Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6030,2,Mod(1,6030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6030, 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("6030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6030.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: | \(48.1497924188\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.70292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2010) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.46640\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6030.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.08313 | 0.787349 | 0.393675 | − | 0.919250i | \(-0.371204\pi\) | ||||
0.393675 | + | 0.919250i | \(0.371204\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −2.20503 | −0.664842 | −0.332421 | − | 0.943131i | \(-0.607866\pi\) | ||||
−0.332421 | + | 0.943131i | \(0.607866\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.28816 | −1.18932 | −0.594661 | − | 0.803976i | \(-0.702714\pi\) | ||||
−0.594661 | + | 0.803976i | \(0.702714\pi\) | |||||||
\(14\) | 2.08313 | 0.556740 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.93280 | 1.19638 | 0.598190 | − | 0.801354i | \(-0.295887\pi\) | ||||
0.598190 | + | 0.801354i | \(0.295887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.93280 | 1.13166 | 0.565831 | − | 0.824521i | \(-0.308555\pi\) | ||||
0.565831 | + | 0.824521i | \(0.308555\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.20503 | −0.470114 | ||||||||
\(23\) | 3.35536 | 0.699641 | 0.349821 | − | 0.936817i | \(-0.386243\pi\) | ||||
0.349821 | + | 0.936817i | \(0.386243\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.28816 | −0.840978 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.08313 | 0.393675 | ||||||||
\(29\) | 2.81090 | 0.521971 | 0.260985 | − | 0.965343i | \(-0.415953\pi\) | ||||
0.260985 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.28816 | −0.410966 | −0.205483 | − | 0.978661i | \(-0.565877\pi\) | ||||
−0.205483 | + | 0.978661i | \(0.565877\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.93280 | 0.845968 | ||||||||
\(35\) | 2.08313 | 0.352113 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.727768 | −0.119644 | −0.0598222 | − | 0.998209i | \(-0.519053\pi\) | ||||
−0.0598222 | + | 0.998209i | \(0.519053\pi\) | |||||||
\(38\) | 4.93280 | 0.800206 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 1.47726 | 0.230710 | 0.115355 | − | 0.993324i | \(-0.463199\pi\) | ||||
0.115355 | + | 0.993324i | \(0.463199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.41006 | 0.672529 | 0.336264 | − | 0.941768i | \(-0.390836\pi\) | ||||
0.336264 | + | 0.941768i | \(0.390836\pi\) | |||||||
\(44\) | −2.20503 | −0.332421 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.35536 | 0.494721 | ||||||||
\(47\) | −9.38722 | −1.36927 | −0.684634 | − | 0.728887i | \(-0.740038\pi\) | ||||
−0.684634 | + | 0.728887i | \(0.740038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.66057 | −0.380081 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.28816 | −0.594661 | ||||||||
\(53\) | 6.16626 | 0.847001 | 0.423500 | − | 0.905896i | \(-0.360801\pi\) | ||||
0.423500 | + | 0.905896i | \(0.360801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.20503 | −0.297326 | ||||||||
\(56\) | 2.08313 | 0.278370 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.81090 | 0.369089 | ||||||||
\(59\) | 1.47726 | 0.192323 | 0.0961617 | − | 0.995366i | \(-0.469343\pi\) | ||||
0.0961617 | + | 0.995366i | \(0.469343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.08313 | 0.522791 | 0.261396 | − | 0.965232i | \(-0.415817\pi\) | ||||
0.261396 | + | 0.965232i | \(0.415817\pi\) | |||||||
\(62\) | −2.28816 | −0.290597 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.28816 | −0.531881 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | 4.93280 | 0.598190 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.08313 | 0.248982 | ||||||||
\(71\) | 4.84967 | 0.575550 | 0.287775 | − | 0.957698i | \(-0.407084\pi\) | ||||
0.287775 | + | 0.957698i | \(0.407084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.544464 | −0.0637246 | −0.0318623 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318623 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(74\) | −0.727768 | −0.0846013 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.93280 | 0.565831 | ||||||||
\(77\) | −4.59337 | −0.523463 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.83263 | 0.543713 | 0.271856 | − | 0.962338i | \(-0.412362\pi\) | ||||
0.271856 | + | 0.962338i | \(0.412362\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.47726 | 0.163137 | ||||||||
\(83\) | 16.5934 | 1.82136 | 0.910679 | − | 0.413114i | \(-0.135559\pi\) | ||||
0.910679 | + | 0.413114i | \(0.135559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.93280 | 0.535037 | ||||||||
\(86\) | 4.41006 | 0.475549 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.20503 | −0.235057 | ||||||||
\(89\) | −2.18330 | −0.231430 | −0.115715 | − | 0.993282i | \(-0.536916\pi\) | ||||
−0.115715 | + | 0.993282i | \(0.536916\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.93280 | −0.936412 | ||||||||
\(92\) | 3.35536 | 0.349821 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.38722 | −0.968218 | ||||||||
\(95\) | 4.93280 | 0.506095 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.20503 | 0.223887 | 0.111944 | − | 0.993715i | \(-0.464292\pi\) | ||||
0.111944 | + | 0.993715i | \(0.464292\pi\) | |||||||
\(98\) | −2.66057 | −0.268758 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.13783 | 0.909248 | 0.454624 | − | 0.890683i | \(-0.349774\pi\) | ||||
0.454624 | + | 0.890683i | \(0.349774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.410065 | 0.0404049 | 0.0202024 | − | 0.999796i | \(-0.493569\pi\) | ||||
0.0202024 | + | 0.999796i | \(0.493569\pi\) | |||||||
\(104\) | −4.28816 | −0.420489 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.16626 | 0.598920 | ||||||||
\(107\) | −0.576325 | −0.0557154 | −0.0278577 | − | 0.999612i | \(-0.508869\pi\) | ||||
−0.0278577 | + | 0.999612i | \(0.508869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.78247 | 0.553860 | 0.276930 | − | 0.960890i | \(-0.410683\pi\) | ||||
0.276930 | + | 0.960890i | \(0.410683\pi\) | |||||||
\(110\) | −2.20503 | −0.210242 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.08313 | 0.196837 | ||||||||
\(113\) | 13.8268 | 1.30072 | 0.650359 | − | 0.759627i | \(-0.274618\pi\) | ||||
0.650359 | + | 0.759627i | \(0.274618\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.35536 | 0.312889 | ||||||||
