Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7350,2,Mod(1,7350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7350.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7350.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: | \(58.6900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1470) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.16053\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7350.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.46967 | 1.34766 | 0.673828 | − | 0.738889i | \(-0.264649\pi\) | ||||
0.673828 | + | 0.738889i | \(0.264649\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.88388 | 1.63189 | 0.815947 | − | 0.578126i | \(-0.196216\pi\) | ||||
0.815947 | + | 0.578126i | \(0.196216\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.73528 | −1.87608 | −0.938040 | − | 0.346527i | \(-0.887361\pi\) | ||||
−0.938040 | + | 0.346527i | \(0.887361\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.61827 | 1.51834 | 0.759168 | − | 0.650895i | \(-0.225606\pi\) | ||||
0.759168 | + | 0.650895i | \(0.225606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.46967 | −0.952936 | ||||||||
\(23\) | 2.61827 | 0.545947 | 0.272974 | − | 0.962022i | \(-0.411993\pi\) | ||||
0.272974 | + | 0.962022i | \(0.411993\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.88388 | −1.15392 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.17246 | −1.51759 | −0.758794 | − | 0.651331i | \(-0.774211\pi\) | ||||
−0.758794 | + | 0.651331i | \(0.774211\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.46967 | 1.52120 | 0.760598 | − | 0.649223i | \(-0.224906\pi\) | ||||
0.760598 | + | 0.649223i | \(0.224906\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.46967 | −0.778069 | ||||||||
\(34\) | 7.73528 | 1.32659 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.18719 | 0.523970 | 0.261985 | − | 0.965072i | \(-0.415623\pi\) | ||||
0.261985 | + | 0.965072i | \(0.415623\pi\) | |||||||
\(38\) | −6.61827 | −1.07363 | ||||||||
\(39\) | −5.88388 | −0.942175 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.56282 | 0.556419 | 0.278209 | − | 0.960520i | \(-0.410259\pi\) | ||||
0.278209 | + | 0.960520i | \(0.410259\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.43108 | 0.218238 | 0.109119 | − | 0.994029i | \(-0.465197\pi\) | ||||
0.109119 | + | 0.994029i | \(0.465197\pi\) | |||||||
\(44\) | 4.46967 | 0.673828 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.61827 | −0.386043 | ||||||||
\(47\) | 6.79073 | 0.990530 | 0.495265 | − | 0.868742i | \(-0.335071\pi\) | ||||
0.495265 | + | 0.868742i | \(0.335071\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.73528 | 1.08316 | ||||||||
\(52\) | 5.88388 | 0.815947 | ||||||||
\(53\) | −1.38173 | −0.189795 | −0.0948976 | − | 0.995487i | \(-0.530252\pi\) | ||||
−0.0948976 | + | 0.995487i | \(0.530252\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.61827 | −0.876611 | ||||||||
\(58\) | 8.17246 | 1.07310 | ||||||||
\(59\) | 4.66421 | 0.607228 | 0.303614 | − | 0.952795i | \(-0.401807\pi\) | ||||
0.303614 | + | 0.952795i | \(0.401807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.79683 | 1.25436 | 0.627178 | − | 0.778876i | \(-0.284210\pi\) | ||||
0.627178 | + | 0.778876i | \(0.284210\pi\) | |||||||
\(62\) | −8.46967 | −1.07565 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.46967 | 0.550178 | ||||||||
\(67\) | 1.85140 | 0.226184 | 0.113092 | − | 0.993585i | \(-0.463925\pi\) | ||||
0.113092 | + | 0.993585i | \(0.463925\pi\) | |||||||
\(68\) | −7.73528 | −0.938040 | ||||||||
\(69\) | −2.61827 | −0.315203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.02386 | 0.240187 | 0.120094 | − | 0.992763i | \(-0.461680\pi\) | ||||
0.120094 | + | 0.992763i | \(0.461680\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 4.01687 | 0.470139 | 0.235069 | − | 0.971979i | \(-0.424468\pi\) | ||||
0.235069 | + | 0.971979i | \(0.424468\pi\) | |||||||
\(74\) | −3.18719 | −0.370503 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.61827 | 0.759168 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.88388 | 0.666218 | ||||||||
\(79\) | −6.98527 | −0.785904 | −0.392952 | − | 0.919559i | \(-0.628546\pi\) | ||||
−0.392952 | + | 0.919559i | \(0.628546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.56282 | −0.393447 | ||||||||
\(83\) | 5.35965 | 0.588298 | 0.294149 | − | 0.955760i | \(-0.404964\pi\) | ||||
0.294149 | + | 0.955760i | \(0.404964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.43108 | −0.154318 | ||||||||
\(87\) | 8.17246 | 0.876180 | ||||||||
\(88\) | −4.46967 | −0.476468 | ||||||||
\(89\) | 14.3912 | 1.52547 | 0.762734 | − | 0.646712i | \(-0.223856\pi\) | ||||
0.762734 | + | 0.646712i | \(0.223856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.61827 | 0.272974 | ||||||||
\(93\) | −8.46967 | −0.878263 | ||||||||
\(94\) | −6.79073 | −0.700410 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.71966 | −0.783813 | −0.391906 | − | 0.920005i | \(-0.628184\pi\) | ||||
−0.391906 | + | 0.920005i | \(0.628184\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.46967 | 0.449218 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3544 | −1.32882 | −0.664408 | − | 0.747370i | \(-0.731316\pi\) | ||||
−0.664408 | + | 0.747370i | \(0.731316\pi\) | |||||||
\(102\) | −7.73528 | −0.765906 | ||||||||
\(103\) | −9.35965 | −0.922233 | −0.461117 | − | 0.887339i | \(-0.652551\pi\) | ||||
−0.461117 | + | 0.887339i | \(0.652551\pi\) | |||||||
\(104\) | −5.88388 | −0.576962 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.38173 | 0.134205 | ||||||||
\(107\) | 11.0165 | 1.06501 | 0.532503 | − | 0.846428i | \(-0.321252\pi\) | ||||
0.532503 | + | 0.846428i | \(0.321252\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −4.69544 | −0.449741 | −0.224871 | − | 0.974389i | \(-0.572196\pi\) | ||||
−0.224871 | + | 0.974389i | \(0.572196\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.18719 | −0.302514 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5723 | −1.18271 | −0.591353 | − | 0.806413i | \(-0.701406\pi\) | ||||
−0.591353 | + | 0.806413i | \(0.701406\pi\) | |||||||
\(114\) | 6.61827 | 0.619858 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.17246 | −0.758794 | ||||||||
\(117\) | 5.88388 | 0.543965 | ||||||||
\(118\) | −4.66421 | −0.429375 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.97792 | 0.816174 | ||||||||
\(122\) | −9.79683 | −0.886963 | ||||||||
\(123\) | −3.56282 | −0.321248 | ||||||||
