Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,2,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1617.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(12.9118100068\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −1.70711 | −0.853553 | − | 0.521005i | \(-0.825557\pi\) | ||||
−0.853553 | + | 0.521005i | \(0.825557\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.82843 | 1.91421 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | −2.41421 | −0.985599 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.82843 | 1.52688 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.82843 | 1.10517 | ||||||||
\(13\) | −0.828427 | −0.229764 | −0.114882 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114882 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | −4.41421 | −1.07060 | −0.535302 | − | 0.844661i | \(-0.679802\pi\) | ||||
−0.535302 | + | 0.844661i | \(0.679802\pi\) | |||||||
\(18\) | −2.41421 | −0.569036 | ||||||||
\(19\) | 7.24264 | 1.66158 | 0.830788 | − | 0.556589i | \(-0.187890\pi\) | ||||
0.830788 | + | 0.556589i | \(0.187890\pi\) | |||||||
\(20\) | −7.65685 | −1.71212 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.41421 | −0.514712 | ||||||||
\(23\) | −7.00000 | −1.45960 | −0.729800 | − | 0.683660i | \(-0.760387\pi\) | ||||
−0.729800 | + | 0.683660i | \(0.760387\pi\) | |||||||
\(24\) | −4.41421 | −0.901048 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.24264 | 0.602143 | 0.301072 | − | 0.953602i | \(-0.402656\pi\) | ||||
0.301072 | + | 0.953602i | \(0.402656\pi\) | |||||||
\(30\) | 4.82843 | 0.881546 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 1.58579 | 0.280330 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 10.6569 | 1.82764 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.82843 | 0.638071 | ||||||||
\(37\) | −9.48528 | −1.55937 | −0.779685 | − | 0.626172i | \(-0.784621\pi\) | ||||
−0.779685 | + | 0.626172i | \(0.784621\pi\) | |||||||
\(38\) | −17.4853 | −2.83649 | ||||||||
\(39\) | −0.828427 | −0.132655 | ||||||||
\(40\) | 8.82843 | 1.39590 | ||||||||
\(41\) | −1.17157 | −0.182969 | −0.0914845 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914845 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.75736 | −0.420493 | −0.210247 | − | 0.977648i | \(-0.567427\pi\) | ||||
−0.210247 | + | 0.977648i | \(0.567427\pi\) | |||||||
\(44\) | 3.82843 | 0.577157 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 16.8995 | 2.49169 | ||||||||
\(47\) | 9.82843 | 1.43362 | 0.716812 | − | 0.697267i | \(-0.245601\pi\) | ||||
0.716812 | + | 0.697267i | \(0.245601\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.41421 | 0.341421 | ||||||||
\(51\) | −4.41421 | −0.618114 | ||||||||
\(52\) | −3.17157 | −0.439818 | ||||||||
\(53\) | −7.17157 | −0.985091 | −0.492546 | − | 0.870287i | \(-0.663934\pi\) | ||||
−0.492546 | + | 0.870287i | \(0.663934\pi\) | |||||||
\(54\) | −2.41421 | −0.328533 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.24264 | 0.959311 | ||||||||
\(58\) | −7.82843 | −1.02792 | ||||||||
\(59\) | −8.65685 | −1.12703 | −0.563513 | − | 0.826107i | \(-0.690551\pi\) | ||||
−0.563513 | + | 0.826107i | \(0.690551\pi\) | |||||||
\(60\) | −7.65685 | −0.988496 | ||||||||
\(61\) | −4.00000 | −0.512148 | −0.256074 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(62\) | −13.6569 | −1.73442 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 1.65685 | 0.205507 | ||||||||
\(66\) | −2.41421 | −0.297169 | ||||||||
\(67\) | −3.17157 | −0.387469 | −0.193735 | − | 0.981054i | \(-0.562060\pi\) | ||||
−0.193735 | + | 0.981054i | \(0.562060\pi\) | |||||||
\(68\) | −16.8995 | −2.04936 | ||||||||
\(69\) | −7.00000 | −0.842701 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.17157 | −0.495075 | −0.247537 | − | 0.968878i | \(-0.579621\pi\) | ||||
−0.247537 | + | 0.968878i | \(0.579621\pi\) | |||||||
\(72\) | −4.41421 | −0.520220 | ||||||||
\(73\) | 0.343146 | 0.0401622 | 0.0200811 | − | 0.999798i | \(-0.493608\pi\) | ||||
0.0200811 | + | 0.999798i | \(0.493608\pi\) | |||||||
\(74\) | 22.8995 | 2.66201 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 27.7279 | 3.18061 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | 13.3137 | 1.49791 | 0.748955 | − | 0.662621i | \(-0.230556\pi\) | ||||
0.748955 | + | 0.662621i | \(0.230556\pi\) | |||||||
\(80\) | −6.00000 | −0.670820 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.82843 | 0.312348 | ||||||||
\(83\) | −2.82843 | −0.310460 | −0.155230 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155230 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.82843 | 0.957577 | ||||||||
\(86\) | 6.65685 | 0.717827 | ||||||||
\(87\) | 3.24264 | 0.347648 | ||||||||
\(88\) | −4.41421 | −0.470557 | ||||||||
\(89\) | −14.1421 | −1.49906 | −0.749532 | − | 0.661968i | \(-0.769721\pi\) | ||||
−0.749532 | + | 0.661968i | \(0.769721\pi\) | |||||||
\(90\) | 4.82843 | 0.508961 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −26.7990 | −2.79399 | ||||||||
\(93\) | 5.65685 | 0.586588 | ||||||||
\(94\) | −23.7279 | −2.44735 | ||||||||
\(95\) | −14.4853 | −1.48616 | ||||||||
\(96\) | 1.58579 | 0.161849 | ||||||||
\(97\) | −11.4853 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −3.82843 | −0.382843 | ||||||||
\(101\) | 4.89949 | 0.487518 | 0.243759 | − | 0.969836i | \(-0.421619\pi\) | ||||
0.243759 | + | 0.969836i | \(0.421619\pi\) | |||||||
\(102\) | 10.6569 | 1.05519 | ||||||||
\(103\) | 12.4853 | 1.23021 | 0.615106 | − | 0.788445i | \(-0.289113\pi\) | ||||
0.615106 | + | 0.788445i | \(0.289113\pi\) | |||||||
\(104\) | 3.65685 | 0.358584 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.3137 | 1.68166 | ||||||||
\(107\) | 9.65685 | 0.933563 | 0.466782 | − | 0.884373i | \(-0.345413\pi\) | ||||
0.466782 | + | 0.884373i | \(0.345413\pi\) | |||||||
\(108\) | 3.82843 | 0.368391 | ||||||||
\(109\) | −6.82843 | −0.654045 | −0.327022 | − | 0.945017i | \(-0.606045\pi\) | ||||
−0.327022 | + | 0.945017i | \(0.606045\pi\) | |||||||
\(110\) | 4.82843 | 0.460372 | ||||||||
\(111\) | −9.48528 | −0.900303 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.65685 | −0.720296 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(114\) | −17.4853 | −1.63765 | ||||||||
\(115\) | 14.0000 | 1.30551 | ||||||||
\(116\) | 12.4142 | 1.15263 | ||||||||
\(117\) | −0.828427 | −0.0765881 | ||||||||
\(118\) | 20.8995 | 1.92395 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.82843 | 0.805921 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.65685 | 0.874291 | ||||||||
\(123\) | −1.17157 | −0.105637 | ||||||||
\(124\) | 21.6569 | 1.94484 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0711 | −1.42608 | −0.713038 | − | 0.701125i | \(-0.752681\pi\) | ||||
−0.713038 | + | 0.701125i | \(0.752681\pi\) | |||||||
