Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1755,2,Mod(1,1755)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1755, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1755.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1755 = 3^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1755.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: | \(14.0137455547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1957.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.06150\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1755.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.514916 | 0.364101 | 0.182050 | − | 0.983289i | \(-0.441727\pi\) | ||||
0.182050 | + | 0.983289i | \(0.441727\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73486 | −0.867431 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.44964 | −1.68180 | −0.840902 | − | 0.541187i | \(-0.817975\pi\) | ||||
−0.840902 | + | 0.541187i | \(0.817975\pi\) | |||||||
\(8\) | −1.92314 | −0.679933 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.514916 | −0.162831 | ||||||||
\(11\) | −5.37278 | −1.61995 | −0.809976 | − | 0.586463i | \(-0.800520\pi\) | ||||
−0.809976 | + | 0.586463i | \(0.800520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.29119 | −0.612346 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.47947 | 0.619867 | ||||||||
\(17\) | 4.15845 | 1.00857 | 0.504286 | − | 0.863537i | \(-0.331756\pi\) | ||||
0.504286 | + | 0.863537i | \(0.331756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.50517 | −0.574726 | −0.287363 | − | 0.957822i | \(-0.592779\pi\) | ||||
−0.287363 | + | 0.957822i | \(0.592779\pi\) | |||||||
\(20\) | 1.73486 | 0.387927 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.76653 | −0.589826 | ||||||||
\(23\) | 2.60625 | 0.543440 | 0.271720 | − | 0.962376i | \(-0.412408\pi\) | ||||
0.271720 | + | 0.962376i | \(0.412408\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.514916 | 0.100983 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.71950 | 1.45885 | ||||||||
\(29\) | −3.18450 | −0.591346 | −0.295673 | − | 0.955289i | \(-0.595544\pi\) | ||||
−0.295673 | + | 0.955289i | \(0.595544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.19424 | 0.753308 | 0.376654 | − | 0.926354i | \(-0.377075\pi\) | ||||
0.376654 | + | 0.926354i | \(0.377075\pi\) | |||||||
\(32\) | 5.12300 | 0.905627 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.14125 | 0.367221 | ||||||||
\(35\) | 4.44964 | 0.752126 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.57641 | −0.916757 | −0.458378 | − | 0.888757i | \(-0.651570\pi\) | ||||
−0.458378 | + | 0.888757i | \(0.651570\pi\) | |||||||
\(38\) | −1.28995 | −0.209258 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.92314 | 0.304075 | ||||||||
\(41\) | −4.43244 | −0.692231 | −0.346115 | − | 0.938192i | \(-0.612499\pi\) | ||||
−0.346115 | + | 0.938192i | \(0.612499\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.18739 | 1.24857 | 0.624283 | − | 0.781199i | \(-0.285391\pi\) | ||||
0.624283 | + | 0.781199i | \(0.285391\pi\) | |||||||
\(44\) | 9.32102 | 1.40520 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.34200 | 0.197867 | ||||||||
\(47\) | 1.07975 | 0.157498 | 0.0787490 | − | 0.996894i | \(-0.474907\pi\) | ||||
0.0787490 | + | 0.996894i | \(0.474907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.7993 | 1.82846 | ||||||||
\(50\) | 0.514916 | 0.0728201 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.73486 | −0.240582 | ||||||||
\(53\) | 12.0816 | 1.65953 | 0.829767 | − | 0.558110i | \(-0.188473\pi\) | ||||
0.829767 | + | 0.558110i | \(0.188473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.37278 | 0.724465 | ||||||||
\(56\) | 8.55727 | 1.14351 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.63975 | −0.215310 | ||||||||
\(59\) | 10.9790 | 1.42935 | 0.714673 | − | 0.699458i | \(-0.246575\pi\) | ||||
0.714673 | + | 0.699458i | \(0.246575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.66213 | −0.852998 | −0.426499 | − | 0.904488i | \(-0.640253\pi\) | ||||
−0.426499 | + | 0.904488i | \(0.640253\pi\) | |||||||
\(62\) | 2.15968 | 0.274280 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.32102 | −0.290128 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.83777 | −0.468858 | −0.234429 | − | 0.972133i | \(-0.575322\pi\) | ||||
−0.234429 | + | 0.972133i | \(0.575322\pi\) | |||||||
\(68\) | −7.21433 | −0.874866 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.29119 | 0.273849 | ||||||||
\(71\) | 5.54842 | 0.658476 | 0.329238 | − | 0.944247i | \(-0.393208\pi\) | ||||
0.329238 | + | 0.944247i | \(0.393208\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.2270 | −1.54810 | −0.774050 | − | 0.633125i | \(-0.781772\pi\) | ||||
−0.774050 | + | 0.633125i | \(0.781772\pi\) | |||||||
\(74\) | −2.87139 | −0.333792 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.34613 | 0.498535 | ||||||||
\(77\) | 23.9069 | 2.72444 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.82530 | −0.767907 | −0.383953 | − | 0.923353i | \(-0.625438\pi\) | ||||
−0.383953 | + | 0.923353i | \(0.625438\pi\) | |||||||
\(80\) | −2.47947 | −0.277213 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.28233 | −0.252042 | ||||||||
\(83\) | −7.79453 | −0.855560 | −0.427780 | − | 0.903883i | \(-0.640704\pi\) | ||||
−0.427780 | + | 0.903883i | \(0.640704\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.15845 | −0.451047 | ||||||||
\(86\) | 4.21582 | 0.454603 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.3326 | 1.10146 | ||||||||
\(89\) | 14.5602 | 1.54337 | 0.771687 | − | 0.636002i | \(-0.219413\pi\) | ||||
0.771687 | + | 0.636002i | \(0.219413\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.44964 | −0.466448 | ||||||||
\(92\) | −4.52148 | −0.471397 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.555982 | 0.0573451 | ||||||||
\(95\) | 2.50517 | 0.257025 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.49070 | −0.151358 | −0.0756789 | − | 0.997132i | \(-0.524112\pi\) | ||||
−0.0756789 | + | 0.997132i | \(0.524112\pi\) | |||||||
\(98\) | 6.59054 | 0.665745 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.73486 | −0.173486 | ||||||||
\(101\) | 9.39972 | 0.935307 | 0.467653 | − | 0.883912i | \(-0.345100\pi\) | ||||
0.467653 | + | 0.883912i | \(0.345100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.66485 | −0.755240 | −0.377620 | − | 0.925961i | \(-0.623258\pi\) | ||||
−0.377620 | + | 0.925961i | \(0.623258\pi\) | |||||||
\(104\) | −1.92314 | −0.188579 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.22100 | 0.604237 | ||||||||
\(107\) | −14.2422 | −1.37685 | −0.688423 | − | 0.725309i | \(-0.741697\pi\) | ||||