\(124\) | 8.46967 | 0.760598 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.59619 | −0.585317 | −0.292658 | − | 0.956217i | \(-0.594540\pi\) | ||||
−0.292658 | + | 0.956217i | \(0.594540\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.43108 | −0.126000 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.32106 | −0.202792 | −0.101396 | − | 0.994846i | \(-0.532331\pi\) | ||||
−0.101396 | + | 0.994846i | \(0.532331\pi\) | |||||||
\(132\) | −4.46967 | −0.389035 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.85140 | −0.159936 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.73528 | 0.663294 | ||||||||
\(137\) | −14.2751 | −1.21961 | −0.609803 | − | 0.792553i | \(-0.708751\pi\) | ||||
−0.609803 | + | 0.792553i | \(0.708751\pi\) | |||||||
\(138\) | 2.61827 | 0.222882 | ||||||||
\(139\) | −14.9632 | −1.26916 | −0.634581 | − | 0.772857i | \(-0.718827\pi\) | ||||
−0.634581 | + | 0.772857i | \(0.718827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.79073 | −0.571883 | ||||||||
\(142\) | −2.02386 | −0.169838 | ||||||||
\(143\) | 26.2990 | 2.19923 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.01687 | −0.332438 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.18719 | 0.261985 | ||||||||
\(149\) | 11.1651 | 0.914681 | 0.457341 | − | 0.889292i | \(-0.348802\pi\) | ||||
0.457341 | + | 0.889292i | \(0.348802\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.664208 | 0.0540525 | 0.0270263 | − | 0.999635i | \(-0.491396\pi\) | ||||
0.0270263 | + | 0.999635i | \(0.491396\pi\) | |||||||
\(152\) | −6.61827 | −0.536813 | ||||||||
\(153\) | −7.73528 | −0.625360 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.88388 | −0.471087 | ||||||||
\(157\) | −8.08184 | −0.645001 | −0.322500 | − | 0.946569i | \(-0.604523\pi\) | ||||
−0.322500 | + | 0.946569i | \(0.604523\pi\) | |||||||
\(158\) | 6.98527 | 0.555718 | ||||||||
\(159\) | 1.38173 | 0.109578 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.836668 | −0.0655329 | −0.0327664 | − | 0.999463i | \(-0.510432\pi\) | ||||
−0.0327664 | + | 0.999463i | \(0.510432\pi\) | |||||||
\(164\) | 3.56282 | 0.278209 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.35965 | −0.415989 | ||||||||
\(167\) | 2.66762 | 0.206427 | 0.103213 | − | 0.994659i | \(-0.467088\pi\) | ||||
0.103213 | + | 0.994659i | \(0.467088\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.6200 | 1.66308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.61827 | 0.506112 | ||||||||
\(172\) | 1.43108 | 0.109119 | ||||||||
\(173\) | 0.647340 | 0.0492164 | 0.0246082 | − | 0.999697i | \(-0.492166\pi\) | ||||
0.0246082 | + | 0.999697i | \(0.492166\pi\) | |||||||
\(174\) | −8.17246 | −0.619553 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.46967 | 0.336914 | ||||||||
\(177\) | −4.66421 | −0.350583 | ||||||||
\(178\) | −14.3912 | −1.07867 | ||||||||
\(179\) | −25.7374 | −1.92371 | −0.961853 | − | 0.273566i | \(-0.911797\pi\) | ||||
−0.961853 | + | 0.273566i | \(0.911797\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.42245 | 0.551707 | 0.275853 | − | 0.961200i | \(-0.411040\pi\) | ||||
0.275853 | + | 0.961200i | \(0.411040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.79683 | −0.724203 | ||||||||
\(184\) | −2.61827 | −0.193021 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.46967 | 0.621026 | ||||||||
\(187\) | −34.5741 | −2.52831 | ||||||||
\(188\) | 6.79073 | 0.495265 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.08452 | −0.0784733 | −0.0392367 | − | 0.999230i | \(-0.512493\pi\) | ||||
−0.0392367 | + | 0.999230i | \(0.512493\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −8.93933 | −0.643467 | −0.321734 | − | 0.946830i | \(-0.604266\pi\) | ||||
−0.321734 | + | 0.946830i | \(0.604266\pi\) | |||||||
\(194\) | 7.71966 | 0.554239 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.45890 | −0.531425 | −0.265712 | − | 0.964052i | \(-0.585607\pi\) | ||||
−0.265712 | + | 0.964052i | \(0.585607\pi\) | |||||||
\(198\) | −4.46967 | −0.317645 | ||||||||
\(199\) | 25.8293 | 1.83099 | 0.915496 | − | 0.402328i | \(-0.131799\pi\) | ||||
0.915496 | + | 0.402328i | \(0.131799\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.85140 | −0.130587 | ||||||||
\(202\) | 13.3544 | 0.939615 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.73528 | 0.541578 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.35965 | 0.652118 | ||||||||
\(207\) | 2.61827 | 0.181982 | ||||||||
\(208\) | 5.88388 | 0.407974 | ||||||||
\(209\) | 29.5815 | 2.04619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.53375 | 0.380959 | 0.190479 | − | 0.981691i | \(-0.438996\pi\) | ||||
0.190479 | + | 0.981691i | \(0.438996\pi\) | |||||||
\(212\) | −1.38173 | −0.0948976 | ||||||||
\(213\) | −2.02386 | −0.138672 | ||||||||
\(214\) | −11.0165 | −0.753073 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.69544 | 0.318015 | ||||||||
\(219\) | −4.01687 | −0.271435 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −45.5134 | −3.06157 | ||||||||
\(222\) | 3.18719 | 0.213910 | ||||||||
\(223\) | −3.28248 | −0.219811 | −0.109906 | − | 0.993942i | \(-0.535055\pi\) | ||||
−0.109906 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.5723 | 0.836299 | ||||||||
\(227\) | −4.42031 | −0.293387 | −0.146693 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146693 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(228\) | −6.61827 | −0.438306 | ||||||||
\(229\) | −7.97270 | −0.526851 | −0.263426 | − | 0.964680i | \(-0.584852\pi\) | ||||
−0.263426 | + | 0.964680i | \(0.584852\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.17246 | 0.536548 | ||||||||
\(233\) | 17.9558 | 1.17633 | 0.588163 | − | 0.808742i | \(-0.299851\pi\) | ||||
0.588163 | + | 0.808742i | \(0.299851\pi\) | |||||||
\(234\) | −5.88388 | −0.384641 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.66421 | 0.303614 | ||||||||
\(237\) | 6.98527 | 0.453742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.41296 | 0.350135 | 0.175068 | − | 0.984556i | \(-0.443986\pi\) | ||||
0.175068 | + | 0.984556i | \(0.443986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.69669 | −0.302541 | −0.151270 | − | 0.988492i | \(-0.548336\pi\) | ||||
−0.151270 | + | 0.988492i | \(0.548336\pi\) | |||||||
\(242\) | −8.97792 | −0.577122 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.79683 | 0.627178 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.56282 | 0.227157 | ||||||||
\(247\) | 38.9411 | 2.47776 | ||||||||
\(248\) | −8.46967 | −0.537824 | ||||||||
