Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.41421 | 1.24211 | 0.621053 | − | 0.783769i | \(-0.286705\pi\) | ||||
0.621053 | + | 0.783769i | \(0.286705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 7.65685 | 1.59656 | 0.798282 | − | 0.602284i | \(-0.205742\pi\) | ||||
0.798282 | + | 0.602284i | \(0.205742\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | −1.41421 | −0.277350 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.65685 | −1.05045 | −0.525226 | − | 0.850963i | \(-0.676019\pi\) | ||||
−0.525226 | + | 0.850963i | \(0.676019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.07107 | −0.551580 | −0.275790 | − | 0.961218i | \(-0.588939\pi\) | ||||
−0.275790 | + | 0.961218i | \(0.588939\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.65685 | 0.601183 | 0.300592 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300592 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(38\) | −5.41421 | −0.878301 | ||||||||
\(39\) | −1.41421 | −0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.65685 | 1.50815 | 0.754074 | − | 0.656790i | \(-0.228086\pi\) | ||||
0.754074 | + | 0.656790i | \(0.228086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.65685 | −1.12894 | ||||||||
\(47\) | −1.41421 | −0.206284 | −0.103142 | − | 0.994667i | \(-0.532890\pi\) | ||||
−0.103142 | + | 0.994667i | \(0.532890\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 1.41421 | 0.196116 | ||||||||
\(53\) | −3.65685 | −0.502308 | −0.251154 | − | 0.967947i | \(-0.580810\pi\) | ||||
−0.251154 | + | 0.967947i | \(0.580810\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.41421 | −0.717130 | ||||||||
\(58\) | 5.65685 | 0.742781 | ||||||||
\(59\) | 6.82843 | 0.888985 | 0.444493 | − | 0.895782i | \(-0.353384\pi\) | ||||
0.444493 | + | 0.895782i | \(0.353384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41421 | −0.181071 | −0.0905357 | − | 0.995893i | \(-0.528858\pi\) | ||||
−0.0905357 | + | 0.995893i | \(0.528858\pi\) | |||||||
\(62\) | 3.07107 | 0.390026 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −11.3137 | −1.38219 | −0.691095 | − | 0.722764i | \(-0.742871\pi\) | ||||
−0.691095 | + | 0.722764i | \(0.742871\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | −7.65685 | −0.921777 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6569 | 1.62077 | 0.810385 | − | 0.585897i | \(-0.199258\pi\) | ||||
0.810385 | + | 0.585897i | \(0.199258\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | −3.65685 | −0.425101 | ||||||||
\(75\) | 5.00000 | 0.577350 | ||||||||
\(76\) | 5.41421 | 0.621053 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.41421 | 0.160128 | ||||||||
\(79\) | 1.65685 | 0.186411 | 0.0932053 | − | 0.995647i | \(-0.470289\pi\) | ||||
0.0932053 | + | 0.995647i | \(0.470289\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.65685 | −1.06642 | ||||||||
\(83\) | −15.0711 | −1.65426 | −0.827132 | − | 0.562007i | \(-0.810029\pi\) | ||||
−0.827132 | + | 0.562007i | \(0.810029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.0000 | 1.07833 | ||||||||
\(87\) | 5.65685 | 0.606478 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 2.58579 | 0.274093 | 0.137046 | − | 0.990565i | \(-0.456239\pi\) | ||||
0.137046 | + | 0.990565i | \(0.456239\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.65685 | 0.798282 | ||||||||
\(93\) | 3.07107 | 0.318455 | ||||||||
\(94\) | 1.41421 | 0.145865 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 12.7279 | 1.29232 | 0.646162 | − | 0.763200i | \(-0.276373\pi\) | ||||
0.646162 | + | 0.763200i | \(0.276373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | −0.242641 | −0.0241437 | −0.0120718 | − | 0.999927i | \(-0.503843\pi\) | ||||
−0.0120718 | + | 0.999927i | \(0.503843\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 13.8995 | 1.36956 | 0.684779 | − | 0.728751i | \(-0.259899\pi\) | ||||
0.684779 | + | 0.728751i | \(0.259899\pi\) | |||||||
\(104\) | −1.41421 | −0.138675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.65685 | 0.355185 | ||||||||
\(107\) | 17.3137 | 1.67378 | 0.836890 | − | 0.547372i | \(-0.184372\pi\) | ||||
0.836890 | + | 0.547372i | \(0.184372\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.65685 | −0.347093 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.65685 | −0.532152 | −0.266076 | − | 0.963952i | \(-0.585727\pi\) | ||||
−0.266076 | + | 0.963952i | \(0.585727\pi\) | |||||||
\(114\) | 5.41421 | 0.507088 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.65685 | −0.525226 | ||||||||
\(117\) | 1.41421 | 0.130744 | ||||||||
\(118\) | −6.82843 | −0.628608 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.41421 | 0.128037 | ||||||||
\(123\) | −9.65685 | −0.870729 | ||||||||
\(124\) | −3.07107 | −0.275790 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.3137 | −1.35887 | −0.679436 | − | 0.733735i | \(-0.737775\pi\) | ||||
−0.679436 | + | 0.733735i | \(0.737775\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.0000 | 0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.75736 | 0.328282 | 0.164141 | − | 0.986437i | \(-0.447515\pi\) | ||||
0.164141 | + | 0.986437i | \(0.447515\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.3137 | 0.977356 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | −9.31371 | −0.795724 | −0.397862 | − | 0.917445i | \(-0.630248\pi\) | ||||
−0.397862 | + | 0.917445i | \(0.630248\pi\) | |||||||
\(138\) | 7.65685 | 0.651795 | ||||||||
\(139\) | 2.10051 | 0.178163 | 0.0890813 | − | 0.996024i | \(-0.471607\pi\) | ||||
0.0890813 | + | 0.996024i | \(0.471607\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.41421 | 0.119098 | ||||||||
\(142\) | −13.6569 | −1.14606 | ||||||||
\(143\) | 1.41421 | 0.118262 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.65685 | 0.300592 | ||||||||
\(149\) | 12.9706 | 1.06259 | 0.531295 | − | 0.847187i | \(-0.321706\pi\) | ||||
