Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.585786 | −0.261972 | −0.130986 | − | 0.991384i | \(-0.541814\pi\) | ||||
−0.130986 | + | 0.991384i | \(0.541814\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.585786 | −0.185242 | ||||||||
\(11\) | −0.414214 | −0.124890 | −0.0624450 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624450 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.585786 | 0.151249 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.41421 | −0.585533 | −0.292766 | − | 0.956184i | \(-0.594576\pi\) | ||||
−0.292766 | + | 0.956184i | \(0.594576\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −2.17157 | −0.498193 | −0.249096 | − | 0.968479i | \(-0.580134\pi\) | ||||
−0.249096 | + | 0.968479i | \(0.580134\pi\) | |||||||
\(20\) | −0.585786 | −0.130986 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.414214 | −0.0883106 | ||||||||
\(23\) | 1.41421 | 0.294884 | 0.147442 | − | 0.989071i | \(-0.452896\pi\) | ||||
0.147442 | + | 0.989071i | \(0.452896\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.65685 | −0.931371 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.82843 | −0.339530 | −0.169765 | − | 0.985485i | \(-0.554301\pi\) | ||||
−0.169765 | + | 0.985485i | \(0.554301\pi\) | |||||||
\(30\) | 0.585786 | 0.106949 | ||||||||
\(31\) | −8.48528 | −1.52400 | −0.762001 | − | 0.647576i | \(-0.775783\pi\) | ||||
−0.762001 | + | 0.647576i | \(0.775783\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.414214 | 0.0721053 | ||||||||
\(34\) | −2.41421 | −0.414034 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.41421 | 0.232495 | 0.116248 | − | 0.993220i | \(-0.462913\pi\) | ||||
0.116248 | + | 0.993220i | \(0.462913\pi\) | |||||||
\(38\) | −2.17157 | −0.352276 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.585786 | −0.0926210 | ||||||||
\(41\) | −9.89949 | −1.54604 | −0.773021 | − | 0.634381i | \(-0.781255\pi\) | ||||
−0.773021 | + | 0.634381i | \(0.781255\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.48528 | 0.988996 | 0.494498 | − | 0.869179i | \(-0.335352\pi\) | ||||
0.494498 | + | 0.869179i | \(0.335352\pi\) | |||||||
\(44\) | −0.414214 | −0.0624450 | ||||||||
\(45\) | −0.585786 | −0.0873239 | ||||||||
\(46\) | 1.41421 | 0.208514 | ||||||||
\(47\) | 1.00000 | 0.145865 | 0.0729325 | − | 0.997337i | \(-0.476764\pi\) | ||||
0.0729325 | + | 0.997337i | \(0.476764\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.65685 | −0.658579 | ||||||||
\(51\) | 2.41421 | 0.338058 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 9.48528 | 1.30290 | 0.651452 | − | 0.758690i | \(-0.274160\pi\) | ||||
0.651452 | + | 0.758690i | \(0.274160\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.242641 | 0.0327177 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.17157 | 0.287632 | ||||||||
\(58\) | −1.82843 | −0.240084 | ||||||||
\(59\) | 2.07107 | 0.269630 | 0.134815 | − | 0.990871i | \(-0.456956\pi\) | ||||
0.134815 | + | 0.990871i | \(0.456956\pi\) | |||||||
\(60\) | 0.585786 | 0.0756247 | ||||||||
\(61\) | −4.41421 | −0.565182 | −0.282591 | − | 0.959240i | \(-0.591194\pi\) | ||||
−0.282591 | + | 0.959240i | \(0.591194\pi\) | |||||||
\(62\) | −8.48528 | −1.07763 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.585786 | −0.0726579 | ||||||||
\(66\) | 0.414214 | 0.0509862 | ||||||||
\(67\) | 1.82843 | 0.223378 | 0.111689 | − | 0.993743i | \(-0.464374\pi\) | ||||
0.111689 | + | 0.993743i | \(0.464374\pi\) | |||||||
\(68\) | −2.41421 | −0.292766 | ||||||||
\(69\) | −1.41421 | −0.170251 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.00000 | −0.593391 | −0.296695 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 1.41421 | 0.165521 | 0.0827606 | − | 0.996569i | \(-0.473626\pi\) | ||||
0.0827606 | + | 0.996569i | \(0.473626\pi\) | |||||||
\(74\) | 1.41421 | 0.164399 | ||||||||
\(75\) | 4.65685 | 0.537727 | ||||||||
\(76\) | −2.17157 | −0.249096 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −11.6569 | −1.31150 | −0.655749 | − | 0.754979i | \(-0.727647\pi\) | ||||
−0.655749 | + | 0.754979i | \(0.727647\pi\) | |||||||
\(80\) | −0.585786 | −0.0654929 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.89949 | −1.09322 | ||||||||
\(83\) | 7.65685 | 0.840449 | 0.420224 | − | 0.907420i | \(-0.361951\pi\) | ||||
0.420224 | + | 0.907420i | \(0.361951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41421 | 0.153393 | ||||||||
\(86\) | 6.48528 | 0.699326 | ||||||||
\(87\) | 1.82843 | 0.196028 | ||||||||
\(88\) | −0.414214 | −0.0441553 | ||||||||
\(89\) | 2.58579 | 0.274093 | 0.137046 | − | 0.990565i | \(-0.456239\pi\) | ||||
0.137046 | + | 0.990565i | \(0.456239\pi\) | |||||||
\(90\) | −0.585786 | −0.0617473 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.41421 | 0.147442 | ||||||||
\(93\) | 8.48528 | 0.879883 | ||||||||
\(94\) | 1.00000 | 0.103142 | ||||||||
\(95\) | 1.27208 | 0.130512 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −0.928932 | −0.0943188 | −0.0471594 | − | 0.998887i | \(-0.515017\pi\) | ||||
−0.0471594 | + | 0.998887i | \(0.515017\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.414214 | −0.0416300 | ||||||||
\(100\) | −4.65685 | −0.465685 | ||||||||
\(101\) | −14.8284 | −1.47548 | −0.737742 | − | 0.675083i | \(-0.764108\pi\) | ||||
−0.737742 | + | 0.675083i | \(0.764108\pi\) | |||||||
\(102\) | 2.41421 | 0.239043 | ||||||||
\(103\) | −16.8284 | −1.65815 | −0.829077 | − | 0.559134i | \(-0.811134\pi\) | ||||
−0.829077 | + | 0.559134i | \(0.811134\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.48528 | 0.921292 | ||||||||
\(107\) | −19.3137 | −1.86713 | −0.933563 | − | 0.358412i | \(-0.883318\pi\) | ||||
−0.933563 | + | 0.358412i | \(0.883318\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.65685 | −0.924959 | −0.462479 | − | 0.886630i | \(-0.653040\pi\) | ||||
−0.462479 | + | 0.886630i | \(0.653040\pi\) | |||||||
\(110\) | 0.242641 | 0.0231349 | ||||||||
\(111\) | −1.41421 | −0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.89949 | 0.460906 | 0.230453 | − | 0.973083i | \(-0.425979\pi\) | ||||
0.230453 | + | 0.973083i | \(0.425979\pi\) | |||||||
\(114\) | 2.17157 | 0.203386 | ||||||||
\(115\) | −0.828427 | −0.0772512 | ||||||||
\(116\) | −1.82843 | −0.169765 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 2.07107 | 0.190657 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.585786 | 0.0534747 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | −4.41421 | −0.399644 | ||||||||
\(123\) | 9.89949 | 0.892607 | ||||||||
\(124\) | −8.48528 | −0.762001 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.89949 | −0.700967 | −0.350483 | − | 0.936569i | \(-0.613983\pi\) | ||||
−0.350483 | + | 0.936569i | \(0.613983\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.48528 | −0.570997 | ||||||||