\(249\) | −5.35965 | −0.339654 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.73402 | 0.488167 | 0.244084 | − | 0.969754i | \(-0.421513\pi\) | ||||
0.244084 | + | 0.969754i | \(0.421513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.7028 | 0.735748 | ||||||||
\(254\) | 6.59619 | 0.413882 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.34442 | 0.0838626 | 0.0419313 | − | 0.999120i | \(-0.486649\pi\) | ||||
0.0419313 | + | 0.999120i | \(0.486649\pi\) | |||||||
\(258\) | 1.43108 | 0.0890953 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.17246 | −0.505863 | ||||||||
\(262\) | 2.32106 | 0.143396 | ||||||||
\(263\) | −4.36700 | −0.269281 | −0.134640 | − | 0.990895i | \(-0.542988\pi\) | ||||
−0.134640 | + | 0.990895i | \(0.542988\pi\) | |||||||
\(264\) | 4.46967 | 0.275089 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.3912 | −0.880730 | ||||||||
\(268\) | 1.85140 | 0.113092 | ||||||||
\(269\) | 23.0671 | 1.40643 | 0.703213 | − | 0.710979i | \(-0.251748\pi\) | ||||
0.703213 | + | 0.710979i | \(0.251748\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.7209 | 0.894233 | 0.447117 | − | 0.894476i | \(-0.352451\pi\) | ||||
0.447117 | + | 0.894476i | \(0.352451\pi\) | |||||||
\(272\) | −7.73528 | −0.469020 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.2751 | 0.862392 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.61827 | −0.157601 | ||||||||
\(277\) | −3.21104 | −0.192933 | −0.0964665 | − | 0.995336i | \(-0.530754\pi\) | ||||
−0.0964665 | + | 0.995336i | \(0.530754\pi\) | |||||||
\(278\) | 14.9632 | 0.897432 | ||||||||
\(279\) | 8.46967 | 0.507066 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.72488 | −0.460827 | −0.230414 | − | 0.973093i | \(-0.574008\pi\) | ||||
−0.230414 | + | 0.973093i | \(0.574008\pi\) | |||||||
\(282\) | 6.79073 | 0.404382 | ||||||||
\(283\) | −29.5594 | −1.75712 | −0.878561 | − | 0.477630i | \(-0.841496\pi\) | ||||
−0.878561 | + | 0.477630i | \(0.841496\pi\) | |||||||
\(284\) | 2.02386 | 0.120094 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −26.2990 | −1.55509 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 42.8345 | 2.51968 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.71966 | 0.452535 | ||||||||
\(292\) | 4.01687 | 0.235069 | ||||||||
\(293\) | 1.17679 | 0.0687487 | 0.0343743 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343743 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.18719 | −0.185252 | ||||||||
\(297\) | −4.46967 | −0.259356 | ||||||||
\(298\) | −11.1651 | −0.646777 | ||||||||
\(299\) | 15.4056 | 0.890928 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.664208 | −0.0382209 | ||||||||
\(303\) | 13.3544 | 0.767192 | ||||||||
\(304\) | 6.61827 | 0.379584 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.73528 | 0.442196 | ||||||||
\(307\) | 20.3761 | 1.16293 | 0.581464 | − | 0.813572i | \(-0.302480\pi\) | ||||
0.581464 | + | 0.813572i | \(0.302480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.35965 | 0.532452 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8934 | −1.07135 | −0.535673 | − | 0.844425i | \(-0.679942\pi\) | ||||
−0.535673 | + | 0.844425i | \(0.679942\pi\) | |||||||
\(312\) | 5.88388 | 0.333109 | ||||||||
\(313\) | 16.4849 | 0.931781 | 0.465891 | − | 0.884842i | \(-0.345734\pi\) | ||||
0.465891 | + | 0.884842i | \(0.345734\pi\) | |||||||
\(314\) | 8.08184 | 0.456084 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.98527 | −0.392952 | ||||||||
\(317\) | −10.3211 | −0.579689 | −0.289844 | − | 0.957074i | \(-0.593604\pi\) | ||||
−0.289844 | + | 0.957074i | \(0.593604\pi\) | |||||||
\(318\) | −1.38173 | −0.0774836 | ||||||||
\(319\) | −36.5282 | −2.04518 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0165 | −0.614881 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −51.1941 | −2.84852 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.836668 | 0.0463387 | ||||||||
\(327\) | 4.69544 | 0.259658 | ||||||||
\(328\) | −3.56282 | −0.196724 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.1906 | −1.05481 | −0.527405 | − | 0.849614i | \(-0.676835\pi\) | ||||
−0.527405 | + | 0.849614i | \(0.676835\pi\) | |||||||
\(332\) | 5.35965 | 0.294149 | ||||||||
\(333\) | 3.18719 | 0.174657 | ||||||||
\(334\) | −2.66762 | −0.145966 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6035 | 1.50366 | 0.751830 | − | 0.659357i | \(-0.229171\pi\) | ||||
0.751830 | + | 0.659357i | \(0.229171\pi\) | |||||||
\(338\) | −21.6200 | −1.17598 | ||||||||
\(339\) | 12.5723 | 0.682835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.8566 | 2.05005 | ||||||||
\(342\) | −6.61827 | −0.357875 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.43108 | −0.0771588 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.647340 | −0.0348012 | ||||||||
\(347\) | 20.3761 | 1.09385 | 0.546924 | − | 0.837182i | \(-0.315798\pi\) | ||||
0.546924 | + | 0.837182i | \(0.315798\pi\) | |||||||
\(348\) | 8.17246 | 0.438090 | ||||||||
\(349\) | −17.8281 | −0.954314 | −0.477157 | − | 0.878818i | \(-0.658333\pi\) | ||||
−0.477157 | + | 0.878818i | \(0.658333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.88388 | −0.314058 | ||||||||
\(352\) | −4.46967 | −0.238234 | ||||||||
\(353\) | 3.51347 | 0.187003 | 0.0935014 | − | 0.995619i | \(-0.470194\pi\) | ||||
0.0935014 | + | 0.995619i | \(0.470194\pi\) | |||||||
\(354\) | 4.66421 | 0.247900 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.3912 | 0.762734 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.7374 | 1.36027 | ||||||||
\(359\) | −2.19796 | −0.116004 | −0.0580018 | − | 0.998316i | \(-0.518473\pi\) | ||||
−0.0580018 | + | 0.998316i | \(0.518473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.8015 | 1.30534 | ||||||||
\(362\) | −7.42245 | −0.390116 | ||||||||
\(363\) | −8.97792 | −0.471218 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.79683 | 0.512089 | ||||||||
\(367\) | 28.7721 | 1.50189 | 0.750945 | − | 0.660365i | \(-0.229598\pi\) | ||||
0.750945 | + | 0.660365i | \(0.229598\pi\) | |||||||
\(368\) | 2.61827 | 0.136487 | ||||||||
\(369\) | 3.56282 | 0.185473 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.46967 | −0.439132 | ||||||||
\(373\) | 14.5689 | 0.754350 | 0.377175 | − | 0.926142i | \(-0.376896\pi\) | ||||
0.377175 | + | 0.926142i | \(0.376896\pi\) | |||||||
\(374\) | 34.5741 | 1.78778 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.79073 | −0.350205 | ||||||||
