Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(1,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.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: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.267949 | 0.119831 | 0.0599153 | − | 0.998203i | \(-0.480917\pi\) | ||||
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.267949 | −0.0847330 | ||||||||
\(11\) | 6.19615 | 1.86821 | 0.934105 | − | 0.356998i | \(-0.116200\pi\) | ||||
0.934105 | + | 0.356998i | \(0.116200\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.46410 | −1.79282 | −0.896410 | − | 0.443227i | \(-0.853834\pi\) | ||||
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.00000 | 1.69775 | 0.848875 | − | 0.528594i | \(-0.177281\pi\) | ||||
0.848875 | + | 0.528594i | \(0.177281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.732051 | 0.167944 | 0.0839720 | − | 0.996468i | \(-0.473239\pi\) | ||||
0.0839720 | + | 0.996468i | \(0.473239\pi\) | |||||||
\(20\) | 0.267949 | 0.0599153 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.19615 | −1.32102 | ||||||||
\(23\) | −4.19615 | −0.874958 | −0.437479 | − | 0.899229i | \(-0.644129\pi\) | ||||
−0.437479 | + | 0.899229i | \(0.644129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92820 | −0.985641 | ||||||||
\(26\) | 6.46410 | 1.26771 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 1.53590 | 0.285209 | 0.142605 | − | 0.989780i | \(-0.454452\pi\) | ||||
0.142605 | + | 0.989780i | \(0.454452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.19615 | 1.47207 | 0.736036 | − | 0.676942i | \(-0.236695\pi\) | ||||
0.736036 | + | 0.676942i | \(0.236695\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.00000 | −1.20049 | ||||||||
\(35\) | −0.267949 | −0.0452917 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6603 | 1.75253 | 0.876267 | − | 0.481825i | \(-0.160026\pi\) | ||||
0.876267 | + | 0.481825i | \(0.160026\pi\) | |||||||
\(38\) | −0.732051 | −0.118754 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.267949 | −0.0423665 | ||||||||
\(41\) | 2.53590 | 0.396041 | 0.198020 | − | 0.980198i | \(-0.436549\pi\) | ||||
0.198020 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.46410 | −0.223273 | −0.111637 | − | 0.993749i | \(-0.535609\pi\) | ||||
−0.111637 | + | 0.993749i | \(0.535609\pi\) | |||||||
\(44\) | 6.19615 | 0.934105 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.19615 | 0.618689 | ||||||||
\(47\) | 4.73205 | 0.690241 | 0.345120 | − | 0.938558i | \(-0.387838\pi\) | ||||
0.345120 | + | 0.938558i | \(0.387838\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.92820 | 0.696953 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.46410 | −0.896410 | ||||||||
\(53\) | −9.46410 | −1.29999 | −0.649997 | − | 0.759937i | \(-0.725230\pi\) | ||||
−0.649997 | + | 0.759937i | \(0.725230\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.66025 | 0.223869 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.53590 | −0.201673 | ||||||||
\(59\) | 4.19615 | 0.546293 | 0.273146 | − | 0.961973i | \(-0.411936\pi\) | ||||
0.273146 | + | 0.961973i | \(0.411936\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.92820 | 0.502955 | 0.251477 | − | 0.967863i | \(-0.419084\pi\) | ||||
0.251477 | + | 0.967863i | \(0.419084\pi\) | |||||||
\(62\) | −8.19615 | −1.04091 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.73205 | −0.214834 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.73205 | −0.822451 | −0.411225 | − | 0.911534i | \(-0.634899\pi\) | ||||
−0.411225 | + | 0.911534i | \(0.634899\pi\) | |||||||
\(68\) | 7.00000 | 0.848875 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.267949 | 0.0320261 | ||||||||
\(71\) | 6.53590 | 0.775668 | 0.387834 | − | 0.921729i | \(-0.373223\pi\) | ||||
0.387834 | + | 0.921729i | \(0.373223\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.26795 | 0.967690 | 0.483845 | − | 0.875154i | \(-0.339240\pi\) | ||||
0.483845 | + | 0.875154i | \(0.339240\pi\) | |||||||
\(74\) | −10.6603 | −1.23923 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.732051 | 0.0839720 | ||||||||
\(77\) | −6.19615 | −0.706117 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.12436 | −1.02657 | −0.513285 | − | 0.858218i | \(-0.671572\pi\) | ||||
−0.513285 | + | 0.858218i | \(0.671572\pi\) | |||||||
\(80\) | 0.267949 | 0.0299576 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.53590 | −0.280043 | ||||||||
\(83\) | 16.5885 | 1.82082 | 0.910410 | − | 0.413707i | \(-0.135766\pi\) | ||||
0.910410 | + | 0.413707i | \(0.135766\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.87564 | 0.203442 | ||||||||
\(86\) | 1.46410 | 0.157878 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.19615 | −0.660512 | ||||||||
\(89\) | 9.92820 | 1.05239 | 0.526194 | − | 0.850365i | \(-0.323619\pi\) | ||||
0.526194 | + | 0.850365i | \(0.323619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.46410 | 0.677622 | ||||||||
\(92\) | −4.19615 | −0.437479 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.73205 | −0.488074 | ||||||||
\(95\) | 0.196152 | 0.0201248 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9282 | 1.10959 | 0.554795 | − | 0.831987i | \(-0.312797\pi\) | ||||
0.554795 | + | 0.831987i | \(0.312797\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.92820 | −0.492820 | ||||||||
\(101\) | 8.92820 | 0.888389 | 0.444195 | − | 0.895930i | \(-0.353490\pi\) | ||||
0.444195 | + | 0.895930i | \(0.353490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.39230 | −0.826918 | −0.413459 | − | 0.910523i | \(-0.635680\pi\) | ||||
−0.413459 | + | 0.910523i | \(0.635680\pi\) | |||||||
\(104\) | 6.46410 | 0.633857 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.46410 | 0.919235 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.19615 | 0.306136 | 0.153068 | − | 0.988216i | \(-0.451085\pi\) | ||||
0.153068 | + | 0.988216i | \(0.451085\pi\) | |||||||
\(110\) | −1.66025 | −0.158299 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −5.73205 | −0.539226 | −0.269613 | − | 0.962969i | \(-0.586896\pi\) | ||||
−0.269613 | + | 0.962969i | \(0.586896\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.12436 | −0.104847 | ||||||||
\(116\) | 1.53590 | 0.142605 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.19615 | −0.386287 | ||||||||
\(119\) | −7.00000 | −0.641689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.3923 | 2.49021 | ||||||||
\(122\) | −3.92820 | −0.355643 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.19615 | 0.736036 | ||||||||
