Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6534,2,Mod(1,6534)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6534, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6534.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6534.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: | \(52.1742526807\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6534.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.54138 | 1.58375 | 0.791877 | − | 0.610681i | \(-0.209104\pi\) | ||||
0.791877 | + | 0.610681i | \(0.209104\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.54138 | 1.11988 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.458619 | 0.127198 | 0.0635990 | − | 0.997976i | \(-0.479742\pi\) | ||||
0.0635990 | + | 0.997976i | \(0.479742\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.08276 | 1.71782 | 0.858911 | − | 0.512125i | \(-0.171141\pi\) | ||||
0.858911 | + | 0.512125i | \(0.171141\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.54138 | 1.04186 | 0.520932 | − | 0.853598i | \(-0.325584\pi\) | ||||
0.520932 | + | 0.853598i | \(0.325584\pi\) | |||||||
\(20\) | 3.54138 | 0.791877 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.541381 | −0.112886 | −0.0564429 | − | 0.998406i | \(-0.517976\pi\) | ||||
−0.0564429 | + | 0.998406i | \(0.517976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.54138 | 1.50828 | ||||||||
\(26\) | 0.458619 | 0.0899425 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.54138 | 0.456446 | 0.228223 | − | 0.973609i | \(-0.426709\pi\) | ||||
0.228223 | + | 0.973609i | \(0.426709\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.08276 | 1.21468 | ||||||||
\(35\) | 3.54138 | 0.598603 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.08276 | −0.342404 | −0.171202 | − | 0.985236i | \(-0.554765\pi\) | ||||
−0.171202 | + | 0.985236i | \(0.554765\pi\) | |||||||
\(38\) | 4.54138 | 0.736709 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.54138 | 0.559942 | ||||||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.08276 | −0.927613 | −0.463806 | − | 0.885937i | \(-0.653517\pi\) | ||||
−0.463806 | + | 0.885937i | \(0.653517\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.541381 | −0.0798223 | ||||||||
\(47\) | 10.6241 | 1.54969 | 0.774845 | − | 0.632151i | \(-0.217828\pi\) | ||||
0.774845 | + | 0.632151i | \(0.217828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 7.54138 | 1.06651 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.458619 | 0.0635990 | ||||||||
\(53\) | −10.0828 | −1.38497 | −0.692487 | − | 0.721430i | \(-0.743485\pi\) | ||||
−0.692487 | + | 0.721430i | \(0.743485\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | 0.393919 | ||||||||
\(59\) | −7.62414 | −0.992579 | −0.496289 | − | 0.868157i | \(-0.665305\pi\) | ||||
−0.496289 | + | 0.868157i | \(0.665305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.08276 | −0.778818 | −0.389409 | − | 0.921065i | \(-0.627321\pi\) | ||||
−0.389409 | + | 0.921065i | \(0.627321\pi\) | |||||||
\(62\) | 2.54138 | 0.322756 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.62414 | 0.201450 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.1655 | −1.85276 | −0.926382 | − | 0.376585i | \(-0.877098\pi\) | ||||
−0.926382 | + | 0.376585i | \(0.877098\pi\) | |||||||
\(68\) | 7.08276 | 0.858911 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.54138 | 0.423276 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.54138 | −0.999693 | −0.499847 | − | 0.866114i | \(-0.666610\pi\) | ||||
−0.499847 | + | 0.866114i | \(0.666610\pi\) | |||||||
\(74\) | −2.08276 | −0.242116 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.54138 | 0.520932 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6241 | 1.64534 | 0.822672 | − | 0.568516i | \(-0.192482\pi\) | ||||
0.822672 | + | 0.568516i | \(0.192482\pi\) | |||||||
\(80\) | 3.54138 | 0.395938 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.00000 | −0.993884 | ||||||||
\(83\) | −5.45862 | −0.599161 | −0.299581 | − | 0.954071i | \(-0.596847\pi\) | ||||
−0.299581 | + | 0.954071i | \(0.596847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.0828 | 2.72061 | ||||||||
\(86\) | −6.08276 | −0.655921 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.54138 | −0.693385 | −0.346693 | − | 0.937979i | \(-0.612695\pi\) | ||||
−0.346693 | + | 0.937979i | \(0.612695\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.458619 | 0.0480763 | ||||||||
\(92\) | −0.541381 | −0.0564429 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.6241 | 1.09580 | ||||||||
\(95\) | 16.0828 | 1.65006 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.1655 | −1.84443 | −0.922215 | − | 0.386678i | \(-0.873623\pi\) | ||||
−0.922215 | + | 0.386678i | \(0.873623\pi\) | |||||||
\(98\) | −6.00000 | −0.606092 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.54138 | 0.754138 | ||||||||
\(101\) | 19.0828 | 1.89881 | 0.949403 | − | 0.314061i | \(-0.101690\pi\) | ||||
0.949403 | + | 0.314061i | \(0.101690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1655 | 1.29724 | 0.648619 | − | 0.761113i | \(-0.275347\pi\) | ||||
0.648619 | + | 0.761113i | \(0.275347\pi\) | |||||||
\(104\) | 0.458619 | 0.0449713 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0828 | −0.979324 | ||||||||
\(107\) | −13.0828 | −1.26476 | −0.632379 | − | 0.774659i | \(-0.717922\pi\) | ||||
−0.632379 | + | 0.774659i | \(0.717922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.45862 | 0.905971 | 0.452986 | − | 0.891518i | \(-0.350359\pi\) | ||||
0.452986 | + | 0.891518i | \(0.350359\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 15.5414 | 1.46201 | 0.731005 | − | 0.682372i | \(-0.239052\pi\) | ||||
0.731005 | + | 0.682372i | \(0.239052\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.91724 | −0.178783 | ||||||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.62414 | −0.701859 | ||||||||
\(119\) | 7.08276 | 0.649276 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −6.08276 | −0.550707 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.54138 | 0.228223 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.45862 | 0.839317 | 0.419658 | − | 0.907682i | \(-0.362150\pi\) | ||||