\(377\) | −48.0858 | −2.47654 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.7868 | −1.58141 | −0.790705 | − | 0.612197i | \(-0.790286\pi\) | ||||
−0.790705 | + | 0.612197i | \(0.790286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.59619 | 0.337933 | ||||||||
\(382\) | 1.08452 | 0.0554890 | ||||||||
\(383\) | 23.3410 | 1.19267 | 0.596334 | − | 0.802736i | \(-0.296623\pi\) | ||||
0.596334 | + | 0.802736i | \(0.296623\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.93933 | 0.455000 | ||||||||
\(387\) | 1.43108 | 0.0727460 | ||||||||
\(388\) | −7.71966 | −0.391906 | ||||||||
\(389\) | −1.21842 | −0.0617762 | −0.0308881 | − | 0.999523i | \(-0.509834\pi\) | ||||
−0.0308881 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.2530 | −1.02424 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.32106 | 0.117082 | ||||||||
\(394\) | 7.45890 | 0.375774 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.46967 | 0.224609 | ||||||||
\(397\) | 8.40595 | 0.421883 | 0.210941 | − | 0.977499i | \(-0.432347\pi\) | ||||
0.210941 | + | 0.977499i | \(0.432347\pi\) | |||||||
\(398\) | −25.8293 | −1.29471 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.664208 | −0.0331690 | −0.0165845 | − | 0.999862i | \(-0.505279\pi\) | ||||
−0.0165845 | + | 0.999862i | \(0.505279\pi\) | |||||||
\(402\) | 1.85140 | 0.0923393 | ||||||||
\(403\) | 49.8345 | 2.48243 | ||||||||
\(404\) | −13.3544 | −0.664408 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.2457 | 0.706131 | ||||||||
\(408\) | −7.73528 | −0.382953 | ||||||||
\(409\) | −7.38476 | −0.365153 | −0.182576 | − | 0.983192i | \(-0.558444\pi\) | ||||
−0.182576 | + | 0.983192i | \(0.558444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.2751 | 0.704140 | ||||||||
\(412\) | −9.35965 | −0.461117 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.61827 | −0.128681 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.88388 | −0.288481 | ||||||||
\(417\) | 14.9632 | 0.732750 | ||||||||
\(418\) | −29.5815 | −1.44688 | ||||||||
\(419\) | 18.6274 | 0.910009 | 0.455004 | − | 0.890489i | \(-0.349638\pi\) | ||||
0.455004 | + | 0.890489i | \(0.349638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5043 | −0.658159 | −0.329079 | − | 0.944302i | \(-0.606738\pi\) | ||||
−0.329079 | + | 0.944302i | \(0.606738\pi\) | |||||||
\(422\) | −5.53375 | −0.269379 | ||||||||
\(423\) | 6.79073 | 0.330177 | ||||||||
\(424\) | 1.38173 | 0.0671027 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.02386 | 0.0980561 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.0165 | 0.532503 | ||||||||
\(429\) | −26.2990 | −1.26973 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.6807 | −1.52601 | −0.763003 | − | 0.646395i | \(-0.776276\pi\) | ||||
−0.763003 | + | 0.646395i | \(0.776276\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 25.3184 | 1.21672 | 0.608362 | − | 0.793660i | \(-0.291827\pi\) | ||||
0.608362 | + | 0.793660i | \(0.291827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.69544 | −0.224871 | ||||||||
\(437\) | 17.3284 | 0.828931 | ||||||||
\(438\) | 4.01687 | 0.191933 | ||||||||
\(439\) | 32.8146 | 1.56615 | 0.783077 | − | 0.621924i | \(-0.213649\pi\) | ||||
0.783077 | + | 0.621924i | \(0.213649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 45.5134 | 2.16485 | ||||||||
\(443\) | −16.6421 | −0.790691 | −0.395346 | − | 0.918532i | \(-0.629375\pi\) | ||||
−0.395346 | + | 0.918532i | \(0.629375\pi\) | |||||||
\(444\) | −3.18719 | −0.151257 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.28248 | 0.155430 | ||||||||
\(447\) | −11.1651 | −0.528091 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.1759 | 0.952158 | 0.476079 | − | 0.879402i | \(-0.342058\pi\) | ||||
0.476079 | + | 0.879402i | \(0.342058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.9246 | 0.749860 | ||||||||
\(452\) | −12.5723 | −0.591353 | ||||||||
\(453\) | −0.664208 | −0.0312072 | ||||||||
\(454\) | 4.42031 | 0.207456 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.61827 | 0.309929 | ||||||||
\(457\) | 35.4124 | 1.65652 | 0.828261 | − | 0.560342i | \(-0.189330\pi\) | ||||
0.828261 | + | 0.560342i | \(0.189330\pi\) | |||||||
\(458\) | 7.97270 | 0.372540 | ||||||||
\(459\) | 7.73528 | 0.361052 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.5940 | −0.586562 | −0.293281 | − | 0.956026i | \(-0.594747\pi\) | ||||
−0.293281 | + | 0.956026i | \(0.594747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.5061 | −1.51069 | −0.755343 | − | 0.655330i | \(-0.772530\pi\) | ||||
−0.755343 | + | 0.655330i | \(0.772530\pi\) | |||||||
\(464\) | −8.17246 | −0.379397 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9558 | −0.831788 | ||||||||
\(467\) | −9.20531 | −0.425971 | −0.212985 | − | 0.977055i | \(-0.568319\pi\) | ||||
−0.212985 | + | 0.977055i | \(0.568319\pi\) | |||||||
\(468\) | 5.88388 | 0.271982 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.08184 | 0.372391 | ||||||||
\(472\) | −4.66421 | −0.214688 | ||||||||
\(473\) | 6.39646 | 0.294109 | ||||||||
\(474\) | −6.98527 | −0.320844 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.38173 | −0.0632651 | ||||||||
\(478\) | −5.41296 | −0.247583 | ||||||||
\(479\) | −39.4914 | −1.80441 | −0.902203 | − | 0.431312i | \(-0.858051\pi\) | ||||
−0.902203 | + | 0.431312i | \(0.858051\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.7530 | 0.855065 | ||||||||
\(482\) | 4.69669 | 0.213928 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.97792 | 0.408087 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 29.2678 | 1.32625 | 0.663125 | − | 0.748509i | \(-0.269230\pi\) | ||||
0.663125 | + | 0.748509i | \(0.269230\pi\) | |||||||
\(488\) | −9.79683 | −0.443482 | ||||||||
\(489\) | 0.836668 | 0.0378354 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3631 | 0.693325 | 0.346663 | − | 0.937990i | \(-0.387315\pi\) | ||||
0.346663 | + | 0.937990i | \(0.387315\pi\) | |||||||
\(492\) | −3.56282 | −0.160624 | ||||||||
\(493\) | 63.2162 | 2.84712 | ||||||||
\(494\) | −38.9411 | −1.75204 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.46967 | 0.380299 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.35965 | 0.240172 | ||||||||
\(499\) | 20.5502 | 0.919955 | 0.459978 | − | 0.887930i | \(-0.347857\pi\) | ||||
0.459978 | + | 0.887930i | \(0.347857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.66762 | −0.119181 | ||||||||
\(502\) | −7.73402 | −0.345186 | ||||||||
\(503\) | −20.4788 | −0.913105 | −0.456553 | − | 0.889696i | \(-0.650916\pi\) | ||||