\(125\) | −2.66025 | −0.237940 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.73205 | 0.151911 | ||||||||
\(131\) | 10.5359 | 0.920526 | 0.460263 | − | 0.887783i | \(-0.347755\pi\) | ||||
0.460263 | + | 0.887783i | \(0.347755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.732051 | −0.0634769 | ||||||||
\(134\) | 6.73205 | 0.581561 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.00000 | −0.600245 | ||||||||
\(137\) | −8.26795 | −0.706379 | −0.353189 | − | 0.935552i | \(-0.614903\pi\) | ||||
−0.353189 | + | 0.935552i | \(0.614903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.26795 | −0.277184 | −0.138592 | − | 0.990350i | \(-0.544258\pi\) | ||||
−0.138592 | + | 0.990350i | \(0.544258\pi\) | |||||||
\(140\) | −0.267949 | −0.0226458 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.53590 | −0.548480 | ||||||||
\(143\) | −40.0526 | −3.34936 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.411543 | 0.0341768 | ||||||||
\(146\) | −8.26795 | −0.684260 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.6603 | 0.876267 | ||||||||
\(149\) | 9.00000 | 0.737309 | 0.368654 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368654 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.80385 | −0.472310 | −0.236155 | − | 0.971715i | \(-0.575887\pi\) | ||||
−0.236155 | + | 0.971715i | \(0.575887\pi\) | |||||||
\(152\) | −0.732051 | −0.0593772 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.19615 | 0.499300 | ||||||||
\(155\) | 2.19615 | 0.176399 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | −0.0798087 | −0.0399043 | − | 0.999204i | \(-0.512705\pi\) | ||||
−0.0399043 | + | 0.999204i | \(0.512705\pi\) | |||||||
\(158\) | 9.12436 | 0.725895 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.267949 | −0.0211832 | ||||||||
\(161\) | 4.19615 | 0.330703 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4641 | −1.05459 | −0.527295 | − | 0.849682i | \(-0.676794\pi\) | ||||
−0.527295 | + | 0.849682i | \(0.676794\pi\) | |||||||
\(164\) | 2.53590 | 0.198020 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.5885 | −1.28751 | ||||||||
\(167\) | −1.80385 | −0.139586 | −0.0697930 | − | 0.997561i | \(-0.522234\pi\) | ||||
−0.0697930 | + | 0.997561i | \(0.522234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.7846 | 2.21420 | ||||||||
\(170\) | −1.87564 | −0.143855 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.46410 | −0.111637 | ||||||||
\(173\) | 6.26795 | 0.476543 | 0.238272 | − | 0.971199i | \(-0.423419\pi\) | ||||
0.238272 | + | 0.971199i | \(0.423419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.92820 | 0.372537 | ||||||||
\(176\) | 6.19615 | 0.467053 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.92820 | −0.744150 | ||||||||
\(179\) | −2.19615 | −0.164148 | −0.0820741 | − | 0.996626i | \(-0.526154\pi\) | ||||
−0.0820741 | + | 0.996626i | \(0.526154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3923 | −1.21843 | −0.609215 | − | 0.793005i | \(-0.708515\pi\) | ||||
−0.609215 | + | 0.793005i | \(0.708515\pi\) | |||||||
\(182\) | −6.46410 | −0.479151 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.19615 | 0.309344 | ||||||||
\(185\) | 2.85641 | 0.210007 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 43.3731 | 3.17175 | ||||||||
\(188\) | 4.73205 | 0.345120 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.196152 | −0.0142304 | ||||||||
\(191\) | −5.66025 | −0.409562 | −0.204781 | − | 0.978808i | \(-0.565648\pi\) | ||||
−0.204781 | + | 0.978808i | \(0.565648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.8564 | 1.35731 | 0.678657 | − | 0.734455i | \(-0.262562\pi\) | ||||
0.678657 | + | 0.734455i | \(0.262562\pi\) | |||||||
\(194\) | −10.9282 | −0.784599 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 15.7846 | 1.12461 | 0.562303 | − | 0.826931i | \(-0.309915\pi\) | ||||
0.562303 | + | 0.826931i | \(0.309915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.1244 | −1.35569 | −0.677845 | − | 0.735205i | \(-0.737086\pi\) | ||||
−0.677845 | + | 0.735205i | \(0.737086\pi\) | |||||||
\(200\) | 4.92820 | 0.348477 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.92820 | −0.628186 | ||||||||
\(203\) | −1.53590 | −0.107799 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.679492 | 0.0474578 | ||||||||
\(206\) | 8.39230 | 0.584720 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.46410 | −0.448205 | ||||||||
\(209\) | 4.53590 | 0.313755 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.2679 | −1.18877 | −0.594387 | − | 0.804179i | \(-0.702605\pi\) | ||||
−0.594387 | + | 0.804179i | \(0.702605\pi\) | |||||||
\(212\) | −9.46410 | −0.649997 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.392305 | −0.0267550 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.19615 | −0.556391 | ||||||||
\(218\) | −3.19615 | −0.216471 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.66025 | 0.111934 | ||||||||
\(221\) | −45.2487 | −3.04376 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4641 | −1.70520 | −0.852601 | − | 0.522562i | \(-0.824976\pi\) | ||||
−0.852601 | + | 0.522562i | \(0.824976\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.73205 | 0.381290 | ||||||||
\(227\) | −18.9282 | −1.25631 | −0.628154 | − | 0.778089i | \(-0.716189\pi\) | ||||
−0.628154 | + | 0.778089i | \(0.716189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.46410 | −0.162832 | −0.0814162 | − | 0.996680i | \(-0.525944\pi\) | ||||
−0.0814162 | + | 0.996680i | \(0.525944\pi\) | |||||||
\(230\) | 1.12436 | 0.0741378 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.53590 | −0.100837 | ||||||||
\(233\) | −2.80385 | −0.183686 | −0.0918431 | − | 0.995773i | \(-0.529276\pi\) | ||||
−0.0918431 | + | 0.995773i | \(0.529276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.26795 | 0.0827119 | ||||||||
\(236\) | 4.19615 | 0.273146 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.00000 | 0.453743 | ||||||||
\(239\) | −10.0526 | −0.650246 | −0.325123 | − | 0.945672i | \(-0.605406\pi\) | ||||
−0.325123 | + | 0.945672i | \(0.605406\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2679 | −0.919079 | −0.459540 | − | 0.888157i | \(-0.651986\pi\) | ||||
−0.459540 | + | 0.888157i | \(0.651986\pi\) | |||||||
\(242\) | −27.3923 | −1.76084 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.92820 | 0.251477 | ||||||||
\(245\) | 0.267949 | 0.0171186 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.73205 | −0.301093 | ||||||||
