||||
\(484\) | −8.94292 | −0.406496 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 5.44308 | 0.246649 | 0.123325 | − | 0.992366i | \(-0.460644\pi\) | ||||
0.123325 | + | 0.992366i | \(0.460644\pi\) | |||||||
\(488\) | −12.5721 | −0.569111 | ||||||||
\(489\) | −10.1134 | −0.457344 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.873965 | 0.0394415 | 0.0197207 | − | 0.999806i | \(-0.493722\pi\) | ||||
0.0197207 | + | 0.999806i | \(0.493722\pi\) | |||||||
\(492\) | 7.94156 | 0.358033 | ||||||||
\(493\) | 5.93687 | 0.267383 | ||||||||
\(494\) | 1.39952 | 0.0629672 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.33773 | −0.104967 | ||||||||
\(497\) | 5.40211 | 0.242318 | ||||||||
\(498\) | −16.3308 | −0.731802 | ||||||||
\(499\) | −34.9604 | −1.56504 | −0.782522 | − | 0.622623i | \(-0.786067\pi\) | ||||
−0.782522 | + | 0.622623i | \(0.786067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.7885 | 0.571346 | ||||||||
\(502\) | 4.10753 | 0.183328 | ||||||||
\(503\) | 0.319724 | 0.0142558 | 0.00712790 | − | 0.999975i | \(-0.497731\pi\) | ||||
0.00712790 | + | 0.999975i | \(0.497731\pi\) | |||||||
\(504\) | −0.533559 | −0.0237666 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.39854 | −0.239995 | ||||||||
\(507\) | −30.2165 | −1.34196 | ||||||||
\(508\) | 6.48257 | 0.287618 | ||||||||
\(509\) | 20.6259 | 0.914225 | 0.457113 | − | 0.889409i | \(-0.348884\pi\) | ||||
0.457113 | + | 0.889409i | \(0.348884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.45760 | 0.329905 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.212889 | −0.00939928 | ||||||||
\(514\) | −30.7748 | −1.35742 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.3607 | −0.500129 | ||||||||
\(517\) | 14.5561 | 0.640177 | ||||||||
\(518\) | 2.16780 | 0.0952477 | ||||||||
\(519\) | −13.6575 | −0.599500 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.22039 | −0.184899 | −0.0924493 | − | 0.995717i | \(-0.529470\pi\) | ||||
−0.0924493 | + | 0.995717i | \(0.529470\pi\) | |||||||
\(522\) | −6.19448 | −0.271125 | ||||||||
\(523\) | −21.5579 | −0.942659 | −0.471330 | − | 0.881957i | \(-0.656226\pi\) | ||||
−0.471330 | + | 0.881957i | \(0.656226\pi\) | |||||||
\(524\) | −9.45794 | −0.413172 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28.3729 | −1.23712 | ||||||||
\(527\) | −2.24051 | −0.0975982 | ||||||||
\(528\) | 1.43425 | 0.0624178 | ||||||||
\(529\) | −8.83222 | −0.384010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.52455 | 0.326538 | ||||||||
\(532\) | 0.113589 | 0.00492470 | ||||||||
\(533\) | 52.2072 | 2.26135 | ||||||||
\(534\) | 5.62220 | 0.243296 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.91285 | −0.298590 | ||||||||
\(537\) | −2.99142 | −0.129089 | ||||||||
\(538\) | −10.6668 | −0.459877 | ||||||||
\(539\) | 9.63146 | 0.414856 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.93662 | −0.384215 | −0.192108 | − | 0.981374i | \(-0.561532\pi\) | ||||
−0.192108 | + | 0.981374i | \(0.561532\pi\) | |||||||
\(542\) | −22.8439 | −0.981231 | ||||||||
\(543\) | −7.62285 | −0.327128 | ||||||||
\(544\) | −0.958413 | −0.0410916 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.50758 | −0.150110 | ||||||||
\(547\) | 12.0786 | 0.516443 | 0.258222 | − | 0.966086i | \(-0.416864\pi\) | ||||
0.258222 | + | 0.966086i | \(0.416864\pi\) | |||||||
\(548\) | 12.3361 | 0.526971 | ||||||||
\(549\) | 12.5721 | 0.536563 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.31874 | 0.0561801 | ||||||||
\(552\) | −3.76401 | −0.160207 | ||||||||
\(553\) | 8.28507 | 0.352317 | ||||||||
