Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6348,2,Mod(1,6348)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6348, 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("6348.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6348 = 2^{2} \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6348.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: | \(50.6890352031\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 14x^{8} + 65x^{7} + 57x^{6} - 354x^{5} - 46x^{4} + 714x^{3} - 74x^{2} - 323x - 23 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.00266\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6348.1 |
$q$-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 | ||||||||
\(5\) | −2.92409 | −1.30769 | −0.653846 | − | 0.756627i | \(-0.726846\pi\) | ||||
−0.653846 | + | 0.756627i | \(0.726846\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00076 | −0.378251 | −0.189125 | − | 0.981953i | \(-0.560565\pi\) | ||||
−0.189125 | + | 0.981953i | \(0.560565\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.52047 | 0.759951 | 0.379976 | − | 0.924997i | \(-0.375932\pi\) | ||||
0.379976 | + | 0.924997i | \(0.375932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.482825 | −0.133912 | −0.0669558 | − | 0.997756i | \(-0.521329\pi\) | ||||
−0.0669558 | + | 0.997756i | \(0.521329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.92409 | −0.754997 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.13735 | −0.760919 | −0.380460 | − | 0.924798i | \(-0.624234\pi\) | ||||
−0.380460 | + | 0.924798i | \(0.624234\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.552973 | 0.126861 | 0.0634304 | − | 0.997986i | \(-0.479796\pi\) | ||||
0.0634304 | + | 0.997986i | \(0.479796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00076 | −0.218383 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.55030 | 0.710061 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.121648 | 0.0225895 | 0.0112948 | − | 0.999936i | \(-0.496405\pi\) | ||||
0.0112948 | + | 0.999936i | \(0.496405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.23476 | 1.47901 | 0.739503 | − | 0.673153i | \(-0.235061\pi\) | ||||
0.739503 | + | 0.673153i | \(0.235061\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.52047 | 0.438758 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.92630 | 0.494636 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.53165 | −1.56699 | −0.783496 | − | 0.621396i | \(-0.786566\pi\) | ||||
−0.783496 | + | 0.621396i | \(0.786566\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.482825 | −0.0773139 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.39208 | −0.217406 | −0.108703 | − | 0.994074i | \(-0.534670\pi\) | ||||
−0.108703 | + | 0.994074i | \(0.534670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.20411 | 0.946117 | 0.473059 | − | 0.881031i | \(-0.343150\pi\) | ||||
0.473059 | + | 0.881031i | \(0.343150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.92409 | −0.435898 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.69831 | 1.26878 | 0.634389 | − | 0.773014i | \(-0.281252\pi\) | ||||
0.634389 | + | 0.773014i | \(0.281252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.99849 | −0.856926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.13735 | −0.439317 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.72669 | 1.06134 | 0.530671 | − | 0.847578i | \(-0.321940\pi\) | ||||
0.530671 | + | 0.847578i | \(0.321940\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.37009 | −0.993783 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.552973 | 0.0732431 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.236931 | −0.0308458 | −0.0154229 | − | 0.999881i | \(-0.504909\pi\) | ||||
−0.0154229 | + | 0.999881i | \(0.504909\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.83181 | −0.234540 | −0.117270 | − | 0.993100i | \(-0.537414\pi\) | ||||
−0.117270 | + | 0.993100i | \(0.537414\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00076 | −0.126084 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.41182 | 0.175115 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.79746 | −0.341765 | −0.170882 | − | 0.985291i | \(-0.554662\pi\) | ||||
−0.170882 | + | 0.985291i | \(0.554662\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4788 | 1.36228 | 0.681139 | − | 0.732154i | \(-0.261485\pi\) | ||||
0.681139 | + | 0.732154i | \(0.261485\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.6919 | −1.60251 | −0.801257 | − | 0.598321i | \(-0.795835\pi\) | ||||
−0.801257 | + | 0.598321i | \(0.795835\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.55030 | 0.409954 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.52238 | −0.287452 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.0899 | −1.92277 | −0.961383 | − | 0.275214i | \(-0.911251\pi\) | ||||
−0.961383 | + | 0.275214i | \(0.911251\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.06382 | −0.885120 | −0.442560 | − | 0.896739i | \(-0.645930\pi\) | ||||
−0.442560 | + | 0.896739i | \(0.645930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.17389 | 0.995049 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.121648 | 0.0130421 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.93850 | 0.523480 | 0.261740 | − | 0.965138i | \(-0.415704\pi\) | ||||
0.261740 | + | 0.965138i | \(0.415704\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.483191 | 0.0506522 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.23476 | 0.853904 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.61694 | −0.165895 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.6281 | −1.58679 | −0.793396 | − | 0.608706i | \(-0.791689\pi\) | ||||
−0.793396 | + | 0.608706i | \(0.791689\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.52047 | 0.253317 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.25218 | −0.323604 | −0.161802 | − | 0.986823i | \(-0.551731\pi\) | ||||
−0.161802 | + | 0.986823i | \(0.551731\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.40182 | −0.138125 | −0.0690627 | − | 0.997612i | \(-0.522001\pi\) | ||||
−0.0690627 | + | 0.997612i | \(0.522001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.92630 | 0.285578 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0443 | −0.971016 | −0.485508 | − | 0.874232i | \(-0.661365\pi\) | ||||
