Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + 13971 x^{7} - 20311 x^{6} - 22309 x^{5} + 38415 x^{4} + 8429 x^{3} - 22584 x^{2} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-2.90634\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | 2.90634 | 1.67798 | 0.838989 | − | 0.544149i | \(-0.183147\pi\) | ||||
0.838989 | + | 0.544149i | \(0.183147\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.506103 | 0.226336 | 0.113168 | − | 0.993576i | \(-0.463900\pi\) | ||||
0.113168 | + | 0.993576i | \(0.463900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.44682 | 1.81561 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.70801 | 1.72103 | 0.860515 | − | 0.509425i | \(-0.170142\pi\) | ||||
0.860515 | + | 0.509425i | \(0.170142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51313 | 0.697017 | 0.348509 | − | 0.937306i | \(-0.386688\pi\) | ||||
0.348509 | + | 0.937306i | \(0.386688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.47091 | 0.379787 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.03384 | 1.22088 | 0.610442 | − | 0.792061i | \(-0.290992\pi\) | ||||
0.610442 | + | 0.792061i | \(0.290992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.78183 | 1.32644 | 0.663221 | − | 0.748423i | \(-0.269189\pi\) | ||||
0.663221 | + | 0.748423i | \(0.269189\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.51894 | 0.316720 | 0.158360 | − | 0.987381i | \(-0.449379\pi\) | ||||
0.158360 | + | 0.987381i | \(0.449379\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.74386 | −0.948772 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.11130 | 1.36857 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.63143 | 1.23143 | 0.615713 | − | 0.787971i | \(-0.288868\pi\) | ||||
0.615713 | + | 0.787971i | \(0.288868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.27388 | −0.588006 | −0.294003 | − | 0.955805i | \(-0.594988\pi\) | ||||
−0.294003 | + | 0.955805i | \(0.594988\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.5894 | 2.88785 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.82938 | 1.61594 | 0.807970 | − | 0.589224i | \(-0.200566\pi\) | ||||
0.807970 | + | 0.589224i | \(0.200566\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.30402 | 1.16958 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.37684 | −1.27746 | −0.638728 | − | 0.769433i | \(-0.720539\pi\) | ||||
−0.638728 | + | 0.769433i | \(0.720539\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.75665 | 0.410937 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.2065 | −1.78051 | −0.890253 | − | 0.455466i | \(-0.849472\pi\) | ||||
−0.890253 | + | 0.455466i | \(0.849472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.6300 | 2.04862 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1084 | −1.66321 | −0.831606 | − | 0.555366i | \(-0.812578\pi\) | ||||
−0.831606 | + | 0.555366i | \(0.812578\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.88884 | 0.389531 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.8040 | 2.22574 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.79288 | −1.14474 | −0.572368 | − | 0.819997i | \(-0.693975\pi\) | ||||
−0.572368 | + | 0.819997i | \(0.693975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.07381 | −0.777672 | −0.388836 | − | 0.921307i | \(-0.627123\pi\) | ||||
−0.388836 | + | 0.921307i | \(0.627123\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.27190 | 0.157760 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2129 | −1.36987 | −0.684935 | − | 0.728604i | \(-0.740169\pi\) | ||||
−0.684935 | + | 0.728604i | \(0.740169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.41455 | 0.531449 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.46228 | −0.648254 | −0.324127 | − | 0.946014i | \(-0.605070\pi\) | ||||
−0.324127 | + | 0.946014i | \(0.605070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.85721 | 0.568494 | 0.284247 | − | 0.958751i | \(-0.408256\pi\) | ||||
0.284247 | + | 0.958751i | \(0.408256\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.7873 | −1.59202 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.19722 | −0.247207 | −0.123603 | − | 0.992332i | \(-0.539445\pi\) | ||||
−0.123603 | + | 0.992332i | \(0.539445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.32740 | 0.480822 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.906091 | 0.0994564 | 0.0497282 | − | 0.998763i | \(-0.484164\pi\) | ||||
0.0497282 | + | 0.998763i | \(0.484164\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.54764 | 0.276330 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.2732 | 2.06630 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.03213 | −0.533405 | −0.266702 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266702 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.51501 | −0.986661 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.92620 | 0.300222 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.21457 | −0.529460 | −0.264730 | − | 0.964323i | \(-0.585283\pi\) | ||||
−0.264730 | + | 0.964323i | \(0.585283\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 31.0905 | 3.12472 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1869 | −1.01364 | −0.506819 | − | 0.862052i | \(-0.669179\pi\) | ||||
−0.506819 | + | 0.862052i | \(0.669179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.42232 | −0.435744 | −0.217872 | − | 0.975977i | \(-0.569912\pi\) | ||||
−0.217872 | + | 0.975977i | \(0.569912\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.67421 | 0.548547 | 0.274273 | − | 0.961652i | \(-0.411563\pi\) | ||||
0.274273 | + | 0.961652i | \(0.411563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.63092 | 0.635127 | 0.317563 | − | 0.948237i | \(-0.397135\pi\) | ||||
