Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(721,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.o (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: | \(74.5506003290\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.1 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.721 |
Dual form | 2736.3.o.l.721.2 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.27492 | −0.254983 | −0.127492 | − | 0.991840i | \(-0.540693\pi\) | ||||
−0.127492 | + | 0.991840i | \(0.540693\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.72508 | −0.675012 | −0.337506 | − | 0.941323i | \(-0.609583\pi\) | ||||
−0.337506 | + | 0.941323i | \(0.609583\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.27492 | −0.661356 | −0.330678 | − | 0.943744i | \(-0.607277\pi\) | ||||
−0.330678 | + | 0.943744i | \(0.607277\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.30136i | − | 0.330873i | −0.986220 | − | 0.165437i | \(-0.947097\pi\) | ||
0.986220 | − | 0.165437i | \(-0.0529034\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 20.3746 | 1.19851 | 0.599253 | − | 0.800560i | \(-0.295465\pi\) | ||||
0.599253 | + | 0.800560i | \(0.295465\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.54983 | + | 17.4356i | 0.397360 | + | 0.917663i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.45017 | 0.236964 | 0.118482 | − | 0.992956i | \(-0.462197\pi\) | ||||
0.118482 | + | 0.992956i | \(0.462197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.3746 | −0.934983 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.60271i | − | 0.296645i | −0.988939 | − | 0.148323i | \(-0.952613\pi\) | ||
0.988939 | − | 0.148323i | \(-0.0473874\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 20.0624i | − | 0.647176i | −0.946198 | − | 0.323588i | \(-0.895111\pi\) | ||
0.946198 | − | 0.323588i | \(-0.104889\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.02409 | 0.172117 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.6169i | 1.09775i | 0.835903 | + | 0.548877i | \(0.184944\pi\) | ||||
−0.835903 | + | 0.548877i | \(0.815056\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 31.2920i | 0.763220i | 0.924324 | + | 0.381610i | \(0.124630\pi\) | ||||
−0.924324 | + | 0.381610i | \(0.875370\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −65.1238 | −1.51451 | −0.757253 | − | 0.653122i | \(-0.773459\pi\) | ||||
−0.757253 | + | 0.653122i | \(0.773459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 55.4743 | 1.18030 | 0.590152 | − | 0.807292i | \(-0.299068\pi\) | ||||
0.590152 | + | 0.807292i | \(0.299068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.6736 | −0.544359 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 78.1149i | 1.47387i | 0.675966 | + | 0.736933i | \(0.263727\pi\) | ||||
−0.675966 | + | 0.736933i | \(0.736273\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.27492 | 0.168635 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 69.5122i | − | 1.17817i | −0.808070 | − | 0.589087i | \(-0.799488\pi\) | ||
0.808070 | − | 0.589087i | \(-0.200512\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.17525 | −0.101234 | −0.0506168 | − | 0.998718i | \(-0.516119\pi\) | ||||
−0.0506168 | + | 0.998718i | \(0.516119\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.48387i | 0.0843673i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 123.724i | − | 1.84662i | −0.384053 | − | 0.923311i | \(-0.625472\pi\) | ||
0.384053 | − | 0.923311i | \(-0.374528\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.11884i | 0.0439273i | 0.999759 | + | 0.0219637i | \(0.00699181\pi\) | ||||
−0.999759 | + | 0.0219637i | \(0.993008\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.8248 | 0.463353 | 0.231676 | − | 0.972793i | \(-0.425579\pi\) | ||||
0.231676 | + | 0.972793i | \(0.425579\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 34.3746 | 0.446423 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 87.6700i | 1.10975i | 0.831935 | + | 0.554873i | \(0.187233\pi\) | ||||
−0.831935 | + | 0.554873i | \(0.812767\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 121.698 | 1.46624 | 0.733119 | − | 0.680101i | \(-0.238064\pi\) | ||||
0.733119 | + | 0.680101i | \(0.238064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25.9759 | −0.305599 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 69.9726i | − | 0.786209i | −0.919494 | − | 0.393104i | \(-0.871401\pi\) | ||
0.919494 | − | 0.393104i | \(-0.128599\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.3243i | 0.223344i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.62541 | − | 22.2289i | −0.101320 | − | 0.233989i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 111.081i | − | 1.14517i | −0.819846 | − | 0.572585i | \(-0.805941\pi\) | ||
