Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9702,2,Mod(1,9702)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9702, 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("9702.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9702.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: | \(77.4708600410\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1386) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9702.1 |
$q$-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 | ||||||||
\(5\) | 0.414214 | 0.185242 | 0.0926210 | − | 0.995701i | \(-0.470476\pi\) | ||||
0.0926210 | + | 0.995701i | \(0.470476\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.414214 | 0.130986 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17157 | 0.324936 | 0.162468 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162468 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.17157 | 0.526684 | 0.263342 | − | 0.964703i | \(-0.415175\pi\) | ||||
0.263342 | + | 0.964703i | \(0.415175\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.828427 | −0.190054 | −0.0950271 | − | 0.995475i | \(-0.530294\pi\) | ||||
−0.0950271 | + | 0.995475i | \(0.530294\pi\) | |||||||
\(20\) | 0.414214 | 0.0926210 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −3.24264 | −0.676137 | −0.338069 | − | 0.941121i | \(-0.609774\pi\) | ||||
−0.338069 | + | 0.941121i | \(0.609774\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.82843 | −0.965685 | ||||||||
\(26\) | 1.17157 | 0.229764 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.48528 | 1.16479 | 0.582395 | − | 0.812906i | \(-0.302116\pi\) | ||||
0.582395 | + | 0.812906i | \(0.302116\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.17157 | 0.372422 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.65685 | 1.58758 | 0.793789 | − | 0.608194i | \(-0.208106\pi\) | ||||
0.793789 | + | 0.608194i | \(0.208106\pi\) | |||||||
\(38\) | −0.828427 | −0.134389 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.414214 | 0.0654929 | ||||||||
\(41\) | −4.65685 | −0.727278 | −0.363639 | − | 0.931540i | \(-0.618466\pi\) | ||||
−0.363639 | + | 0.931540i | \(0.618466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.82843 | −0.431331 | −0.215666 | − | 0.976467i | \(-0.569192\pi\) | ||||
−0.215666 | + | 0.976467i | \(0.569192\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.24264 | −0.478101 | ||||||||
\(47\) | 9.24264 | 1.34818 | 0.674089 | − | 0.738650i | \(-0.264536\pi\) | ||||
0.674089 | + | 0.738650i | \(0.264536\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.82843 | −0.682843 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.17157 | 0.162468 | ||||||||
\(53\) | −5.17157 | −0.710370 | −0.355185 | − | 0.934796i | \(-0.615582\pi\) | ||||
−0.355185 | + | 0.934796i | \(0.615582\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.414214 | 0.0558525 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.82843 | 0.371391 | ||||||||
\(59\) | 3.65685 | 0.476082 | 0.238041 | − | 0.971255i | \(-0.423495\pi\) | ||||
0.238041 | + | 0.971255i | \(0.423495\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.58579 | 0.203039 | 0.101520 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101520 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(62\) | 6.48528 | 0.823632 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.485281 | 0.0601917 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.4853 | −1.64749 | −0.823745 | − | 0.566961i | \(-0.808119\pi\) | ||||
−0.823745 | + | 0.566961i | \(0.808119\pi\) | |||||||
\(68\) | 2.17157 | 0.263342 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3137 | 1.58005 | 0.790023 | − | 0.613077i | \(-0.210068\pi\) | ||||
0.790023 | + | 0.613077i | \(0.210068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.82843 | 0.565125 | 0.282562 | − | 0.959249i | \(-0.408816\pi\) | ||||
0.282562 | + | 0.959249i | \(0.408816\pi\) | |||||||
\(74\) | 9.65685 | 1.12259 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.828427 | −0.0950271 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.75736 | 0.535245 | 0.267622 | − | 0.963524i | \(-0.413762\pi\) | ||||
0.267622 | + | 0.963524i | \(0.413762\pi\) | |||||||
\(80\) | 0.414214 | 0.0463105 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.65685 | −0.514264 | ||||||||
\(83\) | 9.82843 | 1.07881 | 0.539405 | − | 0.842046i | \(-0.318649\pi\) | ||||
0.539405 | + | 0.842046i | \(0.318649\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.899495 | 0.0975639 | ||||||||
\(86\) | −2.82843 | −0.304997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −12.4853 | −1.32344 | −0.661719 | − | 0.749752i | \(-0.730173\pi\) | ||||
−0.661719 | + | 0.749752i | \(0.730173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.24264 | −0.338069 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.24264 | 0.953306 | ||||||||
\(95\) | −0.343146 | −0.0352060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1716 | 1.03277 | 0.516383 | − | 0.856358i | \(-0.327278\pi\) | ||||
0.516383 | + | 0.856358i | \(0.327278\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.82843 | −0.482843 | ||||||||
\(101\) | 14.1421 | 1.40720 | 0.703598 | − | 0.710599i | \(-0.251576\pi\) | ||||
0.703598 | + | 0.710599i | \(0.251576\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.17157 | 0.903702 | 0.451851 | − | 0.892093i | \(-0.350764\pi\) | ||||
0.451851 | + | 0.892093i | \(0.350764\pi\) | |||||||
\(104\) | 1.17157 | 0.114882 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.17157 | −0.502308 | ||||||||
\(107\) | −16.6569 | −1.61028 | −0.805139 | − | 0.593086i | \(-0.797910\pi\) | ||||
−0.805139 | + | 0.593086i | \(0.797910\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.24264 | 0.310589 | 0.155294 | − | 0.987868i | \(-0.450367\pi\) | ||||
0.155294 | + | 0.987868i | \(0.450367\pi\) | |||||||
\(110\) | 0.414214 | 0.0394937 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.65685 | 0.344008 | 0.172004 | − | 0.985096i | \(-0.444976\pi\) | ||||
