Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(1,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.37228 | 1.94699 | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) | ||||
0.973494 | + | 0.228714i | \(0.0734519\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.37228 | 2.79076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.627719 | 0.189264 | 0.0946322 | − | 0.995512i | \(-0.469833\pi\) | ||||
0.0946322 | + | 0.995512i | \(0.469833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37228 | 0.380602 | 0.190301 | − | 0.981726i | \(-0.439054\pi\) | ||||
0.190301 | + | 0.981726i | \(0.439054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.37228 | 0.870719 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.37228 | −1.30297 | −0.651485 | − | 0.758662i | \(-0.725854\pi\) | ||||
−0.651485 | + | 0.758662i | \(0.725854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.74456 | −1.54731 | −0.773654 | − | 0.633608i | \(-0.781573\pi\) | ||||
−0.773654 | + | 0.633608i | \(0.781573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.74456 | 1.40634 | 0.703169 | − | 0.711022i | \(-0.251768\pi\) | ||||
0.703169 | + | 0.711022i | \(0.251768\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.1168 | 3.48659 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.37228 | 0.254826 | 0.127413 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127413 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.11684 | 0.368495 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.62772 | 0.741028 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.74456 | 0.740976 | 0.370488 | − | 0.928837i | \(-0.379190\pi\) | ||||
0.370488 | + | 0.928837i | \(0.379190\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.74456 | 0.418542 | 0.209271 | − | 0.977858i | \(-0.432891\pi\) | ||||
0.209271 | + | 0.977858i | \(0.432891\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.37228 | 1.24807 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.1168 | −1.47569 | −0.737847 | − | 0.674968i | \(-0.764157\pi\) | ||||
−0.737847 | + | 0.674968i | \(0.764157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.1168 | −2.53687 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.744563 | −0.102274 | −0.0511368 | − | 0.998692i | \(-0.516284\pi\) | ||||
−0.0511368 | + | 0.998692i | \(0.516284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.627719 | 0.0846416 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22.7446 | −3.01259 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.74456 | −1.11963 | −0.559813 | − | 0.828619i | \(-0.689127\pi\) | ||||
−0.559813 | + | 0.828619i | \(0.689127\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.37228 | 0.170211 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22.7446 | 2.73812 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.37228 | 0.389398 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.11684 | −0.238164 | −0.119082 | − | 0.992884i | \(-0.537995\pi\) | ||||
−0.119082 | + | 0.992884i | \(0.537995\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4891 | −1.48062 | −0.740312 | − | 0.672264i | \(-0.765322\pi\) | ||||
−0.740312 | + | 0.672264i | \(0.765322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.37228 | −0.582706 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.62772 | 0.496144 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.25544 | −0.345076 | −0.172538 | − | 0.985003i | \(-0.555197\pi\) | ||||
−0.172538 | + | 0.985003i | \(0.555197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.9783 | 2.79751 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.74456 | −0.691978 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.8614 | −1.91509 | −0.957543 | − | 0.288291i | \(-0.906913\pi\) | ||||
−0.957543 | + | 0.288291i | \(0.906913\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.25544 | 0.528191 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3723 | 1.12054 | 0.560272 | − | 0.828309i | \(-0.310697\pi\) | ||||
0.560272 | + | 0.828309i | \(0.310697\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.74456 | −0.265327 | −0.132663 | − | 0.991161i | \(-0.542353\pi\) | ||||
−0.132663 | + | 0.991161i | \(0.542353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.37228 | −0.514571 | −0.257286 | − | 0.966335i | \(-0.582828\pi\) | ||||
−0.257286 | + | 0.966335i | \(0.582828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.74456 | −0.640166 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.74456 | 0.628934 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.4891 | 1.06217 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6060 | −0.964179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.0000 | 1.44267 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.25544 | 0.814896 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.74456 | −0.589275 | −0.294638 | − | 0.955609i | \(-0.595199\pi\) | ||||
−0.294638 | + | 0.955609i | \(0.595199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.1168 | 1.55925 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.25544 | 0.278131 | 0.139065 | − | 0.990283i | \(-0.455590\pi\) | ||||