\(130\) | −0.585786 | −0.0513769 | ||||||||
\(131\) | −9.55635 | −0.834942 | −0.417471 | − | 0.908690i | \(-0.637083\pi\) | ||||
−0.417471 | + | 0.908690i | \(0.637083\pi\) | |||||||
\(132\) | 0.414214 | 0.0360527 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.82843 | 0.157952 | ||||||||
\(135\) | 0.585786 | 0.0504165 | ||||||||
\(136\) | −2.41421 | −0.207017 | ||||||||
\(137\) | 11.0711 | 0.945865 | 0.472933 | − | 0.881099i | \(-0.343195\pi\) | ||||
0.472933 | + | 0.881099i | \(0.343195\pi\) | |||||||
\(138\) | −1.41421 | −0.120386 | ||||||||
\(139\) | −13.0711 | −1.10867 | −0.554337 | − | 0.832292i | \(-0.687028\pi\) | ||||
−0.554337 | + | 0.832292i | \(0.687028\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | −5.00000 | −0.419591 | ||||||||
\(143\) | −0.414214 | −0.0346383 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 1.07107 | 0.0889473 | ||||||||
\(146\) | 1.41421 | 0.117041 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.41421 | 0.116248 | ||||||||
\(149\) | −4.92893 | −0.403794 | −0.201897 | − | 0.979407i | \(-0.564711\pi\) | ||||
−0.201897 | + | 0.979407i | \(0.564711\pi\) | |||||||
\(150\) | 4.65685 | 0.380231 | ||||||||
\(151\) | 4.07107 | 0.331299 | 0.165649 | − | 0.986185i | \(-0.447028\pi\) | ||||
0.165649 | + | 0.986185i | \(0.447028\pi\) | |||||||
\(152\) | −2.17157 | −0.176138 | ||||||||
\(153\) | −2.41421 | −0.195178 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.97056 | 0.399245 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 9.72792 | 0.776373 | 0.388186 | − | 0.921581i | \(-0.373102\pi\) | ||||
0.388186 | + | 0.921581i | \(0.373102\pi\) | |||||||
\(158\) | −11.6569 | −0.927370 | ||||||||
\(159\) | −9.48528 | −0.752232 | ||||||||
\(160\) | −0.585786 | −0.0463105 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −18.6569 | −1.46132 | −0.730659 | − | 0.682743i | \(-0.760787\pi\) | ||||
−0.730659 | + | 0.682743i | \(0.760787\pi\) | |||||||
\(164\) | −9.89949 | −0.773021 | ||||||||
\(165\) | −0.242641 | −0.0188896 | ||||||||
\(166\) | 7.65685 | 0.594287 | ||||||||
\(167\) | −0.656854 | −0.0508289 | −0.0254145 | − | 0.999677i | \(-0.508091\pi\) | ||||
−0.0254145 | + | 0.999677i | \(0.508091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.41421 | 0.108465 | ||||||||
\(171\) | −2.17157 | −0.166064 | ||||||||
\(172\) | 6.48528 | 0.494498 | ||||||||
\(173\) | 5.48528 | 0.417038 | 0.208519 | − | 0.978018i | \(-0.433136\pi\) | ||||
0.208519 | + | 0.978018i | \(0.433136\pi\) | |||||||
\(174\) | 1.82843 | 0.138613 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.414214 | −0.0312225 | ||||||||
\(177\) | −2.07107 | −0.155671 | ||||||||
\(178\) | 2.58579 | 0.193813 | ||||||||
\(179\) | 19.6569 | 1.46922 | 0.734611 | − | 0.678488i | \(-0.237365\pi\) | ||||
0.734611 | + | 0.678488i | \(0.237365\pi\) | |||||||
\(180\) | −0.585786 | −0.0436619 | ||||||||
\(181\) | 2.89949 | 0.215518 | 0.107759 | − | 0.994177i | \(-0.465633\pi\) | ||||
0.107759 | + | 0.994177i | \(0.465633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.41421 | 0.326308 | ||||||||
\(184\) | 1.41421 | 0.104257 | ||||||||
\(185\) | −0.828427 | −0.0609072 | ||||||||
\(186\) | 8.48528 | 0.622171 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 1.00000 | 0.0729325 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.27208 | 0.0922862 | ||||||||
\(191\) | −10.3431 | −0.748404 | −0.374202 | − | 0.927347i | \(-0.622083\pi\) | ||||
−0.374202 | + | 0.927347i | \(0.622083\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −2.92893 | −0.210829 | −0.105415 | − | 0.994428i | \(-0.533617\pi\) | ||||
−0.105415 | + | 0.994428i | \(0.533617\pi\) | |||||||
\(194\) | −0.928932 | −0.0666934 | ||||||||
\(195\) | 0.585786 | 0.0419490 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.5563 | −1.10834 | −0.554172 | − | 0.832402i | \(-0.686965\pi\) | ||||
−0.554172 | + | 0.832402i | \(0.686965\pi\) | |||||||
\(198\) | −0.414214 | −0.0294369 | ||||||||
\(199\) | 2.72792 | 0.193377 | 0.0966886 | − | 0.995315i | \(-0.469175\pi\) | ||||
0.0966886 | + | 0.995315i | \(0.469175\pi\) | |||||||
\(200\) | −4.65685 | −0.329289 | ||||||||
\(201\) | −1.82843 | −0.128967 | ||||||||
\(202\) | −14.8284 | −1.04332 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.41421 | 0.169029 | ||||||||
\(205\) | 5.79899 | 0.405019 | ||||||||
\(206\) | −16.8284 | −1.17249 | ||||||||
\(207\) | 1.41421 | 0.0982946 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0.899495 | 0.0622194 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.9289 | −0.890064 | −0.445032 | − | 0.895515i | \(-0.646808\pi\) | ||||
−0.445032 | + | 0.895515i | \(0.646808\pi\) | |||||||
\(212\) | 9.48528 | 0.651452 | ||||||||
\(213\) | 5.00000 | 0.342594 | ||||||||
\(214\) | −19.3137 | −1.32026 | ||||||||
\(215\) | −3.79899 | −0.259089 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.65685 | −0.654045 | ||||||||
\(219\) | −1.41421 | −0.0955637 | ||||||||
\(220\) | 0.242641 | 0.0163588 | ||||||||
\(221\) | −2.41421 | −0.162398 | ||||||||
\(222\) | −1.41421 | −0.0949158 | ||||||||
\(223\) | −7.92893 | −0.530961 | −0.265480 | − | 0.964116i | \(-0.585531\pi\) | ||||
−0.265480 | + | 0.964116i | \(0.585531\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.65685 | −0.310457 | ||||||||
\(226\) | 4.89949 | 0.325910 | ||||||||
\(227\) | −21.1716 | −1.40521 | −0.702603 | − | 0.711582i | \(-0.747979\pi\) | ||||
−0.702603 | + | 0.711582i | \(0.747979\pi\) | |||||||
\(228\) | 2.17157 | 0.143816 | ||||||||
\(229\) | 26.4853 | 1.75020 | 0.875098 | − | 0.483945i | \(-0.160797\pi\) | ||||
0.875098 | + | 0.483945i | \(0.160797\pi\) | |||||||
\(230\) | −0.828427 | −0.0546249 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.82843 | −0.120042 | ||||||||
\(233\) | −17.7279 | −1.16139 | −0.580697 | − | 0.814119i | \(-0.697220\pi\) | ||||
−0.580697 | + | 0.814119i | \(0.697220\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −0.585786 | −0.0382125 | ||||||||
\(236\) | 2.07107 | 0.134815 | ||||||||
\(237\) | 11.6569 | 0.757194 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.51472 | 0.292033 | 0.146016 | − | 0.989282i | \(-0.453355\pi\) | ||||
0.146016 | + | 0.989282i | \(0.453355\pi\) | |||||||
\(240\) | 0.585786 | 0.0378124 | ||||||||
\(241\) | −2.14214 | −0.137987 | −0.0689935 | − | 0.997617i | \(-0.521979\pi\) | ||||
−0.0689935 | + | 0.997617i | \(0.521979\pi\) | |||||||
\(242\) | −10.8284 | −0.696078 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.41421 | −0.282591 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.89949 | 0.631169 | ||||||||
\(247\) | −2.17157 | −0.138174 | ||||||||
\(248\) | −8.48528 | −0.538816 | ||||||||
\(249\) | −7.65685 | −0.485233 | ||||||||
\(250\) | 5.65685 | 0.357771 | ||||||||
\(251\) | 24.8284 | 1.56716 | 0.783578 | − | 0.621293i | \(-0.213392\pi\) | ||||