\(554\) | −31.4592 | −1.33657 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.53918 | 0.192504 | ||||||||
\(557\) | −8.23596 | −0.348969 | −0.174484 | − | 0.984660i | \(-0.555826\pi\) | ||||
−0.174484 | + | 0.984660i | \(0.555826\pi\) | |||||||
\(558\) | 2.33773 | 0.0989640 | ||||||||
\(559\) | −74.6846 | −3.15882 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.37461 | 0.0580360 | ||||||||
\(562\) | 10.7785 | 0.454664 | ||||||||
\(563\) | 14.6358 | 0.616825 | 0.308413 | − | 0.951253i | \(-0.400202\pi\) | ||||
0.308413 | + | 0.951253i | \(0.400202\pi\) | |||||||
\(564\) | 10.1489 | 0.427347 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.16428 | −0.175038 | ||||||||
\(567\) | 0.533559 | 0.0224074 | ||||||||
\(568\) | −10.1247 | −0.424822 | ||||||||
\(569\) | 31.2471 | 1.30995 | 0.654974 | − | 0.755651i | \(-0.272679\pi\) | ||||
0.654974 | + | 0.755651i | \(0.272679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.2261 | 1.09753 | 0.548763 | − | 0.835978i | \(-0.315099\pi\) | ||||
0.548763 | + | 0.835978i | \(0.315099\pi\) | |||||||
\(572\) | 9.42867 | 0.394233 | ||||||||
\(573\) | 8.40045 | 0.350934 | ||||||||
\(574\) | 4.23729 | 0.176861 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.93340 | −0.371902 | −0.185951 | − | 0.982559i | \(-0.559537\pi\) | ||||
−0.185951 | + | 0.982559i | \(0.559537\pi\) | |||||||
\(578\) | 16.0814 | 0.668900 | ||||||||
\(579\) | −10.5266 | −0.437471 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.71346 | −0.361495 | ||||||||
\(582\) | 5.56558 | 0.230701 | ||||||||
\(583\) | −4.63772 | −0.192075 | ||||||||
\(584\) | −13.9771 | −0.578376 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.9603 | −0.741933 | ||||||||
\(587\) | −3.99360 | −0.164833 | −0.0824167 | − | 0.996598i | \(-0.526264\pi\) | ||||
−0.0824167 | + | 0.996598i | \(0.526264\pi\) | |||||||
\(588\) | 6.71531 | 0.276935 | ||||||||
\(589\) | −0.497677 | −0.0205064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.2080 | −0.419903 | ||||||||
\(592\) | −4.06291 | −0.166985 | ||||||||
\(593\) | −11.2114 | −0.460396 | −0.230198 | − | 0.973144i | \(-0.573937\pi\) | ||||
−0.230198 | + | 0.973144i | \(0.573937\pi\) | |||||||
\(594\) | −1.43425 | −0.0588481 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.0750 | 0.453651 | ||||||||
\(597\) | −3.84318 | −0.157291 | ||||||||
\(598\) | −24.7443 | −1.01187 | ||||||||
\(599\) | −6.64762 | −0.271614 | −0.135807 | − | 0.990735i | \(-0.543363\pi\) | ||||
−0.135807 | + | 0.990735i | \(0.543363\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.7465 | −0.438359 | −0.219179 | − | 0.975685i | \(-0.570338\pi\) | ||||
−0.219179 | + | 0.975685i | \(0.570338\pi\) | |||||||
\(602\) | −6.06163 | −0.247053 | ||||||||
\(603\) | 6.91285 | 0.281513 | ||||||||
\(604\) | −1.63387 | −0.0664812 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.42708 | −0.382949 | ||||||||
\(607\) | −15.4591 | −0.627466 | −0.313733 | − | 0.949511i | \(-0.601580\pi\) | ||||
−0.313733 | + | 0.949511i | \(0.601580\pi\) | |||||||
\(608\) | −0.212889 | −0.00863379 | ||||||||
\(609\) | −3.30512 | −0.133930 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 66.7182 | 2.69913 | ||||||||
\(612\) | 0.958413 | 0.0387416 | ||||||||
\(613\) | 24.4867 | 0.989007 | 0.494503 | − | 0.869176i | \(-0.335350\pi\) | ||||
0.494503 | + | 0.869176i | \(0.335350\pi\) | |||||||
\(614\) | −20.8174 | −0.840122 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.765259 | 0.0308332 | ||||||||
\(617\) | 18.9157 | 0.761515 | 0.380758 | − | 0.924675i | \(-0.375663\pi\) | ||||
0.380758 | + | 0.924675i | \(0.375663\pi\) | |||||||
