Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2800,2,Mod(1,2800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2800, 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("2800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2800.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: | \(22.3581125660\) |
Analytic rank: | \(1\) |
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 | 1.1 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2800.1 |
$q$-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 | \(-0.926548\pi\) | ||||
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.37228 | 2.79076 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.627719 | −0.189264 | −0.0946322 | − | 0.995512i | \(-0.530167\pi\) | ||||
−0.0946322 | + | 0.995512i | \(0.530167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37228 | 0.380602 | 0.190301 | − | 0.981726i | \(-0.439054\pi\) | ||||
0.190301 | + | 0.981726i | \(0.439054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | ||||||||
\(21\) | 3.37228 | 0.735892 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.74456 | 1.40634 | 0.703169 | − | 0.711022i | \(-0.251768\pi\) | ||||
0.703169 | + | 0.711022i | \(0.251768\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 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 | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.62772 | −0.741028 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.74456 | −0.740976 | −0.370488 | − | 0.928837i | \(-0.620810\pi\) | ||||
−0.370488 | + | 0.928837i | \(0.620810\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.74456 | 0.418542 | 0.209271 | − | 0.977858i | \(-0.432891\pi\) | ||||
0.209271 | + | 0.977858i | \(0.432891\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.1168 | 1.47569 | 0.737847 | − | 0.674968i | \(-0.235843\pi\) | ||||
0.737847 | + | 0.674968i | \(0.235843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.1168 | 2.53687 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.744563 | 0.102274 | 0.0511368 | − | 0.998692i | \(-0.483716\pi\) | ||||
0.0511368 | + | 0.998692i | \(0.483716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | \(-0.310873\pi\) | ||||
0.559813 | + | 0.828619i | \(0.310873\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.37228 | −1.05481 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 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 | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.627719 | 0.0715352 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.11684 | 0.238164 | 0.119082 | − | 0.992884i | \(-0.462005\pi\) | ||||
0.119082 | + | 0.992884i | \(0.462005\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.9783 | 3.99758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.4891 | 1.48062 | 0.740312 | − | 0.672264i | \(-0.234678\pi\) | ||||
0.740312 | + | 0.672264i | \(0.234678\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.62772 | −0.496144 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.25544 | 0.345076 | 0.172538 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172538 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.37228 | −0.143854 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.9783 | −2.79751 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 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 | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.3723 | −1.12054 | −0.560272 | − | 0.828309i | \(-0.689303\pi\) | ||||
−0.560272 | + | 0.828309i | \(0.689303\pi\) | |||||||
\(104\) | 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 | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.4891 | 1.06217 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.37228 | 0.492476 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6060 | −0.964179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.0000 | 1.44267 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 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 | ||||||||
\(133\) | 6.74456 | 0.584828 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.25544 | −0.278131 | −0.139065 | − | 0.990283i | \(-0.544410\pi\) | ||||
−0.139065 | + | 0.990283i | \(0.544410\pi\) | |||||||
\(138\) | 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 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.37228 | −0.278141 | ||||||||
\(148\) | 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 | \(-0.472549\pi\) | ||||
0.0861332 | + | 0.996284i | \(0.472549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −44.9783 | −3.63628 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 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 | ||||||||
\(161\) | −6.74456 | −0.531546 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.25544 | −0.411638 | −0.205819 | − | 0.978590i | \(-0.565986\pi\) | ||||
−0.205819 | + | 0.978590i | \(0.565986\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.3723 | −0.880014 | −0.440007 | − | 0.897994i | \(-0.645024\pi\) | ||||
−0.440007 | + | 0.897994i | \(0.645024\pi\) | |||||||
\(168\) | 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 | \(-0.828751\pi\) | ||||
−0.858738 | + | 0.512416i | \(0.828751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.2337 | −1.35530 | −0.677650 | − | 0.735385i | \(-0.737001\pi\) | ||||