0.783578 | + | 0.621293i | \(0.213392\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.585786 | −0.0368281 | ||||||||
\(254\) | −7.89949 | −0.495658 | ||||||||
\(255\) | −1.41421 | −0.0885615 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.4853 | 1.65211 | 0.826053 | − | 0.563592i | \(-0.190581\pi\) | ||||
0.826053 | + | 0.563592i | \(0.190581\pi\) | |||||||
\(258\) | −6.48528 | −0.403756 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.585786 | −0.0363289 | ||||||||
\(261\) | −1.82843 | −0.113177 | ||||||||
\(262\) | −9.55635 | −0.590393 | ||||||||
\(263\) | 20.5858 | 1.26937 | 0.634687 | − | 0.772769i | \(-0.281129\pi\) | ||||
0.634687 | + | 0.772769i | \(0.281129\pi\) | |||||||
\(264\) | 0.414214 | 0.0254931 | ||||||||
\(265\) | −5.55635 | −0.341324 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.58579 | −0.158248 | ||||||||
\(268\) | 1.82843 | 0.111689 | ||||||||
\(269\) | −9.14214 | −0.557406 | −0.278703 | − | 0.960377i | \(-0.589904\pi\) | ||||
−0.278703 | + | 0.960377i | \(0.589904\pi\) | |||||||
\(270\) | 0.585786 | 0.0356498 | ||||||||
\(271\) | 26.2132 | 1.59234 | 0.796169 | − | 0.605074i | \(-0.206856\pi\) | ||||
0.796169 | + | 0.605074i | \(0.206856\pi\) | |||||||
\(272\) | −2.41421 | −0.146383 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.0711 | 0.668828 | ||||||||
\(275\) | 1.92893 | 0.116319 | ||||||||
\(276\) | −1.41421 | −0.0851257 | ||||||||
\(277\) | 18.0711 | 1.08579 | 0.542893 | − | 0.839802i | \(-0.317329\pi\) | ||||
0.542893 | + | 0.839802i | \(0.317329\pi\) | |||||||
\(278\) | −13.0711 | −0.783951 | ||||||||
\(279\) | −8.48528 | −0.508001 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.686292 | 0.0409407 | 0.0204704 | − | 0.999790i | \(-0.493484\pi\) | ||||
0.0204704 | + | 0.999790i | \(0.493484\pi\) | |||||||
\(282\) | −1.00000 | −0.0595491 | ||||||||
\(283\) | −15.7574 | −0.936678 | −0.468339 | − | 0.883549i | \(-0.655147\pi\) | ||||
−0.468339 | + | 0.883549i | \(0.655147\pi\) | |||||||
\(284\) | −5.00000 | −0.296695 | ||||||||
\(285\) | −1.27208 | −0.0753514 | ||||||||
\(286\) | −0.414214 | −0.0244930 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −11.1716 | −0.657151 | ||||||||
\(290\) | 1.07107 | 0.0628953 | ||||||||
\(291\) | 0.928932 | 0.0544550 | ||||||||
\(292\) | 1.41421 | 0.0827606 | ||||||||
\(293\) | −9.89949 | −0.578335 | −0.289167 | − | 0.957279i | \(-0.593378\pi\) | ||||
−0.289167 | + | 0.957279i | \(0.593378\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.21320 | −0.0706354 | ||||||||
\(296\) | 1.41421 | 0.0821995 | ||||||||
\(297\) | 0.414214 | 0.0240351 | ||||||||
\(298\) | −4.92893 | −0.285525 | ||||||||
\(299\) | 1.41421 | 0.0817861 | ||||||||
\(300\) | 4.65685 | 0.268864 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.07107 | 0.234264 | ||||||||
\(303\) | 14.8284 | 0.851871 | ||||||||
\(304\) | −2.17157 | −0.124548 | ||||||||
\(305\) | 2.58579 | 0.148062 | ||||||||
\(306\) | −2.41421 | −0.138011 | ||||||||
\(307\) | −28.1127 | −1.60448 | −0.802238 | − | 0.597004i | \(-0.796358\pi\) | ||||
−0.802238 | + | 0.597004i | \(0.796358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.8284 | 0.957336 | ||||||||
\(310\) | 4.97056 | 0.282309 | ||||||||
\(311\) | −8.10051 | −0.459338 | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229669 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | 3.51472 | 0.198664 | 0.0993318 | − | 0.995054i | \(-0.468329\pi\) | ||||
0.0993318 | + | 0.995054i | \(0.468329\pi\) | |||||||
\(314\) | 9.72792 | 0.548978 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.6569 | −0.655749 | ||||||||
\(317\) | 29.7990 | 1.67368 | 0.836839 | − | 0.547449i | \(-0.184401\pi\) | ||||
0.836839 | + | 0.547449i | \(0.184401\pi\) | |||||||
\(318\) | −9.48528 | −0.531908 | ||||||||
\(319\) | 0.757359 | 0.0424040 | ||||||||
\(320\) | −0.585786 | −0.0327465 | ||||||||
\(321\) | 19.3137 | 1.07799 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.24264 | 0.291708 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.65685 | −0.258316 | ||||||||
\(326\) | −18.6569 | −1.03331 | ||||||||
\(327\) | 9.65685 | 0.534025 | ||||||||
\(328\) | −9.89949 | −0.546608 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.242641 | −0.0133569 | ||||||||
\(331\) | −22.4853 | −1.23590 | −0.617951 | − | 0.786216i | \(-0.712037\pi\) | ||||
−0.617951 | + | 0.786216i | \(0.712037\pi\) | |||||||
\(332\) | 7.65685 | 0.420224 | ||||||||
\(333\) | 1.41421 | 0.0774984 | ||||||||
\(334\) | −0.656854 | −0.0359415 | ||||||||
\(335\) | −1.07107 | −0.0585187 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.3137 | −1.10656 | −0.553279 | − | 0.832996i | \(-0.686624\pi\) | ||||
−0.553279 | + | 0.832996i | \(0.686624\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −4.89949 | −0.266104 | ||||||||
\(340\) | 1.41421 | 0.0766965 | ||||||||
\(341\) | 3.51472 | 0.190333 | ||||||||
\(342\) | −2.17157 | −0.117425 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.48528 | 0.349663 | ||||||||
\(345\) | 0.828427 | 0.0446010 | ||||||||
\(346\) | 5.48528 | 0.294891 | ||||||||
\(347\) | −8.72792 | −0.468539 | −0.234270 | − | 0.972172i | \(-0.575270\pi\) | ||||
−0.234270 | + | 0.972172i | \(0.575270\pi\) | |||||||
\(348\) | 1.82843 | 0.0980140 | ||||||||
\(349\) | −6.72792 | −0.360137 | −0.180069 | − | 0.983654i | \(-0.557632\pi\) | ||||
−0.180069 | + | 0.983654i | \(0.557632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −0.414214 | −0.0220777 | ||||||||
\(353\) | 12.6274 | 0.672090 | 0.336045 | − | 0.941846i | \(-0.390911\pi\) | ||||
0.336045 | + | 0.941846i | \(0.390911\pi\) | |||||||
\(354\) | −2.07107 | −0.110076 | ||||||||
\(355\) | 2.92893 | 0.155452 | ||||||||
\(356\) | 2.58579 | 0.137046 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.6569 | 1.03890 | ||||||||
\(359\) | −0.828427 | −0.0437227 | −0.0218614 | − | 0.999761i | \(-0.506959\pi\) | ||||
−0.0218614 | + | 0.999761i | \(0.506959\pi\) | |||||||
\(360\) | −0.585786 | −0.0308737 | ||||||||
\(361\) | −14.2843 | −0.751804 | ||||||||
\(362\) | 2.89949 | 0.152394 | ||||||||
\(363\) | 10.8284 | 0.568345 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.828427 | −0.0433619 | ||||||||
\(366\) | 4.41421 | 0.230735 | ||||||||
\(367\) | 12.6274 | 0.659146 | 0.329573 | − | 0.944130i | \(-0.393095\pi\) | ||||
0.329573 | + | 0.944130i | \(0.393095\pi\) | |||||||
\(368\) | 1.41421 | 0.0737210 | ||||||||
\(369\) | −9.89949 | −0.515347 | ||||||||
\(370\) | −0.828427 | −0.0430679 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.48528 | 0.439941 | ||||||||
\(373\) | −5.58579 | −0.289221 | −0.144611 | − | 0.989489i | \(-0.546193\pi\) | ||||
−0.144611 | + | 0.989489i | \(0.546193\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | −5.65685 | −0.292119 | ||||||||
\(376\) | 1.00000 | 0.0515711 | ||||||||