\(128\) | 20.5563 | 1.81694 | ||||||||
\(129\) | −2.75736 | −0.242772 | ||||||||
\(130\) | −4.00000 | −0.350823 | ||||||||
\(131\) | −5.17157 | −0.451842 | −0.225921 | − | 0.974146i | \(-0.572539\pi\) | ||||
−0.225921 | + | 0.974146i | \(0.572539\pi\) | |||||||
\(132\) | 3.82843 | 0.333222 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 7.65685 | 0.661451 | ||||||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | 19.4853 | 1.67085 | ||||||||
\(137\) | 0.485281 | 0.0414604 | 0.0207302 | − | 0.999785i | \(-0.493401\pi\) | ||||
0.0207302 | + | 0.999785i | \(0.493401\pi\) | |||||||
\(138\) | 16.8995 | 1.43858 | ||||||||
\(139\) | 8.41421 | 0.713684 | 0.356842 | − | 0.934165i | \(-0.383853\pi\) | ||||
0.356842 | + | 0.934165i | \(0.383853\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.82843 | 0.827703 | ||||||||
\(142\) | 10.0711 | 0.845145 | ||||||||
\(143\) | −0.828427 | −0.0692766 | ||||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | −6.48528 | −0.538573 | ||||||||
\(146\) | −0.828427 | −0.0685611 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −36.3137 | −2.98497 | ||||||||
\(149\) | −22.2132 | −1.81978 | −0.909888 | − | 0.414853i | \(-0.863833\pi\) | ||||
−0.909888 | + | 0.414853i | \(0.863833\pi\) | |||||||
\(150\) | 2.41421 | 0.197120 | ||||||||
\(151\) | −18.8995 | −1.53802 | −0.769010 | − | 0.639237i | \(-0.779250\pi\) | ||||
−0.769010 | + | 0.639237i | \(0.779250\pi\) | |||||||
\(152\) | −31.9706 | −2.59316 | ||||||||
\(153\) | −4.41421 | −0.356868 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.3137 | −0.908739 | ||||||||
\(156\) | −3.17157 | −0.253929 | ||||||||
\(157\) | 7.00000 | 0.558661 | 0.279330 | − | 0.960195i | \(-0.409888\pi\) | ||||
0.279330 | + | 0.960195i | \(0.409888\pi\) | |||||||
\(158\) | −32.1421 | −2.55709 | ||||||||
\(159\) | −7.17157 | −0.568743 | ||||||||
\(160\) | −3.17157 | −0.250735 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.41421 | −0.189679 | ||||||||
\(163\) | −20.9706 | −1.64254 | −0.821271 | − | 0.570539i | \(-0.806734\pi\) | ||||
−0.821271 | + | 0.570539i | \(0.806734\pi\) | |||||||
\(164\) | −4.48528 | −0.350242 | ||||||||
\(165\) | −2.00000 | −0.155700 | ||||||||
\(166\) | 6.82843 | 0.529989 | ||||||||
\(167\) | 5.17157 | 0.400188 | 0.200094 | − | 0.979777i | \(-0.435875\pi\) | ||||
0.200094 | + | 0.979777i | \(0.435875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3137 | −0.947208 | ||||||||
\(170\) | −21.3137 | −1.63469 | ||||||||
\(171\) | 7.24264 | 0.553859 | ||||||||
\(172\) | −10.5563 | −0.804914 | ||||||||
\(173\) | −14.8284 | −1.12738 | −0.563692 | − | 0.825985i | \(-0.690620\pi\) | ||||
−0.563692 | + | 0.825985i | \(0.690620\pi\) | |||||||
\(174\) | −7.82843 | −0.593472 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | −8.65685 | −0.650689 | ||||||||
\(178\) | 34.1421 | 2.55906 | ||||||||
\(179\) | 17.8284 | 1.33256 | 0.666280 | − | 0.745702i | \(-0.267886\pi\) | ||||
0.666280 | + | 0.745702i | \(0.267886\pi\) | |||||||
\(180\) | −7.65685 | −0.570708 | ||||||||
\(181\) | −11.6569 | −0.866447 | −0.433224 | − | 0.901286i | \(-0.642624\pi\) | ||||
−0.433224 | + | 0.901286i | \(0.642624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | 30.8995 | 2.27794 | ||||||||
\(185\) | 18.9706 | 1.39474 | ||||||||
\(186\) | −13.6569 | −1.00137 | ||||||||
\(187\) | −4.41421 | −0.322799 | ||||||||
\(188\) | 37.6274 | 2.74426 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 34.9706 | 2.53703 | ||||||||
\(191\) | −21.6569 | −1.56703 | −0.783517 | − | 0.621370i | \(-0.786577\pi\) | ||||
−0.783517 | + | 0.621370i | \(0.786577\pi\) | |||||||
\(192\) | −9.82843 | −0.709306 | ||||||||
\(193\) | −12.1421 | −0.874010 | −0.437005 | − | 0.899459i | \(-0.643961\pi\) | ||||
−0.437005 | + | 0.899459i | \(0.643961\pi\) | |||||||
\(194\) | 27.7279 | 1.99075 | ||||||||
\(195\) | 1.65685 | 0.118650 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.4142 | −1.16946 | −0.584732 | − | 0.811226i | \(-0.698800\pi\) | ||||
−0.584732 | + | 0.811226i | \(0.698800\pi\) | |||||||
\(198\) | −2.41421 | −0.171571 | ||||||||
\(199\) | −19.7990 | −1.40351 | −0.701757 | − | 0.712417i | \(-0.747601\pi\) | ||||
−0.701757 | + | 0.712417i | \(0.747601\pi\) | |||||||
\(200\) | 4.41421 | 0.312132 | ||||||||
\(201\) | −3.17157 | −0.223706 | ||||||||
\(202\) | −11.8284 | −0.832245 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −16.8995 | −1.18320 | ||||||||
\(205\) | 2.34315 | 0.163652 | ||||||||
\(206\) | −30.1421 | −2.10010 | ||||||||
\(207\) | −7.00000 | −0.486534 | ||||||||
\(208\) | −2.48528 | −0.172323 | ||||||||
\(209\) | 7.24264 | 0.500984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9706 | 1.03062 | 0.515308 | − | 0.857005i | \(-0.327678\pi\) | ||||
0.515308 | + | 0.857005i | \(0.327678\pi\) | |||||||
\(212\) | −27.4558 | −1.88568 | ||||||||
\(213\) | −4.17157 | −0.285831 | ||||||||
\(214\) | −23.3137 | −1.59369 | ||||||||
\(215\) | 5.51472 | 0.376101 | ||||||||
\(216\) | −4.41421 | −0.300349 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.4853 | 1.11652 | ||||||||
\(219\) | 0.343146 | 0.0231876 | ||||||||
\(220\) | −7.65685 | −0.516225 | ||||||||
\(221\) | 3.65685 | 0.245987 | ||||||||
\(222\) | 22.8995 | 1.53691 | ||||||||
\(223\) | −22.9706 | −1.53822 | −0.769111 | − | 0.639115i | \(-0.779301\pi\) | ||||
−0.769111 | + | 0.639115i | \(0.779301\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 18.4853 | 1.22962 | ||||||||
\(227\) | 14.9706 | 0.993631 | 0.496816 | − | 0.867856i | \(-0.334503\pi\) | ||||
0.496816 | + | 0.867856i | \(0.334503\pi\) | |||||||
\(228\) | 27.7279 | 1.83633 | ||||||||
\(229\) | −15.6569 | −1.03463 | −0.517317 | − | 0.855794i | \(-0.673069\pi\) | ||||
−0.517317 | + | 0.855794i | \(0.673069\pi\) | |||||||
\(230\) | −33.7990 | −2.22864 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.3137 | −0.939741 | ||||||||
\(233\) | 10.4142 | 0.682258 | 0.341129 | − | 0.940017i | \(-0.389191\pi\) | ||||
0.341129 | + | 0.940017i | \(0.389191\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | −19.6569 | −1.28227 | ||||||||
\(236\) | −33.1421 | −2.15737 | ||||||||
\(237\) | 13.3137 | 0.864818 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.48528 | −0.419498 | −0.209749 | − | 0.977755i | \(-0.567265\pi\) | ||||
−0.209749 | + | 0.977755i | \(0.567265\pi\) | |||||||
\(240\) | −6.00000 | −0.387298 | ||||||||
\(241\) | 7.31371 | 0.471117 | 0.235559 | − | 0.971860i | \(-0.424308\pi\) | ||||
0.235559 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(242\) | −2.41421 | −0.155192 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −15.3137 | −0.980360 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.82843 | 0.180334 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | −24.9706 | −1.58563 | ||||||||