−0.485508 | + | 0.874232i | \(0.661365\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.75809 | −0.647308 | −0.323654 | − | 0.946176i | \(-0.604911\pi\) | ||||
−0.323654 | + | 0.946176i | \(0.604911\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.53165 | −0.904704 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0242 | −0.943000 | −0.471500 | − | 0.881866i | \(-0.656287\pi\) | ||||
−0.471500 | + | 0.881866i | \(0.656287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.482825 | −0.0446372 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.13973 | 0.287818 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.64722 | −0.422474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.39208 | −0.125519 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.23904 | 0.379151 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6982 | 1.48173 | 0.740865 | − | 0.671654i | \(-0.234416\pi\) | ||||
0.740865 | + | 0.671654i | \(0.234416\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.20411 | 0.546241 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.3899 | −1.25725 | −0.628627 | − | 0.777707i | \(-0.716383\pi\) | ||||
−0.628627 | + | 0.777707i | \(0.716383\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.553392 | −0.0479852 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.92409 | −0.251666 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.88176 | 0.160769 | 0.0803847 | − | 0.996764i | \(-0.474385\pi\) | ||||
0.0803847 | + | 0.996764i | \(0.474385\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.46292 | 0.293721 | 0.146860 | − | 0.989157i | \(-0.453083\pi\) | ||||
0.146860 | + | 0.989157i | \(0.453083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.69831 | 0.732530 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.21695 | −0.101766 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.355710 | −0.0295401 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.99849 | −0.494747 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.5705 | −1.76712 | −0.883560 | − | 0.468318i | \(-0.844860\pi\) | ||||
−0.883560 | + | 0.468318i | \(0.844860\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.27239 | 0.266303 | 0.133151 | − | 0.991096i | \(-0.457490\pi\) | ||||
0.133151 | + | 0.991096i | \(0.457490\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.13735 | −0.253640 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.0792 | −1.93409 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7962 | 1.81934 | 0.909668 | − | 0.415335i | \(-0.136336\pi\) | ||||
0.909668 | + | 0.415335i | \(0.136336\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.72669 | 0.612766 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0872 | −0.946741 | −0.473371 | − | 0.880863i | \(-0.656963\pi\) | ||||
−0.473371 | + | 0.880863i | \(0.656963\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.37009 | −0.573761 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.29559 | 0.641932 | 0.320966 | − | 0.947091i | \(-0.395992\pi\) | ||||
0.320966 | + | 0.947091i | \(0.395992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7669 | −0.982068 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.552973 | 0.0422869 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.6611 | −1.57083 | −0.785417 | − | 0.618967i | \(-0.787551\pi\) | ||||
−0.785417 | + | 0.618967i | \(0.787551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.55299 | −0.268581 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.236931 | −0.0178089 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.88071 | 0.290058 | 0.145029 | − | 0.989427i | \(-0.453672\pi\) | ||||
0.145029 | + | 0.989427i | \(0.453672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.97115 | 0.592491 | 0.296246 | − | 0.955112i | \(-0.404265\pi\) | ||||
0.296246 | + | 0.955112i | \(0.404265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.83181 | −0.135412 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.8714 | 2.04915 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.90760 | −0.578261 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00076 | −0.0727944 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.8859 | 1.22182 | 0.610910 | − | 0.791700i | \(-0.290804\pi\) | ||||
0.610910 | + | 0.791700i | \(0.290804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.3002 | −1.53322 | −0.766611 | − | 0.642112i | \(-0.778058\pi\) | ||||
−0.766611 | + | 0.642112i | \(0.778058\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.41182 | 0.101103 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.9334 | 1.91893 | 0.959463 | − | 0.281835i | \(-0.0909431\pi\) | ||||
0.959463 | + | 0.281835i | \(0.0909431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.28577 | −0.516474 | −0.258237 | − | 0.966082i | \(-0.583142\pi\) | ||||
−0.258237 | + | 0.966082i | \(0.583142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.79746 | −0.197318 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.121740 | −0.00854449 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.07056 | 0.284300 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.39375 | 0.0964080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.6084 | 1.07453 | 0.537264 | − | 0.843414i | \(-0.319458\pi\) | ||||
0.537264 | + | 0.843414i | \(0.319458\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4788 | 0.786512 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.1414 | −1.23723 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.24099 | −0.559435 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.6919 | −0.925212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.51479 | 0.101896 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.40582 | −0.0941407 | −0.0470704 | − | 0.998892i | \(-0.514989\pi\) | ||||
−0.0470704 | + | 0.998892i | \(0.514989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.55030 | 0.236687 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.43994 | −0.294689 | −0.147344 | − | 0.989085i | \(-0.547073\pi\) | ||||
−0.147344 | + | 0.989085i | \(0.547073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.67523 | −0.110702 | −0.0553512 | − | 0.998467i | \(-0.517628\pi\) | ||||