0.419658 | + | 0.907682i | \(0.362150\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.62414 | 0.142447 | ||||||||
\(131\) | −4.08276 | −0.356713 | −0.178356 | − | 0.983966i | \(-0.557078\pi\) | ||||
−0.178356 | + | 0.983966i | \(0.557078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.54138 | 0.393788 | ||||||||
\(134\) | −15.1655 | −1.31010 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.08276 | 0.607342 | ||||||||
\(137\) | −11.4586 | −0.978976 | −0.489488 | − | 0.872010i | \(-0.662816\pi\) | ||||
−0.489488 | + | 0.872010i | \(0.662816\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.2483 | 1.37816 | 0.689081 | − | 0.724684i | \(-0.258014\pi\) | ||||
0.689081 | + | 0.724684i | \(0.258014\pi\) | |||||||
\(140\) | 3.54138 | 0.299301 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.6241 | 0.882287 | ||||||||
\(146\) | −8.54138 | −0.706890 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.08276 | −0.171202 | ||||||||
\(149\) | −0.541381 | −0.0443517 | −0.0221758 | − | 0.999754i | \(-0.507059\pi\) | ||||
−0.0221758 | + | 0.999754i | \(0.507059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9172 | 0.969811 | 0.484906 | − | 0.874567i | \(-0.338854\pi\) | ||||
0.484906 | + | 0.874567i | \(0.338854\pi\) | |||||||
\(152\) | 4.54138 | 0.368355 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.00000 | 0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.2483 | −1.29675 | −0.648377 | − | 0.761319i | \(-0.724552\pi\) | ||||
−0.648377 | + | 0.761319i | \(0.724552\pi\) | |||||||
\(158\) | 14.6241 | 1.16343 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.54138 | 0.279971 | ||||||||
\(161\) | −0.541381 | −0.0426668 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.5414 | −1.53060 | −0.765300 | − | 0.643674i | \(-0.777409\pi\) | ||||
−0.765300 | + | 0.643674i | \(0.777409\pi\) | |||||||
\(164\) | −9.00000 | −0.702782 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.45862 | −0.423671 | ||||||||
\(167\) | 1.37586 | 0.106467 | 0.0532335 | − | 0.998582i | \(-0.483047\pi\) | ||||
0.0532335 | + | 0.998582i | \(0.483047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7897 | −0.983821 | ||||||||
\(170\) | 25.0828 | 1.92376 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.08276 | −0.463806 | ||||||||
\(173\) | 10.0828 | 0.766578 | 0.383289 | − | 0.923628i | \(-0.374791\pi\) | ||||
0.383289 | + | 0.923628i | \(0.374791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.54138 | 0.570075 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.54138 | −0.490297 | ||||||||
\(179\) | −14.7069 | −1.09925 | −0.549623 | − | 0.835413i | \(-0.685229\pi\) | ||||
−0.549623 | + | 0.835413i | \(0.685229\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5414 | −0.783535 | −0.391767 | − | 0.920064i | \(-0.628136\pi\) | ||||
−0.391767 | + | 0.920064i | \(0.628136\pi\) | |||||||
\(182\) | 0.458619 | 0.0339951 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.541381 | −0.0399112 | ||||||||
\(185\) | −7.37586 | −0.542284 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.6241 | 0.774845 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.0828 | 1.16677 | ||||||||
\(191\) | 16.6241 | 1.20288 | 0.601440 | − | 0.798918i | \(-0.294594\pi\) | ||||
0.601440 | + | 0.798918i | \(0.294594\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.54138 | 0.542841 | 0.271420 | − | 0.962461i | \(-0.412507\pi\) | ||||
0.271420 | + | 0.962461i | \(0.412507\pi\) | |||||||
\(194\) | −18.1655 | −1.30421 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | −13.0828 | −0.932108 | −0.466054 | − | 0.884756i | \(-0.654325\pi\) | ||||
−0.466054 | + | 0.884756i | \(0.654325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 7.54138 | 0.533256 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.0828 | 1.34266 | ||||||||
\(203\) | 3.00000 | 0.210559 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.8724 | −2.22607 | ||||||||
\(206\) | 13.1655 | 0.917286 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.458619 | 0.0317995 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.00000 | 0.481900 | 0.240950 | − | 0.970538i | \(-0.422541\pi\) | ||||
0.240950 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(212\) | −10.0828 | −0.692487 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.0828 | −0.894319 | ||||||||
\(215\) | −21.5414 | −1.46911 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.54138 | 0.172520 | ||||||||
\(218\) | 9.45862 | 0.640618 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.24829 | 0.218503 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.5414 | 1.57645 | 0.788224 | − | 0.615389i | \(-0.211001\pi\) | ||||
0.788224 | + | 0.615389i | \(0.211001\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.5414 | 1.03380 | ||||||||
\(227\) | 7.37586 | 0.489553 | 0.244776 | − | 0.969580i | \(-0.421285\pi\) | ||||
0.244776 | + | 0.969580i | \(0.421285\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3759 | −0.751738 | −0.375869 | − | 0.926673i | \(-0.622656\pi\) | ||||
−0.375869 | + | 0.926673i | \(0.622656\pi\) | |||||||
\(230\) | −1.91724 | −0.126419 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −11.4586 | −0.750679 | −0.375340 | − | 0.926887i | \(-0.622474\pi\) | ||||
−0.375340 | + | 0.926887i | \(0.622474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.6241 | 2.45433 | ||||||||
\(236\) | −7.62414 | −0.496289 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.08276 | 0.459107 | ||||||||
\(239\) | 4.08276 | 0.264092 | 0.132046 | − | 0.991244i | \(-0.457845\pi\) | ||||
0.132046 | + | 0.991244i | \(0.457845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.16553 | 0.397156 | 0.198578 | − | 0.980085i | \(-0.436368\pi\) | ||||
0.198578 | + | 0.980085i | \(0.436368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.08276 | −0.389409 | ||||||||
\(245\) | −21.2483 | −1.35750 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.08276 | 0.132523 | ||||||||
\(248\) | 2.54138 | 0.161378 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.00000 | 0.569210 | ||||||||