\(377\) | −1.82843 | −0.0941688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6274 | 0.956826 | 0.478413 | − | 0.878135i | \(-0.341212\pi\) | ||||
0.478413 | + | 0.878135i | \(0.341212\pi\) | |||||||
\(380\) | 1.27208 | 0.0652562 | ||||||||
\(381\) | 7.89949 | 0.404703 | ||||||||
\(382\) | −10.3431 | −0.529201 | ||||||||
\(383\) | 11.1716 | 0.570841 | 0.285420 | − | 0.958402i | \(-0.407867\pi\) | ||||
0.285420 | + | 0.958402i | \(0.407867\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.92893 | −0.149079 | ||||||||
\(387\) | 6.48528 | 0.329665 | ||||||||
\(388\) | −0.928932 | −0.0471594 | ||||||||
\(389\) | −4.51472 | −0.228905 | −0.114453 | − | 0.993429i | \(-0.536511\pi\) | ||||
−0.114453 | + | 0.993429i | \(0.536511\pi\) | |||||||
\(390\) | 0.585786 | 0.0296624 | ||||||||
\(391\) | −3.41421 | −0.172664 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.55635 | 0.482054 | ||||||||
\(394\) | −15.5563 | −0.783718 | ||||||||
\(395\) | 6.82843 | 0.343575 | ||||||||
\(396\) | −0.414214 | −0.0208150 | ||||||||
\(397\) | −9.55635 | −0.479619 | −0.239810 | − | 0.970820i | \(-0.577085\pi\) | ||||
−0.239810 | + | 0.970820i | \(0.577085\pi\) | |||||||
\(398\) | 2.72792 | 0.136738 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.65685 | −0.232843 | ||||||||
\(401\) | 19.8995 | 0.993733 | 0.496867 | − | 0.867827i | \(-0.334484\pi\) | ||||
0.496867 | + | 0.867827i | \(0.334484\pi\) | |||||||
\(402\) | −1.82843 | −0.0911937 | ||||||||
\(403\) | −8.48528 | −0.422682 | ||||||||
\(404\) | −14.8284 | −0.737742 | ||||||||
\(405\) | −0.585786 | −0.0291080 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.585786 | −0.0290364 | ||||||||
\(408\) | 2.41421 | 0.119521 | ||||||||
\(409\) | 32.5858 | 1.61126 | 0.805632 | − | 0.592417i | \(-0.201826\pi\) | ||||
0.805632 | + | 0.592417i | \(0.201826\pi\) | |||||||
\(410\) | 5.79899 | 0.286392 | ||||||||
\(411\) | −11.0711 | −0.546096 | ||||||||
\(412\) | −16.8284 | −0.829077 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.41421 | 0.0695048 | ||||||||
\(415\) | −4.48528 | −0.220174 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 13.0711 | 0.640093 | ||||||||
\(418\) | 0.899495 | 0.0439957 | ||||||||
\(419\) | 27.4558 | 1.34131 | 0.670653 | − | 0.741771i | \(-0.266014\pi\) | ||||
0.670653 | + | 0.741771i | \(0.266014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.07107 | 0.0522007 | 0.0261003 | − | 0.999659i | \(-0.491691\pi\) | ||||
0.0261003 | + | 0.999659i | \(0.491691\pi\) | |||||||
\(422\) | −12.9289 | −0.629371 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 9.48528 | 0.460646 | ||||||||
\(425\) | 11.2426 | 0.545348 | ||||||||
\(426\) | 5.00000 | 0.242251 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −19.3137 | −0.933563 | ||||||||
\(429\) | 0.414214 | 0.0199984 | ||||||||
\(430\) | −3.79899 | −0.183204 | ||||||||
\(431\) | 30.4853 | 1.46842 | 0.734212 | − | 0.678920i | \(-0.237552\pi\) | ||||
0.734212 | + | 0.678920i | \(0.237552\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 29.9706 | 1.44029 | 0.720147 | − | 0.693822i | \(-0.244074\pi\) | ||||
0.720147 | + | 0.693822i | \(0.244074\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.07107 | −0.0513538 | ||||||||
\(436\) | −9.65685 | −0.462479 | ||||||||
\(437\) | −3.07107 | −0.146909 | ||||||||
\(438\) | −1.41421 | −0.0675737 | ||||||||
\(439\) | 16.5858 | 0.791596 | 0.395798 | − | 0.918338i | \(-0.370468\pi\) | ||||
0.395798 | + | 0.918338i | \(0.370468\pi\) | |||||||
\(440\) | 0.242641 | 0.0115674 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.41421 | −0.114832 | ||||||||
\(443\) | −33.6985 | −1.60106 | −0.800532 | − | 0.599290i | \(-0.795449\pi\) | ||||
−0.800532 | + | 0.599290i | \(0.795449\pi\) | |||||||
\(444\) | −1.41421 | −0.0671156 | ||||||||
\(445\) | −1.51472 | −0.0718045 | ||||||||
\(446\) | −7.92893 | −0.375446 | ||||||||
\(447\) | 4.92893 | 0.233130 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.9706 | 1.17843 | 0.589217 | − | 0.807975i | \(-0.299436\pi\) | ||||
0.589217 | + | 0.807975i | \(0.299436\pi\) | |||||||
\(450\) | −4.65685 | −0.219526 | ||||||||
\(451\) | 4.10051 | 0.193085 | ||||||||
\(452\) | 4.89949 | 0.230453 | ||||||||
\(453\) | −4.07107 | −0.191275 | ||||||||
\(454\) | −21.1716 | −0.993631 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.17157 | 0.101693 | ||||||||
\(457\) | −3.07107 | −0.143658 | −0.0718292 | − | 0.997417i | \(-0.522884\pi\) | ||||
−0.0718292 | + | 0.997417i | \(0.522884\pi\) | |||||||
\(458\) | 26.4853 | 1.23758 | ||||||||
\(459\) | 2.41421 | 0.112686 | ||||||||
\(460\) | −0.828427 | −0.0386256 | ||||||||
\(461\) | −4.48528 | −0.208900 | −0.104450 | − | 0.994530i | \(-0.533308\pi\) | ||||
−0.104450 | + | 0.994530i | \(0.533308\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9706 | −0.974585 | −0.487292 | − | 0.873239i | \(-0.662015\pi\) | ||||
−0.487292 | + | 0.873239i | \(0.662015\pi\) | |||||||
\(464\) | −1.82843 | −0.0848826 | ||||||||
\(465\) | −4.97056 | −0.230504 | ||||||||
\(466\) | −17.7279 | −0.821230 | ||||||||
\(467\) | −11.4142 | −0.528187 | −0.264093 | − | 0.964497i | \(-0.585073\pi\) | ||||
−0.264093 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.585786 | −0.0270203 | ||||||||
\(471\) | −9.72792 | −0.448239 | ||||||||
\(472\) | 2.07107 | 0.0953286 | ||||||||
\(473\) | −2.68629 | −0.123516 | ||||||||
\(474\) | 11.6569 | 0.535417 | ||||||||
\(475\) | 10.1127 | 0.464002 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.48528 | 0.434301 | ||||||||
\(478\) | 4.51472 | 0.206498 | ||||||||
\(479\) | −32.1127 | −1.46727 | −0.733633 | − | 0.679546i | \(-0.762177\pi\) | ||||
−0.733633 | + | 0.679546i | \(0.762177\pi\) | |||||||
\(480\) | 0.585786 | 0.0267374 | ||||||||
\(481\) | 1.41421 | 0.0644826 | ||||||||
\(482\) | −2.14214 | −0.0975716 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8284 | −0.492201 | ||||||||
\(485\) | 0.544156 | 0.0247088 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 16.2132 | 0.734690 | 0.367345 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367345 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(488\) | −4.41421 | −0.199822 | ||||||||
\(489\) | 18.6569 | 0.843692 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.6569 | 1.06762 | 0.533809 | − | 0.845605i | \(-0.320760\pi\) | ||||
0.533809 | + | 0.845605i | \(0.320760\pi\) | |||||||
\(492\) | 9.89949 | 0.446304 | ||||||||
\(493\) | 4.41421 | 0.198806 | ||||||||
\(494\) | −2.17157 | −0.0977037 | ||||||||
\(495\) | 0.242641 | 0.0109059 | ||||||||
\(496\) | −8.48528 | −0.381000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.65685 | −0.343112 | ||||||||
\(499\) | 3.65685 | 0.163703 | 0.0818516 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818516 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(500\) | 5.65685 | 0.252982 | ||||||||
