Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1002) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.21432 | −1.43749 | −0.718744 | − | 0.695275i | \(-0.755283\pi\) | ||||
−0.718744 | + | 0.695275i | \(0.755283\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.525428 | −0.198593 | −0.0992965 | − | 0.995058i | \(-0.531659\pi\) | ||||
−0.0992965 | + | 0.995058i | \(0.531659\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.28100 | −0.687746 | −0.343873 | − | 0.939016i | \(-0.611739\pi\) | ||||
−0.343873 | + | 0.939016i | \(0.611739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.474572 | −0.131623 | −0.0658114 | − | 0.997832i | \(-0.520964\pi\) | ||||
−0.0658114 | + | 0.997832i | \(0.520964\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.21432 | −0.829934 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.09679 | −0.751081 | −0.375541 | − | 0.926806i | \(-0.622543\pi\) | ||||
−0.375541 | + | 0.926806i | \(0.622543\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.33185 | 1.68204 | 0.841021 | − | 0.541002i | \(-0.181955\pi\) | ||||
0.841021 | + | 0.541002i | \(0.181955\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.525428 | −0.114658 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.52543 | 0.735102 | 0.367551 | − | 0.930003i | \(-0.380196\pi\) | ||||
0.367551 | + | 0.930003i | \(0.380196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.33185 | 1.06637 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.28100 | −0.423570 | −0.211785 | − | 0.977316i | \(-0.567928\pi\) | ||||
−0.211785 | + | 0.977316i | \(0.567928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.56199 | 1.35817 | 0.679087 | − | 0.734058i | \(-0.262376\pi\) | ||||
0.679087 | + | 0.734058i | \(0.262376\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.28100 | −0.397070 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.68889 | 0.285475 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.02074 | 0.825405 | 0.412703 | − | 0.910866i | \(-0.364585\pi\) | ||||
0.412703 | + | 0.910866i | \(0.364585\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.474572 | −0.0759924 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.05086 | −1.41351 | −0.706753 | − | 0.707460i | \(-0.749841\pi\) | ||||
−0.706753 | + | 0.707460i | \(0.749841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.95407 | −0.907987 | −0.453993 | − | 0.891005i | \(-0.650001\pi\) | ||||
−0.453993 | + | 0.891005i | \(0.650001\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.21432 | −0.479162 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.57628 | 1.10511 | 0.552557 | − | 0.833475i | \(-0.313652\pi\) | ||||
0.552557 | + | 0.833475i | \(0.313652\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.72393 | −0.960561 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.09679 | −0.433637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.9240 | −1.91260 | −0.956301 | − | 0.292383i | \(-0.905552\pi\) | ||||
−0.956301 | + | 0.292383i | \(0.905552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.33185 | 0.988627 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.33185 | 0.971127 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.458751 | −0.0597243 | −0.0298621 | − | 0.999554i | \(-0.509507\pi\) | ||||
−0.0298621 | + | 0.999554i | \(0.509507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.61285 | 0.974725 | 0.487363 | − | 0.873200i | \(-0.337959\pi\) | ||||
0.487363 | + | 0.873200i | \(0.337959\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.525428 | −0.0661977 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.52543 | 0.189206 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.77631 | −0.950028 | −0.475014 | − | 0.879978i | \(-0.657557\pi\) | ||||
−0.475014 | + | 0.879978i | \(0.657557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.52543 | 0.424412 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.95407 | 0.943974 | 0.471987 | − | 0.881605i | \(-0.343537\pi\) | ||||
0.471987 | + | 0.881605i | \(0.343537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.0049 | 1.52211 | 0.761056 | − | 0.648687i | \(-0.224681\pi\) | ||||
0.761056 | + | 0.648687i | \(0.224681\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.33185 | 0.615669 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.19850 | 0.136582 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.19358 | −0.696832 | −0.348416 | − | 0.937340i | \(-0.613280\pi\) | ||||
−0.348416 | + | 0.937340i | \(0.613280\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.06668 | −0.117083 | −0.0585415 | − | 0.998285i | \(-0.518645\pi\) | ||||
−0.0585415 | + | 0.998285i | \(0.518645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.95407 | 1.07967 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.28100 | −0.244548 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.13828 | 0.226657 | 0.113328 | − | 0.993558i | \(-0.463849\pi\) | ||||
0.113328 | + | 0.993558i | \(0.463849\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.249353 | 0.0261393 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.56199 | 0.784142 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −23.5669 | −2.41791 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.95407 | −0.503009 | −0.251505 | − | 0.967856i | \(-0.580925\pi\) | ||||
−0.251505 | + | 0.967856i | \(0.580925\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.28100 | −0.229249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2192 | 1.21586 | 0.607930 | − | 0.793991i | \(-0.292000\pi\) | ||||
0.607930 | + | 0.793991i | \(0.292000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0415 | 0.989417 | 0.494709 | − | 0.869059i | \(-0.335275\pi\) | ||||
0.494709 | + | 0.869059i | \(0.335275\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.68889 | 0.164819 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.0602231 | −0.00582198 | −0.00291099 | − | 0.999996i | \(-0.500927\pi\) | ||||
−0.00291099 | + | 0.999996i | \(0.500927\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7699 | 1.22313 | 0.611565 | − | 0.791194i | \(-0.290540\pi\) | ||||
0.611565 | + | 0.791194i | \(0.290540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.02074 | 0.476548 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.1526 | −1.61358 | −0.806789 | − | 0.590840i | \(-0.798796\pi\) | ||||
