Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, 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("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.830830\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-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 | ||||||||
\(5\) | 3.20362 | 1.43270 | 0.716350 | − | 0.697741i | \(-0.245811\pi\) | ||||
0.716350 | + | 0.697741i | \(0.245811\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.51334 | 0.571988 | 0.285994 | − | 0.958231i | \(-0.407676\pi\) | ||||
0.285994 | + | 0.958231i | \(0.407676\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.20362 | −1.01307 | ||||||||
\(11\) | 6.53843 | 1.97141 | 0.985705 | − | 0.168479i | \(-0.0538855\pi\) | ||||
0.985705 | + | 0.168479i | \(0.0538855\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88612 | 0.800466 | 0.400233 | − | 0.916413i | \(-0.368929\pi\) | ||||
0.400233 | + | 0.916413i | \(0.368929\pi\) | |||||||
\(14\) | −1.51334 | −0.404456 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.19647 | 0.290188 | 0.145094 | − | 0.989418i | \(-0.453652\pi\) | ||||
0.145094 | + | 0.989418i | \(0.453652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.555554 | 0.127453 | 0.0637264 | − | 0.997967i | \(-0.479701\pi\) | ||||
0.0637264 | + | 0.997967i | \(0.479701\pi\) | |||||||
\(20\) | 3.20362 | 0.716350 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.53843 | −1.39400 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.26315 | 1.05263 | ||||||||
\(26\) | −2.88612 | −0.566015 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.51334 | 0.285994 | ||||||||
\(29\) | 8.66918 | 1.60983 | 0.804913 | − | 0.593393i | \(-0.202212\pi\) | ||||
0.804913 | + | 0.593393i | \(0.202212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.73559 | −1.20975 | −0.604874 | − | 0.796321i | \(-0.706776\pi\) | ||||
−0.604874 | + | 0.796321i | \(0.706776\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.19647 | −0.205194 | ||||||||
\(35\) | 4.84815 | 0.819487 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.45380 | −0.239003 | −0.119502 | − | 0.992834i | \(-0.538130\pi\) | ||||
−0.119502 | + | 0.992834i | \(0.538130\pi\) | |||||||
\(38\) | −0.555554 | −0.0901228 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.20362 | −0.506536 | ||||||||
\(41\) | 1.84796 | 0.288602 | 0.144301 | − | 0.989534i | \(-0.453907\pi\) | ||||
0.144301 | + | 0.989534i | \(0.453907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.17379 | 0.331500 | 0.165750 | − | 0.986168i | \(-0.446996\pi\) | ||||
0.165750 | + | 0.986168i | \(0.446996\pi\) | |||||||
\(44\) | 6.53843 | 0.985705 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.4135 | 1.66483 | 0.832416 | − | 0.554152i | \(-0.186957\pi\) | ||||
0.832416 | + | 0.554152i | \(0.186957\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.70981 | −0.672830 | ||||||||
\(50\) | −5.26315 | −0.744322 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.88612 | 0.400233 | ||||||||
\(53\) | −12.0613 | −1.65675 | −0.828375 | − | 0.560175i | \(-0.810734\pi\) | ||||
−0.828375 | + | 0.560175i | \(0.810734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.9466 | 2.82444 | ||||||||
\(56\) | −1.51334 | −0.202228 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.66918 | −1.13832 | ||||||||
\(59\) | −3.96140 | −0.515730 | −0.257865 | − | 0.966181i | \(-0.583019\pi\) | ||||
−0.257865 | + | 0.966181i | \(0.583019\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.03450 | 1.15675 | 0.578375 | − | 0.815771i | \(-0.303687\pi\) | ||||
0.578375 | + | 0.815771i | \(0.303687\pi\) | |||||||
\(62\) | 6.73559 | 0.855420 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.24603 | 1.14683 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.66794 | −0.936788 | −0.468394 | − | 0.883520i | \(-0.655167\pi\) | ||||
−0.468394 | + | 0.883520i | \(0.655167\pi\) | |||||||
\(68\) | 1.19647 | 0.145094 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.84815 | −0.579465 | ||||||||
\(71\) | 9.45607 | 1.12223 | 0.561114 | − | 0.827738i | \(-0.310373\pi\) | ||||
0.561114 | + | 0.827738i | \(0.310373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.627598 | −0.0734548 | −0.0367274 | − | 0.999325i | \(-0.511693\pi\) | ||||
−0.0367274 | + | 0.999325i | \(0.511693\pi\) | |||||||
\(74\) | 1.45380 | 0.169001 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.555554 | 0.0637264 | ||||||||
\(77\) | 9.89485 | 1.12762 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.7721 | −1.54949 | −0.774743 | − | 0.632276i | \(-0.782121\pi\) | ||||
−0.774743 | + | 0.632276i | \(0.782121\pi\) | |||||||
\(80\) | 3.20362 | 0.358175 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.84796 | −0.204073 | ||||||||
\(83\) | 15.5888 | 1.71110 | 0.855549 | − | 0.517722i | \(-0.173220\pi\) | ||||
0.855549 | + | 0.517722i | \(0.173220\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.83304 | 0.415752 | ||||||||
\(86\) | −2.17379 | −0.234406 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.53843 | −0.696999 | ||||||||
\(89\) | 5.61844 | 0.595553 | 0.297777 | − | 0.954636i | \(-0.403755\pi\) | ||||
0.297777 | + | 0.954636i | \(0.403755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.36768 | 0.457857 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.4135 | −1.17721 | ||||||||
\(95\) | 1.77978 | 0.182602 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.24727 | −0.735848 | −0.367924 | − | 0.929856i | \(-0.619931\pi\) | ||||
−0.367924 | + | 0.929856i | \(0.619931\pi\) | |||||||
\(98\) | 4.70981 | 0.475763 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.26315 | 0.526315 | ||||||||
\(101\) | 1.02378 | 0.101870 | 0.0509348 | − | 0.998702i | \(-0.483780\pi\) | ||||
0.0509348 | + | 0.998702i | \(0.483780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.54925 | 0.448251 | 0.224125 | − | 0.974560i | \(-0.428048\pi\) | ||||
0.224125 | + | 0.974560i | \(0.428048\pi\) | |||||||
\(104\) | −2.88612 | −0.283008 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0613 | 1.17150 | ||||||||
\(107\) | 0.602987 | 0.0582929 | 0.0291465 | − | 0.999575i | \(-0.490721\pi\) | ||||
0.0291465 | + | 0.999575i | \(0.490721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.87577 | −0.562796 | −0.281398 | − | 0.959591i | \(-0.590798\pi\) | ||||
−0.281398 | + | 0.959591i | \(0.590798\pi\) | |||||||
\(110\) | −20.9466 | −1.99718 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.51334 | 0.142997 | ||||||||
\(113\) | −12.3076 | −1.15781 | −0.578903 | − | 0.815397i | \(-0.696519\pi\) | ||||