\(248\) | −8.19615 | −0.520456 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.66025 | 0.168249 | ||||||||
\(251\) | −22.0526 | −1.39195 | −0.695973 | − | 0.718068i | \(-0.745027\pi\) | ||||
−0.695973 | + | 0.718068i | \(0.745027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.0000 | −1.63461 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.46410 | 0.403220 | 0.201610 | − | 0.979466i | \(-0.435383\pi\) | ||||
0.201610 | + | 0.979466i | \(0.435383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6603 | −0.662396 | ||||||||
\(260\) | −1.73205 | −0.107417 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.5359 | −0.650910 | ||||||||
\(263\) | −6.33975 | −0.390925 | −0.195463 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195463 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.53590 | −0.155779 | ||||||||
\(266\) | 0.732051 | 0.0448849 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.73205 | −0.411225 | ||||||||
\(269\) | 5.58846 | 0.340734 | 0.170367 | − | 0.985381i | \(-0.445505\pi\) | ||||
0.170367 | + | 0.985381i | \(0.445505\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.5167 | −1.18555 | −0.592776 | − | 0.805367i | \(-0.701968\pi\) | ||||
−0.592776 | + | 0.805367i | \(0.701968\pi\) | |||||||
\(272\) | 7.00000 | 0.424437 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.26795 | 0.499485 | ||||||||
\(275\) | −30.5359 | −1.84138 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7846 | −1.12866 | −0.564329 | − | 0.825550i | \(-0.690865\pi\) | ||||
−0.564329 | + | 0.825550i | \(0.690865\pi\) | |||||||
\(278\) | 3.26795 | 0.195999 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.267949 | 0.0160130 | ||||||||
\(281\) | −13.1962 | −0.787216 | −0.393608 | − | 0.919278i | \(-0.628773\pi\) | ||||
−0.393608 | + | 0.919278i | \(0.628773\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3205 | 0.910710 | 0.455355 | − | 0.890310i | \(-0.349512\pi\) | ||||
0.455355 | + | 0.890310i | \(0.349512\pi\) | |||||||
\(284\) | 6.53590 | 0.387834 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 40.0526 | 2.36836 | ||||||||
\(287\) | −2.53590 | −0.149689 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.0000 | 1.88235 | ||||||||
\(290\) | −0.411543 | −0.0241666 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.26795 | 0.483845 | ||||||||
\(293\) | 3.33975 | 0.195110 | 0.0975550 | − | 0.995230i | \(-0.468898\pi\) | ||||
0.0975550 | + | 0.995230i | \(0.468898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.12436 | 0.0654625 | ||||||||
\(296\) | −10.6603 | −0.619615 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.00000 | −0.521356 | ||||||||
\(299\) | 27.1244 | 1.56864 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.46410 | 0.0843894 | ||||||||
\(302\) | 5.80385 | 0.333974 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.732051 | 0.0419860 | ||||||||
\(305\) | 1.05256 | 0.0602693 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.8564 | −1.24741 | −0.623706 | − | 0.781659i | \(-0.714374\pi\) | ||||
−0.623706 | + | 0.781659i | \(0.714374\pi\) | |||||||
\(308\) | −6.19615 | −0.353059 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.19615 | −0.124733 | ||||||||
\(311\) | 10.1962 | 0.578171 | 0.289085 | − | 0.957303i | \(-0.406649\pi\) | ||||
0.289085 | + | 0.957303i | \(0.406649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5885 | 1.44635 | 0.723173 | − | 0.690667i | \(-0.242683\pi\) | ||||
0.723173 | + | 0.690667i | \(0.242683\pi\) | |||||||
\(314\) | 1.00000 | 0.0564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.12436 | −0.513285 | ||||||||
\(317\) | −31.3923 | −1.76317 | −0.881584 | − | 0.472028i | \(-0.843522\pi\) | ||||
−0.881584 | + | 0.472028i | \(0.843522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.51666 | 0.532831 | ||||||||
\(320\) | 0.267949 | 0.0149788 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.19615 | −0.233842 | ||||||||
\(323\) | 5.12436 | 0.285127 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.8564 | 1.76708 | ||||||||
\(326\) | 13.4641 | 0.745708 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.53590 | −0.140022 | ||||||||
\(329\) | −4.73205 | −0.260886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3923 | 0.681143 | 0.340571 | − | 0.940219i | \(-0.389380\pi\) | ||||
0.340571 | + | 0.940219i | \(0.389380\pi\) | |||||||
\(332\) | 16.5885 | 0.910410 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.80385 | 0.0987021 | ||||||||
\(335\) | −1.80385 | −0.0985547 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.3923 | −0.892946 | −0.446473 | − | 0.894797i | \(-0.647320\pi\) | ||||
−0.446473 | + | 0.894797i | \(0.647320\pi\) | |||||||
\(338\) | −28.7846 | −1.56568 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.87564 | 0.101721 | ||||||||
\(341\) | 50.7846 | 2.75014 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 1.46410 | 0.0789391 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.26795 | −0.336967 | ||||||||
\(347\) | 21.4641 | 1.15225 | 0.576127 | − | 0.817360i | \(-0.304563\pi\) | ||||
0.576127 | + | 0.817360i | \(0.304563\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.46410 | 0.0783716 | 0.0391858 | − | 0.999232i | \(-0.487524\pi\) | ||||
0.0391858 | + | 0.999232i | \(0.487524\pi\) | |||||||
\(350\) | −4.92820 | −0.263424 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.19615 | −0.330256 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.75129 | 0.0929488 | ||||||||
\(356\) | 9.92820 | 0.526194 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.19615 | 0.116070 | ||||||||
\(359\) | −10.9282 | −0.576769 | −0.288384 | − | 0.957515i | \(-0.593118\pi\) | ||||
−0.288384 | + | 0.957515i | \(0.593118\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4641 | −0.971795 | ||||||||
\(362\) | 16.3923 | 0.861560 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.46410 | 0.338811 | ||||||||
\(365\) | 2.21539 | 0.115959 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1244 | 0.580687 | 0.290343 | − | 0.956923i | \(-0.406230\pi\) | ||||
0.290343 | + | 0.956923i | \(0.406230\pi\) | |||||||
\(368\) | −4.19615 | −0.218740 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.85641 | −0.148498 | ||||||||
\(371\) | 9.46410 | 0.491352 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.14359 | −0.318103 | −0.159052 | − | 0.987270i | \(-0.550844\pi\) | ||||
−0.159052 | + | 0.987270i | \(0.550844\pi\) | |||||||
\(374\) | −43.3731 | −2.24277 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.73205 | −0.244037 | ||||||||