0.317563 | + | 0.948237i | \(0.397135\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.5675 | 2.71151 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.8269 | −1.48887 | −0.744436 | − | 0.667694i | \(-0.767281\pi\) | ||||
−0.744436 | + | 0.667694i | \(0.767281\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.768738 | 0.0716852 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.6886 | 1.26551 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.5814 | 1.96195 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.90634 | −0.262056 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.93139 | −0.441077 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.0228 | −1.51053 | −0.755266 | − | 0.655419i | \(-0.772492\pi\) | ||||
−0.755266 | + | 0.655419i | \(0.772492\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.3460 | −2.14354 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.6734 | 1.63150 | 0.815749 | − | 0.578406i | \(-0.196325\pi\) | ||||
0.815749 | + | 0.578406i | \(0.196325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.59905 | 0.309757 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.31324 | 0.539376 | 0.269688 | − | 0.962948i | \(-0.413079\pi\) | ||||
0.269688 | + | 0.962948i | \(0.413079\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.3708 | 1.72783 | 0.863915 | − | 0.503637i | \(-0.168005\pi\) | ||||
0.863915 | + | 0.503637i | \(0.168005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −35.4764 | −2.98765 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.3450 | 1.19959 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.35618 | 0.278716 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5744 | 1.35783 | 0.678913 | − | 0.734219i | \(-0.262451\pi\) | ||||
0.678913 | + | 0.734219i | \(0.262451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.8198 | −1.61291 | −0.806455 | − | 0.591295i | \(-0.798617\pi\) | ||||
−0.806455 | + | 0.591295i | \(0.798617\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 27.4184 | 2.21665 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.65692 | −0.133087 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.507136 | 0.0404739 | 0.0202369 | − | 0.999795i | \(-0.493558\pi\) | ||||
0.0202369 | + | 0.999795i | \(0.493558\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −35.1910 | −2.79083 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.5778 | −0.828520 | −0.414260 | − | 0.910159i | \(-0.635960\pi\) | ||||
−0.414260 | + | 0.910159i | \(0.635960\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.39596 | 0.653624 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.40151 | −0.340599 | −0.170300 | − | 0.985392i | \(-0.554474\pi\) | ||||
−0.170300 | + | 0.985392i | \(0.554474\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.68417 | −0.514167 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.4926 | 2.40830 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.58786 | 0.728951 | 0.364476 | − | 0.931213i | \(-0.381248\pi\) | ||||
0.364476 | + | 0.931213i | \(0.381248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.5551 | −1.92084 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.38187 | 0.327516 | 0.163758 | − | 0.986501i | \(-0.447638\pi\) | ||||
0.163758 | + | 0.986501i | \(0.447638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8224 | −1.54772 | −0.773858 | − | 0.633359i | \(-0.781676\pi\) | ||||
−0.773858 | + | 0.633359i | \(0.781676\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.6526 | −1.30492 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.97467 | 0.365745 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.7332 | 2.10118 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.5815 | 1.34451 | 0.672254 | − | 0.740320i | \(-0.265326\pi\) | ||||
0.672254 | + | 0.740320i | \(0.265326\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.45059 | −0.320361 | −0.160180 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160180 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.69658 | 0.264718 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.25530 | 0.160684 | 0.0803419 | − | 0.996767i | \(-0.474399\pi\) | ||||
0.0803419 | + | 0.996767i | \(0.474399\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.734053 | −0.0520356 | −0.0260178 | − | 0.999661i | \(-0.508283\pi\) | ||||
−0.0260178 | + | 0.999661i | \(0.508283\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −32.5884 | −2.29861 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.506103 | −0.0353477 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.27338 | 0.575040 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 33.0028 | 2.28285 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.9104 | −1.92143 | −0.960716 | − | 0.277532i | \(-0.910484\pi\) | ||||
−0.960716 | + | 0.277532i | \(0.910484\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.8753 | −1.08775 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.23954 | −0.289134 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.1167 | 0.953919 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.6507 | 0.850978 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.10011 | −0.408493 | −0.204247 | − | 0.978919i | \(-0.565474\pi\) | ||||
−0.204247 | + | 0.978919i | \(0.565474\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.8390 | −1.72260 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.54979 | 0.169235 | 0.0846177 | − | 0.996413i | \(-0.473033\pi\) | ||||
0.0846177 | + | 0.996413i | \(0.473033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.39344 | −0.554654 | −0.277327 | − | 0.960776i | \(-0.589449\pi\) | ||||
−0.277327 | + | 0.960776i | \(0.589449\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8195 | 1.29842 | 0.649209 | − | 0.760610i | \(-0.275100\pi\) | ||||