−0.578903 | + | 0.815397i | \(0.696519\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.66918 | 0.804913 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.96140 | 0.364676 | ||||||||
\(119\) | 1.81067 | 0.165984 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.7511 | 2.88646 | ||||||||
\(122\) | −9.03450 | −0.817945 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.73559 | −0.604874 | ||||||||
\(125\) | 0.843041 | 0.0754039 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.86983 | 0.787070 | 0.393535 | − | 0.919310i | \(-0.371252\pi\) | ||||
0.393535 | + | 0.919310i | \(0.371252\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.24603 | −0.810930 | ||||||||
\(131\) | −12.5385 | −1.09549 | −0.547745 | − | 0.836645i | \(-0.684514\pi\) | ||||
−0.547745 | + | 0.836645i | \(0.684514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.840741 | 0.0729015 | ||||||||
\(134\) | 7.66794 | 0.662409 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.19647 | −0.102597 | ||||||||
\(137\) | 13.6483 | 1.16606 | 0.583028 | − | 0.812452i | \(-0.301868\pi\) | ||||
0.583028 | + | 0.812452i | \(0.301868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6537 | −0.988455 | −0.494227 | − | 0.869333i | \(-0.664549\pi\) | ||||
−0.494227 | + | 0.869333i | \(0.664549\pi\) | |||||||
\(140\) | 4.84815 | 0.409743 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.45607 | −0.793536 | ||||||||
\(143\) | 18.8707 | 1.57805 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.7727 | 2.30640 | ||||||||
\(146\) | 0.627598 | 0.0519404 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.45380 | −0.119502 | ||||||||
\(149\) | −17.3034 | −1.41755 | −0.708776 | − | 0.705434i | \(-0.750752\pi\) | ||||
−0.708776 | + | 0.705434i | \(0.750752\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.83249 | −0.393262 | −0.196631 | − | 0.980478i | \(-0.563000\pi\) | ||||
−0.196631 | + | 0.980478i | \(0.563000\pi\) | |||||||
\(152\) | −0.555554 | −0.0450614 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.89485 | −0.797349 | ||||||||
\(155\) | −21.5782 | −1.73321 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.05031 | −0.403059 | −0.201529 | − | 0.979482i | \(-0.564591\pi\) | ||||
−0.201529 | + | 0.979482i | \(0.564591\pi\) | |||||||
\(158\) | 13.7721 | 1.09565 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.20362 | −0.253268 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.56743 | 0.279423 | 0.139711 | − | 0.990192i | \(-0.455383\pi\) | ||||
0.139711 | + | 0.990192i | \(0.455383\pi\) | |||||||
\(164\) | 1.84796 | 0.144301 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.5888 | −1.20993 | ||||||||
\(167\) | −4.56038 | −0.352893 | −0.176446 | − | 0.984310i | \(-0.556460\pi\) | ||||
−0.176446 | + | 0.984310i | \(0.556460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.67030 | −0.359254 | ||||||||
\(170\) | −3.83304 | −0.293981 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.17379 | 0.165750 | ||||||||
\(173\) | 15.6132 | 1.18705 | 0.593525 | − | 0.804816i | \(-0.297736\pi\) | ||||
0.593525 | + | 0.804816i | \(0.297736\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.96492 | 0.602092 | ||||||||
\(176\) | 6.53843 | 0.492853 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.61844 | −0.421120 | ||||||||
\(179\) | −6.40521 | −0.478748 | −0.239374 | − | 0.970927i | \(-0.576942\pi\) | ||||
−0.239374 | + | 0.970927i | \(0.576942\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.1363 | −1.64538 | −0.822691 | − | 0.568489i | \(-0.807528\pi\) | ||||
−0.822691 | + | 0.568489i | \(0.807528\pi\) | |||||||
\(182\) | −4.36768 | −0.323754 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.65742 | −0.342420 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.82306 | 0.572079 | ||||||||
\(188\) | 11.4135 | 0.832416 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.77978 | −0.129119 | ||||||||
\(191\) | 2.14915 | 0.155507 | 0.0777534 | − | 0.996973i | \(-0.475225\pi\) | ||||
0.0777534 | + | 0.996973i | \(0.475225\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2460 | −0.809506 | −0.404753 | − | 0.914426i | \(-0.632643\pi\) | ||||
−0.404753 | + | 0.914426i | \(0.632643\pi\) | |||||||
\(194\) | 7.24727 | 0.520323 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.70981 | −0.336415 | ||||||||
\(197\) | −10.4125 | −0.741860 | −0.370930 | − | 0.928661i | \(-0.620961\pi\) | ||||
−0.370930 | + | 0.928661i | \(0.620961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0998 | 1.07039 | 0.535197 | − | 0.844727i | \(-0.320237\pi\) | ||||
0.535197 | + | 0.844727i | \(0.320237\pi\) | |||||||
\(200\) | −5.26315 | −0.372161 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.02378 | −0.0720327 | ||||||||
\(203\) | 13.1194 | 0.920800 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.92014 | 0.413480 | ||||||||
\(206\) | −4.54925 | −0.316961 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.88612 | 0.200117 | ||||||||
\(209\) | 3.63245 | 0.251262 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4828 | 0.790512 | 0.395256 | − | 0.918571i | \(-0.370656\pi\) | ||||
0.395256 | + | 0.918571i | \(0.370656\pi\) | |||||||
\(212\) | −12.0613 | −0.828375 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.602987 | −0.0412193 | ||||||||
\(215\) | 6.96398 | 0.474940 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.1932 | −0.691961 | ||||||||
\(218\) | 5.87577 | 0.397957 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.9466 | 1.41222 | ||||||||
\(221\) | 3.45317 | 0.232285 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.8063 | −1.05847 | −0.529235 | − | 0.848475i | \(-0.677521\pi\) | ||||
−0.529235 | + | 0.848475i | \(0.677521\pi\) | |||||||
\(224\) | −1.51334 | −0.101114 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.3076 | 0.818692 | ||||||||
\(227\) | 2.59469 | 0.172216 | 0.0861079 | − | 0.996286i | \(-0.472557\pi\) | ||||
0.0861079 | + | 0.996286i | \(0.472557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.99374 | 0.660405 | 0.330202 | − | 0.943910i | \(-0.392883\pi\) | ||||
0.330202 | + | 0.943910i | \(0.392883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.66918 | −0.569159 | ||||||||
\(233\) | 27.2948 | 1.78814 | 0.894070 | − | 0.447927i | \(-0.147838\pi\) | ||||
0.894070 | + | 0.447927i | \(0.147838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.5645 | 2.38520 | ||||||||
\(236\) | −3.96140 | −0.257865 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.81067 | −0.117368 | ||||||||
\(239\) | −14.3187 | −0.926198 | −0.463099 | − | 0.886306i | \(-0.653263\pi\) | ||||