−0.806789 | + | 0.590840i | \(0.798796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.3319 | −1.05670 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.474572 | −0.0438742 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.62714 | 0.149159 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.79706 | −0.527005 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.05086 | −0.816088 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.06668 | −0.0954065 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.184208 | −0.0163458 | −0.00817292 | − | 0.999967i | \(-0.502602\pi\) | ||||
−0.00817292 | + | 0.999967i | \(0.502602\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.95407 | −0.524226 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9541 | −1.56865 | −0.784327 | − | 0.620348i | \(-0.786992\pi\) | ||||
−0.784327 | + | 0.620348i | \(0.786992\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.85236 | −0.334042 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.21432 | −0.276645 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.95407 | 0.594126 | 0.297063 | − | 0.954858i | \(-0.403993\pi\) | ||||
0.297063 | + | 0.954858i | \(0.403993\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.34767 | −0.623221 | −0.311611 | − | 0.950210i | \(-0.600868\pi\) | ||||
−0.311611 | + | 0.950210i | \(0.600868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.57628 | 0.638038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.08250 | 0.0905230 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.33185 | 0.608877 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.72393 | −0.554580 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.4035 | −1.09805 | −0.549027 | − | 0.835805i | \(-0.685001\pi\) | ||||
−0.549027 | + | 0.835805i | \(0.685001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.3368 | −1.32947 | −0.664734 | − | 0.747080i | \(-0.731455\pi\) | ||||
−0.664734 | + | 0.747080i | \(0.731455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.09679 | −0.250360 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.3067 | −1.95236 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.2859 | −1.53918 | −0.769592 | − | 0.638536i | \(-0.779540\pi\) | ||||
−0.769592 | + | 0.638536i | \(0.779540\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.9240 | −1.10424 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.85236 | −0.145986 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.97481 | 0.702961 | 0.351481 | − | 0.936195i | \(-0.385678\pi\) | ||||
0.351481 | + | 0.936195i | \(0.385678\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.33185 | 0.570784 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7748 | −0.982675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.33185 | 0.560681 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.84791 | 0.748723 | 0.374361 | − | 0.927283i | \(-0.377862\pi\) | ||||
0.374361 | + | 0.927283i | \(0.377862\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.80150 | −0.211774 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.458751 | −0.0344818 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.84299 | −0.511469 | −0.255735 | − | 0.966747i | \(-0.582317\pi\) | ||||
−0.255735 | + | 0.966747i | \(0.582317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.5161 | −1.07897 | −0.539485 | − | 0.841995i | \(-0.681381\pi\) | ||||
−0.539485 | + | 0.841995i | \(0.681381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.61285 | 0.562758 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.1383 | −1.18651 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.06376 | 0.516553 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.525428 | −0.0382192 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.66370 | 0.554526 | 0.277263 | − | 0.960794i | \(-0.410573\pi\) | ||||
0.277263 | + | 0.960794i | \(0.410573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.3733 | −1.25056 | −0.625280 | − | 0.780400i | \(-0.715015\pi\) | ||||
−0.625280 | + | 0.780400i | \(0.715015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.52543 | 0.109238 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.4558 | −1.59991 | −0.799956 | − | 0.600059i | \(-0.795144\pi\) | ||||
−0.799956 | + | 0.600059i | \(0.795144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9906 | −0.920881 | −0.460441 | − | 0.887690i | \(-0.652309\pi\) | ||||
−0.460441 | + | 0.887690i | \(0.652309\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.77631 | −0.548499 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.19850 | 0.0841181 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.0923 | 2.03190 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.52543 | 0.245034 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.7239 | −1.15682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.4701 | −1.82228 | −0.911139 | − | 0.412098i | \(-0.864796\pi\) | ||||
−0.911139 | + | 0.412098i | \(0.864796\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.95407 | 0.545004 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.1383 | 1.30522 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.97328 | −0.269724 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.0049 | 0.878791 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.46965 | 0.0988594 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.23951 | 0.216934 | 0.108467 | − | 0.994100i | \(-0.465406\pi\) | ||||
0.108467 | + | 0.994100i | \(0.465406\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.33185 | 0.355457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.6336 | −1.23675 | −0.618377 | − | 0.785881i | \(-0.712210\pi\) | ||||
−0.618377 | + | 0.785881i | \(0.712210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.73329 | 0.246703 | 0.123351 | − | 0.992363i | \(-0.460636\pi\) | ||||
0.123351 | + | 0.992363i | \(0.460636\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.19850 | 0.0788554 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.1334 | −0.991419 | −0.495709 | − | 0.868488i | \(-0.665092\pi\) | ||||
−0.495709 | + | 0.868488i | \(0.665092\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.3526 | −1.58859 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.19358 | −0.402316 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.0923 | −0.717504 | −0.358752 | − | 0.933433i | \(-0.616798\pi\) | ||||