−0.677650 | + | 0.735385i | \(0.737001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.4891 | −2.17990 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.37228 | 0.246606 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.1168 | 1.31781 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.8614 | 1.79891 | 0.899454 | − | 0.437015i | \(-0.143964\pi\) | ||||
0.899454 | + | 0.437015i | \(0.143964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.74456 | 0.341521 | 0.170761 | − | 0.985313i | \(-0.445378\pi\) | ||||
0.170761 | + | 0.985313i | \(0.445378\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.2337 | −1.86907 | −0.934536 | − | 0.355867i | \(-0.884185\pi\) | ||||
−0.934536 | + | 0.355867i | \(0.884185\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −1.37228 | −0.0963153 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | \(-0.404021\pi\) | ||||
0.296978 | + | 0.954884i | \(0.404021\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 26.9783 | 1.84852 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.00000 | −0.543075 | ||||||||
\(218\) | 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 | \(-0.624342\pi\) | ||||
−0.380772 | + | 0.924669i | \(0.624342\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.86141 | −0.588152 | −0.294076 | − | 0.955782i | \(-0.595012\pi\) | ||||
−0.294076 | + | 0.955782i | \(0.595012\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.2337 | 1.46924 | 0.734622 | − | 0.678477i | \(-0.237360\pi\) | ||||
0.734622 | + | 0.678477i | \(0.237360\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.11684 | −0.139278 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.7446 | 0.834924 | 0.417462 | − | 0.908694i | \(-0.362920\pi\) | ||||
0.417462 | + | 0.908694i | \(0.362920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.13859 | −0.463701 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.3723 | −1.25309 | −0.626544 | − | 0.779386i | \(-0.715531\pi\) | ||||
−0.626544 | + | 0.779386i | \(0.715531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.0000 | 1.67481 | 0.837404 | − | 0.546585i | \(-0.184072\pi\) | ||||
0.837404 | + | 0.546585i | \(0.184072\pi\) | |||||||
\(242\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.510875 | 0.0318675 | 0.0159337 | − | 0.999873i | \(-0.494928\pi\) | ||||
0.0159337 | + | 0.999873i | \(0.494928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 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 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9783 | −0.671858 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.4891 | 0.819406 | 0.409703 | − | 0.912219i | \(-0.365632\pi\) | ||||
0.409703 | + | 0.912219i | \(0.365632\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.62772 | 0.280082 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9783 | 1.26046 | 0.630230 | − | 0.776408i | \(-0.282960\pi\) | ||||
0.630230 | + | 0.776408i | \(0.282960\pi\) | |||||||
\(278\) | 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 | \(-0.782877\pi\) | ||||
−0.776243 | + | 0.630434i | \(0.782877\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.74456 | 0.280063 | ||||||||
\(288\) | 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 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.3723 | 0.659887 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.25544 | 0.535256 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.74456 | −0.158194 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.2337 | 1.16240 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.8832 | 0.792354 | 0.396177 | − | 0.918174i | \(-0.370337\pi\) | ||||
0.396177 | + | 0.918174i | \(0.370337\pi\) | |||||||
\(308\) | 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 | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.1168 | 1.00186 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.1168 | −0.557760 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.7446 | 0.917596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4891 | −0.843746 | −0.421873 | − | 0.906655i | \(-0.638627\pi\) | ||||
−0.421873 | + | 0.906655i | \(0.638627\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.74456 | 0.366314 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.02175 | −0.271943 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | \(-0.529769\pi\) | ||||
−0.0933843 | + | 0.995630i | \(0.529769\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.1168 | −0.958845 | ||||||||
\(358\) | 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 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.86141 | −0.462562 | −0.231281 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231281 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −39.7228 | −2.06789 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.744563 | −0.0386558 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.2554 | 0.997009 | 0.498504 | − | 0.866887i | \(-0.333883\pi\) | ||||
0.498504 | + | 0.866887i | \(0.333883\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.88316 | 0.0969875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.9783 | −1.38214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.48913 | 0.280481 | 0.140241 | − | 0.990117i | \(-0.455212\pi\) | ||||