0.649209 | + | 0.760610i | \(0.275100\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.17776 | −0.402993 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.38587 | −0.414807 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.0248 | 1.61872 | 0.809361 | − | 0.587312i | \(-0.199814\pi\) | ||||
0.809361 | + | 0.587312i | \(0.199814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7542 | 1.14365 | 0.571823 | − | 0.820377i | \(-0.306236\pi\) | ||||
0.571823 | + | 0.820377i | \(0.306236\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.75699 | −0.561761 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.5305 | 0.924554 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.63341 | 0.166886 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7916 | 0.681158 | 0.340579 | − | 0.940216i | \(-0.389377\pi\) | ||||
0.340579 | + | 0.940216i | \(0.389377\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.67011 | 0.545085 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.40430 | 0.463676 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.34062 | −0.0836258 | −0.0418129 | − | 0.999125i | \(-0.513313\pi\) | ||||
−0.0418129 | + | 0.999125i | \(0.513313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 36.1202 | 2.23579 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.69500 | 0.166181 | 0.0830903 | − | 0.996542i | \(-0.473521\pi\) | ||||
0.0830903 | + | 0.996542i | \(0.473521\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.12807 | −0.376445 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.6251 | −0.895041 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.8105 | −0.781069 | −0.390534 | − | 0.920588i | \(-0.627710\pi\) | ||||
−0.390534 | + | 0.920588i | \(0.627710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.59766 | 0.583016 | 0.291508 | − | 0.956568i | \(-0.405843\pi\) | ||||
0.291508 | + | 0.956568i | \(0.405843\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −27.0780 | −1.63287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.1317 | 0.969259 | 0.484629 | − | 0.874720i | \(-0.338954\pi\) | ||||
0.484629 | + | 0.874720i | \(0.338954\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.8322 | −1.06759 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9010 | 0.829261 | 0.414631 | − | 0.909990i | \(-0.363911\pi\) | ||||
0.414631 | + | 0.909990i | \(0.363911\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.8856 | −1.18207 | −0.591037 | − | 0.806645i | \(-0.701281\pi\) | ||||
−0.591037 | + | 0.806645i | \(0.701281\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.50454 | 0.503765 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.33950 | 0.490559 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.1553 | −0.888421 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.9804 | −0.758325 | −0.379163 | − | 0.925330i | \(-0.623788\pi\) | ||||
−0.379163 | + | 0.925330i | \(0.623788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.45010 | −0.259095 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 40.5914 | 2.35535 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.81729 | 0.220759 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.6067 | −1.70086 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.07397 | −0.176015 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.91179 | −0.394477 | −0.197238 | − | 0.980356i | \(-0.563197\pi\) | ||||
−0.197238 | + | 0.980356i | \(0.563197\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8528 | −0.731169 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0462826 | 0.00262445 | 0.00131222 | − | 0.999999i | \(-0.499582\pi\) | ||||
0.00131222 | + | 0.999999i | \(0.499582\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.5865 | 1.22014 | 0.610071 | − | 0.792346i | \(-0.291141\pi\) | ||||
0.610071 | + | 0.792346i | \(0.291141\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.24013 | −0.125818 | −0.0629091 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629091 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.8523 | 2.11932 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.4912 | 0.920449 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 29.1048 | 1.61943 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9219 | −0.661310 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.2717 | 1.06573 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.7385 | 1.52464 | 0.762322 | − | 0.647198i | \(-0.224059\pi\) | ||||
0.762322 | + | 0.647198i | \(0.224059\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 53.5389 | 2.93391 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.67486 | −0.310051 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2599 | 0.776785 | 0.388393 | − | 0.921494i | \(-0.373030\pi\) | ||||
0.388393 | + | 0.921494i | \(0.373030\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −45.9984 | −2.49829 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.6873 | −1.01198 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.23422 | 0.120286 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.4476 | 0.560857 | 0.280428 | − | 0.959875i | \(-0.409523\pi\) | ||||
0.280428 | + | 0.959875i | \(0.409523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.5661 | −1.63616 | −0.818082 | − | 0.575101i | \(-0.804963\pi\) | ||||
−0.818082 | + | 0.575101i | \(0.804963\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.8716 | 0.953917 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.3571 | 1.56252 | 0.781261 | − | 0.624204i | \(-0.214577\pi\) | ||||
0.781261 | + | 0.624204i | \(0.214577\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.76448 | −0.146723 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.5299 | −1.40019 | −0.700097 | − | 0.714047i | \(-0.746860\pi\) | ||||