−0.688423 | + | 0.725309i | \(0.741697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.35452 | 0.417088 | 0.208544 | − | 0.978013i | \(-0.433128\pi\) | ||||
0.208544 | + | 0.978013i | \(0.433128\pi\) | |||||||
\(110\) | 2.76653 | 0.263778 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.0327 | −1.04249 | ||||||||
\(113\) | 14.0078 | 1.31774 | 0.658871 | − | 0.752256i | \(-0.271034\pi\) | ||||
0.658871 | + | 0.752256i | \(0.271034\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.60625 | −0.243034 | ||||||||
\(116\) | 5.52466 | 0.512952 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.65327 | 0.520426 | ||||||||
\(119\) | −18.5036 | −1.69622 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.8667 | 1.62425 | ||||||||
\(122\) | −3.43044 | −0.310577 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.27643 | −0.653442 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.7783 | −1.66630 | −0.833151 | − | 0.553045i | \(-0.813466\pi\) | ||||
−0.833151 | + | 0.553045i | \(0.813466\pi\) | |||||||
\(128\) | −11.4411 | −1.01126 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.514916 | −0.0451611 | ||||||||
\(131\) | −6.57369 | −0.574346 | −0.287173 | − | 0.957879i | \(-0.592715\pi\) | ||||
−0.287173 | + | 0.957879i | \(0.592715\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.1471 | 0.966576 | ||||||||
\(134\) | −1.97613 | −0.170712 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.99728 | −0.685761 | ||||||||
\(137\) | −10.4744 | −0.894893 | −0.447446 | − | 0.894311i | \(-0.647666\pi\) | ||||
−0.447446 | + | 0.894311i | \(0.647666\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.96639 | 0.675700 | 0.337850 | − | 0.941200i | \(-0.390300\pi\) | ||||
0.337850 | + | 0.941200i | \(0.390300\pi\) | |||||||
\(140\) | −7.71950 | −0.652417 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.85697 | 0.239752 | ||||||||
\(143\) | −5.37278 | −0.449294 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.18450 | 0.264458 | ||||||||
\(146\) | −6.81078 | −0.563664 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.67431 | 0.795223 | ||||||||
\(149\) | 21.9611 | 1.79912 | 0.899562 | − | 0.436792i | \(-0.143886\pi\) | ||||
0.899562 | + | 0.436792i | \(0.143886\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0281 | −1.30434 | −0.652172 | − | 0.758071i | \(-0.726142\pi\) | ||||
−0.652172 | + | 0.758071i | \(0.726142\pi\) | |||||||
\(152\) | 4.81780 | 0.390775 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.3100 | 0.991971 | ||||||||
\(155\) | −4.19424 | −0.336890 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.9483 | 1.75167 | 0.875833 | − | 0.482615i | \(-0.160313\pi\) | ||||
0.875833 | + | 0.482615i | \(0.160313\pi\) | |||||||
\(158\) | −3.51446 | −0.279595 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.12300 | −0.405009 | ||||||||
\(161\) | −11.5968 | −0.913960 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.4245 | 0.973164 | 0.486582 | − | 0.873635i | \(-0.338243\pi\) | ||||
0.486582 | + | 0.873635i | \(0.338243\pi\) | |||||||
\(164\) | 7.68967 | 0.600462 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.01353 | −0.311510 | ||||||||
\(167\) | 17.8284 | 1.37960 | 0.689800 | − | 0.724000i | \(-0.257698\pi\) | ||||
0.689800 | + | 0.724000i | \(0.257698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.14125 | −0.164226 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.2040 | −1.08304 | ||||||||
\(173\) | 21.3699 | 1.62473 | 0.812363 | − | 0.583152i | \(-0.198181\pi\) | ||||
0.812363 | + | 0.583152i | \(0.198181\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.44964 | −0.336361 | ||||||||
\(176\) | −13.3216 | −1.00415 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.49726 | 0.561944 | ||||||||
\(179\) | 9.24978 | 0.691361 | 0.345680 | − | 0.938352i | \(-0.387648\pi\) | ||||
0.345680 | + | 0.938352i | \(0.387648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.01596 | 0.224175 | 0.112087 | − | 0.993698i | \(-0.464246\pi\) | ||||
0.112087 | + | 0.993698i | \(0.464246\pi\) | |||||||
\(182\) | −2.29119 | −0.169834 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.01218 | −0.369503 | ||||||||
\(185\) | 5.57641 | 0.409986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.3424 | −1.63384 | ||||||||
\(188\) | −1.87322 | −0.136619 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.28995 | 0.0935830 | ||||||||
\(191\) | 13.4334 | 0.972006 | 0.486003 | − | 0.873957i | \(-0.338454\pi\) | ||||
0.486003 | + | 0.873957i | \(0.338454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.1970 | −1.45381 | −0.726907 | − | 0.686736i | \(-0.759043\pi\) | ||||
−0.726907 | + | 0.686736i | \(0.759043\pi\) | |||||||
\(194\) | −0.767586 | −0.0551094 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.2049 | −1.58607 | ||||||||
\(197\) | −3.86855 | −0.275623 | −0.137811 | − | 0.990458i | \(-0.544007\pi\) | ||||
−0.137811 | + | 0.990458i | \(0.544007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.8742 | 1.12529 | 0.562645 | − | 0.826699i | \(-0.309784\pi\) | ||||
0.562645 | + | 0.826699i | \(0.309784\pi\) | |||||||
\(200\) | −1.92314 | −0.135987 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.84006 | 0.340546 | ||||||||
\(203\) | 14.1698 | 0.994528 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.43244 | 0.309575 | ||||||||
\(206\) | −3.94676 | −0.274984 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.47947 | 0.171920 | ||||||||
\(209\) | 13.4597 | 0.931029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.1776 | −1.38909 | −0.694543 | − | 0.719451i | \(-0.744393\pi\) | ||||
−0.694543 | + | 0.719451i | \(0.744393\pi\) | |||||||
\(212\) | −20.9599 | −1.43953 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.33354 | −0.501311 | ||||||||
\(215\) | −8.18739 | −0.558375 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.6628 | −1.26692 | ||||||||
\(218\) | 2.24221 | 0.151862 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.32102 | −0.628423 | ||||||||
\(221\) | 4.15845 | 0.279727 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.6146 | 1.11260 | 0.556299 | − | 0.830982i | \(-0.312221\pi\) | ||||
0.556299 | + | 0.830982i | \(0.312221\pi\) | |||||||
\(224\) | −22.7955 | −1.52309 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.21284 | 0.479791 | ||||||||
\(227\) | −21.1905 | −1.40646 | −0.703230 | − | 0.710962i | \(-0.748260\pi\) | ||||
−0.703230 | + | 0.710962i | \(0.748260\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1066 | 0.800025 | 0.400013 | − | 0.916510i | \(-0.369006\pi\) | ||||
0.400013 | + | 0.916510i | \(0.369006\pi\) | |||||||
\(230\) | −1.34200 | −0.0884888 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.12423 | 0.402076 | ||||||||