\(251\) | −14.4586 | −0.912620 | −0.456310 | − | 0.889821i | \(-0.650829\pi\) | ||||
−0.456310 | + | 0.889821i | \(0.650829\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 9.45862 | 0.593487 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.16553 | 0.322217 | 0.161108 | − | 0.986937i | \(-0.448493\pi\) | ||||
0.161108 | + | 0.986937i | \(0.448493\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.08276 | −0.129417 | ||||||||
\(260\) | 1.62414 | 0.100725 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.08276 | −0.252234 | ||||||||
\(263\) | −15.2483 | −0.940250 | −0.470125 | − | 0.882600i | \(-0.655791\pi\) | ||||
−0.470125 | + | 0.882600i | \(0.655791\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.7069 | −2.19346 | ||||||||
\(266\) | 4.54138 | 0.278450 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.1655 | −0.926382 | ||||||||
\(269\) | −14.7069 | −0.896696 | −0.448348 | − | 0.893859i | \(-0.647987\pi\) | ||||
−0.448348 | + | 0.893859i | \(0.647987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.62414 | 0.523879 | 0.261940 | − | 0.965084i | \(-0.415638\pi\) | ||||
0.261940 | + | 0.965084i | \(0.415638\pi\) | |||||||
\(272\) | 7.08276 | 0.429456 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.4586 | −0.692240 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.2483 | −0.856097 | −0.428048 | − | 0.903756i | \(-0.640799\pi\) | ||||
−0.428048 | + | 0.903756i | \(0.640799\pi\) | |||||||
\(278\) | 16.2483 | 0.974508 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.54138 | 0.211638 | ||||||||
\(281\) | −15.7897 | −0.941933 | −0.470966 | − | 0.882151i | \(-0.656095\pi\) | ||||
−0.470966 | + | 0.882151i | \(0.656095\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 33.1655 | 1.97149 | 0.985743 | − | 0.168258i | \(-0.0538143\pi\) | ||||
0.985743 | + | 0.168258i | \(0.0538143\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.00000 | −0.531253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.1655 | 1.95091 | ||||||||
\(290\) | 10.6241 | 0.623871 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.54138 | −0.499847 | ||||||||
\(293\) | 18.5414 | 1.08320 | 0.541600 | − | 0.840637i | \(-0.317819\pi\) | ||||
0.541600 | + | 0.840637i | \(0.317819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.0000 | −1.57200 | ||||||||
\(296\) | −2.08276 | −0.121058 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.541381 | −0.0313614 | ||||||||
\(299\) | −0.248288 | −0.0143588 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.08276 | −0.350605 | ||||||||
\(302\) | 11.9172 | 0.685760 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.54138 | 0.260466 | ||||||||
\(305\) | −21.5414 | −1.23346 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.29309 | 0.0738008 | 0.0369004 | − | 0.999319i | \(-0.488252\pi\) | ||||
0.0369004 | + | 0.999319i | \(0.488252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | 0.511166 | ||||||||
\(311\) | 10.0828 | 0.571741 | 0.285871 | − | 0.958268i | \(-0.407717\pi\) | ||||
0.285871 | + | 0.958268i | \(0.407717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.62414 | −0.148325 | −0.0741627 | − | 0.997246i | \(-0.523628\pi\) | ||||
−0.0741627 | + | 0.997246i | \(0.523628\pi\) | |||||||
\(314\) | −16.2483 | −0.916944 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.6241 | 0.822672 | ||||||||
\(317\) | −9.24829 | −0.519436 | −0.259718 | − | 0.965685i | \(-0.583630\pi\) | ||||
−0.259718 | + | 0.965685i | \(0.583630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.54138 | 0.197969 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.541381 | −0.0301700 | ||||||||
\(323\) | 32.1655 | 1.78974 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.45862 | 0.191850 | ||||||||
\(326\) | −19.5414 | −1.08230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 10.6241 | 0.585728 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.24829 | 0.453367 | 0.226683 | − | 0.973968i | \(-0.427212\pi\) | ||||
0.226683 | + | 0.973968i | \(0.427212\pi\) | |||||||
\(332\) | −5.45862 | −0.299581 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.37586 | 0.0752835 | ||||||||
\(335\) | −53.7069 | −2.93432 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.917237 | −0.0499651 | −0.0249826 | − | 0.999688i | \(-0.507953\pi\) | ||||
−0.0249826 | + | 0.999688i | \(0.507953\pi\) | |||||||
\(338\) | −12.7897 | −0.695666 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 25.0828 | 1.36030 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −6.08276 | −0.327961 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.0828 | 0.542053 | ||||||||
\(347\) | −36.7897 | −1.97497 | −0.987486 | − | 0.157704i | \(-0.949591\pi\) | ||||
−0.987486 | + | 0.157704i | \(0.949591\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.7069 | 1.32253 | 0.661265 | − | 0.750152i | \(-0.270020\pi\) | ||||
0.661265 | + | 0.750152i | \(0.270020\pi\) | |||||||
\(350\) | 7.54138 | 0.403104 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0000 | 1.59674 | 0.798369 | − | 0.602168i | \(-0.205696\pi\) | ||||
0.798369 | + | 0.602168i | \(0.205696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.2483 | 1.12774 | ||||||||
\(356\) | −6.54138 | −0.346693 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.7069 | −0.777284 | ||||||||
\(359\) | −24.2483 | −1.27978 | −0.639888 | − | 0.768468i | \(-0.721019\pi\) | ||||
−0.639888 | + | 0.768468i | \(0.721019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.62414 | 0.0854813 | ||||||||
\(362\) | −10.5414 | −0.554043 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.458619 | 0.0240382 | ||||||||
\(365\) | −30.2483 | −1.58327 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.6241 | 1.91176 | 0.955882 | − | 0.293750i | \(-0.0949032\pi\) | ||||
0.955882 | + | 0.293750i | \(0.0949032\pi\) | |||||||
\(368\) | −0.541381 | −0.0282214 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.37586 | −0.383453 | ||||||||
\(371\) | −10.0828 | −0.523471 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.5414 | 1.01181 | 0.505907 | − | 0.862588i | \(-0.331158\pi\) | ||||