0.172004 | + | 0.985096i | \(0.444976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.34315 | −0.125249 | ||||||||
\(116\) | 2.82843 | 0.262613 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.65685 | 0.336641 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.58579 | 0.143570 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.48528 | 0.582395 | ||||||||
\(125\) | −4.07107 | −0.364127 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.24264 | 0.110267 | 0.0551333 | − | 0.998479i | \(-0.482442\pi\) | ||||
0.0551333 | + | 0.998479i | \(0.482442\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.485281 | 0.0425620 | ||||||||
\(131\) | −15.3137 | −1.33796 | −0.668982 | − | 0.743278i | \(-0.733270\pi\) | ||||
−0.668982 | + | 0.743278i | \(0.733270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.4853 | −1.16495 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.17157 | 0.186211 | ||||||||
\(137\) | −4.82843 | −0.412520 | −0.206260 | − | 0.978497i | \(-0.566129\pi\) | ||||
−0.206260 | + | 0.978497i | \(0.566129\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.3137 | 1.11726 | ||||||||
\(143\) | 1.17157 | 0.0979718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.17157 | 0.0972938 | ||||||||
\(146\) | 4.82843 | 0.399603 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.65685 | 0.793789 | ||||||||
\(149\) | 11.3137 | 0.926855 | 0.463428 | − | 0.886135i | \(-0.346619\pi\) | ||||
0.463428 | + | 0.886135i | \(0.346619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.24264 | 0.101125 | 0.0505623 | − | 0.998721i | \(-0.483899\pi\) | ||||
0.0505623 | + | 0.998721i | \(0.483899\pi\) | |||||||
\(152\) | −0.828427 | −0.0671943 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.68629 | 0.215768 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.17157 | 0.731971 | 0.365986 | − | 0.930621i | \(-0.380732\pi\) | ||||
0.365986 | + | 0.930621i | \(0.380732\pi\) | |||||||
\(158\) | 4.75736 | 0.378475 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.414214 | 0.0327465 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.00000 | 0.234978 | 0.117489 | − | 0.993074i | \(-0.462515\pi\) | ||||
0.117489 | + | 0.993074i | \(0.462515\pi\) | |||||||
\(164\) | −4.65685 | −0.363639 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.82843 | 0.762834 | ||||||||
\(167\) | 16.4853 | 1.27567 | 0.637835 | − | 0.770173i | \(-0.279830\pi\) | ||||
0.637835 | + | 0.770173i | \(0.279830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6274 | −0.894417 | ||||||||
\(170\) | 0.899495 | 0.0689881 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.82843 | −0.215666 | ||||||||
\(173\) | 12.1421 | 0.923149 | 0.461575 | − | 0.887101i | \(-0.347285\pi\) | ||||
0.461575 | + | 0.887101i | \(0.347285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.4853 | −0.935811 | ||||||||
\(179\) | −3.17157 | −0.237054 | −0.118527 | − | 0.992951i | \(-0.537817\pi\) | ||||
−0.118527 | + | 0.992951i | \(0.537817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34315 | 0.174165 | 0.0870823 | − | 0.996201i | \(-0.472246\pi\) | ||||
0.0870823 | + | 0.996201i | \(0.472246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.24264 | −0.239051 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.17157 | 0.158801 | ||||||||
\(188\) | 9.24264 | 0.674089 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.343146 | −0.0248944 | ||||||||
\(191\) | −9.31371 | −0.673916 | −0.336958 | − | 0.941520i | \(-0.609398\pi\) | ||||
−0.336958 | + | 0.941520i | \(0.609398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.17157 | −0.660184 | −0.330092 | − | 0.943949i | \(-0.607080\pi\) | ||||
−0.330092 | + | 0.943949i | \(0.607080\pi\) | |||||||
\(194\) | 10.1716 | 0.730276 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.51472 | −0.250413 | −0.125207 | − | 0.992131i | \(-0.539959\pi\) | ||||
−0.125207 | + | 0.992131i | \(0.539959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.34315 | 0.591430 | 0.295715 | − | 0.955276i | \(-0.404442\pi\) | ||||
0.295715 | + | 0.955276i | \(0.404442\pi\) | |||||||
\(200\) | −4.82843 | −0.341421 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.1421 | 0.995037 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.92893 | −0.134722 | ||||||||
\(206\) | 9.17157 | 0.639014 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.17157 | 0.0812340 | ||||||||
\(209\) | −0.828427 | −0.0573035 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8284 | 1.02083 | 0.510416 | − | 0.859928i | \(-0.329492\pi\) | ||||
0.510416 | + | 0.859928i | \(0.329492\pi\) | |||||||
\(212\) | −5.17157 | −0.355185 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.6569 | −1.13864 | ||||||||
\(215\) | −1.17157 | −0.0799006 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.24264 | 0.219619 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.414214 | 0.0279263 | ||||||||
\(221\) | 2.54416 | 0.171138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.3137 | 0.891552 | 0.445776 | − | 0.895145i | \(-0.352928\pi\) | ||||
0.445776 | + | 0.895145i | \(0.352928\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.65685 | 0.243250 | ||||||||
\(227\) | −12.3137 | −0.817290 | −0.408645 | − | 0.912694i | \(-0.633998\pi\) | ||||
−0.408645 | + | 0.912694i | \(0.633998\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3137 | 0.747631 | 0.373815 | − | 0.927503i | \(-0.378049\pi\) | ||||
0.373815 | + | 0.927503i | \(0.378049\pi\) | |||||||
\(230\) | −1.34315 | −0.0885644 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.82843 | 0.185695 | ||||||||
\(233\) | 8.31371 | 0.544649 | 0.272325 | − | 0.962205i | \(-0.412208\pi\) | ||||
0.272325 | + | 0.962205i | \(0.412208\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.82843 | 0.249739 | ||||||||
\(236\) | 3.65685 | 0.238041 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9706 | −1.60850 | −0.804248 | − | 0.594294i | \(-0.797431\pi\) | ||||