\(377\) | −9.92820 | −0.511328 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.5167 | −1.41344 | −0.706718 | − | 0.707495i | \(-0.749825\pi\) | ||||
−0.706718 | + | 0.707495i | \(0.749825\pi\) | |||||||
\(380\) | 0.196152 | 0.0100624 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.66025 | 0.289604 | ||||||||
\(383\) | 19.7128 | 1.00728 | 0.503639 | − | 0.863914i | \(-0.331994\pi\) | ||||
0.503639 | + | 0.863914i | \(0.331994\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.66025 | −0.0846144 | ||||||||
\(386\) | −18.8564 | −0.959766 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.9282 | 0.554795 | ||||||||
\(389\) | −13.4641 | −0.682657 | −0.341329 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341329 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.3731 | −1.48546 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.7846 | −0.795217 | ||||||||
\(395\) | −2.44486 | −0.123014 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0000 | −1.05396 | −0.526980 | − | 0.849878i | \(-0.676676\pi\) | ||||
−0.526980 | + | 0.849878i | \(0.676676\pi\) | |||||||
\(398\) | 19.1244 | 0.958617 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.92820 | −0.246410 | ||||||||
\(401\) | 10.5167 | 0.525177 | 0.262588 | − | 0.964908i | \(-0.415424\pi\) | ||||
0.262588 | + | 0.964908i | \(0.415424\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −52.9808 | −2.63916 | ||||||||
\(404\) | 8.92820 | 0.444195 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.53590 | 0.0762254 | ||||||||
\(407\) | 66.0526 | 3.27410 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3397 | 0.857395 | 0.428698 | − | 0.903448i | \(-0.358973\pi\) | ||||
0.428698 | + | 0.903448i | \(0.358973\pi\) | |||||||
\(410\) | −0.679492 | −0.0335577 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.39230 | −0.413459 | ||||||||
\(413\) | −4.19615 | −0.206479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.44486 | 0.218190 | ||||||||
\(416\) | 6.46410 | 0.316929 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.53590 | −0.221858 | ||||||||
\(419\) | −9.46410 | −0.462352 | −0.231176 | − | 0.972912i | \(-0.574257\pi\) | ||||
−0.231176 | + | 0.972912i | \(0.574257\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.124356 | 0.00606072 | 0.00303036 | − | 0.999995i | \(-0.499035\pi\) | ||||
0.00303036 | + | 0.999995i | \(0.499035\pi\) | |||||||
\(422\) | 17.2679 | 0.840591 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.46410 | 0.459617 | ||||||||
\(425\) | −34.4974 | −1.67337 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.92820 | −0.190099 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.392305 | 0.0189186 | ||||||||
\(431\) | −14.5359 | −0.700170 | −0.350085 | − | 0.936718i | \(-0.613847\pi\) | ||||
−0.350085 | + | 0.936718i | \(0.613847\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7321 | 0.756034 | 0.378017 | − | 0.925799i | \(-0.376606\pi\) | ||||
0.378017 | + | 0.925799i | \(0.376606\pi\) | |||||||
\(434\) | 8.19615 | 0.393428 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.19615 | 0.153068 | ||||||||
\(437\) | −3.07180 | −0.146944 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.3205 | 1.11303 | 0.556514 | − | 0.830839i | \(-0.312139\pi\) | ||||
0.556514 | + | 0.830839i | \(0.312139\pi\) | |||||||
\(440\) | −1.66025 | −0.0791495 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 45.2487 | 2.15226 | ||||||||
\(443\) | −15.2679 | −0.725402 | −0.362701 | − | 0.931906i | \(-0.618145\pi\) | ||||
−0.362701 | + | 0.931906i | \(0.618145\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.66025 | 0.126108 | ||||||||
\(446\) | 25.4641 | 1.20576 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 15.8564 | 0.748310 | 0.374155 | − | 0.927366i | \(-0.377933\pi\) | ||||
0.374155 | + | 0.927366i | \(0.377933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7128 | 0.739887 | ||||||||
\(452\) | −5.73205 | −0.269613 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.9282 | 0.888345 | ||||||||
\(455\) | 1.73205 | 0.0811998 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.85641 | −0.320729 | −0.160365 | − | 0.987058i | \(-0.551267\pi\) | ||||
−0.160365 | + | 0.987058i | \(0.551267\pi\) | |||||||
\(458\) | 2.46410 | 0.115140 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.12436 | −0.0524234 | ||||||||
\(461\) | −6.78461 | −0.315991 | −0.157995 | − | 0.987440i | \(-0.550503\pi\) | ||||
−0.157995 | + | 0.987440i | \(0.550503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.41154 | −0.0656000 | −0.0328000 | − | 0.999462i | \(-0.510442\pi\) | ||||
−0.0328000 | + | 0.999462i | \(0.510442\pi\) | |||||||
\(464\) | 1.53590 | 0.0713023 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.80385 | 0.129886 | ||||||||
\(467\) | −16.5885 | −0.767622 | −0.383811 | − | 0.923412i | \(-0.625389\pi\) | ||||
−0.383811 | + | 0.923412i | \(0.625389\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.73205 | 0.310857 | ||||||||
\(470\) | −1.26795 | −0.0584861 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.19615 | −0.193144 | ||||||||
\(473\) | −9.07180 | −0.417122 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.60770 | −0.165532 | ||||||||
\(476\) | −7.00000 | −0.320844 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.0526 | 0.459793 | ||||||||
\(479\) | −21.5167 | −0.983121 | −0.491561 | − | 0.870843i | \(-0.663573\pi\) | ||||
−0.491561 | + | 0.870843i | \(0.663573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −68.9090 | −3.14198 | ||||||||
\(482\) | 14.2679 | 0.649887 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27.3923 | 1.24510 | ||||||||
\(485\) | 2.92820 | 0.132963 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.58846 | 0.117294 | 0.0586471 | − | 0.998279i | \(-0.481321\pi\) | ||||
0.0586471 | + | 0.998279i | \(0.481321\pi\) | |||||||
\(488\) | −3.92820 | −0.177821 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.267949 | −0.0121047 | ||||||||
\(491\) | 26.5359 | 1.19755 | 0.598774 | − | 0.800918i | \(-0.295655\pi\) | ||||
0.598774 | + | 0.800918i | \(0.295655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.7513 | 0.484214 | ||||||||
\(494\) | 4.73205 | 0.212905 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.19615 | 0.368018 | ||||||||
\(497\) | −6.53590 | −0.293175 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.8038 | 0.886542 | 0.443271 | − | 0.896388i | \(-0.353818\pi\) | ||||