−0.0553512 | + | 0.998467i | \(0.517628\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.52238 | −0.165960 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.7578 | −1.42540 | −0.712700 | − | 0.701469i | \(-0.752528\pi\) | ||||
−0.712700 | + | 0.701469i | \(0.752528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.4346 | −1.65917 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.0899 | −1.11011 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.0054 | −1.35872 | −0.679362 | − | 0.733803i | \(-0.737743\pi\) | ||||
−0.679362 | + | 0.733803i | \(0.737743\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.3357 | −1.69643 | −0.848217 | − | 0.529649i | \(-0.822324\pi\) | ||||
−0.848217 | + | 0.529649i | \(0.822324\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.5401 | 1.12060 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.266989 | −0.0169881 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.06382 | −0.511024 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.0533 | 1.64447 | 0.822236 | − | 0.569146i | \(-0.192726\pi\) | ||||
0.822236 | + | 0.569146i | \(0.192726\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.17389 | 0.574492 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.89900 | 0.492726 | 0.246363 | − | 0.969178i | \(-0.420764\pi\) | ||||
0.246363 | + | 0.969178i | \(0.420764\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.53886 | 0.592716 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.121648 | 0.00752983 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.3421 | −0.761044 | −0.380522 | − | 0.924772i | \(-0.624256\pi\) | ||||
−0.380522 | + | 0.924772i | \(0.624256\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5935 | −1.38791 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.93850 | 0.302231 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.1897 | −0.682245 | −0.341123 | − | 0.940019i | \(-0.610807\pi\) | ||||
−0.341123 | + | 0.940019i | \(0.610807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8348 | 1.44786 | 0.723932 | − | 0.689871i | \(-0.242333\pi\) | ||||
0.723932 | + | 0.689871i | \(0.242333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.483191 | 0.0292440 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.94844 | 0.539612 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8542 | −1.07275 | −0.536376 | − | 0.843979i | \(-0.680207\pi\) | ||||
−0.536376 | + | 0.843979i | \(0.680207\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.23476 | 0.493002 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.65517 | −0.0987390 | −0.0493695 | − | 0.998781i | \(-0.515721\pi\) | ||||
−0.0493695 | + | 0.998781i | \(0.515721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.36434 | −0.0811013 | −0.0405507 | − | 0.999177i | \(-0.512911\pi\) | ||||
−0.0405507 | + | 0.999177i | \(0.512911\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.61694 | −0.0957795 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.39313 | 0.0822340 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.15704 | −0.421002 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.6281 | −0.916135 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.6055 | −0.619578 | −0.309789 | − | 0.950805i | \(-0.600258\pi\) | ||||
−0.309789 | + | 0.950805i | \(0.600258\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.692809 | 0.0403369 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.52047 | 0.146253 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.20880 | −0.357870 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.25218 | −0.186833 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.35639 | 0.306706 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3224 | −0.589130 | −0.294565 | − | 0.955631i | \(-0.595175\pi\) | ||||
−0.294565 | + | 0.955631i | \(0.595175\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.40182 | −0.0797468 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.04897 | −0.399710 | −0.199855 | − | 0.979825i | \(-0.564047\pi\) | ||||
−0.199855 | + | 0.979825i | \(0.564047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.26256 | 0.127887 | 0.0639436 | − | 0.997954i | \(-0.479632\pi\) | ||||
0.0639436 | + | 0.997954i | \(0.479632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.92630 | 0.164879 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.17358 | −0.178246 | −0.0891230 | − | 0.996021i | \(-0.528406\pi\) | ||||
−0.0891230 | + | 0.996021i | \(0.528406\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.306611 | 0.0171669 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0443 | −0.560616 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.73487 | −0.0965308 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.71418 | −0.0950854 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.75809 | −0.373723 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.70489 | −0.479916 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7849 | −1.14244 | −0.571221 | − | 0.820797i | \(-0.693530\pi\) | ||||
−0.571221 | + | 0.820797i | \(0.693530\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.53165 | −0.522331 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.18004 | 0.446923 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.1082 | −1.42221 | −0.711103 | − | 0.703088i | \(-0.751804\pi\) | ||||
−0.711103 | + | 0.703088i | \(0.751804\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.0242 | −0.544441 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7555 | 1.12397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0083 | 0.702384 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.4891 | −0.616769 | −0.308385 | − | 0.951262i | \(-0.599788\pi\) | ||||
−0.308385 | + | 0.951262i | \(0.599788\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.2230 | −1.56427 | −0.782136 | − | 0.623108i | \(-0.785870\pi\) | ||||
−0.782136 | + | 0.623108i | \(0.785870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.482825 | −0.0257713 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.5949 | −1.73485 | −0.867426 | − | 0.497565i | \(-0.834227\pi\) | ||||
−0.867426 | + | 0.497565i | \(0.834227\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.5649 | −1.78144 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.13973 | 0.166172 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.1497 | −1.53846 | −0.769231 | − | 0.638970i | \(-0.779361\pi\) | ||||