\(116\) | 2.81090 | 0.260985 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.47726 | 0.135993 | ||||||||
\(119\) | 10.2757 | 0.941969 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.13783 | −0.557985 | ||||||||
\(122\) | 4.08313 | 0.369669 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.28816 | −0.205483 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1208 | −0.986810 | −0.493405 | − | 0.869800i | \(-0.664248\pi\) | ||||
−0.493405 | + | 0.869800i | \(0.664248\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.28816 | −0.376097 | ||||||||
\(131\) | 17.6435 | 1.54152 | 0.770761 | − | 0.637124i | \(-0.219876\pi\) | ||||
0.770761 | + | 0.637124i | \(0.219876\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.2757 | 0.891013 | ||||||||
\(134\) | −1.00000 | −0.0863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.93280 | 0.422984 | ||||||||
\(137\) | 4.72777 | 0.403920 | 0.201960 | − | 0.979394i | \(-0.435269\pi\) | ||||
0.201960 | + | 0.979394i | \(0.435269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0855 | −1.70363 | −0.851813 | − | 0.523846i | \(-0.824497\pi\) | ||||
−0.851813 | + | 0.523846i | \(0.824497\pi\) | |||||||
\(140\) | 2.08313 | 0.176057 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.84967 | 0.406975 | ||||||||
\(143\) | 9.45554 | 0.790712 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.81090 | 0.233432 | ||||||||
\(146\) | −0.544464 | −0.0450601 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.727768 | −0.0598222 | ||||||||
\(149\) | 2.81090 | 0.230278 | 0.115139 | − | 0.993349i | \(-0.463269\pi\) | ||||
0.115139 | + | 0.993349i | \(0.463269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7142 | 0.953285 | 0.476642 | − | 0.879097i | \(-0.341854\pi\) | ||||
0.476642 | + | 0.879097i | \(0.341854\pi\) | |||||||
\(152\) | 4.93280 | 0.400103 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.59337 | −0.370144 | ||||||||
\(155\) | −2.28816 | −0.183790 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.1981 | −1.61199 | −0.805993 | − | 0.591925i | \(-0.798368\pi\) | ||||
−0.805993 | + | 0.591925i | \(0.798368\pi\) | |||||||
\(158\) | 4.83263 | 0.384463 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 6.98966 | 0.550862 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.7278 | −0.840264 | −0.420132 | − | 0.907463i | \(-0.638016\pi\) | ||||
−0.420132 | + | 0.907463i | \(0.638016\pi\) | |||||||
\(164\) | 1.47726 | 0.115355 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.5934 | 1.28790 | ||||||||
\(167\) | −3.93169 | −0.304243 | −0.152122 | − | 0.988362i | \(-0.548611\pi\) | ||||
−0.152122 | + | 0.988362i | \(0.548611\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.38834 | 0.414487 | ||||||||
\(170\) | 4.93280 | 0.378329 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.41006 | 0.336264 | ||||||||
\(173\) | −9.04779 | −0.687891 | −0.343945 | − | 0.938990i | \(-0.611764\pi\) | ||||
−0.343945 | + | 0.938990i | \(0.611764\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.08313 | 0.157470 | ||||||||
\(176\) | −2.20503 | −0.166211 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.18330 | −0.163646 | ||||||||
\(179\) | −13.6754 | −1.02215 | −0.511073 | − | 0.859537i | \(-0.670752\pi\) | ||||
−0.511073 | + | 0.859537i | \(0.670752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.876984 | 0.0651857 | 0.0325929 | − | 0.999469i | \(-0.489624\pi\) | ||||
0.0325929 | + | 0.999469i | \(0.489624\pi\) | |||||||
\(182\) | −8.93280 | −0.662143 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.35536 | 0.247361 | ||||||||
\(185\) | −0.727768 | −0.0535066 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8770 | −0.795404 | ||||||||
\(188\) | −9.38722 | −0.684634 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.93280 | 0.357863 | ||||||||
\(191\) | 16.4101 | 1.18739 | 0.593695 | − | 0.804690i | \(-0.297668\pi\) | ||||
0.593695 | + | 0.804690i | \(0.297668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.17660 | −0.228657 | −0.114329 | − | 0.993443i | \(-0.536472\pi\) | ||||
−0.114329 | + | 0.993443i | \(0.536472\pi\) | |||||||
\(194\) | 2.20503 | 0.158312 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.66057 | −0.190041 | ||||||||
\(197\) | 10.5763 | 0.753532 | 0.376766 | − | 0.926308i | \(-0.377036\pi\) | ||||
0.376766 | + | 0.926308i | \(0.377036\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.59337 | 0.609168 | 0.304584 | − | 0.952486i | \(-0.401483\pi\) | ||||
0.304584 | + | 0.952486i | \(0.401483\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.13783 | 0.642936 | ||||||||
\(203\) | 5.85547 | 0.410973 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.47726 | 0.103177 | ||||||||
\(206\) | 0.410065 | 0.0285705 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.28816 | −0.297331 | ||||||||
\(209\) | −10.8770 | −0.752377 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.8553 | −0.884992 | −0.442496 | − | 0.896770i | \(-0.645907\pi\) | ||||
−0.442496 | + | 0.896770i | \(0.645907\pi\) | |||||||
\(212\) | 6.16626 | 0.423500 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.576325 | −0.0393968 | ||||||||
\(215\) | 4.41006 | 0.300764 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.76654 | −0.323574 | ||||||||
\(218\) | 5.78247 | 0.391638 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.20503 | −0.148663 | ||||||||
\(221\) | −21.1526 | −1.42288 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.8520 | 1.26242 | 0.631211 | − | 0.775611i | \(-0.282558\pi\) | ||||
0.631211 | + | 0.775611i | \(0.282558\pi\) | |||||||
\(224\) | 2.08313 | 0.139185 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8268 | 0.919747 | ||||||||
\(227\) | 22.1094 | 1.46745 | 0.733726 | − | 0.679445i | \(-0.237779\pi\) | ||||
0.733726 | + | 0.679445i | \(0.237779\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.326934 | 0.0216044 | 0.0108022 | − | 0.999942i | \(-0.496561\pi\) | ||||
0.0108022 | + | 0.999942i | \(0.496561\pi\) | |||||||
\(230\) | 3.35536 | 0.221246 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.81090 | 0.184545 | ||||||||
\(233\) | 2.14922 | 0.140800 | 0.0703999 | − | 0.997519i | \(-0.477572\pi\) | ||||
0.0703999 | + | 0.997519i | \(0.477572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.38722 | −0.612355 | ||||||||
\(236\) | 1.47726 | 0.0961617 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.2757 | 0.666072 | ||||||||
\(239\) | −11.1208 | −0.719344 | −0.359672 | − | 0.933079i | \(-0.617111\pi\) | ||||