−0.804248 | + | 0.594294i | \(0.797431\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.58579 | 0.101520 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.970563 | −0.0617554 | ||||||||
\(248\) | 6.48528 | 0.411816 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.07107 | −0.257477 | ||||||||
\(251\) | −26.1421 | −1.65008 | −0.825038 | − | 0.565077i | \(-0.808847\pi\) | ||||
−0.825038 | + | 0.565077i | \(0.808847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.24264 | −0.203863 | ||||||||
\(254\) | 1.24264 | 0.0779702 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.1716 | −1.57016 | −0.785080 | − | 0.619395i | \(-0.787378\pi\) | ||||
−0.785080 | + | 0.619395i | \(0.787378\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.485281 | 0.0300959 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.3137 | −0.946084 | ||||||||
\(263\) | 9.31371 | 0.574308 | 0.287154 | − | 0.957884i | \(-0.407291\pi\) | ||||
0.287154 | + | 0.957884i | \(0.407291\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.14214 | −0.131590 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.4853 | −0.823745 | ||||||||
\(269\) | 8.07107 | 0.492102 | 0.246051 | − | 0.969257i | \(-0.420867\pi\) | ||||
0.246051 | + | 0.969257i | \(0.420867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3137 | 0.808750 | 0.404375 | − | 0.914593i | \(-0.367489\pi\) | ||||
0.404375 | + | 0.914593i | \(0.367489\pi\) | |||||||
\(272\) | 2.17157 | 0.131671 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.82843 | −0.291696 | ||||||||
\(275\) | −4.82843 | −0.291165 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.82843 | −0.410280 | −0.205140 | − | 0.978733i | \(-0.565765\pi\) | ||||
−0.205140 | + | 0.978733i | \(0.565765\pi\) | |||||||
\(278\) | 6.00000 | 0.359856 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.51472 | 0.150016 | 0.0750078 | − | 0.997183i | \(-0.476102\pi\) | ||||
0.0750078 | + | 0.997183i | \(0.476102\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.85786 | 0.110439 | 0.0552193 | − | 0.998474i | \(-0.482414\pi\) | ||||
0.0552193 | + | 0.998474i | \(0.482414\pi\) | |||||||
\(284\) | 13.3137 | 0.790023 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.17157 | 0.0692766 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2843 | −0.722604 | ||||||||
\(290\) | 1.17157 | 0.0687971 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.82843 | 0.282562 | ||||||||
\(293\) | −12.8284 | −0.749445 | −0.374722 | − | 0.927137i | \(-0.622262\pi\) | ||||
−0.374722 | + | 0.927137i | \(0.622262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.51472 | 0.0881903 | ||||||||
\(296\) | 9.65685 | 0.561293 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.3137 | 0.655386 | ||||||||
\(299\) | −3.79899 | −0.219701 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.24264 | 0.0715059 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.828427 | −0.0475136 | ||||||||
\(305\) | 0.656854 | 0.0376114 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.6274 | 1.97629 | 0.988146 | − | 0.153520i | \(-0.0490610\pi\) | ||||
0.988146 | + | 0.153520i | \(0.0490610\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.68629 | 0.152571 | ||||||||
\(311\) | −10.2132 | −0.579138 | −0.289569 | − | 0.957157i | \(-0.593512\pi\) | ||||
−0.289569 | + | 0.957157i | \(0.593512\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.3137 | 1.65691 | 0.828454 | − | 0.560057i | \(-0.189221\pi\) | ||||
0.828454 | + | 0.560057i | \(0.189221\pi\) | |||||||
\(314\) | 9.17157 | 0.517582 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.75736 | 0.267622 | ||||||||
\(317\) | −33.8701 | −1.90233 | −0.951166 | − | 0.308680i | \(-0.900113\pi\) | ||||
−0.951166 | + | 0.308680i | \(0.900113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.82843 | 0.158362 | ||||||||
\(320\) | 0.414214 | 0.0231552 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.79899 | −0.100098 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.65685 | −0.313786 | ||||||||
\(326\) | 3.00000 | 0.166155 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.65685 | −0.257132 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.31371 | 0.347033 | 0.173516 | − | 0.984831i | \(-0.444487\pi\) | ||||
0.173516 | + | 0.984831i | \(0.444487\pi\) | |||||||
\(332\) | 9.82843 | 0.539405 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.4853 | 0.902034 | ||||||||
\(335\) | −5.58579 | −0.305184 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.51472 | 0.518300 | 0.259150 | − | 0.965837i | \(-0.416558\pi\) | ||||
0.259150 | + | 0.965837i | \(0.416558\pi\) | |||||||
\(338\) | −11.6274 | −0.632448 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.899495 | 0.0487820 | ||||||||
\(341\) | 6.48528 | 0.351198 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.82843 | −0.152499 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1421 | 0.652765 | ||||||||
\(347\) | 4.85786 | 0.260784 | 0.130392 | − | 0.991463i | \(-0.458376\pi\) | ||||
0.130392 | + | 0.991463i | \(0.458376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7279 | 0.841896 | 0.420948 | − | 0.907085i | \(-0.361697\pi\) | ||||
0.420948 | + | 0.907085i | \(0.361697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 16.8284 | 0.895687 | 0.447843 | − | 0.894112i | \(-0.352192\pi\) | ||||
0.447843 | + | 0.894112i | \(0.352192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.51472 | 0.292691 | ||||||||
\(356\) | −12.4853 | −0.661719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.17157 | −0.167623 | ||||||||
\(359\) | −8.48528 | −0.447836 | −0.223918 | − | 0.974608i | \(-0.571885\pi\) | ||||
−0.223918 | + | 0.974608i | \(0.571885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3137 | −0.963879 | ||||||||
\(362\) | 2.34315 | 0.123153 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.51472 | −0.287866 | −0.143933 | − | 0.989587i | \(-0.545975\pi\) | ||||
−0.143933 | + | 0.989587i | \(0.545975\pi\) | |||||||