−0.769231 | + | 0.638970i | \(0.779361\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6942 | −0.983906 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.64722 | −0.243916 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 40.0363 | 2.09560 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.4367 | −1.17119 | −0.585593 | − | 0.810605i | \(-0.699138\pi\) | ||||
−0.585593 | + | 0.810605i | \(0.699138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.39208 | −0.0724687 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.73254 | −0.401453 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.6209 | −0.705263 | −0.352631 | − | 0.935762i | \(-0.614713\pi\) | ||||
−0.352631 | + | 0.935762i | \(0.614713\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.23904 | 0.218903 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0587348 | −0.00302500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.63466 | 0.238066 | 0.119033 | − | 0.992890i | \(-0.462021\pi\) | ||||
0.119033 | + | 0.992890i | \(0.462021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.6982 | 0.855477 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.4370 | 1.55526 | 0.777629 | − | 0.628724i | \(-0.216422\pi\) | ||||
0.777629 | + | 0.628724i | \(0.216422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.37567 | 0.375899 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.20411 | 0.315372 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.00516 | 0.152368 | 0.0761839 | − | 0.997094i | \(-0.475726\pi\) | ||||
0.0761839 | + | 0.997094i | \(0.475726\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.3899 | −0.725876 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 49.9725 | 2.51439 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.74084 | −0.488879 | −0.244439 | − | 0.969665i | \(-0.578604\pi\) | ||||
−0.244439 | + | 0.969665i | \(0.578604\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.553392 | −0.0277042 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9647 | 0.996988 | 0.498494 | − | 0.866893i | \(-0.333887\pi\) | ||||
0.498494 | + | 0.866893i | \(0.333887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.97595 | −0.198056 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.92409 | −0.145299 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0243 | −1.19084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3311 | 1.20310 | 0.601548 | − | 0.798837i | \(-0.294551\pi\) | ||||
0.601548 | + | 0.798837i | \(0.294551\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.88176 | 0.0928202 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.237111 | 0.0116675 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.5793 | 1.15746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.46292 | 0.169580 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0882 | 0.639399 | 0.319699 | − | 0.947519i | \(-0.396418\pi\) | ||||
0.319699 | + | 0.947519i | \(0.396418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.11443 | −0.297999 | −0.148999 | − | 0.988837i | \(-0.547605\pi\) | ||||
−0.148999 | + | 0.988837i | \(0.547605\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.69831 | 0.422926 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.1385 | −0.540299 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.83320 | 0.0887148 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.21695 | −0.0587548 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.4286 | −1.17668 | −0.588341 | − | 0.808613i | \(-0.700219\pi\) | ||||
−0.588341 | + | 0.808613i | \(0.700219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4567 | −0.790860 | −0.395430 | − | 0.918496i | \(-0.629404\pi\) | ||||
−0.395430 | + | 0.918496i | \(0.629404\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.355710 | −0.0170550 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.05639 | −0.0504187 | −0.0252093 | − | 0.999682i | \(-0.508025\pi\) | ||||
−0.0252093 | + | 0.999682i | \(0.508025\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.99849 | −0.285642 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.9171 | −0.946291 | −0.473146 | − | 0.880984i | \(-0.656882\pi\) | ||||
−0.473146 | + | 0.880984i | \(0.656882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.4406 | −0.684551 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.5705 | −1.02025 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.4526 | 1.15399 | 0.576995 | − | 0.816748i | \(-0.304225\pi\) | ||||
0.576995 | + | 0.816748i | \(0.304225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.50869 | −0.165218 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.27239 | 0.153750 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.41289 | −0.0662375 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.76318 | 0.456703 | 0.228351 | − | 0.973579i | \(-0.426667\pi\) | ||||
0.228351 | + | 0.973579i | \(0.426667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.13735 | −0.146439 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.8585 | 1.34408 | 0.672038 | − | 0.740517i | \(-0.265419\pi\) | ||||
0.672038 | + | 0.740517i | \(0.265419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.2836 | 0.942658 | 0.471329 | − | 0.881958i | \(-0.343774\pi\) | ||||
0.471329 | + | 0.881958i | \(0.343774\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −24.0792 | −1.11664 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.6590 | 1.27991 | 0.639953 | − | 0.768414i | \(-0.278954\pi\) | ||||
0.639953 | + | 0.768414i | \(0.278954\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.79958 | 0.129273 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.7962 | 1.05039 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.6373 | 0.719003 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.96322 | 0.0900789 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.72669 | 0.353781 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.4525 | 0.934500 | 0.467250 | − | 0.884125i | \(-0.345245\pi\) | ||||
0.467250 | + | 0.884125i | \(0.345245\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.60212 | 0.209839 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 45.6980 | 2.07504 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.11420 | 0.141118 | 0.0705589 | − | 0.997508i | \(-0.477522\pi\) | ||||