−0.358752 | + | 0.933433i | \(0.616798\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8430 | 0.956121 | 0.478060 | − | 0.878327i | \(-0.341340\pi\) | ||||
0.478060 | + | 0.878327i | \(0.341340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.6128 | 1.38079 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.47949 | −0.221395 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.06668 | −0.0675979 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.16992 | −0.452561 | −0.226281 | − | 0.974062i | \(-0.572657\pi\) | ||||
−0.226281 | + | 0.974062i | \(0.572657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.04149 | −0.505564 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.95407 | 0.623348 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.9447 | 1.43125 | 0.715626 | − | 0.698484i | \(-0.246142\pi\) | ||||
0.715626 | + | 0.698484i | \(0.246142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.63804 | −0.163920 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.28100 | −0.141190 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.6494 | 1.58161 | 0.790805 | − | 0.612068i | \(-0.209662\pi\) | ||||
0.790805 | + | 0.612068i | \(0.209662\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 44.7560 | 2.74934 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.13828 | 0.130860 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.03011 | −0.245720 | −0.122860 | − | 0.992424i | \(-0.539207\pi\) | ||||
−0.122860 | + | 0.992424i | \(0.539207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.2716 | −1.04918 | −0.524588 | − | 0.851356i | \(-0.675781\pi\) | ||||
−0.524588 | + | 0.851356i | \(0.675781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.249353 | 0.0150916 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.1619 | −0.733392 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.0760445 | −0.00456907 | −0.00228453 | − | 0.999997i | \(-0.500727\pi\) | ||||
−0.00228453 | + | 0.999997i | \(0.500727\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.56199 | 0.452725 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.93978 | 0.175372 | 0.0876862 | − | 0.996148i | \(-0.472053\pi\) | ||||
0.0876862 | + | 0.996148i | \(0.472053\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3082 | 1.20720 | 0.603598 | − | 0.797289i | \(-0.293733\pi\) | ||||
0.603598 | + | 0.797289i | \(0.293733\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −23.5669 | −1.39598 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.75557 | 0.280712 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.40990 | −0.435877 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.95407 | −0.290413 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.53972 | −0.0899513 | −0.0449756 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449756 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.47457 | 0.0858529 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.28100 | −0.132357 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.67307 | −0.0967562 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.12843 | 0.180320 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.2192 | 0.701977 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.4701 | −1.40116 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.68889 | −0.0963902 | −0.0481951 | − | 0.998838i | \(-0.515347\pi\) | ||||
−0.0481951 | + | 0.998838i | \(0.515347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0415 | 0.571240 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.67307 | −0.151576 | −0.0757880 | − | 0.997124i | \(-0.524147\pi\) | ||||
−0.0757880 | + | 0.997124i | \(0.524147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.9541 | −1.24092 | −0.620459 | − | 0.784239i | \(-0.713054\pi\) | ||||
−0.620459 | + | 0.784239i | \(0.713054\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.68889 | 0.0951583 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.2400 | −0.743632 | −0.371816 | − | 0.928307i | \(-0.621265\pi\) | ||||
−0.371816 | + | 0.928307i | \(0.621265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.20294 | 0.291309 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0602231 | −0.00336132 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.7052 | −1.26335 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.53035 | −0.140359 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.7699 | 0.706175 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.98079 | −0.219468 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.92549 | 0.105834 | 0.0529172 | − | 0.998599i | \(-0.483148\pi\) | ||||
0.0529172 | + | 0.998599i | \(0.483148\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.02074 | 0.275135 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.9956 | 1.36565 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5620 | 0.738769 | 0.369384 | − | 0.929277i | \(-0.379569\pi\) | ||||
0.369384 | + | 0.929277i | \(0.379569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.1526 | −0.931599 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.2489 | −0.934079 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.21093 | 0.389354 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.3319 | −0.610086 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.6015 | −0.837531 | −0.418765 | − | 0.908094i | \(-0.637537\pi\) | ||||
−0.418765 | + | 0.908094i | \(0.637537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.2652 | −1.19183 | −0.595914 | − | 0.803048i | \(-0.703210\pi\) | ||||
−0.595914 | + | 0.803048i | \(0.703210\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.474572 | −0.0253308 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.14272 | −0.326944 | −0.163472 | − | 0.986548i | \(-0.552269\pi\) | ||||
−0.163472 | + | 0.986548i | \(0.552269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.5669 | −1.35695 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.62714 | 0.0861173 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9684 | 1.15945 | 0.579723 | − | 0.814814i | \(-0.303161\pi\) | ||||
0.579723 | + | 0.814814i | \(0.303161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.7560 | 1.82927 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.79706 | −0.304267 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −41.8020 | −2.18802 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0923 | −0.579016 | −0.289508 | − | 0.957176i | \(-0.593492\pi\) | ||||