0.531295 | + | 0.847187i | \(0.321706\pi\) | |||||||
\(150\) | −5.00000 | −0.408248 | ||||||||
\(151\) | −1.65685 | −0.134833 | −0.0674164 | − | 0.997725i | \(-0.521476\pi\) | ||||
−0.0674164 | + | 0.997725i | \(0.521476\pi\) | |||||||
\(152\) | −5.41421 | −0.439151 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.41421 | −0.113228 | ||||||||
\(157\) | −2.82843 | −0.225733 | −0.112867 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112867 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(158\) | −1.65685 | −0.131812 | ||||||||
\(159\) | 3.65685 | 0.290007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 5.65685 | 0.443079 | 0.221540 | − | 0.975151i | \(-0.428892\pi\) | ||||
0.221540 | + | 0.975151i | \(0.428892\pi\) | |||||||
\(164\) | 9.65685 | 0.754074 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0711 | 1.16974 | ||||||||
\(167\) | 10.8284 | 0.837929 | 0.418964 | − | 0.908003i | \(-0.362393\pi\) | ||||
0.418964 | + | 0.908003i | \(0.362393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.41421 | 0.414035 | ||||||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | 4.92893 | 0.374740 | 0.187370 | − | 0.982289i | \(-0.440004\pi\) | ||||
0.187370 | + | 0.982289i | \(0.440004\pi\) | |||||||
\(174\) | −5.65685 | −0.428845 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −6.82843 | −0.513256 | ||||||||
\(178\) | −2.58579 | −0.193813 | ||||||||
\(179\) | 2.34315 | 0.175135 | 0.0875675 | − | 0.996159i | \(-0.472091\pi\) | ||||
0.0875675 | + | 0.996159i | \(0.472091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.6569 | −1.60974 | −0.804871 | − | 0.593450i | \(-0.797765\pi\) | ||||
−0.804871 | + | 0.593450i | \(0.797765\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.41421 | 0.104542 | ||||||||
\(184\) | −7.65685 | −0.564471 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.07107 | −0.225182 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | −1.41421 | −0.103142 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.9706 | −0.793802 | −0.396901 | − | 0.917861i | \(-0.629914\pi\) | ||||
−0.396901 | + | 0.917861i | \(0.629914\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 7.65685 | 0.551152 | 0.275576 | − | 0.961279i | \(-0.411131\pi\) | ||||
0.275576 | + | 0.961279i | \(0.411131\pi\) | |||||||
\(194\) | −12.7279 | −0.913812 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3137 | 1.51854 | 0.759269 | − | 0.650776i | \(-0.225556\pi\) | ||||
0.759269 | + | 0.650776i | \(0.225556\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | 10.5858 | 0.750407 | 0.375203 | − | 0.926943i | \(-0.377573\pi\) | ||||
0.375203 | + | 0.926943i | \(0.377573\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 11.3137 | 0.798007 | ||||||||
\(202\) | 0.242641 | 0.0170721 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.8995 | −0.968424 | ||||||||
\(207\) | 7.65685 | 0.532188 | ||||||||
\(208\) | 1.41421 | 0.0980581 | ||||||||
\(209\) | 5.41421 | 0.374509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3137 | 1.19192 | 0.595962 | − | 0.803012i | \(-0.296771\pi\) | ||||
0.595962 | + | 0.803012i | \(0.296771\pi\) | |||||||
\(212\) | −3.65685 | −0.251154 | ||||||||
\(213\) | −13.6569 | −0.935752 | ||||||||
\(214\) | −17.3137 | −1.18354 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.65685 | 0.380521 | ||||||||
\(222\) | 3.65685 | 0.245432 | ||||||||
\(223\) | 19.5563 | 1.30959 | 0.654795 | − | 0.755807i | \(-0.272755\pi\) | ||||
0.654795 | + | 0.755807i | \(0.272755\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 5.65685 | 0.376288 | ||||||||
\(227\) | 23.5563 | 1.56349 | 0.781745 | − | 0.623598i | \(-0.214330\pi\) | ||||
0.781745 | + | 0.623598i | \(0.214330\pi\) | |||||||
\(228\) | −5.41421 | −0.358565 | ||||||||
\(229\) | 5.65685 | 0.373815 | 0.186908 | − | 0.982377i | \(-0.440153\pi\) | ||||
0.186908 | + | 0.982377i | \(0.440153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.65685 | 0.371391 | ||||||||
\(233\) | 12.3431 | 0.808626 | 0.404313 | − | 0.914621i | \(-0.367511\pi\) | ||||
0.404313 | + | 0.914621i | \(0.367511\pi\) | |||||||
\(234\) | −1.41421 | −0.0924500 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.82843 | 0.444493 | ||||||||
\(237\) | −1.65685 | −0.107624 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.3431 | 0.927781 | 0.463890 | − | 0.885893i | \(-0.346453\pi\) | ||||
0.463890 | + | 0.885893i | \(0.346453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.31371 | −0.471117 | −0.235559 | − | 0.971860i | \(-0.575692\pi\) | ||||
−0.235559 | + | 0.971860i | \(0.575692\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.41421 | −0.0905357 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.65685 | 0.615699 | ||||||||
\(247\) | 7.65685 | 0.487194 | ||||||||
\(248\) | 3.07107 | 0.195013 | ||||||||
\(249\) | 15.0711 | 0.955090 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.8284 | 0.935962 | 0.467981 | − | 0.883739i | \(-0.344982\pi\) | ||||
0.467981 | + | 0.883739i | \(0.344982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.65685 | 0.481382 | ||||||||
\(254\) | 15.3137 | 0.960868 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −16.7279 | −1.04346 | −0.521730 | − | 0.853111i | \(-0.674713\pi\) | ||||
−0.521730 | + | 0.853111i | \(0.674713\pi\) | |||||||
\(258\) | −10.0000 | −0.622573 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.65685 | −0.350150 | ||||||||
\(262\) | −3.75736 | −0.232130 | ||||||||
\(263\) | 13.6569 | 0.842118 | 0.421059 | − | 0.907033i | \(-0.361659\pi\) | ||||
0.421059 | + | 0.907033i | \(0.361659\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.58579 | −0.158248 | ||||||||
\(268\) | −11.3137 | −0.691095 | ||||||||
\(269\) | 22.6274 | 1.37962 | 0.689809 | − | 0.723991i | \(-0.257694\pi\) | ||||
0.689809 | + | 0.723991i | \(0.257694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1716 | 1.28608 | 0.643041 | − | 0.765832i | \(-0.277673\pi\) | ||||
