Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3136,2,Mod(3135,3136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3136.3135");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3136 = 2^{6} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3136.f (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(25.0410860739\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1212153856.10 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 196) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3135.3 | ||
Root | \(-1.07072 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3136.3135 |
Dual form | 3136.2.f.i.3135.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3136\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −2.14144 | −1.23636 | −0.618182 | − | 0.786035i | \(-0.712130\pi\) | ||||
−0.618182 | + | 0.786035i | \(0.712130\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.61313i | − 1.16863i | −0.811529 | − | 0.584313i | \(-0.801364\pi\) | ||||
0.811529 | − | 0.584313i | \(-0.198636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.58579 | 0.528595 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.95687i | 1.19304i | 0.802597 | + | 0.596521i | \(0.203451\pi\) | ||||
−0.802597 | + | 0.596521i | \(0.796549\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.08239i | − 0.300202i | −0.988671 | − | 0.150101i | \(-0.952040\pi\) | ||||
0.988671 | − | 0.150101i | \(-0.0479598\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.59587i | 1.44485i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.317025i | 0.0768899i | 0.999261 | + | 0.0384450i | \(0.0122404\pi\) | ||||
−0.999261 | + | 0.0384450i | \(0.987760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.16991 | −1.18606 | −0.593029 | − | 0.805181i | \(-0.702068\pi\) | ||||
−0.593029 | + | 0.805181i | \(0.702068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 2.31788i | − 0.483312i | −0.970362 | − | 0.241656i | \(-0.922309\pi\) | ||||
0.970362 | − | 0.241656i | \(-0.0776906\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.82843 | −0.365685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.02846 | 0.582827 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.82843 | 1.26801 | 0.634004 | − | 0.773330i | \(-0.281410\pi\) | ||||
0.634004 | + | 0.773330i | \(0.281410\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.05692 | 1.08786 | 0.543928 | − | 0.839132i | \(-0.316937\pi\) | ||||
0.543928 | + | 0.839132i | \(0.316937\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 8.47343i | − 1.47503i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.31788i | 0.371158i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2.29610i | − 0.358591i | −0.983795 | − | 0.179295i | \(-0.942618\pi\) | ||||
0.983795 | − | 0.179295i | \(-0.0573818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.23486i | 1.10331i | 0.834074 | + | 0.551653i | \(0.186003\pi\) | ||||
−0.834074 | + | 0.551653i | \(0.813997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 4.14386i | − 0.617730i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.28289 | −0.624724 | −0.312362 | − | 0.949963i | \(-0.601120\pi\) | ||||
−0.312362 | + | 0.949963i | \(0.601120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 0.678892i | − 0.0950639i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4853 | −1.44026 | −0.720132 | − | 0.693837i | \(-0.755919\pi\) | ||||
−0.720132 | + | 0.693837i | \(0.755919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3398 | 1.39422 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.0711 | 1.46640 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2268 | 1.46161 | 0.730804 | − | 0.682587i | \(-0.239145\pi\) | ||||
0.730804 | + | 0.682587i | \(0.239145\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 5.41196i | − 0.692931i | −0.938063 | − | 0.346465i | \(-0.887382\pi\) | ||||
0.938063 | − | 0.346465i | \(-0.112618\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.82843 | −0.350823 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.27798i | − 0.400469i | −0.979748 | − | 0.200235i | \(-0.935830\pi\) | ||||
0.979748 | − | 0.200235i | \(-0.0641704\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.96362i | 0.597550i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 14.0167i | − 1.64053i | −0.571983 | − | 0.820266i | \(-0.693826\pi\) | ||||
0.571983 | − | 0.820266i | \(-0.306174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.91548 | 0.452120 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.91375i | 0.890366i | 0.895440 | + | 0.445183i | \(0.146861\pi\) | ||||
−0.895440 | + | 0.445183i | \(0.853139\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2426 | −1.24918 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.45280 | 1.03758 | 0.518790 | − | 0.854902i | \(-0.326383\pi\) | ||||
0.518790 | + | 0.854902i | \(0.326383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.828427 | 0.0898555 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.6227 | −1.56772 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.99162i | 0.635110i | 0.948240 | + | 0.317555i | \(0.102862\pi\) | ||||
−0.948240 | + | 0.317555i | \(0.897138\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.9706 | −1.34498 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.5096i | 1.38606i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.23880i | 0.938058i | 0.883183 | + | 0.469029i | \(0.155396\pi\) | ||||
−0.883183 | + | 0.469029i | \(0.844604\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.27476i | 0.630637i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 15.2304i | − 1.51548i | −0.652555 | − | 0.757741i | \(-0.726303\pi\) | ||||
0.652555 | − | 0.757741i | \(-0.273697\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.1138 | −1.19361 | −0.596806 | − | 0.802385i | \(-0.703564\pi\) | ||||
−0.596806 | + | 0.802385i | \(0.703564\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.31788i | 0.224078i | 0.993704 | + | 0.112039i | \(0.0357382\pi\) | ||||