0.505907 | + | 0.862588i | \(0.331158\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6241 | 0.547898 | ||||||||
\(377\) | 1.37586 | 0.0708602 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.62414 | 0.186160 | 0.0930799 | − | 0.995659i | \(-0.470329\pi\) | ||||
0.0930799 | + | 0.995659i | \(0.470329\pi\) | |||||||
\(380\) | 16.0828 | 0.825028 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.6241 | 0.850565 | ||||||||
\(383\) | 1.91724 | 0.0979663 | 0.0489831 | − | 0.998800i | \(-0.484402\pi\) | ||||
0.0489831 | + | 0.998800i | \(0.484402\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.54138 | 0.383846 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.1655 | −0.922215 | ||||||||
\(389\) | −36.2483 | −1.83786 | −0.918931 | − | 0.394419i | \(-0.870946\pi\) | ||||
−0.918931 | + | 0.394419i | \(0.870946\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.83447 | −0.193918 | ||||||||
\(392\) | −6.00000 | −0.303046 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.0828 | −0.659100 | ||||||||
\(395\) | 51.7897 | 2.60582 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.0828 | 1.35924 | 0.679622 | − | 0.733562i | \(-0.262144\pi\) | ||||
0.679622 | + | 0.733562i | \(0.262144\pi\) | |||||||
\(398\) | 8.00000 | 0.401004 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.54138 | 0.377069 | ||||||||
\(401\) | −9.54138 | −0.476474 | −0.238237 | − | 0.971207i | \(-0.576569\pi\) | ||||
−0.238237 | + | 0.971207i | \(0.576569\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.16553 | 0.0580589 | ||||||||
\(404\) | 19.0828 | 0.949403 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.00000 | 0.148888 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.7069 | −1.27112 | −0.635562 | − | 0.772050i | \(-0.719232\pi\) | ||||
−0.635562 | + | 0.772050i | \(0.719232\pi\) | |||||||
\(410\) | −31.8724 | −1.57407 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.1655 | 0.648619 | ||||||||
\(413\) | −7.62414 | −0.375160 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.3311 | −0.948924 | ||||||||
\(416\) | 0.458619 | 0.0224856 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.0000 | −1.02592 | −0.512959 | − | 0.858413i | \(-0.671451\pi\) | ||||
−0.512959 | + | 0.858413i | \(0.671451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 7.00000 | 0.340755 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.0828 | −0.489662 | ||||||||
\(425\) | 53.4138 | 2.59095 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.08276 | −0.294366 | ||||||||
\(428\) | −13.0828 | −0.632379 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.5414 | −1.03882 | ||||||||
\(431\) | 3.24829 | 0.156465 | 0.0782323 | − | 0.996935i | \(-0.475072\pi\) | ||||
0.0782323 | + | 0.996935i | \(0.475072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.375856 | 0.0180625 | 0.00903125 | − | 0.999959i | \(-0.497125\pi\) | ||||
0.00903125 | + | 0.999959i | \(0.497125\pi\) | |||||||
\(434\) | 2.54138 | 0.121990 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.45862 | 0.452986 | ||||||||
\(437\) | −2.45862 | −0.117612 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3311 | −0.731711 | −0.365856 | − | 0.930672i | \(-0.619224\pi\) | ||||
−0.365856 | + | 0.930672i | \(0.619224\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.24829 | 0.154505 | ||||||||
\(443\) | 1.08276 | 0.0514436 | 0.0257218 | − | 0.999669i | \(-0.491812\pi\) | ||||
0.0257218 | + | 0.999669i | \(0.491812\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.1655 | −1.09815 | ||||||||
\(446\) | 23.5414 | 1.11472 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −12.8345 | −0.605696 | −0.302848 | − | 0.953039i | \(-0.597938\pi\) | ||||
−0.302848 | + | 0.953039i | \(0.597938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 15.5414 | 0.731005 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.37586 | 0.346166 | ||||||||
\(455\) | 1.62414 | 0.0761410 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.1655 | 1.13042 | 0.565208 | − | 0.824949i | \(-0.308796\pi\) | ||||
0.565208 | + | 0.824949i | \(0.308796\pi\) | |||||||
\(458\) | −11.3759 | −0.531559 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.91724 | −0.0893917 | ||||||||
\(461\) | −17.1655 | −0.799478 | −0.399739 | − | 0.916629i | \(-0.630899\pi\) | ||||
−0.399739 | + | 0.916629i | \(0.630899\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.78967 | 0.129647 | 0.0648235 | − | 0.997897i | \(-0.479352\pi\) | ||||
0.0648235 | + | 0.997897i | \(0.479352\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.4586 | −0.530810 | ||||||||
\(467\) | 10.6241 | 0.491627 | 0.245813 | − | 0.969317i | \(-0.420945\pi\) | ||||
0.245813 | + | 0.969317i | \(0.420945\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.1655 | −0.700279 | ||||||||
\(470\) | 37.6241 | 1.73547 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.62414 | −0.350930 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 34.2483 | 1.57142 | ||||||||
\(476\) | 7.08276 | 0.324638 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.08276 | 0.186741 | ||||||||
\(479\) | 19.8724 | 0.907995 | 0.453997 | − | 0.891003i | \(-0.349998\pi\) | ||||
0.453997 | + | 0.891003i | \(0.349998\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.955194 | −0.0435531 | ||||||||
\(482\) | 6.16553 | 0.280832 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −64.3311 | −2.92112 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0000 | 0.498458 | 0.249229 | − | 0.968445i | \(-0.419823\pi\) | ||||
0.249229 | + | 0.968445i | \(0.419823\pi\) | |||||||
\(488\) | −6.08276 | −0.275354 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21.2483 | −0.959900 | ||||||||
\(491\) | −7.91724 | −0.357300 | −0.178650 | − | 0.983913i | \(-0.557173\pi\) | ||||
−0.178650 | + | 0.983913i | \(0.557173\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.2483 | 0.956975 | ||||||||
\(494\) | 2.08276 | 0.0937079 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.54138 | 0.114111 | ||||||||
\(497\) | 6.00000 | 0.269137 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.75171 | −0.167950 | −0.0839749 | − | 0.996468i | \(-0.526762\pi\) | ||||