−0.289508 | + | 0.957176i | \(0.593492\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.05086 | −0.471169 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.31603 | 0.379829 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0988 | 0.937120 | 0.468560 | − | 0.883432i | \(-0.344773\pi\) | ||||
0.468560 | + | 0.883432i | \(0.344773\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.06668 | −0.0550829 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.08250 | 0.0557515 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4543 | 0.639735 | 0.319867 | − | 0.947462i | \(-0.396362\pi\) | ||||
0.319867 | + | 0.947462i | \(0.396362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.184208 | −0.00943727 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.42864 | −0.430683 | −0.215342 | − | 0.976539i | \(-0.569087\pi\) | ||||
−0.215342 | + | 0.976539i | \(0.569087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.85236 | −0.196334 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.95407 | −0.302662 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.5892 | −1.55093 | −0.775467 | − | 0.631388i | \(-0.782485\pi\) | ||||
−0.775467 | + | 0.631388i | \(0.782485\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.9175 | −0.552122 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.9541 | −0.905663 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.9081 | 1.00169 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.3733 | −0.871943 | −0.435971 | − | 0.899961i | \(-0.643595\pi\) | ||||
−0.435971 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.85236 | −0.192859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.2672 | 1.16191 | 0.580954 | − | 0.813937i | \(-0.302680\pi\) | ||||
0.580954 | + | 0.813937i | \(0.302680\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.58871 | −0.178767 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.21432 | −0.159721 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.4523 | −0.567669 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5718 | 1.41279 | 0.706393 | − | 0.707820i | \(-0.250321\pi\) | ||||
0.706393 | + | 0.707820i | \(0.250321\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.95407 | 0.343019 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.241040 | 0.0118608 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.42864 | 0.168305 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.34767 | −0.359817 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.47013 | −0.413793 | −0.206896 | − | 0.978363i | \(-0.566336\pi\) | ||||
−0.206896 | + | 0.978363i | \(0.566336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.9032 | −1.21371 | −0.606854 | − | 0.794813i | \(-0.707569\pi\) | ||||
−0.606854 | + | 0.794813i | \(0.707569\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.57628 | 0.368371 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.5116 | −0.800931 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | −0.193574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.08250 | 0.0522635 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.8163 | −1.19536 | −0.597679 | − | 0.801736i | \(-0.703910\pi\) | ||||
−0.597679 | + | 0.801736i | \(0.703910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2761 | −0.493837 | −0.246918 | − | 0.969036i | \(-0.579418\pi\) | ||||
−0.246918 | + | 0.969036i | \(0.579418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.33185 | 0.351535 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.8479 | 1.23647 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.9906 | 0.620009 | 0.310005 | − | 0.950735i | \(-0.399669\pi\) | ||||
0.310005 | + | 0.950735i | \(0.399669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.72393 | −0.320187 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.1318 | −0.576400 | −0.288200 | − | 0.957570i | \(-0.593057\pi\) | ||||
−0.288200 | + | 0.957570i | \(0.593057\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.87310 | −0.325816 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.4035 | −0.633961 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.43356 | 0.114847 | 0.0574234 | − | 0.998350i | \(-0.481711\pi\) | ||||
0.0574234 | + | 0.998350i | \(0.481711\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6450 | 0.972134 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.3368 | −0.767569 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.801502 | −0.0375750 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.43801 | 0.0672671 | 0.0336336 | − | 0.999434i | \(-0.489292\pi\) | ||||
0.0336336 | + | 0.999434i | \(0.489292\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.09679 | −0.144546 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.8015 | −0.503076 | −0.251538 | − | 0.967847i | \(-0.580936\pi\) | ||||
−0.251538 | + | 0.967847i | \(0.580936\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9813 | 0.928608 | 0.464304 | − | 0.885676i | \(-0.346304\pi\) | ||||
0.464304 | + | 0.885676i | \(0.346304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.3067 | −1.12719 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000 | 0.277647 | 0.138823 | − | 0.990317i | \(-0.455668\pi\) | ||||
0.138823 | + | 0.990317i | \(0.455668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.08589 | 0.188669 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.2859 | −0.888648 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.5812 | 0.624464 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.0923 | 1.79368 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.9240 | −0.637534 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.3145 | −0.973884 | −0.486942 | − | 0.873434i | \(-0.661888\pi\) | ||||
−0.486942 | + | 0.873434i | \(0.661888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.38271 | −0.108642 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.85236 | −0.0842852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.9240 | 0.723070 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.5575 | −0.569037 | −0.284518 | − | 0.958671i | \(-0.591834\pi\) | ||||