\(249\) | −2.82843 | −0.179244 | ||||||||
\(250\) | −28.9706 | −1.83226 | ||||||||
\(251\) | −2.51472 | −0.158728 | −0.0793638 | − | 0.996846i | \(-0.525289\pi\) | ||||
−0.0793638 | + | 0.996846i | \(0.525289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.00000 | −0.440086 | ||||||||
\(254\) | 38.7990 | 2.43447 | ||||||||
\(255\) | 8.82843 | 0.552858 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 21.4558 | 1.33838 | 0.669189 | − | 0.743092i | \(-0.266641\pi\) | ||||
0.669189 | + | 0.743092i | \(0.266641\pi\) | |||||||
\(258\) | 6.65685 | 0.414438 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.34315 | 0.393385 | ||||||||
\(261\) | 3.24264 | 0.200714 | ||||||||
\(262\) | 12.4853 | 0.771343 | ||||||||
\(263\) | 18.0000 | 1.10993 | 0.554964 | − | 0.831875i | \(-0.312732\pi\) | ||||
0.554964 | + | 0.831875i | \(0.312732\pi\) | |||||||
\(264\) | −4.41421 | −0.271676 | ||||||||
\(265\) | 14.3431 | 0.881092 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.1421 | −0.865485 | ||||||||
\(268\) | −12.1421 | −0.741699 | ||||||||
\(269\) | −27.7990 | −1.69493 | −0.847467 | − | 0.530848i | \(-0.821874\pi\) | ||||
−0.847467 | + | 0.530848i | \(0.821874\pi\) | |||||||
\(270\) | 4.82843 | 0.293849 | ||||||||
\(271\) | −22.9706 | −1.39536 | −0.697681 | − | 0.716408i | \(-0.745785\pi\) | ||||
−0.697681 | + | 0.716408i | \(0.745785\pi\) | |||||||
\(272\) | −13.2426 | −0.802953 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.17157 | −0.0707773 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −26.7990 | −1.61311 | ||||||||
\(277\) | −25.6569 | −1.54157 | −0.770785 | − | 0.637095i | \(-0.780136\pi\) | ||||
−0.770785 | + | 0.637095i | \(0.780136\pi\) | |||||||
\(278\) | −20.3137 | −1.21834 | ||||||||
\(279\) | 5.65685 | 0.338667 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4142 | 0.859880 | 0.429940 | − | 0.902857i | \(-0.358535\pi\) | ||||
0.429940 | + | 0.902857i | \(0.358535\pi\) | |||||||
\(282\) | −23.7279 | −1.41298 | ||||||||
\(283\) | 20.3431 | 1.20927 | 0.604637 | − | 0.796501i | \(-0.293318\pi\) | ||||
0.604637 | + | 0.796501i | \(0.293318\pi\) | |||||||
\(284\) | −15.9706 | −0.947679 | ||||||||
\(285\) | −14.4853 | −0.858034 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.58579 | 0.0934434 | ||||||||
\(289\) | 2.48528 | 0.146193 | ||||||||
\(290\) | 15.6569 | 0.919402 | ||||||||
\(291\) | −11.4853 | −0.673279 | ||||||||
\(292\) | 1.31371 | 0.0768790 | ||||||||
\(293\) | 5.72792 | 0.334629 | 0.167314 | − | 0.985904i | \(-0.446491\pi\) | ||||
0.167314 | + | 0.985904i | \(0.446491\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.3137 | 1.00804 | ||||||||
\(296\) | 41.8701 | 2.43365 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 53.6274 | 3.10655 | ||||||||
\(299\) | 5.79899 | 0.335364 | ||||||||
\(300\) | −3.82843 | −0.221034 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 45.6274 | 2.62556 | ||||||||
\(303\) | 4.89949 | 0.281469 | ||||||||
\(304\) | 21.7279 | 1.24618 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 10.6569 | 0.609212 | ||||||||
\(307\) | −17.3137 | −0.988146 | −0.494073 | − | 0.869421i | \(-0.664492\pi\) | ||||
−0.494073 | + | 0.869421i | \(0.664492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.4853 | 0.710263 | ||||||||
\(310\) | 27.3137 | 1.55131 | ||||||||
\(311\) | 29.6274 | 1.68002 | 0.840008 | − | 0.542573i | \(-0.182550\pi\) | ||||
0.840008 | + | 0.542573i | \(0.182550\pi\) | |||||||
\(312\) | 3.65685 | 0.207029 | ||||||||
\(313\) | 4.79899 | 0.271255 | 0.135627 | − | 0.990760i | \(-0.456695\pi\) | ||||
0.135627 | + | 0.990760i | \(0.456695\pi\) | |||||||
\(314\) | −16.8995 | −0.953694 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 50.9706 | 2.86732 | ||||||||
\(317\) | −25.3137 | −1.42176 | −0.710880 | − | 0.703314i | \(-0.751703\pi\) | ||||
−0.710880 | + | 0.703314i | \(0.751703\pi\) | |||||||
\(318\) | 17.3137 | 0.970905 | ||||||||
\(319\) | 3.24264 | 0.181553 | ||||||||
\(320\) | 19.6569 | 1.09885 | ||||||||
\(321\) | 9.65685 | 0.538993 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.9706 | −1.77889 | ||||||||
\(324\) | 3.82843 | 0.212690 | ||||||||
\(325\) | 0.828427 | 0.0459529 | ||||||||
\(326\) | 50.6274 | 2.80399 | ||||||||
\(327\) | −6.82843 | −0.377613 | ||||||||
\(328\) | 5.17157 | 0.285552 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 4.82843 | 0.265796 | ||||||||
\(331\) | 22.4853 | 1.23590 | 0.617951 | − | 0.786216i | \(-0.287963\pi\) | ||||
0.617951 | + | 0.786216i | \(0.287963\pi\) | |||||||
\(332\) | −10.8284 | −0.594287 | ||||||||
\(333\) | −9.48528 | −0.519790 | ||||||||
\(334\) | −12.4853 | −0.683164 | ||||||||
\(335\) | 6.34315 | 0.346563 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.85786 | 0.210151 | 0.105076 | − | 0.994464i | \(-0.466492\pi\) | ||||
0.105076 | + | 0.994464i | \(0.466492\pi\) | |||||||
\(338\) | 29.7279 | 1.61699 | ||||||||
\(339\) | −7.65685 | −0.415863 | ||||||||
\(340\) | 33.7990 | 1.83301 | ||||||||
\(341\) | 5.65685 | 0.306336 | ||||||||
\(342\) | −17.4853 | −0.945496 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.1716 | 0.656247 | ||||||||
\(345\) | 14.0000 | 0.753735 | ||||||||
\(346\) | 35.7990 | 1.92457 | ||||||||
\(347\) | 14.9706 | 0.803662 | 0.401831 | − | 0.915714i | \(-0.368374\pi\) | ||||
0.401831 | + | 0.915714i | \(0.368374\pi\) | |||||||
\(348\) | 12.4142 | 0.665472 | ||||||||
\(349\) | 10.9706 | 0.587241 | 0.293620 | − | 0.955922i | \(-0.405140\pi\) | ||||
0.293620 | + | 0.955922i | \(0.405140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.828427 | −0.0442182 | ||||||||
\(352\) | 1.58579 | 0.0845227 | ||||||||
\(353\) | 13.3137 | 0.708617 | 0.354309 | − | 0.935129i | \(-0.384716\pi\) | ||||
0.354309 | + | 0.935129i | \(0.384716\pi\) | |||||||
\(354\) | 20.8995 | 1.11080 | ||||||||
\(355\) | 8.34315 | 0.442808 | ||||||||
\(356\) | −54.1421 | −2.86953 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −43.0416 | −2.27482 | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 8.82843 | 0.465299 | ||||||||
\(361\) | 33.4558 | 1.76083 | ||||||||
\(362\) | 28.1421 | 1.47912 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.686292 | −0.0359221 | ||||||||
\(366\) | 9.65685 | 0.504772 | ||||||||
\(367\) | −4.14214 | −0.216218 | −0.108109 | − | 0.994139i | \(-0.534480\pi\) | ||||
−0.108109 | + | 0.994139i | \(0.534480\pi\) | |||||||
\(368\) | −21.0000 | −1.09470 | ||||||||
\(369\) | −1.17157 | −0.0609896 | ||||||||
\(370\) | −45.7990 | −2.38098 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 21.6569 | 1.12286 | ||||||||
\(373\) | −1.65685 | −0.0857887 | −0.0428943 | − | 0.999080i | \(-0.513658\pi\) | ||||
−0.0428943 | + | 0.999080i | \(0.513658\pi\) | |||||||
\(374\) | 10.6569 | 0.551053 | ||||||||
\(375\) | 12.0000 | 0.619677 | ||||||||