0.443271 | + | 0.896388i | \(0.353818\pi\) | |||||||
\(500\) | −2.66025 | −0.118970 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.0526 | 0.984254 | ||||||||
\(503\) | 40.0526 | 1.78586 | 0.892928 | − | 0.450200i | \(-0.148647\pi\) | ||||
0.892928 | + | 0.450200i | \(0.148647\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.39230 | 0.106456 | ||||||||
\(506\) | 26.0000 | 1.15584 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | 31.8564 | 1.41201 | 0.706005 | − | 0.708207i | \(-0.250496\pi\) | ||||
0.706005 | + | 0.708207i | \(0.250496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.26795 | −0.365753 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.46410 | −0.285119 | ||||||||
\(515\) | −2.24871 | −0.0990901 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.3205 | 1.28951 | ||||||||
\(518\) | 10.6603 | 0.468385 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.73205 | 0.0759555 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.1769 | 1.45073 | 0.725363 | − | 0.688367i | \(-0.241672\pi\) | ||||
0.725363 | + | 0.688367i | \(0.241672\pi\) | |||||||
\(524\) | 10.5359 | 0.460263 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.33975 | 0.276426 | ||||||||
\(527\) | 57.3731 | 2.49921 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.39230 | −0.234448 | ||||||||
\(530\) | 2.53590 | 0.110152 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.732051 | −0.0317384 | ||||||||
\(533\) | −16.3923 | −0.710030 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.73205 | 0.290780 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.58846 | −0.240936 | ||||||||
\(539\) | 6.19615 | 0.266887 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.33975 | 0.143587 | 0.0717934 | − | 0.997420i | \(-0.477128\pi\) | ||||
0.0717934 | + | 0.997420i | \(0.477128\pi\) | |||||||
\(542\) | 19.5167 | 0.838312 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.00000 | −0.300123 | ||||||||
\(545\) | 0.856406 | 0.0366844 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.7321 | −0.971952 | −0.485976 | − | 0.873972i | \(-0.661536\pi\) | ||||
−0.485976 | + | 0.873972i | \(0.661536\pi\) | |||||||
\(548\) | −8.26795 | −0.353189 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 30.5359 | 1.30206 | ||||||||
\(551\) | 1.12436 | 0.0478992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.12436 | 0.388007 | ||||||||
\(554\) | 18.7846 | 0.798082 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.26795 | −0.138592 | ||||||||
\(557\) | 23.9282 | 1.01387 | 0.506935 | − | 0.861984i | \(-0.330778\pi\) | ||||
0.506935 | + | 0.861984i | \(0.330778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.46410 | 0.400289 | ||||||||
\(560\) | −0.267949 | −0.0113229 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.1962 | 0.556646 | ||||||||
\(563\) | 19.7128 | 0.830796 | 0.415398 | − | 0.909640i | \(-0.363642\pi\) | ||||
0.415398 | + | 0.909640i | \(0.363642\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.53590 | −0.0646157 | ||||||||
\(566\) | −15.3205 | −0.643969 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.53590 | −0.274240 | ||||||||
\(569\) | 23.1962 | 0.972433 | 0.486217 | − | 0.873838i | \(-0.338377\pi\) | ||||
0.486217 | + | 0.873838i | \(0.338377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.7321 | −0.951307 | −0.475653 | − | 0.879633i | \(-0.657788\pi\) | ||||
−0.475653 | + | 0.879633i | \(0.657788\pi\) | |||||||
\(572\) | −40.0526 | −1.67468 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.53590 | 0.105846 | ||||||||
\(575\) | 20.6795 | 0.862394 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.6603 | 1.02662 | 0.513310 | − | 0.858203i | \(-0.328419\pi\) | ||||
0.513310 | + | 0.858203i | \(0.328419\pi\) | |||||||
\(578\) | −32.0000 | −1.33102 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.411543 | 0.0170884 | ||||||||
\(581\) | −16.5885 | −0.688205 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −58.6410 | −2.42866 | ||||||||
\(584\) | −8.26795 | −0.342130 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.33975 | −0.137964 | ||||||||
\(587\) | 14.7321 | 0.608057 | 0.304028 | − | 0.952663i | \(-0.401668\pi\) | ||||
0.304028 | + | 0.952663i | \(0.401668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | −1.12436 | −0.0462890 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.6603 | 0.438134 | ||||||||
\(593\) | −22.1769 | −0.910697 | −0.455348 | − | 0.890313i | \(-0.650485\pi\) | ||||
−0.455348 | + | 0.890313i | \(0.650485\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.87564 | −0.0768939 | ||||||||
\(596\) | 9.00000 | 0.368654 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.1244 | −1.10920 | ||||||||
\(599\) | −15.1244 | −0.617964 | −0.308982 | − | 0.951068i | \(-0.599988\pi\) | ||||
−0.308982 | + | 0.951068i | \(0.599988\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.1962 | 0.783027 | 0.391514 | − | 0.920172i | \(-0.371952\pi\) | ||||
0.391514 | + | 0.920172i | \(0.371952\pi\) | |||||||
\(602\) | −1.46410 | −0.0596723 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.80385 | −0.236155 | ||||||||
\(605\) | 7.33975 | 0.298403 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5885 | −0.998015 | −0.499007 | − | 0.866598i | \(-0.666302\pi\) | ||||
−0.499007 | + | 0.866598i | \(0.666302\pi\) | |||||||
\(608\) | −0.732051 | −0.0296886 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.05256 | −0.0426169 | ||||||||
\(611\) | −30.5885 | −1.23748 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.7846 | 1.08182 | 0.540910 | − | 0.841080i | \(-0.318080\pi\) | ||||
0.540910 | + | 0.841080i | \(0.318080\pi\) | |||||||
\(614\) | 21.8564 | 0.882053 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.19615 | 0.249650 | ||||||||
\(617\) | 11.9808 | 0.482327 | 0.241164 | − | 0.970484i | \(-0.422471\pi\) | ||||
0.241164 | + | 0.970484i | \(0.422471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7128 | −0.953098 | −0.476549 | − | 0.879148i | \(-0.658113\pi\) | ||||
−0.476549 | + | 0.879148i | \(0.658113\pi\) | |||||||
\(620\) | 2.19615 | 0.0881996 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.1962 | −0.408828 | ||||||||
\(623\) | −9.92820 | −0.397765 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | −25.5885 | −1.02272 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | −0.0399043 | ||||||||
\(629\) | 74.6218 | 2.97537 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.66025 | −0.145712 | −0.0728562 | − | 0.997342i | \(-0.523211\pi\) | ||||