0.139065 | + | 0.990283i | \(0.455590\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.74456 | −0.572066 | −0.286033 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286033 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −34.1168 | −2.87316 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.861407 | 0.0720344 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.37228 | 0.113962 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.48913 | −0.613533 | −0.306767 | − | 0.951785i | \(-0.599247\pi\) | ||||
−0.306767 | + | 0.951785i | \(0.599247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.11684 | −0.172266 | −0.0861332 | − | 0.996284i | \(-0.527451\pi\) | ||||
−0.0861332 | + | 0.996284i | \(0.527451\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −44.9783 | −3.63628 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.48913 | −0.597697 | −0.298849 | − | 0.954301i | \(-0.596603\pi\) | ||||
−0.298849 | + | 0.954301i | \(0.596603\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.51087 | −0.199125 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.25544 | −0.411638 | −0.205819 | − | 0.978590i | \(-0.565986\pi\) | ||||
−0.205819 | + | 0.978590i | \(0.565986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.11684 | 0.164796 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3723 | 0.880014 | 0.440007 | − | 0.897994i | \(-0.354976\pi\) | ||||
0.440007 | + | 0.897994i | \(0.354976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1168 | −0.855142 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −56.4674 | −4.31817 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.37228 | −0.408447 | −0.204223 | − | 0.978924i | \(-0.565467\pi\) | ||||
−0.204223 | + | 0.978924i | \(0.565467\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.9783 | −2.02781 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.9783 | 1.71748 | 0.858738 | − | 0.512416i | \(-0.171249\pi\) | ||||
0.858738 | + | 0.512416i | \(0.171249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2337 | 1.35530 | 0.677650 | − | 0.735385i | \(-0.262999\pi\) | ||||
0.677650 | + | 0.735385i | \(0.262999\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.4891 | −2.17990 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.37228 | −0.246606 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.8614 | −1.79891 | −0.899454 | − | 0.437015i | \(-0.856036\pi\) | ||||
−0.899454 | + | 0.437015i | \(0.856036\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.74456 | −0.341521 | −0.170761 | − | 0.985313i | \(-0.554622\pi\) | ||||
−0.170761 | + | 0.985313i | \(0.554622\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.62772 | 0.331398 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.2337 | 1.86907 | 0.934536 | − | 0.355867i | \(-0.115815\pi\) | ||||
0.934536 | + | 0.355867i | \(0.115815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4891 | −0.951450 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.74456 | 0.331375 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 56.4674 | 3.92475 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.23369 | −0.292850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.62772 | −0.593957 | −0.296978 | − | 0.954884i | \(-0.595979\pi\) | ||||
−0.296978 | + | 0.954884i | \(0.595979\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.9783 | 1.84852 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.74456 | 0.187178 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.2337 | 1.36727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.37228 | −0.495913 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3723 | 0.761544 | 0.380772 | − | 0.924669i | \(-0.375658\pi\) | ||||
0.380772 | + | 0.924669i | \(0.375658\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.37228 | 0.558152 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.86141 | 0.588152 | 0.294076 | − | 0.955782i | \(-0.404988\pi\) | ||||
0.294076 | + | 0.955782i | \(0.404988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.2337 | −1.46924 | −0.734622 | − | 0.678477i | \(-0.762640\pi\) | ||||
−0.734622 | + | 0.678477i | \(0.762640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7446 | −0.834924 | −0.417462 | − | 0.908694i | \(-0.637080\pi\) | ||||
−0.417462 | + | 0.908694i | \(0.637080\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1168 | −0.659950 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.13859 | −0.463701 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3723 | 1.25309 | 0.626544 | − | 0.779386i | \(-0.284469\pi\) | ||||
0.626544 | + | 0.779386i | \(0.284469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0000 | −1.67481 | −0.837404 | − | 0.546585i | \(-0.815928\pi\) | ||||
−0.837404 | + | 0.546585i | \(0.815928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 66.9783 | 4.29666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.25544 | −0.588909 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −45.4891 | −2.88276 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.74456 | 0.425713 | 0.212857 | − | 0.977083i | \(-0.431723\pi\) | ||||
0.212857 | + | 0.977083i | \(0.431723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.23369 | 0.266170 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.1168 | −1.13452 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.510875 | 0.0318675 | 0.0159337 | − | 0.999873i | \(-0.494928\pi\) | ||||
0.0159337 | + | 0.999873i | \(0.494928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.4891 | 0.711159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.2337 | −0.754362 | −0.377181 | − | 0.926140i | \(-0.623106\pi\) | ||||