0.643041 | + | 0.765832i | \(0.277673\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.31371 | 0.562662 | ||||||||
\(275\) | −5.00000 | −0.301511 | ||||||||
\(276\) | −7.65685 | −0.460888 | ||||||||
\(277\) | 4.00000 | 0.240337 | 0.120168 | − | 0.992754i | \(-0.461657\pi\) | ||||
0.120168 | + | 0.992754i | \(0.461657\pi\) | |||||||
\(278\) | −2.10051 | −0.125980 | ||||||||
\(279\) | −3.07107 | −0.183860 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.9706 | −1.13169 | −0.565844 | − | 0.824512i | \(-0.691450\pi\) | ||||
−0.565844 | + | 0.824512i | \(0.691450\pi\) | |||||||
\(282\) | −1.41421 | −0.0842152 | ||||||||
\(283\) | 15.7574 | 0.936678 | 0.468339 | − | 0.883549i | \(-0.344853\pi\) | ||||
0.468339 | + | 0.883549i | \(0.344853\pi\) | |||||||
\(284\) | 13.6569 | 0.810385 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.41421 | −0.0836242 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.7279 | −0.746124 | ||||||||
\(292\) | 4.00000 | 0.234082 | ||||||||
\(293\) | −3.07107 | −0.179414 | −0.0897068 | − | 0.995968i | \(-0.528593\pi\) | ||||
−0.0897068 | + | 0.995968i | \(0.528593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.65685 | −0.212550 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −12.9706 | −0.751365 | ||||||||
\(299\) | 10.8284 | 0.626224 | ||||||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.65685 | 0.0953412 | ||||||||
\(303\) | 0.242641 | 0.0139393 | ||||||||
\(304\) | 5.41421 | 0.310526 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | −0.727922 | −0.0415447 | −0.0207724 | − | 0.999784i | \(-0.506613\pi\) | ||||
−0.0207724 | + | 0.999784i | \(0.506613\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.8995 | −0.790715 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.2426 | 1.14785 | 0.573927 | − | 0.818906i | \(-0.305419\pi\) | ||||
0.573927 | + | 0.818906i | \(0.305419\pi\) | |||||||
\(312\) | 1.41421 | 0.0800641 | ||||||||
\(313\) | −12.2426 | −0.691995 | −0.345997 | − | 0.938235i | \(-0.612459\pi\) | ||||
−0.345997 | + | 0.938235i | \(0.612459\pi\) | |||||||
\(314\) | 2.82843 | 0.159617 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.65685 | 0.0932053 | ||||||||
\(317\) | −5.31371 | −0.298448 | −0.149224 | − | 0.988803i | \(-0.547677\pi\) | ||||
−0.149224 | + | 0.988803i | \(0.547677\pi\) | |||||||
\(318\) | −3.65685 | −0.205066 | ||||||||
\(319\) | −5.65685 | −0.316723 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.3137 | −0.966357 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.6569 | 1.20502 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −7.07107 | −0.392232 | ||||||||
\(326\) | −5.65685 | −0.313304 | ||||||||
\(327\) | 10.0000 | 0.553001 | ||||||||
\(328\) | −9.65685 | −0.533211 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.9706 | 1.59237 | 0.796183 | − | 0.605056i | \(-0.206849\pi\) | ||||
0.796183 | + | 0.605056i | \(0.206849\pi\) | |||||||
\(332\) | −15.0711 | −0.827132 | ||||||||
\(333\) | 3.65685 | 0.200394 | ||||||||
\(334\) | −10.8284 | −0.592505 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.3137 | −0.943138 | −0.471569 | − | 0.881829i | \(-0.656312\pi\) | ||||
−0.471569 | + | 0.881829i | \(0.656312\pi\) | |||||||
\(338\) | 11.0000 | 0.598321 | ||||||||
\(339\) | 5.65685 | 0.307238 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.07107 | −0.166308 | ||||||||
\(342\) | −5.41421 | −0.292767 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.92893 | −0.264981 | ||||||||
\(347\) | −2.00000 | −0.107366 | −0.0536828 | − | 0.998558i | \(-0.517096\pi\) | ||||
−0.0536828 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(348\) | 5.65685 | 0.303239 | ||||||||
\(349\) | 22.5858 | 1.20899 | 0.604495 | − | 0.796609i | \(-0.293375\pi\) | ||||
0.604495 | + | 0.796609i | \(0.293375\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.41421 | −0.0754851 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −13.8995 | −0.739795 | −0.369898 | − | 0.929072i | \(-0.620607\pi\) | ||||
−0.369898 | + | 0.929072i | \(0.620607\pi\) | |||||||
\(354\) | 6.82843 | 0.362927 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.58579 | 0.137046 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.34315 | −0.123839 | ||||||||
\(359\) | −4.00000 | −0.211112 | −0.105556 | − | 0.994413i | \(-0.533662\pi\) | ||||
−0.105556 | + | 0.994413i | \(0.533662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.3137 | 0.542827 | ||||||||
\(362\) | 21.6569 | 1.13826 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.41421 | −0.0739221 | ||||||||
\(367\) | −30.8701 | −1.61140 | −0.805702 | − | 0.592321i | \(-0.798212\pi\) | ||||
−0.805702 | + | 0.592321i | \(0.798212\pi\) | |||||||
\(368\) | 7.65685 | 0.399141 | ||||||||
\(369\) | 9.65685 | 0.502716 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.07107 | 0.159227 | ||||||||
\(373\) | −36.6274 | −1.89650 | −0.948248 | − | 0.317531i | \(-0.897146\pi\) | ||||
−0.948248 | + | 0.317531i | \(0.897146\pi\) | |||||||
\(374\) | −4.00000 | −0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.41421 | 0.0729325 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.6569 | −0.906972 | −0.453486 | − | 0.891263i | \(-0.649820\pi\) | ||||
−0.453486 | + | 0.891263i | \(0.649820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.3137 | 0.784545 | ||||||||
\(382\) | 10.9706 | 0.561303 | ||||||||
\(383\) | −7.55635 | −0.386111 | −0.193056 | − | 0.981188i | \(-0.561840\pi\) | ||||
−0.193056 | + | 0.981188i | \(0.561840\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.65685 | −0.389724 | ||||||||
\(387\) | −10.0000 | −0.508329 | ||||||||
\(388\) | 12.7279 | 0.646162 | ||||||||
\(389\) | 12.6274 | 0.640235 | 0.320118 | − | 0.947378i | \(-0.396278\pi\) | ||||
0.320118 | + | 0.947378i | \(0.396278\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.6274 | 1.54890 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.75736 | −0.189534 | ||||||||