−0.993704 | + | 0.112039i | \(0.964262\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.65685 | 0.541828 | 0.270914 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270914 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.56578 | −0.813028 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | −0.399114 | −0.199557 | − | 0.979886i | \(-0.563950\pi\) | ||||
−0.199557 | + | 0.979886i | \(0.563950\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.05692 | −0.564811 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 1.71644i | − 0.158685i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.65685 | −0.423350 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.91697i | 0.443349i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 8.28772i | − 0.741276i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 10.2316i | − 0.907911i | −0.891024 | − | 0.453955i | \(-0.850013\pi\) | ||||
0.891024 | − | 0.453955i | \(-0.149987\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 15.4930i | − 1.36409i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.367414 | 0.0321011 | 0.0160505 | − | 0.999871i | \(-0.494891\pi\) | ||||
0.0160505 | + | 0.999871i | \(0.494891\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 7.91375i | − 0.681107i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.24264 | −0.704216 | −0.352108 | − | 0.935959i | \(-0.614535\pi\) | ||||
−0.352108 | + | 0.935959i | \(0.614535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.8211 | −1.93566 | −0.967829 | − | 0.251610i | \(-0.919040\pi\) | ||||
−0.967829 | + | 0.251610i | \(0.919040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.17157 | 0.772386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.28289 | 0.358153 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 17.8435i | − 1.48183i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.82843 | −0.395560 | −0.197780 | − | 0.980246i | \(-0.563373\pi\) | ||||
−0.197780 | + | 0.980246i | \(0.563373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 21.4234i | − 1.74341i | −0.490032 | − | 0.871704i | \(-0.663015\pi\) | ||||
0.490032 | − | 0.871704i | \(-0.336985\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.502734i | 0.0406437i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 15.8275i | − 1.27130i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 19.1886i | − 1.53141i | −0.643189 | − | 0.765707i | \(-0.722389\pi\) | ||||
0.643189 | − | 0.765707i | \(-0.277611\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.4537 | 1.78069 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 15.1486i | − 1.18653i | −0.805007 | − | 0.593265i | \(-0.797839\pi\) | ||||
0.805007 | − | 0.593265i | \(-0.202161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −22.1421 | −1.72376 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.83095 | −0.605977 | −0.302989 | − | 0.952994i | \(-0.597984\pi\) | ||||
−0.302989 | + | 0.952994i | \(0.597984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8284 | 0.909879 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.19837 | −0.626945 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 6.57128i | − 0.499605i | −0.968297 | − | 0.249802i | \(-0.919634\pi\) | ||||
0.968297 | − | 0.249802i | \(-0.0803657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.0416 | −1.80708 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 13.5096i | − 1.00976i | −0.863191 | − | 0.504878i | \(-0.831537\pi\) | ||||
0.863191 | − | 0.504878i | \(-0.168463\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.9874i | 1.63431i | 0.576418 | + | 0.817155i | \(0.304450\pi\) | ||||
−0.576418 | + | 0.817155i | \(0.695550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5894i | 0.856714i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 10.4525i | − 0.768483i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.25443 | −0.0917330 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 6.55596i | − 0.474373i | −0.971464 | − | 0.237186i | \(-0.923775\pi\) | ||||
0.971464 | − | 0.237186i | \(-0.0762252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.5858 | 1.04991 | 0.524954 | − | 0.851131i | \(-0.324083\pi\) | ||||
0.524954 | + | 0.851131i | \(0.324083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.05692 | 0.433745 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.1316 | 1.21442 | 0.607212 | − | 0.794540i | \(-0.292288\pi\) | ||||
0.607212 | + | 0.794540i | \(0.292288\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.01962i | 0.495126i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 3.67567i | − 0.255477i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 20.4567i | − 1.41502i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 14.4697i | − 0.996136i | −0.867138 | − | 0.498068i | \(-0.834043\pi\) | ||||
0.867138 | − | 0.498068i | \(-0.165957\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.9056 | 1.28935 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 30.0160i | 2.02829i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.343146 | 0.0230825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.83095 | −0.524399 | −0.262200 | − | 0.965014i | \(-0.584448\pi\) | ||||
−0.262200 | + | 0.965014i | \(0.584448\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.89949 | −0.193300 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.97240 | −0.661891 | −0.330946 | − | 0.943650i | \(-0.607368\pi\) | ||||
−0.330946 | + | 0.943650i | \(0.607368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.34502i | 0.0888817i | 0.999012 | + | 0.0444409i | \(0.0141506\pi\) | ||||
−0.999012 | + | 0.0444409i | \(0.985849\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.2426 | 1.06409 | 0.532045 | − | 0.846716i | \(-0.321424\pi\) | ||||
0.532045 | + | 0.846716i | \(0.321424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.1917i | 0.730068i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 16.9469i | − 1.10082i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 10.2316i | − 0.661829i | −0.943661 | − | 0.330915i | \(-0.892643\pi\) | ||||