−0.359672 | + | 0.933079i | \(0.617111\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.15956 | −0.461188 | −0.230594 | − | 0.973050i | \(-0.574067\pi\) | ||||
−0.230594 | + | 0.973050i | \(0.574067\pi\) | |||||||
\(242\) | −6.13783 | −0.394555 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.08313 | 0.261396 | ||||||||
\(245\) | −2.66057 | −0.169978 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.1526 | −1.34591 | ||||||||
\(248\) | −2.28816 | −0.145298 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 10.7278 | 0.677131 | 0.338565 | − | 0.940943i | \(-0.390058\pi\) | ||||
0.338565 | + | 0.940943i | \(0.390058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.39868 | −0.465151 | ||||||||
\(254\) | −11.1208 | −0.697780 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.4202 | 1.27378 | 0.636888 | − | 0.770956i | \(-0.280221\pi\) | ||||
0.636888 | + | 0.770956i | \(0.280221\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.51604 | −0.0942019 | ||||||||
\(260\) | −4.28816 | −0.265941 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.6435 | 1.09002 | ||||||||
\(263\) | 3.59917 | 0.221934 | 0.110967 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110967 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.16626 | 0.378790 | ||||||||
\(266\) | 10.2757 | 0.630041 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.00000 | −0.0610847 | ||||||||
\(269\) | −8.94530 | −0.545404 | −0.272702 | − | 0.962098i | \(-0.587917\pi\) | ||||
−0.272702 | + | 0.962098i | \(0.587917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.41118 | −0.450197 | −0.225099 | − | 0.974336i | \(-0.572270\pi\) | ||||
−0.225099 | + | 0.974336i | \(0.572270\pi\) | |||||||
\(272\) | 4.93280 | 0.299095 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.72777 | 0.285615 | ||||||||
\(275\) | −2.20503 | −0.132968 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.2586 | 0.976886 | 0.488443 | − | 0.872596i | \(-0.337565\pi\) | ||||
0.488443 | + | 0.872596i | \(0.337565\pi\) | |||||||
\(278\) | −20.0855 | −1.20465 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.08313 | 0.124491 | ||||||||
\(281\) | −19.1526 | −1.14255 | −0.571276 | − | 0.820758i | \(-0.693551\pi\) | ||||
−0.571276 | + | 0.820758i | \(0.693551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.2905 | −1.44392 | −0.721960 | − | 0.691935i | \(-0.756758\pi\) | ||||
−0.721960 | + | 0.691935i | \(0.756758\pi\) | |||||||
\(284\) | 4.84967 | 0.287775 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.45554 | 0.559118 | ||||||||
\(287\) | 3.07733 | 0.181649 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.33252 | 0.431325 | ||||||||
\(290\) | 2.81090 | 0.165062 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.544464 | −0.0318623 | ||||||||
\(293\) | −13.9705 | −0.816163 | −0.408081 | − | 0.912946i | \(-0.633802\pi\) | ||||
−0.408081 | + | 0.912946i | \(0.633802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.47726 | 0.0860096 | ||||||||
\(296\) | −0.727768 | −0.0423007 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.81090 | 0.162831 | ||||||||
\(299\) | −14.3883 | −0.832099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.18674 | 0.529515 | ||||||||
\(302\) | 11.7142 | 0.674074 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.93280 | 0.282916 | ||||||||
\(305\) | 4.08313 | 0.233799 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.3144 | −1.15941 | −0.579703 | − | 0.814828i | \(-0.696831\pi\) | ||||
−0.579703 | + | 0.814828i | \(0.696831\pi\) | |||||||
\(308\) | −4.59337 | −0.261732 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.28816 | −0.129959 | ||||||||
\(311\) | 7.75620 | 0.439814 | 0.219907 | − | 0.975521i | \(-0.429425\pi\) | ||||
0.219907 | + | 0.975521i | \(0.429425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.8132 | −1.17643 | −0.588216 | − | 0.808704i | \(-0.700170\pi\) | ||||
−0.588216 | + | 0.808704i | \(0.700170\pi\) | |||||||
\(314\) | −20.1981 | −1.13985 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.83263 | 0.271856 | ||||||||
\(317\) | −0.488511 | −0.0274375 | −0.0137188 | − | 0.999906i | \(-0.504367\pi\) | ||||
−0.0137188 | + | 0.999906i | \(0.504367\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.19812 | −0.347028 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.98966 | 0.389518 | ||||||||
\(323\) | 24.3325 | 1.35390 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.28816 | −0.237864 | ||||||||
\(326\) | −10.7278 | −0.594156 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.47726 | 0.0815683 | ||||||||
\(329\) | −19.5548 | −1.07809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.0570 | −1.26733 | −0.633664 | − | 0.773608i | \(-0.718450\pi\) | ||||
−0.633664 | + | 0.773608i | \(0.718450\pi\) | |||||||
\(332\) | 16.5934 | 0.910679 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.93169 | −0.215132 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.3293 | 1.65214 | 0.826070 | − | 0.563568i | \(-0.190572\pi\) | ||||
0.826070 | + | 0.563568i | \(0.190572\pi\) | |||||||
\(338\) | 5.38834 | 0.293087 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.93280 | 0.267519 | ||||||||
\(341\) | 5.04547 | 0.273228 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1242 | −1.08661 | ||||||||
\(344\) | 4.41006 | 0.237775 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.04779 | −0.486412 | ||||||||
\(347\) | −17.5432 | −0.941769 | −0.470885 | − | 0.882195i | \(-0.656065\pi\) | ||||
−0.470885 | + | 0.882195i | \(0.656065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8201 | 0.793303 | 0.396652 | − | 0.917969i | \(-0.370172\pi\) | ||||
0.396652 | + | 0.917969i | \(0.370172\pi\) | |||||||
\(350\) | 2.08313 | 0.111348 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.20503 | −0.117529 | ||||||||
\(353\) | −18.7665 | −0.998842 | −0.499421 | − | 0.866359i | \(-0.666454\pi\) | ||||
−0.499421 | + | 0.866359i | \(0.666454\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.84967 | 0.257394 | ||||||||
\(356\) | −2.18330 | −0.115715 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.6754 | −0.722767 | ||||||||
\(359\) | 6.43738 | 0.339752 | 0.169876 | − | 0.985465i | \(-0.445663\pi\) | ||||
0.169876 | + | 0.985465i | \(0.445663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.33252 | 0.280659 | ||||||||
\(362\) | 0.876984 | 0.0460933 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.93280 | −0.468206 | ||||||||
\(365\) | −0.544464 | −0.0284985 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.1298 | −0.946368 | −0.473184 | − | 0.880964i | \(-0.656895\pi\) | ||||