0.140241 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(384\) | 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 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.3723 | −1.87566 | −0.937831 | − | 0.347094i | \(-0.887169\pi\) | ||||
−0.937831 | + | 0.347094i | \(0.887169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.7446 | −1.13865 | ||||||||
\(400\) | 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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.25544 | −0.0622297 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.4891 | −0.568101 | −0.284050 | − | 0.958809i | \(-0.591678\pi\) | ||||
−0.284050 | + | 0.958809i | \(0.591678\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.9783 | 0.541517 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.74456 | −0.423179 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.90491 | 0.140250 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.6277 | −0.608256 | −0.304128 | − | 0.952631i | \(-0.598365\pi\) | ||||
−0.304128 | + | 0.952631i | \(0.598365\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9783 | 0.815923 | 0.407961 | − | 0.912999i | \(-0.366240\pi\) | ||||
0.407961 | + | 0.912999i | \(0.366240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 8.37228 | 0.398680 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.25544 | −0.249693 | −0.124847 | − | 0.992176i | \(-0.539844\pi\) | ||||
−0.124847 | + | 0.992176i | \(0.539844\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 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 | \(-0.628092\pi\) | ||||
−0.391639 | + | 0.920119i | \(0.628092\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 97.3288 | 4.54292 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.7446 | −0.593573 | −0.296787 | − | 0.954944i | \(-0.595915\pi\) | ||||
−0.296787 | + | 0.954944i | \(0.595915\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4891 | −1.37048 | −0.685238 | − | 0.728319i | \(-0.740302\pi\) | ||||
−0.685238 | + | 0.728319i | \(0.740302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.6060 | −1.46255 | −0.731275 | − | 0.682083i | \(-0.761074\pi\) | ||||
−0.731275 | + | 0.682083i | \(0.761074\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.2554 | 1.16371 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.72281 | −0.0792150 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | ||||||||
\(483\) | 22.7446 | 1.03491 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 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 | \(-0.632216\pi\) | ||||
−0.403528 | + | 0.914967i | \(0.632216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.37228 | −0.332031 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.13859 | −0.140503 | −0.0702514 | − | 0.997529i | \(-0.522380\pi\) | ||||
−0.0702514 | + | 0.997529i | \(0.522380\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 38.3505 | 1.71338 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.6277 | −0.563042 | −0.281521 | − | 0.959555i | \(-0.590839\pi\) | ||||
−0.281521 | + | 0.959555i | \(0.590839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.4891 | 1.66495 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.97825 | 0.220657 | 0.110329 | − | 0.993895i | \(-0.464810\pi\) | ||||
0.110329 | + | 0.993895i | \(0.464810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 122.190 | 5.39483 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 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 | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.4674 | 1.41970 | 0.709850 | − | 0.704353i | \(-0.248763\pi\) | ||||
0.709850 | + | 0.704353i | \(0.248763\pi\) | |||||||
\(524\) | 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 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 77.4891 | 3.34390 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.627719 | −0.0270378 | ||||||||
\(540\) | 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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 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 | ||||||||
\(553\) | −2.11684 | −0.0900174 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.2337 | 1.62001 | 0.810007 | − | 0.586421i | \(-0.199463\pi\) | ||||
0.810007 | + | 0.586421i | \(0.199463\pi\) | |||||||
\(558\) | 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 | \(-0.536901\pi\) | ||||
−0.115670 | + | 0.993288i | \(0.536901\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.9783 | −1.51094 | ||||||||
\(568\) | 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 | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −83.8397 | −3.50245 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 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 | ||||||||
\(581\) | −13.4891 | −0.559623 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.467376 | −0.0193567 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.9783 | 0.453121 | 0.226560 | − | 0.973997i | \(-0.427252\pi\) | ||||
0.226560 | + | 0.973997i | \(0.427252\pi\) | |||||||
\(588\) | 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 | \(-0.549662\pi\) | ||||
−0.155386 | + | 0.987854i | \(0.549662\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.4891 | 1.61080 | 0.805398 | − | 0.592735i | \(-0.201952\pi\) | ||||