−0.456553 | + | 0.889696i | \(0.650916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.7028 | −0.520253 | ||||||||
\(507\) | −21.6200 | −0.960180 | ||||||||
\(508\) | −6.59619 | −0.292658 | ||||||||
\(509\) | 12.0702 | 0.535001 | 0.267501 | − | 0.963558i | \(-0.413802\pi\) | ||||
0.267501 | + | 0.963558i | \(0.413802\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.61827 | −0.292204 | ||||||||
\(514\) | −1.34442 | −0.0592998 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.43108 | −0.0629999 | ||||||||
\(517\) | 30.3523 | 1.33489 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.647340 | −0.0284151 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.7049 | 0.644235 | 0.322117 | − | 0.946700i | \(-0.395605\pi\) | ||||
0.322117 | + | 0.946700i | \(0.395605\pi\) | |||||||
\(522\) | 8.17246 | 0.357699 | ||||||||
\(523\) | −6.44417 | −0.281784 | −0.140892 | − | 0.990025i | \(-0.544997\pi\) | ||||
−0.140892 | + | 0.990025i | \(0.544997\pi\) | |||||||
\(524\) | −2.32106 | −0.101396 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.36700 | 0.190410 | ||||||||
\(527\) | −65.5152 | −2.85389 | ||||||||
\(528\) | −4.46967 | −0.194517 | ||||||||
\(529\) | −16.1447 | −0.701942 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.66421 | 0.202409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.9632 | 0.908016 | ||||||||
\(534\) | 14.3912 | 0.622770 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.85140 | −0.0799681 | ||||||||
\(537\) | 25.7374 | 1.11065 | ||||||||
\(538\) | −23.0671 | −0.994494 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.5815 | −0.497926 | −0.248963 | − | 0.968513i | \(-0.580090\pi\) | ||||
−0.248963 | + | 0.968513i | \(0.580090\pi\) | |||||||
\(542\) | −14.7209 | −0.632318 | ||||||||
\(543\) | −7.42245 | −0.318528 | ||||||||
\(544\) | 7.73528 | 0.331647 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.2656 | −0.823737 | −0.411868 | − | 0.911243i | \(-0.635124\pi\) | ||||
−0.411868 | + | 0.911243i | \(0.635124\pi\) | |||||||
\(548\) | −14.2751 | −0.609803 | ||||||||
\(549\) | 9.79683 | 0.418119 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.0875 | −2.30421 | ||||||||
\(552\) | 2.61827 | 0.111441 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.21104 | 0.136424 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.9632 | −0.634581 | ||||||||
\(557\) | −21.0404 | −0.891509 | −0.445754 | − | 0.895155i | \(-0.647064\pi\) | ||||
−0.445754 | + | 0.895155i | \(0.647064\pi\) | |||||||
\(558\) | −8.46967 | −0.358550 | ||||||||
\(559\) | 8.42031 | 0.356141 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 34.5741 | 1.45972 | ||||||||
\(562\) | 7.72488 | 0.325854 | ||||||||
\(563\) | −3.61092 | −0.152182 | −0.0760910 | − | 0.997101i | \(-0.524244\pi\) | ||||
−0.0760910 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(564\) | −6.79073 | −0.285941 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29.5594 | 1.24247 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.02386 | −0.0849191 | ||||||||
\(569\) | 33.2145 | 1.39242 | 0.696211 | − | 0.717837i | \(-0.254868\pi\) | ||||
0.696211 | + | 0.717837i | \(0.254868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.1776 | −1.34659 | −0.673296 | − | 0.739373i | \(-0.735122\pi\) | ||||
−0.673296 | + | 0.739373i | \(0.735122\pi\) | |||||||
\(572\) | 26.2990 | 1.09962 | ||||||||
\(573\) | 1.08452 | 0.0453066 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 34.1902 | 1.42336 | 0.711679 | − | 0.702505i | \(-0.247935\pi\) | ||||
0.711679 | + | 0.702505i | \(0.247935\pi\) | |||||||
\(578\) | −42.8345 | −1.78168 | ||||||||
\(579\) | 8.93933 | 0.371506 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.71966 | −0.319990 | ||||||||
\(583\) | −6.17587 | −0.255779 | ||||||||
\(584\) | −4.01687 | −0.166219 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.17679 | −0.0486126 | ||||||||
\(587\) | 34.5962 | 1.42794 | 0.713969 | − | 0.700178i | \(-0.246896\pi\) | ||||
0.713969 | + | 0.700178i | \(0.246896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.0545 | 2.30969 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.45890 | 0.306818 | ||||||||
\(592\) | 3.18719 | 0.130993 | ||||||||
\(593\) | −33.0845 | −1.35862 | −0.679309 | − | 0.733853i | \(-0.737720\pi\) | ||||
−0.679309 | + | 0.733853i | \(0.737720\pi\) | |||||||
\(594\) | 4.46967 | 0.183393 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.1651 | 0.457341 | ||||||||
\(597\) | −25.8293 | −1.05712 | ||||||||
\(598\) | −15.4056 | −0.629981 | ||||||||
\(599\) | 6.07485 | 0.248212 | 0.124106 | − | 0.992269i | \(-0.460394\pi\) | ||||
0.124106 | + | 0.992269i | \(0.460394\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7469 | −0.479167 | −0.239584 | − | 0.970876i | \(-0.577011\pi\) | ||||
−0.239584 | + | 0.970876i | \(0.577011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85140 | 0.0753947 | ||||||||
\(604\) | 0.664208 | 0.0270263 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −13.3544 | −0.542487 | ||||||||
\(607\) | −45.8180 | −1.85970 | −0.929848 | − | 0.367944i | \(-0.880062\pi\) | ||||
−0.929848 | + | 0.367944i | \(0.880062\pi\) | |||||||
\(608\) | −6.61827 | −0.268406 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.9558 | 1.61644 | ||||||||
\(612\) | −7.73528 | −0.312680 | ||||||||
\(613\) | 34.2514 | 1.38340 | 0.691701 | − | 0.722184i | \(-0.256862\pi\) | ||||
0.691701 | + | 0.722184i | \(0.256862\pi\) | |||||||
\(614\) | −20.3761 | −0.822314 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.8106 | −1.56246 | −0.781228 | − | 0.624245i | \(-0.785407\pi\) | ||||
−0.781228 | + | 0.624245i | \(0.785407\pi\) | |||||||
\(618\) | −9.35965 | −0.376500 | ||||||||
\(619\) | −4.27512 | −0.171832 | −0.0859159 | − | 0.996302i | \(-0.527382\pi\) | ||||
−0.0859159 | + | 0.996302i | \(0.527382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.61827 | −0.105068 | ||||||||
\(622\) | 18.8934 | 0.757556 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.88388 | −0.235544 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.4849 | −0.658869 | ||||||||
\(627\) | −29.5815 | −1.18137 | ||||||||
\(628\) | −8.08184 | −0.322500 | ||||||||
\(629\) | −24.6538 | −0.983011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.8419 | 1.46665 | 0.733326 | − | 0.679878i | \(-0.237967\pi\) | ||||
0.733326 | + | 0.679878i | \(0.237967\pi\) | |||||||
\(632\) | 6.98527 | 0.277859 | ||||||||
\(633\) | −5.53375 | −0.219947 | ||||||||