−0.284518 | + | 0.958671i | \(0.591834\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.97481 | 0.405855 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.7877 | 1.07352 | 0.536762 | − | 0.843734i | \(-0.319647\pi\) | ||||
0.536762 | + | 0.843734i | \(0.319647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.06376 | 0.318136 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.33185 | 0.329542 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.17929 | −0.187467 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.4242 | 0.645716 | 0.322858 | − | 0.946447i | \(-0.395356\pi\) | ||||
0.322858 | + | 0.946447i | \(0.395356\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.9175 | 1.02184 | 0.510920 | − | 0.859628i | \(-0.329305\pi\) | ||||
0.510920 | + | 0.859628i | \(0.329305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.2766 | −1.74778 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7748 | −0.567348 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.0415 | 1.24292 | 0.621459 | − | 0.783447i | \(-0.286540\pi\) | ||||
0.621459 | + | 0.783447i | \(0.286540\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.83314 | −0.302281 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.33185 | 0.323709 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.2766 | −1.42227 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.2815 | −0.760038 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.84791 | 0.432275 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.25872 | −0.0551456 | −0.0275728 | − | 0.999620i | \(-0.508778\pi\) | ||||
−0.0275728 | + | 0.999620i | \(0.508778\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.23951 | 0.272835 | 0.136417 | − | 0.990651i | \(-0.456441\pi\) | ||||
0.136417 | + | 0.990651i | \(0.456441\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.80150 | −0.122268 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23.4179 | −1.02010 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5714 | −0.459624 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.458751 | −0.0199081 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.29529 | 0.186050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.193576 | 0.00836903 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.84299 | −0.295297 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.3372 | 0.660622 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.67952 | −0.115202 | −0.0576009 | − | 0.998340i | \(-0.518345\pi\) | ||||
−0.0576009 | + | 0.998340i | \(0.518345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.5161 | −0.622944 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.0464 | −1.75823 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.84590 | 0.207196 | 0.103598 | − | 0.994619i | \(-0.466964\pi\) | ||||
0.103598 | + | 0.994619i | \(0.466964\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.61285 | 0.324908 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.7239 | −0.712463 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.25428 | 0.138386 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.1383 | −0.685032 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.73822 | −0.285507 | −0.142754 | − | 0.989758i | \(-0.545596\pi\) | ||||
−0.142754 | + | 0.989758i | \(0.545596\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.82564 | 0.119512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.06376 | 0.298232 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.99555 | −0.421262 | −0.210631 | − | 0.977566i | \(-0.567552\pi\) | ||||
−0.210631 | + | 0.977566i | \(0.567552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 55.1338 | 2.31950 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.525428 | −0.0220659 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0968 | −0.465202 | −0.232601 | − | 0.972572i | \(-0.574724\pi\) | ||||
−0.232601 | + | 0.972572i | \(0.574724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.4449 | −0.981140 | −0.490570 | − | 0.871402i | \(-0.663211\pi\) | ||||
−0.490570 | + | 0.871402i | \(0.663211\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.66370 | 0.320156 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.7971 | 0.783891 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.16055 | 0.381359 | 0.190679 | − | 0.981652i | \(-0.438931\pi\) | ||||
0.190679 | + | 0.981652i | \(0.438931\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.3733 | −0.722011 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.560461 | 0.0232519 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.7605 | 1.31539 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.52543 | 0.0630687 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.1684 | −1.69920 | −0.849601 | − | 0.527427i | \(-0.823157\pi\) | ||||
−0.849601 | + | 0.527427i | \(0.823157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 55.4434 | 2.28451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.4558 | −0.923710 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.6780 | −0.931274 | −0.465637 | − | 0.884976i | \(-0.654175\pi\) | ||||
−0.465637 | + | 0.884976i | \(0.654175\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.23014 | −0.214415 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.9906 | −0.531671 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.2627 | 1.80853 | 0.904263 | − | 0.426975i | \(-0.140421\pi\) | ||||
0.904263 | + | 0.426975i | \(0.140421\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.3230 | −1.40006 | −0.700031 | − | 0.714112i | \(-0.746831\pi\) | ||||
−0.700031 | + | 0.714112i | \(0.746831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.77631 | −0.316676 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.6336 | 0.757563 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.9782 | 1.86620 | 0.933099 | − | 0.359620i | \(-0.117094\pi\) | ||||
0.933099 | + | 0.359620i | \(0.117094\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.19850 | 0.0485656 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.59549 | −0.145458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.3412 | −1.22547 | −0.612735 | − | 0.790288i | \(-0.709931\pi\) | ||||
−0.612735 | + | 0.790288i | \(0.709931\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.0923 | 1.17312 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.0192 | 0.926719 | 0.463359 | − | 0.886171i | \(-0.346644\pi\) | ||||