\(233\) | 19.3182 | 1.26558 | 0.632788 | − | 0.774325i | \(-0.281910\pi\) | ||||
0.632788 | + | 0.774325i | \(0.281910\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.07975 | −0.0704353 | ||||||||
\(236\) | −19.0471 | −1.23986 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.52779 | −0.617595 | ||||||||
\(239\) | −23.8990 | −1.54590 | −0.772948 | − | 0.634469i | \(-0.781219\pi\) | ||||
−0.772948 | + | 0.634469i | \(0.781219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.92710 | −0.124135 | −0.0620677 | − | 0.998072i | \(-0.519769\pi\) | ||||
−0.0620677 | + | 0.998072i | \(0.519769\pi\) | |||||||
\(242\) | 9.19986 | 0.591389 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.5579 | 0.739917 | ||||||||
\(245\) | −12.7993 | −0.817714 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.50517 | −0.159400 | ||||||||
\(248\) | −8.06611 | −0.512199 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.514916 | −0.0325662 | ||||||||
\(251\) | 24.4095 | 1.54071 | 0.770357 | − | 0.637612i | \(-0.220078\pi\) | ||||
0.770357 | + | 0.637612i | \(0.220078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0028 | −0.880347 | ||||||||
\(254\) | −9.66924 | −0.606702 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.24918 | −0.0780736 | ||||||||
\(257\) | −3.50646 | −0.218727 | −0.109364 | − | 0.994002i | \(-0.534881\pi\) | ||||
−0.109364 | + | 0.994002i | \(0.534881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.8130 | 1.54181 | ||||||||
\(260\) | 1.73486 | 0.107592 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.38490 | −0.209120 | ||||||||
\(263\) | −17.3816 | −1.07180 | −0.535899 | − | 0.844282i | \(-0.680027\pi\) | ||||
−0.535899 | + | 0.844282i | \(0.680027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0816 | −0.742166 | ||||||||
\(266\) | 5.73982 | 0.351931 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.65800 | 0.406702 | ||||||||
\(269\) | 0.127670 | 0.00778416 | 0.00389208 | − | 0.999992i | \(-0.498761\pi\) | ||||
0.00389208 | + | 0.999992i | \(0.498761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.61932 | 0.523586 | 0.261793 | − | 0.965124i | \(-0.415686\pi\) | ||||
0.261793 | + | 0.965124i | \(0.415686\pi\) | |||||||
\(272\) | 10.3107 | 0.625180 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.39346 | −0.325831 | ||||||||
\(275\) | −5.37278 | −0.323991 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.60519 | 0.216615 | 0.108307 | − | 0.994117i | \(-0.465457\pi\) | ||||
0.108307 | + | 0.994117i | \(0.465457\pi\) | |||||||
\(278\) | 4.10202 | 0.246023 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.55727 | −0.511395 | ||||||||
\(281\) | −10.4581 | −0.623881 | −0.311940 | − | 0.950102i | \(-0.600979\pi\) | ||||
−0.311940 | + | 0.950102i | \(0.600979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.30153 | −0.196256 | −0.0981279 | − | 0.995174i | \(-0.531285\pi\) | ||||
−0.0981279 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(284\) | −9.62574 | −0.571182 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.76653 | −0.163588 | ||||||||
\(287\) | 19.7227 | 1.16420 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.292678 | 0.0172163 | ||||||||
\(290\) | 1.63975 | 0.0962893 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.9470 | 1.34287 | ||||||||
\(293\) | 3.84339 | 0.224533 | 0.112267 | − | 0.993678i | \(-0.464189\pi\) | ||||
0.112267 | + | 0.993678i | \(0.464189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9790 | −0.639223 | ||||||||
\(296\) | 10.7242 | 0.623333 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.3081 | 0.655062 | ||||||||
\(299\) | 2.60625 | 0.150723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.4309 | −2.09984 | ||||||||
\(302\) | −8.25310 | −0.474913 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.21149 | −0.356253 | ||||||||
\(305\) | 6.66213 | 0.381472 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8062 | 1.01625 | 0.508126 | − | 0.861283i | \(-0.330339\pi\) | ||||
0.508126 | + | 0.861283i | \(0.330339\pi\) | |||||||
\(308\) | −41.4751 | −2.36327 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.15968 | −0.122662 | ||||||||
\(311\) | −34.2196 | −1.94041 | −0.970207 | − | 0.242278i | \(-0.922105\pi\) | ||||
−0.970207 | + | 0.242278i | \(0.922105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.8447 | 0.952118 | 0.476059 | − | 0.879413i | \(-0.342065\pi\) | ||||
0.476059 | + | 0.879413i | \(0.342065\pi\) | |||||||
\(314\) | 11.3015 | 0.637782 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.8410 | 0.666106 | ||||||||
\(317\) | 16.1049 | 0.904542 | 0.452271 | − | 0.891881i | \(-0.350614\pi\) | ||||
0.452271 | + | 0.891881i | \(0.350614\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.1096 | 0.957953 | ||||||||
\(320\) | 2.32102 | 0.129749 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.97140 | −0.332773 | ||||||||
\(323\) | −10.4176 | −0.579652 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 6.39759 | 0.354330 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.52420 | 0.470670 | ||||||||
\(329\) | −4.80450 | −0.264881 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.8658 | 1.58661 | 0.793305 | − | 0.608825i | \(-0.208359\pi\) | ||||
0.793305 | + | 0.608825i | \(0.208359\pi\) | |||||||
\(332\) | 13.5224 | 0.742139 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.18012 | 0.502314 | ||||||||
\(335\) | 3.83777 | 0.209680 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.1297 | −1.64127 | −0.820635 | − | 0.571452i | \(-0.806380\pi\) | ||||
−0.820635 | + | 0.571452i | \(0.806380\pi\) | |||||||
\(338\) | 0.514916 | 0.0280077 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.21433 | 0.391252 | ||||||||
\(341\) | −22.5347 | −1.22032 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −25.8046 | −1.39332 | ||||||||
\(344\) | −15.7455 | −0.848940 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0037 | 0.591564 | ||||||||
\(347\) | −6.65740 | −0.357388 | −0.178694 | − | 0.983905i | \(-0.557187\pi\) | ||||
−0.178694 | + | 0.983905i | \(0.557187\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.5996 | 1.79855 | 0.899273 | − | 0.437387i | \(-0.144096\pi\) | ||||
0.899273 | + | 0.437387i | \(0.144096\pi\) | |||||||
\(350\) | −2.29119 | −0.122469 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.5247 | −1.46707 | ||||||||
\(353\) | 4.03385 | 0.214700 | 0.107350 | − | 0.994221i | \(-0.465763\pi\) | ||||
0.107350 | + | 0.994221i | \(0.465763\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.54842 | −0.294479 | ||||||||
\(356\) | −25.2599 | −1.33877 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.76286 | 0.251725 | ||||||||