−0.473184 | + | 0.880964i | \(0.656895\pi\) | |||||||
\(368\) | 3.35536 | 0.174910 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.727768 | −0.0378349 | ||||||||
\(371\) | 12.8451 | 0.666886 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.6207 | 0.653474 | 0.326737 | − | 0.945115i | \(-0.394051\pi\) | ||||
0.326737 | + | 0.945115i | \(0.394051\pi\) | |||||||
\(374\) | −10.8770 | −0.562435 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.38722 | −0.484109 | ||||||||
\(377\) | −12.0536 | −0.620791 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.4180 | 1.45973 | 0.729867 | − | 0.683590i | \(-0.239582\pi\) | ||||
0.729867 | + | 0.683590i | \(0.239582\pi\) | |||||||
\(380\) | 4.93280 | 0.253047 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.4101 | 0.839612 | ||||||||
\(383\) | −13.6048 | −0.695170 | −0.347585 | − | 0.937648i | \(-0.612998\pi\) | ||||
−0.347585 | + | 0.937648i | \(0.612998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.59337 | −0.234100 | ||||||||
\(386\) | −3.17660 | −0.161685 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.20503 | 0.111944 | ||||||||
\(389\) | 23.6948 | 1.20137 | 0.600686 | − | 0.799485i | \(-0.294894\pi\) | ||||
0.600686 | + | 0.799485i | \(0.294894\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5513 | 0.837037 | ||||||||
\(392\) | −2.66057 | −0.134379 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.5763 | 0.532828 | ||||||||
\(395\) | 4.83263 | 0.243156 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.65022 | −0.233388 | −0.116694 | − | 0.993168i | \(-0.537230\pi\) | ||||
−0.116694 | + | 0.993168i | \(0.537230\pi\) | |||||||
\(398\) | 8.59337 | 0.430747 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −23.5193 | −1.17450 | −0.587248 | − | 0.809407i | \(-0.699789\pi\) | ||||
−0.587248 | + | 0.809407i | \(0.699789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.81201 | 0.488771 | ||||||||
\(404\) | 9.13783 | 0.454624 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.85547 | 0.290602 | ||||||||
\(407\) | 1.60475 | 0.0795446 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5763 | 0.918540 | 0.459270 | − | 0.888297i | \(-0.348111\pi\) | ||||
0.459270 | + | 0.888297i | \(0.348111\pi\) | |||||||
\(410\) | 1.47726 | 0.0729569 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.410065 | 0.0202024 | ||||||||
\(413\) | 3.07733 | 0.151426 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.5934 | 0.814536 | ||||||||
\(416\) | −4.28816 | −0.210244 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.8770 | −0.532011 | ||||||||
\(419\) | 1.97605 | 0.0965361 | 0.0482681 | − | 0.998834i | \(-0.484630\pi\) | ||||
0.0482681 | + | 0.998834i | \(0.484630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.92246 | 0.483591 | 0.241795 | − | 0.970327i | \(-0.422264\pi\) | ||||
0.241795 | + | 0.970327i | \(0.422264\pi\) | |||||||
\(422\) | −12.8553 | −0.625784 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.16626 | 0.299460 | ||||||||
\(425\) | 4.93280 | 0.239276 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.50569 | 0.411619 | ||||||||
\(428\) | −0.576325 | −0.0278577 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.41006 | 0.212672 | ||||||||
\(431\) | −2.38275 | −0.114773 | −0.0573865 | − | 0.998352i | \(-0.518277\pi\) | ||||
−0.0573865 | + | 0.998352i | \(0.518277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.9965 | −1.00903 | −0.504514 | − | 0.863403i | \(-0.668328\pi\) | ||||
−0.504514 | + | 0.863403i | \(0.668328\pi\) | |||||||
\(434\) | −4.76654 | −0.228801 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.78247 | 0.276930 | ||||||||
\(437\) | 16.5513 | 0.791758 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0034 | 0.811530 | 0.405765 | − | 0.913978i | \(-0.367005\pi\) | ||||
0.405765 | + | 0.913978i | \(0.367005\pi\) | |||||||
\(440\) | −2.20503 | −0.105121 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.1526 | −1.00613 | ||||||||
\(443\) | 13.8656 | 0.658775 | 0.329387 | − | 0.944195i | \(-0.393158\pi\) | ||||
0.329387 | + | 0.944195i | \(0.393158\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.18330 | −0.103499 | ||||||||
\(446\) | 18.8520 | 0.892668 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.08313 | 0.0984186 | ||||||||
\(449\) | −39.0922 | −1.84487 | −0.922436 | − | 0.386149i | \(-0.873805\pi\) | ||||
−0.922436 | + | 0.386149i | \(0.873805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.25741 | −0.153386 | ||||||||
\(452\) | 13.8268 | 0.650359 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.1094 | 1.03765 | ||||||||
\(455\) | −8.93280 | −0.418776 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.68900 | −0.312898 | −0.156449 | − | 0.987686i | \(-0.550005\pi\) | ||||
−0.156449 | + | 0.987686i | \(0.550005\pi\) | |||||||
\(458\) | 0.326934 | 0.0152766 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.35536 | 0.156445 | ||||||||
\(461\) | 22.0545 | 1.02718 | 0.513590 | − | 0.858036i | \(-0.328315\pi\) | ||||
0.513590 | + | 0.858036i | \(0.328315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.4191 | 1.83196 | 0.915980 | − | 0.401224i | \(-0.131415\pi\) | ||||
0.915980 | + | 0.401224i | \(0.131415\pi\) | |||||||
\(464\) | 2.81090 | 0.130493 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.14922 | 0.0995605 | ||||||||
\(467\) | −10.0148 | −0.463430 | −0.231715 | − | 0.972784i | \(-0.574434\pi\) | ||||
−0.231715 | + | 0.972784i | \(0.574434\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.08313 | −0.0961900 | ||||||||
\(470\) | −9.38722 | −0.433000 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.47726 | 0.0679966 | ||||||||
\(473\) | −9.72433 | −0.447125 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.93280 | 0.226332 | ||||||||
\(476\) | 10.2757 | 0.470984 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.1208 | −0.508653 | ||||||||
\(479\) | −22.8474 | −1.04393 | −0.521963 | − | 0.852968i | \(-0.674800\pi\) | ||||
−0.521963 | + | 0.852968i | \(0.674800\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.12079 | 0.142296 | ||||||||
\(482\) | −7.15956 | −0.326109 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.13783 | −0.278992 | ||||||||
\(485\) | 2.20503 | 0.100125 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.8896 | 1.62632 | 0.813158 | − | 0.582044i | \(-0.197747\pi\) | ||||
0.813158 | + | 0.582044i | \(0.197747\pi\) | |||||||
\(488\) | 4.08313 | 0.184835 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.66057 | −0.120192 | ||||||||