\(634\) | 10.3211 | 0.409902 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.38173 | 0.0547892 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36.5282 | 1.44616 | ||||||||
\(639\) | 2.02386 | 0.0800625 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.9043 | 1.97110 | 0.985551 | − | 0.169382i | \(-0.0541770\pi\) | ||||
0.985551 | + | 0.169382i | \(0.0541770\pi\) | |||||||
\(642\) | 11.0165 | 0.434787 | ||||||||
\(643\) | 29.0091 | 1.14401 | 0.572004 | − | 0.820251i | \(-0.306166\pi\) | ||||
0.572004 | + | 0.820251i | \(0.306166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 51.1941 | 2.01421 | ||||||||
\(647\) | 4.94329 | 0.194341 | 0.0971705 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971705 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 20.8475 | 0.818334 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.836668 | −0.0327664 | ||||||||
\(653\) | 9.40559 | 0.368069 | 0.184035 | − | 0.982920i | \(-0.441084\pi\) | ||||
0.184035 | + | 0.982920i | \(0.441084\pi\) | |||||||
\(654\) | −4.69544 | −0.183606 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.56282 | 0.139105 | ||||||||
\(657\) | 4.01687 | 0.156713 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4090 | 0.522340 | 0.261170 | − | 0.965293i | \(-0.415892\pi\) | ||||
0.261170 | + | 0.965293i | \(0.415892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2509 | 0.515400 | 0.257700 | − | 0.966225i | \(-0.417035\pi\) | ||||
0.257700 | + | 0.966225i | \(0.417035\pi\) | |||||||
\(662\) | 19.1906 | 0.745864 | ||||||||
\(663\) | 45.5134 | 1.76760 | ||||||||
\(664\) | −5.35965 | −0.207995 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.18719 | −0.123501 | ||||||||
\(667\) | −21.3977 | −0.828522 | ||||||||
\(668\) | 2.66762 | 0.103213 | ||||||||
\(669\) | 3.28248 | 0.126908 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.7886 | 1.69044 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.8236 | 0.841237 | 0.420619 | − | 0.907238i | \(-0.361813\pi\) | ||||
0.420619 | + | 0.907238i | \(0.361813\pi\) | |||||||
\(674\) | −27.6035 | −1.06325 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.6200 | 0.831540 | ||||||||
\(677\) | 41.0572 | 1.57796 | 0.788979 | − | 0.614421i | \(-0.210610\pi\) | ||||
0.788979 | + | 0.614421i | \(0.210610\pi\) | |||||||
\(678\) | −12.5723 | −0.482837 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.42031 | 0.169387 | ||||||||
\(682\) | −37.8566 | −1.44960 | ||||||||
\(683\) | 31.0642 | 1.18864 | 0.594320 | − | 0.804229i | \(-0.297421\pi\) | ||||
0.594320 | + | 0.804229i | \(0.297421\pi\) | |||||||
\(684\) | 6.61827 | 0.253056 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.97270 | 0.304178 | ||||||||
\(688\) | 1.43108 | 0.0545595 | ||||||||
\(689\) | −8.12993 | −0.309726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.0012 | −1.21738 | −0.608692 | − | 0.793407i | \(-0.708305\pi\) | ||||
−0.608692 | + | 0.793407i | \(0.708305\pi\) | |||||||
\(692\) | 0.647340 | 0.0246082 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.3761 | −0.773468 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.17246 | −0.309776 | ||||||||
\(697\) | −27.5594 | −1.04389 | ||||||||
\(698\) | 17.8281 | 0.674802 | ||||||||
\(699\) | −17.9558 | −0.679152 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.4635 | −1.71713 | −0.858567 | − | 0.512701i | \(-0.828645\pi\) | ||||
−0.858567 | + | 0.512701i | \(0.828645\pi\) | |||||||
\(702\) | 5.88388 | 0.222073 | ||||||||
\(703\) | 21.0937 | 0.795563 | ||||||||
\(704\) | 4.46967 | 0.168457 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.51347 | −0.132231 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.66421 | −0.175292 | ||||||||
\(709\) | −47.7597 | −1.79365 | −0.896826 | − | 0.442384i | \(-0.854133\pi\) | ||||
−0.896826 | + | 0.442384i | \(0.854133\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.98527 | −0.261968 | ||||||||
\(712\) | −14.3912 | −0.539335 | ||||||||
\(713\) | 22.1759 | 0.830493 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.7374 | −0.961853 | ||||||||
\(717\) | −5.41296 | −0.202151 | ||||||||
\(718\) | 2.19796 | 0.0820270 | ||||||||
\(719\) | 13.1611 | 0.490828 | 0.245414 | − | 0.969418i | \(-0.421076\pi\) | ||||
0.245414 | + | 0.969418i | \(0.421076\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.8015 | −0.923016 | ||||||||
\(723\) | 4.69669 | 0.174672 | ||||||||
\(724\) | 7.42245 | 0.275853 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.97792 | 0.333202 | ||||||||
\(727\) | −8.17082 | −0.303039 | −0.151519 | − | 0.988454i | \(-0.548417\pi\) | ||||
−0.151519 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.0698 | −0.409432 | ||||||||
\(732\) | −9.79683 | −0.362101 | ||||||||
\(733\) | 2.01510 | 0.0744293 | 0.0372146 | − | 0.999307i | \(-0.488151\pi\) | ||||
0.0372146 | + | 0.999307i | \(0.488151\pi\) | |||||||
\(734\) | −28.7721 | −1.06200 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.61827 | −0.0965107 | ||||||||
\(737\) | 8.27512 | 0.304818 | ||||||||
\(738\) | −3.56282 | −0.131149 | ||||||||
\(739\) | −3.82590 | −0.140738 | −0.0703690 | − | 0.997521i | \(-0.522418\pi\) | ||||
−0.0703690 | + | 0.997521i | \(0.522418\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.9411 | −1.43054 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.6654 | 1.34512 | 0.672562 | − | 0.740041i | \(-0.265194\pi\) | ||||
0.672562 | + | 0.740041i | \(0.265194\pi\) | |||||||
\(744\) | 8.46967 | 0.310513 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.5689 | −0.533406 | ||||||||
\(747\) | 5.35965 | 0.196099 | ||||||||
\(748\) | −34.5741 | −1.26415 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.4657 | −0.746804 | −0.373402 | − | 0.927670i | \(-0.621809\pi\) | ||||
−0.373402 | + | 0.927670i | \(0.621809\pi\) | |||||||
\(752\) | 6.79073 | 0.247632 | ||||||||
\(753\) | −7.73402 | −0.281843 | ||||||||
\(754\) | 48.0858 | 1.75118 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.9575 | 1.37959 | 0.689794 | − | 0.724006i | \(-0.257701\pi\) | ||||
0.689794 | + | 0.724006i | \(0.257701\pi\) | |||||||
\(758\) | 30.7868 | 1.11823 | ||||||||
\(759\) | −11.7028 | −0.424784 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.6131 | −1.25472 | −0.627361 | − | 0.778728i | \(-0.715865\pi\) | ||||
−0.627361 | + | 0.778728i | \(0.715865\pi\) | |||||||
\(762\) | −6.59619 | −0.238955 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.08452 | −0.0392367 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.3410 | −0.843344 | ||||||||