0.463359 | + | 0.886171i | \(0.346644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.2212 | −1.01373 | −0.506864 | − | 0.862026i | \(-0.669195\pi\) | ||||
−0.506864 | + | 0.862026i | \(0.669195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.52543 | 0.141471 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.12351 | −0.0450124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.2306 | −0.929225 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.7239 | −0.667889 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.5482 | −0.619946 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4608 | −0.496055 | −0.248027 | − | 0.968753i | \(-0.579782\pi\) | ||||
−0.248027 | + | 0.968753i | \(0.579782\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −26.4701 | −1.05209 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.592104 | 0.0234969 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.19099 | 0.126432 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.95407 | 0.314658 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.08297 | −0.0822725 | −0.0411363 | − | 0.999154i | \(-0.513098\pi\) | ||||
−0.0411363 | + | 0.999154i | \(0.513098\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9541 | 0.550295 | 0.275147 | − | 0.961402i | \(-0.411273\pi\) | ||||
0.275147 | + | 0.961402i | \(0.411273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.1383 | 0.753569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2859 | 0.679580 | 0.339790 | − | 0.940501i | \(-0.389644\pi\) | ||||
0.339790 | + | 0.940501i | \(0.389644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.04641 | 0.0410752 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.97328 | −0.155725 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.5022 | −1.46758 | −0.733788 | − | 0.679378i | \(-0.762250\pi\) | ||||
−0.733788 | + | 0.679378i | \(0.762250\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.7101 | 2.25492 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.0049 | 0.507370 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.84146 | 0.110687 | 0.0553437 | − | 0.998467i | \(-0.482375\pi\) | ||||
0.0553437 | + | 0.998467i | \(0.482375\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.9545 | −1.51516 | −0.757578 | − | 0.652745i | \(-0.773617\pi\) | ||||
−0.757578 | + | 0.652745i | \(0.773617\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.46965 | 0.0570765 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.3827 | 0.480181 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.04149 | −0.311368 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.23951 | 0.125247 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.3649 | −0.670364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.74128 | 0.336952 | 0.168476 | − | 0.985706i | \(-0.446116\pi\) | ||||
0.168476 | + | 0.985706i | \(0.446116\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.33185 | 0.205223 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.8113 | 0.799845 | 0.399923 | − | 0.916549i | \(-0.369037\pi\) | ||||
0.399923 | + | 0.916549i | \(0.369037\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.60300 | 0.0998941 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.6336 | −0.714041 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.493308 | 0.0188759 | 0.00943796 | − | 0.999955i | \(-0.496996\pi\) | ||||
0.00943796 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.3526 | −0.854049 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.73329 | 0.142434 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.60793 | 0.251742 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.4652 | 0.436157 | 0.218078 | − | 0.975931i | \(-0.430021\pi\) | ||||
0.218078 | + | 0.975931i | \(0.430021\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.19850 | 0.0455272 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.6178 | 0.895873 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.0286 | 1.06166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.1334 | −0.572396 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.7368 | 0.632141 | 0.316071 | − | 0.948736i | \(-0.397636\pi\) | ||||
0.316071 | + | 0.948736i | \(0.397636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.8113 | 1.38837 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.3526 | −0.917172 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.42033 | −0.241461 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.8227 | 0.631791 | 0.315895 | − | 0.948794i | \(-0.397695\pi\) | ||||
0.315895 | + | 0.948794i | \(0.397695\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.19358 | −0.232277 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.6593 | 0.998397 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.47949 | −0.130126 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.0923 | −0.414251 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.3684 | −1.13255 | −0.566275 | − | 0.824216i | \(-0.691616\pi\) | ||||
−0.566275 | + | 0.824216i | \(0.691616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.27607 | −0.196491 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.8430 | 0.552017 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.1619 | −0.451683 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.5669 | 1.61581 | 0.807904 | − | 0.589315i | \(-0.200602\pi\) | ||||
0.807904 | + | 0.589315i | \(0.200602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.4385 | 0.681972 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.85236 | −0.0684184 | −0.0342092 | − | 0.999415i | \(-0.510891\pi\) | ||||
−0.0342092 | + | 0.999415i | \(0.510891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.6128 | 0.797202 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.7377 | 0.653378 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.89231 | −0.143181 | −0.0715905 | − | 0.997434i | \(-0.522807\pi\) | ||||
−0.0715905 | + | 0.997434i | \(0.522807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.47949 | −0.127822 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.496847 | −0.0182276 | −0.00911378 | − | 0.999958i | \(-0.502901\pi\) | ||||
−0.00911378 | + | 0.999958i | \(0.502901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.0830 | 1.57844 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.06668 | −0.0390277 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0316429 | 0.00115620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.6593 | −1.55666 | −0.778329 | − | 0.627856i | \(-0.783933\pi\) | ||||