\(618\) | −7.99871 | −0.321755 | ||||||||
\(619\) | 2.55005 | 0.102495 | 0.0512476 | − | 0.998686i | \(-0.483680\pi\) | ||||
0.0512476 | + | 0.998686i | \(0.483680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.76401 | 0.151045 | ||||||||
\(622\) | 19.4526 | 0.779978 | ||||||||
\(623\) | 2.99977 | 0.120183 | ||||||||
\(624\) | 6.57392 | 0.263168 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.88310 | 0.235136 | ||||||||
\(627\) | 0.305337 | 0.0121940 | ||||||||
\(628\) | −6.64544 | −0.265182 | ||||||||
\(629\) | −3.89395 | −0.155262 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4530 | −1.45117 | −0.725585 | − | 0.688133i | \(-0.758431\pi\) | ||||
−0.725585 | + | 0.688133i | \(0.758431\pi\) | |||||||
\(632\) | −15.5279 | −0.617668 | ||||||||
\(633\) | −5.24920 | −0.208637 | ||||||||
\(634\) | −10.7610 | −0.427375 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.23354 | −0.128218 | ||||||||
\(637\) | 44.1460 | 1.74913 | ||||||||
\(638\) | 8.88445 | 0.351739 | ||||||||
\(639\) | 10.1247 | 0.400526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.3669 | −0.804444 | −0.402222 | − | 0.915542i | \(-0.631762\pi\) | ||||
−0.402222 | + | 0.915542i | \(0.631762\pi\) | |||||||
\(642\) | −18.9260 | −0.746949 | ||||||||
\(643\) | 11.4218 | 0.450433 | 0.225217 | − | 0.974309i | \(-0.427691\pi\) | ||||
0.225217 | + | 0.974309i | \(0.427691\pi\) | |||||||
\(644\) | −2.00832 | −0.0791390 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.204036 | −0.00802768 | ||||||||
\(647\) | −5.89217 | −0.231645 | −0.115823 | − | 0.993270i | \(-0.536950\pi\) | ||||
−0.115823 | + | 0.993270i | \(0.536950\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −10.7921 | −0.423627 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.24732 | 0.0488862 | ||||||||
\(652\) | 10.1134 | 0.396071 | ||||||||
\(653\) | −17.1063 | −0.669422 | −0.334711 | − | 0.942321i | \(-0.608639\pi\) | ||||
−0.334711 | + | 0.942321i | \(0.608639\pi\) | |||||||
\(654\) | −2.65524 | −0.103828 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.94156 | −0.310066 | ||||||||
\(657\) | 13.9771 | 0.545298 | ||||||||
\(658\) | 5.41505 | 0.211101 | ||||||||
\(659\) | −29.7191 | −1.15769 | −0.578846 | − | 0.815437i | \(-0.696497\pi\) | ||||
−0.578846 | + | 0.815437i | \(0.696497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.3036 | 1.80100 | 0.900501 | − | 0.434854i | \(-0.143200\pi\) | ||||
0.900501 | + | 0.434854i | \(0.143200\pi\) | |||||||
\(662\) | 0.617092 | 0.0239840 | ||||||||
\(663\) | 6.30054 | 0.244693 | ||||||||
\(664\) | 16.3308 | 0.633759 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.06291 | 0.157435 | ||||||||
\(667\) | −23.3161 | −0.902803 | ||||||||
\(668\) | −12.7885 | −0.494800 | ||||||||
\(669\) | −19.2782 | −0.745340 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.0315 | −0.696099 | ||||||||
\(672\) | 0.533559 | 0.0205825 | ||||||||
\(673\) | −19.7080 | −0.759689 | −0.379845 | − | 0.925050i | \(-0.624023\pi\) | ||||
−0.379845 | + | 0.925050i | \(0.624023\pi\) | |||||||
\(674\) | −15.4106 | −0.593595 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 30.2165 | 1.16217 | ||||||||
\(677\) | 24.7774 | 0.952273 | 0.476137 | − | 0.879371i | \(-0.342037\pi\) | ||||
0.476137 | + | 0.879371i | \(0.342037\pi\) | |||||||
\(678\) | −3.06283 | −0.117627 | ||||||||
\(679\) | 2.96957 | 0.113961 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.43957 | 0.323405 | ||||||||
\(682\) | −3.35289 | −0.128389 | ||||||||
\(683\) | 16.5874 | 0.634699 | 0.317349 | − | 0.948309i | \(-0.397207\pi\) | ||||