−0.700097 | + | 0.714047i | \(0.746860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4296 | 0.759451 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 62.7229 | 3.29210 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.45825 | 0.128671 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.37178 | 0.228205 | 0.114103 | − | 0.993469i | \(-0.463601\pi\) | ||||
0.114103 | + | 0.993469i | \(0.463601\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.44682 | −0.283550 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.8934 | 0.978261 | 0.489131 | − | 0.872211i | \(-0.337314\pi\) | ||||
0.489131 | + | 0.872211i | \(0.337314\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.3323 | −0.740117 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6657 | 0.858325 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.5558 | 1.41545 | 0.707723 | − | 0.706490i | \(-0.249722\pi\) | ||||
0.707723 | + | 0.706490i | \(0.249722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −49.4741 | −2.53464 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.1536 | −1.43858 | −0.719291 | − | 0.694709i | \(-0.755533\pi\) | ||||
−0.719291 | + | 0.694709i | \(0.755533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −45.6271 | −2.31936 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.5849 | −0.790187 | −0.395093 | − | 0.918641i | \(-0.629288\pi\) | ||||
−0.395093 | + | 0.918641i | \(0.629288\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.64608 | 0.386679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54.2711 | 2.73762 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.11202 | −0.0559518 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.6831 | −1.23881 | −0.619405 | − | 0.785072i | \(-0.712626\pi\) | ||||
−0.619405 | + | 0.785072i | \(0.712626\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4381 | 0.621129 | 0.310564 | − | 0.950552i | \(-0.399482\pi\) | ||||
0.310564 | + | 0.950552i | \(0.399482\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.22769 | −0.409850 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.19011 | 0.108827 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 56.1062 | 2.78108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.7192 | −0.628926 | −0.314463 | − | 0.949270i | \(-0.601824\pi\) | ||||
−0.314463 | + | 0.949270i | \(0.601824\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.3484 | 0.905061 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.458575 | 0.0225106 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 59.2046 | 2.89926 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.02761 | −0.147908 | −0.0739541 | − | 0.997262i | \(-0.523562\pi\) | ||||
−0.0739541 | + | 0.997262i | \(0.523562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.51515 | −0.122581 | −0.0612905 | − | 0.998120i | \(-0.519522\pi\) | ||||
−0.0612905 | + | 0.998120i | \(0.519522\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −66.4868 | −3.23270 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.8798 | −1.15834 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.6914 | 2.01288 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.7281 | −0.805763 | −0.402882 | − | 0.915252i | \(-0.631991\pi\) | ||||
−0.402882 | + | 0.915252i | \(0.631991\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.24985 | −0.444519 | −0.222260 | − | 0.974988i | \(-0.571343\pi\) | ||||
−0.222260 | + | 0.974988i | \(0.571343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.75422 | 0.467679 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.78223 | 0.420111 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.8582 | 1.42506 | 0.712528 | − | 0.701644i | \(-0.247550\pi\) | ||||
0.712528 | + | 0.701644i | \(0.247550\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.8087 | 1.36874 | 0.684372 | − | 0.729133i | \(-0.260076\pi\) | ||||
0.684372 | + | 0.729133i | \(0.260076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.54678 | −0.120729 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 48.1708 | 2.27840 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.35246 | 0.394177 | 0.197088 | − | 0.980386i | \(-0.436851\pi\) | ||||
0.197088 | + | 0.980386i | \(0.436851\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.70801 | −0.268780 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −57.6030 | −2.70643 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.9129 | −1.21215 | −0.606076 | − | 0.795407i | \(-0.707257\pi\) | ||||
−0.606076 | + | 0.795407i | \(0.707257\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.7971 | 1.67087 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.2580 | −0.477762 | −0.238881 | − | 0.971049i | \(-0.576781\pi\) | ||||
−0.238881 | + | 0.971049i | \(0.576781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.55147 | 0.304472 | 0.152236 | − | 0.988344i | \(-0.451353\pi\) | ||||
0.152236 | + | 0.988344i | \(0.451353\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.81557 | −0.223317 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.4972 | −0.855947 | −0.427973 | − | 0.903791i | \(-0.640772\pi\) | ||||
−0.427973 | + | 0.903791i | \(0.640772\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.47391 | 0.0679142 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −47.8151 | −2.19854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.4282 | −1.25849 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −65.9521 | −3.01974 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.1133 | 0.827620 | 0.413810 | − | 0.910363i | \(-0.364198\pi\) | ||||
0.413810 | + | 0.910363i | \(0.364198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.7025 | 1.12634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.63911 | −0.119836 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9867 | 0.679111 | 0.339556 | − | 0.940586i | \(-0.389723\pi\) | ||||