−0.463099 | + | 0.886306i | \(0.653263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1957 | 0.914428 | 0.457214 | − | 0.889357i | \(-0.348847\pi\) | ||||
0.457214 | + | 0.889357i | \(0.348847\pi\) | |||||||
\(242\) | −31.7511 | −2.04103 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.03450 | 0.578375 | ||||||||
\(245\) | −15.0884 | −0.963964 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.60340 | 0.102022 | ||||||||
\(248\) | 6.73559 | 0.427710 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.843041 | −0.0533186 | ||||||||
\(251\) | −11.9645 | −0.755194 | −0.377597 | − | 0.925970i | \(-0.623250\pi\) | ||||
−0.377597 | + | 0.925970i | \(0.623250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.86983 | −0.556543 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.9967 | −1.62163 | −0.810815 | − | 0.585302i | \(-0.800976\pi\) | ||||
−0.810815 | + | 0.585302i | \(0.800976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.20009 | −0.136707 | ||||||||
\(260\) | 9.24603 | 0.573414 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.5385 | 0.774629 | ||||||||
\(263\) | −5.74265 | −0.354107 | −0.177054 | − | 0.984201i | \(-0.556657\pi\) | ||||
−0.177054 | + | 0.984201i | \(0.556657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.6398 | −2.37363 | ||||||||
\(266\) | −0.840741 | −0.0515491 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.66794 | −0.468394 | ||||||||
\(269\) | −8.17926 | −0.498699 | −0.249349 | − | 0.968414i | \(-0.580217\pi\) | ||||
−0.249349 | + | 0.968414i | \(0.580217\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.5053 | −0.820386 | −0.410193 | − | 0.911999i | \(-0.634539\pi\) | ||||
−0.410193 | + | 0.911999i | \(0.634539\pi\) | |||||||
\(272\) | 1.19647 | 0.0725469 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6483 | −0.824526 | ||||||||
\(275\) | 34.4128 | 2.07517 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.9697 | 0.899440 | 0.449720 | − | 0.893169i | \(-0.351524\pi\) | ||||
0.449720 | + | 0.893169i | \(0.351524\pi\) | |||||||
\(278\) | 11.6537 | 0.698943 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.84815 | −0.289732 | ||||||||
\(281\) | −26.9740 | −1.60913 | −0.804566 | − | 0.593863i | \(-0.797602\pi\) | ||||
−0.804566 | + | 0.593863i | \(0.797602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7193 | 0.815528 | 0.407764 | − | 0.913087i | \(-0.366309\pi\) | ||||
0.407764 | + | 0.913087i | \(0.366309\pi\) | |||||||
\(284\) | 9.45607 | 0.561114 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.8707 | −1.11585 | ||||||||
\(287\) | 2.79658 | 0.165077 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5685 | −0.915791 | ||||||||
\(290\) | −27.7727 | −1.63087 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.627598 | −0.0367274 | ||||||||
\(293\) | −9.20499 | −0.537761 | −0.268881 | − | 0.963174i | \(-0.586654\pi\) | ||||
−0.268881 | + | 0.963174i | \(0.586654\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.6908 | −0.738887 | ||||||||
\(296\) | 1.45380 | 0.0845004 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.3034 | 1.00236 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.28968 | 0.189614 | ||||||||
\(302\) | 4.83249 | 0.278078 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.555554 | 0.0318632 | ||||||||
\(305\) | 28.9431 | 1.65728 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.75676 | 0.100264 | 0.0501319 | − | 0.998743i | \(-0.484036\pi\) | ||||
0.0501319 | + | 0.998743i | \(0.484036\pi\) | |||||||
\(308\) | 9.89485 | 0.563811 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21.5782 | 1.22556 | ||||||||
\(311\) | −30.3629 | −1.72172 | −0.860860 | − | 0.508841i | \(-0.830074\pi\) | ||||
−0.860860 | + | 0.508841i | \(0.830074\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0192 | 0.622843 | 0.311421 | − | 0.950272i | \(-0.399195\pi\) | ||||
0.311421 | + | 0.950272i | \(0.399195\pi\) | |||||||
\(314\) | 5.05031 | 0.285006 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.7721 | −0.774743 | ||||||||
\(317\) | 10.1471 | 0.569920 | 0.284960 | − | 0.958539i | \(-0.408020\pi\) | ||||
0.284960 | + | 0.958539i | \(0.408020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 56.6828 | 3.17363 | ||||||||
\(320\) | 3.20362 | 0.179088 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.664706 | 0.0369852 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.1901 | 0.842595 | ||||||||
\(326\) | −3.56743 | −0.197582 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.84796 | −0.102036 | ||||||||
\(329\) | 17.2725 | 0.952263 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.7790 | 1.63680 | 0.818401 | − | 0.574648i | \(-0.194861\pi\) | ||||
0.818401 | + | 0.574648i | \(0.194861\pi\) | |||||||
\(332\) | 15.5888 | 0.855549 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.56038 | 0.249533 | ||||||||
\(335\) | −24.5651 | −1.34214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.0588 | −1.03820 | −0.519100 | − | 0.854714i | \(-0.673733\pi\) | ||||
−0.519100 | + | 0.854714i | \(0.673733\pi\) | |||||||
\(338\) | 4.67030 | 0.254031 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.83304 | 0.207876 | ||||||||
\(341\) | −44.0402 | −2.38491 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.7209 | −0.956838 | ||||||||
\(344\) | −2.17379 | −0.117203 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.6132 | −0.839371 | ||||||||
\(347\) | 12.1929 | 0.654550 | 0.327275 | − | 0.944929i | \(-0.393870\pi\) | ||||
0.327275 | + | 0.944929i | \(0.393870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.4022 | −0.824459 | −0.412229 | − | 0.911080i | \(-0.635250\pi\) | ||||
−0.412229 | + | 0.911080i | \(0.635250\pi\) | |||||||
\(350\) | −7.96492 | −0.425743 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.53843 | −0.348499 | ||||||||
\(353\) | −18.5308 | −0.986295 | −0.493147 | − | 0.869946i | \(-0.664154\pi\) | ||||
−0.493147 | + | 0.869946i | \(0.664154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.2936 | 1.60782 | ||||||||
\(356\) | 5.61844 | 0.297777 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.40521 | 0.338526 | ||||||||
\(359\) | 11.7601 | 0.620673 | 0.310337 | − | 0.950627i | \(-0.399558\pi\) | ||||
0.310337 | + | 0.950627i | \(0.399558\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6914 | −0.983756 | ||||||||
\(362\) | 22.1363 | 1.16346 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.36768 | 0.228928 | ||||||||