0.317349 | + | 0.948309i | \(0.397207\pi\) | |||||||
\(684\) | 0.212889 | 0.00814002 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.31793 | 0.279400 | ||||||||
\(687\) | −5.95568 | −0.227224 | ||||||||
\(688\) | 11.3607 | 0.433124 | ||||||||
\(689\) | −21.2571 | −0.809830 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.2893 | 1.60876 | 0.804381 | − | 0.594114i | \(-0.202497\pi\) | ||||
0.804381 | + | 0.594114i | \(0.202497\pi\) | |||||||
\(692\) | 13.6575 | 0.519182 | ||||||||
\(693\) | −0.765259 | −0.0290698 | ||||||||
\(694\) | 22.6565 | 0.860031 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.19448 | 0.234801 | ||||||||
\(697\) | −7.61130 | −0.288299 | ||||||||
\(698\) | 16.9543 | 0.641731 | ||||||||
\(699\) | −2.09293 | −0.0791617 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.7240 | −0.858273 | −0.429137 | − | 0.903240i | \(-0.641182\pi\) | ||||
−0.429137 | + | 0.903240i | \(0.641182\pi\) | |||||||
\(702\) | −6.57392 | −0.248117 | ||||||||
\(703\) | −0.864949 | −0.0326222 | ||||||||
\(704\) | −1.43425 | −0.0540554 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.06255 | 0.228167 | ||||||||
\(707\) | −5.02990 | −0.189169 | ||||||||
\(708\) | −7.52455 | −0.282790 | ||||||||
\(709\) | 46.4122 | 1.74305 | 0.871524 | − | 0.490353i | \(-0.163132\pi\) | ||||
0.871524 | + | 0.490353i | \(0.163132\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.5279 | 0.582343 | ||||||||
\(712\) | −5.62220 | −0.210701 | ||||||||
\(713\) | 8.79924 | 0.329534 | ||||||||
\(714\) | 0.511370 | 0.0191375 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.99142 | 0.111795 | ||||||||
\(717\) | −9.89840 | −0.369662 | ||||||||
\(718\) | −18.8987 | −0.705294 | ||||||||
\(719\) | −28.2066 | −1.05193 | −0.525964 | − | 0.850507i | \(-0.676295\pi\) | ||||
−0.525964 | + | 0.850507i | \(0.676295\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.26779 | −0.158941 | ||||||||
\(722\) | 18.9547 | 0.705420 | ||||||||
\(723\) | 21.4567 | 0.797983 | ||||||||
\(724\) | 7.62285 | 0.283301 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.94292 | −0.331903 | ||||||||
\(727\) | 0.851592 | 0.0315838 | 0.0157919 | − | 0.999875i | \(-0.494973\pi\) | ||||
0.0157919 | + | 0.999875i | \(0.494973\pi\) | |||||||
\(728\) | 3.50758 | 0.129999 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8883 | 0.402718 | ||||||||
\(732\) | −12.5721 | −0.464677 | ||||||||
\(733\) | 30.7299 | 1.13504 | 0.567518 | − | 0.823361i | \(-0.307904\pi\) | ||||
0.567518 | + | 0.823361i | \(0.307904\pi\) | |||||||
\(734\) | −25.0483 | −0.924551 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.76401 | 0.138743 | ||||||||
\(737\) | −9.91477 | −0.365215 | ||||||||
\(738\) | 7.94156 | 0.292333 | ||||||||
\(739\) | 2.06485 | 0.0759566 | 0.0379783 | − | 0.999279i | \(-0.487908\pi\) | ||||
0.0379783 | + | 0.999279i | \(0.487908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.39952 | 0.0514125 | ||||||||
\(742\) | −1.72529 | −0.0633373 | ||||||||
\(743\) | −37.8972 | −1.39031 | −0.695157 | − | 0.718858i | \(-0.744665\pi\) | ||||
−0.695157 | + | 0.718858i | \(0.744665\pi\) | |||||||
\(744\) | −2.33773 | −0.0857053 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.8954 | −0.435522 | ||||||||
\(747\) | −16.3308 | −0.597514 | ||||||||
\(748\) | −1.37461 | −0.0502606 | ||||||||
\(749\) | −10.0981 | −0.368978 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.6331 | −1.48272 | −0.741361 | − | 0.671106i | \(-0.765819\pi\) | ||||
−0.741361 | + | 0.671106i | \(0.765819\pi\) | |||||||
\(752\) | −10.1489 | −0.370093 | ||||||||