\(359\) | 15.3477 | 0.810019 | 0.405010 | − | 0.914312i | \(-0.367268\pi\) | ||||
0.405010 | + | 0.914312i | \(0.367268\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.7241 | −0.669690 | ||||||||
\(362\) | 1.55297 | 0.0816221 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.71950 | 0.404612 | ||||||||
\(365\) | 13.2270 | 0.692331 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.7870 | −1.34607 | −0.673034 | − | 0.739611i | \(-0.735009\pi\) | ||||
−0.673034 | + | 0.739611i | \(0.735009\pi\) | |||||||
\(368\) | 6.46210 | 0.336860 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.87139 | 0.149276 | ||||||||
\(371\) | −53.7587 | −2.79101 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0741 | 0.728731 | 0.364366 | − | 0.931256i | \(-0.381286\pi\) | ||||
0.364366 | + | 0.931256i | \(0.381286\pi\) | |||||||
\(374\) | −11.5045 | −0.594881 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.07651 | −0.107088 | ||||||||
\(377\) | −3.18450 | −0.164010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7611 | 0.604126 | 0.302063 | − | 0.953288i | \(-0.402325\pi\) | ||||
0.302063 | + | 0.953288i | \(0.402325\pi\) | |||||||
\(380\) | −4.34613 | −0.222952 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.91707 | 0.353908 | ||||||||
\(383\) | 2.54142 | 0.129861 | 0.0649304 | − | 0.997890i | \(-0.479317\pi\) | ||||
0.0649304 | + | 0.997890i | \(0.479317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.9069 | −1.21841 | ||||||||
\(386\) | −10.3998 | −0.529334 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.58616 | 0.131292 | ||||||||
\(389\) | −4.22869 | −0.214403 | −0.107201 | − | 0.994237i | \(-0.534189\pi\) | ||||
−0.107201 | + | 0.994237i | \(0.534189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.8379 | 0.548098 | ||||||||
\(392\) | −24.6148 | −1.24323 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.99198 | −0.100354 | ||||||||
\(395\) | 6.82530 | 0.343418 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.45665 | 0.324050 | 0.162025 | − | 0.986787i | \(-0.448197\pi\) | ||||
0.162025 | + | 0.986787i | \(0.448197\pi\) | |||||||
\(398\) | 8.17386 | 0.409719 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.47947 | 0.123973 | ||||||||
\(401\) | 29.6081 | 1.47856 | 0.739280 | − | 0.673398i | \(-0.235166\pi\) | ||||
0.739280 | + | 0.673398i | \(0.235166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.19424 | 0.208930 | ||||||||
\(404\) | −16.3072 | −0.811314 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.29628 | 0.362108 | ||||||||
\(407\) | 29.9608 | 1.48510 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.1491 | 1.54022 | 0.770112 | − | 0.637909i | \(-0.220200\pi\) | ||||
0.770112 | + | 0.637909i | \(0.220200\pi\) | |||||||
\(410\) | 2.28233 | 0.112716 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.2975 | 0.655119 | ||||||||
\(413\) | −48.8526 | −2.40388 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.79453 | 0.382618 | ||||||||
\(416\) | 5.12300 | 0.251176 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.93063 | 0.338988 | ||||||||
\(419\) | −30.6871 | −1.49916 | −0.749582 | − | 0.661911i | \(-0.769745\pi\) | ||||
−0.749582 | + | 0.661911i | \(0.769745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.27706 | −0.354662 | −0.177331 | − | 0.984151i | \(-0.556746\pi\) | ||||
−0.177331 | + | 0.984151i | \(0.556746\pi\) | |||||||
\(422\) | −10.3898 | −0.505767 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −23.2346 | −1.12837 | ||||||||
\(425\) | 4.15845 | 0.201714 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.6440 | 1.43458 | ||||||||
\(428\) | 24.7083 | 1.19432 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.21582 | −0.203305 | ||||||||
\(431\) | 23.5582 | 1.13476 | 0.567380 | − | 0.823456i | \(-0.307957\pi\) | ||||
0.567380 | + | 0.823456i | \(0.307957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.4881 | −1.75351 | −0.876753 | − | 0.480941i | \(-0.840295\pi\) | ||||
−0.876753 | + | 0.480941i | \(0.840295\pi\) | |||||||
\(434\) | −9.60980 | −0.461285 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.55449 | −0.361795 | ||||||||
\(437\) | −6.52910 | −0.312329 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.5625 | −0.551846 | −0.275923 | − | 0.961180i | \(-0.588983\pi\) | ||||
−0.275923 | + | 0.961180i | \(0.588983\pi\) | |||||||
\(440\) | −10.3326 | −0.492587 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.14125 | 0.101849 | ||||||||
\(443\) | −1.09457 | −0.0520045 | −0.0260023 | − | 0.999662i | \(-0.508278\pi\) | ||||
−0.0260023 | + | 0.999662i | \(0.508278\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.5602 | −0.690218 | ||||||||
\(446\) | 8.55515 | 0.405098 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.3277 | 0.487938 | ||||||||
\(449\) | 36.8476 | 1.73895 | 0.869473 | − | 0.493980i | \(-0.164458\pi\) | ||||
0.869473 | + | 0.493980i | \(0.164458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.8145 | 1.12138 | ||||||||
\(452\) | −24.3016 | −1.14305 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.9113 | −0.512093 | ||||||||
\(455\) | 4.44964 | 0.208602 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.9478 | −0.652450 | −0.326225 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326225 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(458\) | 6.23387 | 0.291290 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.52148 | 0.210815 | ||||||||
\(461\) | 3.29468 | 0.153449 | 0.0767243 | − | 0.997052i | \(-0.475554\pi\) | ||||
0.0767243 | + | 0.997052i | \(0.475554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.6337 | −1.37719 | −0.688597 | − | 0.725144i | \(-0.741773\pi\) | ||||
−0.688597 | + | 0.725144i | \(0.741773\pi\) | |||||||
\(464\) | −7.89585 | −0.366556 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.94724 | 0.460797 | ||||||||
\(467\) | 11.5765 | 0.535695 | 0.267848 | − | 0.963461i | \(-0.413688\pi\) | ||||
0.267848 | + | 0.963461i | \(0.413688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.0767 | 0.788528 | ||||||||
\(470\) | −0.555982 | −0.0256455 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −21.1142 | −0.971860 | ||||||||
\(473\) | −43.9890 | −2.02262 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.50517 | −0.114945 | ||||||||
\(476\) | 32.1011 | 1.47135 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.3060 | −0.562862 | ||||||||
\(479\) | −2.77882 | −0.126967 | −0.0634837 | − | 0.997983i | \(-0.520221\pi\) | ||||
−0.0634837 | + | 0.997983i | \(0.520221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.57641 | −0.254263 | ||||||||
\(482\) | −0.992295 | −0.0451978 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −30.9963 | −1.40892 | ||||||||