\(365\) | −2.01058 | −0.105239 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.81907 | −0.408152 | −0.204076 | − | 0.978955i | \(-0.565419\pi\) | ||||
−0.204076 | + | 0.978955i | \(0.565419\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.65742 | 0.242127 | ||||||||
\(371\) | −18.2528 | −0.947640 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.13817 | 0.110710 | 0.0553550 | − | 0.998467i | \(-0.482371\pi\) | ||||
0.0553550 | + | 0.998467i | \(0.482371\pi\) | |||||||
\(374\) | −7.82306 | −0.404521 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.4135 | −0.588607 | ||||||||
\(377\) | 25.0203 | 1.28861 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6725 | −1.11324 | −0.556621 | − | 0.830767i | \(-0.687902\pi\) | ||||
−0.556621 | + | 0.830767i | \(0.687902\pi\) | |||||||
\(380\) | 1.77978 | 0.0913009 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.14915 | −0.109960 | ||||||||
\(383\) | −5.00975 | −0.255986 | −0.127993 | − | 0.991775i | \(-0.540854\pi\) | ||||
−0.127993 | + | 0.991775i | \(0.540854\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.6993 | 1.61555 | ||||||||
\(386\) | 11.2460 | 0.572407 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.24727 | −0.367924 | ||||||||
\(389\) | 6.02177 | 0.305316 | 0.152658 | − | 0.988279i | \(-0.451217\pi\) | ||||
0.152658 | + | 0.988279i | \(0.451217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 4.70981 | 0.237881 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.4125 | 0.524574 | ||||||||
\(395\) | −44.1206 | −2.21995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.0018 | 1.20461 | 0.602307 | − | 0.798265i | \(-0.294248\pi\) | ||||
0.602307 | + | 0.798265i | \(0.294248\pi\) | |||||||
\(398\) | −15.0998 | −0.756883 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.26315 | 0.263158 | ||||||||
\(401\) | 14.4766 | 0.722926 | 0.361463 | − | 0.932387i | \(-0.382277\pi\) | ||||
0.361463 | + | 0.932387i | \(0.382277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.4397 | −0.968362 | ||||||||
\(404\) | 1.02378 | 0.0509348 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.1194 | −0.651104 | ||||||||
\(407\) | −9.50557 | −0.471173 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.6435 | −1.61412 | −0.807059 | − | 0.590471i | \(-0.798942\pi\) | ||||
−0.807059 | + | 0.590471i | \(0.798942\pi\) | |||||||
\(410\) | −5.92014 | −0.292375 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.54925 | 0.224125 | ||||||||
\(413\) | −5.99493 | −0.294991 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49.9407 | 2.45149 | ||||||||
\(416\) | −2.88612 | −0.141504 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.63245 | −0.177669 | ||||||||
\(419\) | 36.2427 | 1.77057 | 0.885286 | − | 0.465046i | \(-0.153962\pi\) | ||||
0.885286 | + | 0.465046i | \(0.153962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.98570 | 0.340462 | 0.170231 | − | 0.985404i | \(-0.445549\pi\) | ||||
0.170231 | + | 0.985404i | \(0.445549\pi\) | |||||||
\(422\) | −11.4828 | −0.558976 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.0613 | 0.585749 | ||||||||
\(425\) | 6.29722 | 0.305460 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.6722 | 0.661646 | ||||||||
\(428\) | 0.602987 | 0.0291465 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.96398 | −0.335833 | ||||||||
\(431\) | 33.3054 | 1.60426 | 0.802132 | − | 0.597146i | \(-0.203699\pi\) | ||||
0.802132 | + | 0.597146i | \(0.203699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.5646 | −1.03633 | −0.518165 | − | 0.855281i | \(-0.673385\pi\) | ||||
−0.518165 | + | 0.855281i | \(0.673385\pi\) | |||||||
\(434\) | 10.1932 | 0.489290 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.87577 | −0.281398 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.2393 | 0.822785 | 0.411393 | − | 0.911458i | \(-0.365043\pi\) | ||||
0.411393 | + | 0.911458i | \(0.365043\pi\) | |||||||
\(440\) | −20.9466 | −0.998591 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.45317 | −0.164251 | ||||||||
\(443\) | −18.9166 | −0.898754 | −0.449377 | − | 0.893342i | \(-0.648354\pi\) | ||||
−0.449377 | + | 0.893342i | \(0.648354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.9993 | 0.853250 | ||||||||
\(446\) | 15.8063 | 0.748452 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.51334 | 0.0714985 | ||||||||
\(449\) | −23.0511 | −1.08785 | −0.543924 | − | 0.839134i | \(-0.683062\pi\) | ||||
−0.543924 | + | 0.839134i | \(0.683062\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0827 | 0.568953 | ||||||||
\(452\) | −12.3076 | −0.578903 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.59469 | −0.121775 | ||||||||
\(455\) | 13.9924 | 0.655972 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1904 | 0.710578 | 0.355289 | − | 0.934757i | \(-0.384383\pi\) | ||||
0.355289 | + | 0.934757i | \(0.384383\pi\) | |||||||
\(458\) | −9.99374 | −0.466977 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.2440 | −0.896281 | −0.448141 | − | 0.893963i | \(-0.647914\pi\) | ||||
−0.448141 | + | 0.893963i | \(0.647914\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.03240 | −0.140927 | −0.0704637 | − | 0.997514i | \(-0.522448\pi\) | ||||
−0.0704637 | + | 0.997514i | \(0.522448\pi\) | |||||||
\(464\) | 8.66918 | 0.402456 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.2948 | −1.26441 | ||||||||
\(467\) | −2.85012 | −0.131888 | −0.0659439 | − | 0.997823i | \(-0.521006\pi\) | ||||
−0.0659439 | + | 0.997823i | \(0.521006\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.6042 | −0.535831 | ||||||||
\(470\) | −36.5645 | −1.68659 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.96140 | 0.182338 | ||||||||
\(473\) | 14.2132 | 0.653522 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.92397 | 0.134161 | ||||||||
\(476\) | 1.81067 | 0.0829918 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.3187 | 0.654921 | ||||||||
\(479\) | −37.2607 | −1.70249 | −0.851243 | − | 0.524772i | \(-0.824151\pi\) | ||||
−0.851243 | + | 0.524772i | \(0.824151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.19584 | −0.191314 | ||||||||
\(482\) | −14.1957 | −0.646598 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 31.7511 | 1.44323 | ||||||||
\(485\) | −23.2175 | −1.05425 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.7455 | −1.39321 | −0.696606 | − | 0.717454i | \(-0.745307\pi\) | ||||
−0.696606 | + | 0.717454i | \(0.745307\pi\) | |||||||
\(488\) | −9.03450 | −0.408973 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.0884 | 0.681625 | ||||||||
\(491\) | −7.81494 | −0.352683 | −0.176342 | − | 0.984329i | \(-0.556426\pi\) | ||||