0.943661 | − | 0.330915i | \(-0.107357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.09494i | 0.328194i | 0.986444 | + | 0.164097i | \(0.0524710\pi\) | ||||
−0.986444 | + | 0.164097i | \(0.947529\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.9901 | 0.961616 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.59587i | 0.356056i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.2426 | −1.28283 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.91548 | −0.247143 | −0.123571 | − | 0.992336i | \(-0.539435\pi\) | ||||
−0.123571 | + | 0.992336i | \(0.539435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.17157 | 0.576612 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.77403 | −0.111094 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 19.0572i | − 1.18876i | −0.804185 | − | 0.594379i | \(-0.797398\pi\) | ||||
0.804185 | − | 0.594379i | \(-0.202602\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.8284 | 0.670263 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 25.6614i | − 1.58235i | −0.611588 | − | 0.791176i | \(-0.709469\pi\) | ||||
0.611588 | − | 0.791176i | \(-0.290531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.3994i | 1.68313i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 12.8307i | − 0.785227i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.04054i | 0.307327i | 0.988123 | + | 0.153664i | \(0.0491072\pi\) | ||||
−0.988123 | + | 0.153664i | \(0.950893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.28289 | −0.260167 | −0.130084 | − | 0.991503i | \(-0.541525\pi\) | ||||
−0.130084 | + | 0.991503i | \(0.541525\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 7.23486i | − 0.436278i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.14214 | 0.248877 | 0.124438 | − | 0.992227i | \(-0.460287\pi\) | ||||
0.124438 | + | 0.992227i | \(0.460287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.60498 | 0.575035 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3848 | 0.619504 | 0.309752 | − | 0.950817i | \(-0.399754\pi\) | ||||
0.309752 | + | 0.950817i | \(0.399754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.39587 | 0.201864 | 0.100932 | − | 0.994893i | \(-0.467818\pi\) | ||||
0.100932 | + | 0.994893i | \(0.467818\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 28.9301i | − 1.71367i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8995 | 0.994088 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 19.7844i | − 1.15978i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 11.7975i | − 0.689219i | −0.938746 | − | 0.344609i | \(-0.888011\pi\) | ||||
0.938746 | − | 0.344609i | \(-0.111989\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 29.3371i | − 1.70807i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.9832i | 0.695338i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.50886 | −0.145091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.6151i | 1.87369i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.1421 | −0.809776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.91548 | −0.223468 | −0.111734 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111734 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.9411 | 1.47574 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.6796 | −1.17263 | −0.586317 | − | 0.810082i | \(-0.699423\pi\) | ||||
−0.586317 | + | 0.810082i | \(0.699423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7486i | 0.720594i | 0.932838 | + | 0.360297i | \(0.117325\pi\) | ||||
−0.932838 | + | 0.360297i | \(0.882675\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.51472 | 0.309737 | 0.154869 | − | 0.987935i | \(-0.450505\pi\) | ||||
0.154869 | + | 0.987935i | \(0.450505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.0192i | 1.51279i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 4.96362i | − 0.277042i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.63899i | − 0.0911959i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.97908i | 0.109779i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1138 | −0.669897 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 15.1486i | − 0.832643i | −0.909218 | − | 0.416321i | \(-0.863319\pi\) | ||||
0.909218 | − | 0.416321i | \(-0.136681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.34315 | 0.347602 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.56578 | −0.467999 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8284 | 0.589862 | 0.294931 | − | 0.955519i | \(-0.404703\pi\) | ||||
0.294931 | + | 0.955519i | \(0.404703\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.08538 | 0.493450 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.9665i | 1.29786i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.9706 | 0.698312 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.95687i | 0.212416i | 0.994344 | + | 0.106208i | \(0.0338710\pi\) | ||||
−0.994344 | + | 0.106208i | \(0.966129\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.47343i | 0.453572i | 0.973945 | + | 0.226786i | \(0.0728218\pi\) | ||||
−0.973945 | + | 0.226786i | \(0.927178\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 3.27798i | − 0.174966i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 10.0586i | − 0.535363i | −0.963507 | − | 0.267681i | \(-0.913743\pi\) | ||||
0.963507 | − | 0.267681i | \(-0.0862575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 31.2573i | − 1.64970i | −0.565353 | − | 0.824849i | \(-0.691260\pi\) | ||||
0.565353 | − | 0.824849i | \(-0.308740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.72792 | 0.406733 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.97240 | 0.523415 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.6274 | −1.91717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.8487 | −0.670695 | −0.335348 | − | 0.942094i | \(-0.608854\pi\) | ||||