\(501\) | 0.656854 | 0.0293461 | ||||||||
\(502\) | 24.8284 | 1.10815 | ||||||||
\(503\) | 26.1421 | 1.16562 | 0.582810 | − | 0.812608i | \(-0.301953\pi\) | ||||
0.582810 | + | 0.812608i | \(0.301953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.68629 | 0.386535 | ||||||||
\(506\) | −0.585786 | −0.0260414 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −7.89949 | −0.350483 | ||||||||
\(509\) | 10.6274 | 0.471052 | 0.235526 | − | 0.971868i | \(-0.424319\pi\) | ||||
0.235526 | + | 0.971868i | \(0.424319\pi\) | |||||||
\(510\) | −1.41421 | −0.0626224 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.17157 | 0.0958773 | ||||||||
\(514\) | 26.4853 | 1.16822 | ||||||||
\(515\) | 9.85786 | 0.434389 | ||||||||
\(516\) | −6.48528 | −0.285499 | ||||||||
\(517\) | −0.414214 | −0.0182171 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.48528 | −0.240777 | ||||||||
\(520\) | −0.585786 | −0.0256884 | ||||||||
\(521\) | 40.6274 | 1.77992 | 0.889960 | − | 0.456039i | \(-0.150732\pi\) | ||||
0.889960 | + | 0.456039i | \(0.150732\pi\) | |||||||
\(522\) | −1.82843 | −0.0800281 | ||||||||
\(523\) | −16.8284 | −0.735856 | −0.367928 | − | 0.929854i | \(-0.619933\pi\) | ||||
−0.367928 | + | 0.929854i | \(0.619933\pi\) | |||||||
\(524\) | −9.55635 | −0.417471 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.5858 | 0.897583 | ||||||||
\(527\) | 20.4853 | 0.892353 | ||||||||
\(528\) | 0.414214 | 0.0180263 | ||||||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | −5.55635 | −0.241352 | ||||||||
\(531\) | 2.07107 | 0.0898767 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.89949 | −0.428795 | ||||||||
\(534\) | −2.58579 | −0.111898 | ||||||||
\(535\) | 11.3137 | 0.489134 | ||||||||
\(536\) | 1.82843 | 0.0789760 | ||||||||
\(537\) | −19.6569 | −0.848256 | ||||||||
\(538\) | −9.14214 | −0.394145 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.585786 | 0.0252082 | ||||||||
\(541\) | 23.0711 | 0.991903 | 0.495951 | − | 0.868350i | \(-0.334819\pi\) | ||||
0.495951 | + | 0.868350i | \(0.334819\pi\) | |||||||
\(542\) | 26.2132 | 1.12595 | ||||||||
\(543\) | −2.89949 | −0.124429 | ||||||||
\(544\) | −2.41421 | −0.103509 | ||||||||
\(545\) | 5.65685 | 0.242313 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.8701 | −1.31991 | −0.659954 | − | 0.751306i | \(-0.729424\pi\) | ||||
−0.659954 | + | 0.751306i | \(0.729424\pi\) | |||||||
\(548\) | 11.0711 | 0.472933 | ||||||||
\(549\) | −4.41421 | −0.188394 | ||||||||
\(550\) | 1.92893 | 0.0822499 | ||||||||
\(551\) | 3.97056 | 0.169152 | ||||||||
\(552\) | −1.41421 | −0.0601929 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.0711 | 0.767766 | ||||||||
\(555\) | 0.828427 | 0.0351648 | ||||||||
\(556\) | −13.0711 | −0.554337 | ||||||||
\(557\) | −32.6274 | −1.38247 | −0.691234 | − | 0.722631i | \(-0.742933\pi\) | ||||
−0.691234 | + | 0.722631i | \(0.742933\pi\) | |||||||
\(558\) | −8.48528 | −0.359211 | ||||||||
\(559\) | 6.48528 | 0.274298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | 0.686292 | 0.0289495 | ||||||||
\(563\) | −32.7696 | −1.38107 | −0.690536 | − | 0.723298i | \(-0.742625\pi\) | ||||
−0.690536 | + | 0.723298i | \(0.742625\pi\) | |||||||
\(564\) | −1.00000 | −0.0421076 | ||||||||
\(565\) | −2.87006 | −0.120744 | ||||||||
\(566\) | −15.7574 | −0.662331 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.00000 | −0.209795 | ||||||||
\(569\) | 23.7279 | 0.994726 | 0.497363 | − | 0.867542i | \(-0.334302\pi\) | ||||
0.497363 | + | 0.867542i | \(0.334302\pi\) | |||||||
\(570\) | −1.27208 | −0.0532815 | ||||||||
\(571\) | −31.3137 | −1.31044 | −0.655219 | − | 0.755439i | \(-0.727424\pi\) | ||||
−0.655219 | + | 0.755439i | \(0.727424\pi\) | |||||||
\(572\) | −0.414214 | −0.0173191 | ||||||||
\(573\) | 10.3431 | 0.432091 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.58579 | −0.274646 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 16.3431 | 0.680374 | 0.340187 | − | 0.940358i | \(-0.389510\pi\) | ||||
0.340187 | + | 0.940358i | \(0.389510\pi\) | |||||||
\(578\) | −11.1716 | −0.464676 | ||||||||
\(579\) | 2.92893 | 0.121722 | ||||||||
\(580\) | 1.07107 | 0.0444737 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.928932 | 0.0385055 | ||||||||
\(583\) | −3.92893 | −0.162720 | ||||||||
\(584\) | 1.41421 | 0.0585206 | ||||||||
\(585\) | −0.585786 | −0.0242193 | ||||||||
\(586\) | −9.89949 | −0.408944 | ||||||||
\(587\) | −1.58579 | −0.0654524 | −0.0327262 | − | 0.999464i | \(-0.510419\pi\) | ||||
−0.0327262 | + | 0.999464i | \(0.510419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.4264 | 0.759247 | ||||||||
\(590\) | −1.21320 | −0.0499468 | ||||||||
\(591\) | 15.5563 | 0.639903 | ||||||||
\(592\) | 1.41421 | 0.0581238 | ||||||||
\(593\) | −34.3848 | −1.41201 | −0.706007 | − | 0.708205i | \(-0.749505\pi\) | ||||
−0.706007 | + | 0.708205i | \(0.749505\pi\) | |||||||
\(594\) | 0.414214 | 0.0169954 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.92893 | −0.201897 | ||||||||
\(597\) | −2.72792 | −0.111646 | ||||||||
\(598\) | 1.41421 | 0.0578315 | ||||||||
\(599\) | 1.55635 | 0.0635907 | 0.0317954 | − | 0.999494i | \(-0.489878\pi\) | ||||
0.0317954 | + | 0.999494i | \(0.489878\pi\) | |||||||
\(600\) | 4.65685 | 0.190115 | ||||||||
\(601\) | 1.20101 | 0.0489902 | 0.0244951 | − | 0.999700i | \(-0.492202\pi\) | ||||
0.0244951 | + | 0.999700i | \(0.492202\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.82843 | 0.0744593 | ||||||||
\(604\) | 4.07107 | 0.165649 | ||||||||
\(605\) | 6.34315 | 0.257886 | ||||||||
\(606\) | 14.8284 | 0.602364 | ||||||||
\(607\) | 34.5269 | 1.40140 | 0.700702 | − | 0.713454i | \(-0.252870\pi\) | ||||
0.700702 | + | 0.713454i | \(0.252870\pi\) | |||||||
\(608\) | −2.17157 | −0.0880689 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.58579 | 0.104695 | ||||||||
\(611\) | 1.00000 | 0.0404557 | ||||||||
\(612\) | −2.41421 | −0.0975888 | ||||||||
\(613\) | −7.79899 | −0.314998 | −0.157499 | − | 0.987519i | \(-0.550343\pi\) | ||||
−0.157499 | + | 0.987519i | \(0.550343\pi\) | |||||||
\(614\) | −28.1127 | −1.13454 | ||||||||
\(615\) | −5.79899 | −0.233838 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.1421 | −0.971926 | −0.485963 | − | 0.873979i | \(-0.661531\pi\) | ||||
−0.485963 | + | 0.873979i | \(0.661531\pi\) | |||||||
\(618\) | 16.8284 | 0.676939 | ||||||||
\(619\) | 20.8284 | 0.837165 | 0.418583 | − | 0.908179i | \(-0.362527\pi\) | ||||
0.418583 | + | 0.908179i | \(0.362527\pi\) | |||||||
\(620\) | 4.97056 | 0.199623 | ||||||||
\(621\) | −1.41421 | −0.0567504 | ||||||||
\(622\) | −8.10051 | −0.324801 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 3.51472 | 0.140476 | ||||||||
\(627\) | −0.899495 | −0.0359224 | ||||||||