−0.377181 | + | 0.926140i | \(0.623106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.744563 | −0.0457381 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9783 | −0.671858 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.4891 | 0.819406 | 0.409703 | − | 0.912219i | \(-0.365632\pi\) | ||||
0.409703 | + | 0.912219i | \(0.365632\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.627719 | 0.0378529 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.9783 | −1.26046 | −0.630230 | − | 0.776408i | \(-0.717040\pi\) | ||||
−0.630230 | + | 0.776408i | \(0.717040\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 66.9783 | 4.00988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6060 | −1.28890 | −0.644452 | − | 0.764645i | \(-0.722914\pi\) | ||||
−0.644452 | + | 0.764645i | \(0.722914\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1168 | 1.55249 | 0.776243 | − | 0.630434i | \(-0.217123\pi\) | ||||
0.776243 | + | 0.630434i | \(0.217123\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.7446 | −1.34727 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8614 | 0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −63.6060 | −3.72865 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.88316 | −0.460539 | −0.230269 | − | 0.973127i | \(-0.573961\pi\) | ||||
−0.230269 | + | 0.973127i | \(0.573961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.3723 | 0.659887 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.25544 | 0.535256 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.2337 | 1.16240 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.74456 | −0.500712 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.8832 | −0.792354 | −0.396177 | − | 0.918174i | \(-0.629663\pi\) | ||||
−0.396177 | + | 0.918174i | \(0.629663\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 38.3505 | 2.18169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.25544 | 0.0711893 | 0.0355947 | − | 0.999366i | \(-0.488667\pi\) | ||||
0.0355947 | + | 0.999366i | \(0.488667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.1168 | −1.13707 | −0.568536 | − | 0.822659i | \(-0.692490\pi\) | ||||
−0.568536 | + | 0.822659i | \(0.692490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0000 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.861407 | 0.0482295 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.25544 | −0.516588 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.2337 | 2.01610 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.37228 | 0.0761205 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.1168 | −1.00186 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.7446 | −0.917596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.4891 | 0.843746 | 0.421873 | − | 0.906655i | \(-0.361373\pi\) | ||||
0.421873 | + | 0.906655i | \(0.361373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.74456 | 0.366314 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.02175 | 0.271943 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.7446 | 1.22453 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.2554 | −0.711589 | −0.355795 | − | 0.934564i | \(-0.615790\pi\) | ||||
−0.355795 | + | 0.934564i | \(0.615790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.48913 | 0.186769 | 0.0933843 | − | 0.995630i | \(-0.470231\pi\) | ||||
0.0933843 | + | 0.995630i | \(0.470231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.8614 | 1.32700 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.8614 | −1.42969 | −0.714844 | − | 0.699284i | \(-0.753502\pi\) | ||||
−0.714844 | + | 0.699284i | \(0.753502\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.4891 | 1.39416 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −35.7663 | −1.87724 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.86141 | 0.462562 | 0.231281 | − | 0.972887i | \(-0.425708\pi\) | ||||
0.231281 | + | 0.972887i | \(0.425708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 39.7228 | 2.06789 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.2554 | −0.997009 | −0.498504 | − | 0.866887i | \(-0.666117\pi\) | ||||
−0.498504 | + | 0.866887i | \(0.666117\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.37228 | 0.174144 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.88316 | 0.0969875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.9783 | 1.38214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.48913 | −0.280481 | −0.140241 | − | 0.990117i | \(-0.544788\pi\) | ||||
−0.140241 | + | 0.990117i | \(0.544788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.9783 | 1.16805 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.8614 | −0.550695 | −0.275348 | − | 0.961345i | \(-0.588793\pi\) | ||||
−0.275348 | + | 0.961345i | \(0.588793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.2337 | −1.83242 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.7446 | −1.14731 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.11684 | −0.106510 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.3723 | −1.87566 | −0.937831 | − | 0.347094i | \(-0.887169\pi\) | ||||
−0.937831 | + | 0.347094i | \(0.887169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.60597 | 0.0801983 | 0.0400991 | − | 0.999196i | \(-0.487233\pi\) | ||||