\(376\) | −43.3848 | −2.23740 | ||||||||
\(377\) | −2.68629 | −0.138351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8284 | 0.967151 | 0.483576 | − | 0.875303i | \(-0.339338\pi\) | ||||
0.483576 | + | 0.875303i | \(0.339338\pi\) | |||||||
\(380\) | −55.4558 | −2.84482 | ||||||||
\(381\) | −16.0711 | −0.823346 | ||||||||
\(382\) | 52.2843 | 2.67510 | ||||||||
\(383\) | 2.31371 | 0.118225 | 0.0591125 | − | 0.998251i | \(-0.481173\pi\) | ||||
0.0591125 | + | 0.998251i | \(0.481173\pi\) | |||||||
\(384\) | 20.5563 | 1.04901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 29.3137 | 1.49203 | ||||||||
\(387\) | −2.75736 | −0.140164 | ||||||||
\(388\) | −43.9706 | −2.23227 | ||||||||
\(389\) | −11.7990 | −0.598233 | −0.299116 | − | 0.954217i | \(-0.596692\pi\) | ||||
−0.299116 | + | 0.954217i | \(0.596692\pi\) | |||||||
\(390\) | −4.00000 | −0.202548 | ||||||||
\(391\) | 30.8995 | 1.56265 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.17157 | −0.260871 | ||||||||
\(394\) | 39.6274 | 1.99640 | ||||||||
\(395\) | −26.6274 | −1.33977 | ||||||||
\(396\) | 3.82843 | 0.192386 | ||||||||
\(397\) | 17.4853 | 0.877561 | 0.438781 | − | 0.898594i | \(-0.355411\pi\) | ||||
0.438781 | + | 0.898594i | \(0.355411\pi\) | |||||||
\(398\) | 47.7990 | 2.39595 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | 7.51472 | 0.375267 | 0.187634 | − | 0.982239i | \(-0.439918\pi\) | ||||
0.187634 | + | 0.982239i | \(0.439918\pi\) | |||||||
\(402\) | 7.65685 | 0.381889 | ||||||||
\(403\) | −4.68629 | −0.233441 | ||||||||
\(404\) | 18.7574 | 0.933214 | ||||||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.48528 | −0.470168 | ||||||||
\(408\) | 19.4853 | 0.964665 | ||||||||
\(409\) | −7.79899 | −0.385635 | −0.192818 | − | 0.981235i | \(-0.561763\pi\) | ||||
−0.192818 | + | 0.981235i | \(0.561763\pi\) | |||||||
\(410\) | −5.65685 | −0.279372 | ||||||||
\(411\) | 0.485281 | 0.0239372 | ||||||||
\(412\) | 47.7990 | 2.35489 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.8995 | 0.830565 | ||||||||
\(415\) | 5.65685 | 0.277684 | ||||||||
\(416\) | −1.31371 | −0.0644099 | ||||||||
\(417\) | 8.41421 | 0.412046 | ||||||||
\(418\) | −17.4853 | −0.855233 | ||||||||
\(419\) | 14.7990 | 0.722978 | 0.361489 | − | 0.932376i | \(-0.382269\pi\) | ||||
0.361489 | + | 0.932376i | \(0.382269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.00000 | −0.341159 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(422\) | −36.1421 | −1.75937 | ||||||||
\(423\) | 9.82843 | 0.477874 | ||||||||
\(424\) | 31.6569 | 1.53739 | ||||||||
\(425\) | 4.41421 | 0.214121 | ||||||||
\(426\) | 10.0711 | 0.487945 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 36.9706 | 1.78704 | ||||||||
\(429\) | −0.828427 | −0.0399968 | ||||||||
\(430\) | −13.3137 | −0.642044 | ||||||||
\(431\) | 6.97056 | 0.335760 | 0.167880 | − | 0.985807i | \(-0.446308\pi\) | ||||
0.167880 | + | 0.985807i | \(0.446308\pi\) | |||||||
\(432\) | 3.00000 | 0.144338 | ||||||||
\(433\) | 0.857864 | 0.0412263 | 0.0206132 | − | 0.999788i | \(-0.493438\pi\) | ||||
0.0206132 | + | 0.999788i | \(0.493438\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.48528 | −0.310945 | ||||||||
\(436\) | −26.1421 | −1.25198 | ||||||||
\(437\) | −50.6985 | −2.42524 | ||||||||
\(438\) | −0.828427 | −0.0395838 | ||||||||
\(439\) | 30.8995 | 1.47475 | 0.737376 | − | 0.675482i | \(-0.236065\pi\) | ||||
0.737376 | + | 0.675482i | \(0.236065\pi\) | |||||||
\(440\) | 8.82843 | 0.420879 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.82843 | −0.419925 | ||||||||
\(443\) | 33.6274 | 1.59769 | 0.798843 | − | 0.601539i | \(-0.205446\pi\) | ||||
0.798843 | + | 0.601539i | \(0.205446\pi\) | |||||||
\(444\) | −36.3137 | −1.72337 | ||||||||
\(445\) | 28.2843 | 1.34080 | ||||||||
\(446\) | 55.4558 | 2.62591 | ||||||||
\(447\) | −22.2132 | −1.05065 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.00000 | −0.188772 | −0.0943858 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943858 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(450\) | 2.41421 | 0.113807 | ||||||||
\(451\) | −1.17157 | −0.0551672 | ||||||||
\(452\) | −29.3137 | −1.37880 | ||||||||
\(453\) | −18.8995 | −0.887976 | ||||||||
\(454\) | −36.1421 | −1.69623 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −31.9706 | −1.49716 | ||||||||
\(457\) | 18.8284 | 0.880757 | 0.440378 | − | 0.897812i | \(-0.354844\pi\) | ||||
0.440378 | + | 0.897812i | \(0.354844\pi\) | |||||||
\(458\) | 37.7990 | 1.76623 | ||||||||
\(459\) | −4.41421 | −0.206038 | ||||||||
\(460\) | 53.5980 | 2.49902 | ||||||||
\(461\) | 6.75736 | 0.314722 | 0.157361 | − | 0.987541i | \(-0.449701\pi\) | ||||
0.157361 | + | 0.987541i | \(0.449701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6274 | 0.865689 | 0.432845 | − | 0.901468i | \(-0.357510\pi\) | ||||
0.432845 | + | 0.901468i | \(0.357510\pi\) | |||||||
\(464\) | 9.72792 | 0.451607 | ||||||||
\(465\) | −11.3137 | −0.524661 | ||||||||
\(466\) | −25.1421 | −1.16469 | ||||||||
\(467\) | −8.31371 | −0.384713 | −0.192356 | − | 0.981325i | \(-0.561613\pi\) | ||||
−0.192356 | + | 0.981325i | \(0.561613\pi\) | |||||||
\(468\) | −3.17157 | −0.146606 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 47.4558 | 2.18897 | ||||||||
\(471\) | 7.00000 | 0.322543 | ||||||||
\(472\) | 38.2132 | 1.75891 | ||||||||
\(473\) | −2.75736 | −0.126784 | ||||||||
\(474\) | −32.1421 | −1.47634 | ||||||||
\(475\) | −7.24264 | −0.332315 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.17157 | −0.328364 | ||||||||
\(478\) | 15.6569 | 0.716128 | ||||||||
\(479\) | 14.0000 | 0.639676 | 0.319838 | − | 0.947472i | \(-0.396371\pi\) | ||||
0.319838 | + | 0.947472i | \(0.396371\pi\) | |||||||
\(480\) | −3.17157 | −0.144762 | ||||||||
\(481\) | 7.85786 | 0.358288 | ||||||||
\(482\) | −17.6569 | −0.804248 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.82843 | 0.174019 | ||||||||
\(485\) | 22.9706 | 1.04304 | ||||||||
\(486\) | −2.41421 | −0.109511 | ||||||||
\(487\) | −32.6274 | −1.47849 | −0.739245 | − | 0.673437i | \(-0.764817\pi\) | ||||
−0.739245 | + | 0.673437i | \(0.764817\pi\) | |||||||
\(488\) | 17.6569 | 0.799288 | ||||||||
\(489\) | −20.9706 | −0.948322 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.51472 | −0.0683583 | −0.0341791 | − | 0.999416i | \(-0.510882\pi\) | ||||
−0.0341791 | + | 0.999416i | \(0.510882\pi\) | |||||||
\(492\) | −4.48528 | −0.202212 | ||||||||
\(493\) | −14.3137 | −0.644657 | ||||||||
\(494\) | 14.4853 | 0.651724 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | 16.9706 | 0.762001 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.82843 | 0.305989 | ||||||||
\(499\) | −31.7990 | −1.42352 | −0.711759 | − | 0.702424i | \(-0.752101\pi\) | ||||
−0.711759 | + | 0.702424i | \(0.752101\pi\) | |||||||