\(628\) | 9.72792 | 0.388186 | ||||||||
\(629\) | −3.41421 | −0.136134 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.6274 | 1.29888 | 0.649438 | − | 0.760414i | \(-0.275004\pi\) | ||||
0.649438 | + | 0.760414i | \(0.275004\pi\) | |||||||
\(632\) | −11.6569 | −0.463685 | ||||||||
\(633\) | 12.9289 | 0.513879 | ||||||||
\(634\) | 29.7990 | 1.18347 | ||||||||
\(635\) | 4.62742 | 0.183633 | ||||||||
\(636\) | −9.48528 | −0.376116 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.757359 | 0.0299841 | ||||||||
\(639\) | −5.00000 | −0.197797 | ||||||||
\(640\) | −0.585786 | −0.0231552 | ||||||||
\(641\) | 31.7990 | 1.25598 | 0.627992 | − | 0.778220i | \(-0.283877\pi\) | ||||
0.627992 | + | 0.778220i | \(0.283877\pi\) | |||||||
\(642\) | 19.3137 | 0.762251 | ||||||||
\(643\) | −2.51472 | −0.0991708 | −0.0495854 | − | 0.998770i | \(-0.515790\pi\) | ||||
−0.0495854 | + | 0.998770i | \(0.515790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.79899 | 0.149585 | ||||||||
\(646\) | 5.24264 | 0.206269 | ||||||||
\(647\) | −9.02944 | −0.354984 | −0.177492 | − | 0.984122i | \(-0.556798\pi\) | ||||
−0.177492 | + | 0.984122i | \(0.556798\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −0.857864 | −0.0336741 | ||||||||
\(650\) | −4.65685 | −0.182657 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.6569 | −0.730659 | ||||||||
\(653\) | 22.1421 | 0.866489 | 0.433244 | − | 0.901276i | \(-0.357369\pi\) | ||||
0.433244 | + | 0.901276i | \(0.357369\pi\) | |||||||
\(654\) | 9.65685 | 0.377613 | ||||||||
\(655\) | 5.59798 | 0.218731 | ||||||||
\(656\) | −9.89949 | −0.386510 | ||||||||
\(657\) | 1.41421 | 0.0551737 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5858 | 0.412364 | 0.206182 | − | 0.978514i | \(-0.433896\pi\) | ||||
0.206182 | + | 0.978514i | \(0.433896\pi\) | |||||||
\(660\) | −0.242641 | −0.00944478 | ||||||||
\(661\) | 40.2426 | 1.56526 | 0.782629 | − | 0.622489i | \(-0.213878\pi\) | ||||
0.782629 | + | 0.622489i | \(0.213878\pi\) | |||||||
\(662\) | −22.4853 | −0.873915 | ||||||||
\(663\) | 2.41421 | 0.0937603 | ||||||||
\(664\) | 7.65685 | 0.297144 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.41421 | 0.0547997 | ||||||||
\(667\) | −2.58579 | −0.100122 | ||||||||
\(668\) | −0.656854 | −0.0254145 | ||||||||
\(669\) | 7.92893 | 0.306550 | ||||||||
\(670\) | −1.07107 | −0.0413790 | ||||||||
\(671\) | 1.82843 | 0.0705856 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.1421 | 1.62446 | 0.812230 | − | 0.583337i | \(-0.198253\pi\) | ||||
0.812230 | + | 0.583337i | \(0.198253\pi\) | |||||||
\(674\) | −20.3137 | −0.782455 | ||||||||
\(675\) | 4.65685 | 0.179242 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 15.0000 | 0.576497 | 0.288248 | − | 0.957556i | \(-0.406927\pi\) | ||||
0.288248 | + | 0.957556i | \(0.406927\pi\) | |||||||
\(678\) | −4.89949 | −0.188164 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.41421 | 0.0542326 | ||||||||
\(681\) | 21.1716 | 0.811296 | ||||||||
\(682\) | 3.51472 | 0.134586 | ||||||||
\(683\) | −14.1421 | −0.541134 | −0.270567 | − | 0.962701i | \(-0.587211\pi\) | ||||
−0.270567 | + | 0.962701i | \(0.587211\pi\) | |||||||
\(684\) | −2.17157 | −0.0830322 | ||||||||
\(685\) | −6.48528 | −0.247790 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.4853 | −1.01048 | ||||||||
\(688\) | 6.48528 | 0.247249 | ||||||||
\(689\) | 9.48528 | 0.361360 | ||||||||
\(690\) | 0.828427 | 0.0315377 | ||||||||
\(691\) | −20.6569 | −0.785824 | −0.392912 | − | 0.919576i | \(-0.628532\pi\) | ||||
−0.392912 | + | 0.919576i | \(0.628532\pi\) | |||||||
\(692\) | 5.48528 | 0.208519 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.72792 | −0.331307 | ||||||||
\(695\) | 7.65685 | 0.290441 | ||||||||
\(696\) | 1.82843 | 0.0693064 | ||||||||
\(697\) | 23.8995 | 0.905258 | ||||||||
\(698\) | −6.72792 | −0.254656 | ||||||||
\(699\) | 17.7279 | 0.670532 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.1716 | −1.10180 | −0.550898 | − | 0.834573i | \(-0.685715\pi\) | ||||
−0.550898 | + | 0.834573i | \(0.685715\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | −3.07107 | −0.115828 | ||||||||
\(704\) | −0.414214 | −0.0156113 | ||||||||
\(705\) | 0.585786 | 0.0220620 | ||||||||
\(706\) | 12.6274 | 0.475239 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.07107 | −0.0778355 | ||||||||
\(709\) | −36.8701 | −1.38468 | −0.692342 | − | 0.721569i | \(-0.743421\pi\) | ||||
−0.692342 | + | 0.721569i | \(0.743421\pi\) | |||||||
\(710\) | 2.92893 | 0.109921 | ||||||||
\(711\) | −11.6569 | −0.437166 | ||||||||
\(712\) | 2.58579 | 0.0969064 | ||||||||
\(713\) | −12.0000 | −0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.242641 | 0.00907425 | ||||||||
\(716\) | 19.6569 | 0.734611 | ||||||||
\(717\) | −4.51472 | −0.168605 | ||||||||
\(718\) | −0.828427 | −0.0309166 | ||||||||
\(719\) | 9.31371 | 0.347343 | 0.173671 | − | 0.984804i | \(-0.444437\pi\) | ||||
0.173671 | + | 0.984804i | \(0.444437\pi\) | |||||||
\(720\) | −0.585786 | −0.0218310 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −14.2843 | −0.531606 | ||||||||
\(723\) | 2.14214 | 0.0796669 | ||||||||
\(724\) | 2.89949 | 0.107759 | ||||||||
\(725\) | 8.51472 | 0.316229 | ||||||||
\(726\) | 10.8284 | 0.401881 | ||||||||
\(727\) | −50.4264 | −1.87021 | −0.935106 | − | 0.354368i | \(-0.884696\pi\) | ||||
−0.935106 | + | 0.354368i | \(0.884696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.828427 | −0.0306615 | ||||||||
\(731\) | −15.6569 | −0.579090 | ||||||||
\(732\) | 4.41421 | 0.163154 | ||||||||
\(733\) | −28.5858 | −1.05584 | −0.527920 | − | 0.849294i | \(-0.677028\pi\) | ||||
−0.527920 | + | 0.849294i | \(0.677028\pi\) | |||||||
\(734\) | 12.6274 | 0.466086 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.41421 | 0.0521286 | ||||||||
\(737\) | −0.757359 | −0.0278977 | ||||||||
\(738\) | −9.89949 | −0.364405 | ||||||||
\(739\) | −30.0000 | −1.10357 | −0.551784 | − | 0.833987i | \(-0.686053\pi\) | ||||
−0.551784 | + | 0.833987i | \(0.686053\pi\) | |||||||
\(740\) | −0.828427 | −0.0304536 | ||||||||
\(741\) | 2.17157 | 0.0797747 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.1716 | 0.446532 | 0.223266 | − | 0.974758i | \(-0.428328\pi\) | ||||
0.223266 | + | 0.974758i | \(0.428328\pi\) | |||||||
\(744\) | 8.48528 | 0.311086 | ||||||||
\(745\) | 2.88730 | 0.105783 | ||||||||
\(746\) | −5.58579 | −0.204510 | ||||||||
\(747\) | 7.65685 | 0.280150 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.65685 | −0.206559 | ||||||||
\(751\) | −19.3137 | −0.704767 | −0.352384 | − | 0.935856i | \(-0.614629\pi\) | ||||
−0.352384 | + | 0.935856i | \(0.614629\pi\) | |||||||
\(752\) | 1.00000 | 0.0364662 | ||||||||
\(753\) | −24.8284 | −0.904798 | ||||||||
\(754\) | −1.82843 | −0.0665874 | ||||||||