\(491\) | 35.2403 | 1.59037 | 0.795187 | − | 0.606364i | \(-0.207373\pi\) | ||||
0.795187 | + | 0.606364i | \(0.207373\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.8656 | 0.624475 | ||||||||
\(494\) | −21.1526 | −0.951703 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.28816 | −0.102742 | ||||||||
\(497\) | 10.1025 | 0.453159 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.17094 | 0.365782 | 0.182891 | − | 0.983133i | \(-0.441455\pi\) | ||||
0.182891 | + | 0.983133i | \(0.441455\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.7278 | 0.478804 | ||||||||
\(503\) | 0.470564 | 0.0209814 | 0.0104907 | − | 0.999945i | \(-0.496661\pi\) | ||||
0.0104907 | + | 0.999945i | \(0.496661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.13783 | 0.406628 | ||||||||
\(506\) | −7.39868 | −0.328912 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.1208 | −0.493405 | ||||||||
\(509\) | −1.02284 | −0.0453366 | −0.0226683 | − | 0.999743i | \(-0.507216\pi\) | ||||
−0.0226683 | + | 0.999743i | \(0.507216\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.13419 | −0.0501735 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.4202 | 0.900696 | ||||||||
\(515\) | 0.410065 | 0.0180696 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.6991 | 0.910347 | ||||||||
\(518\) | −1.51604 | −0.0666108 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.28816 | −0.188048 | ||||||||
\(521\) | 0.841857 | 0.0368824 | 0.0184412 | − | 0.999830i | \(-0.494130\pi\) | ||||
0.0184412 | + | 0.999830i | \(0.494130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.8987 | 1.70092 | 0.850460 | − | 0.526040i | \(-0.176324\pi\) | ||||
0.850460 | + | 0.526040i | \(0.176324\pi\) | |||||||
\(524\) | 17.6435 | 0.770761 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.59917 | 0.156931 | ||||||||
\(527\) | −11.2870 | −0.491672 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.7415 | −0.510502 | ||||||||
\(530\) | 6.16626 | 0.267845 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.2757 | 0.445507 | ||||||||
\(533\) | −6.33475 | −0.274388 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.576325 | −0.0249167 | ||||||||
\(536\) | −1.00000 | −0.0431934 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.94530 | −0.385659 | ||||||||
\(539\) | 5.86664 | 0.252694 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2644 | −0.484295 | −0.242148 | − | 0.970239i | \(-0.577852\pi\) | ||||
−0.242148 | + | 0.970239i | \(0.577852\pi\) | |||||||
\(542\) | −7.41118 | −0.318337 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.93280 | 0.211492 | ||||||||
\(545\) | 5.78247 | 0.247694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.1092 | 1.41565 | 0.707823 | − | 0.706389i | \(-0.249677\pi\) | ||||
0.707823 | + | 0.706389i | \(0.249677\pi\) | |||||||
\(548\) | 4.72777 | 0.201960 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.20503 | −0.0940229 | ||||||||
\(551\) | 13.8656 | 0.590694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0670 | 0.428092 | ||||||||
\(554\) | 16.2586 | 0.690763 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −20.0855 | −0.851813 | ||||||||
\(557\) | −14.1103 | −0.597873 | −0.298936 | − | 0.954273i | \(-0.596632\pi\) | ||||
−0.298936 | + | 0.954273i | \(0.596632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.9111 | −0.799853 | ||||||||
\(560\) | 2.08313 | 0.0880283 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.1526 | −0.807906 | ||||||||
\(563\) | 16.4101 | 0.691602 | 0.345801 | − | 0.938308i | \(-0.387607\pi\) | ||||
0.345801 | + | 0.938308i | \(0.387607\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.8268 | 0.581699 | ||||||||
\(566\) | −24.2905 | −1.02101 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.84967 | 0.203488 | ||||||||
\(569\) | −30.7255 | −1.28808 | −0.644041 | − | 0.764991i | \(-0.722743\pi\) | ||||
−0.644041 | + | 0.764991i | \(0.722743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.86560 | −0.412863 | −0.206431 | − | 0.978461i | \(-0.566185\pi\) | ||||
−0.206431 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(572\) | 9.45554 | 0.395356 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.07733 | 0.128445 | ||||||||
\(575\) | 3.35536 | 0.139928 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.86685 | −0.119349 | −0.0596743 | − | 0.998218i | \(-0.519006\pi\) | ||||
−0.0596743 | + | 0.998218i | \(0.519006\pi\) | |||||||
\(578\) | 7.33252 | 0.304993 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.81090 | 0.116716 | ||||||||
\(581\) | 34.5661 | 1.43405 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.5968 | −0.563122 | ||||||||
\(584\) | −0.544464 | −0.0225301 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.9705 | −0.577114 | ||||||||
\(587\) | 6.26553 | 0.258606 | 0.129303 | − | 0.991605i | \(-0.458726\pi\) | ||||
0.129303 | + | 0.991605i | \(0.458726\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.2870 | −0.465075 | ||||||||
\(590\) | 1.47726 | 0.0608180 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.727768 | −0.0299111 | ||||||||
\(593\) | 9.77324 | 0.401339 | 0.200669 | − | 0.979659i | \(-0.435688\pi\) | ||||
0.200669 | + | 0.979659i | \(0.435688\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.2757 | 0.421261 | ||||||||
\(596\) | 2.81090 | 0.115139 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.3883 | −0.588383 | ||||||||
\(599\) | 15.1845 | 0.620422 | 0.310211 | − | 0.950668i | \(-0.399600\pi\) | ||||
0.310211 | + | 0.950668i | \(0.399600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2688 | −0.826780 | −0.413390 | − | 0.910554i | \(-0.635655\pi\) | ||||
−0.413390 | + | 0.910554i | \(0.635655\pi\) | |||||||
\(602\) | 9.18674 | 0.374424 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.7142 | 0.476642 | ||||||||
\(605\) | −6.13783 | −0.249538 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.31891 | −0.215888 | −0.107944 | − | 0.994157i | \(-0.534427\pi\) | ||||
−0.107944 | + | 0.994157i | \(0.534427\pi\) | |||||||
\(608\) | 4.93280 | 0.200051 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.08313 | 0.165321 | ||||||||
\(611\) | 40.2539 | 1.62850 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6650 | −0.430757 | −0.215378 | − | 0.976531i | \(-0.569099\pi\) | ||||
−0.215378 | + | 0.976531i | \(0.569099\pi\) | |||||||
\(614\) | −20.3144 | −0.819824 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.59337 | −0.185072 | ||||||||
\(617\) | −37.1628 | −1.49612 | −0.748059 | − | 0.663633i | \(-0.769014\pi\) | ||||