0.0705589 | + | 0.997508i | \(0.477522\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0872 | −0.546601 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.49988 | −0.248206 | −0.124103 | − | 0.992269i | \(-0.539605\pi\) | ||||
−0.124103 | + | 0.992269i | \(0.539605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.381653 | −0.0171888 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.37009 | −0.331261 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.4875 | −0.515283 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.38938 | 0.375560 | 0.187780 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187780 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.29559 | 0.370620 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.69208 | −0.0754461 | −0.0377230 | − | 0.999288i | \(-0.512010\pi\) | ||||
−0.0377230 | + | 0.999288i | \(0.512010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.50967 | 0.423175 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7669 | −0.566997 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.6024 | −0.647241 | −0.323621 | − | 0.946187i | \(-0.604900\pi\) | ||||
−0.323621 | + | 0.946187i | \(0.604900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.7022 | 0.606152 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.552973 | 0.0244144 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.09905 | 0.180626 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.9238 | 0.964210 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.6611 | −0.906921 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.7782 | −1.12937 | −0.564683 | − | 0.825308i | \(-0.691001\pi\) | ||||
−0.564683 | + | 0.825308i | \(0.691001\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0698 | 0.615230 | 0.307615 | − | 0.951511i | \(-0.400469\pi\) | ||||
0.307615 | + | 0.951511i | \(0.400469\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.55299 | −0.155065 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.8353 | −1.12540 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.236931 | −0.0102819 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.672130 | 0.0291132 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.3704 | 1.26979 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.88071 | 0.167465 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.1190 | −0.651222 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0495 | −0.776008 | −0.388004 | − | 0.921658i | \(-0.626835\pi\) | ||||
−0.388004 | + | 0.921658i | \(0.626835\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.97115 | 0.342075 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.7613 | 0.846480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.3113 | −0.697421 | −0.348710 | − | 0.937231i | \(-0.613380\pi\) | ||||
−0.348710 | + | 0.937231i | \(0.613380\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.83181 | −0.0781799 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0672682 | 0.00286572 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1029 | 0.727287 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.8714 | 1.18307 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.3437 | 0.946732 | 0.473366 | − | 0.880866i | \(-0.343039\pi\) | ||||
0.473366 | + | 0.880866i | \(0.343039\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.99550 | −0.126696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.90760 | −0.333859 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.0337 | −0.591452 | −0.295726 | − | 0.955273i | \(-0.595561\pi\) | ||||
−0.295726 | + | 0.955273i | \(0.595561\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.3117 | 1.23315 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00076 | −0.0420278 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.2949 | 1.56348 | 0.781741 | − | 0.623603i | \(-0.214332\pi\) | ||||
0.781741 | + | 0.623603i | \(0.214332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.8538 | −1.54228 | −0.771142 | − | 0.636663i | \(-0.780314\pi\) | ||||
−0.771142 | + | 0.636663i | \(0.780314\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.8859 | 0.705418 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.0650 | 0.876946 | 0.438473 | − | 0.898744i | \(-0.355519\pi\) | ||||
0.438473 | + | 0.898744i | \(0.355519\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.3002 | −0.885206 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.06993 | 0.334797 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.4749 | 0.806568 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.41182 | 0.0583718 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0411633 | 0.00169899 | 0.000849496 | − | 1.00000i | \(-0.499730\pi\) | ||||
0.000849496 | 1.00000i | \(0.499730\pi\) | ||||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.55360 | 0.187628 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.9334 | 1.10789 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.8649 | 0.610427 | 0.305213 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305213 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.18084 | −0.376378 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.28577 | −0.298187 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.0448 | 1.79962 | 0.899811 | − | 0.436280i | \(-0.143704\pi\) | ||||
0.899811 | + | 0.436280i | \(0.143704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.1391 | 1.80047 | 0.900237 | − | 0.435401i | \(-0.143393\pi\) | ||||
0.900237 | + | 0.435401i | \(0.143393\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.79746 | −0.113922 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.5889 | 0.552467 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2355 | −0.861923 | −0.430961 | − | 0.902370i | \(-0.641825\pi\) | ||||
−0.430961 | + | 0.902370i | \(0.641825\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.121740 | −0.00493317 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.19976 | −0.169904 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.1417 | −1.37897 | −0.689485 | − | 0.724300i | \(-0.742163\pi\) | ||||