\(755\) | −2.38478 | −0.0867909 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.7574 | −1.11790 | −0.558948 | − | 0.829203i | \(-0.688795\pi\) | ||||
−0.558948 | + | 0.829203i | \(0.688795\pi\) | |||||||
\(758\) | 18.6274 | 0.676578 | ||||||||
\(759\) | 0.585786 | 0.0212627 | ||||||||
\(760\) | 1.27208 | 0.0461431 | ||||||||
\(761\) | 43.1127 | 1.56283 | 0.781417 | − | 0.624009i | \(-0.214497\pi\) | ||||
0.781417 | + | 0.624009i | \(0.214497\pi\) | |||||||
\(762\) | 7.89949 | 0.286169 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.3431 | −0.374202 | ||||||||
\(765\) | 1.41421 | 0.0511310 | ||||||||
\(766\) | 11.1716 | 0.403645 | ||||||||
\(767\) | 2.07107 | 0.0747819 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 9.89949 | 0.356985 | 0.178492 | − | 0.983941i | \(-0.442878\pi\) | ||||
0.178492 | + | 0.983941i | \(0.442878\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.4853 | −0.953844 | ||||||||
\(772\) | −2.92893 | −0.105415 | ||||||||
\(773\) | 18.9706 | 0.682324 | 0.341162 | − | 0.940005i | \(-0.389180\pi\) | ||||
0.341162 | + | 0.940005i | \(0.389180\pi\) | |||||||
\(774\) | 6.48528 | 0.233109 | ||||||||
\(775\) | 39.5147 | 1.41941 | ||||||||
\(776\) | −0.928932 | −0.0333467 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.51472 | −0.161861 | ||||||||
\(779\) | 21.4975 | 0.770227 | ||||||||
\(780\) | 0.585786 | 0.0209745 | ||||||||
\(781\) | 2.07107 | 0.0741086 | ||||||||
\(782\) | −3.41421 | −0.122092 | ||||||||
\(783\) | 1.82843 | 0.0653427 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.69848 | −0.203388 | ||||||||
\(786\) | 9.55635 | 0.340864 | ||||||||
\(787\) | −26.3137 | −0.937982 | −0.468991 | − | 0.883203i | \(-0.655382\pi\) | ||||
−0.468991 | + | 0.883203i | \(0.655382\pi\) | |||||||
\(788\) | −15.5563 | −0.554172 | ||||||||
\(789\) | −20.5858 | −0.732873 | ||||||||
\(790\) | 6.82843 | 0.242945 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.414214 | −0.0147184 | ||||||||
\(793\) | −4.41421 | −0.156753 | ||||||||
\(794\) | −9.55635 | −0.339142 | ||||||||
\(795\) | 5.55635 | 0.197063 | ||||||||
\(796\) | 2.72792 | 0.0966886 | ||||||||
\(797\) | 34.3431 | 1.21650 | 0.608248 | − | 0.793747i | \(-0.291872\pi\) | ||||
0.608248 | + | 0.793747i | \(0.291872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.41421 | −0.0854087 | ||||||||
\(800\) | −4.65685 | −0.164645 | ||||||||
\(801\) | 2.58579 | 0.0913643 | ||||||||
\(802\) | 19.8995 | 0.702676 | ||||||||
\(803\) | −0.585786 | −0.0206720 | ||||||||
\(804\) | −1.82843 | −0.0644837 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.48528 | −0.298881 | ||||||||
\(807\) | 9.14214 | 0.321818 | ||||||||
\(808\) | −14.8284 | −0.521662 | ||||||||
\(809\) | −17.5858 | −0.618283 | −0.309142 | − | 0.951016i | \(-0.600042\pi\) | ||||
−0.309142 | + | 0.951016i | \(0.600042\pi\) | |||||||
\(810\) | −0.585786 | −0.0205824 | ||||||||
\(811\) | 55.4558 | 1.94732 | 0.973659 | − | 0.228009i | \(-0.0732216\pi\) | ||||
0.973659 | + | 0.228009i | \(0.0732216\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.2132 | −0.919337 | ||||||||
\(814\) | −0.585786 | −0.0205318 | ||||||||
\(815\) | 10.9289 | 0.382824 | ||||||||
\(816\) | 2.41421 | 0.0845144 | ||||||||
\(817\) | −14.0833 | −0.492711 | ||||||||
\(818\) | 32.5858 | 1.13934 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.79899 | 0.202510 | ||||||||
\(821\) | 47.8995 | 1.67170 | 0.835852 | − | 0.548955i | \(-0.184974\pi\) | ||||
0.835852 | + | 0.548955i | \(0.184974\pi\) | |||||||
\(822\) | −11.0711 | −0.386148 | ||||||||
\(823\) | −43.8406 | −1.52819 | −0.764094 | − | 0.645105i | \(-0.776814\pi\) | ||||
−0.764094 | + | 0.645105i | \(0.776814\pi\) | |||||||
\(824\) | −16.8284 | −0.586246 | ||||||||
\(825\) | −1.92893 | −0.0671568 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.3553 | 1.61193 | 0.805967 | − | 0.591961i | \(-0.201646\pi\) | ||||
0.805967 | + | 0.591961i | \(0.201646\pi\) | |||||||
\(828\) | 1.41421 | 0.0491473 | ||||||||
\(829\) | −26.6985 | −0.927277 | −0.463638 | − | 0.886025i | \(-0.653456\pi\) | ||||
−0.463638 | + | 0.886025i | \(0.653456\pi\) | |||||||
\(830\) | −4.48528 | −0.155686 | ||||||||
\(831\) | −18.0711 | −0.626878 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.0711 | 0.452614 | ||||||||
\(835\) | 0.384776 | 0.0133157 | ||||||||
\(836\) | 0.899495 | 0.0311097 | ||||||||
\(837\) | 8.48528 | 0.293294 | ||||||||
\(838\) | 27.4558 | 0.948446 | ||||||||
\(839\) | −31.8284 | −1.09884 | −0.549420 | − | 0.835547i | \(-0.685151\pi\) | ||||
−0.549420 | + | 0.835547i | \(0.685151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6569 | −0.884719 | ||||||||
\(842\) | 1.07107 | 0.0369114 | ||||||||
\(843\) | −0.686292 | −0.0236371 | ||||||||
\(844\) | −12.9289 | −0.445032 | ||||||||
\(845\) | −0.585786 | −0.0201517 | ||||||||
\(846\) | 1.00000 | 0.0343807 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.48528 | 0.325726 | ||||||||
\(849\) | 15.7574 | 0.540791 | ||||||||
\(850\) | 11.2426 | 0.385619 | ||||||||
\(851\) | 2.00000 | 0.0685591 | ||||||||
\(852\) | 5.00000 | 0.171297 | ||||||||
\(853\) | 6.72792 | 0.230360 | 0.115180 | − | 0.993345i | \(-0.463256\pi\) | ||||
0.115180 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.27208 | 0.0435041 | ||||||||
\(856\) | −19.3137 | −0.660129 | ||||||||
\(857\) | 20.5563 | 0.702192 | 0.351096 | − | 0.936340i | \(-0.385809\pi\) | ||||
0.351096 | + | 0.936340i | \(0.385809\pi\) | |||||||
\(858\) | 0.414214 | 0.0141410 | ||||||||
\(859\) | −11.7990 | −0.402576 | −0.201288 | − | 0.979532i | \(-0.564513\pi\) | ||||
−0.201288 | + | 0.979532i | \(0.564513\pi\) | |||||||
\(860\) | −3.79899 | −0.129544 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.4853 | 1.03833 | ||||||||
\(863\) | 39.3137 | 1.33825 | 0.669127 | − | 0.743148i | \(-0.266668\pi\) | ||||
0.669127 | + | 0.743148i | \(0.266668\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −3.21320 | −0.109252 | ||||||||
\(866\) | 29.9706 | 1.01844 | ||||||||
\(867\) | 11.1716 | 0.379407 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.82843 | 0.163793 | ||||||||
\(870\) | −1.07107 | −0.0363126 | ||||||||
\(871\) | 1.82843 | 0.0619539 | ||||||||
\(872\) | −9.65685 | −0.327022 | ||||||||
\(873\) | −0.928932 | −0.0314396 | ||||||||
\(874\) | −3.07107 | −0.103880 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.41421 | −0.0477818 | ||||||||
\(877\) | −40.0416 | −1.35211 | −0.676055 | − | 0.736851i | \(-0.736312\pi\) | ||||
−0.676055 | + | 0.736851i | \(0.736312\pi\) | |||||||
\(878\) | 16.5858 | 0.559743 | ||||||||
\(879\) | 9.89949 | 0.333902 | ||||||||
\(880\) | 0.242641 | 0.00817942 | ||||||||
\(881\) | 18.4853 | 0.622785 | 0.311392 | − | 0.950281i | \(-0.399205\pi\) | ||||
0.311392 | + | 0.950281i | \(0.399205\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.75736 | −0.328361 | −0.164181 | − | 0.986430i | \(-0.552498\pi\) | ||||