\(394\) | −21.3137 | −1.07377 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 11.7990 | 0.592174 | 0.296087 | − | 0.955161i | \(-0.404318\pi\) | ||||
0.296087 | + | 0.955161i | \(0.404318\pi\) | |||||||
\(398\) | −10.5858 | −0.530618 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | −11.3137 | −0.564276 | ||||||||
\(403\) | −4.34315 | −0.216347 | ||||||||
\(404\) | −0.242641 | −0.0120718 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.65685 | 0.181264 | ||||||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | −12.4853 | −0.617357 | −0.308679 | − | 0.951166i | \(-0.599887\pi\) | ||||
−0.308679 | + | 0.951166i | \(0.599887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.31371 | 0.459411 | ||||||||
\(412\) | 13.8995 | 0.684779 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.65685 | −0.376314 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.41421 | −0.0693375 | ||||||||
\(417\) | −2.10051 | −0.102862 | ||||||||
\(418\) | −5.41421 | −0.264818 | ||||||||
\(419\) | 16.2843 | 0.795539 | 0.397769 | − | 0.917485i | \(-0.369784\pi\) | ||||
0.397769 | + | 0.917485i | \(0.369784\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.9706 | −0.729621 | −0.364810 | − | 0.931082i | \(-0.618866\pi\) | ||||
−0.364810 | + | 0.931082i | \(0.618866\pi\) | |||||||
\(422\) | −17.3137 | −0.842818 | ||||||||
\(423\) | −1.41421 | −0.0687614 | ||||||||
\(424\) | 3.65685 | 0.177593 | ||||||||
\(425\) | −20.0000 | −0.970143 | ||||||||
\(426\) | 13.6569 | 0.661677 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 17.3137 | 0.836890 | ||||||||
\(429\) | −1.41421 | −0.0682789 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 37.2132 | 1.78835 | 0.894176 | − | 0.447715i | \(-0.147762\pi\) | ||||
0.894176 | + | 0.447715i | \(0.147762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 41.4558 | 1.98310 | ||||||||
\(438\) | 4.00000 | 0.191127 | ||||||||
\(439\) | 35.7990 | 1.70859 | 0.854296 | − | 0.519786i | \(-0.173988\pi\) | ||||
0.854296 | + | 0.519786i | \(0.173988\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.65685 | −0.269069 | ||||||||
\(443\) | 28.2843 | 1.34383 | 0.671913 | − | 0.740630i | \(-0.265473\pi\) | ||||
0.671913 | + | 0.740630i | \(0.265473\pi\) | |||||||
\(444\) | −3.65685 | −0.173547 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.5563 | −0.926020 | ||||||||
\(447\) | −12.9706 | −0.613487 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.3431 | 0.488123 | 0.244062 | − | 0.969760i | \(-0.421520\pi\) | ||||
0.244062 | + | 0.969760i | \(0.421520\pi\) | |||||||
\(450\) | 5.00000 | 0.235702 | ||||||||
\(451\) | 9.65685 | 0.454724 | ||||||||
\(452\) | −5.65685 | −0.266076 | ||||||||
\(453\) | 1.65685 | 0.0778458 | ||||||||
\(454\) | −23.5563 | −1.10555 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.41421 | 0.253544 | ||||||||
\(457\) | 19.6569 | 0.919509 | 0.459754 | − | 0.888046i | \(-0.347937\pi\) | ||||
0.459754 | + | 0.888046i | \(0.347937\pi\) | |||||||
\(458\) | −5.65685 | −0.264327 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.8995 | 1.76516 | 0.882578 | − | 0.470167i | \(-0.155806\pi\) | ||||
0.882578 | + | 0.470167i | \(0.155806\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.3137 | −1.26938 | −0.634688 | − | 0.772769i | \(-0.718871\pi\) | ||||
−0.634688 | + | 0.772769i | \(0.718871\pi\) | |||||||
\(464\) | −5.65685 | −0.262613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.3431 | −0.571785 | ||||||||
\(467\) | −37.9411 | −1.75571 | −0.877853 | − | 0.478930i | \(-0.841025\pi\) | ||||
−0.877853 | + | 0.478930i | \(0.841025\pi\) | |||||||
\(468\) | 1.41421 | 0.0653720 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.82843 | 0.130327 | ||||||||
\(472\) | −6.82843 | −0.314304 | ||||||||
\(473\) | −10.0000 | −0.459800 | ||||||||
\(474\) | 1.65685 | 0.0761018 | ||||||||
\(475\) | −27.0711 | −1.24211 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.65685 | −0.167436 | ||||||||
\(478\) | −14.3431 | −0.656040 | ||||||||
\(479\) | 32.9706 | 1.50646 | 0.753232 | − | 0.657755i | \(-0.228494\pi\) | ||||
0.753232 | + | 0.657755i | \(0.228494\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.17157 | 0.235803 | ||||||||
\(482\) | 7.31371 | 0.333130 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −0.343146 | −0.0155494 | −0.00777471 | − | 0.999970i | \(-0.502475\pi\) | ||||
−0.00777471 | + | 0.999970i | \(0.502475\pi\) | |||||||
\(488\) | 1.41421 | 0.0640184 | ||||||||
\(489\) | −5.65685 | −0.255812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | −9.65685 | −0.435365 | ||||||||
\(493\) | −22.6274 | −1.01909 | ||||||||
\(494\) | −7.65685 | −0.344498 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.07107 | −0.137895 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.0711 | −0.675351 | ||||||||
\(499\) | −10.6274 | −0.475749 | −0.237874 | − | 0.971296i | \(-0.576451\pi\) | ||||
−0.237874 | + | 0.971296i | \(0.576451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.8284 | −0.483778 | ||||||||
\(502\) | −14.8284 | −0.661825 | ||||||||
\(503\) | −0.485281 | −0.0216376 | −0.0108188 | − | 0.999941i | \(-0.503444\pi\) | ||||
−0.0108188 | + | 0.999941i | \(0.503444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.65685 | −0.340389 | ||||||||
\(507\) | 11.0000 | 0.488527 | ||||||||
\(508\) | −15.3137 | −0.679436 | ||||||||
\(509\) | −41.9411 | −1.85901 | −0.929504 | − | 0.368812i | \(-0.879764\pi\) | ||||
−0.929504 | + | 0.368812i | \(0.879764\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.41421 | −0.239043 | ||||||||
\(514\) | 16.7279 | 0.737837 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.0000 | 0.440225 | ||||||||
\(517\) | −1.41421 | −0.0621970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.92893 | −0.216356 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.27208 | −0.318596 | −0.159298 | − | 0.987231i | \(-0.550923\pi\) | ||||