−0.335348 | + | 0.942094i | \(0.608854\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 3.64113i | − 0.189549i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.1421 | 1.04292 | 0.521460 | − | 0.853276i | \(-0.325388\pi\) | ||||
0.521460 | + | 0.853276i | \(0.325388\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.7477i | 0.916487i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.39104i | − 0.380658i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.7046i | 1.11489i | 0.830214 | + | 0.557444i | \(0.188218\pi\) | ||||
−0.830214 | + | 0.557444i | \(0.811782\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.9105i | 1.12251i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.0194 | −1.58502 | −0.792509 | − | 0.609860i | \(-0.791226\pi\) | ||||
−0.792509 | + | 0.609860i | \(0.791226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4729i | 0.583202i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.1421 | −0.717035 | −0.358517 | − | 0.933523i | \(-0.616718\pi\) | ||||
−0.358517 | + | 0.933523i | \(0.616718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.734828 | 0.0371618 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.786797 | −0.0396886 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.6796 | 1.04050 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 16.1271i | − 0.809396i | −0.914450 | − | 0.404698i | \(-0.867377\pi\) | ||||
0.914450 | − | 0.404698i | \(-0.132623\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.8284 | −0.640621 | −0.320311 | − | 0.947313i | \(-0.603787\pi\) | ||||
−0.320311 | + | 0.947313i | \(0.603787\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.55596i | − 0.326576i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.3784i | 1.45983i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8275i | 0.784540i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.8310i | 0.683899i | 0.939718 | + | 0.341949i | \(0.111087\pi\) | ||||
−0.939718 | + | 0.341949i | \(0.888913\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.6512 | 0.870668 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 24.7013i | − 1.21254i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 48.8701 | 2.39318 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.2837 | −0.844366 | −0.422183 | − | 0.906511i | \(-0.638736\pi\) | ||||
−0.422183 | + | 0.906511i | \(0.638736\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.4853 | 0.511021 | 0.255511 | − | 0.966806i | \(-0.417756\pi\) | ||||
0.255511 | + | 0.966806i | \(0.417756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.79175 | −0.330226 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 0.579658i | − 0.0281175i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.17157 | −0.442808 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 0.960099i | − 0.0462463i | −0.999733 | − | 0.0231232i | \(-0.992639\pi\) | ||||
0.999733 | − | 0.0231232i | \(-0.00736099\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 26.1857i | − 1.25840i | −0.777243 | − | 0.629201i | \(-0.783382\pi\) | ||||
0.777243 | − | 0.629201i | \(-0.216618\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 38.2110i | 1.83208i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.9832i | 0.573236i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.4537 | 1.07165 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 28.3770i | − 1.34823i | −0.738625 | − | 0.674116i | \(-0.764525\pi\) | ||||
0.738625 | − | 0.674116i | \(-0.235475\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.6569 | 0.742206 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.3398 | 0.489056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2843 | −0.768502 | −0.384251 | − | 0.923229i | \(-0.625540\pi\) | ||||
−0.384251 | + | 0.923229i | \(0.625540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.08538 | 0.427814 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 45.8770i | 2.15549i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.727922 | 0.0340508 | 0.0170254 | − | 0.999855i | \(-0.494580\pi\) | ||||
0.0170254 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.960099i | 0.0448136i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 29.7499i | − 1.38559i | −0.721135 | − | 0.692794i | \(-0.756379\pi\) | ||||
0.721135 | − | 0.692794i | \(-0.243621\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.9330i | 1.62347i | 0.584024 | + | 0.811737i | \(0.301477\pi\) | ||||
−0.584024 | + | 0.811737i | \(0.698523\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 33.8937i | 1.57178i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.0755 | −1.11408 | −0.557041 | − | 0.830485i | \(-0.688063\pi\) | ||||
−0.557041 | + | 0.830485i | \(0.688063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 41.0913i | 1.89339i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.6274 | −1.31629 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.45280 | 0.433724 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.6274 | −0.761317 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.7935 | 1.49837 | 0.749186 | − | 0.662360i | \(-0.230445\pi\) | ||||
0.749186 | + | 0.662360i | \(0.230445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 4.32957i | − 0.197411i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.1421 | 1.09624 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5032i | 0.883773i | 0.897071 | + | 0.441886i | \(0.145691\pi\) | ||||
−0.897071 | + | 0.441886i | \(0.854309\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.4399i | 1.46698i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.4697i | 0.653009i | 0.945196 | + | 0.326504i | \(0.105871\pi\) | ||||
−0.945196 | + | 0.326504i | \(0.894129\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.16478i | 0.0974970i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.3967 | 0.736978 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5495i | 0.561793i | 0.959738 | + | 0.280897i | \(0.0906318\pi\) | ||||