0.339556 | + | 0.940586i | \(0.389723\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.7428 | −1.39024 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.81825 | 0.217445 | 0.108722 | − | 0.994072i | \(-0.465324\pi\) | ||||
0.108722 | + | 0.994072i | \(0.465324\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.3815 | 1.50343 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.7350 | 0.707235 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.21602 | 0.367800 | 0.183900 | − | 0.982945i | \(-0.441128\pi\) | ||||
0.183900 | + | 0.982945i | \(0.441128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.7923 | −0.571518 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.3859 | −1.71154 | −0.855772 | − | 0.517354i | \(-0.826917\pi\) | ||||
−0.855772 | + | 0.517354i | \(0.826917\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.15564 | −0.229423 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.4265 | −0.862760 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.9633 | −1.37242 | −0.686211 | − | 0.727402i | \(-0.740727\pi\) | ||||
−0.686211 | + | 0.727402i | \(0.740727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 41.1163 | 1.81533 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.23815 | −0.0986246 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −69.6750 | −3.06430 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.8656 | 1.22316 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.77849 | −0.296971 | −0.148485 | − | 0.988915i | \(-0.547440\pi\) | ||||
−0.148485 | + | 0.988915i | \(0.547440\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.9055 | 0.914134 | 0.457067 | − | 0.889432i | \(-0.348900\pi\) | ||||
0.457067 | + | 0.889432i | \(0.348900\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.4802 | −0.717887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6928 | −0.899688 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −47.8933 | −2.07839 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.51313 | −0.108856 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.87173 | 0.124156 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.7352 | 0.549565 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.18831 | 0.0510894 | 0.0255447 | − | 0.999674i | \(-0.491868\pi\) | ||||
0.0255447 | + | 0.999674i | \(0.491868\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −60.5170 | −2.59703 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.35593 | 0.143752 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.5228 | −0.492680 | −0.246340 | − | 0.969183i | \(-0.579228\pi\) | ||||
−0.246340 | + | 0.969183i | \(0.579228\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −33.0830 | −1.41195 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 38.3418 | 1.63342 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.4581 | 0.613712 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.27508 | −0.0540268 | −0.0270134 | − | 0.999635i | \(-0.508600\pi\) | ||||
−0.0270134 | + | 0.999635i | \(0.508600\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.0521 | −0.890409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 83.5085 | 3.52573 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.02739 | −0.0854443 | −0.0427222 | − | 0.999087i | \(-0.513603\pi\) | ||||
−0.0427222 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.01005 | −0.336985 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.7963 | 1.79411 | 0.897057 | − | 0.441915i | \(-0.145701\pi\) | ||||
0.897057 | + | 0.441915i | \(0.145701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.6779 | 0.488704 | 0.244352 | − | 0.969687i | \(-0.421425\pi\) | ||||
0.244352 | + | 0.969687i | \(0.421425\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 54.0041 | 2.25605 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.20562 | −0.300495 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.29918 | −0.303869 | −0.151934 | − | 0.988391i | \(-0.548550\pi\) | ||||
−0.151934 | + | 0.988391i | \(0.548550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9349 | −0.537558 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −69.1147 | −2.86244 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.92783 | 0.286430 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.35476 | 0.221015 | 0.110507 | − | 0.993875i | \(-0.464752\pi\) | ||||
0.110507 | + | 0.993875i | \(0.464752\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.9290 | −0.779956 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.55468 | 0.269624 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.7874 | −1.30535 | −0.652675 | − | 0.757638i | \(-0.726353\pi\) | ||||
−0.652675 | + | 0.757638i | \(0.726353\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.13341 | −0.0873146 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.7983 | −1.78955 | −0.894776 | − | 0.446516i | \(-0.852665\pi\) | ||||
−0.894776 | + | 0.446516i | \(0.852665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.4183 | 0.873672 | 0.436836 | − | 0.899541i | \(-0.356099\pi\) | ||||
0.436836 | + | 0.899541i | \(0.356099\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −61.0745 | −2.48714 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9224 | 0.444059 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.5754 | −0.875718 | −0.437859 | − | 0.899044i | \(-0.644263\pi\) | ||||
−0.437859 | + | 0.899044i | \(0.644263\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −30.6766 | −1.24104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.8291 | 0.760502 | 0.380251 | − | 0.924883i | \(-0.375838\pi\) | ||||
0.380251 | + | 0.924883i | \(0.375838\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.47091 | −0.0593127 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.74835 | −0.311937 | −0.155968 | − | 0.987762i | \(-0.549850\pi\) | ||||