−0.176342 | + | 0.984329i | \(0.556426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.3724 | 0.467151 | ||||||||
\(494\) | −1.60340 | −0.0721403 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.73559 | −0.302437 | ||||||||
\(497\) | 14.3102 | 0.641901 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9597 | 0.580154 | 0.290077 | − | 0.957003i | \(-0.406319\pi\) | ||||
0.290077 | + | 0.957003i | \(0.406319\pi\) | |||||||
\(500\) | 0.843041 | 0.0377020 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11.9645 | 0.534003 | ||||||||
\(503\) | −19.6304 | −0.875276 | −0.437638 | − | 0.899151i | \(-0.644185\pi\) | ||||
−0.437638 | + | 0.899151i | \(0.644185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.27979 | 0.145949 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.86983 | 0.393535 | ||||||||
\(509\) | −6.25244 | −0.277134 | −0.138567 | − | 0.990353i | \(-0.544250\pi\) | ||||
−0.138567 | + | 0.990353i | \(0.544250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.949767 | −0.0420152 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 25.9967 | 1.14667 | ||||||||
\(515\) | 14.5740 | 0.642209 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 74.6264 | 3.28207 | ||||||||
\(518\) | 2.20009 | 0.0966664 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.24603 | −0.405465 | ||||||||
\(521\) | −23.9904 | −1.05104 | −0.525518 | − | 0.850782i | \(-0.676129\pi\) | ||||
−0.525518 | + | 0.850782i | \(0.676129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.42756 | −0.324784 | −0.162392 | − | 0.986726i | \(-0.551921\pi\) | ||||
−0.162392 | + | 0.986726i | \(0.551921\pi\) | |||||||
\(524\) | −12.5385 | −0.547745 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.74265 | 0.250392 | ||||||||
\(527\) | −8.05895 | −0.351054 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 38.6398 | 1.67841 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.840741 | 0.0364507 | ||||||||
\(533\) | 5.33343 | 0.231016 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.93174 | 0.0835163 | ||||||||
\(536\) | 7.66794 | 0.331204 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.17926 | 0.352633 | ||||||||
\(539\) | −30.7948 | −1.32642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4393 | 0.878752 | 0.439376 | − | 0.898303i | \(-0.355200\pi\) | ||||
0.439376 | + | 0.898303i | \(0.355200\pi\) | |||||||
\(542\) | 13.5053 | 0.580101 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.19647 | −0.0512984 | ||||||||
\(545\) | −18.8237 | −0.806318 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.31027 | −0.398078 | −0.199039 | − | 0.979992i | \(-0.563782\pi\) | ||||
−0.199039 | + | 0.979992i | \(0.563782\pi\) | |||||||
\(548\) | 13.6483 | 0.583028 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −34.4128 | −1.46736 | ||||||||
\(551\) | 4.81620 | 0.205177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.8419 | −0.886287 | ||||||||
\(554\) | −14.9697 | −0.636000 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.6537 | −0.494227 | ||||||||
\(557\) | 31.9209 | 1.35253 | 0.676265 | − | 0.736658i | \(-0.263597\pi\) | ||||
0.676265 | + | 0.736658i | \(0.263597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.27382 | 0.265354 | ||||||||
\(560\) | 4.84815 | 0.204872 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.9740 | 1.13783 | ||||||||
\(563\) | 16.8512 | 0.710195 | 0.355097 | − | 0.934829i | \(-0.384448\pi\) | ||||
0.355097 | + | 0.934829i | \(0.384448\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.4289 | −1.65879 | ||||||||
\(566\) | −13.7193 | −0.576665 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.45607 | −0.396768 | ||||||||
\(569\) | 2.18185 | 0.0914680 | 0.0457340 | − | 0.998954i | \(-0.485437\pi\) | ||||
0.0457340 | + | 0.998954i | \(0.485437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.97740 | −0.375693 | −0.187846 | − | 0.982198i | \(-0.560151\pi\) | ||||
−0.187846 | + | 0.982198i | \(0.560151\pi\) | |||||||
\(572\) | 18.8707 | 0.789024 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.79658 | −0.116727 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.1842 | −1.71452 | −0.857261 | − | 0.514882i | \(-0.827836\pi\) | ||||
−0.857261 | + | 0.514882i | \(0.827836\pi\) | |||||||
\(578\) | 15.5685 | 0.647562 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 27.7727 | 1.15320 | ||||||||
\(581\) | 23.5912 | 0.978727 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −78.8620 | −3.26613 | ||||||||
\(584\) | 0.627598 | 0.0259702 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.20499 | 0.380254 | ||||||||
\(587\) | −9.61116 | −0.396695 | −0.198348 | − | 0.980132i | \(-0.563557\pi\) | ||||
−0.198348 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.74198 | −0.154186 | ||||||||
\(590\) | 12.6908 | 0.522472 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.45380 | −0.0597508 | ||||||||
\(593\) | 36.4575 | 1.49713 | 0.748564 | − | 0.663062i | \(-0.230744\pi\) | ||||
0.748564 | + | 0.663062i | \(0.230744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.80068 | 0.237805 | ||||||||
\(596\) | −17.3034 | −0.708776 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.93439 | 0.283331 | 0.141666 | − | 0.989915i | \(-0.454754\pi\) | ||||
0.141666 | + | 0.989915i | \(0.454754\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.7707 | 0.684089 | 0.342045 | − | 0.939684i | \(-0.388881\pi\) | ||||
0.342045 | + | 0.939684i | \(0.388881\pi\) | |||||||
\(602\) | −3.28968 | −0.134077 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.83249 | −0.196631 | ||||||||
\(605\) | 101.718 | 4.13543 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.8715 | −0.441259 | −0.220629 | − | 0.975358i | \(-0.570811\pi\) | ||||
−0.220629 | + | 0.975358i | \(0.570811\pi\) | |||||||
\(608\) | −0.555554 | −0.0225307 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.9431 | −1.17187 | ||||||||
\(611\) | 32.9408 | 1.33264 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.7458 | 0.837914 | 0.418957 | − | 0.908006i | \(-0.362396\pi\) | ||||
0.418957 | + | 0.908006i | \(0.362396\pi\) | |||||||
\(614\) | −1.75676 | −0.0708972 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.89485 | −0.398675 | ||||||||
\(617\) | −3.09354 | −0.124541 | −0.0622706 | − | 0.998059i | \(-0.519834\pi\) | ||||
−0.0622706 | + | 0.998059i | \(0.519834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0130 | −0.523038 | −0.261519 | − | 0.965198i | \(-0.584223\pi\) | ||||
−0.261519 | + | 0.965198i | \(0.584223\pi\) | |||||||