−0.959738 | + | 0.280897i | \(0.909368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.7696 | 0.749208 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.83095 | 0.349165 | 0.174582 | − | 0.984643i | \(-0.444142\pi\) | ||||
0.174582 | + | 0.984643i | \(0.444142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.7990 | −1.77103 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.3299 | −1.12494 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 6.57128i | − 0.291267i | −0.989339 | − | 0.145633i | \(-0.953478\pi\) | ||||
0.989339 | − | 0.145633i | \(-0.0465220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.6569 | −0.691267 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.6550i | 1.39489i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 16.9469i | − 0.745322i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.0720i | 0.617693i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 12.0376i | − 0.527378i | −0.964608 | − | 0.263689i | \(-0.915061\pi\) | ||||
0.964608 | − | 0.263689i | \(-0.0849393\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.46354 | −0.326358 | −0.163179 | − | 0.986597i | \(-0.552175\pi\) | ||||
−0.163179 | + | 0.986597i | \(0.552175\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.92020i | 0.0836451i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.6274 | 0.766409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.8033 | 0.772600 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.48528 | −0.107649 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.05692 | 0.261864 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 28.9301i | 1.24843i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −45.3137 | −1.94819 | −0.974094 | − | 0.226142i | \(-0.927389\pi\) | ||||
−0.974094 | + | 0.226142i | \(0.927389\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 47.0848i | − 2.02060i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 14.7821i | − 0.633194i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 27.6981i | − 1.18429i | −0.805833 | − | 0.592143i | \(-0.798282\pi\) | ||||
0.805833 | − | 0.592143i | \(-0.201718\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 8.58221i | − 0.366280i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.3023 | −1.50393 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 22.3835i | 0.950125i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.6569 | 0.832888 | 0.416444 | − | 0.909161i | \(-0.363276\pi\) | ||||
0.416444 | + | 0.909161i | \(0.363276\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.83095 | 0.331214 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.68629 | 0.113415 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.0470 | −0.887027 | −0.443513 | − | 0.896268i | \(-0.646268\pi\) | ||||
−0.443513 | + | 0.896268i | \(0.646268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.0866i | 0.466415i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8284 | 0.789329 | 0.394664 | − | 0.918825i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918825i | \(0.370861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.95043i | 0.416412i | 0.978085 | + | 0.208206i | \(0.0667625\pi\) | ||||
−0.978085 | + | 0.208206i | \(0.933237\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.0392i | 0.586497i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.23808i | 0.176740i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 0.842290i | − 0.0350650i | −0.999846 | − | 0.0175325i | \(-0.994419\pi\) | ||||
0.999846 | − | 0.0175325i | \(-0.00558105\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.2347 | −1.29807 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 41.4889i | − 1.71830i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.48528 | −0.185444 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.8211 | 0.941926 | 0.470963 | − | 0.882153i | \(-0.343906\pi\) | ||||
0.470963 | + | 0.882153i | \(0.343906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.3137 | −1.29026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.28289 | 0.176175 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4579i | 1.53821i | 0.639121 | + | 0.769106i | \(0.279298\pi\) | ||||
−0.639121 | + | 0.769106i | \(0.720702\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.6863 | −1.50147 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.2174i | 1.31637i | 0.752857 | + | 0.658184i | \(0.228675\pi\) | ||||
−0.752857 | + | 0.658184i | \(0.771325\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.5516i | 1.04227i | 0.853474 | + | 0.521136i | \(0.174491\pi\) | ||||
−0.853474 | + | 0.521136i | \(0.825509\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.19818i | − 0.211686i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1689i | 0.494738i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.1138 | −0.491686 | −0.245843 | − | 0.969310i | \(-0.579065\pi\) | ||||
−0.245843 | + | 0.969310i | \(0.579065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.63577i | 0.187543i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.68629 | 0.350836 | 0.175418 | − | 0.984494i | \(-0.443872\pi\) | ||||
0.175418 | + | 0.984494i | \(0.443872\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.8487 | 0.518108 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4558 | −1.42740 | −0.713699 | − | 0.700452i | \(-0.752982\pi\) | ||||
−0.713699 | + | 0.700452i | \(0.752982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.5205 | 0.543433 | 0.271717 | − | 0.962377i | \(-0.412409\pi\) | ||||
0.271717 | + | 0.962377i | \(0.412409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 7.01962i | − 0.281688i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7990 | −1.23196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 43.8068i | 1.74948i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.26810i | 0.0505625i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.4633i | 0.814630i | 0.913288 | + | 0.407315i | \(0.133535\pi\) | ||||