\(485\) | 1.49070 | 0.0676892 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5009 | −0.566471 | −0.283236 | − | 0.959050i | \(-0.591408\pi\) | ||||
−0.283236 | + | 0.959050i | \(0.591408\pi\) | |||||||
\(488\) | 12.8122 | 0.579981 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.59054 | −0.297730 | ||||||||
\(491\) | −9.51586 | −0.429445 | −0.214722 | − | 0.976675i | \(-0.568885\pi\) | ||||
−0.214722 | + | 0.976675i | \(0.568885\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.2426 | −0.596415 | ||||||||
\(494\) | −1.28995 | −0.0580377 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3995 | 0.466951 | ||||||||
\(497\) | −24.6884 | −1.10743 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.1460 | 0.812326 | 0.406163 | − | 0.913801i | \(-0.366867\pi\) | ||||
0.406163 | + | 0.913801i | \(0.366867\pi\) | |||||||
\(500\) | 1.73486 | 0.0775854 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.5689 | 0.560975 | ||||||||
\(503\) | 6.11036 | 0.272448 | 0.136224 | − | 0.990678i | \(-0.456503\pi\) | ||||
0.136224 | + | 0.990678i | \(0.456503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.39972 | −0.418282 | ||||||||
\(506\) | −7.21026 | −0.320535 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.5777 | 1.44540 | ||||||||
\(509\) | 16.1158 | 0.714320 | 0.357160 | − | 0.934043i | \(-0.383745\pi\) | ||||
0.357160 | + | 0.934043i | \(0.383745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 58.8552 | 2.60360 | ||||||||
\(512\) | 22.2390 | 0.982836 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.80553 | −0.0796387 | ||||||||
\(515\) | 7.66485 | 0.337754 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.80126 | −0.255139 | ||||||||
\(518\) | 12.7766 | 0.561372 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.92314 | 0.0843353 | ||||||||
\(521\) | −12.1096 | −0.530533 | −0.265266 | − | 0.964175i | \(-0.585460\pi\) | ||||
−0.265266 | + | 0.964175i | \(0.585460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.1965 | 1.18922 | 0.594609 | − | 0.804015i | \(-0.297307\pi\) | ||||
0.594609 | + | 0.804015i | \(0.297307\pi\) | |||||||
\(524\) | 11.4044 | 0.498205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.95008 | −0.390242 | ||||||||
\(527\) | 17.4415 | 0.759765 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2075 | −0.704673 | ||||||||
\(530\) | −6.22100 | −0.270223 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.3387 | −0.838438 | ||||||||
\(533\) | −4.43244 | −0.191990 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.2422 | 0.615745 | ||||||||
\(536\) | 7.38057 | 0.318792 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.0657392 | 0.00283422 | ||||||||
\(539\) | −68.7675 | −2.96203 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.3549 | 1.47703 | 0.738517 | − | 0.674235i | \(-0.235527\pi\) | ||||
0.738517 | + | 0.674235i | \(0.235527\pi\) | |||||||
\(542\) | 4.43822 | 0.190638 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.3037 | 0.913389 | ||||||||
\(545\) | −4.35452 | −0.186527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.8457 | −0.677512 | −0.338756 | − | 0.940874i | \(-0.610006\pi\) | ||||
−0.338756 | + | 0.940874i | \(0.610006\pi\) | |||||||
\(548\) | 18.1717 | 0.776257 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.76653 | −0.117965 | ||||||||
\(551\) | 7.97771 | 0.339862 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.3701 | 1.29147 | ||||||||
\(554\) | 1.85637 | 0.0788696 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.8206 | −0.586123 | ||||||||
\(557\) | 3.13245 | 0.132726 | 0.0663631 | − | 0.997796i | \(-0.478860\pi\) | ||||
0.0663631 | + | 0.997796i | \(0.478860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.18739 | 0.346290 | ||||||||
\(560\) | 11.0327 | 0.466218 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.38507 | −0.227155 | ||||||||
\(563\) | −0.650982 | −0.0274356 | −0.0137178 | − | 0.999906i | \(-0.504367\pi\) | ||||
−0.0137178 | + | 0.999906i | \(0.504367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0078 | −0.589312 | ||||||||
\(566\) | −1.70001 | −0.0714568 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.6704 | −0.447719 | ||||||||
\(569\) | 22.6287 | 0.948644 | 0.474322 | − | 0.880352i | \(-0.342693\pi\) | ||||
0.474322 | + | 0.880352i | \(0.342693\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.5204 | 0.858753 | 0.429376 | − | 0.903126i | \(-0.358733\pi\) | ||||
0.429376 | + | 0.903126i | \(0.358733\pi\) | |||||||
\(572\) | 9.32102 | 0.389731 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.1556 | 0.423885 | ||||||||
\(575\) | 2.60625 | 0.108688 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.90761 | −0.287568 | −0.143784 | − | 0.989609i | \(-0.545927\pi\) | ||||
−0.143784 | + | 0.989609i | \(0.545927\pi\) | |||||||
\(578\) | 0.150704 | 0.00626848 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.52466 | −0.229399 | ||||||||
\(581\) | 34.6828 | 1.43888 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −64.9116 | −2.68837 | ||||||||
\(584\) | 25.4373 | 1.05260 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.97902 | 0.0817527 | ||||||||
\(587\) | 8.27601 | 0.341587 | 0.170794 | − | 0.985307i | \(-0.445367\pi\) | ||||
0.170794 | + | 0.985307i | \(0.445367\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.5073 | −0.432945 | ||||||||
\(590\) | −5.65327 | −0.232742 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.8265 | −0.568267 | ||||||||
\(593\) | 1.17530 | 0.0482637 | 0.0241318 | − | 0.999709i | \(-0.492318\pi\) | ||||
0.0241318 | + | 0.999709i | \(0.492318\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.5036 | 0.758572 | ||||||||
\(596\) | −38.0995 | −1.56062 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.34200 | 0.0548784 | ||||||||
\(599\) | 33.1386 | 1.35401 | 0.677003 | − | 0.735980i | \(-0.263278\pi\) | ||||
0.677003 | + | 0.735980i | \(0.263278\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6751 | 0.802563 | 0.401282 | − | 0.915955i | \(-0.368565\pi\) | ||||
0.401282 | + | 0.915955i | \(0.368565\pi\) | |||||||
\(602\) | −18.7589 | −0.764554 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27.8065 | 1.13143 | ||||||||
\(605\) | −17.8667 | −0.726385 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.81610 | −0.0737133 | −0.0368567 | − | 0.999321i | \(-0.511734\pi\) | ||||
−0.0368567 | + | 0.999321i | \(0.511734\pi\) | |||||||
\(608\) | −12.8340 | −0.520487 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.43044 | 0.138894 | ||||||||
\(611\) | 1.07975 | 0.0436821 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.1676 | 0.572226 | 0.286113 | − | 0.958196i | \(-0.407637\pi\) | ||||