\(753\) | 4.10753 | 0.149687 | ||||||||
\(754\) | 40.7220 | 1.48301 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.533559 | −0.0194054 | ||||||||
\(757\) | 10.0032 | 0.363572 | 0.181786 | − | 0.983338i | \(-0.441812\pi\) | ||||
0.181786 | + | 0.983338i | \(0.441812\pi\) | |||||||
\(758\) | −27.5184 | −0.999514 | ||||||||
\(759\) | −5.39854 | −0.195955 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.1813 | −1.09407 | −0.547035 | − | 0.837110i | \(-0.684244\pi\) | ||||
−0.547035 | + | 0.837110i | \(0.684244\pi\) | |||||||
\(762\) | 6.48257 | 0.234839 | ||||||||
\(763\) | −1.41673 | −0.0512890 | ||||||||
\(764\) | −8.40045 | −0.303917 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.0314 | −0.796028 | ||||||||
\(767\) | −49.4658 | −1.78611 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 21.1468 | 0.762571 | 0.381286 | − | 0.924457i | \(-0.375481\pi\) | ||||
0.381286 | + | 0.924457i | \(0.375481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.7748 | −1.10833 | ||||||||
\(772\) | 10.5266 | 0.378861 | ||||||||
\(773\) | −29.4470 | −1.05913 | −0.529567 | − | 0.848268i | \(-0.677646\pi\) | ||||
−0.529567 | + | 0.848268i | \(0.677646\pi\) | |||||||
\(774\) | −11.3607 | −0.408353 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.56558 | −0.199793 | ||||||||
\(777\) | 2.16780 | 0.0777695 | ||||||||
\(778\) | −17.4892 | −0.627019 | ||||||||
\(779\) | −1.69067 | −0.0605746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.5213 | −0.519614 | ||||||||
\(782\) | 3.60748 | 0.129003 | ||||||||
\(783\) | −6.19448 | −0.221373 | ||||||||
\(784\) | −6.71531 | −0.239833 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.45794 | −0.337353 | ||||||||
\(787\) | −5.16875 | −0.184246 | −0.0921230 | − | 0.995748i | \(-0.529365\pi\) | ||||
−0.0921230 | + | 0.995748i | \(0.529365\pi\) | |||||||
\(788\) | 10.2080 | 0.363647 | ||||||||
\(789\) | −28.3729 | −1.01010 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.63420 | −0.0581055 | ||||||||
\(792\) | 1.43425 | 0.0509640 | ||||||||
\(793\) | −82.6478 | −2.93491 | ||||||||
\(794\) | −24.4990 | −0.869439 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.84318 | 0.136218 | ||||||||
\(797\) | −3.75807 | −0.133118 | −0.0665588 | − | 0.997783i | \(-0.521202\pi\) | ||||
−0.0665588 | + | 0.997783i | \(0.521202\pi\) | |||||||
\(798\) | 0.113589 | 0.00402100 | ||||||||
\(799\) | −9.72686 | −0.344111 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.62220 | 0.198650 | ||||||||
\(802\) | −1.04105 | −0.0367607 | ||||||||
\(803\) | −20.0467 | −0.707432 | ||||||||
\(804\) | −6.91285 | −0.243797 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.3681 | −0.541317 | ||||||||
\(807\) | −10.6668 | −0.375488 | ||||||||
\(808\) | 9.42708 | 0.331643 | ||||||||
\(809\) | −20.8847 | −0.734266 | −0.367133 | − | 0.930168i | \(-0.619661\pi\) | ||||
−0.367133 | + | 0.930168i | \(0.619661\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5032 | −1.28180 | −0.640900 | − | 0.767625i | \(-0.721439\pi\) | ||||
−0.640900 | + | 0.767625i | \(0.721439\pi\) | |||||||
\(812\) | 3.30512 | 0.115987 | ||||||||
\(813\) | −22.8439 | −0.801172 | ||||||||
\(814\) | −5.82724 | −0.204245 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.958413 | −0.0335512 | ||||||||
\(817\) | 2.41858 | 0.0846153 | ||||||||
\(818\) | −22.2568 | −0.778190 | ||||||||
\(819\) | −3.50758 | −0.122565 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.2221 | 1.15946 | 0.579730 | − | 0.814809i | \(-0.303158\pi\) | ||||
0.579730 | + | 0.814809i | \(0.303158\pi\) | |||||||