0.805398 | + | 0.592735i | \(0.201952\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −33.4891 | −1.36378 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.6060 | −0.633427 | −0.316713 | − | 0.948521i | \(-0.602579\pi\) | ||||
−0.316713 | + | 0.948521i | \(0.602579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.62772 | 0.187525 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.8832 | 0.561652 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.4891 | 1.27183 | 0.635917 | − | 0.771758i | \(-0.280622\pi\) | ||||
0.635917 | + | 0.771758i | \(0.280622\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.00000 | 0.241551 | 0.120775 | − | 0.992680i | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | −3.25544 | −0.130426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 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 | \(-0.478618\pi\) | ||||
0.0671242 | + | 0.997745i | \(0.478618\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −29.0951 | −1.15643 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.37228 | 0.0543718 | ||||||||
\(638\) | 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 | \(-0.419900\pi\) | ||||
0.248994 | + | 0.968505i | \(0.419900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.0000 | −0.629025 | −0.314512 | − | 0.949253i | \(-0.601841\pi\) | ||||
−0.314512 | + | 0.949253i | \(0.601841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.02175 | 0.197121 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.9783 | 1.05736 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 50.2337 | 1.95980 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.11684 | −0.238278 | −0.119139 | − | 0.992878i | \(-0.538013\pi\) | ||||
−0.119139 | + | 0.992878i | \(0.538013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.25544 | 0.126622 | 0.0633109 | − | 0.997994i | \(-0.479834\pi\) | ||||
0.0633109 | + | 0.997994i | \(0.479834\pi\) | |||||||
\(662\) | 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 | \(-0.290602\pi\) | ||||
0.611412 | + | 0.791312i | \(0.290602\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.3505 | 1.39706 | 0.698532 | − | 0.715579i | \(-0.253837\pi\) | ||||
0.698532 | + | 0.715579i | \(0.253837\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8614 | 0.723834 | ||||||||
\(680\) | 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 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 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 | ||||||||
\(693\) | 5.25544 | 0.199638 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 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 | 0 | ||||||||
\(716\) | 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 | ||||||||
\(721\) | 11.3723 | 0.423526 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −87.6793 | −3.26083 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.0000 | 1.18681 | 0.593407 | − | 0.804902i | \(-0.297782\pi\) | ||||
0.593407 | + | 0.804902i | \(0.297782\pi\) | |||||||
\(728\) | 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 | \(-0.617431\pi\) | ||||
−0.360609 | + | 0.932717i | \(0.617431\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 112.935 | 4.13207 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.74456 | 0.100284 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.8614 | −1.78298 | −0.891489 | − | 0.453042i | \(-0.850339\pi\) | ||||
−0.891489 | + | 0.453042i | \(0.850339\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.7446 | −0.828858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2337 | 1.38963 | 0.694814 | − | 0.719190i | \(-0.255487\pi\) | ||||
0.694814 | + | 0.719190i | \(0.255487\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.2772 | 0.518229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.9783 | −1.48546 | −0.742730 | − | 0.669591i | \(-0.766469\pi\) | ||||
−0.742730 | + | 0.669591i | \(0.766469\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.37228 | 0.194490 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.9783 | −0.396402 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.4891 | −0.702796 | −0.351398 | − | 0.936226i | \(-0.614294\pi\) | ||||
−0.351398 | + | 0.936226i | \(0.614294\pi\) | |||||||
\(770\) | 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 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.74456 | 0.241960 | ||||||||
\(778\) | 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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8832 | −0.494881 | −0.247441 | − | 0.968903i | \(-0.579589\pi\) | ||||
−0.247441 | + | 0.968903i | \(0.579589\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.2554 | 1.46873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.5109 | −0.647614 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −11.4891 | −0.401463 | ||||||||
\(820\) | 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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | \(-0.373821\pi\) | ||||
0.386104 | + | 0.922455i | \(0.373821\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −70.7446 | −2.45410 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.37228 | −0.186139 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6060 | 0.364425 | ||||||||
\(848\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | ||||||||
\(861\) | −16.0000 | −0.545279 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.51087 | 0.0854712 | 0.0427356 | − | 0.999086i | \(-0.486393\pi\) | ||||