−0.0728562 | + | 0.997342i | \(0.523211\pi\) | |||||||
\(632\) | 9.12436 | 0.362947 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.3923 | 1.24675 | ||||||||
\(635\) | 3.21539 | 0.127599 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.46410 | −0.256117 | ||||||||
\(638\) | −9.51666 | −0.376768 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.267949 | −0.0105916 | ||||||||
\(641\) | 39.4449 | 1.55798 | 0.778989 | − | 0.627037i | \(-0.215733\pi\) | ||||
0.778989 | + | 0.627037i | \(0.215733\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.41154 | −0.371155 | −0.185578 | − | 0.982630i | \(-0.559416\pi\) | ||||
−0.185578 | + | 0.982630i | \(0.559416\pi\) | |||||||
\(644\) | 4.19615 | 0.165352 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.12436 | −0.201615 | ||||||||
\(647\) | −4.39230 | −0.172679 | −0.0863397 | − | 0.996266i | \(-0.527517\pi\) | ||||
−0.0863397 | + | 0.996266i | \(0.527517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.0000 | 1.02059 | ||||||||
\(650\) | −31.8564 | −1.24951 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.4641 | −0.527295 | ||||||||
\(653\) | −30.2487 | −1.18372 | −0.591862 | − | 0.806039i | \(-0.701607\pi\) | ||||
−0.591862 | + | 0.806039i | \(0.701607\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.82309 | 0.110307 | ||||||||
\(656\) | 2.53590 | 0.0990102 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.73205 | 0.184475 | ||||||||
\(659\) | −36.3923 | −1.41764 | −0.708821 | − | 0.705388i | \(-0.750773\pi\) | ||||
−0.708821 | + | 0.705388i | \(0.750773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.8564 | −0.500056 | −0.250028 | − | 0.968239i | \(-0.580440\pi\) | ||||
−0.250028 | + | 0.968239i | \(0.580440\pi\) | |||||||
\(662\) | −12.3923 | −0.481641 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.5885 | −0.643757 | ||||||||
\(665\) | −0.196152 | −0.00760646 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.44486 | −0.249546 | ||||||||
\(668\) | −1.80385 | −0.0697930 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.80385 | 0.0696887 | ||||||||
\(671\) | 24.3397 | 0.939625 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.3205 | −0.706204 | −0.353102 | − | 0.935585i | \(-0.614873\pi\) | ||||
−0.353102 | + | 0.935585i | \(0.614873\pi\) | |||||||
\(674\) | 16.3923 | 0.631408 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.7846 | 1.10710 | ||||||||
\(677\) | 36.0000 | 1.38359 | 0.691796 | − | 0.722093i | \(-0.256820\pi\) | ||||
0.691796 | + | 0.722093i | \(0.256820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9282 | −0.419386 | ||||||||
\(680\) | −1.87564 | −0.0719277 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −50.7846 | −1.94464 | ||||||||
\(683\) | −1.85641 | −0.0710334 | −0.0355167 | − | 0.999369i | \(-0.511308\pi\) | ||||
−0.0355167 | + | 0.999369i | \(0.511308\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.21539 | −0.0846457 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.46410 | −0.0558184 | ||||||||
\(689\) | 61.1769 | 2.33065 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 6.26795 | 0.238272 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.4641 | −0.814766 | ||||||||
\(695\) | −0.875644 | −0.0332151 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.7513 | 0.672378 | ||||||||
\(698\) | −1.46410 | −0.0554171 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.92820 | 0.186269 | ||||||||
\(701\) | 27.3923 | 1.03459 | 0.517297 | − | 0.855806i | \(-0.326938\pi\) | ||||
0.517297 | + | 0.855806i | \(0.326938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.80385 | 0.294328 | ||||||||
\(704\) | 6.19615 | 0.233526 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | −8.92820 | −0.335780 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.87564 | −0.145553 | −0.0727764 | − | 0.997348i | \(-0.523186\pi\) | ||||
−0.0727764 | + | 0.997348i | \(0.523186\pi\) | |||||||
\(710\) | −1.75129 | −0.0657247 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.92820 | −0.372075 | ||||||||
\(713\) | −34.3923 | −1.28800 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.7321 | −0.401356 | ||||||||
\(716\) | −2.19615 | −0.0820741 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.9282 | 0.407837 | ||||||||
\(719\) | −9.46410 | −0.352951 | −0.176476 | − | 0.984305i | \(-0.556470\pi\) | ||||
−0.176476 | + | 0.984305i | \(0.556470\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.39230 | 0.312546 | ||||||||
\(722\) | 18.4641 | 0.687163 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.3923 | −0.609215 | ||||||||
\(725\) | −7.56922 | −0.281114 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.3205 | 1.90337 | 0.951686 | − | 0.307072i | \(-0.0993494\pi\) | ||||
0.951686 | + | 0.307072i | \(0.0993494\pi\) | |||||||
\(728\) | −6.46410 | −0.239576 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.21539 | −0.0819953 | ||||||||
\(731\) | −10.2487 | −0.379062 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 47.3205 | 1.74782 | 0.873911 | − | 0.486085i | \(-0.161576\pi\) | ||||
0.873911 | + | 0.486085i | \(0.161576\pi\) | |||||||
\(734\) | −11.1244 | −0.410607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.19615 | 0.154672 | ||||||||
\(737\) | −41.7128 | −1.53651 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.2679 | −0.488069 | −0.244035 | − | 0.969767i | \(-0.578471\pi\) | ||||
−0.244035 | + | 0.969767i | \(0.578471\pi\) | |||||||
\(740\) | 2.85641 | 0.105004 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.46410 | −0.347438 | ||||||||
\(743\) | −40.3923 | −1.48185 | −0.740925 | − | 0.671588i | \(-0.765613\pi\) | ||||
−0.740925 | + | 0.671588i | \(0.765613\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.41154 | 0.0883521 | ||||||||
\(746\) | 6.14359 | 0.224933 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 43.3731 | 1.58588 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.1436 | −0.808031 | −0.404016 | − | 0.914752i | \(-0.632386\pi\) | ||||
−0.404016 | + | 0.914752i | \(0.632386\pi\) | |||||||
\(752\) | 4.73205 | 0.172560 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.92820 | 0.361564 | ||||||||
\(755\) | −1.55514 | −0.0565972 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.7846 | 0.755429 | 0.377715 | − | 0.925922i | \(-0.376710\pi\) | ||||
0.377715 | + | 0.925922i | \(0.376710\pi\) | |||||||
\(758\) | 27.5167 | 0.999450 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.196152 | −0.00711520 | ||||||||