−0.155968 | + | 0.987762i | \(0.549850\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.9297 | −0.559883 | −0.279942 | − | 0.960017i | \(-0.590315\pi\) | ||||
−0.279942 | + | 0.960017i | \(0.590315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.8016 | 0.433454 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2235 | 0.848940 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 95.9173 | 3.83057 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 49.4795 | 1.97288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8581 | 0.671109 | 0.335554 | − | 0.942021i | \(-0.391076\pi\) | ||||
0.335554 | + | 0.942021i | \(0.391076\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −81.1172 | −3.22412 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.61529 | −0.341888 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.7521 | −1.17697 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.7214 | 1.92438 | 0.962189 | − | 0.272382i | \(-0.0878115\pi\) | ||||
0.962189 | + | 0.272382i | \(0.0878115\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3027 | 0.958407 | 0.479203 | − | 0.877704i | \(-0.340926\pi\) | ||||
0.479203 | + | 0.877704i | \(0.340926\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.3216 | −0.485161 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.57912 | 0.297966 | 0.148983 | − | 0.988840i | \(-0.452400\pi\) | ||||
0.148983 | + | 0.988840i | \(0.452400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −50.1899 | −1.97012 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.9280 | −0.975507 | −0.487754 | − | 0.872981i | \(-0.662184\pi\) | ||||
−0.487754 | + | 0.872981i | \(0.662184\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.45063 | 0.369267 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.4564 | 1.03216 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.3444 | −0.948324 | −0.474162 | − | 0.880438i | \(-0.657249\pi\) | ||||
−0.474162 | + | 0.880438i | \(0.657249\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.3785 | −1.57054 | −0.785271 | − | 0.619152i | \(-0.787477\pi\) | ||||
−0.785271 | + | 0.619152i | \(0.787477\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.7672 | 1.42792 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0727 | 0.390017 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.7290 | −0.685443 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.6694 | −1.33840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0815 | 0.735537 | 0.367769 | − | 0.929917i | \(-0.380122\pi\) | ||||
0.367769 | + | 0.929917i | \(0.380122\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −33.7350 | −1.29846 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.19086 | 0.353234 | 0.176617 | − | 0.984280i | \(-0.443485\pi\) | ||||
0.176617 | + | 0.984280i | \(0.443485\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.41056 | 0.283973 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.78539 | −0.221372 | −0.110686 | − | 0.993855i | \(-0.535305\pi\) | ||||
−0.110686 | + | 0.993855i | \(0.535305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.19515 | 0.122080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.3942 | −0.930697 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.4299 | −1.15929 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0361 | 1.67521 | 0.837607 | − | 0.546274i | \(-0.183954\pi\) | ||||
0.837607 | + | 0.546274i | \(0.183954\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3097 | 0.391070 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.03384 | −0.190670 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 57.6022 | 2.17871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.9512 | 1.39563 | 0.697813 | − | 0.716280i | \(-0.254157\pi\) | ||||
0.697813 | + | 0.716280i | \(0.254157\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 56.8318 | 2.14345 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.9547 | −0.676212 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.6033 | 0.585995 | 0.292997 | − | 0.956113i | \(-0.405347\pi\) | ||||
0.292997 | + | 0.956113i | \(0.405347\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.9679 | −0.448830 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.97281 | −0.186233 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.26003 | 0.271510 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 72.7307 | 2.71618 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.493177 | −0.0183924 | −0.00919619 | − | 0.999958i | \(-0.502927\pi\) | ||||
−0.00919619 | + | 0.999958i | \(0.502927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 51.5997 | 1.91901 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −31.4586 | −1.16834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.29693 | 0.233540 | 0.116770 | − | 0.993159i | \(-0.462746\pi\) | ||||
0.116770 | + | 0.993159i | \(0.462746\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.4330 | −1.42344 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42.1676 | −1.55963 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.44142 | 0.200983 | 0.100492 | − | 0.994938i | \(-0.467958\pi\) | ||||
0.100492 | + | 0.994938i | \(0.467958\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −64.0032 | −2.35759 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.13823 | 0.336155 | 0.168078 | − | 0.985774i | \(-0.446244\pi\) | ||||
0.168078 | + | 0.985774i | \(0.446244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.2306 | 1.55138 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.9354 | −0.511239 | −0.255619 | − | 0.966778i | \(-0.582279\pi\) | ||||