−0.689485 | + | 0.724300i | \(0.742163\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.07056 | 0.164141 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.0131 | 1.65112 | 0.825562 | − | 0.564311i | \(-0.190858\pi\) | ||||
0.825562 | + | 0.564311i | \(0.190858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.04481 | 0.283155 | 0.141577 | − | 0.989927i | \(-0.454783\pi\) | ||||
0.141577 | + | 0.989927i | \(0.454783\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.94224 | −0.198007 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1469 | −1.20587 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.39375 | 0.0556612 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.9041 | 1.19235 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3895 | 0.931120 | 0.465560 | − | 0.885016i | \(-0.345853\pi\) | ||||
0.465560 | + | 0.885016i | \(0.345853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.6084 | 0.620379 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −48.8272 | −1.93765 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.89622 | 0.114752 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.4788 | 0.454093 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5270 | 0.652778 | 0.326389 | − | 0.945235i | \(-0.394168\pi\) | ||||
0.326389 | + | 0.945235i | \(0.394168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.1400 | −1.34635 | −0.673176 | − | 0.739482i | \(-0.735070\pi\) | ||||
−0.673176 | + | 0.739482i | \(0.735070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.1414 | −0.714316 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.66388 | −0.379926 | −0.189963 | − | 0.981791i | \(-0.560837\pi\) | ||||
−0.189963 | + | 0.981791i | \(0.560837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.597179 | −0.0234413 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.24099 | −0.322990 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.96106 | 0.233274 | 0.116637 | − | 0.993175i | \(-0.462789\pi\) | ||||
0.116637 | + | 0.993175i | \(0.462789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42.0774 | 1.64410 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.6919 | −0.534171 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.7022 | 1.46867 | 0.734334 | − | 0.678789i | \(-0.237495\pi\) | ||||
0.734334 | + | 0.678789i | \(0.237495\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.1603 | −1.25089 | −0.625445 | − | 0.780268i | \(-0.715083\pi\) | ||||
−0.625445 | + | 0.780268i | \(0.715083\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.51479 | 0.0588296 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.61817 | 0.0627498 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.40582 | −0.0543522 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.61704 | −0.178239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.2644 | −1.20516 | −0.602578 | − | 0.798060i | \(-0.705860\pi\) | ||||
−0.602578 | + | 0.798060i | \(0.705860\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.55030 | 0.136651 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.46909 | 0.210194 | 0.105097 | − | 0.994462i | \(-0.466485\pi\) | ||||
0.105097 | + | 0.994462i | \(0.466485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.6399 | 0.600205 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.43994 | −0.170139 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.3278 | −1.27525 | −0.637626 | − | 0.770346i | \(-0.720084\pi\) | ||||
−0.637626 | + | 0.770346i | \(0.720084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.50243 | −0.210237 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.67523 | −0.0639141 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.73064 | −0.142126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.4533 | 0.892206 | 0.446103 | − | 0.894982i | \(-0.352811\pi\) | ||||
0.446103 | + | 0.894982i | \(0.352811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.52238 | −0.0958173 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.1259 | −0.384097 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.36744 | 0.165428 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.7578 | −0.822955 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.7674 | 0.557757 | 0.278879 | − | 0.960326i | \(-0.410037\pi\) | ||||
0.278879 | + | 0.960326i | \(0.410037\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.27074 | −0.198790 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.4346 | −0.957924 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.25464 | 0.122403 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.9708 | 0.487130 | 0.243565 | − | 0.969885i | \(-0.421683\pi\) | ||||
0.243565 | + | 0.969885i | \(0.421683\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.0899 | −0.640922 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.55847 | 0.133079 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.0054 | −0.784459 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2138 | −0.679259 | −0.339630 | − | 0.940559i | \(-0.610302\pi\) | ||||
−0.339630 | + | 0.940559i | \(0.610302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.40288 | 0.0522460 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.3357 | −0.979437 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.431888 | 0.0160399 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.57796 | 0.318139 | 0.159069 | − | 0.987267i | \(-0.449151\pi\) | ||||
0.159069 | + | 0.987267i | \(0.449151\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.4645 | −0.719919 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.14291 | −0.116086 | −0.0580431 | − | 0.998314i | \(-0.518486\pi\) | ||||
−0.0580431 | + | 0.998314i | \(0.518486\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.5401 | 0.646977 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.05093 | −0.259724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.5068 | 0.827925 | 0.413962 | − | 0.910294i | \(-0.364145\pi\) | ||||
0.413962 | + | 0.910294i | \(0.364145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.266989 | −0.00980810 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.92937 | 0.180841 | 0.0904206 | − | 0.995904i | \(-0.471179\pi\) | ||||