\(368\) | −3.24264 | −0.169034 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.00000 | 0.207950 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.7279 | −0.814361 | −0.407180 | − | 0.913348i | \(-0.633488\pi\) | ||||
−0.407180 | + | 0.913348i | \(0.633488\pi\) | |||||||
\(374\) | 2.17157 | 0.112289 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.24264 | 0.476653 | ||||||||
\(377\) | 3.31371 | 0.170665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.3431 | 0.993591 | 0.496795 | − | 0.867868i | \(-0.334510\pi\) | ||||
0.496795 | + | 0.867868i | \(0.334510\pi\) | |||||||
\(380\) | −0.343146 | −0.0176030 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.31371 | −0.476531 | ||||||||
\(383\) | 34.2843 | 1.75184 | 0.875922 | − | 0.482452i | \(-0.160254\pi\) | ||||
0.875922 | + | 0.482452i | \(0.160254\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.17157 | −0.466821 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.1716 | 0.516383 | ||||||||
\(389\) | −1.72792 | −0.0876091 | −0.0438046 | − | 0.999040i | \(-0.513948\pi\) | ||||
−0.0438046 | + | 0.999040i | \(0.513948\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.04163 | −0.356111 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.51472 | −0.177069 | ||||||||
\(395\) | 1.97056 | 0.0991498 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.4853 | −0.626618 | −0.313309 | − | 0.949651i | \(-0.601438\pi\) | ||||
−0.313309 | + | 0.949651i | \(0.601438\pi\) | |||||||
\(398\) | 8.34315 | 0.418204 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.82843 | −0.241421 | ||||||||
\(401\) | −15.7990 | −0.788964 | −0.394482 | − | 0.918904i | \(-0.629076\pi\) | ||||
−0.394482 | + | 0.918904i | \(0.629076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.59798 | 0.378482 | ||||||||
\(404\) | 14.1421 | 0.703598 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.65685 | 0.478672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.4558 | 0.566455 | 0.283228 | − | 0.959053i | \(-0.408595\pi\) | ||||
0.283228 | + | 0.959053i | \(0.408595\pi\) | |||||||
\(410\) | −1.92893 | −0.0952632 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.17157 | 0.451851 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.07107 | 0.199841 | ||||||||
\(416\) | 1.17157 | 0.0574411 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.828427 | −0.0405197 | ||||||||
\(419\) | 25.7990 | 1.26036 | 0.630182 | − | 0.776448i | \(-0.282980\pi\) | ||||
0.630182 | + | 0.776448i | \(0.282980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8284 | 0.722693 | 0.361347 | − | 0.932432i | \(-0.382317\pi\) | ||||
0.361347 | + | 0.932432i | \(0.382317\pi\) | |||||||
\(422\) | 14.8284 | 0.721837 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.17157 | −0.251154 | ||||||||
\(425\) | −10.4853 | −0.508611 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −16.6569 | −0.805139 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.17157 | −0.0564983 | ||||||||
\(431\) | −19.1716 | −0.923462 | −0.461731 | − | 0.887020i | \(-0.652771\pi\) | ||||
−0.461731 | + | 0.887020i | \(0.652771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.6569 | 1.28105 | 0.640523 | − | 0.767939i | \(-0.278717\pi\) | ||||
0.640523 | + | 0.767939i | \(0.278717\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.24264 | 0.155294 | ||||||||
\(437\) | 2.68629 | 0.128503 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.38478 | −0.161547 | −0.0807733 | − | 0.996733i | \(-0.525739\pi\) | ||||
−0.0807733 | + | 0.996733i | \(0.525739\pi\) | |||||||
\(440\) | 0.414214 | 0.0197469 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.54416 | 0.121013 | ||||||||
\(443\) | 14.3431 | 0.681463 | 0.340732 | − | 0.940161i | \(-0.389325\pi\) | ||||
0.340732 | + | 0.940161i | \(0.389325\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.17157 | −0.245156 | ||||||||
\(446\) | 13.3137 | 0.630422 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.1127 | 1.09076 | 0.545378 | − | 0.838190i | \(-0.316386\pi\) | ||||
0.545378 | + | 0.838190i | \(0.316386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.65685 | −0.219283 | ||||||||
\(452\) | 3.65685 | 0.172004 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12.3137 | −0.577911 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.6274 | 1.61980 | 0.809901 | − | 0.586566i | \(-0.199521\pi\) | ||||
0.809901 | + | 0.586566i | \(0.199521\pi\) | |||||||
\(458\) | 11.3137 | 0.528655 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.34315 | −0.0626245 | ||||||||
\(461\) | 23.6569 | 1.10181 | 0.550905 | − | 0.834568i | \(-0.314283\pi\) | ||||
0.550905 | + | 0.834568i | \(0.314283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.1127 | 1.07414 | 0.537069 | − | 0.843538i | \(-0.319531\pi\) | ||||
0.537069 | + | 0.843538i | \(0.319531\pi\) | |||||||
\(464\) | 2.82843 | 0.131306 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.31371 | 0.385125 | ||||||||
\(467\) | 2.97056 | 0.137461 | 0.0687306 | − | 0.997635i | \(-0.478105\pi\) | ||||
0.0687306 | + | 0.997635i | \(0.478105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.82843 | 0.176592 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.65685 | 0.168320 | ||||||||
\(473\) | −2.82843 | −0.130051 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.0000 | 0.914779 | ||||||||
\(479\) | −5.17157 | −0.236295 | −0.118148 | − | 0.992996i | \(-0.537696\pi\) | ||||
−0.118148 | + | 0.992996i | \(0.537696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3137 | 0.515861 | ||||||||
\(482\) | −24.9706 | −1.13738 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 4.21320 | 0.191312 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.3137 | −0.965816 | −0.482908 | − | 0.875671i | \(-0.660420\pi\) | ||||
−0.482908 | + | 0.875671i | \(0.660420\pi\) | |||||||
\(488\) | 1.58579 | 0.0717852 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6274 | −0.705255 | −0.352628 | − | 0.935764i | \(-0.614712\pi\) | ||||
−0.352628 | + | 0.935764i | \(0.614712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.14214 | 0.276628 | ||||||||