\(620\) | −21.5782 | −0.866603 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.3629 | 1.21744 | ||||||||
\(623\) | 8.50259 | 0.340649 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.6150 | −0.944599 | ||||||||
\(626\) | −11.0192 | −0.440416 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.05031 | −0.201529 | ||||||||
\(629\) | −1.73943 | −0.0693557 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.82295 | 0.391045 | 0.195523 | − | 0.980699i | \(-0.437360\pi\) | ||||
0.195523 | + | 0.980699i | \(0.437360\pi\) | |||||||
\(632\) | 13.7721 | 0.547826 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.1471 | −0.402994 | ||||||||
\(635\) | 28.4155 | 1.12764 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.5931 | −0.538578 | ||||||||
\(638\) | −56.6828 | −2.24409 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.20362 | −0.126634 | ||||||||
\(641\) | −13.6360 | −0.538590 | −0.269295 | − | 0.963058i | \(-0.586791\pi\) | ||||
−0.269295 | + | 0.963058i | \(0.586791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.57857 | 0.141125 | 0.0705626 | − | 0.997507i | \(-0.477521\pi\) | ||||
0.0705626 | + | 0.997507i | \(0.477521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.664706 | −0.0261525 | ||||||||
\(647\) | 26.2492 | 1.03196 | 0.515982 | − | 0.856599i | \(-0.327427\pi\) | ||||
0.515982 | + | 0.856599i | \(0.327427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.9013 | −1.01672 | ||||||||
\(650\) | −15.1901 | −0.595805 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.56743 | 0.139711 | ||||||||
\(653\) | −25.7390 | −1.00725 | −0.503623 | − | 0.863923i | \(-0.668000\pi\) | ||||
−0.503623 | + | 0.863923i | \(0.668000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.1684 | −1.56951 | ||||||||
\(656\) | 1.84796 | 0.0721505 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.2725 | −0.673352 | ||||||||
\(659\) | 10.1996 | 0.397318 | 0.198659 | − | 0.980069i | \(-0.436341\pi\) | ||||
0.198659 | + | 0.980069i | \(0.436341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.9545 | −1.16509 | −0.582547 | − | 0.812797i | \(-0.697944\pi\) | ||||
−0.582547 | + | 0.812797i | \(0.697944\pi\) | |||||||
\(662\) | −29.7790 | −1.15739 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.5888 | −0.604965 | ||||||||
\(665\) | 2.69341 | 0.104446 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −4.56038 | −0.176446 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.5651 | 0.949034 | ||||||||
\(671\) | 59.0714 | 2.28043 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.02716 | −0.0781413 | −0.0390707 | − | 0.999236i | \(-0.512440\pi\) | ||||
−0.0390707 | + | 0.999236i | \(0.512440\pi\) | |||||||
\(674\) | 19.0588 | 0.734118 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.67030 | −0.179627 | ||||||||
\(677\) | −2.46315 | −0.0946664 | −0.0473332 | − | 0.998879i | \(-0.515072\pi\) | ||||
−0.0473332 | + | 0.998879i | \(0.515072\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9676 | −0.420896 | ||||||||
\(680\) | −3.83304 | −0.146990 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 44.0402 | 1.68638 | ||||||||
\(683\) | 30.3002 | 1.15941 | 0.579703 | − | 0.814828i | \(-0.303169\pi\) | ||||
0.579703 | + | 0.814828i | \(0.303169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.7240 | 1.67061 | ||||||||
\(686\) | 17.7209 | 0.676587 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.17379 | 0.0828749 | ||||||||
\(689\) | −34.8104 | −1.32617 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.71993 | −0.0654294 | −0.0327147 | − | 0.999465i | \(-0.510415\pi\) | ||||
−0.0327147 | + | 0.999465i | \(0.510415\pi\) | |||||||
\(692\) | 15.6132 | 0.593525 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.1929 | −0.462837 | ||||||||
\(695\) | −37.3340 | −1.41616 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.21103 | 0.0837487 | ||||||||
\(698\) | 15.4022 | 0.582980 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.96492 | 0.301046 | ||||||||
\(701\) | 0.739062 | 0.0279140 | 0.0139570 | − | 0.999903i | \(-0.495557\pi\) | ||||
0.0139570 | + | 0.999903i | \(0.495557\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.807665 | −0.0304616 | ||||||||
\(704\) | 6.53843 | 0.246426 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.5308 | 0.697416 | ||||||||
\(707\) | 1.54932 | 0.0582682 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.5819 | 0.848081 | 0.424040 | − | 0.905643i | \(-0.360611\pi\) | ||||
0.424040 | + | 0.905643i | \(0.360611\pi\) | |||||||
\(710\) | −30.2936 | −1.13690 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.61844 | −0.210560 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 60.4545 | 2.26087 | ||||||||
\(716\) | −6.40521 | −0.239374 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.7601 | −0.438882 | ||||||||
\(719\) | −10.9509 | −0.408400 | −0.204200 | − | 0.978929i | \(-0.565459\pi\) | ||||
−0.204200 | + | 0.978929i | \(0.565459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.88454 | 0.256394 | ||||||||
\(722\) | 18.6914 | 0.695620 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.1363 | −0.822691 | ||||||||
\(725\) | 45.6272 | 1.69455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.2793 | 1.38261 | 0.691307 | − | 0.722562i | \(-0.257035\pi\) | ||||
0.691307 | + | 0.722562i | \(0.257035\pi\) | |||||||
\(728\) | −4.36768 | −0.161877 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.01058 | 0.0744150 | ||||||||
\(731\) | 2.60088 | 0.0961971 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.1008 | 1.18567 | 0.592835 | − | 0.805324i | \(-0.298009\pi\) | ||||
0.592835 | + | 0.805324i | \(0.298009\pi\) | |||||||
\(734\) | 7.81907 | 0.288607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.1363 | −1.84679 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.5076 | 1.37974 | 0.689870 | − | 0.723934i | \(-0.257668\pi\) | ||||
0.689870 | + | 0.723934i | \(0.257668\pi\) | |||||||
\(740\) | −4.65742 | −0.171210 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.2528 | 0.670083 | ||||||||
\(743\) | −31.8791 | −1.16953 | −0.584766 | − | 0.811202i | \(-0.698814\pi\) | ||||
−0.584766 | + | 0.811202i | \(0.698814\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −55.4335 | −2.03093 | ||||||||
\(746\) | −2.13817 | −0.0782838 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.82306 | 0.286039 | ||||||||
\(749\) | 0.912522 | 0.0333428 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.9494 | −0.654983 | −0.327491 | − | 0.944854i | \(-0.606203\pi\) | ||||
−0.327491 | + | 0.944854i | \(0.606203\pi\) | |||||||