\(822\) | 12.3361 | 0.430270 | ||||||||
\(823\) | −32.7898 | −1.14298 | −0.571490 | − | 0.820609i | \(-0.693634\pi\) | ||||
−0.571490 | + | 0.820609i | \(0.693634\pi\) | |||||||
\(824\) | 7.99871 | 0.278648 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.01479 | −0.139692 | ||||||||
\(827\) | 5.18915 | 0.180444 | 0.0902222 | − | 0.995922i | \(-0.471242\pi\) | ||||
0.0902222 | + | 0.995922i | \(0.471242\pi\) | |||||||
\(828\) | −3.76401 | −0.130808 | ||||||||
\(829\) | −5.55820 | −0.193044 | −0.0965221 | − | 0.995331i | \(-0.530772\pi\) | ||||
−0.0965221 | + | 0.995331i | \(0.530772\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.4592 | −1.09131 | ||||||||
\(832\) | −6.57392 | −0.227910 | ||||||||
\(833\) | −6.43605 | −0.222996 | ||||||||
\(834\) | 4.53918 | 0.157179 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.305337 | −0.0105603 | ||||||||
\(837\) | 2.33773 | 0.0808037 | ||||||||
\(838\) | 23.1294 | 0.798991 | ||||||||
\(839\) | 43.4383 | 1.49966 | 0.749828 | − | 0.661633i | \(-0.230136\pi\) | ||||
0.749828 | + | 0.661633i | \(0.230136\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.37160 | 0.323159 | ||||||||
\(842\) | −9.76139 | −0.336400 | ||||||||
\(843\) | 10.7785 | 0.371232 | ||||||||
\(844\) | 5.24920 | 0.180685 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 10.1489 | 0.348927 | ||||||||
\(847\) | −4.77158 | −0.163953 | ||||||||
\(848\) | 3.23354 | 0.111040 | ||||||||
\(849\) | −4.16428 | −0.142918 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.2928 | 0.524231 | ||||||||
\(852\) | −10.1247 | −0.346865 | ||||||||
\(853\) | 3.34342 | 0.114477 | 0.0572383 | − | 0.998361i | \(-0.481771\pi\) | ||||
0.0572383 | + | 0.998361i | \(0.481771\pi\) | |||||||
\(854\) | −6.70794 | −0.229541 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9260 | 0.646877 | ||||||||
\(857\) | −34.5415 | −1.17991 | −0.589957 | − | 0.807434i | \(-0.700855\pi\) | ||||
−0.589957 | + | 0.807434i | \(0.700855\pi\) | |||||||
\(858\) | 9.42867 | 0.321889 | ||||||||
\(859\) | −23.8513 | −0.813796 | −0.406898 | − | 0.913474i | \(-0.633390\pi\) | ||||
−0.406898 | + | 0.913474i | \(0.633390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.23729 | 0.144407 | ||||||||
\(862\) | −8.49298 | −0.289272 | ||||||||
\(863\) | 5.73061 | 0.195072 | 0.0975361 | − | 0.995232i | \(-0.468904\pi\) | ||||
0.0975361 | + | 0.995232i | \(0.468904\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.0042 | 0.747733 | ||||||||
\(867\) | 16.0814 | 0.546154 | ||||||||
\(868\) | −1.24732 | −0.0423367 | ||||||||
\(869\) | −22.2710 | −0.755492 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.4445 | −1.53983 | ||||||||
\(872\) | 2.65524 | 0.0899178 | ||||||||
\(873\) | 5.56558 | 0.188366 | ||||||||
\(874\) | 0.801317 | 0.0271049 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13.9771 | −0.472242 | ||||||||
\(877\) | 49.8482 | 1.68325 | 0.841627 | − | 0.540059i | \(-0.181598\pi\) | ||||
0.841627 | + | 0.540059i | \(0.181598\pi\) | |||||||
\(878\) | 38.3582 | 1.29453 | ||||||||
\(879\) | −17.9603 | −0.605786 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.65609 | −0.257940 | −0.128970 | − | 0.991648i | \(-0.541167\pi\) | ||||
−0.128970 | + | 0.991648i | \(0.541167\pi\) | |||||||
\(882\) | 6.71531 | 0.226116 | ||||||||
\(883\) | 38.9959 | 1.31232 | 0.656158 | − | 0.754623i | \(-0.272180\pi\) | ||||
0.656158 | + | 0.754623i | \(0.272180\pi\) | |||||||
\(884\) | −6.30054 | −0.211910 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.7478 | 0.428270 | ||||||||
\(887\) | −32.5338 | −1.09238 | −0.546189 | − | 0.837662i | \(-0.683922\pi\) | ||||