\(494\) | −0.970563 | −0.0436677 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.48528 | 0.291198 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.3431 | 0.642087 | 0.321044 | − | 0.947064i | \(-0.395966\pi\) | ||||
0.321044 | + | 0.947064i | \(0.395966\pi\) | |||||||
\(500\) | −4.07107 | −0.182064 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.1421 | −1.16678 | ||||||||
\(503\) | −8.97056 | −0.399978 | −0.199989 | − | 0.979798i | \(-0.564091\pi\) | ||||
−0.199989 | + | 0.979798i | \(0.564091\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.85786 | 0.260672 | ||||||||
\(506\) | −3.24264 | −0.144153 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.24264 | 0.0551333 | ||||||||
\(509\) | −25.1716 | −1.11571 | −0.557855 | − | 0.829938i | \(-0.688376\pi\) | ||||
−0.557855 | + | 0.829938i | \(0.688376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.1716 | −1.11027 | ||||||||
\(515\) | 3.79899 | 0.167403 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.24264 | 0.406491 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.485281 | 0.0212810 | ||||||||
\(521\) | −29.3137 | −1.28426 | −0.642128 | − | 0.766597i | \(-0.721948\pi\) | ||||
−0.642128 | + | 0.766597i | \(0.721948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.4558 | 1.37547 | 0.687734 | − | 0.725963i | \(-0.258606\pi\) | ||||
0.687734 | + | 0.725963i | \(0.258606\pi\) | |||||||
\(524\) | −15.3137 | −0.668982 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.31371 | 0.406097 | ||||||||
\(527\) | 14.0833 | 0.613476 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4853 | −0.542838 | ||||||||
\(530\) | −2.14214 | −0.0930484 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.45584 | −0.236319 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.89949 | −0.298291 | ||||||||
\(536\) | −13.4853 | −0.582475 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.07107 | 0.347968 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.44365 | −0.234041 | −0.117020 | − | 0.993130i | \(-0.537334\pi\) | ||||
−0.117020 | + | 0.993130i | \(0.537334\pi\) | |||||||
\(542\) | 13.3137 | 0.571873 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.17157 | 0.0931054 | ||||||||
\(545\) | 1.34315 | 0.0575340 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.1421 | −1.54533 | −0.772663 | − | 0.634816i | \(-0.781076\pi\) | ||||
−0.772663 | + | 0.634816i | \(0.781076\pi\) | |||||||
\(548\) | −4.82843 | −0.206260 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.82843 | −0.205885 | ||||||||
\(551\) | −2.34315 | −0.0998214 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −6.82843 | −0.290112 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.00000 | 0.254457 | ||||||||
\(557\) | −4.48528 | −0.190047 | −0.0950237 | − | 0.995475i | \(-0.530293\pi\) | ||||
−0.0950237 | + | 0.995475i | \(0.530293\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.31371 | −0.140155 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.51472 | 0.106077 | ||||||||
\(563\) | −25.6569 | −1.08131 | −0.540654 | − | 0.841245i | \(-0.681823\pi\) | ||||
−0.540654 | + | 0.841245i | \(0.681823\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.51472 | 0.0637247 | ||||||||
\(566\) | 1.85786 | 0.0780919 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.3137 | 0.558631 | ||||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6569 | −0.906311 | −0.453156 | − | 0.891431i | \(-0.649702\pi\) | ||||
−0.453156 | + | 0.891431i | \(0.649702\pi\) | |||||||
\(572\) | 1.17157 | 0.0489859 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.6569 | 0.652936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.14214 | −0.214070 | −0.107035 | − | 0.994255i | \(-0.534136\pi\) | ||||
−0.107035 | + | 0.994255i | \(0.534136\pi\) | |||||||
\(578\) | −12.2843 | −0.510958 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.17157 | 0.0486469 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.17157 | −0.214185 | ||||||||
\(584\) | 4.82843 | 0.199802 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.8284 | −0.529937 | ||||||||
\(587\) | 28.1421 | 1.16155 | 0.580775 | − | 0.814064i | \(-0.302750\pi\) | ||||
0.580775 | + | 0.814064i | \(0.302750\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.37258 | −0.221373 | ||||||||
\(590\) | 1.51472 | 0.0623600 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.65685 | 0.396894 | ||||||||
\(593\) | −39.9411 | −1.64019 | −0.820093 | − | 0.572231i | \(-0.806078\pi\) | ||||
−0.820093 | + | 0.572231i | \(0.806078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.3137 | 0.463428 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.79899 | −0.155352 | ||||||||
\(599\) | 29.0416 | 1.18661 | 0.593304 | − | 0.804978i | \(-0.297823\pi\) | ||||
0.593304 | + | 0.804978i | \(0.297823\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0000 | 0.815817 | 0.407909 | − | 0.913023i | \(-0.366258\pi\) | ||||
0.407909 | + | 0.913023i | \(0.366258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.24264 | 0.0505623 | ||||||||
\(605\) | 0.414214 | 0.0168402 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −46.2132 | −1.87574 | −0.937868 | − | 0.346992i | \(-0.887203\pi\) | ||||
−0.937868 | + | 0.346992i | \(0.887203\pi\) | |||||||
\(608\) | −0.828427 | −0.0335972 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.656854 | 0.0265953 | ||||||||
\(611\) | 10.8284 | 0.438071 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.8995 | −1.24802 | −0.624009 | − | 0.781417i | \(-0.714497\pi\) | ||||
−0.624009 | + | 0.781417i | \(0.714497\pi\) | |||||||
\(614\) | 34.6274 | 1.39745 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.4853 | −0.985740 | −0.492870 | − | 0.870103i | \(-0.664052\pi\) | ||||
−0.492870 | + | 0.870103i | \(0.664052\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.514719 | −0.0206883 | −0.0103441 | − | 0.999946i | \(-0.503293\pi\) | ||||
−0.0103441 | + | 0.999946i | \(0.503293\pi\) | |||||||