\(752\) | 11.4135 | 0.416208 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25.0203 | −0.911186 | ||||||||
\(755\) | −15.4814 | −0.563427 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.9617 | −0.398410 | −0.199205 | − | 0.979958i | \(-0.563836\pi\) | ||||
−0.199205 | + | 0.979958i | \(0.563836\pi\) | |||||||
\(758\) | 21.6725 | 0.787180 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.77978 | −0.0645595 | ||||||||
\(761\) | 0.365855 | 0.0132622 | 0.00663111 | − | 0.999978i | \(-0.497889\pi\) | ||||
0.00663111 | + | 0.999978i | \(0.497889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.89201 | −0.321912 | ||||||||
\(764\) | 2.14915 | 0.0777534 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.00975 | 0.181010 | ||||||||
\(767\) | −11.4331 | −0.412825 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.305975 | 0.0110337 | 0.00551686 | − | 0.999985i | \(-0.498244\pi\) | ||||
0.00551686 | + | 0.999985i | \(0.498244\pi\) | |||||||
\(770\) | −31.6993 | −1.14236 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.2460 | −0.404753 | ||||||||
\(773\) | 3.53034 | 0.126977 | 0.0634887 | − | 0.997983i | \(-0.479777\pi\) | ||||
0.0634887 | + | 0.997983i | \(0.479777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35.4504 | −1.27342 | ||||||||
\(776\) | 7.24727 | 0.260162 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.02177 | −0.215891 | ||||||||
\(779\) | 1.02664 | 0.0367832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 61.8278 | 2.21237 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.70981 | −0.168208 | ||||||||
\(785\) | −16.1793 | −0.577462 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.24943 | −0.0801837 | −0.0400918 | − | 0.999196i | \(-0.512765\pi\) | ||||
−0.0400918 | + | 0.999196i | \(0.512765\pi\) | |||||||
\(788\) | −10.4125 | −0.370930 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 44.1206 | 1.56974 | ||||||||
\(791\) | −18.6256 | −0.662250 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.0747 | 0.925939 | ||||||||
\(794\) | −24.0018 | −0.851790 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.0998 | 0.535197 | ||||||||
\(797\) | 39.6694 | 1.40516 | 0.702581 | − | 0.711604i | \(-0.252031\pi\) | ||||
0.702581 | + | 0.711604i | \(0.252031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6560 | 0.483113 | ||||||||
\(800\) | −5.26315 | −0.186081 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.4766 | −0.511186 | ||||||||
\(803\) | −4.10350 | −0.144810 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 19.4397 | 0.684735 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.02378 | −0.0360164 | ||||||||
\(809\) | 38.4898 | 1.35323 | 0.676614 | − | 0.736338i | \(-0.263447\pi\) | ||||
0.676614 | + | 0.736338i | \(0.263447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.4390 | −0.507021 | −0.253511 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253511 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(812\) | 13.1194 | 0.460400 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.50557 | 0.333170 | ||||||||
\(815\) | 11.4287 | 0.400329 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.20766 | 0.0422506 | ||||||||
\(818\) | 32.6435 | 1.14135 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.92014 | 0.206740 | ||||||||
\(821\) | −29.2724 | −1.02161 | −0.510806 | − | 0.859696i | \(-0.670653\pi\) | ||||
−0.510806 | + | 0.859696i | \(0.670653\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.6990 | −0.582091 | −0.291045 | − | 0.956709i | \(-0.594003\pi\) | ||||
−0.291045 | + | 0.956709i | \(0.594003\pi\) | |||||||
\(824\) | −4.54925 | −0.158481 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.99493 | 0.208590 | ||||||||
\(827\) | 20.3196 | 0.706582 | 0.353291 | − | 0.935514i | \(-0.385063\pi\) | ||||
0.353291 | + | 0.935514i | \(0.385063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.285271 | 0.00990788 | 0.00495394 | − | 0.999988i | \(-0.498423\pi\) | ||||
0.00495394 | + | 0.999988i | \(0.498423\pi\) | |||||||
\(830\) | −49.9407 | −1.73347 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.88612 | 0.100058 | ||||||||
\(833\) | −5.63517 | −0.195247 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6097 | −0.505589 | ||||||||
\(836\) | 3.63245 | 0.125631 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36.2427 | −1.25198 | ||||||||
\(839\) | 24.4524 | 0.844192 | 0.422096 | − | 0.906551i | \(-0.361295\pi\) | ||||
0.422096 | + | 0.906551i | \(0.361295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.1546 | 1.59154 | ||||||||
\(842\) | −6.98570 | −0.240743 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.4828 | 0.395256 | ||||||||
\(845\) | −14.9618 | −0.514703 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.0500 | 1.65102 | ||||||||
\(848\) | −12.0613 | −0.414187 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.29722 | −0.215993 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9592 | 0.991545 | 0.495773 | − | 0.868452i | \(-0.334885\pi\) | ||||
0.495773 | + | 0.868452i | \(0.334885\pi\) | |||||||
\(854\) | −13.6722 | −0.467855 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.602987 | −0.0206097 | ||||||||
\(857\) | 30.4523 | 1.04023 | 0.520116 | − | 0.854096i | \(-0.325889\pi\) | ||||
0.520116 | + | 0.854096i | \(0.325889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.3725 | 1.44573 | 0.722866 | − | 0.690988i | \(-0.242824\pi\) | ||||
0.722866 | + | 0.690988i | \(0.242824\pi\) | |||||||
\(860\) | 6.96398 | 0.237470 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.3054 | −1.13439 | ||||||||
\(863\) | 49.6854 | 1.69131 | 0.845655 | − | 0.533729i | \(-0.179210\pi\) | ||||
0.845655 | + | 0.533729i | \(0.179210\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.0187 | 1.70069 | ||||||||
\(866\) | 21.5646 | 0.732796 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.1932 | −0.345980 | ||||||||
\(869\) | −90.0482 | −3.05467 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.1306 | −0.749867 | ||||||||
\(872\) | 5.87577 | 0.198979 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.27581 | 0.0431301 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.98560 | 0.168352 | 0.0841759 | − | 0.996451i | \(-0.473174\pi\) | ||||
0.0841759 | + | 0.996451i | \(0.473174\pi\) | |||||||
\(878\) | −17.2393 | −0.581797 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 20.9466 | 0.706110 | ||||||||
\(881\) | −49.2503 | −1.65928 | −0.829642 | − | 0.558296i | \(-0.811455\pi\) | ||||