0.0904206 | + | 0.995904i | \(0.471179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 63.0740 | 2.31085 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.06382 | −0.295040 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.0519 | 0.367288 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.04768 | 0.0382306 | 0.0191153 | − | 0.999817i | \(-0.493915\pi\) | ||||
0.0191153 | + | 0.999817i | \(0.493915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.0533 | 0.949437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.56875 | −0.348242 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.83671 | −0.103102 | −0.0515509 | − | 0.998670i | \(-0.516416\pi\) | ||||
−0.0515509 | + | 0.998670i | \(0.516416\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.1788 | −1.05773 | −0.528865 | − | 0.848706i | \(-0.677382\pi\) | ||||
−0.528865 | + | 0.848706i | \(0.677382\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.76321 | 0.244845 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.17389 | 0.331683 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.114396 | 0.00413062 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.3225 | 0.732849 | 0.366424 | − | 0.930448i | \(-0.380582\pi\) | ||||
0.366424 | + | 0.930448i | \(0.380582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.89900 | 0.284475 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.4407 | −0.807135 | −0.403568 | − | 0.914950i | \(-0.632230\pi\) | ||||
−0.403568 | + | 0.914950i | \(0.632230\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.2359 | 1.05018 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.53886 | 0.342205 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.769782 | −0.0275803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.9319 | 1.03526 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.121648 | 0.00434735 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −66.6582 | −2.37913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0329 | −0.500219 | −0.250109 | − | 0.968218i | \(-0.580467\pi\) | ||||
−0.250109 | + | 0.968218i | \(0.580467\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.3421 | −0.439389 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.0318 | 0.356690 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.884446 | 0.0314076 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −22.5935 | −0.801310 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.6768 | 1.86591 | 0.932954 | − | 0.359994i | \(-0.117221\pi\) | ||||
0.932954 | + | 0.359994i | \(0.117221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2896 | −0.965438 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.93850 | 0.174493 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.5100 | −1.21783 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.1897 | −0.393895 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.8291 | 1.85737 | 0.928686 | − | 0.370868i | \(-0.120940\pi\) | ||||
0.928686 | + | 0.370868i | \(0.120940\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.5497 | 1.49412 | 0.747061 | − | 0.664756i | \(-0.231464\pi\) | ||||
0.747061 | + | 0.664756i | \(0.231464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.8348 | 0.835925 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.3440 | 1.23805 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.43070 | 0.120025 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.483191 | 0.0168841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.3213 | 0.360214 | 0.180107 | − | 0.983647i | \(-0.442356\pi\) | ||||
0.180107 | + | 0.983647i | \(0.442356\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.3933 | −1.89603 | −0.948016 | − | 0.318223i | \(-0.896914\pi\) | ||||
−0.948016 | + | 0.318223i | \(0.896914\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.94844 | 0.311545 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.7576 | 0.965227 | 0.482613 | − | 0.875834i | \(-0.339688\pi\) | ||||
0.482613 | + | 0.875834i | \(0.339688\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.3925 | −1.09031 | −0.545153 | − | 0.838336i | \(-0.683529\pi\) | ||||
−0.545153 | + | 0.838336i | \(0.683529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.8542 | −0.619354 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.8193 | 0.652052 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.2571 | −0.839450 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.23476 | 0.284635 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.42802 | 0.118348 | 0.0591742 | − | 0.998248i | \(-0.481153\pi\) | ||||
0.0591742 | + | 0.998248i | \(0.481153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9852 | −0.999490 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.65517 | −0.0570070 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 37.3315 | 1.28424 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.65074 | 0.159801 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.36434 | −0.0468239 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.5301 | 1.11381 | 0.556904 | − | 0.830577i | \(-0.311989\pi\) | ||||
0.556904 | + | 0.830577i | \(0.311989\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.61694 | −0.0552983 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.8564 | −1.22483 | −0.612416 | − | 0.790536i | \(-0.709802\pi\) | ||||
−0.612416 | + | 0.790536i | \(0.709802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.07094 | 0.309497 | 0.154748 | − | 0.987954i | \(-0.450543\pi\) | ||||
0.154748 | + | 0.987954i | \(0.450543\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.39313 | 0.0474778 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42.4039 | 1.44344 | 0.721722 | − | 0.692183i | \(-0.243351\pi\) | ||||
0.721722 | + | 0.692183i | \(0.243351\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 60.4149 | 2.05417 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.15704 | −0.243066 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.0747 | −1.46121 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.35069 | 0.0457662 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.6281 | −0.528931 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.24225 | −0.143414 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.3885 | 1.39759 | 0.698795 | − | 0.715322i | \(-0.253720\pi\) | ||||
0.698795 | + | 0.715322i | \(0.253720\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.6055 | −0.357714 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.7850 | 0.599192 | 0.299596 | − | 0.954066i | \(-0.403148\pi\) | ||||