−0.0839749 | + | 0.996468i | \(0.526762\pi\) | |||||||
\(500\) | 9.00000 | 0.402492 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.4586 | −0.645320 | ||||||||
\(503\) | −30.5414 | −1.36177 | −0.680886 | − | 0.732389i | \(-0.738405\pi\) | ||||
−0.680886 | + | 0.732389i | \(0.738405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 67.5793 | 3.00724 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.45862 | 0.419658 | ||||||||
\(509\) | 20.4138 | 0.904826 | 0.452413 | − | 0.891808i | \(-0.350563\pi\) | ||||
0.452413 | + | 0.891808i | \(0.350563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.54138 | −0.377848 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.16553 | 0.227842 | ||||||||
\(515\) | 46.6241 | 2.05451 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.08276 | −0.0915113 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.62414 | 0.0712234 | ||||||||
\(521\) | −7.37586 | −0.323142 | −0.161571 | − | 0.986861i | \(-0.551656\pi\) | ||||
−0.161571 | + | 0.986861i | \(0.551656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.6241 | 1.16419 | 0.582096 | − | 0.813120i | \(-0.302233\pi\) | ||||
0.582096 | + | 0.813120i | \(0.302233\pi\) | |||||||
\(524\) | −4.08276 | −0.178356 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.2483 | −0.664857 | ||||||||
\(527\) | 18.0000 | 0.784092 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7069 | −0.987257 | ||||||||
\(530\) | −35.7069 | −1.55101 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.54138 | 0.196894 | ||||||||
\(533\) | −4.12757 | −0.178785 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.3311 | −2.00307 | ||||||||
\(536\) | −15.1655 | −0.655051 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.7069 | −0.634060 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.3311 | −0.917093 | −0.458547 | − | 0.888670i | \(-0.651630\pi\) | ||||
−0.458547 | + | 0.888670i | \(0.651630\pi\) | |||||||
\(542\) | 8.62414 | 0.370439 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.08276 | 0.303671 | ||||||||
\(545\) | 33.4966 | 1.43484 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8724 | −1.70482 | −0.852411 | − | 0.522872i | \(-0.824860\pi\) | ||||
−0.852411 | + | 0.522872i | \(0.824860\pi\) | |||||||
\(548\) | −11.4586 | −0.489488 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.6241 | 0.580408 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6241 | 0.621882 | ||||||||
\(554\) | −14.2483 | −0.605352 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.2483 | 0.689081 | ||||||||
\(557\) | −13.8724 | −0.587794 | −0.293897 | − | 0.955837i | \(-0.594952\pi\) | ||||
−0.293897 | + | 0.955837i | \(0.594952\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.78967 | −0.117990 | ||||||||
\(560\) | 3.54138 | 0.149651 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.7897 | −0.666047 | ||||||||
\(563\) | 17.4138 | 0.733905 | 0.366952 | − | 0.930240i | \(-0.380401\pi\) | ||||
0.366952 | + | 0.930240i | \(0.380401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 55.0380 | 2.31546 | ||||||||
\(566\) | 33.1655 | 1.39405 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 29.1655 | 1.22268 | 0.611341 | − | 0.791367i | \(-0.290630\pi\) | ||||
0.611341 | + | 0.791367i | \(0.290630\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0828 | −0.505648 | −0.252824 | − | 0.967512i | \(-0.581359\pi\) | ||||
−0.252824 | + | 0.967512i | \(0.581359\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.00000 | −0.375653 | ||||||||
\(575\) | −4.08276 | −0.170263 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.2483 | −1.55067 | −0.775333 | − | 0.631552i | \(-0.782418\pi\) | ||||
−0.775333 | + | 0.631552i | \(0.782418\pi\) | |||||||
\(578\) | 33.1655 | 1.37950 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.6241 | 0.441144 | ||||||||
\(581\) | −5.45862 | −0.226462 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −8.54138 | −0.353445 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.5414 | 0.765937 | ||||||||
\(587\) | −46.6241 | −1.92438 | −0.962192 | − | 0.272371i | \(-0.912192\pi\) | ||||
−0.962192 | + | 0.272371i | \(0.912192\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.5414 | 0.475554 | ||||||||
\(590\) | −27.0000 | −1.11157 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.08276 | −0.0856010 | ||||||||
\(593\) | 13.3759 | 0.549281 | 0.274640 | − | 0.961547i | \(-0.411441\pi\) | ||||
0.274640 | + | 0.961547i | \(0.411441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.0828 | 1.02829 | ||||||||
\(596\) | −0.541381 | −0.0221758 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.248288 | −0.0101532 | ||||||||
\(599\) | 4.62414 | 0.188937 | 0.0944687 | − | 0.995528i | \(-0.469885\pi\) | ||||
0.0944687 | + | 0.995528i | \(0.469885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.4138 | 1.48535 | 0.742675 | − | 0.669652i | \(-0.233557\pi\) | ||||
0.742675 | + | 0.669652i | \(0.233557\pi\) | |||||||
\(602\) | −6.08276 | −0.247915 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.9172 | 0.484906 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.4138 | 1.23446 | 0.617229 | − | 0.786783i | \(-0.288255\pi\) | ||||
0.617229 | + | 0.786783i | \(0.288255\pi\) | |||||||
\(608\) | 4.54138 | 0.184177 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.5414 | −0.872185 | ||||||||
\(611\) | 4.87243 | 0.197117 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3311 | 0.578826 | 0.289413 | − | 0.957204i | \(-0.406540\pi\) | ||||
0.289413 | + | 0.957204i | \(0.406540\pi\) | |||||||
\(614\) | 1.29309 | 0.0521850 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.5414 | 1.22955 | 0.614775 | − | 0.788703i | \(-0.289247\pi\) | ||||
0.614775 | + | 0.788703i | \(0.289247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.62414 | −0.105473 | −0.0527366 | − | 0.998608i | \(-0.516794\pi\) | ||||
−0.0527366 | + | 0.998608i | \(0.516794\pi\) | |||||||
\(620\) | 9.00000 | 0.361449 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.0828 | 0.404282 | ||||||||