\(620\) | 2.68629 | 0.107884 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.2132 | −0.409512 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4558 | 0.898234 | ||||||||
\(626\) | 29.3137 | 1.17161 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.17157 | 0.365986 | ||||||||
\(629\) | 20.9706 | 0.836151 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.02944 | −0.0409812 | −0.0204906 | − | 0.999790i | \(-0.506523\pi\) | ||||
−0.0204906 | + | 0.999790i | \(0.506523\pi\) | |||||||
\(632\) | 4.75736 | 0.189238 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.8701 | −1.34515 | ||||||||
\(635\) | 0.514719 | 0.0204260 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.82843 | 0.111979 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.414214 | 0.0163732 | ||||||||
\(641\) | −27.3137 | −1.07883 | −0.539413 | − | 0.842041i | \(-0.681354\pi\) | ||||
−0.539413 | + | 0.842041i | \(0.681354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.6569 | −0.696318 | −0.348159 | − | 0.937435i | \(-0.613193\pi\) | ||||
−0.348159 | + | 0.937435i | \(0.613193\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.79899 | −0.0707803 | ||||||||
\(647\) | −42.6985 | −1.67865 | −0.839325 | − | 0.543629i | \(-0.817050\pi\) | ||||
−0.839325 | + | 0.543629i | \(0.817050\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.65685 | 0.143544 | ||||||||
\(650\) | −5.65685 | −0.221880 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.00000 | 0.117489 | ||||||||
\(653\) | 44.3553 | 1.73576 | 0.867879 | − | 0.496775i | \(-0.165483\pi\) | ||||
0.867879 | + | 0.496775i | \(0.165483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.34315 | −0.247847 | ||||||||
\(656\) | −4.65685 | −0.181820 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.9411 | −1.43902 | −0.719511 | − | 0.694481i | \(-0.755634\pi\) | ||||
−0.719511 | + | 0.694481i | \(0.755634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.9706 | 1.51578 | 0.757890 | − | 0.652383i | \(-0.226231\pi\) | ||||
0.757890 | + | 0.652383i | \(0.226231\pi\) | |||||||
\(662\) | 6.31371 | 0.245389 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.82843 | 0.381417 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.17157 | −0.355125 | ||||||||
\(668\) | 16.4853 | 0.637835 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.58579 | −0.215798 | ||||||||
\(671\) | 1.58579 | 0.0612186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6274 | 0.949317 | 0.474659 | − | 0.880170i | \(-0.342572\pi\) | ||||
0.474659 | + | 0.880170i | \(0.342572\pi\) | |||||||
\(674\) | 9.51472 | 0.366493 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.6274 | −0.447208 | ||||||||
\(677\) | −42.7696 | −1.64377 | −0.821884 | − | 0.569655i | \(-0.807077\pi\) | ||||
−0.821884 | + | 0.569655i | \(0.807077\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.899495 | 0.0344941 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.48528 | 0.248334 | ||||||||
\(683\) | 17.6569 | 0.675621 | 0.337810 | − | 0.941214i | \(-0.390314\pi\) | ||||
0.337810 | + | 0.941214i | \(0.390314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.82843 | −0.107833 | ||||||||
\(689\) | −6.05887 | −0.230825 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.1421 | −1.10862 | −0.554310 | − | 0.832311i | \(-0.687018\pi\) | ||||
−0.554310 | + | 0.832311i | \(0.687018\pi\) | |||||||
\(692\) | 12.1421 | 0.461575 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.85786 | 0.184402 | ||||||||
\(695\) | 2.48528 | 0.0942721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.1127 | −0.383046 | ||||||||
\(698\) | 15.7279 | 0.595311 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.1421 | 1.06291 | 0.531457 | − | 0.847085i | \(-0.321645\pi\) | ||||
0.531457 | + | 0.847085i | \(0.321645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.8284 | 0.633346 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.85786 | 0.144885 | 0.0724426 | − | 0.997373i | \(-0.476921\pi\) | ||||
0.0724426 | + | 0.997373i | \(0.476921\pi\) | |||||||
\(710\) | 5.51472 | 0.206964 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.4853 | −0.467906 | ||||||||
\(713\) | −21.0294 | −0.787559 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.485281 | 0.0181485 | ||||||||
\(716\) | −3.17157 | −0.118527 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.48528 | −0.316668 | ||||||||
\(719\) | 16.2132 | 0.604650 | 0.302325 | − | 0.953205i | \(-0.402237\pi\) | ||||
0.302325 | + | 0.953205i | \(0.402237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.3137 | −0.681566 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.34315 | 0.0870823 | ||||||||
\(725\) | −13.6569 | −0.507203 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.4853 | 1.20481 | 0.602406 | − | 0.798190i | \(-0.294209\pi\) | ||||
0.602406 | + | 0.798190i | \(0.294209\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.00000 | 0.0740233 | ||||||||
\(731\) | −6.14214 | −0.227175 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7574 | 0.545076 | 0.272538 | − | 0.962145i | \(-0.412137\pi\) | ||||
0.272538 | + | 0.962145i | \(0.412137\pi\) | |||||||
\(734\) | −5.51472 | −0.203552 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.24264 | −0.119525 | ||||||||
\(737\) | −13.4853 | −0.496737 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.0000 | −1.25071 | −0.625355 | − | 0.780340i | \(-0.715046\pi\) | ||||
−0.625355 | + | 0.780340i | \(0.715046\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6569 | −0.501021 | −0.250511 | − | 0.968114i | \(-0.580599\pi\) | ||||
−0.250511 | + | 0.968114i | \(0.580599\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.68629 | 0.171692 | ||||||||
\(746\) | −15.7279 | −0.575840 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.17157 | 0.0794006 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7990 | 1.08738 | 0.543690 | − | 0.839286i | \(-0.317027\pi\) | ||||
0.543690 | + | 0.839286i | \(0.317027\pi\) | |||||||
\(752\) | 9.24264 | 0.337044 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.31371 | 0.120678 | ||||||||