\(767\) | 27.4436 | 0.990932 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −1.48961 | −0.0537167 | −0.0268584 | − | 0.999639i | \(-0.508550\pi\) | ||||
−0.0268584 | + | 0.999639i | \(0.508550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.34442 | −0.0484181 | ||||||||
\(772\) | −8.93933 | −0.321734 | ||||||||
\(773\) | −0.992258 | −0.0356891 | −0.0178445 | − | 0.999841i | \(-0.505680\pi\) | ||||
−0.0178445 | + | 0.999841i | \(0.505680\pi\) | |||||||
\(774\) | −1.43108 | −0.0514392 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.71966 | 0.277120 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21842 | 0.0436824 | ||||||||
\(779\) | 23.5797 | 0.844830 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.04596 | 0.323690 | ||||||||
\(782\) | 20.2530 | 0.724247 | ||||||||
\(783\) | 8.17246 | 0.292060 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.32106 | −0.0827896 | ||||||||
\(787\) | 10.2513 | 0.365418 | 0.182709 | − | 0.983167i | \(-0.441513\pi\) | ||||
0.182709 | + | 0.983167i | \(0.441513\pi\) | |||||||
\(788\) | −7.45890 | −0.265712 | ||||||||
\(789\) | 4.36700 | 0.155469 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.46967 | −0.158823 | ||||||||
\(793\) | 57.6434 | 2.04698 | ||||||||
\(794\) | −8.40595 | −0.298316 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.8293 | 0.915496 | ||||||||
\(797\) | 32.6811 | 1.15762 | 0.578812 | − | 0.815461i | \(-0.303517\pi\) | ||||
0.578812 | + | 0.815461i | \(0.303517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −52.5282 | −1.85831 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3912 | 0.508490 | ||||||||
\(802\) | 0.664208 | 0.0234540 | ||||||||
\(803\) | 17.9541 | 0.633585 | ||||||||
\(804\) | −1.85140 | −0.0652937 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −49.8345 | −1.75535 | ||||||||
\(807\) | −23.0671 | −0.812001 | ||||||||
\(808\) | 13.3544 | 0.469807 | ||||||||
\(809\) | 22.4515 | 0.789354 | 0.394677 | − | 0.918820i | \(-0.370856\pi\) | ||||
0.394677 | + | 0.918820i | \(0.370856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.6581 | 1.32235 | 0.661177 | − | 0.750230i | \(-0.270057\pi\) | ||||
0.661177 | + | 0.750230i | \(0.270057\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.7209 | −0.516286 | ||||||||
\(814\) | −14.2457 | −0.499310 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.73528 | 0.270789 | ||||||||
\(817\) | 9.47129 | 0.331358 | ||||||||
\(818\) | 7.38476 | 0.258202 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4838 | −0.749791 | −0.374896 | − | 0.927067i | \(-0.622321\pi\) | ||||
−0.374896 | + | 0.927067i | \(0.622321\pi\) | |||||||
\(822\) | −14.2751 | −0.497902 | ||||||||
\(823\) | −18.6127 | −0.648797 | −0.324398 | − | 0.945921i | \(-0.605162\pi\) | ||||
−0.324398 | + | 0.945921i | \(0.605162\pi\) | |||||||
\(824\) | 9.35965 | 0.326059 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.4254 | −0.640713 | −0.320356 | − | 0.947297i | \(-0.603803\pi\) | ||||
−0.320356 | + | 0.947297i | \(0.603803\pi\) | |||||||
\(828\) | 2.61827 | 0.0909912 | ||||||||
\(829\) | 32.0377 | 1.11271 | 0.556357 | − | 0.830943i | \(-0.312199\pi\) | ||||
0.556357 | + | 0.830943i | \(0.312199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.21104 | 0.111390 | ||||||||
\(832\) | 5.88388 | 0.203987 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.9632 | −0.518133 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 29.5815 | 1.02310 | ||||||||
\(837\) | −8.46967 | −0.292754 | ||||||||
\(838\) | −18.6274 | −0.643473 | ||||||||
\(839\) | 8.45154 | 0.291780 | 0.145890 | − | 0.989301i | \(-0.453395\pi\) | ||||
0.145890 | + | 0.989301i | \(0.453395\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.7891 | 1.30307 | ||||||||
\(842\) | 13.5043 | 0.465389 | ||||||||
\(843\) | 7.72488 | 0.266059 | ||||||||
\(844\) | 5.53375 | 0.190479 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.79073 | −0.233470 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.38173 | −0.0474488 | ||||||||
\(849\) | 29.5594 | 1.01448 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.34492 | 0.286060 | ||||||||
\(852\) | −2.02386 | −0.0693361 | ||||||||
\(853\) | 50.6270 | 1.73344 | 0.866718 | − | 0.498798i | \(-0.166225\pi\) | ||||
0.866718 | + | 0.498798i | \(0.166225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.0165 | −0.376536 | ||||||||
\(857\) | 12.0013 | 0.409955 | 0.204978 | − | 0.978767i | \(-0.434288\pi\) | ||||
0.204978 | + | 0.978767i | \(0.434288\pi\) | |||||||
\(858\) | 26.2990 | 0.897832 | ||||||||
\(859\) | −35.7119 | −1.21848 | −0.609238 | − | 0.792988i | \(-0.708525\pi\) | ||||
−0.609238 | + | 0.792988i | \(0.708525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 31.6807 | 1.07905 | ||||||||
\(863\) | 1.28425 | 0.0437164 | 0.0218582 | − | 0.999761i | \(-0.493042\pi\) | ||||
0.0218582 | + | 0.999761i | \(0.493042\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.3184 | −0.860353 | ||||||||
\(867\) | −42.8345 | −1.45474 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.2218 | −1.05913 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.8934 | 0.369109 | ||||||||
\(872\) | 4.69544 | 0.159008 | ||||||||
\(873\) | −7.71966 | −0.261271 | ||||||||
\(874\) | −17.3284 | −0.586142 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.01687 | −0.135717 | ||||||||
\(877\) | −38.3501 | −1.29499 | −0.647496 | − | 0.762069i | \(-0.724184\pi\) | ||||
−0.647496 | + | 0.762069i | \(0.724184\pi\) | |||||||
\(878\) | −32.8146 | −1.10744 | ||||||||
\(879\) | −1.17679 | −0.0396921 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.389472 | 0.0131216 | 0.00656082 | − | 0.999978i | \(-0.497912\pi\) | ||||
0.00656082 | + | 0.999978i | \(0.497912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.5412 | 0.623962 | 0.311981 | − | 0.950088i | \(-0.399007\pi\) | ||||
0.311981 | + | 0.950088i | \(0.399007\pi\) | |||||||
\(884\) | −45.5134 | −1.53078 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.6421 | 0.559103 | ||||||||
\(887\) | 42.4806 | 1.42636 | 0.713179 | − | 0.700982i | \(-0.247255\pi\) | ||||
0.713179 | + | 0.700982i | \(0.247255\pi\) | |||||||
\(888\) | 3.18719 | 0.106955 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.46967 | 0.149739 | ||||||||
\(892\) | −3.28248 | −0.109906 | ||||||||
\(893\) | 44.9429 | 1.50396 | ||||||||
\(894\) | 11.1651 | 0.373417 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.4056 | −0.514378 | ||||||||
\(898\) | −20.1759 | −0.673278 | ||||||||