−0.748059 | + | 0.663633i | \(0.769014\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0672 | −0.605602 | −0.302801 | − | 0.953054i | \(-0.597922\pi\) | ||||
−0.302801 | + | 0.953054i | \(0.597922\pi\) | |||||||
\(620\) | −2.28816 | −0.0918948 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.75620 | 0.310995 | ||||||||
\(623\) | −4.54811 | −0.182216 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −20.8132 | −0.831864 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.1981 | −0.805993 | ||||||||
\(629\) | −3.58994 | −0.143140 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4226 | −0.494534 | −0.247267 | − | 0.968947i | \(-0.579533\pi\) | ||||
−0.247267 | + | 0.968947i | \(0.579533\pi\) | |||||||
\(632\) | 4.83263 | 0.192232 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.488511 | −0.0194013 | ||||||||
\(635\) | −11.1208 | −0.441315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11.4090 | 0.452039 | ||||||||
\(638\) | −6.19812 | −0.245386 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −31.8177 | −1.25672 | −0.628362 | − | 0.777921i | \(-0.716274\pi\) | ||||
−0.628362 | + | 0.777921i | \(0.716274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.3427 | −1.59096 | −0.795479 | − | 0.605981i | \(-0.792781\pi\) | ||||
−0.795479 | + | 0.605981i | \(0.792781\pi\) | |||||||
\(644\) | 6.98966 | 0.275431 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.3325 | 0.957350 | ||||||||
\(647\) | −43.6662 | −1.71670 | −0.858349 | − | 0.513067i | \(-0.828509\pi\) | ||||
−0.858349 | + | 0.513067i | \(0.828509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.25741 | −0.127865 | ||||||||
\(650\) | −4.28816 | −0.168196 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.7278 | −0.420132 | ||||||||
\(653\) | −33.1411 | −1.29691 | −0.648455 | − | 0.761253i | \(-0.724584\pi\) | ||||
−0.648455 | + | 0.761253i | \(0.724584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.6435 | 0.689390 | ||||||||
\(656\) | 1.47726 | 0.0576775 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.5548 | −0.762326 | ||||||||
\(659\) | −34.6640 | −1.35032 | −0.675159 | − | 0.737672i | \(-0.735925\pi\) | ||||
−0.675159 | + | 0.737672i | \(0.735925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8884 | −0.423511 | −0.211756 | − | 0.977323i | \(-0.567918\pi\) | ||||
−0.211756 | + | 0.977323i | \(0.567918\pi\) | |||||||
\(662\) | −23.0570 | −0.896137 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 16.5934 | 0.643948 | ||||||||
\(665\) | 10.2757 | 0.398473 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.43158 | 0.365192 | ||||||||
\(668\) | −3.93169 | −0.152122 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.00000 | −0.0386334 | ||||||||
\(671\) | −9.00343 | −0.347574 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.48865 | −0.327213 | −0.163607 | − | 0.986526i | \(-0.552313\pi\) | ||||
−0.163607 | + | 0.986526i | \(0.552313\pi\) | |||||||
\(674\) | 30.3293 | 1.16824 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.38834 | 0.207244 | ||||||||
\(677\) | 15.1526 | 0.582364 | 0.291182 | − | 0.956668i | \(-0.405952\pi\) | ||||
0.291182 | + | 0.956668i | \(0.405952\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.59337 | 0.176277 | ||||||||
\(680\) | 4.93280 | 0.189164 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.04547 | 0.193201 | ||||||||
\(683\) | −5.01138 | −0.191755 | −0.0958776 | − | 0.995393i | \(-0.530566\pi\) | ||||
−0.0958776 | + | 0.995393i | \(0.530566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.72777 | 0.180639 | ||||||||
\(686\) | −20.1242 | −0.768346 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.41006 | 0.168132 | ||||||||
\(689\) | −26.4419 | −1.00736 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.89969 | −0.376602 | −0.188301 | − | 0.982111i | \(-0.560298\pi\) | ||||
−0.188301 | + | 0.982111i | \(0.560298\pi\) | |||||||
\(692\) | −9.04779 | −0.343945 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.5432 | −0.665931 | ||||||||
\(695\) | −20.0855 | −0.761885 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.28705 | 0.276017 | ||||||||
\(698\) | 14.8201 | 0.560950 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.08313 | 0.0787349 | ||||||||
\(701\) | −11.3609 | −0.429097 | −0.214549 | − | 0.976713i | \(-0.568828\pi\) | ||||
−0.214549 | + | 0.976713i | \(0.568828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.58994 | −0.135397 | ||||||||
\(704\) | −2.20503 | −0.0831053 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.7665 | −0.706288 | ||||||||
\(707\) | 19.0353 | 0.715896 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.5170 | −1.85965 | −0.929826 | − | 0.368001i | \(-0.880042\pi\) | ||||
−0.929826 | + | 0.368001i | \(0.880042\pi\) | |||||||
\(710\) | 4.84967 | 0.182005 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.18330 | −0.0818228 | ||||||||
\(713\) | −7.67761 | −0.287529 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.45554 | 0.353617 | ||||||||
\(716\) | −13.6754 | −0.511073 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.43738 | 0.240241 | ||||||||
\(719\) | 28.4863 | 1.06236 | 0.531180 | − | 0.847259i | \(-0.321749\pi\) | ||||
0.531180 | + | 0.847259i | \(0.321749\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.854218 | 0.0318127 | ||||||||
\(722\) | 5.33252 | 0.198456 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.876984 | 0.0325929 | ||||||||
\(725\) | 2.81090 | 0.104394 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.4191 | −0.720214 | −0.360107 | − | 0.932911i | \(-0.617260\pi\) | ||||
−0.360107 | + | 0.932911i | \(0.617260\pi\) | |||||||
\(728\) | −8.93280 | −0.331072 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.544464 | −0.0201515 | ||||||||
\(731\) | 21.7540 | 0.804600 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0628 | 0.741037 | 0.370519 | − | 0.928825i | \(-0.379180\pi\) | ||||
0.370519 | + | 0.928825i | \(0.379180\pi\) | |||||||
\(734\) | −18.1298 | −0.669183 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.35536 | 0.123680 | ||||||||
\(737\) | 2.20503 | 0.0812234 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.21985 | 0.228801 | 0.114400 | − | 0.993435i | \(-0.463505\pi\) | ||||
0.114400 | + | 0.993435i | \(0.463505\pi\) | |||||||
\(740\) | −0.727768 | −0.0267533 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.8451 | 0.471559 | ||||||||
\(743\) | −51.6925 | −1.89641 | −0.948207 | − | 0.317652i | \(-0.897106\pi\) | ||||
−0.948207 | + | 0.317652i | \(0.897106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.81090 | 0.102983 | ||||||||