0.299596 | + | 0.954066i | \(0.403148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.22699 | 0.276860 | 0.138430 | − | 0.990372i | \(-0.455794\pi\) | ||||
0.138430 | + | 0.990372i | \(0.455794\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.692809 | 0.0232885 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.6339 | −1.49866 | −0.749330 | − | 0.662197i | \(-0.769624\pi\) | ||||
−0.749330 | + | 0.662197i | \(0.769624\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.7109 | −0.560465 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.52047 | 0.0844390 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.80993 | 0.160958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.3476 | −0.379307 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.00174 | 0.0334100 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.2413 | −0.807596 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.20880 | −0.206616 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3084 | −0.774797 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.8967 | 1.35795 | 0.678977 | − | 0.734160i | \(-0.262424\pi\) | ||||
0.678977 | + | 0.734160i | \(0.262424\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.25218 | −0.107868 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.868077 | 0.0287607 | 0.0143803 | − | 0.999897i | \(-0.495422\pi\) | ||||
0.0143803 | + | 0.999897i | \(0.495422\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.3246 | −0.672648 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.35639 | 0.177077 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.4008 | 0.475557 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.6469 | −1.76965 | −0.884824 | − | 0.465926i | \(-0.845721\pi\) | ||||
−0.884824 | + | 0.465926i | \(0.845721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3224 | −0.340135 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.54224 | −0.182425 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33.8402 | −1.11266 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.40182 | −0.0460418 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.37588 | −0.143568 | −0.0717840 | − | 0.997420i | \(-0.522869\pi\) | ||||
−0.0717840 | + | 0.997420i | \(0.522869\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.31700 | −0.108710 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.04897 | −0.230773 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23.1225 | 0.756188 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.70488 | 0.186370 | 0.0931851 | − | 0.995649i | \(-0.470295\pi\) | ||||
0.0931851 | + | 0.995649i | \(0.470295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.26256 | 0.0738357 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.1076 | −0.362098 | −0.181049 | − | 0.983474i | \(-0.557949\pi\) | ||||
−0.181049 | + | 0.983474i | \(0.557949\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.92630 | 0.0951927 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.9499 | −0.485807 | −0.242904 | − | 0.970050i | \(-0.578100\pi\) | ||||
−0.242904 | + | 0.970050i | \(0.578100\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.61079 | 0.214595 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.17358 | −0.102910 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.5217 | −0.956301 | −0.478150 | − | 0.878278i | \(-0.658693\pi\) | ||||
−0.478150 | + | 0.878278i | \(0.658693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49.3758 | −1.59776 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.306611 | 0.00991132 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.88318 | −0.0608111 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.8112 | 1.18746 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.0443 | −0.323672 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 62.2837 | 2.00498 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.5676 | −1.43320 | −0.716598 | − | 0.697486i | \(-0.754302\pi\) | ||||
−0.716598 | + | 0.697486i | \(0.754302\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.73487 | −0.0557321 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.2047 | 1.70742 | 0.853710 | − | 0.520749i | \(-0.174347\pi\) | ||||
0.853710 | + | 0.520749i | \(0.174347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.46554 | −0.111100 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.71418 | −0.0548976 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.8076 | −1.17758 | −0.588790 | − | 0.808286i | \(-0.700396\pi\) | ||||
−0.588790 | + | 0.808286i | \(0.700396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.4474 | 0.397819 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.75809 | −0.215769 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.2307 | −1.31506 | −0.657528 | − | 0.753430i | \(-0.728398\pi\) | ||||
−0.657528 | + | 0.753430i | \(0.728398\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −78.7557 | −2.50937 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.70489 | −0.277080 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.3806 | −1.28273 | −0.641366 | − | 0.767235i | \(-0.721632\pi\) | ||||
−0.641366 | + | 0.767235i | \(0.721632\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.7849 | −0.659589 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3042 | 0.675390 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.4577 | 0.837923 | 0.418961 | − | 0.908004i | \(-0.362394\pi\) | ||||
0.418961 | + | 0.908004i | \(0.362394\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.53165 | −0.301568 |
(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 | 6348.2.a.s.1.2 | 10 | ||
23.4 | even | 11 | 276.2.i.a.85.1 | yes | 20 | ||
23.6 | even | 11 | 276.2.i.a.13.1 | ✓ | 20 | ||
23.22 | odd | 2 | 6348.2.a.t.1.9 | 10 | |||
69.29 | odd | 22 | 828.2.q.c.289.2 | 20 | |||
69.50 | odd | 22 | 828.2.q.c.361.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.13.1 | ✓ | 20 | 23.6 | even | 11 | ||
276.2.i.a.85.1 | yes | 20 | 23.4 | even | 11 | ||
828.2.q.c.289.2 | 20 | 69.29 | odd | 22 | |||
828.2.q.c.361.2 | 20 | 69.50 | odd | 22 | |||
6348.2.a.s.1.2 | 10 | 1.1 | even | 1 | trivial | ||
6348.2.a.t.1.9 | 10 | 23.22 | odd | 2 |