−0.159298 | + | 0.987231i | \(0.550923\pi\) | |||||||
\(522\) | 5.65685 | 0.247594 | ||||||||
\(523\) | −31.7574 | −1.38865 | −0.694326 | − | 0.719660i | \(-0.744297\pi\) | ||||
−0.694326 | + | 0.719660i | \(0.744297\pi\) | |||||||
\(524\) | 3.75736 | 0.164141 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6569 | −0.595467 | ||||||||
\(527\) | −12.2843 | −0.535111 | ||||||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 35.6274 | 1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.82843 | 0.296328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.6569 | 0.591544 | ||||||||
\(534\) | 2.58579 | 0.111898 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.3137 | 0.488678 | ||||||||
\(537\) | −2.34315 | −0.101114 | ||||||||
\(538\) | −22.6274 | −0.975537 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.62742 | −0.370922 | −0.185461 | − | 0.982652i | \(-0.559378\pi\) | ||||
−0.185461 | + | 0.982652i | \(0.559378\pi\) | |||||||
\(542\) | −21.1716 | −0.909397 | ||||||||
\(543\) | 21.6569 | 0.929385 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.65685 | −0.0708420 | −0.0354210 | − | 0.999372i | \(-0.511277\pi\) | ||||
−0.0354210 | + | 0.999372i | \(0.511277\pi\) | |||||||
\(548\) | −9.31371 | −0.397862 | ||||||||
\(549\) | −1.41421 | −0.0603572 | ||||||||
\(550\) | 5.00000 | 0.213201 | ||||||||
\(551\) | −30.6274 | −1.30477 | ||||||||
\(552\) | 7.65685 | 0.325897 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.00000 | −0.169944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.10051 | 0.0890813 | ||||||||
\(557\) | 31.9411 | 1.35339 | 0.676694 | − | 0.736264i | \(-0.263412\pi\) | ||||
0.676694 | + | 0.736264i | \(0.263412\pi\) | |||||||
\(558\) | 3.07107 | 0.130009 | ||||||||
\(559\) | −14.1421 | −0.598149 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | 18.9706 | 0.800225 | ||||||||
\(563\) | −22.5858 | −0.951877 | −0.475939 | − | 0.879478i | \(-0.657892\pi\) | ||||
−0.475939 | + | 0.879478i | \(0.657892\pi\) | |||||||
\(564\) | 1.41421 | 0.0595491 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.7574 | −0.662331 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.6569 | −0.573029 | ||||||||
\(569\) | −6.68629 | −0.280304 | −0.140152 | − | 0.990130i | \(-0.544759\pi\) | ||||
−0.140152 | + | 0.990130i | \(0.544759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.2843 | 1.68584 | 0.842922 | − | 0.538036i | \(-0.180833\pi\) | ||||
0.842922 | + | 0.538036i | \(0.180833\pi\) | |||||||
\(572\) | 1.41421 | 0.0591312 | ||||||||
\(573\) | 10.9706 | 0.458302 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.2843 | −1.59656 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −27.7574 | −1.15555 | −0.577777 | − | 0.816195i | \(-0.696080\pi\) | ||||
−0.577777 | + | 0.816195i | \(0.696080\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −7.65685 | −0.318208 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12.7279 | 0.527589 | ||||||||
\(583\) | −3.65685 | −0.151451 | ||||||||
\(584\) | −4.00000 | −0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.07107 | 0.126865 | ||||||||
\(587\) | 3.51472 | 0.145068 | 0.0725340 | − | 0.997366i | \(-0.476891\pi\) | ||||
0.0725340 | + | 0.997366i | \(0.476891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.6274 | −0.685121 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.3137 | −0.876729 | ||||||||
\(592\) | 3.65685 | 0.150296 | ||||||||
\(593\) | −23.3137 | −0.957379 | −0.478690 | − | 0.877984i | \(-0.658888\pi\) | ||||
−0.478690 | + | 0.877984i | \(0.658888\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.9706 | 0.531295 | ||||||||
\(597\) | −10.5858 | −0.433247 | ||||||||
\(598\) | −10.8284 | −0.442807 | ||||||||
\(599\) | −32.9706 | −1.34714 | −0.673570 | − | 0.739123i | \(-0.735240\pi\) | ||||
−0.673570 | + | 0.739123i | \(0.735240\pi\) | |||||||
\(600\) | −5.00000 | −0.204124 | ||||||||
\(601\) | 13.4558 | 0.548875 | 0.274438 | − | 0.961605i | \(-0.411508\pi\) | ||||
0.274438 | + | 0.961605i | \(0.411508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.3137 | −0.460730 | ||||||||
\(604\) | −1.65685 | −0.0674164 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.242641 | −0.00985660 | ||||||||
\(607\) | 3.31371 | 0.134499 | 0.0672496 | − | 0.997736i | \(-0.478578\pi\) | ||||
0.0672496 | + | 0.997736i | \(0.478578\pi\) | |||||||
\(608\) | −5.41421 | −0.219575 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.00000 | −0.0809113 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | 12.0000 | 0.484675 | 0.242338 | − | 0.970192i | \(-0.422086\pi\) | ||||
0.242338 | + | 0.970192i | \(0.422086\pi\) | |||||||
\(614\) | 0.727922 | 0.0293765 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3431 | 0.577433 | 0.288717 | − | 0.957415i | \(-0.406771\pi\) | ||||
0.288717 | + | 0.957415i | \(0.406771\pi\) | |||||||
\(618\) | 13.8995 | 0.559120 | ||||||||
\(619\) | −7.31371 | −0.293963 | −0.146981 | − | 0.989139i | \(-0.546956\pi\) | ||||
−0.146981 | + | 0.989139i | \(0.546956\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.65685 | −0.307259 | ||||||||
\(622\) | −20.2426 | −0.811656 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.41421 | −0.0566139 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 12.2426 | 0.489314 | ||||||||
\(627\) | −5.41421 | −0.216223 | ||||||||
\(628\) | −2.82843 | −0.112867 | ||||||||
\(629\) | 14.6274 | 0.583233 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.5980 | 1.49675 | 0.748376 | − | 0.663275i | \(-0.230834\pi\) | ||||
0.748376 | + | 0.663275i | \(0.230834\pi\) | |||||||
\(632\) | −1.65685 | −0.0659061 | ||||||||
\(633\) | −17.3137 | −0.688158 | ||||||||
\(634\) | 5.31371 | 0.211034 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.65685 | 0.145004 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.65685 | 0.223957 | ||||||||