0.819846 | − | 0.572585i | \(-0.194059\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −75.2508 | −0.745058 | −0.372529 | − | 0.928021i | \(-0.621509\pi\) | ||||
−0.372529 | + | 0.928021i | \(0.621509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 188.474i | − | 1.82985i | −0.403628 | − | 0.914923i | \(-0.632251\pi\) | ||
0.403628 | − | 0.914923i | \(-0.367749\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.14236i | 0.0760968i | 0.999276 | + | 0.0380484i | \(0.0121141\pi\) | ||||
−0.999276 | + | 0.0380484i | \(0.987886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 119.192i | − | 1.09351i | −0.837294 | − | 0.546753i | \(-0.815864\pi\) | ||
0.837294 | − | 0.546753i | \(-0.184136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 196.355i | − | 1.73765i | −0.495117 | − | 0.868826i | \(-0.664875\pi\) | ||
0.495117 | − | 0.868826i | \(-0.335125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.94851 | −0.0604218 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −96.2716 | −0.809005 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −68.0756 | −0.562608 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 61.6736 | 0.493389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.0229i | − | 0.126165i | −0.998008 | − | 0.0630823i | \(-0.979907\pi\) | ||
0.998008 | − | 0.0630823i | \(-0.0200931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 165.921 | 1.26657 | 0.633287 | − | 0.773917i | \(-0.281705\pi\) | ||||
0.633287 | + | 0.773917i | \(0.281705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −35.6736 | − | 82.3846i | −0.268223 | − | 0.619433i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 199.674 | 1.45747 | 0.728736 | − | 0.684795i | \(-0.240108\pi\) | ||||
0.728736 | + | 0.684795i | \(0.240108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 54.5739 | 0.392618 | 0.196309 | − | 0.980542i | \(-0.437104\pi\) | ||||
0.196309 | + | 0.980542i | \(0.437104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 31.2920i | 0.218825i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.9677i | 0.0756396i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 245.323 | 1.64646 | 0.823232 | − | 0.567705i | \(-0.192169\pi\) | ||||
0.823232 | + | 0.567705i | \(0.192169\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 79.2974i | 0.525149i | 0.964912 | + | 0.262574i | \(0.0845715\pi\) | ||||
−0.964912 | + | 0.262574i | \(0.915429\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.5780i | 0.165019i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −53.6977 | −0.342023 | −0.171012 | − | 0.985269i | \(-0.554704\pi\) | ||||
−0.171012 | + | 0.985269i | \(0.554704\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.7525 | −0.159953 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −78.3987 | −0.480973 | −0.240487 | − | 0.970652i | \(-0.577307\pi\) | ||||
−0.240487 | + | 0.970652i | \(0.577307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 293.350i | − | 1.75658i | −0.478124 | − | 0.878292i | \(-0.658683\pi\) | ||
0.478124 | − | 0.878292i | \(-0.341317\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 150.498 | 0.890523 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 10.5074i | − | 0.0607364i | −0.999539 | − | 0.0303682i | \(-0.990332\pi\) | ||
0.999539 | − | 0.0303682i | \(-0.00966798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 110.447 | 0.631125 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.4121i | − | 0.0693412i | −0.999399 | − | 0.0346706i | \(-0.988962\pi\) | ||
0.999399 | − | 0.0346706i | \(-0.0110382\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 106.780i | 0.589945i | 0.955506 | + | 0.294973i | \(0.0953105\pi\) | ||||
−0.955506 | + | 0.294973i | \(0.904689\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 51.7832i | − | 0.279909i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −148.223 | −0.792639 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.0274 | −0.0996199 | −0.0498099 | − | 0.998759i | \(-0.515862\pi\) | ||||
−0.0498099 | + | 0.998759i | \(0.515862\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 110.391i | 0.571974i | 0.958234 | + | 0.285987i | \(0.0923213\pi\) | ||||
−0.958234 | + | 0.285987i | \(0.907679\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −328.749 | −1.66878 | −0.834389 | − | 0.551176i | \(-0.814179\pi\) | ||||
−0.834389 | + | 0.551176i | \(0.814179\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 266.973 | 1.34157 | 0.670785 | − | 0.741651i | \(-0.265957\pi\) | ||||
0.670785 | + | 0.741651i | \(0.265957\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 40.6485i | 0.200239i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 39.8947i | − | 0.194608i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −54.9244 | − | 126.843i | −0.262796 | − | 0.606902i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 70.4329i | − | 0.333805i | −0.985973 | − | 0.166903i | \(-0.946623\pi\) | ||