\(500\) | 45.9411 | 2.05455 | ||||||||
\(501\) | 5.17157 | 0.231049 | ||||||||
\(502\) | 6.07107 | 0.270965 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.79899 | −0.436049 | ||||||||
\(506\) | 16.8995 | 0.751274 | ||||||||
\(507\) | −12.3137 | −0.546871 | ||||||||
\(508\) | −61.5269 | −2.72982 | ||||||||
\(509\) | −12.0000 | −0.531891 | −0.265945 | − | 0.963988i | \(-0.585684\pi\) | ||||
−0.265945 | + | 0.963988i | \(0.585684\pi\) | |||||||
\(510\) | −21.3137 | −0.943787 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 7.24264 | 0.319770 | ||||||||
\(514\) | −51.7990 | −2.28476 | ||||||||
\(515\) | −24.9706 | −1.10033 | ||||||||
\(516\) | −10.5563 | −0.464717 | ||||||||
\(517\) | 9.82843 | 0.432254 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.8284 | −0.650896 | ||||||||
\(520\) | −7.31371 | −0.320727 | ||||||||
\(521\) | 31.1716 | 1.36565 | 0.682826 | − | 0.730581i | \(-0.260751\pi\) | ||||
0.682826 | + | 0.730581i | \(0.260751\pi\) | |||||||
\(522\) | −7.82843 | −0.342641 | ||||||||
\(523\) | −22.2843 | −0.974423 | −0.487212 | − | 0.873284i | \(-0.661986\pi\) | ||||
−0.487212 | + | 0.873284i | \(0.661986\pi\) | |||||||
\(524\) | −19.7990 | −0.864923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −43.4558 | −1.89476 | ||||||||
\(527\) | −24.9706 | −1.08773 | ||||||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | 26.0000 | 1.13043 | ||||||||
\(530\) | −34.6274 | −1.50412 | ||||||||
\(531\) | −8.65685 | −0.375675 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.970563 | 0.0420397 | ||||||||
\(534\) | 34.1421 | 1.47747 | ||||||||
\(535\) | −19.3137 | −0.835004 | ||||||||
\(536\) | 14.0000 | 0.604708 | ||||||||
\(537\) | 17.8284 | 0.769353 | ||||||||
\(538\) | 67.1127 | 2.89343 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.65685 | −0.329499 | ||||||||
\(541\) | 19.6569 | 0.845114 | 0.422557 | − | 0.906336i | \(-0.361133\pi\) | ||||
0.422557 | + | 0.906336i | \(0.361133\pi\) | |||||||
\(542\) | 55.4558 | 2.38203 | ||||||||
\(543\) | −11.6569 | −0.500243 | ||||||||
\(544\) | −7.00000 | −0.300123 | ||||||||
\(545\) | 13.6569 | 0.584995 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.2132 | −1.03528 | −0.517641 | − | 0.855598i | \(-0.673190\pi\) | ||||
−0.517641 | + | 0.855598i | \(0.673190\pi\) | |||||||
\(548\) | 1.85786 | 0.0793640 | ||||||||
\(549\) | −4.00000 | −0.170716 | ||||||||
\(550\) | 2.41421 | 0.102942 | ||||||||
\(551\) | 23.4853 | 1.00051 | ||||||||
\(552\) | 30.8995 | 1.31517 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 61.9411 | 2.63163 | ||||||||
\(555\) | 18.9706 | 0.805256 | ||||||||
\(556\) | 32.2132 | 1.36614 | ||||||||
\(557\) | −8.55635 | −0.362544 | −0.181272 | − | 0.983433i | \(-0.558021\pi\) | ||||
−0.181272 | + | 0.983433i | \(0.558021\pi\) | |||||||
\(558\) | −13.6569 | −0.578141 | ||||||||
\(559\) | 2.28427 | 0.0966144 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.41421 | −0.186368 | ||||||||
\(562\) | −34.7990 | −1.46791 | ||||||||
\(563\) | 24.8284 | 1.04639 | 0.523197 | − | 0.852212i | \(-0.324739\pi\) | ||||
0.523197 | + | 0.852212i | \(0.324739\pi\) | |||||||
\(564\) | 37.6274 | 1.58440 | ||||||||
\(565\) | 15.3137 | 0.644253 | ||||||||
\(566\) | −49.1127 | −2.06436 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.4142 | 0.772643 | ||||||||
\(569\) | 1.24264 | 0.0520942 | 0.0260471 | − | 0.999661i | \(-0.491708\pi\) | ||||
0.0260471 | + | 0.999661i | \(0.491708\pi\) | |||||||
\(570\) | 34.9706 | 1.46476 | ||||||||
\(571\) | −3.92893 | −0.164421 | −0.0822103 | − | 0.996615i | \(-0.526198\pi\) | ||||
−0.0822103 | + | 0.996615i | \(0.526198\pi\) | |||||||
\(572\) | −3.17157 | −0.132610 | ||||||||
\(573\) | −21.6569 | −0.904728 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.00000 | 0.291920 | ||||||||
\(576\) | −9.82843 | −0.409518 | ||||||||
\(577\) | 7.65685 | 0.318759 | 0.159380 | − | 0.987217i | \(-0.449051\pi\) | ||||
0.159380 | + | 0.987217i | \(0.449051\pi\) | |||||||
\(578\) | −6.00000 | −0.249567 | ||||||||
\(579\) | −12.1421 | −0.504610 | ||||||||
\(580\) | −24.8284 | −1.03094 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 27.7279 | 1.14936 | ||||||||
\(583\) | −7.17157 | −0.297016 | ||||||||
\(584\) | −1.51472 | −0.0626795 | ||||||||
\(585\) | 1.65685 | 0.0685025 | ||||||||
\(586\) | −13.8284 | −0.571247 | ||||||||
\(587\) | 8.68629 | 0.358522 | 0.179261 | − | 0.983802i | \(-0.442629\pi\) | ||||
0.179261 | + | 0.983802i | \(0.442629\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.9706 | 1.68816 | ||||||||
\(590\) | −41.7990 | −1.72084 | ||||||||
\(591\) | −16.4142 | −0.675191 | ||||||||
\(592\) | −28.4558 | −1.16953 | ||||||||
\(593\) | −22.2721 | −0.914605 | −0.457302 | − | 0.889311i | \(-0.651184\pi\) | ||||
−0.457302 | + | 0.889311i | \(0.651184\pi\) | |||||||
\(594\) | −2.41421 | −0.0990564 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −85.0416 | −3.48344 | ||||||||
\(597\) | −19.7990 | −0.810319 | ||||||||
\(598\) | −14.0000 | −0.572503 | ||||||||
\(599\) | −1.37258 | −0.0560822 | −0.0280411 | − | 0.999607i | \(-0.508927\pi\) | ||||
−0.0280411 | + | 0.999607i | \(0.508927\pi\) | |||||||
\(600\) | 4.41421 | 0.180210 | ||||||||
\(601\) | −14.4853 | −0.590867 | −0.295433 | − | 0.955363i | \(-0.595464\pi\) | ||||
−0.295433 | + | 0.955363i | \(0.595464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.17157 | −0.129156 | ||||||||
\(604\) | −72.3553 | −2.94410 | ||||||||
\(605\) | −2.00000 | −0.0813116 | ||||||||
\(606\) | −11.8284 | −0.480497 | ||||||||
\(607\) | −18.6863 | −0.758453 | −0.379227 | − | 0.925304i | \(-0.623810\pi\) | ||||
−0.379227 | + | 0.925304i | \(0.623810\pi\) | |||||||
\(608\) | 11.4853 | 0.465790 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.3137 | −0.781989 | ||||||||
\(611\) | −8.14214 | −0.329396 | ||||||||
\(612\) | −16.8995 | −0.683122 | ||||||||
\(613\) | 25.1716 | 1.01667 | 0.508335 | − | 0.861159i | \(-0.330261\pi\) | ||||
0.508335 | + | 0.861159i | \(0.330261\pi\) | |||||||
\(614\) | 41.7990 | 1.68687 | ||||||||
\(615\) | 2.34315 | 0.0944848 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.1716 | 0.530268 | 0.265134 | − | 0.964212i | \(-0.414584\pi\) | ||||
0.265134 | + | 0.964212i | \(0.414584\pi\) | |||||||
\(618\) | −30.1421 | −1.21249 | ||||||||
\(619\) | 34.6274 | 1.39179 | 0.695897 | − | 0.718142i | \(-0.255007\pi\) | ||||
0.695897 | + | 0.718142i | \(0.255007\pi\) | |||||||
\(620\) | −43.3137 | −1.73952 | ||||||||
\(621\) | −7.00000 | −0.280900 | ||||||||
\(622\) | −71.5269 | −2.86797 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.48528 | −0.0994909 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −11.5858 | −0.463061 | ||||||||
\(627\) | 7.24264 | 0.289243 | ||||||||
\(628\) | 26.7990 | 1.06940 | ||||||||