0.286113 | + | 0.958196i | \(0.407637\pi\) | |||||||
\(614\) | 9.16868 | 0.370018 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −45.9763 | −1.85244 | ||||||||
\(617\) | −46.9789 | −1.89130 | −0.945649 | − | 0.325189i | \(-0.894572\pi\) | ||||
−0.945649 | + | 0.325189i | \(0.894572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.62966 | 0.105695 | 0.0528475 | − | 0.998603i | \(-0.483170\pi\) | ||||
0.0528475 | + | 0.998603i | \(0.483170\pi\) | |||||||
\(620\) | 7.27643 | 0.292228 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.6202 | −0.706506 | ||||||||
\(623\) | −64.7874 | −2.59565 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.67360 | 0.346667 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −38.0773 | −1.51945 | ||||||||
\(629\) | −23.1892 | −0.924615 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.4482 | 1.45098 | 0.725490 | − | 0.688233i | \(-0.241613\pi\) | ||||
0.725490 | + | 0.688233i | \(0.241613\pi\) | |||||||
\(632\) | 13.1260 | 0.522125 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.29268 | 0.329344 | ||||||||
\(635\) | 18.7783 | 0.745193 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.7993 | 0.507125 | ||||||||
\(638\) | 8.81000 | 0.348791 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.4411 | 0.452250 | ||||||||
\(641\) | 40.8350 | 1.61289 | 0.806444 | − | 0.591311i | \(-0.201389\pi\) | ||||
0.806444 | + | 0.591311i | \(0.201389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.6445 | −1.01132 | −0.505660 | − | 0.862733i | \(-0.668751\pi\) | ||||
−0.505660 | + | 0.862733i | \(0.668751\pi\) | |||||||
\(644\) | 20.1189 | 0.792797 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.36420 | −0.211052 | ||||||||
\(647\) | −17.8129 | −0.700298 | −0.350149 | − | 0.936694i | \(-0.613869\pi\) | ||||
−0.350149 | + | 0.936694i | \(0.613869\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.9878 | −2.31547 | ||||||||
\(650\) | 0.514916 | 0.0201967 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.5548 | −0.844153 | ||||||||
\(653\) | 21.7875 | 0.852611 | 0.426305 | − | 0.904579i | \(-0.359815\pi\) | ||||
0.426305 | + | 0.904579i | \(0.359815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.57369 | 0.256855 | ||||||||
\(656\) | −10.9901 | −0.429091 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.47392 | −0.0964433 | ||||||||
\(659\) | −15.8255 | −0.616475 | −0.308238 | − | 0.951309i | \(-0.599739\pi\) | ||||
−0.308238 | + | 0.951309i | \(0.599739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1484 | −0.394725 | −0.197363 | − | 0.980331i | \(-0.563238\pi\) | ||||
−0.197363 | + | 0.980331i | \(0.563238\pi\) | |||||||
\(662\) | 14.8635 | 0.577685 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.9900 | 0.581723 | ||||||||
\(665\) | −11.1471 | −0.432266 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.29958 | −0.321361 | ||||||||
\(668\) | −30.9298 | −1.19671 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.97613 | 0.0763446 | ||||||||
\(671\) | 35.7941 | 1.38182 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.8157 | 1.03367 | 0.516835 | − | 0.856085i | \(-0.327110\pi\) | ||||
0.516835 | + | 0.856085i | \(0.327110\pi\) | |||||||
\(674\) | −15.5143 | −0.597588 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.73486 | −0.0667254 | ||||||||
\(677\) | 20.8477 | 0.801241 | 0.400620 | − | 0.916244i | \(-0.368795\pi\) | ||||
0.400620 | + | 0.916244i | \(0.368795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.63307 | 0.254554 | ||||||||
\(680\) | 7.99728 | 0.306682 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.6035 | −0.444320 | ||||||||
\(683\) | −30.5434 | −1.16871 | −0.584356 | − | 0.811498i | \(-0.698653\pi\) | ||||
−0.584356 | + | 0.811498i | \(0.698653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4744 | 0.400208 | ||||||||
\(686\) | −13.2872 | −0.507307 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.3004 | 0.773944 | ||||||||
\(689\) | 12.0816 | 0.460272 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.3125 | 0.848808 | 0.424404 | − | 0.905473i | \(-0.360484\pi\) | ||||
0.424404 | + | 0.905473i | \(0.360484\pi\) | |||||||
\(692\) | −37.0739 | −1.40934 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.42800 | −0.130125 | ||||||||
\(695\) | −7.96639 | −0.302182 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.4321 | −0.698164 | ||||||||
\(698\) | 17.3010 | 0.654852 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.71950 | 0.291770 | ||||||||
\(701\) | −38.2280 | −1.44385 | −0.721925 | − | 0.691971i | \(-0.756743\pi\) | ||||
−0.721925 | + | 0.691971i | \(0.756743\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.9699 | 0.526884 | ||||||||
\(704\) | 12.4703 | 0.469993 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.07709 | 0.0781724 | ||||||||
\(707\) | −41.8253 | −1.57300 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.8893 | 0.634290 | 0.317145 | − | 0.948377i | \(-0.397276\pi\) | ||||
0.317145 | + | 0.948377i | \(0.397276\pi\) | |||||||
\(710\) | −2.85697 | −0.107220 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −28.0012 | −1.04939 | ||||||||
\(713\) | 10.9312 | 0.409378 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.37278 | 0.200930 | ||||||||
\(716\) | −16.0471 | −0.599708 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.90276 | 0.294928 | ||||||||
\(719\) | 12.0803 | 0.450518 | 0.225259 | − | 0.974299i | \(-0.427677\pi\) | ||||
0.225259 | + | 0.974299i | \(0.427677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 34.1058 | 1.27017 | ||||||||
\(722\) | −6.55185 | −0.243835 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.23227 | −0.194456 | ||||||||
\(725\) | −3.18450 | −0.118269 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.66912 | −0.247344 | −0.123672 | − | 0.992323i | \(-0.539467\pi\) | ||||
−0.123672 | + | 0.992323i | \(0.539467\pi\) | |||||||
\(728\) | 8.55727 | 0.317154 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.81078 | 0.252078 | ||||||||
\(731\) | 34.0468 | 1.25927 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.95393 | 0.330721 | 0.165360 | − | 0.986233i | \(-0.447121\pi\) | ||||
0.165360 | + | 0.986233i | \(0.447121\pi\) | |||||||
\(734\) | −13.2781 | −0.490104 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.3518 | 0.492154 | ||||||||
\(737\) | 20.6195 | 0.759528 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9855 | −0.882322 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(740\) | −9.67431 | −0.355635 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.6812 | −1.01621 | ||||||||
\(743\) | −4.48597 | −0.164574 | −0.0822872 | − | 0.996609i | \(-0.526222\pi\) | ||||