−0.913288 | + | 0.407315i | \(0.866465\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.9861i | 1.23159i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.7365 | −1.06101 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 49.4558 | 1.95339 | 0.976694 | − | 0.214636i | \(-0.0688564\pi\) | ||||
0.976694 | + | 0.214636i | \(0.0688564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.7267 | 1.64554 | 0.822769 | − | 0.568375i | \(-0.192428\pi\) | ||||
0.822769 | + | 0.568375i | \(0.192428\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.4853 | −1.59411 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.8681 | 1.72463 | 0.862317 | − | 0.506370i | \(-0.169013\pi\) | ||||
0.862317 | + | 0.506370i | \(0.169013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.4231i | 1.74376i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7990 | 0.931326 | 0.465663 | − | 0.884962i | \(-0.345816\pi\) | ||||
0.465663 | + | 0.884962i | \(0.345816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 0.960099i | − 0.0375142i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 22.2275i | − 0.867177i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 13.2284i | − 0.515306i | −0.966238 | − | 0.257653i | \(-0.917051\pi\) | ||||
0.966238 | − | 0.257653i | \(-0.0829491\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.6662i | 1.46504i | 0.680744 | + | 0.732522i | \(0.261657\pi\) | ||||
−0.680744 | + | 0.732522i | \(0.738343\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.734828 | −0.0285383 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 15.8275i | − 0.612843i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.7696 | 0.648348 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.4144 | 0.826696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3848 | 0.400304 | 0.200152 | − | 0.979765i | \(-0.435856\pi\) | ||||
0.200152 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.53732 | −0.213132 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8532i | 1.10892i | 0.832211 | + | 0.554459i | \(0.187075\pi\) | ||||
−0.832211 | + | 0.554459i | \(0.812925\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.3553 | 0.818338 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 32.2174i | − 1.23276i | −0.787447 | − | 0.616382i | \(-0.788598\pi\) | ||||
0.787447 | − | 0.616382i | \(-0.211402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.5391i | 0.822965i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 2.88030i | − 0.109890i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3492i | 0.432370i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.19837 | 0.311881 | 0.155940 | − | 0.987766i | \(-0.450159\pi\) | ||||
0.155940 | + | 0.987766i | \(0.450159\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 59.6343i | 2.26206i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.727922 | 0.0275720 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.7827 | −1.31560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.0000 | −0.604312 | −0.302156 | − | 0.953259i | \(-0.597706\pi\) | ||||
−0.302156 | + | 0.953259i | \(0.597706\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.6796 | −0.779947 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 23.9665i | − 0.902630i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.6274 | 1.75113 | 0.875565 | − | 0.483101i | \(-0.160490\pi\) | ||||
0.875565 | + | 0.483101i | \(0.160490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5495i | 0.470644i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 14.0392i | − 0.525774i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 11.1917i | − 0.418547i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.9105i | 0.818262i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.5283 | 1.25039 | 0.625197 | − | 0.780467i | \(-0.285019\pi\) | ||||
0.625197 | + | 0.780467i | \(0.285019\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 10.9105i | − 0.405767i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.4853 | −0.463692 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.9802 | −1.11191 | −0.555953 | − | 0.831214i | \(-0.687646\pi\) | ||||
−0.555953 | + | 0.831214i | \(0.687646\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.62742 | 0.0602747 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.29363 | −0.0848331 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4567i | 0.755584i | 0.925890 | + | 0.377792i | \(0.123317\pi\) | ||||
−0.925890 | + | 0.377792i | \(0.876683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9706 | 0.477777 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.4330i | 0.457357i | 0.973502 | + | 0.228678i | \(0.0734404\pi\) | ||||
−0.973502 | + | 0.228678i | \(0.926560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 11.9832i | − 0.440215i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 45.1646i | − 1.65693i | −0.560042 | − | 0.828464i | \(-0.689215\pi\) | ||||
0.560042 | − | 0.828464i | \(-0.310785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.6173i | 0.462262i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.9901 | 0.548460 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 37.2509i | − 1.35930i | −0.733535 | − | 0.679652i | \(-0.762131\pi\) | ||||
0.733535 | − | 0.679652i | \(-0.237869\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.38478 | 0.305558 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −55.9819 | −2.03739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.2843 | 1.60954 | 0.804770 | − | 0.593587i | \(-0.202289\pi\) | ||||
0.804770 | + | 0.593587i | \(0.202289\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.6404 | −0.712902 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0543929i | 0.00197174i | 1.00000 | 0.000985871i | \(0.000313813\pi\) | |||||
−1.00000 | 0.000985871i | \(0.999686\pi\) | ||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.31371 | 0.0474972 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 12.1518i | − 0.438777i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.1342i | 0.689996i | 0.938603 | + | 0.344998i | \(0.112120\pi\) | ||||