−0.164181 | + | 0.986430i | \(0.552498\pi\) | |||||||
\(884\) | −2.41421 | −0.0811988 | ||||||||
\(885\) | 1.21320 | 0.0407814 | ||||||||
\(886\) | −33.6985 | −1.13212 | ||||||||
\(887\) | 48.9117 | 1.64229 | 0.821147 | − | 0.570717i | \(-0.193335\pi\) | ||||
0.821147 | + | 0.570717i | \(0.193335\pi\) | |||||||
\(888\) | −1.41421 | −0.0474579 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.51472 | −0.0507735 | ||||||||
\(891\) | −0.414214 | −0.0138767 | ||||||||
\(892\) | −7.92893 | −0.265480 | ||||||||
\(893\) | −2.17157 | −0.0726689 | ||||||||
\(894\) | 4.92893 | 0.164848 | ||||||||
\(895\) | −11.5147 | −0.384895 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.41421 | −0.0472192 | ||||||||
\(898\) | 24.9706 | 0.833278 | ||||||||
\(899\) | 15.5147 | 0.517445 | ||||||||
\(900\) | −4.65685 | −0.155228 | ||||||||
\(901\) | −22.8995 | −0.762893 | ||||||||
\(902\) | 4.10051 | 0.136532 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.89949 | 0.162955 | ||||||||
\(905\) | −1.69848 | −0.0564595 | ||||||||
\(906\) | −4.07107 | −0.135252 | ||||||||
\(907\) | 54.3848 | 1.80582 | 0.902908 | − | 0.429833i | \(-0.141428\pi\) | ||||
0.902908 | + | 0.429833i | \(0.141428\pi\) | |||||||
\(908\) | −21.1716 | −0.702603 | ||||||||
\(909\) | −14.8284 | −0.491828 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.34315 | −0.143895 | −0.0719474 | − | 0.997408i | \(-0.522921\pi\) | ||||
−0.0719474 | + | 0.997408i | \(0.522921\pi\) | |||||||
\(912\) | 2.17157 | 0.0719080 | ||||||||
\(913\) | −3.17157 | −0.104964 | ||||||||
\(914\) | −3.07107 | −0.101582 | ||||||||
\(915\) | −2.58579 | −0.0854835 | ||||||||
\(916\) | 26.4853 | 0.875098 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.41421 | 0.0796809 | ||||||||
\(919\) | 1.79899 | 0.0593432 | 0.0296716 | − | 0.999560i | \(-0.490554\pi\) | ||||
0.0296716 | + | 0.999560i | \(0.490554\pi\) | |||||||
\(920\) | −0.828427 | −0.0273124 | ||||||||
\(921\) | 28.1127 | 0.926345 | ||||||||
\(922\) | −4.48528 | −0.147715 | ||||||||
\(923\) | −5.00000 | −0.164577 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.58579 | −0.216539 | ||||||||
\(926\) | −20.9706 | −0.689135 | ||||||||
\(927\) | −16.8284 | −0.552718 | ||||||||
\(928\) | −1.82843 | −0.0600211 | ||||||||
\(929\) | 34.6863 | 1.13802 | 0.569010 | − | 0.822330i | \(-0.307327\pi\) | ||||
0.569010 | + | 0.822330i | \(0.307327\pi\) | |||||||
\(930\) | −4.97056 | −0.162991 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17.7279 | −0.580697 | ||||||||
\(933\) | 8.10051 | 0.265199 | ||||||||
\(934\) | −11.4142 | −0.373484 | ||||||||
\(935\) | −0.585786 | −0.0191573 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 42.6569 | 1.39354 | 0.696769 | − | 0.717295i | \(-0.254620\pi\) | ||||
0.696769 | + | 0.717295i | \(0.254620\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.51472 | −0.114699 | ||||||||
\(940\) | −0.585786 | −0.0191062 | ||||||||
\(941\) | −12.9706 | −0.422828 | −0.211414 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211414 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(942\) | −9.72792 | −0.316953 | ||||||||
\(943\) | −14.0000 | −0.455903 | ||||||||
\(944\) | 2.07107 | 0.0674075 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.68629 | −0.0873389 | ||||||||
\(947\) | 8.41421 | 0.273425 | 0.136713 | − | 0.990611i | \(-0.456346\pi\) | ||||
0.136713 | + | 0.990611i | \(0.456346\pi\) | |||||||
\(948\) | 11.6569 | 0.378597 | ||||||||
\(949\) | 1.41421 | 0.0459073 | ||||||||
\(950\) | 10.1127 | 0.328099 | ||||||||
\(951\) | −29.7990 | −0.966298 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.5858 | −1.34710 | −0.673548 | − | 0.739144i | \(-0.735230\pi\) | ||||
−0.673548 | + | 0.739144i | \(0.735230\pi\) | |||||||
\(954\) | 9.48528 | 0.307097 | ||||||||
\(955\) | 6.05887 | 0.196061 | ||||||||
\(956\) | 4.51472 | 0.146016 | ||||||||
\(957\) | −0.757359 | −0.0244819 | ||||||||
\(958\) | −32.1127 | −1.03751 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.585786 | 0.0189062 | ||||||||
\(961\) | 41.0000 | 1.32258 | ||||||||
\(962\) | 1.41421 | 0.0455961 | ||||||||
\(963\) | −19.3137 | −0.622376 | ||||||||
\(964\) | −2.14214 | −0.0689935 | ||||||||
\(965\) | 1.71573 | 0.0552313 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5858 | −0.436889 | −0.218445 | − | 0.975849i | \(-0.570098\pi\) | ||||
−0.218445 | + | 0.975849i | \(0.570098\pi\) | |||||||
\(968\) | −10.8284 | −0.348039 | ||||||||
\(969\) | −5.24264 | −0.168418 | ||||||||
\(970\) | 0.544156 | 0.0174718 | ||||||||
\(971\) | −32.5269 | −1.04384 | −0.521919 | − | 0.852995i | \(-0.674784\pi\) | ||||
−0.521919 | + | 0.852995i | \(0.674784\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 16.2132 | 0.519505 | ||||||||
\(975\) | 4.65685 | 0.149139 | ||||||||
\(976\) | −4.41421 | −0.141296 | ||||||||
\(977\) | 43.1716 | 1.38118 | 0.690590 | − | 0.723246i | \(-0.257351\pi\) | ||||
0.690590 | + | 0.723246i | \(0.257351\pi\) | |||||||
\(978\) | 18.6569 | 0.596580 | ||||||||
\(979\) | −1.07107 | −0.0342315 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.65685 | −0.308320 | ||||||||
\(982\) | 23.6569 | 0.754921 | ||||||||
\(983\) | −29.4853 | −0.940434 | −0.470217 | − | 0.882551i | \(-0.655824\pi\) | ||||
−0.470217 | + | 0.882551i | \(0.655824\pi\) | |||||||
\(984\) | 9.89949 | 0.315584 | ||||||||
\(985\) | 9.11270 | 0.290355 | ||||||||
\(986\) | 4.41421 | 0.140577 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.17157 | −0.0690869 | ||||||||
\(989\) | 9.17157 | 0.291639 | ||||||||
\(990\) | 0.242641 | 0.00771163 | ||||||||
\(991\) | −0.686292 | −0.0218008 | −0.0109004 | − | 0.999941i | \(-0.503470\pi\) | ||||
−0.0109004 | + | 0.999941i | \(0.503470\pi\) | |||||||
\(992\) | −8.48528 | −0.269408 | ||||||||
\(993\) | 22.4853 | 0.713549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.59798 | −0.0506594 | ||||||||
\(996\) | −7.65685 | −0.242617 | ||||||||
\(997\) | 52.4975 | 1.66261 | 0.831306 | − | 0.555815i | \(-0.187594\pi\) | ||||
0.831306 | + | 0.555815i | \(0.187594\pi\) | |||||||
\(998\) | 3.65685 | 0.115756 | ||||||||
\(999\) | −1.41421 | −0.0447437 |
(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 | 3822.2.a.bn.1.2 | 2 | ||
7.2 | even | 3 | 546.2.i.i.235.1 | yes | 4 | ||
7.4 | even | 3 | 546.2.i.i.79.1 | ✓ | 4 | ||
7.6 | odd | 2 | 3822.2.a.bu.1.1 | 2 | |||
21.2 | odd | 6 | 1638.2.j.m.235.2 | 4 | |||
21.11 | odd | 6 | 1638.2.j.m.1171.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.i.79.1 | ✓ | 4 | 7.4 | even | 3 | ||
546.2.i.i.235.1 | yes | 4 | 7.2 | even | 3 | ||
1638.2.j.m.235.2 | 4 | 21.2 | odd | 6 | |||
1638.2.j.m.1171.2 | 4 | 21.11 | odd | 6 | |||
3822.2.a.bn.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3822.2.a.bu.1.1 | 2 | 7.6 | odd | 2 |