−0.778329 | + | 0.627856i | \(0.783933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.16992 | −0.261286 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 52.5116 | 1.91109 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.4143 | 0.960046 | 0.480023 | − | 0.877256i | \(-0.340628\pi\) | ||||
0.480023 | + | 0.877256i | \(0.340628\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.04149 | −0.291887 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.9491 | −0.578156 | −0.289078 | − | 0.957306i | \(-0.593349\pi\) | ||||
−0.289078 | + | 0.957306i | \(0.593349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.70964 | −0.242905 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.95407 | 0.359890 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.217711 | 0.00786107 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.3541 | −0.373379 | −0.186690 | − | 0.982419i | \(-0.559776\pi\) | ||||
−0.186690 | + | 0.982419i | \(0.559776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.9447 | 0.826333 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.0163 | −1.11558 | −0.557789 | − | 0.829983i | \(-0.688350\pi\) | ||||
−0.557789 | + | 0.829983i | \(0.688350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.3194 | 1.44832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.63804 | −0.0946391 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −66.3595 | −2.37758 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.1432 | −0.649215 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.28100 | −0.0815162 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 61.9911 | 2.21256 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0370 | 0.642951 | 0.321476 | − | 0.946918i | \(-0.395821\pi\) | ||||
0.321476 | + | 0.946918i | \(0.395821\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.6494 | 0.913143 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.01243 | 0.320445 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.61285 | −0.128296 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 44.7560 | 1.58733 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −48.4943 | −1.71775 | −0.858877 | − | 0.512181i | \(-0.828838\pi\) | ||||
−0.858877 | + | 0.512181i | \(0.828838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.4621 | −0.830031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.13828 | 0.0755522 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.6642 | −1.04683 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.95407 | 0.209853 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.03011 | −0.141867 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.0781 | 1.54970 | 0.774851 | − | 0.632144i | \(-0.217825\pi\) | ||||
0.774851 | + | 0.632144i | \(0.217825\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.6523 | 0.654972 | 0.327486 | − | 0.944856i | \(-0.393799\pi\) | ||||
0.327486 | + | 0.944856i | \(0.393799\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.2716 | −0.605742 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.8479 | −1.01050 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.6543 | −1.52727 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.249353 | 0.00871311 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.1669 | 0.808529 | 0.404264 | − | 0.914642i | \(-0.367528\pi\) | ||||
0.404264 | + | 0.914642i | \(0.367528\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.2623 | −1.75203 | −0.876016 | − | 0.482282i | \(-0.839808\pi\) | ||||
−0.876016 | + | 0.482282i | \(0.839808\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.1619 | −0.423424 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −49.5036 | −1.72141 | −0.860705 | − | 0.509104i | \(-0.829977\pi\) | ||||
−0.860705 | + | 0.509104i | \(0.829977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.0765 | 1.21826 | 0.609129 | − | 0.793071i | \(-0.291519\pi\) | ||||
0.609129 | + | 0.793071i | \(0.291519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.0760445 | −0.00263795 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.8226 | 0.721459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.21432 | 0.111236 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.56199 | 0.261381 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1971 | 0.559187 | 0.279593 | − | 0.960119i | \(-0.409800\pi\) | ||||
0.279593 | + | 0.960119i | \(0.409800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.7971 | −0.820588 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.93978 | 0.101251 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.0622 | 1.41258 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.04593 | 0.104659 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.3082 | 0.696975 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.7003 | 0.606757 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3497 | 1.38155 | 0.690773 | − | 0.723071i | \(-0.257270\pi\) | ||||
0.690773 | + | 0.723071i | \(0.257270\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.5669 | −0.805971 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.9590 | −0.476830 | −0.238415 | − | 0.971163i | \(-0.576628\pi\) | ||||
−0.238415 | + | 0.971163i | \(0.576628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.3220 | −0.386302 | −0.193151 | − | 0.981169i | \(-0.561871\pi\) | ||||
−0.193151 | + | 0.981169i | \(0.561871\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.75557 | 0.162069 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.7556 | 1.04693 | 0.523466 | − | 0.852047i | \(-0.324639\pi\) | ||||
0.523466 | + | 0.852047i | \(0.324639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.6543 | −1.07628 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.40990 | −0.251654 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1275 | 0.479243 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.69042 | 0.125045 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.95407 | −0.167670 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.560461 | 0.0189470 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.566438 | 0.0191273 | 0.00956363 | − | 0.999954i | \(-0.496956\pi\) | ||||