0.985973 | − | 0.166903i | \(-0.0533766\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 83.0274 | 0.386174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 94.7967i | 0.436851i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 87.6383i | − | 0.396554i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 237.432i | 1.06472i | 0.846519 | + | 0.532359i | \(0.178694\pi\) | ||||
−0.846519 | + | 0.532359i | \(0.821306\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 269.740i | − | 1.18828i | −0.804362 | − | 0.594140i | \(-0.797492\pi\) | ||
0.804362 | − | 0.594140i | \(-0.202508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 259.419 | 1.13284 | 0.566418 | − | 0.824118i | \(-0.308329\pi\) | ||||
0.566418 | + | 0.824118i | \(0.308329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 52.6769 | 0.226081 | 0.113041 | − | 0.993590i | \(-0.463941\pi\) | ||||
0.113041 | + | 0.993590i | \(0.463941\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −70.7251 | −0.300958 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −346.120 | −1.44820 | −0.724101 | − | 0.689694i | \(-0.757745\pi\) | ||||
−0.724101 | + | 0.689694i | \(0.757745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 300.278i | − | 1.24597i | −0.782235 | − | 0.622983i | \(-0.785921\pi\) | ||
0.782235 | − | 0.622983i | \(-0.214079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 34.0066 | 0.138803 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 74.9967 | − | 32.4745i | 0.303630 | − | 0.131476i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 190.223 | 0.757862 | 0.378931 | − | 0.925425i | \(-0.376292\pi\) | ||||
0.378931 | + | 0.925425i | \(0.376292\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −39.6495 | −0.156717 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 25.3478i | − | 0.0986295i | −0.998783 | − | 0.0493147i | \(-0.984296\pi\) | ||
0.998783 | − | 0.0493147i | \(-0.0157037\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 191.918i | − | 0.740997i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −450.120 | −1.71148 | −0.855742 | − | 0.517402i | \(-0.826899\pi\) | ||||
−0.855742 | + | 0.517402i | \(0.826899\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 99.5901i | − | 0.375812i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 485.141i | − | 1.80350i | −0.432259 | − | 0.901749i | \(-0.642284\pi\) | ||
0.432259 | − | 0.901749i | \(-0.357716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −156.997 | −0.579324 | −0.289662 | − | 0.957129i | \(-0.593543\pi\) | ||||
−0.289662 | + | 0.957129i | \(0.593543\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 170.048 | 0.618357 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 156.629 | 0.565447 | 0.282723 | − | 0.959202i | \(-0.408762\pi\) | ||||
0.282723 | + | 0.959202i | \(0.408762\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 457.658i | − | 1.62868i | −0.580390 | − | 0.814339i | \(-0.697100\pi\) | ||
0.580390 | − | 0.814339i | \(-0.302900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 46.5739 | 0.164572 | 0.0822861 | − | 0.996609i | \(-0.473778\pi\) | ||||
0.0822861 | + | 0.996609i | \(0.473778\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 147.857i | − | 0.515182i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 126.124 | 0.436414 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 222.163i | − | 0.758235i | −0.925349 | − | 0.379117i | \(-0.876228\pi\) | ||
0.925349 | − | 0.379117i | \(-0.123772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 88.6223i | 0.300415i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 23.4431i | − | 0.0784050i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 307.715 | 1.02231 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.87293 | 0.0258129 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 492.069i | − | 1.60283i | −0.598108 | − | 0.801416i | \(-0.704080\pi\) | ||
0.598108 | − | 0.801416i | \(-0.295920\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 162.773 | 0.523387 | 0.261693 | − | 0.965151i | \(-0.415719\pi\) | ||||
0.261693 | + | 0.965151i | \(0.415719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 414.894 | 1.32554 | 0.662770 | − | 0.748823i | \(-0.269381\pi\) | ||||
0.662770 | + | 0.748823i | \(0.269381\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 365.750i | 1.15379i | 0.816819 | + | 0.576893i | \(0.195735\pi\) | ||||
−0.816819 | + | 0.576893i | \(0.804265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 62.5840i | 0.196188i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 153.825 | + | 355.243i | 0.476238 | + | 1.09982i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 100.542i | 0.309361i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −262.120 | −0.796719 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 220.258i | 0.665433i | 0.943027 | + | 0.332716i | \(0.107965\pi\) | ||||