−0.938603 | + | 0.344998i | \(0.887880\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.8100i | 1.46974i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 49.4955i | − 1.78023i | −0.455735 | − | 0.890116i | \(-0.650624\pi\) | ||||
0.455735 | − | 0.890116i | \(-0.349376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.0746 | −0.397813 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.8706i | 0.425309i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.6796 | 0.739029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50.1421 | −1.78965 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.2071 | 1.46887 | 0.734436 | − | 0.678677i | \(-0.237447\pi\) | ||||
0.734436 | + | 0.678677i | \(0.237447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 54.9526i | 1.95636i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.85786 | −0.208019 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 58.6742i | − 2.08096i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 20.1940i | − 0.715309i | −0.933854 | − | 0.357655i | \(-0.883576\pi\) | ||||
0.933854 | − | 0.357655i | \(-0.116424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.35778i | − 0.0480350i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.50143i | 0.335716i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 55.4623 | 1.95722 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 10.7940i | − 0.379968i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.0416306 | −0.00146365 | −0.000731826 | − | 1.00000i | \(-0.500233\pi\) | ||||
−0.000731826 | 1.00000i | \(0.500233\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.4330 | 1.38468 | 0.692340 | − | 0.721571i | \(-0.256580\pi\) | ||||
0.692340 | + | 0.721571i | \(0.256580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.17157 | 0.321661 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.5852 | −1.38661 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 37.4035i | − 1.30858i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0000 | 0.628204 | 0.314102 | − | 0.949389i | \(-0.398297\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 17.1853i | − 0.599041i | −0.954090 | − | 0.299521i | \(-0.903173\pi\) | ||||
0.954090 | − | 0.299521i | \(-0.0968267\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.4930i | 0.539399i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.1646i | 1.57053i | 0.619162 | + | 0.785264i | \(0.287473\pi\) | ||||
−0.619162 | + | 0.785264i | \(0.712527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.2220i | 1.64009i | 0.572301 | + | 0.820044i | \(0.306051\pi\) | ||||
−0.572301 | + | 0.820044i | \(0.693949\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.87016 | −0.307702 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.4633i | 0.708160i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.3431 | 0.634032 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.3984 | −1.46376 | −0.731878 | − | 0.681435i | \(-0.761356\pi\) | ||||
−0.731878 | + | 0.681435i | \(0.761356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.2384 | −0.765932 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 30.9092i | − 1.06331i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.27208 | −0.249577 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 9.27153i | − 0.317824i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.3002i | 1.31137i | 0.755033 | + | 0.655687i | \(0.227621\pi\) | ||||
−0.755033 | + | 0.655687i | \(0.772379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.4234i | 0.732664i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.45542i | 0.118035i | 0.998257 | + | 0.0590174i | \(0.0187967\pi\) | ||||
−0.998257 | + | 0.0590174i | \(0.981203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.66105 | 0.0907937 | 0.0453969 | − | 0.998969i | \(-0.485545\pi\) | ||||
0.0453969 | + | 0.998969i | \(0.485545\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 12.5495i | − 0.427190i | −0.976922 | − | 0.213595i | \(-0.931483\pi\) | ||||
0.976922 | − | 0.213595i | \(-0.0685174\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.1716 | −0.583851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.1893 | −1.22905 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.3137 | −1.06224 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.54806 | −0.120221 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.6508i | 0.495853i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.4264 | −1.02743 | −0.513713 | − | 0.857962i | \(-0.671731\pi\) | ||||
−0.513713 | + | 0.857962i | \(0.671731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.2638i | 0.852125i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 26.1857i | − 0.882217i | −0.897454 | − | 0.441109i | \(-0.854585\pi\) | ||||
0.897454 | − | 0.441109i | \(-0.145415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 24.7013i | − 0.831266i | −0.909532 | − | 0.415633i | \(-0.863560\pi\) | ||||
0.909532 | − | 0.415633i | \(-0.136440\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 62.8238i | 2.11180i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4537 | 0.753920 | 0.376960 | − | 0.926230i | \(-0.376969\pi\) | ||||
0.376960 | + | 0.926230i | \(0.376969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 44.4857i | − 1.49033i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.1421 | 0.740958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.3023 | −1.18003 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.37258 | 0.179385 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.3592 | 1.37941 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 3.32410i | − 0.110742i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 57.4558 | 1.90990 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 33.9729i | − 1.12805i | −0.825757 | − | 0.564025i | \(-0.809252\pi\) | ||||