0.0400991 | + | 0.999196i | \(0.487233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.9783 | 0.546866 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35.9783 | 1.78777 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.25544 | −0.0622297 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.4891 | 0.568101 | 0.284050 | − | 0.958809i | \(-0.408322\pi\) | ||||
0.284050 | + | 0.958809i | \(0.408322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.9783 | 0.541517 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.4891 | −0.662155 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.7446 | −1.11381 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.4891 | 1.83146 | 0.915732 | − | 0.401790i | \(-0.131612\pi\) | ||||
0.915732 | + | 0.401790i | \(0.131612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.6060 | 1.05301 | 0.526505 | − | 0.850172i | \(-0.323502\pi\) | ||||
0.526505 | + | 0.850172i | \(0.323502\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −84.7011 | −4.11831 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.37228 | −0.260594 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.90491 | 0.140250 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.6277 | 0.608256 | 0.304128 | − | 0.952631i | \(-0.401635\pi\) | ||||
0.304128 | + | 0.952631i | \(0.401635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9783 | 0.815923 | 0.407961 | − | 0.912999i | \(-0.366240\pi\) | ||||
0.407961 | + | 0.912999i | \(0.366240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.62772 | 0.221882 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −45.4891 | −2.17604 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.2337 | −1.34752 | −0.673760 | − | 0.738950i | \(-0.735322\pi\) | ||||
−0.673760 | + | 0.738950i | \(0.735322\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.25544 | −0.249693 | −0.124847 | − | 0.992176i | \(-0.539844\pi\) | ||||
−0.124847 | + | 0.992176i | \(0.539844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.25544 | −0.154323 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.2554 | −1.19454 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.116844 | −0.00551421 | −0.00275710 | − | 0.999996i | \(-0.500878\pi\) | ||||
−0.00275710 | + | 0.999996i | \(0.500878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.97825 | 0.140240 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.13859 | −0.335400 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7446 | 0.783278 | 0.391639 | − | 0.920119i | \(-0.371908\pi\) | ||||
0.391639 | + | 0.920119i | \(0.371908\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −97.3288 | −4.54292 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.7446 | 0.593573 | 0.296787 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296787 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4891 | −1.37048 | −0.685238 | − | 0.728319i | \(-0.740302\pi\) | ||||
−0.685238 | + | 0.728319i | \(0.740302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 26.9783 | 1.25109 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.6060 | 1.46255 | 0.731275 | − | 0.682083i | \(-0.238926\pi\) | ||||
0.731275 | + | 0.682083i | \(0.238926\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.2554 | −1.16371 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.72281 | 0.0792150 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.74456 | −0.309462 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.23369 | −0.285421 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.2337 | 0.558971 | 0.279486 | − | 0.960150i | \(-0.409836\pi\) | ||||
0.279486 | + | 0.960150i | \(0.409836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.74456 | −0.125141 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.8614 | −0.856452 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.23369 | −0.191847 | −0.0959234 | − | 0.995389i | \(-0.530580\pi\) | ||||
−0.0959234 | + | 0.995389i | \(0.530580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.7228 | −0.801453 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8832 | 0.807056 | 0.403528 | − | 0.914967i | \(-0.367784\pi\) | ||||
0.403528 | + | 0.914967i | \(0.367784\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.37228 | −0.332031 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.25544 | 0.236214 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.13859 | 0.140503 | 0.0702514 | − | 0.997529i | \(-0.477620\pi\) | ||||
0.0702514 | + | 0.997529i | \(0.477620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.3505 | 1.71338 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.6277 | 0.563042 | 0.281521 | − | 0.959555i | \(-0.409161\pi\) | ||||
0.281521 | + | 0.959555i | \(0.409161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.4891 | −1.66495 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.97825 | −0.220657 | −0.110329 | − | 0.993895i | \(-0.535190\pi\) | ||||
−0.110329 | + | 0.993895i | \(0.535190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −122.190 | −5.39483 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.3723 | 0.501123 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.35053 | −0.279296 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.1168 | −0.795241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.4674 | −1.41970 | −0.709850 | − | 0.704353i | \(-0.751237\pi\) | ||||