−0.255619 | + | 0.966778i | \(0.582279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.38833 | 0.307325 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.93532 | 0.180574 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.6521 | 0.534663 | 0.267331 | − | 0.963605i | \(-0.413858\pi\) | ||||
0.267331 | + | 0.963605i | \(0.413858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.3640 | 1.14297 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0308 | −0.365060 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.3236 | 1.64732 | 0.823658 | − | 0.567087i | \(-0.191930\pi\) | ||||
0.823658 | + | 0.567087i | \(0.191930\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.1983 | 0.914640 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.2630 | −0.988283 | −0.494141 | − | 0.869382i | \(-0.664517\pi\) | ||||
−0.494141 | + | 0.869382i | \(0.664517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.8765 | 0.501707 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.0977 | −0.797900 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.5462 | 1.20971 | 0.604853 | − | 0.796337i | \(-0.293232\pi\) | ||||
0.604853 | + | 0.796337i | \(0.293232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.89631 | −0.140322 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.2586 | −0.620749 | −0.310375 | − | 0.950614i | \(-0.600455\pi\) | ||||
−0.310375 | + | 0.950614i | \(0.600455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.5308 | 0.557884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.78183 | −0.207156 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.1788 | −1.11566 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 47.1581 | 1.68529 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.256663 | 0.00916069 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.9158 | −1.85060 | −0.925299 | − | 0.379239i | \(-0.876186\pi\) | ||||
−0.925299 | + | 0.379239i | \(0.876186\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.83258 | 0.278847 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2643 | −0.542051 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.8103 | −0.631666 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.8432 | −0.561194 | −0.280597 | − | 0.959826i | \(-0.590532\pi\) | ||||
−0.280597 | + | 0.959826i | \(0.590532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −61.4457 | −2.17379 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.4091 | −0.968454 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.7250 | 0.978395 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.2316 | −1.31062 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.7929 | 0.555248 | 0.277624 | − | 0.960690i | \(-0.410453\pi\) | ||||
0.277624 | + | 0.960690i | \(0.410453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.92918 | 0.0677427 | 0.0338714 | − | 0.999426i | \(-0.489216\pi\) | ||||
0.0338714 | + | 0.999426i | \(0.489216\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.8941 | 0.978288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.35347 | −0.187524 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −48.4335 | −1.69447 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.6731 | −0.861098 | −0.430549 | − | 0.902567i | \(-0.641680\pi\) | ||||
−0.430549 | + | 0.902567i | \(0.641680\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.8147 | 0.551264 | 0.275632 | − | 0.961263i | \(-0.411113\pi\) | ||||
0.275632 | + | 0.961263i | \(0.411113\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −78.6980 | −2.73991 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.0722 | −0.802300 | −0.401150 | − | 0.916012i | \(-0.631389\pi\) | ||||
−0.401150 | + | 0.916012i | \(0.631389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.20726 | −0.111393 | −0.0556964 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556964 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 46.8842 | 1.62639 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.22762 | −0.0770898 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.2815 | −0.804728 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.0822 | −0.451647 | −0.225823 | − | 0.974168i | \(-0.572507\pi\) | ||||
−0.225823 | + | 0.974168i | \(0.572507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.9759 | 0.516409 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 40.4009 | 1.39148 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.38288 | −0.116374 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −57.7942 | −1.98349 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.9302 | 0.511801 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.4104 | 0.767317 | 0.383658 | − | 0.923475i | \(-0.374664\pi\) | ||||
0.383658 | + | 0.923475i | \(0.374664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.9385 | 0.545085 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.4971 | 0.631849 | 0.315925 | − | 0.948784i | \(-0.397685\pi\) | ||||
0.315925 | + | 0.948784i | \(0.397685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.9579 | −1.36335 | −0.681673 | − | 0.731657i | \(-0.738747\pi\) | ||||
−0.681673 | + | 0.731657i | \(0.738747\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.1995 | −0.755678 | −0.377839 | − | 0.925871i | \(-0.623333\pi\) | ||||
−0.377839 | + | 0.925871i | \(0.623333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.85244 | 0.164988 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.2374 | 0.823147 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.5418 | −0.425450 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.1794 | −0.954823 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.4029 | −0.961291 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.32226 | 0.314790 | 0.157395 | − | 0.987536i | \(-0.449690\pi\) | ||||