\(761\) | 37.0000 | 1.34125 | 0.670624 | − | 0.741797i | \(-0.266026\pi\) | ||||
0.670624 | + | 0.741797i | \(0.266026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.19615 | −0.115708 | ||||||||
\(764\) | −5.66025 | −0.204781 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.7128 | −0.712253 | ||||||||
\(767\) | −27.1244 | −0.979404 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.41154 | −0.159084 | −0.0795421 | − | 0.996832i | \(-0.525346\pi\) | ||||
−0.0795421 | + | 0.996832i | \(0.525346\pi\) | |||||||
\(770\) | 1.66025 | 0.0598314 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.8564 | 0.678657 | ||||||||
\(773\) | −4.12436 | −0.148343 | −0.0741714 | − | 0.997246i | \(-0.523631\pi\) | ||||
−0.0741714 | + | 0.997246i | \(0.523631\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −40.3923 | −1.45093 | ||||||||
\(776\) | −10.9282 | −0.392300 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.4641 | 0.482711 | ||||||||
\(779\) | 1.85641 | 0.0665127 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.4974 | 1.44911 | ||||||||
\(782\) | 29.3731 | 1.05038 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −0.267949 | −0.00956352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.3923 | −1.01208 | −0.506038 | − | 0.862511i | \(-0.668891\pi\) | ||||
−0.506038 | + | 0.862511i | \(0.668891\pi\) | |||||||
\(788\) | 15.7846 | 0.562303 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.44486 | 0.0869843 | ||||||||
\(791\) | 5.73205 | 0.203808 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.3923 | −0.901707 | ||||||||
\(794\) | 21.0000 | 0.745262 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.1244 | −0.677845 | ||||||||
\(797\) | −29.4449 | −1.04299 | −0.521495 | − | 0.853254i | \(-0.674626\pi\) | ||||
−0.521495 | + | 0.853254i | \(0.674626\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.1244 | 1.17186 | ||||||||
\(800\) | 4.92820 | 0.174238 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.5167 | −0.371356 | ||||||||
\(803\) | 51.2295 | 1.80785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.12436 | 0.0396283 | ||||||||
\(806\) | 52.9808 | 1.86617 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.92820 | −0.314093 | ||||||||
\(809\) | 32.1244 | 1.12943 | 0.564716 | − | 0.825285i | \(-0.308986\pi\) | ||||
0.564716 | + | 0.825285i | \(0.308986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.1962 | 0.638953 | 0.319477 | − | 0.947594i | \(-0.396493\pi\) | ||||
0.319477 | + | 0.947594i | \(0.396493\pi\) | |||||||
\(812\) | −1.53590 | −0.0538995 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −66.0526 | −2.31514 | ||||||||
\(815\) | −3.60770 | −0.126372 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.07180 | −0.0374974 | ||||||||
\(818\) | −17.3397 | −0.606270 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.679492 | 0.0237289 | ||||||||
\(821\) | 25.9282 | 0.904901 | 0.452450 | − | 0.891790i | \(-0.350550\pi\) | ||||
0.452450 | + | 0.891790i | \(0.350550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.784610 | 0.0273498 | 0.0136749 | − | 0.999906i | \(-0.495647\pi\) | ||||
0.0136749 | + | 0.999906i | \(0.495647\pi\) | |||||||
\(824\) | 8.39230 | 0.292360 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.19615 | 0.146003 | ||||||||
\(827\) | −23.3205 | −0.810934 | −0.405467 | − | 0.914110i | \(-0.632891\pi\) | ||||
−0.405467 | + | 0.914110i | \(0.632891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.0000 | −0.486240 | −0.243120 | − | 0.969996i | \(-0.578171\pi\) | ||||
−0.243120 | + | 0.969996i | \(0.578171\pi\) | |||||||
\(830\) | −4.44486 | −0.154283 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.46410 | −0.224102 | ||||||||
\(833\) | 7.00000 | 0.242536 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.483340 | −0.0167267 | ||||||||
\(836\) | 4.53590 | 0.156877 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.46410 | 0.326932 | ||||||||
\(839\) | 1.46410 | 0.0505464 | 0.0252732 | − | 0.999681i | \(-0.491954\pi\) | ||||
0.0252732 | + | 0.999681i | \(0.491954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6410 | −0.918656 | ||||||||
\(842\) | −0.124356 | −0.00428558 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.2679 | −0.594387 | ||||||||
\(845\) | 7.71281 | 0.265329 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.3923 | −0.941211 | ||||||||
\(848\) | −9.46410 | −0.324999 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34.4974 | 1.18325 | ||||||||
\(851\) | −44.7321 | −1.53339 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.7128 | −1.70213 | −0.851067 | − | 0.525057i | \(-0.824044\pi\) | ||||
−0.851067 | + | 0.525057i | \(0.824044\pi\) | |||||||
\(854\) | 3.92820 | 0.134420 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.8564 | −0.575804 | −0.287902 | − | 0.957660i | \(-0.592958\pi\) | ||||
−0.287902 | + | 0.957660i | \(0.592958\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.3923 | 0.832255 | 0.416127 | − | 0.909306i | \(-0.363387\pi\) | ||||
0.416127 | + | 0.909306i | \(0.363387\pi\) | |||||||
\(860\) | −0.392305 | −0.0133775 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.5359 | 0.495095 | ||||||||
\(863\) | −7.12436 | −0.242516 | −0.121258 | − | 0.992621i | \(-0.538693\pi\) | ||||
−0.121258 | + | 0.992621i | \(0.538693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.67949 | 0.0571044 | ||||||||
\(866\) | −15.7321 | −0.534597 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.19615 | −0.278196 | ||||||||
\(869\) | −56.5359 | −1.91785 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43.5167 | 1.47451 | ||||||||
\(872\) | −3.19615 | −0.108235 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.07180 | 0.103905 | ||||||||
\(875\) | 2.66025 | 0.0899330 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.5167 | −1.23308 | −0.616540 | − | 0.787324i | \(-0.711466\pi\) | ||||
−0.616540 | + | 0.787324i | \(0.711466\pi\) | |||||||
\(878\) | −23.3205 | −0.787029 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.66025 | 0.0559672 | ||||||||
\(881\) | 30.2487 | 1.01910 | 0.509552 | − | 0.860440i | \(-0.329811\pi\) | ||||
0.509552 | + | 0.860440i | \(0.329811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.66025 | −0.325093 | −0.162547 | − | 0.986701i | \(-0.551971\pi\) | ||||
−0.162547 | + | 0.986701i | \(0.551971\pi\) | |||||||
\(884\) | −45.2487 | −1.52188 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.2679 | 0.512937 | ||||||||