−0.546189 | + | 0.837662i | \(0.683922\pi\) | |||||||
\(888\) | −4.06291 | −0.136342 | ||||||||
\(889\) | 3.45884 | 0.116006 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.43425 | −0.0480493 | ||||||||
\(892\) | 19.2782 | 0.645483 | ||||||||
\(893\) | −2.16059 | −0.0723015 | ||||||||
\(894\) | 11.0750 | 0.370405 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.533559 | −0.0178250 | ||||||||
\(897\) | −24.7443 | −0.826189 | ||||||||
\(898\) | −18.0358 | −0.601862 | ||||||||
\(899\) | −14.4810 | −0.482969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.09907 | 0.103245 | ||||||||
\(902\) | −11.3902 | −0.379253 | ||||||||
\(903\) | −6.06163 | −0.201718 | ||||||||
\(904\) | 3.06283 | 0.101868 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.63387 | −0.0542817 | ||||||||
\(907\) | 16.5820 | 0.550595 | 0.275297 | − | 0.961359i | \(-0.411224\pi\) | ||||
0.275297 | + | 0.961359i | \(0.411224\pi\) | |||||||
\(908\) | −8.43957 | −0.280077 | ||||||||
\(909\) | −9.42708 | −0.312676 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.5720 | −0.946633 | −0.473316 | − | 0.880893i | \(-0.656943\pi\) | ||||
−0.473316 | + | 0.880893i | \(0.656943\pi\) | |||||||
\(912\) | −0.212889 | −0.00704946 | ||||||||
\(913\) | 23.4225 | 0.775173 | ||||||||
\(914\) | −21.1495 | −0.699565 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.95568 | 0.196781 | ||||||||
\(917\) | −5.04637 | −0.166646 | ||||||||
\(918\) | 0.958413 | 0.0316324 | ||||||||
\(919\) | −0.382861 | −0.0126294 | −0.00631471 | − | 0.999980i | \(-0.502010\pi\) | ||||
−0.00631471 | + | 0.999980i | \(0.502010\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.8174 | −0.685957 | ||||||||
\(922\) | −32.0085 | −1.05414 | ||||||||
\(923\) | −66.5588 | −2.19081 | ||||||||
\(924\) | 0.765259 | 0.0251752 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 28.7776 | 0.945689 | ||||||||
\(927\) | −7.99871 | −0.262712 | ||||||||
\(928\) | −6.19448 | −0.203344 | ||||||||
\(929\) | −6.25711 | −0.205289 | −0.102645 | − | 0.994718i | \(-0.532730\pi\) | ||||
−0.102645 | + | 0.994718i | \(0.532730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.42962 | −0.0468538 | ||||||||
\(932\) | 2.09293 | 0.0685561 | ||||||||
\(933\) | 19.4526 | 0.636849 | ||||||||
\(934\) | 5.20326 | 0.170256 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.57392 | 0.214875 | ||||||||
\(937\) | −4.93214 | −0.161126 | −0.0805630 | − | 0.996750i | \(-0.525672\pi\) | ||||
−0.0805630 | + | 0.996750i | \(0.525672\pi\) | |||||||
\(938\) | −3.68841 | −0.120431 | ||||||||
\(939\) | 5.88310 | 0.191988 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.8107 | 0.971801 | 0.485901 | − | 0.874014i | \(-0.338492\pi\) | ||||
0.485901 | + | 0.874014i | \(0.338492\pi\) | |||||||
\(942\) | −6.64544 | −0.216520 | ||||||||
\(943\) | 29.8921 | 0.973422 | ||||||||
\(944\) | 7.52455 | 0.244903 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.2942 | 0.529769 | ||||||||
\(947\) | −26.9125 | −0.874539 | −0.437270 | − | 0.899330i | \(-0.644054\pi\) | ||||
−0.437270 | + | 0.899330i | \(0.644054\pi\) | |||||||
\(948\) | −15.5279 | −0.504324 | ||||||||
\(949\) | −91.8843 | −2.98269 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.7610 | −0.348950 | ||||||||
\(952\) | −0.511370 | −0.0165736 | ||||||||
\(953\) | 37.2337 | 1.20612 | 0.603059 | − | 0.797697i | \(-0.293949\pi\) | ||||
0.603059 | + | 0.797697i | \(0.293949\pi\) | |||||||
\(954\) | −3.23354 | −0.104690 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.89840 | 0.320137 | ||||||||
\(957\) | 8.88445 | 0.287194 | ||||||||