−0.0822872 | + | 0.996609i | \(0.526222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.9611 | −0.804593 | ||||||||
\(746\) | 7.24700 | 0.265331 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 38.7610 | 1.41724 | ||||||||
\(749\) | 63.3727 | 2.31559 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.5617 | −0.531365 | −0.265682 | − | 0.964061i | \(-0.585597\pi\) | ||||
−0.265682 | + | 0.964061i | \(0.585597\pi\) | |||||||
\(752\) | 2.67721 | 0.0976278 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.63975 | −0.0597161 | ||||||||
\(755\) | 16.0281 | 0.583321 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.01931 | −0.182430 | −0.0912150 | − | 0.995831i | \(-0.529075\pi\) | ||||
−0.0912150 | + | 0.995831i | \(0.529075\pi\) | |||||||
\(758\) | 6.05597 | 0.219963 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.81780 | −0.174760 | ||||||||
\(761\) | 8.77091 | 0.317945 | 0.158973 | − | 0.987283i | \(-0.449182\pi\) | ||||
0.158973 | + | 0.987283i | \(0.449182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.3760 | −0.701460 | ||||||||
\(764\) | −23.3051 | −0.843147 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.30862 | 0.0472824 | ||||||||
\(767\) | 10.9790 | 0.396430 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.35285 | −0.120907 | −0.0604535 | − | 0.998171i | \(-0.519255\pi\) | ||||
−0.0604535 | + | 0.998171i | \(0.519255\pi\) | |||||||
\(770\) | −12.3100 | −0.443623 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 35.0390 | 1.26108 | ||||||||
\(773\) | −32.3940 | −1.16513 | −0.582566 | − | 0.812783i | \(-0.697951\pi\) | ||||
−0.582566 | + | 0.812783i | \(0.697951\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.19424 | 0.150662 | ||||||||
\(776\) | 2.86683 | 0.102913 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.17742 | −0.0780642 | ||||||||
\(779\) | 11.1040 | 0.397843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.8104 | −1.06670 | ||||||||
\(782\) | 5.58063 | 0.199563 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 31.7353 | 1.13340 | ||||||||
\(785\) | −21.9483 | −0.783368 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.7890 | 0.562819 | 0.281409 | − | 0.959588i | \(-0.409198\pi\) | ||||
0.281409 | + | 0.959588i | \(0.409198\pi\) | |||||||
\(788\) | 6.71140 | 0.239084 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.51446 | 0.125039 | ||||||||
\(791\) | −62.3296 | −2.21618 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.66213 | −0.236579 | ||||||||
\(794\) | 3.32464 | 0.117987 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.5395 | −0.976111 | ||||||||
\(797\) | −5.98197 | −0.211892 | −0.105946 | − | 0.994372i | \(-0.533787\pi\) | ||||
−0.105946 | + | 0.994372i | \(0.533787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.49009 | 0.158848 | ||||||||
\(800\) | 5.12300 | 0.181125 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.2457 | 0.538345 | ||||||||
\(803\) | 71.0655 | 2.50785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.5968 | 0.408735 | ||||||||
\(806\) | 2.15968 | 0.0760716 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.0770 | −0.635946 | ||||||||
\(809\) | 17.5389 | 0.616636 | 0.308318 | − | 0.951283i | \(-0.400234\pi\) | ||||
0.308318 | + | 0.951283i | \(0.400234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.2599 | 0.957223 | 0.478612 | − | 0.878027i | \(-0.341140\pi\) | ||||
0.478612 | + | 0.878027i | \(0.341140\pi\) | |||||||
\(812\) | −24.5827 | −0.862684 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.4273 | 0.540727 | ||||||||
\(815\) | −12.4245 | −0.435212 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.5108 | −0.717583 | ||||||||
\(818\) | 16.0392 | 0.560797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.68967 | −0.268535 | ||||||||
\(821\) | 27.6454 | 0.964832 | 0.482416 | − | 0.875942i | \(-0.339759\pi\) | ||||
0.482416 | + | 0.875942i | \(0.339759\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.5070 | −0.993692 | −0.496846 | − | 0.867839i | \(-0.665509\pi\) | ||||
−0.496846 | + | 0.867839i | \(0.665509\pi\) | |||||||
\(824\) | 14.7406 | 0.513513 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −25.1550 | −0.875255 | ||||||||
\(827\) | −12.6993 | −0.441599 | −0.220799 | − | 0.975319i | \(-0.570867\pi\) | ||||
−0.220799 | + | 0.975319i | \(0.570867\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.935064 | 0.0324761 | 0.0162381 | − | 0.999868i | \(-0.494831\pi\) | ||||
0.0162381 | + | 0.999868i | \(0.494831\pi\) | |||||||
\(830\) | 4.01353 | 0.139312 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.32102 | −0.0804669 | ||||||||
\(833\) | 53.2250 | 1.84414 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.8284 | −0.616976 | ||||||||
\(836\) | −23.3508 | −0.807603 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.8013 | −0.545847 | ||||||||
\(839\) | −32.1537 | −1.11007 | −0.555034 | − | 0.831828i | \(-0.687295\pi\) | ||||
−0.555034 | + | 0.831828i | \(0.687295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.8590 | −0.650310 | ||||||||
\(842\) | −3.74708 | −0.129133 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.0054 | 1.20494 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −79.5004 | −2.73166 | ||||||||
\(848\) | 29.9559 | 1.02869 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.14125 | 0.0734443 | ||||||||
\(851\) | −14.5335 | −0.498202 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.7177 | −0.846319 | −0.423159 | − | 0.906055i | \(-0.639079\pi\) | ||||
−0.423159 | + | 0.906055i | \(0.639079\pi\) | |||||||
\(854\) | 15.2642 | 0.522330 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 27.3898 | 0.936163 | ||||||||
\(857\) | 27.6460 | 0.944368 | 0.472184 | − | 0.881500i | \(-0.343466\pi\) | ||||
0.472184 | + | 0.881500i | \(0.343466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.0622 | −1.02571 | −0.512855 | − | 0.858475i | \(-0.671412\pi\) | ||||
−0.512855 | + | 0.858475i | \(0.671412\pi\) | |||||||
\(860\) | 14.2040 | 0.484352 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.1305 | 0.413167 | ||||||||
\(863\) | 28.9538 | 0.985599 | 0.492799 | − | 0.870143i | \(-0.335974\pi\) | ||||
0.492799 | + | 0.870143i | \(0.335974\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.3699 | −0.726600 | ||||||||
\(866\) | −18.7883 | −0.638453 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.3774 | 1.09896 | ||||||||
\(869\) | 36.6708 | 1.24397 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.83777 | −0.130038 | ||||||||
\(872\) | −8.37436 | −0.283591 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.36194 | −0.113719 | ||||||||
\(875\) | 4.44964 | 0.150425 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0412 | 0.744280 | 0.372140 | − | 0.928177i | \(-0.378624\pi\) | ||||