\(746\) | 12.6207 | 0.462076 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.8770 | −0.397702 | ||||||||
\(749\) | −1.20056 | −0.0438675 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.8201 | −0.467813 | −0.233907 | − | 0.972259i | \(-0.575151\pi\) | ||||
−0.233907 | + | 0.972259i | \(0.575151\pi\) | |||||||
\(752\) | −9.38722 | −0.342317 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.0536 | −0.438966 | ||||||||
\(755\) | 11.7142 | 0.426322 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.4613 | −1.10713 | −0.553567 | − | 0.832805i | \(-0.686734\pi\) | ||||
−0.553567 | + | 0.832805i | \(0.686734\pi\) | |||||||
\(758\) | 28.4180 | 1.03219 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.93280 | 0.178931 | ||||||||
\(761\) | −0.937484 | −0.0339838 | −0.0169919 | − | 0.999856i | \(-0.505409\pi\) | ||||
−0.0169919 | + | 0.999856i | \(0.505409\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.0456 | 0.436081 | ||||||||
\(764\) | 16.4101 | 0.593695 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.6048 | −0.491560 | ||||||||
\(767\) | −6.33475 | −0.228734 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.2734 | −1.09169 | −0.545844 | − | 0.837887i | \(-0.683791\pi\) | ||||
−0.545844 | + | 0.837887i | \(0.683791\pi\) | |||||||
\(770\) | −4.59337 | −0.165534 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.17660 | −0.114329 | ||||||||
\(773\) | 26.8949 | 0.967343 | 0.483672 | − | 0.875249i | \(-0.339303\pi\) | ||||
0.483672 | + | 0.875249i | \(0.339303\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.28816 | −0.0821932 | ||||||||
\(776\) | 2.20503 | 0.0791560 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.6948 | 0.849498 | ||||||||
\(779\) | 7.28705 | 0.261086 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.6937 | −0.382650 | ||||||||
\(782\) | 16.5513 | 0.591874 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.66057 | −0.0950203 | ||||||||
\(785\) | −20.1981 | −0.720902 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.0936 | 1.17966 | 0.589829 | − | 0.807528i | \(-0.299195\pi\) | ||||
0.589829 | + | 0.807528i | \(0.299195\pi\) | |||||||
\(788\) | 10.5763 | 0.376766 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.83263 | 0.171937 | ||||||||
\(791\) | 28.8031 | 1.02412 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.5091 | −0.621767 | ||||||||
\(794\) | −4.65022 | −0.165030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.59337 | 0.304584 | ||||||||
\(797\) | −22.6243 | −0.801395 | −0.400697 | − | 0.916210i | \(-0.631232\pi\) | ||||
−0.400697 | + | 0.916210i | \(0.631232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −46.3053 | −1.63816 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.5193 | −0.830494 | ||||||||
\(803\) | 1.20056 | 0.0423668 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.98966 | 0.246353 | ||||||||
\(806\) | 9.81201 | 0.345613 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.13783 | 0.321468 | ||||||||
\(809\) | −26.0000 | −0.914111 | −0.457056 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457056 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.5217 | −1.52825 | −0.764127 | − | 0.645066i | \(-0.776830\pi\) | ||||
−0.764127 | + | 0.645066i | \(0.776830\pi\) | |||||||
\(812\) | 5.85547 | 0.205487 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.60475 | 0.0562465 | ||||||||
\(815\) | −10.7278 | −0.375777 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.7540 | 0.761075 | ||||||||
\(818\) | 18.5763 | 0.649506 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.47726 | 0.0515883 | ||||||||
\(821\) | −10.9431 | −0.381916 | −0.190958 | − | 0.981598i | \(-0.561159\pi\) | ||||
−0.190958 | + | 0.981598i | \(0.561159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.63541 | 0.301011 | 0.150506 | − | 0.988609i | \(-0.451910\pi\) | ||||
0.150506 | + | 0.988609i | \(0.451910\pi\) | |||||||
\(824\) | 0.410065 | 0.0142853 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.07733 | 0.107074 | ||||||||
\(827\) | 23.9395 | 0.832458 | 0.416229 | − | 0.909260i | \(-0.363351\pi\) | ||||
0.416229 | + | 0.909260i | \(0.363351\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.6993 | −0.545261 | −0.272630 | − | 0.962119i | \(-0.587894\pi\) | ||||
−0.272630 | + | 0.962119i | \(0.587894\pi\) | |||||||
\(830\) | 16.5934 | 0.575964 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.28816 | −0.148665 | ||||||||
\(833\) | −13.1241 | −0.454722 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.93169 | −0.136062 | ||||||||
\(836\) | −10.8770 | −0.376188 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.97605 | 0.0682613 | ||||||||
\(839\) | −25.1742 | −0.869111 | −0.434556 | − | 0.900645i | \(-0.643095\pi\) | ||||
−0.434556 | + | 0.900645i | \(0.643095\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0989 | −0.727547 | ||||||||
\(842\) | 9.92246 | 0.341950 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.8553 | −0.442496 | ||||||||
\(845\) | 5.38834 | 0.185364 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7859 | −0.439329 | ||||||||
\(848\) | 6.16626 | 0.211750 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.93280 | 0.169194 | ||||||||
\(851\) | −2.44193 | −0.0837081 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.33029 | 0.285224 | 0.142612 | − | 0.989779i | \(-0.454450\pi\) | ||||
0.142612 | + | 0.989779i | \(0.454450\pi\) | |||||||
\(854\) | 8.50569 | 0.291059 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.576325 | −0.0196984 | ||||||||
\(857\) | 35.7562 | 1.22141 | 0.610703 | − | 0.791859i | \(-0.290887\pi\) | ||||
0.610703 | + | 0.791859i | \(0.290887\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.5410 | −1.75856 | −0.879278 | − | 0.476309i | \(-0.841974\pi\) | ||||
−0.879278 | + | 0.476309i | \(0.841974\pi\) | |||||||
\(860\) | 4.41006 | 0.150382 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.38275 | −0.0811568 | ||||||||
\(863\) | 3.65825 | 0.124528 | 0.0622641 | − | 0.998060i | \(-0.480168\pi\) | ||||
0.0622641 | + | 0.998060i | \(0.480168\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.04779 | −0.307634 | ||||||||
\(866\) | −20.9965 | −0.713491 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.76654 | −0.161787 | ||||||||
\(869\) | −10.6561 | −0.361483 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.28816 | 0.145299 | ||||||||
\(872\) | 5.78247 | 0.195819 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.5513 | 0.559857 | ||||||||