\(639\) | 13.6569 | 0.540257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.28427 | 0.327209 | 0.163605 | − | 0.986526i | \(-0.447688\pi\) | ||||
0.163605 | + | 0.986526i | \(0.447688\pi\) | |||||||
\(642\) | 17.3137 | 0.683318 | ||||||||
\(643\) | −46.8284 | −1.84673 | −0.923366 | − | 0.383920i | \(-0.874574\pi\) | ||||
−0.923366 | + | 0.383920i | \(0.874574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.6569 | −0.852078 | ||||||||
\(647\) | 17.8995 | 0.703702 | 0.351851 | − | 0.936056i | \(-0.385552\pi\) | ||||
0.351851 | + | 0.936056i | \(0.385552\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 6.82843 | 0.268039 | ||||||||
\(650\) | 7.07107 | 0.277350 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.65685 | 0.221540 | ||||||||
\(653\) | −32.6274 | −1.27681 | −0.638405 | − | 0.769701i | \(-0.720405\pi\) | ||||
−0.638405 | + | 0.769701i | \(0.720405\pi\) | |||||||
\(654\) | −10.0000 | −0.391031 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.65685 | 0.377037 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.3137 | −0.986082 | −0.493041 | − | 0.870006i | \(-0.664115\pi\) | ||||
−0.493041 | + | 0.870006i | \(0.664115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.9706 | −0.971242 | −0.485621 | − | 0.874169i | \(-0.661407\pi\) | ||||
−0.485621 | + | 0.874169i | \(0.661407\pi\) | |||||||
\(662\) | −28.9706 | −1.12597 | ||||||||
\(663\) | −5.65685 | −0.219694 | ||||||||
\(664\) | 15.0711 | 0.584871 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.65685 | −0.141700 | ||||||||
\(667\) | −43.3137 | −1.67711 | ||||||||
\(668\) | 10.8284 | 0.418964 | ||||||||
\(669\) | −19.5563 | −0.756092 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.41421 | −0.0545951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6569 | 0.757716 | 0.378858 | − | 0.925455i | \(-0.376317\pi\) | ||||
0.378858 | + | 0.925455i | \(0.376317\pi\) | |||||||
\(674\) | 17.3137 | 0.666899 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | −11.0000 | −0.423077 | ||||||||
\(677\) | −18.5858 | −0.714310 | −0.357155 | − | 0.934045i | \(-0.616253\pi\) | ||||
−0.357155 | + | 0.934045i | \(0.616253\pi\) | |||||||
\(678\) | −5.65685 | −0.217250 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.5563 | −0.902681 | ||||||||
\(682\) | 3.07107 | 0.117597 | ||||||||
\(683\) | −48.2843 | −1.84755 | −0.923773 | − | 0.382940i | \(-0.874912\pi\) | ||||
−0.923773 | + | 0.382940i | \(0.874912\pi\) | |||||||
\(684\) | 5.41421 | 0.207018 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.65685 | −0.215822 | ||||||||
\(688\) | −10.0000 | −0.381246 | ||||||||
\(689\) | −5.17157 | −0.197021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.48528 | 0.170628 | 0.0853141 | − | 0.996354i | \(-0.472811\pi\) | ||||
0.0853141 | + | 0.996354i | \(0.472811\pi\) | |||||||
\(692\) | 4.92893 | 0.187370 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.00000 | 0.0759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.65685 | −0.214423 | ||||||||
\(697\) | 38.6274 | 1.46312 | ||||||||
\(698\) | −22.5858 | −0.854885 | ||||||||
\(699\) | −12.3431 | −0.466861 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.3137 | −1.56040 | −0.780199 | − | 0.625532i | \(-0.784882\pi\) | ||||
−0.780199 | + | 0.625532i | \(0.784882\pi\) | |||||||
\(702\) | 1.41421 | 0.0533761 | ||||||||
\(703\) | 19.7990 | 0.746733 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.8995 | 0.523114 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.82843 | −0.256628 | ||||||||
\(709\) | 0.627417 | 0.0235631 | 0.0117816 | − | 0.999931i | \(-0.496250\pi\) | ||||
0.0117816 | + | 0.999931i | \(0.496250\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.65685 | 0.0621369 | ||||||||
\(712\) | −2.58579 | −0.0969064 | ||||||||
\(713\) | −23.5147 | −0.880633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.34315 | 0.0875675 | ||||||||
\(717\) | −14.3431 | −0.535655 | ||||||||
\(718\) | 4.00000 | 0.149279 | ||||||||
\(719\) | 14.5858 | 0.543958 | 0.271979 | − | 0.962303i | \(-0.412322\pi\) | ||||
0.271979 | + | 0.962303i | \(0.412322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.3137 | −0.383836 | ||||||||
\(723\) | 7.31371 | 0.272000 | ||||||||
\(724\) | −21.6569 | −0.804871 | ||||||||
\(725\) | 28.2843 | 1.05045 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −39.3553 | −1.45961 | −0.729804 | − | 0.683656i | \(-0.760389\pi\) | ||||
−0.729804 | + | 0.683656i | \(0.760389\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.0000 | −1.47945 | ||||||||
\(732\) | 1.41421 | 0.0522708 | ||||||||
\(733\) | −35.7574 | −1.32073 | −0.660364 | − | 0.750946i | \(-0.729598\pi\) | ||||
−0.660364 | + | 0.750946i | \(0.729598\pi\) | |||||||
\(734\) | 30.8701 | 1.13943 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.65685 | −0.282235 | ||||||||
\(737\) | −11.3137 | −0.416746 | ||||||||
\(738\) | −9.65685 | −0.355474 | ||||||||
\(739\) | 6.34315 | 0.233336 | 0.116668 | − | 0.993171i | \(-0.462779\pi\) | ||||
0.116668 | + | 0.993171i | \(0.462779\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.65685 | −0.281282 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.97056 | −0.182352 | −0.0911761 | − | 0.995835i | \(-0.529063\pi\) | ||||
−0.0911761 | + | 0.995835i | \(0.529063\pi\) | |||||||
\(744\) | −3.07107 | −0.112591 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 36.6274 | 1.34103 | ||||||||
\(747\) | −15.0711 | −0.551422 | ||||||||
\(748\) | 4.00000 | 0.146254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.9706 | 0.984170 | 0.492085 | − | 0.870547i | \(-0.336235\pi\) | ||||
0.492085 | + | 0.870547i | \(0.336235\pi\) | |||||||
\(752\) | −1.41421 | −0.0515711 | ||||||||
\(753\) | −14.8284 | −0.540378 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.68629 | −0.243017 | −0.121509 | − | 0.992590i | \(-0.538773\pi\) | ||||
−0.121509 | + | 0.992590i | \(0.538773\pi\) | |||||||