\(623\) | −6.54138 | −0.262075 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.83447 | −0.233379 | ||||||||
\(626\) | −2.62414 | −0.104882 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −16.2483 | −0.648377 | ||||||||
\(629\) | −14.7517 | −0.588189 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.08276 | 0.361579 | 0.180790 | − | 0.983522i | \(-0.442135\pi\) | ||||
0.180790 | + | 0.983522i | \(0.442135\pi\) | |||||||
\(632\) | 14.6241 | 0.581717 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.24829 | −0.367296 | ||||||||
\(635\) | 33.4966 | 1.32927 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.75171 | −0.109027 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.54138 | 0.139985 | ||||||||
\(641\) | 4.62414 | 0.182643 | 0.0913213 | − | 0.995821i | \(-0.470891\pi\) | ||||
0.0913213 | + | 0.995821i | \(0.470891\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000 | 0.788723 | 0.394362 | − | 0.918955i | \(-0.370966\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(644\) | −0.541381 | −0.0213334 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.1655 | 1.26554 | ||||||||
\(647\) | −19.3311 | −0.759982 | −0.379991 | − | 0.924990i | \(-0.624073\pi\) | ||||
−0.379991 | + | 0.924990i | \(0.624073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.45862 | 0.135658 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.5414 | −0.765300 | ||||||||
\(653\) | −27.2483 | −1.06631 | −0.533154 | − | 0.846018i | \(-0.678993\pi\) | ||||
−0.533154 | + | 0.846018i | \(0.678993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.4586 | −0.564945 | ||||||||
\(656\) | −9.00000 | −0.351391 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.6241 | 0.414172 | ||||||||
\(659\) | 31.8724 | 1.24157 | 0.620787 | − | 0.783979i | \(-0.286813\pi\) | ||||
0.620787 | + | 0.783979i | \(0.286813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.4138 | 0.638423 | 0.319212 | − | 0.947683i | \(-0.396582\pi\) | ||||
0.319212 | + | 0.947683i | \(0.396582\pi\) | |||||||
\(662\) | 8.24829 | 0.320579 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.45862 | −0.211835 | ||||||||
\(665\) | 16.0828 | 0.623663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.62414 | −0.0628871 | ||||||||
\(668\) | 1.37586 | 0.0532335 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −53.7069 | −2.07488 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.00000 | 0.154189 | 0.0770943 | − | 0.997024i | \(-0.475436\pi\) | ||||
0.0770943 | + | 0.997024i | \(0.475436\pi\) | |||||||
\(674\) | −0.917237 | −0.0353307 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7897 | −0.491910 | ||||||||
\(677\) | 15.5414 | 0.597304 | 0.298652 | − | 0.954362i | \(-0.403463\pi\) | ||||
0.298652 | + | 0.954362i | \(0.403463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.1655 | −0.697129 | ||||||||
\(680\) | 25.0828 | 0.961880 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.3759 | −0.856188 | −0.428094 | − | 0.903734i | \(-0.640815\pi\) | ||||
−0.428094 | + | 0.903734i | \(0.640815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −40.5793 | −1.55046 | ||||||||
\(686\) | −13.0000 | −0.496342 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.08276 | −0.231903 | ||||||||
\(689\) | −4.62414 | −0.176166 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.45862 | −0.131572 | −0.0657860 | − | 0.997834i | \(-0.520955\pi\) | ||||
−0.0657860 | + | 0.997834i | \(0.520955\pi\) | |||||||
\(692\) | 10.0828 | 0.383289 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36.7897 | −1.39652 | ||||||||
\(695\) | 57.5414 | 2.18267 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −63.7449 | −2.41451 | ||||||||
\(698\) | 24.7069 | 0.935170 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.54138 | 0.285037 | ||||||||
\(701\) | −46.8724 | −1.77035 | −0.885174 | − | 0.465261i | \(-0.845961\pi\) | ||||
−0.885174 | + | 0.465261i | \(0.845961\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.45862 | −0.356739 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.0000 | 1.12906 | ||||||||
\(707\) | 19.0828 | 0.717681 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.1655 | 1.17045 | 0.585223 | − | 0.810872i | \(-0.301007\pi\) | ||||
0.585223 | + | 0.810872i | \(0.301007\pi\) | |||||||
\(710\) | 21.2483 | 0.797434 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.54138 | −0.245149 | ||||||||
\(713\) | −1.37586 | −0.0515262 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −14.7069 | −0.549623 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.2483 | −0.904938 | ||||||||
\(719\) | −45.4966 | −1.69674 | −0.848368 | − | 0.529407i | \(-0.822414\pi\) | ||||
−0.848368 | + | 0.529407i | \(0.822414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1655 | 0.490310 | ||||||||
\(722\) | 1.62414 | 0.0604444 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.5414 | −0.391767 | ||||||||
\(725\) | 22.6241 | 0.840240 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.9172 | 0.701602 | 0.350801 | − | 0.936450i | \(-0.385909\pi\) | ||||
0.350801 | + | 0.936450i | \(0.385909\pi\) | |||||||
\(728\) | 0.458619 | 0.0169975 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.2483 | −1.11954 | ||||||||
\(731\) | −43.0828 | −1.59347 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.8724 | −1.36191 | −0.680957 | − | 0.732323i | \(-0.738436\pi\) | ||||
−0.680957 | + | 0.732323i | \(0.738436\pi\) | |||||||
\(734\) | 36.6241 | 1.35182 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.541381 | −0.0199556 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.37586 | 0.197754 | 0.0988770 | − | 0.995100i | \(-0.468475\pi\) | ||||
0.0988770 | + | 0.995100i | \(0.468475\pi\) | |||||||
\(740\) | −7.37586 | −0.271142 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.0828 | −0.370150 | ||||||||
\(743\) | −20.7069 | −0.759663 | −0.379831 | − | 0.925056i | \(-0.624018\pi\) | ||||
−0.379831 | + | 0.925056i | \(0.624018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.91724 | −0.0702421 | ||||||||
\(746\) | 19.5414 | 0.715461 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.0828 | −0.478034 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0000 | −0.802791 | −0.401396 | − | 0.915905i | \(-0.631475\pi\) | ||||