0.825757 | − | 0.564025i | \(-0.190748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 24.1522i | − 0.801077i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 18.7078i | − 0.619817i | −0.950766 | − | 0.309908i | \(-0.899702\pi\) | ||||
0.950766 | − | 0.309908i | \(-0.100298\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.4035i | 1.23788i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.2846 | 1.00118 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.8403i | 1.61109i | 0.592533 | + | 0.805546i | \(0.298128\pi\) | ||||
−0.592533 | + | 0.805546i | \(0.701872\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.38478 | 0.276288 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.31371 | −0.240473 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.2100 | −0.630938 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.8812i | 0.980369i | 0.871619 | + | 0.490185i | \(0.163071\pi\) | ||||
−0.871619 | + | 0.490185i | \(0.836929\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 44.2843 | 1.44980 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.27798i | 0.107201i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 29.8042i | − 0.973662i | −0.873496 | − | 0.486831i | \(-0.838153\pi\) | ||||
0.873496 | − | 0.486831i | \(-0.161847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 27.3004i | − 0.890916i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 24.7862i | − 0.808008i | −0.914757 | − | 0.404004i | \(-0.867618\pi\) | ||||
0.914757 | − | 0.404004i | \(-0.132382\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.32209 | −0.173311 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 9.15505i | − 0.297499i | −0.988875 | − | 0.148750i | \(-0.952475\pi\) | ||||
0.988875 | − | 0.148750i | \(-0.0475249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.1716 | −0.492490 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.8095 | −0.382948 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.3431 | 0.853338 | 0.426669 | − | 0.904408i | \(-0.359687\pi\) | ||||
0.426669 | + | 0.904408i | \(0.359687\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.1316 | −0.554364 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 57.8602i | − 1.87035i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.68629 | 0.183429 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.67567i | 0.118447i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 38.1145i | − 1.22695i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 45.1646i | − 1.45240i | −0.687486 | − | 0.726198i | \(-0.741286\pi\) | ||||
0.687486 | − | 0.726198i | \(-0.258714\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.50981i | 0.112751i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.0009 | −0.417217 | −0.208609 | − | 0.977999i | \(-0.566894\pi\) | ||||
−0.208609 | + | 0.977999i | \(0.566894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 4.23808i | − 0.135727i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.6152 | 0.563561 | 0.281780 | − | 0.959479i | \(-0.409075\pi\) | ||||
0.281780 | + | 0.959479i | \(0.409075\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.7081 | −0.757714 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.97056 | 0.286408 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.60498 | −0.306351 | −0.153176 | − | 0.988199i | \(-0.548950\pi\) | ||||
−0.153176 | + | 0.988199i | \(0.548950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.22625i | 0.166522i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.7696 | 0.533241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 25.6614i | − 0.815163i | −0.913169 | − | 0.407581i | \(-0.866372\pi\) | ||||
0.913169 | − | 0.407581i | \(-0.133628\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.4399i | 1.02945i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 44.7669i | − 1.41921i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.9092i | 0.978903i | 0.872030 | + | 0.489452i | \(0.162803\pi\) | ||||
−0.872030 | + | 0.489452i | \(0.837197\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.1138 | 0.383265 |
(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 | 3136.2.f.i.3135.3 | 8 | ||
4.3 | odd | 2 | inner | 3136.2.f.i.3135.5 | 8 | ||
7.6 | odd | 2 | inner | 3136.2.f.i.3135.6 | 8 | ||
8.3 | odd | 2 | 196.2.d.c.195.5 | ✓ | 8 | ||
8.5 | even | 2 | 196.2.d.c.195.8 | yes | 8 | ||
24.5 | odd | 2 | 1764.2.b.k.1567.1 | 8 | |||
24.11 | even | 2 | 1764.2.b.k.1567.3 | 8 | |||
28.27 | even | 2 | inner | 3136.2.f.i.3135.4 | 8 | ||
56.3 | even | 6 | 196.2.f.d.19.5 | 16 | |||
56.5 | odd | 6 | 196.2.f.d.31.6 | 16 | |||
56.11 | odd | 6 | 196.2.f.d.19.6 | 16 | |||
56.13 | odd | 2 | 196.2.d.c.195.7 | yes | 8 | ||
56.19 | even | 6 | 196.2.f.d.31.1 | 16 | |||
56.27 | even | 2 | 196.2.d.c.195.6 | yes | 8 | ||
56.37 | even | 6 | 196.2.f.d.31.5 | 16 | |||
56.45 | odd | 6 | 196.2.f.d.19.2 | 16 | |||
56.51 | odd | 6 | 196.2.f.d.31.2 | 16 | |||
56.53 | even | 6 | 196.2.f.d.19.1 | 16 | |||
168.83 | odd | 2 | 1764.2.b.k.1567.4 | 8 | |||
168.125 | even | 2 | 1764.2.b.k.1567.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
196.2.d.c.195.5 | ✓ | 8 | 8.3 | odd | 2 | ||
196.2.d.c.195.6 | yes | 8 | 56.27 | even | 2 | ||
196.2.d.c.195.7 | yes | 8 | 56.13 | odd | 2 | ||
196.2.d.c.195.8 | yes | 8 | 8.5 | even | 2 | ||
196.2.f.d.19.1 | 16 | 56.53 | even | 6 | |||
196.2.f.d.19.2 | 16 | 56.45 | odd | 6 | |||
196.2.f.d.19.5 | 16 | 56.3 | even | 6 | |||
196.2.f.d.19.6 | 16 | 56.11 | odd | 6 | |||
196.2.f.d.31.1 | 16 | 56.19 | even | 6 | |||
196.2.f.d.31.2 | 16 | 56.51 | odd | 6 | |||
196.2.f.d.31.5 | 16 | 56.37 | even | 6 | |||
196.2.f.d.31.6 | 16 | 56.5 | odd | 6 | |||
1764.2.b.k.1567.1 | 8 | 24.5 | odd | 2 | |||
1764.2.b.k.1567.2 | 8 | 168.125 | even | 2 | |||
1764.2.b.k.1567.3 | 8 | 24.11 | even | 2 | |||
1764.2.b.k.1567.4 | 8 | 168.83 | odd | 2 | |||
3136.2.f.i.3135.3 | 8 | 1.1 | even | 1 | trivial | ||
3136.2.f.i.3135.4 | 8 | 28.27 | even | 2 | inner | ||
3136.2.f.i.3135.5 | 8 | 4.3 | odd | 2 | inner | ||
3136.2.f.i.3135.6 | 8 | 7.6 | odd | 2 | inner |