0.0427356 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 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 | \(-0.147550\pi\) | ||||
0.894474 | + | 0.447120i | \(0.147550\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.5842 | 0.896663 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.7446 | −1.23796 | −0.618978 | − | 0.785408i | \(-0.712453\pi\) | ||||
−0.618978 | + | 0.785408i | \(0.712453\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.4891 | −1.12700 | −0.563499 | − | 0.826116i | \(-0.690545\pi\) | ||||
−0.563499 | + | 0.826116i | \(0.690545\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −58.9783 | −1.98030 | −0.990148 | − | 0.140025i | \(-0.955282\pi\) | ||||
−0.990148 | + | 0.140025i | \(0.955282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.5842 | −0.756600 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −68.2337 | −2.28335 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 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 | ||||||||
\(903\) | 9.25544 | 0.308002 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 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 | \(-0.775440\pi\) | ||||
−0.761303 | + | 0.648396i | \(0.775440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.46738 | −0.280229 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.74456 | 0.222725 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.3723 | −0.639033 | −0.319516 | − | 0.947581i | \(-0.603520\pi\) | ||||
−0.319516 | + | 0.947581i | \(0.603520\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −46.8179 | −1.54270 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9783 | −0.361354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −95.2119 | −3.12717 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.2337 | −1.38564 | −0.692821 | − | 0.721109i | \(-0.743632\pi\) | ||||
−0.692821 | + | 0.721109i | \(0.743632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.74456 | −0.221044 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.23369 | −0.138605 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 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 | \(-0.511592\pi\) | ||||
−0.0364081 | + | 0.999337i | \(0.511592\pi\) | |||||||
\(942\) | 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 | \(-0.789658\pi\) | ||||
−0.789496 | + | 0.613756i | \(0.789658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.90491 | 0.0939023 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.25544 | 0.105124 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.9783 | −0.740464 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 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 | ||||||||
\(973\) | 6.74456 | 0.216221 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.02175 | −0.224646 | −0.112323 | − | 0.993672i | \(-0.535829\pi\) | ||||
−0.112323 | + | 0.993672i | \(0.535829\pi\) | |||||||
\(978\) | 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 | \(-0.523513\pi\) | ||||
−0.0738007 | + | 0.997273i | \(0.523513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 34.1168 | 1.08595 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.5109 | 0.588612 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.9565 | −1.71398 | −0.856992 | − | 0.515329i | \(-0.827670\pi\) | ||||
−0.856992 | + | 0.515329i | \(0.827670\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.4674 | 1.28419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 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 | 2800.2.a.bk.1.1 | 2 | ||
4.3 | odd | 2 | 1400.2.a.r.1.2 | 2 | |||
5.2 | odd | 4 | 2800.2.g.r.449.4 | 4 | |||
5.3 | odd | 4 | 2800.2.g.r.449.1 | 4 | |||
5.4 | even | 2 | 560.2.a.h.1.2 | 2 | |||
15.14 | odd | 2 | 5040.2.a.by.1.1 | 2 | |||
20.3 | even | 4 | 1400.2.g.i.449.4 | 4 | |||
20.7 | even | 4 | 1400.2.g.i.449.1 | 4 | |||
20.19 | odd | 2 | 280.2.a.c.1.1 | ✓ | 2 | ||
28.27 | even | 2 | 9800.2.a.bu.1.1 | 2 | |||
35.34 | odd | 2 | 3920.2.a.bt.1.1 | 2 | |||
40.19 | odd | 2 | 2240.2.a.bk.1.2 | 2 | |||
40.29 | even | 2 | 2240.2.a.bg.1.1 | 2 | |||
60.59 | even | 2 | 2520.2.a.x.1.2 | 2 | |||
140.19 | even | 6 | 1960.2.q.r.361.1 | 4 | |||
140.39 | odd | 6 | 1960.2.q.t.961.2 | 4 | |||
140.59 | even | 6 | 1960.2.q.r.961.1 | 4 | |||
140.79 | odd | 6 | 1960.2.q.t.361.2 | 4 | |||
140.139 | even | 2 | 1960.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.c.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
560.2.a.h.1.2 | 2 | 5.4 | even | 2 | |||
1400.2.a.r.1.2 | 2 | 4.3 | odd | 2 | |||
1400.2.g.i.449.1 | 4 | 20.7 | even | 4 | |||
1400.2.g.i.449.4 | 4 | 20.3 | even | 4 | |||
1960.2.a.s.1.2 | 2 | 140.139 | even | 2 | |||
1960.2.q.r.361.1 | 4 | 140.19 | even | 6 | |||
1960.2.q.r.961.1 | 4 | 140.59 | even | 6 | |||
1960.2.q.t.361.2 | 4 | 140.79 | odd | 6 | |||
1960.2.q.t.961.2 | 4 | 140.39 | odd | 6 | |||
2240.2.a.bg.1.1 | 2 | 40.29 | even | 2 | |||
2240.2.a.bk.1.2 | 2 | 40.19 | odd | 2 | |||
2520.2.a.x.1.2 | 2 | 60.59 | even | 2 | |||
2800.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2800.2.g.r.449.1 | 4 | 5.3 | odd | 4 | |||
2800.2.g.r.449.4 | 4 | 5.2 | odd | 4 | |||
3920.2.a.bt.1.1 | 2 | 35.34 | odd | 2 | |||
5040.2.a.by.1.1 | 2 | 15.14 | odd | 2 | |||
9800.2.a.bu.1.1 | 2 | 28.27 | even | 2 |