\(629\) | 41.8701 | 1.66947 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.2843 | 1.04636 | 0.523180 | − | 0.852222i | \(-0.324745\pi\) | ||||
0.523180 | + | 0.852222i | \(0.324745\pi\) | |||||||
\(632\) | −58.7696 | −2.33773 | ||||||||
\(633\) | 14.9706 | 0.595026 | ||||||||
\(634\) | 61.1127 | 2.42710 | ||||||||
\(635\) | 32.1421 | 1.27552 | ||||||||
\(636\) | −27.4558 | −1.08870 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.82843 | −0.309930 | ||||||||
\(639\) | −4.17157 | −0.165025 | ||||||||
\(640\) | −41.1127 | −1.62512 | ||||||||
\(641\) | −12.4853 | −0.493139 | −0.246569 | − | 0.969125i | \(-0.579303\pi\) | ||||
−0.246569 | + | 0.969125i | \(0.579303\pi\) | |||||||
\(642\) | −23.3137 | −0.920119 | ||||||||
\(643\) | 2.00000 | 0.0788723 | 0.0394362 | − | 0.999222i | \(-0.487444\pi\) | ||||
0.0394362 | + | 0.999222i | \(0.487444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.51472 | 0.217142 | ||||||||
\(646\) | 77.1838 | 3.03675 | ||||||||
\(647\) | −19.3137 | −0.759300 | −0.379650 | − | 0.925130i | \(-0.623956\pi\) | ||||
−0.379650 | + | 0.925130i | \(0.623956\pi\) | |||||||
\(648\) | −4.41421 | −0.173407 | ||||||||
\(649\) | −8.65685 | −0.339811 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −80.2843 | −3.14417 | ||||||||
\(653\) | 31.1127 | 1.21753 | 0.608767 | − | 0.793349i | \(-0.291664\pi\) | ||||
0.608767 | + | 0.793349i | \(0.291664\pi\) | |||||||
\(654\) | 16.4853 | 0.644626 | ||||||||
\(655\) | 10.3431 | 0.404140 | ||||||||
\(656\) | −3.51472 | −0.137227 | ||||||||
\(657\) | 0.343146 | 0.0133874 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.4853 | 1.34336 | 0.671678 | − | 0.740843i | \(-0.265574\pi\) | ||||
0.671678 | + | 0.740843i | \(0.265574\pi\) | |||||||
\(660\) | −7.65685 | −0.298043 | ||||||||
\(661\) | 11.9706 | 0.465601 | 0.232800 | − | 0.972525i | \(-0.425211\pi\) | ||||
0.232800 | + | 0.972525i | \(0.425211\pi\) | |||||||
\(662\) | −54.2843 | −2.10982 | ||||||||
\(663\) | 3.65685 | 0.142020 | ||||||||
\(664\) | 12.4853 | 0.484523 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 22.8995 | 0.887337 | ||||||||
\(667\) | −22.6985 | −0.878889 | ||||||||
\(668\) | 19.7990 | 0.766046 | ||||||||
\(669\) | −22.9706 | −0.888093 | ||||||||
\(670\) | −15.3137 | −0.591620 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.1716 | 1.04739 | 0.523694 | − | 0.851907i | \(-0.324554\pi\) | ||||
0.523694 | + | 0.851907i | \(0.324554\pi\) | |||||||
\(674\) | −9.31371 | −0.358751 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −47.1421 | −1.81316 | ||||||||
\(677\) | −32.0122 | −1.23033 | −0.615164 | − | 0.788399i | \(-0.710910\pi\) | ||||
−0.615164 | + | 0.788399i | \(0.710910\pi\) | |||||||
\(678\) | 18.4853 | 0.709923 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −38.9706 | −1.49445 | ||||||||
\(681\) | 14.9706 | 0.573673 | ||||||||
\(682\) | −13.6569 | −0.522948 | ||||||||
\(683\) | 3.20101 | 0.122483 | 0.0612416 | − | 0.998123i | \(-0.480494\pi\) | ||||
0.0612416 | + | 0.998123i | \(0.480494\pi\) | |||||||
\(684\) | 27.7279 | 1.06020 | ||||||||
\(685\) | −0.970563 | −0.0370833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.6569 | −0.597346 | ||||||||
\(688\) | −8.27208 | −0.315370 | ||||||||
\(689\) | 5.94113 | 0.226339 | ||||||||
\(690\) | −33.7990 | −1.28671 | ||||||||
\(691\) | −11.4558 | −0.435801 | −0.217900 | − | 0.975971i | \(-0.569921\pi\) | ||||
−0.217900 | + | 0.975971i | \(0.569921\pi\) | |||||||
\(692\) | −56.7696 | −2.15805 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.1421 | −1.37194 | ||||||||
\(695\) | −16.8284 | −0.638339 | ||||||||
\(696\) | −14.3137 | −0.542560 | ||||||||
\(697\) | 5.17157 | 0.195887 | ||||||||
\(698\) | −26.4853 | −1.00248 | ||||||||
\(699\) | 10.4142 | 0.393902 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.89949 | −0.109512 | −0.0547562 | − | 0.998500i | \(-0.517438\pi\) | ||||
−0.0547562 | + | 0.998500i | \(0.517438\pi\) | |||||||
\(702\) | 2.00000 | 0.0754851 | ||||||||
\(703\) | −68.6985 | −2.59101 | ||||||||
\(704\) | −9.82843 | −0.370423 | ||||||||
\(705\) | −19.6569 | −0.740320 | ||||||||
\(706\) | −32.1421 | −1.20969 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −33.1421 | −1.24556 | ||||||||
\(709\) | 25.7696 | 0.967796 | 0.483898 | − | 0.875124i | \(-0.339221\pi\) | ||||
0.483898 | + | 0.875124i | \(0.339221\pi\) | |||||||
\(710\) | −20.1421 | −0.755921 | ||||||||
\(711\) | 13.3137 | 0.499303 | ||||||||
\(712\) | 62.4264 | 2.33953 | ||||||||
\(713\) | −39.5980 | −1.48296 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.65685 | 0.0619628 | ||||||||
\(716\) | 68.2548 | 2.55080 | ||||||||
\(717\) | −6.48528 | −0.242197 | ||||||||
\(718\) | 19.3137 | 0.720781 | ||||||||
\(719\) | 11.2010 | 0.417727 | 0.208864 | − | 0.977945i | \(-0.433024\pi\) | ||||
0.208864 | + | 0.977945i | \(0.433024\pi\) | |||||||
\(720\) | −6.00000 | −0.223607 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −80.7696 | −3.00593 | ||||||||
\(723\) | 7.31371 | 0.272000 | ||||||||
\(724\) | −44.6274 | −1.65856 | ||||||||
\(725\) | −3.24264 | −0.120429 | ||||||||
\(726\) | −2.41421 | −0.0895999 | ||||||||
\(727\) | 46.0833 | 1.70913 | 0.854567 | − | 0.519342i | \(-0.173823\pi\) | ||||
0.854567 | + | 0.519342i | \(0.173823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.65685 | 0.0613229 | ||||||||
\(731\) | 12.1716 | 0.450182 | ||||||||
\(732\) | −15.3137 | −0.566011 | ||||||||
\(733\) | 9.65685 | 0.356684 | 0.178342 | − | 0.983969i | \(-0.442927\pi\) | ||||
0.178342 | + | 0.983969i | \(0.442927\pi\) | |||||||
\(734\) | 10.0000 | 0.369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.1005 | −0.409170 | ||||||||
\(737\) | −3.17157 | −0.116826 | ||||||||
\(738\) | 2.82843 | 0.104116 | ||||||||
\(739\) | −39.6569 | −1.45880 | −0.729400 | − | 0.684087i | \(-0.760201\pi\) | ||||
−0.729400 | + | 0.684087i | \(0.760201\pi\) | |||||||
\(740\) | 72.6274 | 2.66984 | ||||||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.7990 | 1.23996 | 0.619982 | − | 0.784616i | \(-0.287140\pi\) | ||||
0.619982 | + | 0.784616i | \(0.287140\pi\) | |||||||
\(744\) | −24.9706 | −0.915465 | ||||||||
\(745\) | 44.4264 | 1.62766 | ||||||||
\(746\) | 4.00000 | 0.146450 | ||||||||
\(747\) | −2.82843 | −0.103487 | ||||||||
\(748\) | −16.8995 | −0.617907 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −28.9706 | −1.05786 | ||||||||
\(751\) | −29.3137 | −1.06967 | −0.534836 | − | 0.844956i | \(-0.679627\pi\) | ||||
−0.534836 | + | 0.844956i | \(0.679627\pi\) | |||||||
\(752\) | 29.4853 | 1.07522 | ||||||||
\(753\) | −2.51472 | −0.0916414 | ||||||||
\(754\) | 6.48528 | 0.236180 | ||||||||
\(755\) | 37.7990 | 1.37565 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.68629 | −0.279363 | −0.139682 | − | 0.990196i | \(-0.544608\pi\) | ||||