0.157395 | + | 0.987536i | \(0.449690\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.7256 | −1.27245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.5285 | 0.590550 | 0.295275 | − | 0.955412i | \(-0.404589\pi\) | ||||
0.295275 | + | 0.955412i | \(0.404589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.47657 | 0.0496905 | 0.0248453 | − | 0.999691i | \(-0.492091\pi\) | ||||
0.0248453 | + | 0.999691i | \(0.492091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.9335 | −0.434755 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.7404 | 0.998586 | 0.499293 | − | 0.866433i | \(-0.333593\pi\) | ||||
0.499293 | + | 0.866433i | \(0.333593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.7009 | 0.827510 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −70.5761 | −2.36174 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.21768 | 0.0741287 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.0943 | 0.370429 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.7105 | −0.724086 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −60.9515 | −2.03059 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.5383 | −0.350304 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.67663 | −0.288103 | −0.144051 | − | 0.989570i | \(-0.546013\pi\) | ||||
−0.144051 | + | 0.989570i | \(0.546013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −55.4865 | −1.84037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.7245 | −0.752895 | −0.376448 | − | 0.926438i | \(-0.622855\pi\) | ||||
−0.376448 | + | 0.926438i | \(0.622855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.17198 | 0.171168 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.93401 | −0.295349 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8906 | 0.887040 | 0.443520 | − | 0.896265i | \(-0.353730\pi\) | ||||
0.443520 | + | 0.896265i | \(0.353730\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0880 | −0.661923 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.7274 | −0.451844 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.6292 | −1.53316 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.0876 | −0.791140 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.7302 | −1.04103 | −0.520517 | − | 0.853851i | \(-0.674261\pi\) | ||||
−0.520517 | + | 0.853851i | \(0.674261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.134513 | 0.00440376 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.5419 | 0.475572 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.9242 | −0.748901 | −0.374450 | − | 0.927247i | \(-0.622169\pi\) | ||||
−0.374450 | + | 0.927247i | \(0.622169\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.7378 | 2.04737 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.7909 | −0.514767 | −0.257384 | − | 0.966309i | \(-0.582860\pi\) | ||||
−0.257384 | + | 0.966309i | \(0.582860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.51894 | −0.0494634 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.0933 | 0.425474 | 0.212737 | − | 0.977109i | \(-0.431762\pi\) | ||||
0.212737 | + | 0.977109i | \(0.431762\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.2068 | 0.396250 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.51059 | −0.211120 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.95732 | −0.290156 | −0.145078 | − | 0.989420i | \(-0.546343\pi\) | ||||
−0.145078 | + | 0.989420i | \(0.546343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.40414 | 0.304311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 110.012 | 3.55617 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.2817 | −0.654249 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.9064 | 0.995946 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.25246 | −0.0725091 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.9003 | 1.12232 | 0.561160 | − | 0.827708i | \(-0.310355\pi\) | ||||
0.561160 | + | 0.827708i | \(0.310355\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 84.5884 | 2.71737 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.18663 | 0.294813 | 0.147407 | − | 0.989076i | \(-0.452907\pi\) | ||||
0.147407 | + | 0.989076i | \(0.452907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −34.6492 | −1.10966 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.9209 | −1.53312 | −0.766562 | − | 0.642170i | \(-0.778034\pi\) | ||||
−0.766562 | + | 0.642170i | \(0.778034\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.7235 | −0.918006 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.1174 | 1.15314 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.6952 | 1.23419 | 0.617093 | − | 0.786890i | \(-0.288310\pi\) | ||||
0.617093 | + | 0.786890i | \(0.288310\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.14142 | 0.0363685 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.7239 | −0.404596 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.2144 | 1.37275 | 0.686375 | − | 0.727248i | \(-0.259201\pi\) | ||||
0.686375 | + | 0.727248i | \(0.259201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 80.6175 | 2.55832 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.371506 | −0.0117775 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.9844 | −0.506230 | −0.253115 | − | 0.967436i | \(-0.581455\pi\) | ||||
−0.253115 | + | 0.967436i | \(0.581455\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 69.8996 | 2.21153 |
(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 | 8036.2.a.q.1.14 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.2 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.2 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.2 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.2 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.2 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.14 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.2 | 15 | 7.6 | odd | 2 |