−0.829642 | + | 0.558296i | \(0.811455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.1640 | −0.981448 | −0.490724 | − | 0.871315i | \(-0.663268\pi\) | ||||
−0.490724 | + | 0.871315i | \(0.663268\pi\) | |||||||
\(884\) | 3.45317 | 0.116143 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.9166 | 0.635515 | ||||||||
\(887\) | −6.09320 | −0.204590 | −0.102295 | − | 0.994754i | \(-0.532619\pi\) | ||||
−0.102295 | + | 0.994754i | \(0.532619\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4230 | 0.450194 | ||||||||
\(890\) | −17.9993 | −0.603339 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.8063 | −0.529235 | ||||||||
\(893\) | 6.34082 | 0.212188 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.5198 | −0.685903 | ||||||||
\(896\) | −1.51334 | −0.0505570 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.0511 | 0.769225 | ||||||||
\(899\) | −58.3920 | −1.94748 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4310 | −0.480768 | ||||||||
\(902\) | −12.0827 | −0.402311 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.3076 | 0.409346 | ||||||||
\(905\) | −70.9163 | −2.35734 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.46052 | −0.0817004 | −0.0408502 | − | 0.999165i | \(-0.513007\pi\) | ||||
−0.0408502 | + | 0.999165i | \(0.513007\pi\) | |||||||
\(908\) | 2.59469 | 0.0861079 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.9924 | −0.463842 | ||||||||
\(911\) | 52.4143 | 1.73656 | 0.868281 | − | 0.496073i | \(-0.165225\pi\) | ||||
0.868281 | + | 0.496073i | \(0.165225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 101.927 | 3.37328 | ||||||||
\(914\) | −15.1904 | −0.502454 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.99374 | 0.330202 | ||||||||
\(917\) | −18.9749 | −0.626607 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.0132 | −0.396280 | −0.198140 | − | 0.980174i | \(-0.563490\pi\) | ||||
−0.198140 | + | 0.980174i | \(0.563490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.2440 | 0.633767 | ||||||||
\(923\) | 27.2914 | 0.898306 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.65157 | −0.251582 | ||||||||
\(926\) | 3.03240 | 0.0996507 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.66918 | −0.284580 | ||||||||
\(929\) | 17.2437 | 0.565747 | 0.282874 | − | 0.959157i | \(-0.408712\pi\) | ||||
0.282874 | + | 0.959157i | \(0.408712\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.61656 | −0.0857541 | ||||||||
\(932\) | 27.2948 | 0.894070 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.85012 | 0.0932588 | ||||||||
\(935\) | 25.0621 | 0.819617 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.8875 | 0.649696 | 0.324848 | − | 0.945766i | \(-0.394687\pi\) | ||||
0.324848 | + | 0.945766i | \(0.394687\pi\) | |||||||
\(938\) | 11.6042 | 0.378890 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 36.5645 | 1.19260 | ||||||||
\(941\) | 14.7942 | 0.482278 | 0.241139 | − | 0.970491i | \(-0.422479\pi\) | ||||
0.241139 | + | 0.970491i | \(0.422479\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.96140 | −0.128933 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.2132 | −0.462110 | ||||||||
\(947\) | 18.1501 | 0.589799 | 0.294900 | − | 0.955528i | \(-0.404714\pi\) | ||||
0.294900 | + | 0.955528i | \(0.404714\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.81132 | −0.0587981 | ||||||||
\(950\) | −2.92397 | −0.0948660 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.81067 | −0.0586841 | ||||||||
\(953\) | 26.1661 | 0.847605 | 0.423802 | − | 0.905755i | \(-0.360695\pi\) | ||||
0.423802 | + | 0.905755i | \(0.360695\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.88504 | 0.222795 | ||||||||
\(956\) | −14.3187 | −0.463099 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37.2607 | 1.20384 | ||||||||
\(959\) | 20.6545 | 0.666969 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.3681 | 0.463488 | ||||||||
\(962\) | 4.19584 | 0.135279 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.1957 | 0.457214 | ||||||||
\(965\) | −36.0279 | −1.15978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.8164 | −0.733726 | −0.366863 | − | 0.930275i | \(-0.619568\pi\) | ||||
−0.366863 | + | 0.930275i | \(0.619568\pi\) | |||||||
\(968\) | −31.7511 | −1.02052 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.2175 | 0.745468 | ||||||||
\(971\) | 2.27238 | 0.0729240 | 0.0364620 | − | 0.999335i | \(-0.488391\pi\) | ||||
0.0364620 | + | 0.999335i | \(0.488391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.6360 | −0.565384 | ||||||||
\(974\) | 30.7455 | 0.985150 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.03450 | 0.289187 | ||||||||
\(977\) | 37.7855 | 1.20887 | 0.604433 | − | 0.796656i | \(-0.293400\pi\) | ||||
0.604433 | + | 0.796656i | \(0.293400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.7358 | 1.17408 | ||||||||
\(980\) | −15.0884 | −0.481982 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.81494 | 0.249385 | ||||||||
\(983\) | 53.3063 | 1.70021 | 0.850104 | − | 0.526615i | \(-0.176539\pi\) | ||||
0.850104 | + | 0.526615i | \(0.176539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.3577 | −1.06286 | ||||||||
\(986\) | −10.3724 | −0.330326 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.60340 | 0.0510109 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.1670 | 0.545328 | 0.272664 | − | 0.962109i | \(-0.412095\pi\) | ||||
0.272664 | + | 0.962109i | \(0.412095\pi\) | |||||||
\(992\) | 6.73559 | 0.213855 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.3102 | −0.453893 | ||||||||
\(995\) | 48.3739 | 1.53356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.8767 | −0.914535 | −0.457268 | − | 0.889329i | \(-0.651172\pi\) | ||||
−0.457268 | + | 0.889329i | \(0.651172\pi\) | |||||||
\(998\) | −12.9597 | −0.410231 | ||||||||
\(999\) | 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 | 9522.2.a.bt.1.5 | 5 | ||
3.2 | odd | 2 | 3174.2.a.bc.1.1 | 5 | |||
23.3 | even | 11 | 414.2.i.d.55.1 | 10 | |||
23.8 | even | 11 | 414.2.i.d.271.1 | 10 | |||
23.22 | odd | 2 | 9522.2.a.bq.1.1 | 5 | |||
69.8 | odd | 22 | 138.2.e.a.133.1 | yes | 10 | ||
69.26 | odd | 22 | 138.2.e.a.55.1 | ✓ | 10 | ||
69.68 | even | 2 | 3174.2.a.bd.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.a.55.1 | ✓ | 10 | 69.26 | odd | 22 | ||
138.2.e.a.133.1 | yes | 10 | 69.8 | odd | 22 | ||
414.2.i.d.55.1 | 10 | 23.3 | even | 11 | |||
414.2.i.d.271.1 | 10 | 23.8 | even | 11 | |||
3174.2.a.bc.1.1 | 5 | 3.2 | odd | 2 | |||
3174.2.a.bd.1.5 | 5 | 69.68 | even | 2 | |||
9522.2.a.bq.1.1 | 5 | 23.22 | odd | 2 | |||
9522.2.a.bt.1.5 | 5 | 1.1 | even | 1 | trivial |