\(887\) | −56.4449 | −1.89523 | −0.947617 | − | 0.319410i | \(-0.896515\pi\) | ||||
−0.947617 | + | 0.319410i | \(0.896515\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | −2.66025 | −0.0891719 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.4641 | −0.852601 | ||||||||
\(893\) | 3.46410 | 0.115922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.588457 | −0.0196700 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15.8564 | −0.529135 | ||||||||
\(899\) | 12.5885 | 0.419849 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −66.2487 | −2.20706 | ||||||||
\(902\) | −15.7128 | −0.523179 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.73205 | 0.190645 | ||||||||
\(905\) | −4.39230 | −0.146005 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.0000 | −1.19536 | −0.597680 | − | 0.801735i | \(-0.703911\pi\) | ||||
−0.597680 | + | 0.801735i | \(0.703911\pi\) | |||||||
\(908\) | −18.9282 | −0.628154 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.73205 | −0.0574169 | ||||||||
\(911\) | 42.2487 | 1.39976 | 0.699881 | − | 0.714259i | \(-0.253236\pi\) | ||||
0.699881 | + | 0.714259i | \(0.253236\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 102.785 | 3.40167 | ||||||||
\(914\) | 6.85641 | 0.226790 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.46410 | −0.0814162 | ||||||||
\(917\) | −10.5359 | −0.347926 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.9808 | 0.890013 | 0.445007 | − | 0.895527i | \(-0.353201\pi\) | ||||
0.445007 | + | 0.895527i | \(0.353201\pi\) | |||||||
\(920\) | 1.12436 | 0.0370689 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.78461 | 0.223439 | ||||||||
\(923\) | −42.2487 | −1.39063 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.5359 | −1.72737 | ||||||||
\(926\) | 1.41154 | 0.0463862 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.53590 | −0.0504183 | ||||||||
\(929\) | −51.4974 | −1.68958 | −0.844788 | − | 0.535101i | \(-0.820273\pi\) | ||||
−0.844788 | + | 0.535101i | \(0.820273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.732051 | 0.0239920 | ||||||||
\(932\) | −2.80385 | −0.0918431 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.5885 | 0.542791 | ||||||||
\(935\) | 11.6218 | 0.380073 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.8372 | −0.844064 | −0.422032 | − | 0.906581i | \(-0.638683\pi\) | ||||
−0.422032 | + | 0.906581i | \(0.638683\pi\) | |||||||
\(938\) | −6.73205 | −0.219809 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.26795 | 0.0413559 | ||||||||
\(941\) | −34.1244 | −1.11242 | −0.556211 | − | 0.831041i | \(-0.687745\pi\) | ||||
−0.556211 | + | 0.831041i | \(0.687745\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.6410 | −0.346519 | ||||||||
\(944\) | 4.19615 | 0.136573 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.07180 | 0.294950 | ||||||||
\(947\) | −46.2487 | −1.50288 | −0.751441 | − | 0.659801i | \(-0.770641\pi\) | ||||
−0.751441 | + | 0.659801i | \(0.770641\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53.4449 | −1.73489 | ||||||||
\(950\) | 3.60770 | 0.117049 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.00000 | 0.226871 | ||||||||
\(953\) | −41.5885 | −1.34718 | −0.673591 | − | 0.739104i | \(-0.735249\pi\) | ||||
−0.673591 | + | 0.739104i | \(0.735249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.51666 | −0.0490780 | ||||||||
\(956\) | −10.0526 | −0.325123 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.5167 | 0.695172 | ||||||||
\(959\) | 8.26795 | 0.266986 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 36.1769 | 1.16700 | ||||||||
\(962\) | 68.9090 | 2.22171 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.2679 | −0.459540 | ||||||||
\(965\) | 5.05256 | 0.162648 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.66025 | −0.117706 | −0.0588529 | − | 0.998267i | \(-0.518744\pi\) | ||||
−0.0588529 | + | 0.998267i | \(0.518744\pi\) | |||||||
\(968\) | −27.3923 | −0.880422 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.92820 | −0.0940189 | ||||||||
\(971\) | 8.87564 | 0.284833 | 0.142416 | − | 0.989807i | \(-0.454513\pi\) | ||||
0.142416 | + | 0.989807i | \(0.454513\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.26795 | 0.104766 | ||||||||
\(974\) | −2.58846 | −0.0829395 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.92820 | 0.125739 | ||||||||
\(977\) | 57.7128 | 1.84640 | 0.923198 | − | 0.384324i | \(-0.125565\pi\) | ||||
0.923198 | + | 0.384324i | \(0.125565\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61.5167 | 1.96608 | ||||||||
\(980\) | 0.267949 | 0.00855932 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.5359 | −0.846795 | ||||||||
\(983\) | 58.6410 | 1.87036 | 0.935179 | − | 0.354176i | \(-0.115238\pi\) | ||||
0.935179 | + | 0.354176i | \(0.115238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.22947 | 0.134762 | ||||||||
\(986\) | −10.7513 | −0.342391 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.73205 | −0.150547 | ||||||||
\(989\) | 6.14359 | 0.195355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.6603 | −0.878657 | −0.439328 | − | 0.898327i | \(-0.644784\pi\) | ||||
−0.439328 | + | 0.898327i | \(0.644784\pi\) | |||||||
\(992\) | −8.19615 | −0.260228 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.53590 | 0.207306 | ||||||||
\(995\) | −5.12436 | −0.162453 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.2487 | 1.30636 | 0.653180 | − | 0.757203i | \(-0.273435\pi\) | ||||
0.653180 | + | 0.757203i | \(0.273435\pi\) | |||||||
\(998\) | −19.8038 | −0.626880 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.a.l.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1134.2.a.m.1.2 | yes | 2 | ||
4.3 | odd | 2 | 9072.2.a.bp.1.1 | 2 | |||
7.6 | odd | 2 | 7938.2.a.bg.1.2 | 2 | |||
9.2 | odd | 6 | 1134.2.f.r.757.1 | 4 | |||
9.4 | even | 3 | 1134.2.f.s.379.2 | 4 | |||
9.5 | odd | 6 | 1134.2.f.r.379.1 | 4 | |||
9.7 | even | 3 | 1134.2.f.s.757.2 | 4 | |||
12.11 | even | 2 | 9072.2.a.y.1.2 | 2 | |||
21.20 | even | 2 | 7938.2.a.bt.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.a.l.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1134.2.a.m.1.2 | yes | 2 | 3.2 | odd | 2 | ||
1134.2.f.r.379.1 | 4 | 9.5 | odd | 6 | |||
1134.2.f.r.757.1 | 4 | 9.2 | odd | 6 | |||
1134.2.f.s.379.2 | 4 | 9.4 | even | 3 | |||
1134.2.f.s.757.2 | 4 | 9.7 | even | 3 | |||
7938.2.a.bg.1.2 | 2 | 7.6 | odd | 2 | |||
7938.2.a.bt.1.1 | 2 | 21.20 | even | 2 | |||
9072.2.a.y.1.2 | 2 | 12.11 | even | 2 | |||
9072.2.a.bp.1.1 | 2 | 4.3 | odd | 2 |