−0.709850 | + | 0.704353i | \(0.751237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.9783 | −1.87216 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4891 | 0.977788 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −66.9783 | −2.90661 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.51087 | 0.282017 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.74456 | −0.118658 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 77.4891 | 3.34390 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.3505 | 0.874938 | 0.437469 | − | 0.899234i | \(-0.355875\pi\) | ||||
0.437469 | + | 0.899234i | \(0.355875\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 61.4891 | 2.63875 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.37228 | −0.230123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9783 | 0.640424 | 0.320212 | − | 0.947346i | \(-0.396246\pi\) | ||||
0.320212 | + | 0.947346i | \(0.396246\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −73.2119 | −3.12461 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.25544 | −0.394295 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.74456 | −0.286291 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.2337 | −1.62001 | −0.810007 | − | 0.586421i | \(-0.800537\pi\) | ||||
−0.810007 | + | 0.586421i | \(0.800537\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.76631 | 0.159298 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.3723 | −0.480138 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.48913 | 0.231339 | 0.115670 | − | 0.993288i | \(-0.463099\pi\) | ||||
0.115670 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.9783 | 0.879454 | 0.439727 | − | 0.898131i | \(-0.355075\pi\) | ||||
0.439727 | + | 0.898131i | \(0.355075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −83.8397 | −3.50245 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.74456 | 0.281268 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.6060 | −0.732946 | −0.366473 | − | 0.930429i | \(-0.619435\pi\) | ||||
−0.366473 | + | 0.930429i | \(0.619435\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.0000 | −0.664937 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.467376 | −0.0193567 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.4891 | 0.475017 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.9783 | −0.453121 | −0.226560 | − | 0.973997i | \(-0.572748\pi\) | ||||
−0.226560 | + | 0.973997i | \(0.572748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.9565 | −2.22324 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 88.4674 | 3.63906 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.3723 | 1.04191 | 0.520957 | − | 0.853583i | \(-0.325575\pi\) | ||||
0.520957 | + | 0.853583i | \(0.325575\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 53.9565 | 2.20829 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.60597 | 0.310771 | 0.155386 | − | 0.987854i | \(-0.450338\pi\) | ||||
0.155386 | + | 0.987854i | \(0.450338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.4891 | −1.61080 | −0.805398 | − | 0.592735i | \(-0.798048\pi\) | ||||
−0.805398 | + | 0.592735i | \(0.798048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.4891 | −1.36378 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.6060 | −0.431194 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.6060 | 0.633427 | 0.316713 | − | 0.948521i | \(-0.397421\pi\) | ||||
0.316713 | + | 0.948521i | \(0.397421\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.8832 | −0.561652 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.4891 | −1.27183 | −0.635917 | − | 0.771758i | \(-0.719378\pi\) | ||||
−0.635917 | + | 0.771758i | \(0.719378\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0000 | 0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.25544 | 0.0504603 | 0.0252301 | − | 0.999682i | \(-0.491968\pi\) | ||||
0.0252301 | + | 0.999682i | \(0.491968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 122.190 | 4.90332 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.2772 | −0.570176 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.7446 | 0.428414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.37228 | −0.134248 | −0.0671242 | − | 0.997745i | \(-0.521382\pi\) | ||||
−0.0671242 | + | 0.997745i | \(0.521382\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.0951 | −1.15643 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.00000 | 0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 66.9783 | 2.64962 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.6277 | −0.497989 | −0.248994 | − | 0.968505i | \(-0.580100\pi\) | ||||
−0.248994 | + | 0.968505i | \(0.580100\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.25544 | 0.364432 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.0000 | 0.629025 | 0.314512 | − | 0.949253i | \(-0.398159\pi\) | ||||
0.314512 | + | 0.949253i | \(0.398159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.02175 | −0.197121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.74456 | −0.263532 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 50.2337 | 1.95980 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.11684 | 0.238278 | 0.119139 | − | 0.992878i | \(-0.461987\pi\) | ||||