\(875\) | 2.08313 | 0.0704227 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.0185 | 0.338299 | 0.169150 | − | 0.985590i | \(-0.445898\pi\) | ||||
0.169150 | + | 0.985590i | \(0.445898\pi\) | |||||||
\(878\) | 17.0034 | 0.573838 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.20503 | −0.0743316 | ||||||||
\(881\) | −13.9145 | −0.468792 | −0.234396 | − | 0.972141i | \(-0.575311\pi\) | ||||
−0.234396 | + | 0.972141i | \(0.575311\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.7562 | −0.664849 | −0.332424 | − | 0.943130i | \(-0.607867\pi\) | ||||
−0.332424 | + | 0.943130i | \(0.607867\pi\) | |||||||
\(884\) | −21.1526 | −0.711441 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.8656 | 0.465824 | ||||||||
\(887\) | 8.75182 | 0.293857 | 0.146929 | − | 0.989147i | \(-0.453061\pi\) | ||||
0.146929 | + | 0.989147i | \(0.453061\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.1660 | −0.776964 | ||||||||
\(890\) | −2.18330 | −0.0731845 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.8520 | 0.631211 | ||||||||
\(893\) | −46.3053 | −1.54955 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.6754 | −0.457118 | ||||||||
\(896\) | 2.08313 | 0.0695925 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.0922 | −1.30452 | ||||||||
\(899\) | −6.43179 | −0.214512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.4169 | 1.01333 | ||||||||
\(902\) | −3.25741 | −0.108460 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.8268 | 0.459873 | ||||||||
\(905\) | 0.876984 | 0.0291519 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.3920 | −0.809922 | −0.404961 | − | 0.914334i | \(-0.632715\pi\) | ||||
−0.404961 | + | 0.914334i | \(0.632715\pi\) | |||||||
\(908\) | 22.1094 | 0.733726 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.93280 | −0.296119 | ||||||||
\(911\) | 6.94061 | 0.229953 | 0.114976 | − | 0.993368i | \(-0.463321\pi\) | ||||
0.114976 | + | 0.993368i | \(0.463321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36.5889 | −1.21092 | ||||||||
\(914\) | −6.68900 | −0.221252 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.326934 | 0.0108022 | ||||||||
\(917\) | 36.7538 | 1.21372 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.0764 | −0.563299 | −0.281650 | − | 0.959517i | \(-0.590882\pi\) | ||||
−0.281650 | + | 0.959517i | \(0.590882\pi\) | |||||||
\(920\) | 3.35536 | 0.110623 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.0545 | 0.726326 | ||||||||
\(923\) | −20.7962 | −0.684514 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.727768 | −0.0239289 | ||||||||
\(926\) | 39.4191 | 1.29539 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.81090 | 0.0922723 | ||||||||
\(929\) | −16.6433 | −0.546049 | −0.273025 | − | 0.962007i | \(-0.588024\pi\) | ||||
−0.273025 | + | 0.962007i | \(0.588024\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.1241 | −0.430124 | ||||||||
\(932\) | 2.14922 | 0.0703999 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.0148 | −0.327695 | ||||||||
\(935\) | −10.8770 | −0.355715 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.72652 | 0.317752 | 0.158876 | − | 0.987299i | \(-0.449213\pi\) | ||||
0.158876 | + | 0.987299i | \(0.449213\pi\) | |||||||
\(938\) | −2.08313 | −0.0680166 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.38722 | −0.306177 | ||||||||
\(941\) | 7.20056 | 0.234732 | 0.117366 | − | 0.993089i | \(-0.462555\pi\) | ||||
0.117366 | + | 0.993089i | \(0.462555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.95676 | 0.161414 | ||||||||
\(944\) | 1.47726 | 0.0480808 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.72433 | −0.316165 | ||||||||
\(947\) | −30.1561 | −0.979941 | −0.489971 | − | 0.871739i | \(-0.662992\pi\) | ||||
−0.489971 | + | 0.871739i | \(0.662992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.33475 | 0.0757891 | ||||||||
\(950\) | 4.93280 | 0.160041 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.2757 | 0.333036 | ||||||||
\(953\) | 19.0193 | 0.616095 | 0.308048 | − | 0.951371i | \(-0.400324\pi\) | ||||
0.308048 | + | 0.951371i | \(0.400324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4101 | 0.531017 | ||||||||
\(956\) | −11.1208 | −0.359672 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.8474 | −0.738167 | ||||||||
\(959\) | 9.84856 | 0.318026 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7643 | −0.831107 | ||||||||
\(962\) | 3.12079 | 0.100618 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.15956 | −0.230594 | ||||||||
\(965\) | −3.17660 | −0.102259 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.1865 | 1.29231 | 0.646156 | − | 0.763206i | \(-0.276376\pi\) | ||||
0.646156 | + | 0.763206i | \(0.276376\pi\) | |||||||
\(968\) | −6.13783 | −0.197277 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.20503 | 0.0707993 | ||||||||
\(971\) | 50.4387 | 1.61865 | 0.809327 | − | 0.587359i | \(-0.199832\pi\) | ||||
0.809327 | + | 0.587359i | \(0.199832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.8406 | −1.34135 | ||||||||
\(974\) | 35.8896 | 1.14998 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.08313 | 0.130698 | ||||||||
\(977\) | −58.8142 | −1.88163 | −0.940817 | − | 0.338916i | \(-0.889940\pi\) | ||||
−0.940817 | + | 0.338916i | \(0.889940\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.81426 | 0.153864 | ||||||||
\(980\) | −2.66057 | −0.0849888 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 35.2403 | 1.12456 | ||||||||
\(983\) | −13.2643 | −0.423065 | −0.211532 | − | 0.977371i | \(-0.567845\pi\) | ||||
−0.211532 | + | 0.977371i | \(0.567845\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.5763 | 0.336990 | ||||||||
\(986\) | 13.8656 | 0.441571 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.1526 | −0.672955 | ||||||||
\(989\) | 14.7974 | 0.470529 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.6071 | −0.495775 | −0.247887 | − | 0.968789i | \(-0.579736\pi\) | ||||
−0.247887 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(992\) | −2.28816 | −0.0726492 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.1025 | 0.320432 | ||||||||
\(995\) | 8.59337 | 0.272428 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.5911 | −0.652128 | −0.326064 | − | 0.945348i | \(-0.605722\pi\) | ||||
−0.326064 | + | 0.945348i | \(0.605722\pi\) | |||||||
\(998\) | 8.17094 | 0.258647 | ||||||||
\(999\) | 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 | 6030.2.a.bu.1.3 | 4 | ||
3.2 | odd | 2 | 2010.2.a.r.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2010.2.a.r.1.3 | ✓ | 4 | 3.2 | odd | 2 | ||
6030.2.a.bu.1.3 | 4 | 1.1 | even | 1 | trivial |