\(758\) | 17.6569 | 0.641326 | ||||||||
\(759\) | −7.65685 | −0.277926 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.8579 | −0.502347 | −0.251174 | − | 0.967942i | \(-0.580817\pi\) | ||||
−0.251174 | + | 0.967942i | \(0.580817\pi\) | |||||||
\(762\) | −15.3137 | −0.554757 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10.9706 | −0.396901 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.55635 | 0.273022 | ||||||||
\(767\) | 9.65685 | 0.348689 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 39.7990 | 1.43519 | 0.717594 | − | 0.696462i | \(-0.245243\pi\) | ||||
0.717594 | + | 0.696462i | \(0.245243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.7279 | 0.602441 | ||||||||
\(772\) | 7.65685 | 0.275576 | ||||||||
\(773\) | −14.1421 | −0.508657 | −0.254329 | − | 0.967118i | \(-0.581854\pi\) | ||||
−0.254329 | + | 0.967118i | \(0.581854\pi\) | |||||||
\(774\) | 10.0000 | 0.359443 | ||||||||
\(775\) | 15.3553 | 0.551580 | ||||||||
\(776\) | −12.7279 | −0.456906 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.6274 | −0.452715 | ||||||||
\(779\) | 52.2843 | 1.87328 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6569 | 0.488681 | ||||||||
\(782\) | −30.6274 | −1.09523 | ||||||||
\(783\) | 5.65685 | 0.202159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.75736 | 0.134021 | ||||||||
\(787\) | −38.3848 | −1.36827 | −0.684135 | − | 0.729356i | \(-0.739820\pi\) | ||||
−0.684135 | + | 0.729356i | \(0.739820\pi\) | |||||||
\(788\) | 21.3137 | 0.759269 | ||||||||
\(789\) | −13.6569 | −0.486197 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −2.00000 | −0.0710221 | ||||||||
\(794\) | −11.7990 | −0.418730 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.5858 | 0.375203 | ||||||||
\(797\) | −50.8284 | −1.80044 | −0.900218 | − | 0.435440i | \(-0.856593\pi\) | ||||
−0.900218 | + | 0.435440i | \(0.856593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.65685 | −0.200125 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | 2.58579 | 0.0913643 | ||||||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | 4.00000 | 0.141157 | ||||||||
\(804\) | 11.3137 | 0.399004 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.34315 | 0.152981 | ||||||||
\(807\) | −22.6274 | −0.796523 | ||||||||
\(808\) | 0.242641 | 0.00853607 | ||||||||
\(809\) | 18.9706 | 0.666969 | 0.333485 | − | 0.942755i | \(-0.391775\pi\) | ||||
0.333485 | + | 0.942755i | \(0.391775\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.12994 | 0.0396776 | 0.0198388 | − | 0.999803i | \(-0.493685\pi\) | ||||
0.0198388 | + | 0.999803i | \(0.493685\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.1716 | −0.742519 | ||||||||
\(814\) | −3.65685 | −0.128173 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | −54.1421 | −1.89419 | ||||||||
\(818\) | 12.4853 | 0.436538 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.02944 | 0.105728 | 0.0528640 | − | 0.998602i | \(-0.483165\pi\) | ||||
0.0528640 | + | 0.998602i | \(0.483165\pi\) | |||||||
\(822\) | −9.31371 | −0.324853 | ||||||||
\(823\) | −53.5980 | −1.86831 | −0.934154 | − | 0.356870i | \(-0.883844\pi\) | ||||
−0.934154 | + | 0.356870i | \(0.883844\pi\) | |||||||
\(824\) | −13.8995 | −0.484212 | ||||||||
\(825\) | 5.00000 | 0.174078 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | 7.65685 | 0.266094 | ||||||||
\(829\) | 19.3137 | 0.670793 | 0.335396 | − | 0.942077i | \(-0.391130\pi\) | ||||
0.335396 | + | 0.942077i | \(0.391130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | −0.138758 | ||||||||
\(832\) | 1.41421 | 0.0490290 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.10051 | 0.0727345 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.41421 | 0.187254 | ||||||||
\(837\) | 3.07107 | 0.106152 | ||||||||
\(838\) | −16.2843 | −0.562531 | ||||||||
\(839\) | 12.7279 | 0.439417 | 0.219708 | − | 0.975566i | \(-0.429489\pi\) | ||||
0.219708 | + | 0.975566i | \(0.429489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | 14.9706 | 0.515920 | ||||||||
\(843\) | 18.9706 | 0.653381 | ||||||||
\(844\) | 17.3137 | 0.595962 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.41421 | 0.0486217 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.65685 | −0.125577 | ||||||||
\(849\) | −15.7574 | −0.540791 | ||||||||
\(850\) | 20.0000 | 0.685994 | ||||||||
\(851\) | 28.0000 | 0.959828 | ||||||||
\(852\) | −13.6569 | −0.467876 | ||||||||
\(853\) | −52.7279 | −1.80537 | −0.902685 | − | 0.430302i | \(-0.858407\pi\) | ||||
−0.902685 | + | 0.430302i | \(0.858407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.3137 | −0.591770 | ||||||||
\(857\) | −14.8284 | −0.506529 | −0.253265 | − | 0.967397i | \(-0.581504\pi\) | ||||
−0.253265 | + | 0.967397i | \(0.581504\pi\) | |||||||
\(858\) | 1.41421 | 0.0482805 | ||||||||
\(859\) | 46.4264 | 1.58405 | 0.792024 | − | 0.610490i | \(-0.209027\pi\) | ||||
0.792024 | + | 0.610490i | \(0.209027\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | 49.5980 | 1.68833 | 0.844167 | − | 0.536080i | \(-0.180095\pi\) | ||||
0.844167 | + | 0.536080i | \(0.180095\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −37.2132 | −1.26456 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.65685 | 0.0562049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 10.0000 | 0.338643 | ||||||||
\(873\) | 12.7279 | 0.430775 | ||||||||
\(874\) | −41.4558 | −1.40226 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | 53.3137 | 1.80028 | 0.900138 | − | 0.435605i | \(-0.143465\pi\) | ||||
0.900138 | + | 0.435605i | \(0.143465\pi\) | |||||||
\(878\) | −35.7990 | −1.20816 | ||||||||
\(879\) | 3.07107 | 0.103585 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.8995 | −0.737813 | −0.368906 | − | 0.929467i | \(-0.620268\pi\) | ||||
−0.368906 | + | 0.929467i | \(0.620268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.6274 | −0.896084 | −0.448042 | − | 0.894013i | \(-0.647878\pi\) | ||||