0.119139 | + | 0.992878i | \(0.461987\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.25544 | −0.126622 | −0.0633109 | − | 0.997994i | \(-0.520166\pi\) | ||||
−0.0633109 | + | 0.997994i | \(0.520166\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −24.8614 | −0.965537 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.25544 | 0.358372 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.3505 | 1.48272 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.48913 | −0.211905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.7228 | −1.22282 | −0.611412 | − | 0.791312i | \(-0.709398\pi\) | ||||
−0.611412 | + | 0.791312i | \(0.709398\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 18.1168 | 0.697318 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.3505 | 1.39706 | 0.698532 | − | 0.715579i | \(-0.253837\pi\) | ||||
0.698532 | + | 0.715579i | \(0.253837\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.8832 | 1.14513 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.25544 | 0.124384 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −74.9783 | −2.86060 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.02175 | −0.0389256 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4891 | −0.513151 | −0.256575 | − | 0.966524i | \(-0.582594\pi\) | ||||
−0.256575 | + | 0.966524i | \(0.582594\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.74456 | −0.255836 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.4891 | −0.965469 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −42.9783 | −1.62559 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.8614 | 1.16562 | 0.582810 | − | 0.812609i | \(-0.301953\pi\) | ||||
0.582810 | + | 0.812609i | \(0.301953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.4891 | 0.508752 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.1168 | −1.28491 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.6060 | −1.26210 | −0.631049 | − | 0.775743i | \(-0.717375\pi\) | ||||
−0.631049 | + | 0.775743i | \(0.717375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.7228 | −0.664657 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 53.9565 | 2.02069 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.861407 | 0.0322148 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 65.3288 | 2.43975 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.7446 | −0.549879 | −0.274940 | − | 0.961461i | \(-0.588658\pi\) | ||||
−0.274940 | + | 0.961461i | \(0.588658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −87.6793 | −3.26083 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.37228 | 0.0509652 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.0000 | −1.18681 | −0.593407 | − | 0.804902i | \(-0.702218\pi\) | ||||
−0.593407 | + | 0.804902i | \(0.702218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 117.935 | 4.36795 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.7446 | −0.545347 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.8614 | 1.43538 | 0.717689 | − | 0.696363i | \(-0.245200\pi\) | ||||
0.717689 | + | 0.696363i | \(0.245200\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.51087 | −0.0924893 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.6060 | 0.721217 | 0.360609 | − | 0.932717i | \(-0.382569\pi\) | ||||
0.360609 | + | 0.932717i | \(0.382569\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.2119 | −1.14660 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.4891 | −1.08185 | −0.540926 | − | 0.841070i | \(-0.681926\pi\) | ||||
−0.540926 | + | 0.841070i | \(0.681926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.48913 | −0.274380 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −112.935 | −4.13207 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.8614 | 1.78298 | 0.891489 | − | 0.453042i | \(-0.149661\pi\) | ||||
0.891489 | + | 0.453042i | \(0.149661\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.7446 | 0.828858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.11684 | −0.0770398 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.2337 | −1.38963 | −0.694814 | − | 0.719190i | \(-0.744513\pi\) | ||||
−0.694814 | + | 0.719190i | \(0.744513\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.2772 | 0.518229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.9783 | 1.48546 | 0.742730 | − | 0.669591i | \(-0.233531\pi\) | ||||
0.742730 | + | 0.669591i | \(0.233531\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −44.9783 | −1.62619 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.9783 | −0.396402 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4891 | 0.702796 | 0.351398 | − | 0.936226i | \(-0.385706\pi\) | ||||
0.351398 | + | 0.936226i | \(0.385706\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.72281 | 0.0620456 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.37228 | 0.0493575 | 0.0246788 | − | 0.999695i | \(-0.492144\pi\) | ||||
0.0246788 | + | 0.999695i | \(0.492144\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | 0.287368 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.0000 | −1.14652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.02175 | 0.179692 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.8614 | 0.888474 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.48913 | −0.267298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8832 | 0.494881 | 0.247441 | − | 0.968903i | \(-0.420411\pi\) | ||||