\(755\) | 0.514719 | 0.0187325 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.6569 | 0.714441 | 0.357220 | − | 0.934020i | \(-0.383725\pi\) | ||||
0.357220 | + | 0.934020i | \(0.383725\pi\) | |||||||
\(758\) | 19.3431 | 0.702575 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.343146 | −0.0124472 | ||||||||
\(761\) | −24.4558 | −0.886524 | −0.443262 | − | 0.896392i | \(-0.646179\pi\) | ||||
−0.443262 | + | 0.896392i | \(0.646179\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9.31371 | −0.336958 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.2843 | 1.23874 | ||||||||
\(767\) | 4.28427 | 0.154696 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.4853 | −0.955084 | −0.477542 | − | 0.878609i | \(-0.658472\pi\) | ||||
−0.477542 | + | 0.878609i | \(0.658472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.17157 | −0.330092 | ||||||||
\(773\) | −31.2426 | −1.12372 | −0.561860 | − | 0.827232i | \(-0.689914\pi\) | ||||
−0.561860 | + | 0.827232i | \(0.689914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.3137 | −1.12482 | ||||||||
\(776\) | 10.1716 | 0.365138 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.72792 | −0.0619490 | ||||||||
\(779\) | 3.85786 | 0.138222 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.3137 | 0.476402 | ||||||||
\(782\) | −7.04163 | −0.251808 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.79899 | 0.135592 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.7696 | 1.38199 | 0.690993 | − | 0.722862i | \(-0.257174\pi\) | ||||
0.690993 | + | 0.722862i | \(0.257174\pi\) | |||||||
\(788\) | −3.51472 | −0.125207 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.97056 | 0.0701095 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.85786 | 0.0659747 | ||||||||
\(794\) | −12.4853 | −0.443086 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.34315 | 0.295715 | ||||||||
\(797\) | −52.8995 | −1.87380 | −0.936898 | − | 0.349602i | \(-0.886317\pi\) | ||||
−0.936898 | + | 0.349602i | \(0.886317\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.0711 | 0.710063 | ||||||||
\(800\) | −4.82843 | −0.170711 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.7990 | −0.557882 | ||||||||
\(803\) | 4.82843 | 0.170391 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.59798 | 0.267627 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.1421 | 0.497519 | ||||||||
\(809\) | −9.34315 | −0.328488 | −0.164244 | − | 0.986420i | \(-0.552518\pi\) | ||||
−0.164244 | + | 0.986420i | \(0.552518\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.65685 | 0.268869 | 0.134434 | − | 0.990923i | \(-0.457078\pi\) | ||||
0.134434 | + | 0.990923i | \(0.457078\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.65685 | 0.338473 | ||||||||
\(815\) | 1.24264 | 0.0435278 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.34315 | 0.0819763 | ||||||||
\(818\) | 11.4558 | 0.400544 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.92893 | −0.0673612 | ||||||||
\(821\) | 21.5147 | 0.750869 | 0.375434 | − | 0.926849i | \(-0.377494\pi\) | ||||
0.375434 | + | 0.926849i | \(0.377494\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.5147 | −0.749956 | −0.374978 | − | 0.927034i | \(-0.622350\pi\) | ||||
−0.374978 | + | 0.927034i | \(0.622350\pi\) | |||||||
\(824\) | 9.17157 | 0.319507 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.17157 | 0.0755130 | 0.0377565 | − | 0.999287i | \(-0.487979\pi\) | ||||
0.0377565 | + | 0.999287i | \(0.487979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.0000 | 0.972480 | 0.486240 | − | 0.873825i | \(-0.338368\pi\) | ||||
0.486240 | + | 0.873825i | \(0.338368\pi\) | |||||||
\(830\) | 4.07107 | 0.141309 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.17157 | 0.0406170 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.82843 | 0.236307 | ||||||||
\(836\) | −0.828427 | −0.0286518 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.7990 | 0.891211 | ||||||||
\(839\) | −8.21320 | −0.283551 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 14.8284 | 0.511021 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.8284 | 0.510416 | ||||||||
\(845\) | −4.81623 | −0.165683 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.17157 | −0.177593 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.4853 | −0.359642 | ||||||||
\(851\) | −31.3137 | −1.07342 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.2426 | 0.795813 | 0.397906 | − | 0.917426i | \(-0.369737\pi\) | ||||
0.397906 | + | 0.917426i | \(0.369737\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.6569 | −0.569320 | ||||||||
\(857\) | −21.6863 | −0.740790 | −0.370395 | − | 0.928874i | \(-0.620778\pi\) | ||||
−0.370395 | + | 0.928874i | \(0.620778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.9411 | 1.73809 | 0.869044 | − | 0.494734i | \(-0.164735\pi\) | ||||
0.869044 | + | 0.494734i | \(0.164735\pi\) | |||||||
\(860\) | −1.17157 | −0.0399503 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.1716 | −0.652986 | ||||||||
\(863\) | −39.1838 | −1.33383 | −0.666915 | − | 0.745133i | \(-0.732386\pi\) | ||||
−0.666915 | + | 0.745133i | \(0.732386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.02944 | 0.171006 | ||||||||
\(866\) | 26.6569 | 0.905837 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.75736 | 0.161382 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.7990 | −0.535328 | ||||||||
\(872\) | 3.24264 | 0.109810 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.68629 | 0.0908652 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.5563 | 0.829209 | 0.414604 | − | 0.910002i | \(-0.363920\pi\) | ||||
0.414604 | + | 0.910002i | \(0.363920\pi\) | |||||||
\(878\) | −3.38478 | −0.114231 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.414214 | 0.0139631 | ||||||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.514719 | 0.0173217 | 0.00866083 | − | 0.999962i | \(-0.497243\pi\) | ||||
0.00866083 | + | 0.999962i | \(0.497243\pi\) | |||||||