−0.448042 | + | 0.894013i | \(0.647878\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.2843 | −0.950229 | ||||||||
\(887\) | −4.28427 | −0.143852 | −0.0719259 | − | 0.997410i | \(-0.522915\pi\) | ||||
−0.0719259 | + | 0.997410i | \(0.522915\pi\) | |||||||
\(888\) | 3.65685 | 0.122716 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 19.5563 | 0.654795 | ||||||||
\(893\) | −7.65685 | −0.256227 | ||||||||
\(894\) | 12.9706 | 0.433801 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.8284 | −0.361551 | ||||||||
\(898\) | −10.3431 | −0.345155 | ||||||||
\(899\) | 17.3726 | 0.579408 | ||||||||
\(900\) | −5.00000 | −0.166667 | ||||||||
\(901\) | −14.6274 | −0.487310 | ||||||||
\(902\) | −9.65685 | −0.321538 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.65685 | 0.188144 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.65685 | −0.0550453 | ||||||||
\(907\) | −33.9411 | −1.12700 | −0.563498 | − | 0.826117i | \(-0.690545\pi\) | ||||
−0.563498 | + | 0.826117i | \(0.690545\pi\) | |||||||
\(908\) | 23.5563 | 0.781745 | ||||||||
\(909\) | −0.242641 | −0.00804788 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.5980 | 1.37820 | 0.689101 | − | 0.724665i | \(-0.258006\pi\) | ||||
0.689101 | + | 0.724665i | \(0.258006\pi\) | |||||||
\(912\) | −5.41421 | −0.179283 | ||||||||
\(913\) | −15.0711 | −0.498780 | ||||||||
\(914\) | −19.6569 | −0.650191 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.65685 | 0.186908 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | 14.6274 | 0.482514 | 0.241257 | − | 0.970461i | \(-0.422440\pi\) | ||||
0.241257 | + | 0.970461i | \(0.422440\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.727922 | 0.0239858 | ||||||||
\(922\) | −37.8995 | −1.24815 | ||||||||
\(923\) | 19.3137 | 0.635718 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.2843 | −0.601183 | ||||||||
\(926\) | 27.3137 | 0.897584 | ||||||||
\(927\) | 13.8995 | 0.456519 | ||||||||
\(928\) | 5.65685 | 0.185695 | ||||||||
\(929\) | −35.0711 | −1.15064 | −0.575322 | − | 0.817927i | \(-0.695123\pi\) | ||||
−0.575322 | + | 0.817927i | \(0.695123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.3431 | 0.404313 | ||||||||
\(933\) | −20.2426 | −0.662714 | ||||||||
\(934\) | 37.9411 | 1.24147 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.41421 | −0.0462250 | ||||||||
\(937\) | −50.6274 | −1.65393 | −0.826963 | − | 0.562257i | \(-0.809933\pi\) | ||||
−0.826963 | + | 0.562257i | \(0.809933\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.2426 | 0.399523 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.69848 | 0.0553690 | 0.0276845 | − | 0.999617i | \(-0.491187\pi\) | ||||
0.0276845 | + | 0.999617i | \(0.491187\pi\) | |||||||
\(942\) | −2.82843 | −0.0921551 | ||||||||
\(943\) | 73.9411 | 2.40785 | ||||||||
\(944\) | 6.82843 | 0.222246 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0000 | 0.325128 | ||||||||
\(947\) | −24.6863 | −0.802197 | −0.401098 | − | 0.916035i | \(-0.631371\pi\) | ||||
−0.401098 | + | 0.916035i | \(0.631371\pi\) | |||||||
\(948\) | −1.65685 | −0.0538121 | ||||||||
\(949\) | 5.65685 | 0.183629 | ||||||||
\(950\) | 27.0711 | 0.878301 | ||||||||
\(951\) | 5.31371 | 0.172309 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 3.65685 | 0.118395 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.3431 | 0.463890 | ||||||||
\(957\) | 5.65685 | 0.182860 | ||||||||
\(958\) | −32.9706 | −1.06523 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5685 | −0.695759 | ||||||||
\(962\) | −5.17157 | −0.166738 | ||||||||
\(963\) | 17.3137 | 0.557926 | ||||||||
\(964\) | −7.31371 | −0.235559 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.2843 | 1.42409 | 0.712043 | − | 0.702136i | \(-0.247770\pi\) | ||||
0.712043 | + | 0.702136i | \(0.247770\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −21.6569 | −0.695718 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.9117 | 1.50547 | 0.752734 | − | 0.658325i | \(-0.228735\pi\) | ||||
0.752734 | + | 0.658325i | \(0.228735\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0.343146 | 0.0109951 | ||||||||
\(975\) | 7.07107 | 0.226455 | ||||||||
\(976\) | −1.41421 | −0.0452679 | ||||||||
\(977\) | 26.3431 | 0.842792 | 0.421396 | − | 0.906877i | \(-0.361540\pi\) | ||||
0.421396 | + | 0.906877i | \(0.361540\pi\) | |||||||
\(978\) | 5.65685 | 0.180886 | ||||||||
\(979\) | 2.58579 | 0.0826421 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | −20.0000 | −0.638226 | ||||||||
\(983\) | 41.0122 | 1.30809 | 0.654043 | − | 0.756457i | \(-0.273072\pi\) | ||||
0.654043 | + | 0.756457i | \(0.273072\pi\) | |||||||
\(984\) | 9.65685 | 0.307849 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.6274 | 0.720604 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.65685 | 0.243597 | ||||||||
\(989\) | −76.5685 | −2.43474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.3137 | 1.37591 | 0.687953 | − | 0.725756i | \(-0.258510\pi\) | ||||
0.687953 | + | 0.725756i | \(0.258510\pi\) | |||||||
\(992\) | 3.07107 | 0.0975065 | ||||||||
\(993\) | −28.9706 | −0.919353 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.0711 | 0.477545 | ||||||||
\(997\) | 9.89949 | 0.313520 | 0.156760 | − | 0.987637i | \(-0.449895\pi\) | ||||
0.156760 | + | 0.987637i | \(0.449895\pi\) | |||||||
\(998\) | 10.6274 | 0.336405 | ||||||||
\(999\) | −3.65685 | −0.115698 |
(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 | 3234.2.a.y.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9702.2.a.de.1.2 | 2 | |||
7.6 | odd | 2 | 3234.2.a.z.1.1 | yes | 2 | ||
21.20 | even | 2 | 9702.2.a.dl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.y.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3234.2.a.z.1.1 | yes | 2 | 7.6 | odd | 2 | ||
9702.2.a.de.1.2 | 2 | 3.2 | odd | 2 | |||
9702.2.a.dl.1.1 | 2 | 21.20 | even | 2 |