0.247441 | + | 0.968903i | \(0.420411\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.2554 | −1.46873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0000 | −0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.51087 | −0.0890515 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.3723 | −0.757045 | −0.378523 | − | 0.925592i | \(-0.623568\pi\) | ||||
−0.378523 | + | 0.925592i | \(0.623568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.3505 | 1.92278 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.2554 | −0.963024 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.76631 | 0.132910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.2337 | 0.712260 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.6277 | 0.514283 | 0.257142 | − | 0.966374i | \(-0.417219\pi\) | ||||
0.257142 | + | 0.966374i | \(0.417219\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.25544 | −0.0440844 | −0.0220422 | − | 0.999757i | \(-0.507017\pi\) | ||||
−0.0220422 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 45.4891 | 1.59537 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.25544 | −0.184090 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.5109 | −0.647614 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.88316 | −0.275124 | −0.137562 | − | 0.990493i | \(-0.543927\pi\) | ||||
−0.137562 | + | 0.990493i | \(0.543927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | −0.278862 | −0.139431 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139431 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.11684 | 0.0736990 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.2554 | 0.460937 | 0.230468 | − | 0.973080i | \(-0.425974\pi\) | ||||
0.230468 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2337 | −0.772208 | −0.386104 | − | 0.922455i | \(-0.626179\pi\) | ||||
−0.386104 | + | 0.922455i | \(0.626179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −70.7446 | −2.45410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.3723 | 0.393554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 144.935 | 5.00968 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.7446 | 0.785230 | 0.392615 | − | 0.919703i | \(-0.371571\pi\) | ||||
0.392615 | + | 0.919703i | \(0.371571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.1168 | −0.935064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −72.8614 | −2.50948 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1168 | −0.382431 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 88.0733 | 3.02267 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.4891 | −0.462401 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5109 | 0.565322 | 0.282661 | − | 0.959220i | \(-0.408783\pi\) | ||||
0.282661 | + | 0.959220i | \(0.408783\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −56.4674 | −1.93114 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.0000 | −0.614868 | −0.307434 | − | 0.951569i | \(-0.599470\pi\) | ||||
−0.307434 | + | 0.951569i | \(0.599470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.4674 | 0.834816 | 0.417408 | − | 0.908719i | \(-0.362939\pi\) | ||||
0.417408 | + | 0.908719i | \(0.362939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.51087 | 0.0854712 | 0.0427356 | − | 0.999086i | \(-0.486393\pi\) | ||||
0.0427356 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.37228 | −0.182663 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.0000 | 1.35847 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.32878 | −0.0450759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.48913 | −0.185992 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −157.913 | −5.34455 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.9783 | −1.78895 | −0.894474 | − | 0.447120i | \(-0.852450\pi\) | ||||
−0.894474 | + | 0.447120i | \(0.852450\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.5842 | −0.896663 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.7446 | 1.23796 | 0.618978 | − | 0.785408i | \(-0.287547\pi\) | ||||
0.618978 | + | 0.785408i | \(0.287547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.4891 | −1.12700 | −0.563499 | − | 0.826116i | \(-0.690545\pi\) | ||||
−0.563499 | + | 0.826116i | \(0.690545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.9783 | −0.906864 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 58.9783 | 1.98030 | 0.990148 | − | 0.140025i | \(-0.0447184\pi\) | ||||
0.990148 | + | 0.140025i | \(0.0447184\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.5842 | 0.756600 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 68.2337 | 2.28335 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.9783 | 0.768078 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.2119 | 1.04214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.9783 | 0.366145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.2337 | 0.606108 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.7228 | −1.51820 | −0.759101 | − | 0.650973i | \(-0.774361\pi\) | ||||
−0.759101 | + | 0.650973i | \(0.774361\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 50.2337 | 1.66615 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.9565 | 1.52261 | 0.761303 | − | 0.648396i | \(-0.224560\pi\) | ||||