−0.401396 | + | 0.915905i | \(0.631475\pi\) | |||||||
\(752\) | 10.6241 | 0.387423 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.37586 | 0.0501057 | ||||||||
\(755\) | 42.2035 | 1.53594 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2483 | 0.954010 | 0.477005 | − | 0.878901i | \(-0.341722\pi\) | ||||
0.477005 | + | 0.878901i | \(0.341722\pi\) | |||||||
\(758\) | 3.62414 | 0.131635 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.0828 | 0.583383 | ||||||||
\(761\) | −36.2483 | −1.31400 | −0.657000 | − | 0.753891i | \(-0.728175\pi\) | ||||
−0.657000 | + | 0.753891i | \(0.728175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.45862 | 0.342425 | ||||||||
\(764\) | 16.6241 | 0.601440 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.91724 | 0.0692726 | ||||||||
\(767\) | −3.49658 | −0.126254 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.7897 | 1.47091 | 0.735457 | − | 0.677572i | \(-0.236968\pi\) | ||||
0.735457 | + | 0.677572i | \(0.236968\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.54138 | 0.271420 | ||||||||
\(773\) | −11.7517 | −0.422680 | −0.211340 | − | 0.977413i | \(-0.567783\pi\) | ||||
−0.211340 | + | 0.977413i | \(0.567783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.1655 | 0.688446 | ||||||||
\(776\) | −18.1655 | −0.652104 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.2483 | −1.29956 | ||||||||
\(779\) | −40.8724 | −1.46441 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −3.83447 | −0.137121 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | −57.5414 | −2.05374 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.3311 | −1.18812 | −0.594062 | − | 0.804419i | \(-0.702477\pi\) | ||||
−0.594062 | + | 0.804419i | \(0.702477\pi\) | |||||||
\(788\) | −13.0828 | −0.466054 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 51.7897 | 1.84259 | ||||||||
\(791\) | 15.5414 | 0.552588 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.78967 | −0.0990640 | ||||||||
\(794\) | 27.0828 | 0.961131 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | 0.283552 | ||||||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 75.2483 | 2.66209 | ||||||||
\(800\) | 7.54138 | 0.266628 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.54138 | −0.336918 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.91724 | −0.0675737 | ||||||||
\(806\) | 1.16553 | 0.0410539 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.0828 | 0.671329 | ||||||||
\(809\) | −6.83447 | −0.240287 | −0.120144 | − | 0.992757i | \(-0.538336\pi\) | ||||
−0.120144 | + | 0.992757i | \(0.538336\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.6241 | −0.443294 | −0.221647 | − | 0.975127i | \(-0.571143\pi\) | ||||
−0.221647 | + | 0.975127i | \(0.571143\pi\) | |||||||
\(812\) | 3.00000 | 0.105279 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −69.2035 | −2.42409 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.6241 | −0.966446 | ||||||||
\(818\) | −25.7069 | −0.898821 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −31.8724 | −1.11303 | ||||||||
\(821\) | 18.2931 | 0.638433 | 0.319217 | − | 0.947682i | \(-0.396580\pi\) | ||||
0.319217 | + | 0.947682i | \(0.396580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.1207 | −1.46824 | −0.734118 | − | 0.679022i | \(-0.762404\pi\) | ||||
−0.734118 | + | 0.679022i | \(0.762404\pi\) | |||||||
\(824\) | 13.1655 | 0.458643 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.62414 | −0.265278 | ||||||||
\(827\) | −44.1655 | −1.53579 | −0.767893 | − | 0.640578i | \(-0.778695\pi\) | ||||
−0.767893 | + | 0.640578i | \(0.778695\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.70691 | 0.267672 | 0.133836 | − | 0.991003i | \(-0.457270\pi\) | ||||
0.133836 | + | 0.991003i | \(0.457270\pi\) | |||||||
\(830\) | −19.3311 | −0.670991 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.458619 | 0.0158997 | ||||||||
\(833\) | −42.4966 | −1.47242 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.87243 | 0.168617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.0000 | −0.725433 | ||||||||
\(839\) | 43.6241 | 1.50607 | 0.753036 | − | 0.657979i | \(-0.228588\pi\) | ||||
0.753036 | + | 0.657979i | \(0.228588\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −1.00000 | −0.0344623 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.00000 | 0.240950 | ||||||||
\(845\) | −45.2931 | −1.55813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10.0828 | −0.346243 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 53.4138 | 1.83208 | ||||||||
\(851\) | 1.12757 | 0.0386526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.3311 | 0.593404 | 0.296702 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296702 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(854\) | −6.08276 | −0.208148 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.0828 | −0.447160 | ||||||||
\(857\) | −9.54138 | −0.325927 | −0.162964 | − | 0.986632i | \(-0.552105\pi\) | ||||
−0.162964 | + | 0.986632i | \(0.552105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.5793 | 1.65751 | 0.828753 | − | 0.559615i | \(-0.189051\pi\) | ||||
0.828753 | + | 0.559615i | \(0.189051\pi\) | |||||||
\(860\) | −21.5414 | −0.734555 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.24829 | 0.110637 | ||||||||
\(863\) | −7.08276 | −0.241100 | −0.120550 | − | 0.992707i | \(-0.538466\pi\) | ||||
−0.120550 | + | 0.992707i | \(0.538466\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.7069 | 1.21407 | ||||||||
\(866\) | 0.375856 | 0.0127721 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.54138 | 0.0862601 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.95519 | −0.235668 | ||||||||
\(872\) | 9.45862 | 0.320309 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.45862 | −0.0831640 | ||||||||
\(875\) | 9.00000 | 0.304256 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.5793 | 1.70794 | 0.853971 | − | 0.520320i | \(-0.174187\pi\) | ||||
0.853971 | + | 0.520320i | \(0.174187\pi\) | |||||||