\(899\) | −69.2180 | −2.30855 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6881 | 0.356071 | ||||||||
\(902\) | −15.9246 | −0.530231 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.5723 | 0.418150 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.664208 | 0.0220668 | ||||||||
\(907\) | 41.1686 | 1.36698 | 0.683491 | − | 0.729959i | \(-0.260461\pi\) | ||||
0.683491 | + | 0.729959i | \(0.260461\pi\) | |||||||
\(908\) | −4.42031 | −0.146693 | ||||||||
\(909\) | −13.3544 | −0.442939 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1703 | −0.833929 | −0.416964 | − | 0.908923i | \(-0.636906\pi\) | ||||
−0.416964 | + | 0.908923i | \(0.636906\pi\) | |||||||
\(912\) | −6.61827 | −0.219153 | ||||||||
\(913\) | 23.9558 | 0.792822 | ||||||||
\(914\) | −35.4124 | −1.17134 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.97270 | −0.263426 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −7.73528 | −0.255302 | ||||||||
\(919\) | −5.03681 | −0.166149 | −0.0830745 | − | 0.996543i | \(-0.526474\pi\) | ||||
−0.0830745 | + | 0.996543i | \(0.526474\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.3761 | −0.671417 | ||||||||
\(922\) | 12.5940 | 0.414762 | ||||||||
\(923\) | 11.9081 | 0.391961 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.5061 | 1.06822 | ||||||||
\(927\) | −9.35965 | −0.307411 | ||||||||
\(928\) | 8.17246 | 0.268274 | ||||||||
\(929\) | −14.2846 | −0.468663 | −0.234332 | − | 0.972157i | \(-0.575290\pi\) | ||||
−0.234332 | + | 0.972157i | \(0.575290\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.9558 | 0.588163 | ||||||||
\(933\) | 18.8934 | 0.618542 | ||||||||
\(934\) | 9.20531 | 0.301207 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.88388 | −0.192321 | ||||||||
\(937\) | 19.8403 | 0.648153 | 0.324077 | − | 0.946031i | \(-0.394946\pi\) | ||||
0.324077 | + | 0.946031i | \(0.394946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.4849 | −0.537964 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.9054 | 0.518502 | 0.259251 | − | 0.965810i | \(-0.416524\pi\) | ||||
0.259251 | + | 0.965810i | \(0.416524\pi\) | |||||||
\(942\) | −8.08184 | −0.263320 | ||||||||
\(943\) | 9.32842 | 0.303775 | ||||||||
\(944\) | 4.66421 | 0.151807 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.39646 | −0.207967 | ||||||||
\(947\) | −9.55815 | −0.310598 | −0.155299 | − | 0.987867i | \(-0.549634\pi\) | ||||
−0.155299 | + | 0.987867i | \(0.549634\pi\) | |||||||
\(948\) | 6.98527 | 0.226871 | ||||||||
\(949\) | 23.6348 | 0.767217 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.3211 | 0.334683 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.7505 | −0.769354 | −0.384677 | − | 0.923051i | \(-0.625687\pi\) | ||||
−0.384677 | + | 0.923051i | \(0.625687\pi\) | |||||||
\(954\) | 1.38173 | 0.0447352 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.41296 | 0.175068 | ||||||||
\(957\) | 36.5282 | 1.18079 | ||||||||
\(958\) | 39.4914 | 1.27591 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7352 | 1.31404 | ||||||||
\(962\) | −18.7530 | −0.604622 | ||||||||
\(963\) | 11.0165 | 0.355002 | ||||||||
\(964\) | −4.69669 | −0.151270 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.9706 | 1.83205 | 0.916025 | − | 0.401121i | \(-0.131379\pi\) | ||||
0.916025 | + | 0.401121i | \(0.131379\pi\) | |||||||
\(968\) | −8.97792 | −0.288561 | ||||||||
\(969\) | 51.1941 | 1.64459 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.0857 | 1.06177 | 0.530886 | − | 0.847443i | \(-0.321859\pi\) | ||||
0.530886 | + | 0.847443i | \(0.321859\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29.2678 | −0.937800 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.79683 | 0.313589 | ||||||||
\(977\) | 24.6127 | 0.787429 | 0.393715 | − | 0.919233i | \(-0.371190\pi\) | ||||
0.393715 | + | 0.919233i | \(0.371190\pi\) | |||||||
\(978\) | −0.836668 | −0.0267537 | ||||||||
\(979\) | 64.3241 | 2.05581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.69544 | −0.149914 | ||||||||
\(982\) | −15.3631 | −0.490255 | ||||||||
\(983\) | −42.4806 | −1.35492 | −0.677460 | − | 0.735559i | \(-0.736919\pi\) | ||||
−0.677460 | + | 0.735559i | \(0.736919\pi\) | |||||||
\(984\) | 3.56282 | 0.113578 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −63.2162 | −2.01321 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.9411 | 1.23888 | ||||||||
\(989\) | 3.74696 | 0.119146 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.838308 | −0.0266297 | −0.0133149 | − | 0.999911i | \(-0.504238\pi\) | ||||
−0.0133149 | + | 0.999911i | \(0.504238\pi\) | |||||||
\(992\) | −8.46967 | −0.268912 | ||||||||
\(993\) | 19.1906 | 0.608995 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.35965 | −0.169827 | ||||||||
\(997\) | 31.5940 | 1.00059 | 0.500297 | − | 0.865854i | \(-0.333224\pi\) | ||||
0.500297 | + | 0.865854i | \(0.333224\pi\) | |||||||
\(998\) | −20.5502 | −0.650507 | ||||||||
\(999\) | −3.18719 | −0.100838 |
(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 | 7350.2.a.dr.1.4 | 4 | ||
5.2 | odd | 4 | 1470.2.g.k.589.3 | yes | 8 | ||
5.3 | odd | 4 | 1470.2.g.k.589.7 | yes | 8 | ||
5.4 | even | 2 | 7350.2.a.du.1.4 | 4 | |||
7.6 | odd | 2 | 7350.2.a.ds.1.4 | 4 | |||
35.2 | odd | 12 | 1470.2.n.k.949.3 | 16 | |||
35.3 | even | 12 | 1470.2.n.l.79.2 | 16 | |||
35.12 | even | 12 | 1470.2.n.l.949.2 | 16 | |||
35.13 | even | 4 | 1470.2.g.j.589.6 | yes | 8 | ||
35.17 | even | 12 | 1470.2.n.l.79.8 | 16 | |||
35.18 | odd | 12 | 1470.2.n.k.79.3 | 16 | |||
35.23 | odd | 12 | 1470.2.n.k.949.5 | 16 | |||
35.27 | even | 4 | 1470.2.g.j.589.2 | ✓ | 8 | ||
35.32 | odd | 12 | 1470.2.n.k.79.5 | 16 | |||
35.33 | even | 12 | 1470.2.n.l.949.8 | 16 | |||
35.34 | odd | 2 | 7350.2.a.dt.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.2 | ✓ | 8 | 35.27 | even | 4 | ||
1470.2.g.j.589.6 | yes | 8 | 35.13 | even | 4 | ||
1470.2.g.k.589.3 | yes | 8 | 5.2 | odd | 4 | ||
1470.2.g.k.589.7 | yes | 8 | 5.3 | odd | 4 | ||
1470.2.n.k.79.3 | 16 | 35.18 | odd | 12 | |||
1470.2.n.k.79.5 | 16 | 35.32 | odd | 12 | |||
1470.2.n.k.949.3 | 16 | 35.2 | odd | 12 | |||
1470.2.n.k.949.5 | 16 | 35.23 | odd | 12 | |||
1470.2.n.l.79.2 | 16 | 35.3 | even | 12 | |||
1470.2.n.l.79.8 | 16 | 35.17 | even | 12 | |||
1470.2.n.l.949.2 | 16 | 35.12 | even | 12 | |||
1470.2.n.l.949.8 | 16 | 35.33 | even | 12 | |||
7350.2.a.dr.1.4 | 4 | 1.1 | even | 1 | trivial | ||
7350.2.a.ds.1.4 | 4 | 7.6 | odd | 2 | |||
7350.2.a.dt.1.4 | 4 | 35.34 | odd | 2 | |||
7350.2.a.du.1.4 | 4 | 5.4 | even | 2 |