0.00956363 | + | 0.999954i | \(0.496956\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.53972 | −0.0519334 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.9906 | −1.11148 | −0.555741 | − | 0.831355i | \(-0.687566\pi\) | ||||
−0.555741 | + | 0.831355i | \(0.687566\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.1798 | 1.85695 | 0.928473 | − | 0.371399i | \(-0.121122\pi\) | ||||
0.928473 | + | 0.371399i | \(0.121122\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.47457 | 0.0495672 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.8988 | 1.03748 | 0.518740 | − | 0.854932i | \(-0.326401\pi\) | ||||
0.518740 | + | 0.854932i | \(0.326401\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0967881 | 0.00324617 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.28100 | −0.0764163 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 55.5482 | 1.85885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.9956 | 0.735230 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.67307 | −0.0558622 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.2489 | −0.575282 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.1195 | 1.43652 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.12843 | 0.104108 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46.6593 | 1.55101 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.3131 | 1.43819 | 0.719094 | − | 0.694913i | \(-0.244557\pi\) | ||||
0.719094 | + | 0.694913i | \(0.244557\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.2192 | 0.405287 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.2578 | 1.89704 | 0.948518 | − | 0.316723i | \(-0.102583\pi\) | ||||
0.948518 | + | 0.316723i | \(0.102583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.43309 | 0.0805234 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.4701 | −0.808957 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.43356 | 0.311524 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.0879 | 1.71822 | 0.859111 | − | 0.511790i | \(-0.171017\pi\) | ||||
0.859111 | + | 0.511790i | \(0.171017\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.68889 | −0.0556509 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.77478 | −0.124248 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.7699 | 0.880188 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.0415 | 0.329806 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 55.7338 | 1.82857 | 0.914283 | − | 0.405076i | \(-0.132755\pi\) | ||||
0.914283 | + | 0.405076i | \(0.132755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −49.2988 | −1.61570 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.67307 | −0.0875124 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.7052 | −0.742539 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.2405 | 1.90263 | 0.951316 | − | 0.308216i | \(-0.0997319\pi\) | ||||
0.951316 | + | 0.308216i | \(0.0997319\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.9541 | −0.716444 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.9224 | −0.975443 | −0.487722 | − | 0.872999i | \(-0.662172\pi\) | ||||
−0.487722 | + | 0.872999i | \(0.662172\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.9081 | −1.03907 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.68889 | 0.0549397 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.58427 | −0.311447 | −0.155723 | − | 0.987801i | \(-0.549771\pi\) | ||||
−0.155723 | + | 0.987801i | \(0.549771\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.17178 | −0.200344 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.2400 | −0.429336 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.20834 | 0.298287 | 0.149144 | − | 0.988816i | \(-0.452348\pi\) | ||||
0.149144 | + | 0.988816i | \(0.452348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.6336 | −0.797124 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.20294 | 0.168187 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.65386 | −0.117989 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.1837 | 0.844637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0602231 | −0.00194066 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 55.8435 | 1.79766 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.2257 | −0.489625 | −0.244813 | − | 0.969570i | \(-0.578726\pi\) | ||||
−0.244813 | + | 0.969570i | \(0.578726\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.7052 | −0.729396 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.6889 | −0.760213 | −0.380106 | − | 0.924943i | \(-0.624113\pi\) | ||||
−0.380106 | + | 0.924943i | \(0.624113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.86067 | 0.123767 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.53035 | −0.0810360 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.3827 | 1.16399 | 0.581993 | − | 0.813194i | \(-0.302273\pi\) | ||||
0.581993 | + | 0.813194i | \(0.302273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.87740 | −0.155882 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.7699 | 0.407710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.6222 | −0.976697 | −0.488348 | − | 0.872649i | \(-0.662401\pi\) | ||||
−0.488348 | + | 0.872649i | \(0.662401\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 72.1802 | 2.29985 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.98079 | −0.126710 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.9906 | −0.667463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.7605 | −1.32657 | −0.663283 | − | 0.748369i | \(-0.730837\pi\) | ||||
−0.663283 | + | 0.748369i | \(0.730837\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.92549 | 0.0611035 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.7560 | 1.32376 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.33185 | 0.232202 | 0.116101 | − | 0.993237i | \(-0.462960\pi\) | ||||
0.116101 | + | 0.993237i | \(0.462960\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.02074 | 0.158849 |
(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 | 8016.2.a.l.1.1 | 3 | ||
4.3 | odd | 2 | 1002.2.a.h.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 3006.2.a.o.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1002.2.a.h.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
3006.2.a.o.1.3 | 3 | 12.11 | even | 2 | |||
8016.2.a.l.1.1 | 3 | 1.1 | even | 1 | trivial |