0.761303 | + | 0.648396i | \(0.224560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.46738 | −0.280229 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.4891 | −0.974880 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.3723 | 0.639033 | 0.319516 | − | 0.947581i | \(-0.396480\pi\) | ||||
0.319516 | + | 0.947581i | \(0.396480\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.8179 | −1.54270 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.9783 | 0.361354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 95.2119 | 3.12717 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.2337 | 1.38564 | 0.692821 | − | 0.721109i | \(-0.256368\pi\) | ||||
0.692821 | + | 0.721109i | \(0.256368\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.23369 | 0.138605 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.37228 | −0.110285 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0951 | 1.14651 | 0.573253 | − | 0.819378i | \(-0.305681\pi\) | ||||
0.573253 | + | 0.819378i | \(0.305681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −67.8397 | −2.21386 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.23369 | 0.0728161 | 0.0364081 | − | 0.999337i | \(-0.488408\pi\) | ||||
0.0364081 | + | 0.999337i | \(0.488408\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000 | 1.04206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0000 | −0.909878 | −0.454939 | − | 0.890523i | \(-0.650339\pi\) | ||||
−0.454939 | + | 0.890523i | \(0.650339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.23369 | 0.267277 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 47.2119 | 1.53095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.7446 | 1.57899 | 0.789496 | − | 0.613756i | \(-0.210342\pi\) | ||||
0.789496 | + | 0.613756i | \(0.210342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.8614 | −0.804496 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.90491 | 0.0939023 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.9783 | −0.740464 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.74456 | −0.152733 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2337 | 1.16520 | 0.582598 | − | 0.812760i | \(-0.302036\pi\) | ||||
0.582598 | + | 0.812760i | \(0.302036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 122.190 | 3.92531 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.5109 | −0.337310 | −0.168655 | − | 0.985675i | \(-0.553942\pi\) | ||||
−0.168655 | + | 0.985675i | \(0.553942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.62772 | 0.148206 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.02175 | 0.224646 | 0.112323 | − | 0.993672i | \(-0.464171\pi\) | ||||
0.112323 | + | 0.993672i | \(0.464171\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.04350 | −0.0653105 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.9783 | −1.43605 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.62772 | 0.147601 | 0.0738007 | − | 0.997273i | \(-0.476487\pi\) | ||||
0.0738007 | + | 0.997273i | \(0.476487\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.2337 | 0.835875 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.5109 | 0.588612 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.9565 | 1.71398 | 0.856992 | − | 0.515329i | \(-0.172330\pi\) | ||||
0.856992 | + | 0.515329i | \(0.172330\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.4674 | 1.28419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1168 | 0.763788 | 0.381894 | − | 0.924206i | \(-0.375272\pi\) | ||||
0.381894 | + | 0.924206i | \(0.375272\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −36.2337 | −1.14638 |
(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 | 1960.2.a.s.1.2 | 2 | ||
4.3 | odd | 2 | 3920.2.a.bt.1.1 | 2 | |||
5.4 | even | 2 | 9800.2.a.bu.1.1 | 2 | |||
7.2 | even | 3 | 1960.2.q.r.361.1 | 4 | |||
7.3 | odd | 6 | 1960.2.q.t.961.2 | 4 | |||
7.4 | even | 3 | 1960.2.q.r.961.1 | 4 | |||
7.5 | odd | 6 | 1960.2.q.t.361.2 | 4 | |||
7.6 | odd | 2 | 280.2.a.c.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 2520.2.a.x.1.2 | 2 | |||
28.27 | even | 2 | 560.2.a.h.1.2 | 2 | |||
35.13 | even | 4 | 1400.2.g.i.449.1 | 4 | |||
35.27 | even | 4 | 1400.2.g.i.449.4 | 4 | |||
35.34 | odd | 2 | 1400.2.a.r.1.2 | 2 | |||
56.13 | odd | 2 | 2240.2.a.bk.1.2 | 2 | |||
56.27 | even | 2 | 2240.2.a.bg.1.1 | 2 | |||
84.83 | odd | 2 | 5040.2.a.by.1.1 | 2 | |||
140.27 | odd | 4 | 2800.2.g.r.449.1 | 4 | |||
140.83 | odd | 4 | 2800.2.g.r.449.4 | 4 | |||
140.139 | even | 2 | 2800.2.a.bk.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.c.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
560.2.a.h.1.2 | 2 | 28.27 | even | 2 | |||
1400.2.a.r.1.2 | 2 | 35.34 | odd | 2 | |||
1400.2.g.i.449.1 | 4 | 35.13 | even | 4 | |||
1400.2.g.i.449.4 | 4 | 35.27 | even | 4 | |||
1960.2.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1960.2.q.r.361.1 | 4 | 7.2 | even | 3 | |||
1960.2.q.r.961.1 | 4 | 7.4 | even | 3 | |||
1960.2.q.t.361.2 | 4 | 7.5 | odd | 6 | |||
1960.2.q.t.961.2 | 4 | 7.3 | odd | 6 | |||
2240.2.a.bg.1.1 | 2 | 56.27 | even | 2 | |||
2240.2.a.bk.1.2 | 2 | 56.13 | odd | 2 | |||
2520.2.a.x.1.2 | 2 | 21.20 | even | 2 | |||
2800.2.a.bk.1.1 | 2 | 140.139 | even | 2 | |||
2800.2.g.r.449.1 | 4 | 140.27 | odd | 4 | |||
2800.2.g.r.449.4 | 4 | 140.83 | odd | 4 | |||
3920.2.a.bt.1.1 | 2 | 4.3 | odd | 2 | |||
5040.2.a.by.1.1 | 2 | 84.83 | odd | 2 | |||
9800.2.a.bu.1.1 | 2 | 5.4 | even | 2 |