−0.139682 | + | 0.990196i | \(0.544608\pi\) | |||||||
\(758\) | −45.4558 | −1.65103 | ||||||||
\(759\) | −7.00000 | −0.254084 | ||||||||
\(760\) | 63.9411 | 2.31939 | ||||||||
\(761\) | −0.201010 | −0.00728661 | −0.00364331 | − | 0.999993i | \(-0.501160\pi\) | ||||
−0.00364331 | + | 0.999993i | \(0.501160\pi\) | |||||||
\(762\) | 38.7990 | 1.40554 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −82.9117 | −2.99964 | ||||||||
\(765\) | 8.82843 | 0.319192 | ||||||||
\(766\) | −5.58579 | −0.201823 | ||||||||
\(767\) | 7.17157 | 0.258950 | ||||||||
\(768\) | −29.9706 | −1.08147 | ||||||||
\(769\) | 33.7990 | 1.21882 | 0.609411 | − | 0.792854i | \(-0.291406\pi\) | ||||
0.609411 | + | 0.792854i | \(0.291406\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.4558 | 0.772713 | ||||||||
\(772\) | −46.4853 | −1.67304 | ||||||||
\(773\) | −51.6569 | −1.85797 | −0.928984 | − | 0.370120i | \(-0.879317\pi\) | ||||
−0.928984 | + | 0.370120i | \(0.879317\pi\) | |||||||
\(774\) | 6.65685 | 0.239276 | ||||||||
\(775\) | −5.65685 | −0.203200 | ||||||||
\(776\) | 50.6985 | 1.81997 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.4853 | 1.02125 | ||||||||
\(779\) | −8.48528 | −0.304017 | ||||||||
\(780\) | 6.34315 | 0.227121 | ||||||||
\(781\) | −4.17157 | −0.149271 | ||||||||
\(782\) | −74.5980 | −2.66762 | ||||||||
\(783\) | 3.24264 | 0.115883 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.0000 | −0.499681 | ||||||||
\(786\) | 12.4853 | 0.445335 | ||||||||
\(787\) | 29.5269 | 1.05252 | 0.526260 | − | 0.850323i | \(-0.323594\pi\) | ||||
0.526260 | + | 0.850323i | \(0.323594\pi\) | |||||||
\(788\) | −62.8406 | −2.23860 | ||||||||
\(789\) | 18.0000 | 0.640817 | ||||||||
\(790\) | 64.2843 | 2.28713 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.41421 | −0.156852 | ||||||||
\(793\) | 3.31371 | 0.117673 | ||||||||
\(794\) | −42.2132 | −1.49809 | ||||||||
\(795\) | 14.3431 | 0.508699 | ||||||||
\(796\) | −75.7990 | −2.68662 | ||||||||
\(797\) | 11.1716 | 0.395717 | 0.197859 | − | 0.980231i | \(-0.436601\pi\) | ||||
0.197859 | + | 0.980231i | \(0.436601\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.3848 | −1.53484 | ||||||||
\(800\) | −1.58579 | −0.0560660 | ||||||||
\(801\) | −14.1421 | −0.499688 | ||||||||
\(802\) | −18.1421 | −0.640621 | ||||||||
\(803\) | 0.343146 | 0.0121094 | ||||||||
\(804\) | −12.1421 | −0.428220 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.3137 | 0.398508 | ||||||||
\(807\) | −27.7990 | −0.978571 | ||||||||
\(808\) | −21.6274 | −0.760850 | ||||||||
\(809\) | 10.8284 | 0.380707 | 0.190354 | − | 0.981716i | \(-0.439037\pi\) | ||||
0.190354 | + | 0.981716i | \(0.439037\pi\) | |||||||
\(810\) | 4.82843 | 0.169654 | ||||||||
\(811\) | 14.9706 | 0.525688 | 0.262844 | − | 0.964838i | \(-0.415340\pi\) | ||||
0.262844 | + | 0.964838i | \(0.415340\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.9706 | −0.805613 | ||||||||
\(814\) | 22.8995 | 0.802627 | ||||||||
\(815\) | 41.9411 | 1.46913 | ||||||||
\(816\) | −13.2426 | −0.463585 | ||||||||
\(817\) | −19.9706 | −0.698682 | ||||||||
\(818\) | 18.8284 | 0.658321 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.97056 | 0.313266 | ||||||||
\(821\) | 38.8284 | 1.35512 | 0.677561 | − | 0.735467i | \(-0.263037\pi\) | ||||
0.677561 | + | 0.735467i | \(0.263037\pi\) | |||||||
\(822\) | −1.17157 | −0.0408633 | ||||||||
\(823\) | −33.1716 | −1.15629 | −0.578144 | − | 0.815935i | \(-0.696223\pi\) | ||||
−0.578144 | + | 0.815935i | \(0.696223\pi\) | |||||||
\(824\) | −55.1127 | −1.91994 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.3137 | −1.29752 | −0.648762 | − | 0.760991i | \(-0.724713\pi\) | ||||
−0.648762 | + | 0.760991i | \(0.724713\pi\) | |||||||
\(828\) | −26.7990 | −0.931329 | ||||||||
\(829\) | −6.17157 | −0.214348 | −0.107174 | − | 0.994240i | \(-0.534180\pi\) | ||||
−0.107174 | + | 0.994240i | \(0.534180\pi\) | |||||||
\(830\) | −13.6569 | −0.474036 | ||||||||
\(831\) | −25.6569 | −0.890026 | ||||||||
\(832\) | 8.14214 | 0.282278 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20.3137 | −0.703406 | ||||||||
\(835\) | −10.3431 | −0.357939 | ||||||||
\(836\) | 27.7279 | 0.958990 | ||||||||
\(837\) | 5.65685 | 0.195529 | ||||||||
\(838\) | −35.7279 | −1.23420 | ||||||||
\(839\) | 8.97056 | 0.309698 | 0.154849 | − | 0.987938i | \(-0.450511\pi\) | ||||
0.154849 | + | 0.987938i | \(0.450511\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.4853 | −0.637423 | ||||||||
\(842\) | 16.8995 | 0.582395 | ||||||||
\(843\) | 14.4142 | 0.496452 | ||||||||
\(844\) | 57.3137 | 1.97282 | ||||||||
\(845\) | 24.6274 | 0.847209 | ||||||||
\(846\) | −23.7279 | −0.815783 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −21.5147 | −0.738818 | ||||||||
\(849\) | 20.3431 | 0.698175 | ||||||||
\(850\) | −10.6569 | −0.365527 | ||||||||
\(851\) | 66.3970 | 2.27606 | ||||||||
\(852\) | −15.9706 | −0.547142 | ||||||||
\(853\) | −12.4853 | −0.427488 | −0.213744 | − | 0.976890i | \(-0.568566\pi\) | ||||
−0.213744 | + | 0.976890i | \(0.568566\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.4853 | −0.495386 | ||||||||
\(856\) | −42.6274 | −1.45698 | ||||||||
\(857\) | −44.3553 | −1.51515 | −0.757575 | − | 0.652748i | \(-0.773616\pi\) | ||||
−0.757575 | + | 0.652748i | \(0.773616\pi\) | |||||||
\(858\) | 2.00000 | 0.0682789 | ||||||||
\(859\) | −24.4853 | −0.835427 | −0.417714 | − | 0.908579i | \(-0.637168\pi\) | ||||
−0.417714 | + | 0.908579i | \(0.637168\pi\) | |||||||
\(860\) | 21.1127 | 0.719937 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.8284 | −0.573179 | ||||||||
\(863\) | 2.62742 | 0.0894383 | 0.0447192 | − | 0.999000i | \(-0.485761\pi\) | ||||
0.0447192 | + | 0.999000i | \(0.485761\pi\) | |||||||
\(864\) | 1.58579 | 0.0539496 | ||||||||
\(865\) | 29.6569 | 1.00836 | ||||||||
\(866\) | −2.07107 | −0.0703777 | ||||||||
\(867\) | 2.48528 | 0.0844046 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3137 | 0.451637 | ||||||||
\(870\) | 15.6569 | 0.530817 | ||||||||
\(871\) | 2.62742 | 0.0890266 | ||||||||
\(872\) | 30.1421 | 1.02074 | ||||||||
\(873\) | −11.4853 | −0.388718 | ||||||||
\(874\) | 122.397 | 4.14014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.31371 | 0.0443861 | ||||||||
\(877\) | 2.48528 | 0.0839220 | 0.0419610 | − | 0.999119i | \(-0.486639\pi\) | ||||
0.0419610 | + | 0.999119i | \(0.486639\pi\) | |||||||
\(878\) | −74.5980 | −2.51756 | ||||||||
\(879\) | 5.72792 | 0.193198 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | 16.6863 | 0.562175 | 0.281088 | − | 0.959682i | \(-0.409305\pi\) | ||||
0.281088 | + | 0.959682i | \(0.409305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.6569 | 1.33456 | 0.667280 | − | 0.744807i | \(-0.267459\pi\) | ||||
0.667280 | + | 0.744807i | \(0.267459\pi\) | |||||||