\(878\) | −15.3311 | −0.517398 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.541381 | −0.0182396 | −0.00911980 | − | 0.999958i | \(-0.502903\pi\) | ||||
−0.00911980 | + | 0.999958i | \(0.502903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.5793 | 1.02908 | 0.514538 | − | 0.857467i | \(-0.327963\pi\) | ||||
0.514538 | + | 0.857467i | \(0.327963\pi\) | |||||||
\(884\) | 3.24829 | 0.109252 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.08276 | 0.0363761 | ||||||||
\(887\) | 0.248288 | 0.00833668 | 0.00416834 | − | 0.999991i | \(-0.498673\pi\) | ||||
0.00416834 | + | 0.999991i | \(0.498673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.45862 | 0.317232 | ||||||||
\(890\) | −23.1655 | −0.776510 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 23.5414 | 0.788224 | ||||||||
\(893\) | 48.2483 | 1.61457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −52.0828 | −1.74093 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8345 | −0.428292 | ||||||||
\(899\) | 7.62414 | 0.254279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −71.4138 | −2.37914 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.5414 | 0.516899 | ||||||||
\(905\) | −37.3311 | −1.24093 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5414 | −0.848088 | −0.424044 | − | 0.905642i | \(-0.639390\pi\) | ||||
−0.424044 | + | 0.905642i | \(0.639390\pi\) | |||||||
\(908\) | 7.37586 | 0.244776 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.62414 | 0.0538398 | ||||||||
\(911\) | 54.2483 | 1.79733 | 0.898663 | − | 0.438640i | \(-0.144540\pi\) | ||||
0.898663 | + | 0.438640i | \(0.144540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 24.1655 | 0.799325 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.3759 | −0.375869 | ||||||||
\(917\) | −4.08276 | −0.134825 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3759 | 0.573177 | 0.286588 | − | 0.958054i | \(-0.407479\pi\) | ||||
0.286588 | + | 0.958054i | \(0.407479\pi\) | |||||||
\(920\) | −1.91724 | −0.0632094 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.1655 | −0.565316 | ||||||||
\(923\) | 2.75171 | 0.0905737 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.7069 | −0.516440 | ||||||||
\(926\) | 2.78967 | 0.0916742 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | −28.6241 | −0.939128 | −0.469564 | − | 0.882899i | \(-0.655589\pi\) | ||||
−0.469564 | + | 0.882899i | \(0.655589\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.2483 | −0.893027 | ||||||||
\(932\) | −11.4586 | −0.375340 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.6241 | 0.347633 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.0827625 | −0.00270373 | −0.00135187 | − | 0.999999i | \(-0.500430\pi\) | ||||
−0.00135187 | + | 0.999999i | \(0.500430\pi\) | |||||||
\(938\) | −15.1655 | −0.495172 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 37.6241 | 1.22716 | ||||||||
\(941\) | 18.0000 | 0.586783 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.87243 | 0.158668 | ||||||||
\(944\) | −7.62414 | −0.248145 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.2483 | 0.982937 | 0.491469 | − | 0.870895i | \(-0.336460\pi\) | ||||
0.491469 | + | 0.870895i | \(0.336460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.91724 | −0.127159 | ||||||||
\(950\) | 34.2483 | 1.11116 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.08276 | 0.229554 | ||||||||
\(953\) | −5.75171 | −0.186316 | −0.0931581 | − | 0.995651i | \(-0.529696\pi\) | ||||
−0.0931581 | + | 0.995651i | \(0.529696\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 58.8724 | 1.90507 | ||||||||
\(956\) | 4.08276 | 0.132046 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.8724 | 0.642049 | ||||||||
\(959\) | −11.4586 | −0.370018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5414 | −0.791657 | ||||||||
\(962\) | −0.955194 | −0.0307967 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.16553 | 0.198578 | ||||||||
\(965\) | 26.7069 | 0.859726 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.9552 | −1.12408 | −0.562042 | − | 0.827109i | \(-0.689984\pi\) | ||||
−0.562042 | + | 0.827109i | \(0.689984\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −64.3311 | −2.06555 | ||||||||
\(971\) | 42.0000 | 1.34784 | 0.673922 | − | 0.738802i | \(-0.264608\pi\) | ||||
0.673922 | + | 0.738802i | \(0.264608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.2483 | 0.520896 | ||||||||
\(974\) | 11.0000 | 0.352463 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.08276 | −0.194704 | ||||||||
\(977\) | 2.16553 | 0.0692813 | 0.0346406 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346406 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −21.2483 | −0.678752 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.91724 | −0.252649 | ||||||||
\(983\) | 33.4966 | 1.06837 | 0.534187 | − | 0.845366i | \(-0.320618\pi\) | ||||
0.534187 | + | 0.845366i | \(0.320618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46.3311 | −1.47623 | ||||||||
\(986\) | 21.2483 | 0.676683 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.08276 | 0.0662615 | ||||||||
\(989\) | 3.29309 | 0.104714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.00000 | −0.222362 | −0.111181 | − | 0.993800i | \(-0.535463\pi\) | ||||
−0.111181 | + | 0.993800i | \(0.535463\pi\) | |||||||
\(992\) | 2.54138 | 0.0806889 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | 0.190308 | ||||||||
\(995\) | 28.3311 | 0.898155 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.54138 | 0.238838 | 0.119419 | − | 0.992844i | \(-0.461897\pi\) | ||||
0.119419 | + | 0.992844i | \(0.461897\pi\) | |||||||
\(998\) | −3.75171 | −0.118758 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6534.2.a.cl.1.2 | yes | 2 | |
3.2 | odd | 2 | 6534.2.a.bk.1.1 | ✓ | 2 | ||
11.10 | odd | 2 | 6534.2.a.bp.1.2 | yes | 2 | ||
33.32 | even | 2 | 6534.2.a.cc.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6534.2.a.bk.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
6534.2.a.bp.1.2 | yes | 2 | 11.10 | odd | 2 | ||
6534.2.a.cc.1.1 | yes | 2 | 33.32 | even | 2 | ||
6534.2.a.cl.1.2 | yes | 2 | 1.1 | even | 1 | trivial |