\(884\) | 2.54416 | 0.0855692 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.3431 | 0.481867 | ||||||||
\(887\) | −8.34315 | −0.280135 | −0.140068 | − | 0.990142i | \(-0.544732\pi\) | ||||
−0.140068 | + | 0.990142i | \(0.544732\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5.17157 | −0.173352 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.3137 | 0.445776 | ||||||||
\(893\) | −7.65685 | −0.256227 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.31371 | −0.0439124 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.1127 | 0.771281 | ||||||||
\(899\) | 18.3431 | 0.611778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.2304 | −0.374140 | ||||||||
\(902\) | −4.65685 | −0.155056 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.65685 | 0.121625 | ||||||||
\(905\) | 0.970563 | 0.0322626 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.8579 | 0.360529 | 0.180265 | − | 0.983618i | \(-0.442305\pi\) | ||||
0.180265 | + | 0.983618i | \(0.442305\pi\) | |||||||
\(908\) | −12.3137 | −0.408645 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.2132 | 1.66364 | 0.831819 | − | 0.555047i | \(-0.187300\pi\) | ||||
0.831819 | + | 0.555047i | \(0.187300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.82843 | 0.325273 | ||||||||
\(914\) | 34.6274 | 1.14537 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.3137 | 0.373815 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.8995 | −0.755385 | −0.377692 | − | 0.925931i | \(-0.623282\pi\) | ||||
−0.377692 | + | 0.925931i | \(0.623282\pi\) | |||||||
\(920\) | −1.34315 | −0.0442822 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.6569 | 0.779097 | ||||||||
\(923\) | 15.5980 | 0.513414 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.6274 | −1.53310 | ||||||||
\(926\) | 23.1127 | 0.759530 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.82843 | 0.0928477 | ||||||||
\(929\) | −7.45584 | −0.244618 | −0.122309 | − | 0.992492i | \(-0.539030\pi\) | ||||
−0.122309 | + | 0.992492i | \(0.539030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8.31371 | 0.272325 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.97056 | 0.0971998 | ||||||||
\(935\) | 0.899495 | 0.0294166 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.6569 | −0.380813 | −0.190406 | − | 0.981705i | \(-0.560981\pi\) | ||||
−0.190406 | + | 0.981705i | \(0.560981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.82843 | 0.124870 | ||||||||
\(941\) | −11.3726 | −0.370736 | −0.185368 | − | 0.982669i | \(-0.559348\pi\) | ||||
−0.185368 | + | 0.982669i | \(0.559348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.1005 | 0.491740 | ||||||||
\(944\) | 3.65685 | 0.119020 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.82843 | −0.0919601 | ||||||||
\(947\) | 12.6274 | 0.410336 | 0.205168 | − | 0.978727i | \(-0.434226\pi\) | ||||
0.205168 | + | 0.978727i | \(0.434226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.65685 | 0.183629 | ||||||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.31371 | −0.204521 | −0.102261 | − | 0.994758i | \(-0.532608\pi\) | ||||
−0.102261 | + | 0.994758i | \(0.532608\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.85786 | −0.124838 | ||||||||
\(956\) | 20.0000 | 0.646846 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.17157 | −0.167086 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0589 | 0.356738 | ||||||||
\(962\) | 11.3137 | 0.364769 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −24.9706 | −0.804248 | ||||||||
\(965\) | −3.79899 | −0.122294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.10051 | 0.0997055 | 0.0498528 | − | 0.998757i | \(-0.484125\pi\) | ||||
0.0498528 | + | 0.998757i | \(0.484125\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.21320 | 0.135278 | ||||||||
\(971\) | 10.0000 | 0.320915 | 0.160458 | − | 0.987043i | \(-0.448703\pi\) | ||||
0.160458 | + | 0.987043i | \(0.448703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −21.3137 | −0.682935 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.58579 | 0.0507598 | ||||||||
\(977\) | 31.9411 | 1.02189 | 0.510944 | − | 0.859614i | \(-0.329296\pi\) | ||||
0.510944 | + | 0.859614i | \(0.329296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.4853 | −0.399031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.6274 | −0.498691 | ||||||||
\(983\) | −36.7574 | −1.17238 | −0.586189 | − | 0.810174i | \(-0.699372\pi\) | ||||
−0.586189 | + | 0.810174i | \(0.699372\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.45584 | −0.0463871 | ||||||||
\(986\) | 6.14214 | 0.195605 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.970563 | −0.0308777 | ||||||||
\(989\) | 9.17157 | 0.291639 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3431 | 0.709753 | 0.354877 | − | 0.934913i | \(-0.384523\pi\) | ||||
0.354877 | + | 0.934913i | \(0.384523\pi\) | |||||||
\(992\) | 6.48528 | 0.205908 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.45584 | 0.109558 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.7990 | −1.51381 | −0.756905 | − | 0.653525i | \(-0.773289\pi\) | ||||
−0.756905 | + | 0.653525i | \(0.773289\pi\) | |||||||
\(998\) | 14.3431 | 0.454024 | ||||||||
\(999\) | 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 | 9702.2.a.da.1.2 | 2 | ||
3.2 | odd | 2 | 9702.2.a.cv.1.1 | 2 | |||
7.3 | odd | 6 | 1386.2.k.q.793.2 | ✓ | 4 | ||
7.5 | odd | 6 | 1386.2.k.q.991.2 | yes | 4 | ||
7.6 | odd | 2 | 9702.2.a.ds.1.1 | 2 | |||
21.5 | even | 6 | 1386.2.k.u.991.1 | yes | 4 | ||
21.17 | even | 6 | 1386.2.k.u.793.1 | yes | 4 | ||
21.20 | even | 2 | 9702.2.a.cj.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.k.q.793.2 | ✓ | 4 | 7.3 | odd | 6 | ||
1386.2.k.q.991.2 | yes | 4 | 7.5 | odd | 6 | ||
1386.2.k.u.793.1 | yes | 4 | 21.17 | even | 6 | ||
1386.2.k.u.991.1 | yes | 4 | 21.5 | even | 6 | ||
9702.2.a.cj.1.2 | 2 | 21.20 | even | 2 | |||
9702.2.a.cv.1.1 | 2 | 3.2 | odd | 2 | |||
9702.2.a.da.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9702.2.a.ds.1.1 | 2 | 7.6 | odd | 2 |