\(884\) | 14.0000 | 0.470871 | ||||||||
\(885\) | 17.3137 | 0.581994 | ||||||||
\(886\) | −81.1838 | −2.72742 | ||||||||
\(887\) | −13.3137 | −0.447031 | −0.223515 | − | 0.974700i | \(-0.571753\pi\) | ||||
−0.223515 | + | 0.974700i | \(0.571753\pi\) | |||||||
\(888\) | 41.8701 | 1.40507 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −68.2843 | −2.28889 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −87.9411 | −2.94449 | ||||||||
\(893\) | 71.1838 | 2.38207 | ||||||||
\(894\) | 53.6274 | 1.79357 | ||||||||
\(895\) | −35.6569 | −1.19188 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.79899 | 0.193623 | ||||||||
\(898\) | 9.65685 | 0.322253 | ||||||||
\(899\) | 18.3431 | 0.611778 | ||||||||
\(900\) | −3.82843 | −0.127614 | ||||||||
\(901\) | 31.6569 | 1.05464 | ||||||||
\(902\) | 2.82843 | 0.0941763 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 33.7990 | 1.12414 | ||||||||
\(905\) | 23.3137 | 0.774974 | ||||||||
\(906\) | 45.6274 | 1.51587 | ||||||||
\(907\) | −17.5147 | −0.581567 | −0.290783 | − | 0.956789i | \(-0.593916\pi\) | ||||
−0.290783 | + | 0.956789i | \(0.593916\pi\) | |||||||
\(908\) | 57.3137 | 1.90202 | ||||||||
\(909\) | 4.89949 | 0.162506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.51472 | −0.149579 | −0.0747897 | − | 0.997199i | \(-0.523829\pi\) | ||||
−0.0747897 | + | 0.997199i | \(0.523829\pi\) | |||||||
\(912\) | 21.7279 | 0.719483 | ||||||||
\(913\) | −2.82843 | −0.0936073 | ||||||||
\(914\) | −45.4558 | −1.50355 | ||||||||
\(915\) | 8.00000 | 0.264472 | ||||||||
\(916\) | −59.9411 | −1.98051 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.6569 | 0.351729 | ||||||||
\(919\) | 56.3553 | 1.85899 | 0.929496 | − | 0.368833i | \(-0.120243\pi\) | ||||
0.929496 | + | 0.368833i | \(0.120243\pi\) | |||||||
\(920\) | −61.7990 | −2.03745 | ||||||||
\(921\) | −17.3137 | −0.570506 | ||||||||
\(922\) | −16.3137 | −0.537263 | ||||||||
\(923\) | 3.45584 | 0.113750 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.48528 | 0.311874 | ||||||||
\(926\) | −44.9706 | −1.47782 | ||||||||
\(927\) | 12.4853 | 0.410070 | ||||||||
\(928\) | 5.14214 | 0.168799 | ||||||||
\(929\) | −22.8284 | −0.748976 | −0.374488 | − | 0.927232i | \(-0.622182\pi\) | ||||
−0.374488 | + | 0.927232i | \(0.622182\pi\) | |||||||
\(930\) | 27.3137 | 0.895652 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39.8701 | 1.30599 | ||||||||
\(933\) | 29.6274 | 0.969958 | ||||||||
\(934\) | 20.0711 | 0.656745 | ||||||||
\(935\) | 8.82843 | 0.288720 | ||||||||
\(936\) | 3.65685 | 0.119528 | ||||||||
\(937\) | 5.85786 | 0.191368 | 0.0956840 | − | 0.995412i | \(-0.469496\pi\) | ||||
0.0956840 | + | 0.995412i | \(0.469496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.79899 | 0.156609 | ||||||||
\(940\) | −75.2548 | −2.45454 | ||||||||
\(941\) | −12.0711 | −0.393506 | −0.196753 | − | 0.980453i | \(-0.563040\pi\) | ||||
−0.196753 | + | 0.980453i | \(0.563040\pi\) | |||||||
\(942\) | −16.8995 | −0.550615 | ||||||||
\(943\) | 8.20101 | 0.267062 | ||||||||
\(944\) | −25.9706 | −0.845270 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.65685 | 0.216433 | ||||||||
\(947\) | 37.4853 | 1.21811 | 0.609054 | − | 0.793129i | \(-0.291549\pi\) | ||||
0.609054 | + | 0.793129i | \(0.291549\pi\) | |||||||
\(948\) | 50.9706 | 1.65545 | ||||||||
\(949\) | −0.284271 | −0.00922784 | ||||||||
\(950\) | 17.4853 | 0.567297 | ||||||||
\(951\) | −25.3137 | −0.820853 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.1421 | −0.458109 | −0.229054 | − | 0.973414i | \(-0.573563\pi\) | ||||
−0.229054 | + | 0.973414i | \(0.573563\pi\) | |||||||
\(954\) | 17.3137 | 0.560552 | ||||||||
\(955\) | 43.3137 | 1.40160 | ||||||||
\(956\) | −24.8284 | −0.803009 | ||||||||
\(957\) | 3.24264 | 0.104820 | ||||||||
\(958\) | −33.7990 | −1.09200 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 19.6569 | 0.634422 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −18.9706 | −0.611635 | ||||||||
\(963\) | 9.65685 | 0.311188 | ||||||||
\(964\) | 28.0000 | 0.901819 | ||||||||
\(965\) | 24.2843 | 0.781738 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.0416 | −0.676653 | −0.338327 | − | 0.941029i | \(-0.609861\pi\) | ||||
−0.338327 | + | 0.941029i | \(0.609861\pi\) | |||||||
\(968\) | −4.41421 | −0.141878 | ||||||||
\(969\) | −31.9706 | −1.02704 | ||||||||
\(970\) | −55.4558 | −1.78058 | ||||||||
\(971\) | 4.97056 | 0.159513 | 0.0797565 | − | 0.996814i | \(-0.474586\pi\) | ||||
0.0797565 | + | 0.996814i | \(0.474586\pi\) | |||||||
\(972\) | 3.82843 | 0.122797 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 78.7696 | 2.52394 | ||||||||
\(975\) | 0.828427 | 0.0265309 | ||||||||
\(976\) | −12.0000 | −0.384111 | ||||||||
\(977\) | −12.8284 | −0.410418 | −0.205209 | − | 0.978718i | \(-0.565787\pi\) | ||||
−0.205209 | + | 0.978718i | \(0.565787\pi\) | |||||||
\(978\) | 50.6274 | 1.61889 | ||||||||
\(979\) | −14.1421 | −0.451985 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.82843 | −0.218015 | ||||||||
\(982\) | 3.65685 | 0.116695 | ||||||||
\(983\) | −2.02944 | −0.0647290 | −0.0323645 | − | 0.999476i | \(-0.510304\pi\) | ||||
−0.0323645 | + | 0.999476i | \(0.510304\pi\) | |||||||
\(984\) | 5.17157 | 0.164864 | ||||||||
\(985\) | 32.8284 | 1.04600 | ||||||||
\(986\) | 34.5563 | 1.10050 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.9706 | −0.730791 | ||||||||
\(989\) | 19.3015 | 0.613752 | ||||||||
\(990\) | 4.82843 | 0.153457 | ||||||||
\(991\) | −24.6863 | −0.784186 | −0.392093 | − | 0.919926i | \(-0.628249\pi\) | ||||
−0.392093 | + | 0.919926i | \(0.628249\pi\) | |||||||
\(992\) | 8.97056 | 0.284816 | ||||||||
\(993\) | 22.4853 | 0.713549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.5980 | 1.25534 | ||||||||
\(996\) | −10.8284 | −0.343112 | ||||||||
\(997\) | 9.85786 | 0.312202 | 0.156101 | − | 0.987741i | \(-0.450108\pi\) | ||||
0.156101 | + | 0.987741i | \(0.450108\pi\) | |||||||
\(998\) | 76.7696 | 2.43010 | ||||||||
\(999\) | −9.48528 | −0.300101 |
(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 | 1617.2.a.n.1.1 | 2 | ||
3.2 | odd | 2 | 4851.2.a.be.1.2 | 2 | |||
7.2 | even | 3 | 231.2.i.d.67.2 | ✓ | 4 | ||
7.4 | even | 3 | 231.2.i.d.100.2 | yes | 4 | ||
7.6 | odd | 2 | 1617.2.a.m.1.1 | 2 | |||
21.2 | odd | 6 | 693.2.i.f.298.1 | 4 | |||
21.11 | odd | 6 | 693.2.i.f.100.1 | 4 | |||
21.20 | even | 2 | 4851.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.i.d.67.2 | ✓ | 4 | 7.2 | even | 3 | ||
231.2.i.d.100.2 | yes | 4 | 7.4 | even | 3 | ||
693.2.i.f.100.1 | 4 | 21.11 | odd | 6 | |||
693.2.i.f.298.1 | 4 | 21.2 | odd | 6 | |||
1617.2.a.m.1.1 | 2 | 7.6 | odd | 2 | |||
1617.2.a.n.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4851.2.a.bd.1.2 | 2 | 21.20 | even | 2 | |||
4851.2.a.be.1.2 | 2 | 3.2 | odd | 2 |