\(958\) | 39.6385 | 1.28066 | ||||||||
\(959\) | 6.58203 | 0.212545 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5350 | −0.823710 | ||||||||
\(962\) | −26.7093 | −0.861141 | ||||||||
\(963\) | −18.9260 | −0.609882 | ||||||||
\(964\) | −21.4567 | −0.691074 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.00832 | −0.0646167 | ||||||||
\(967\) | 16.0845 | 0.517244 | 0.258622 | − | 0.965979i | \(-0.416732\pi\) | ||||
0.258622 | + | 0.965979i | \(0.416732\pi\) | |||||||
\(968\) | 8.94292 | 0.287436 | ||||||||
\(969\) | −0.204036 | −0.00655457 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2569 | 0.393342 | 0.196671 | − | 0.980470i | \(-0.436987\pi\) | ||||
0.196671 | + | 0.980470i | \(0.436987\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 2.42192 | 0.0776431 | ||||||||
\(974\) | −5.44308 | −0.174407 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.5721 | 0.402422 | ||||||||
\(977\) | 18.0218 | 0.576569 | 0.288285 | − | 0.957545i | \(-0.406915\pi\) | ||||
0.288285 | + | 0.957545i | \(0.406915\pi\) | |||||||
\(978\) | 10.1134 | 0.323391 | ||||||||
\(979\) | −8.06365 | −0.257715 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.65524 | −0.0847753 | ||||||||
\(982\) | −0.873965 | −0.0278893 | ||||||||
\(983\) | 49.4029 | 1.57571 | 0.787854 | − | 0.615862i | \(-0.211192\pi\) | ||||
0.787854 | + | 0.615862i | \(0.211192\pi\) | |||||||
\(984\) | −7.94156 | −0.253168 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.93687 | −0.189069 | ||||||||
\(987\) | 5.41505 | 0.172363 | ||||||||
\(988\) | −1.39952 | −0.0445246 | ||||||||
\(989\) | −42.7619 | −1.35975 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.5664 | −0.970972 | −0.485486 | − | 0.874244i | \(-0.661357\pi\) | ||||
−0.485486 | + | 0.874244i | \(0.661357\pi\) | |||||||
\(992\) | 2.33773 | 0.0742230 | ||||||||
\(993\) | 0.617092 | 0.0195828 | ||||||||
\(994\) | −5.40211 | −0.171345 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.3308 | 0.517462 | ||||||||
\(997\) | 6.81050 | 0.215691 | 0.107845 | − | 0.994168i | \(-0.465605\pi\) | ||||
0.107845 | + | 0.994168i | \(0.465605\pi\) | |||||||
\(998\) | 34.9604 | 1.10665 | ||||||||
\(999\) | 4.06291 | 0.128545 |
(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 | 3750.2.a.u.1.6 | 8 | ||
5.2 | odd | 4 | 3750.2.c.k.1249.6 | 16 | |||
5.3 | odd | 4 | 3750.2.c.k.1249.11 | 16 | |||
5.4 | even | 2 | 3750.2.a.v.1.3 | 8 | |||
25.3 | odd | 20 | 150.2.h.b.109.3 | ✓ | 16 | ||
25.4 | even | 10 | 750.2.g.f.451.2 | 16 | |||
25.6 | even | 5 | 750.2.g.g.301.3 | 16 | |||
25.8 | odd | 20 | 750.2.h.d.199.1 | 16 | |||
25.17 | odd | 20 | 150.2.h.b.139.3 | yes | 16 | ||
25.19 | even | 10 | 750.2.g.f.301.2 | 16 | |||
25.21 | even | 5 | 750.2.g.g.451.3 | 16 | |||
25.22 | odd | 20 | 750.2.h.d.49.2 | 16 | |||
75.17 | even | 20 | 450.2.l.c.289.2 | 16 | |||
75.53 | even | 20 | 450.2.l.c.109.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.b.109.3 | ✓ | 16 | 25.3 | odd | 20 | ||
150.2.h.b.139.3 | yes | 16 | 25.17 | odd | 20 | ||
450.2.l.c.109.2 | 16 | 75.53 | even | 20 | |||
450.2.l.c.289.2 | 16 | 75.17 | even | 20 | |||
750.2.g.f.301.2 | 16 | 25.19 | even | 10 | |||
750.2.g.f.451.2 | 16 | 25.4 | even | 10 | |||
750.2.g.g.301.3 | 16 | 25.6 | even | 5 | |||
750.2.g.g.451.3 | 16 | 25.21 | even | 5 | |||
750.2.h.d.49.2 | 16 | 25.22 | odd | 20 | |||
750.2.h.d.199.1 | 16 | 25.8 | odd | 20 | |||
3750.2.a.u.1.6 | 8 | 1.1 | even | 1 | trivial | ||
3750.2.a.v.1.3 | 8 | 5.4 | even | 2 | |||
3750.2.c.k.1249.6 | 16 | 5.2 | odd | 4 | |||
3750.2.c.k.1249.11 | 16 | 5.3 | odd | 4 |