0.372140 | + | 0.928177i | \(0.378624\pi\) | |||||||
\(878\) | −5.95369 | −0.200927 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 13.3216 | 0.449072 | ||||||||
\(881\) | 21.2728 | 0.716699 | 0.358350 | − | 0.933587i | \(-0.383340\pi\) | ||||
0.358350 | + | 0.933587i | \(0.383340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5673 | 1.19694 | 0.598468 | − | 0.801147i | \(-0.295777\pi\) | ||||
0.598468 | + | 0.801147i | \(0.295777\pi\) | |||||||
\(884\) | −7.21433 | −0.242644 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.563611 | −0.0189349 | ||||||||
\(887\) | 26.8853 | 0.902720 | 0.451360 | − | 0.892342i | \(-0.350939\pi\) | ||||
0.451360 | + | 0.892342i | \(0.350939\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 83.5565 | 2.80239 | ||||||||
\(890\) | −7.49726 | −0.251309 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28.8241 | −0.965102 | ||||||||
\(893\) | −2.70496 | −0.0905182 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.24978 | −0.309186 | ||||||||
\(896\) | 50.9088 | 1.70074 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.9734 | 0.633152 | ||||||||
\(899\) | −13.3565 | −0.445466 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.2406 | 1.67376 | ||||||||
\(902\) | 12.2625 | 0.408296 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.9390 | −0.895976 | ||||||||
\(905\) | −3.01596 | −0.100254 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.0379 | 0.632143 | 0.316071 | − | 0.948735i | \(-0.397636\pi\) | ||||
0.316071 | + | 0.948735i | \(0.397636\pi\) | |||||||
\(908\) | 36.7625 | 1.22001 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.29119 | 0.0759522 | ||||||||
\(911\) | 52.1035 | 1.72626 | 0.863132 | − | 0.504978i | \(-0.168499\pi\) | ||||
0.863132 | + | 0.504978i | \(0.168499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.8782 | 1.38597 | ||||||||
\(914\) | −7.18194 | −0.237557 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.0032 | −0.693967 | ||||||||
\(917\) | 29.2505 | 0.965937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.5433 | −1.50233 | −0.751167 | − | 0.660113i | \(-0.770509\pi\) | ||||
−0.751167 | + | 0.660113i | \(0.770509\pi\) | |||||||
\(920\) | 5.01218 | 0.165247 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.69648 | 0.0558707 | ||||||||
\(923\) | 5.54842 | 0.182628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.57641 | −0.183351 | ||||||||
\(926\) | −15.2589 | −0.501438 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.3142 | −0.535539 | ||||||||
\(929\) | −10.1464 | −0.332894 | −0.166447 | − | 0.986050i | \(-0.553229\pi\) | ||||
−0.166447 | + | 0.986050i | \(0.553229\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.0643 | −1.05087 | ||||||||
\(932\) | −33.5144 | −1.09780 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.96091 | 0.195047 | ||||||||
\(935\) | 22.3424 | 0.730675 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9000 | 0.911452 | 0.455726 | − | 0.890120i | \(-0.349380\pi\) | ||||
0.455726 | + | 0.890120i | \(0.349380\pi\) | |||||||
\(938\) | 8.79306 | 0.287104 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.87322 | 0.0610977 | ||||||||
\(941\) | −51.4135 | −1.67603 | −0.838017 | − | 0.545645i | \(-0.816285\pi\) | ||||
−0.838017 | + | 0.545645i | \(0.816285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5520 | −0.376186 | ||||||||
\(944\) | 27.2221 | 0.886005 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.6506 | −0.736436 | ||||||||
\(947\) | −2.63195 | −0.0855269 | −0.0427635 | − | 0.999085i | \(-0.513616\pi\) | ||||
−0.0427635 | + | 0.999085i | \(0.513616\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.2270 | −0.429365 | ||||||||
\(950\) | −1.28995 | −0.0418516 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 35.5850 | 1.15332 | ||||||||
\(953\) | −19.4156 | −0.628933 | −0.314466 | − | 0.949269i | \(-0.601826\pi\) | ||||
−0.314466 | + | 0.949269i | \(0.601826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.4334 | −0.434694 | ||||||||
\(956\) | 41.4614 | 1.34096 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.43086 | −0.0462289 | ||||||||
\(959\) | 46.6075 | 1.50503 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.4083 | −0.432527 | ||||||||
\(962\) | −2.87139 | −0.0925772 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.34325 | 0.107679 | ||||||||
\(965\) | 20.1970 | 0.650165 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.8150 | 1.31252 | 0.656260 | − | 0.754535i | \(-0.272137\pi\) | ||||
0.656260 | + | 0.754535i | \(0.272137\pi\) | |||||||
\(968\) | −34.3602 | −1.10438 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.767586 | 0.0246457 | ||||||||
\(971\) | 34.5822 | 1.10980 | 0.554898 | − | 0.831919i | \(-0.312757\pi\) | ||||
0.554898 | + | 0.831919i | \(0.312757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.4475 | −1.13639 | ||||||||
\(974\) | −6.43693 | −0.206253 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.5185 | −0.528745 | ||||||||
\(977\) | 55.3685 | 1.77140 | 0.885698 | − | 0.464262i | \(-0.153681\pi\) | ||||
0.885698 | + | 0.464262i | \(0.153681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −78.2285 | −2.50019 | ||||||||
\(980\) | 22.2049 | 0.709310 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.89987 | −0.156361 | ||||||||
\(983\) | 38.6556 | 1.23292 | 0.616461 | − | 0.787386i | \(-0.288566\pi\) | ||||
0.616461 | + | 0.787386i | \(0.288566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.86855 | 0.123262 | ||||||||
\(986\) | −6.81881 | −0.217155 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.34613 | 0.138269 | ||||||||
\(989\) | 21.3384 | 0.678520 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.73406 | 0.277446 | 0.138723 | − | 0.990331i | \(-0.455700\pi\) | ||||
0.138723 | + | 0.990331i | \(0.455700\pi\) | |||||||
\(992\) | 21.4871 | 0.682216 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.7125 | −0.403215 | ||||||||
\(995\) | −15.8742 | −0.503245 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.3184 | −0.516807 | −0.258404 | − | 0.966037i | \(-0.583196\pi\) | ||||
−0.258404 | + | 0.966037i | \(0.583196\pi\) | |||||||
\(998\) | 9.34366 | 0.295768 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1755.2.a.s.1.2 | yes | 4 | |
3.2 | odd | 2 | 1755.2.a.m.1.3 | ✓ | 4 | ||
5.4 | even | 2 | 8775.2.a.bh.1.3 | 4 | |||
15.14 | odd | 2 | 8775.2.a.bt.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1755.2.a.m.1.3 | ✓ | 4 | 3.2 | odd | 2 | ||
1755.2.a.s.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
8775.2.a.bh.1.3 | 4 | 5.4 | even | 2 | |||
8775.2.a.bt.1.2 | 4 | 15.14 | odd | 2 |