−0.943027 | + | 0.332716i | \(0.892035\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 157.737i | 0.470858i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 240.980i | − | 0.715073i | −0.933899 | − | 0.357536i | \(-0.883617\pi\) | ||
0.933899 | − | 0.357536i | \(-0.116383\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 145.953i | 0.428014i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 357.564 | 1.04246 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −234.876 | −0.676877 | −0.338438 | − | 0.940989i | \(-0.609899\pi\) | ||||
−0.338438 | + | 0.940989i | \(0.609899\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −440.677 | −1.26268 | −0.631342 | − | 0.775504i | \(-0.717496\pi\) | ||||
−0.631342 | + | 0.775504i | \(0.717496\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 543.292 | 1.53907 | 0.769536 | − | 0.638603i | \(-0.220488\pi\) | ||||
0.769536 | + | 0.638603i | \(0.220488\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.97626i | − | 0.0112007i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −38.5191 | −0.107296 | −0.0536478 | − | 0.998560i | \(-0.517085\pi\) | ||||
−0.0536478 | + | 0.998560i | \(0.517085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −247.000 | + | 263.272i | −0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.1238 | −0.118147 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 568.997 | 1.55040 | 0.775200 | − | 0.631716i | \(-0.217649\pi\) | ||||
0.775200 | + | 0.631716i | \(0.217649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 369.099i | − | 0.994877i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 61.8618i | − | 0.165849i | −0.996556 | − | 0.0829247i | \(-0.973574\pi\) | ||
0.996556 | − | 0.0829247i | \(-0.0264261\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.0033 | −0.0981520 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 342.601i | 0.903960i | 0.892028 | + | 0.451980i | \(0.149282\pi\) | ||||
−0.892028 | + | 0.451980i | \(0.850718\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 77.1309i | − | 0.201386i | −0.994918 | − | 0.100693i | \(-0.967894\pi\) | ||
0.994918 | − | 0.100693i | \(-0.0321060\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −43.8248 | −0.113831 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −433.770 | −1.11509 | −0.557545 | − | 0.830147i | \(-0.688257\pi\) | ||||
−0.557545 | + | 0.830147i | \(0.688257\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 111.045 | 0.284002 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 111.772i | − | 0.282967i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −283.069 | −0.713020 | −0.356510 | − | 0.934291i | \(-0.616033\pi\) | ||||
−0.356510 | + | 0.934291i | \(0.616033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 323.491i | 0.806710i | 0.915044 | + | 0.403355i | \(0.132156\pi\) | ||||
−0.915044 | + | 0.403355i | \(0.867844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −86.2957 | −0.214133 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 295.484i | − | 0.726006i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 546.741i | − | 1.33678i | −0.743813 | − | 0.668388i | \(-0.766985\pi\) | ||
0.743813 | − | 0.668388i | \(-0.233015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 328.451i | 0.795281i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −155.154 | −0.373866 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −352.997 | −0.842474 | −0.421237 | − | 0.906951i | \(-0.638404\pi\) | ||||
−0.421237 | + | 0.906951i | \(0.638404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 578.525i | 1.37417i | 0.726578 | + | 0.687084i | \(0.241110\pi\) | ||||
−0.726578 | + | 0.687084i | \(0.758890\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −476.248 | −1.12058 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.1786 | 0.0683339 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 628.896i | − | 1.45915i | −0.683898 | − | 0.729577i | \(-0.739717\pi\) | ||
0.683898 | − | 0.729577i | \(-0.260283\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 122.803i | − | 0.283610i | −0.989895 | − | 0.141805i | \(-0.954709\pi\) | ||
0.989895 | − | 0.141805i | \(-0.0452905\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.1478 | + | 95.0269i | 0.0941598 | + | 0.217453i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 63.3694i | 0.144350i | 0.997392 | + | 0.0721748i | \(0.0229939\pi\) | ||||
−0.997392 | + | 0.0721748i | \(0.977006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 610.320 | 1.37770 | 0.688849 | − | 0.724905i | \(-0.258117\pi\) | ||||
0.688849 | + | 0.724905i | \(0.258117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 89.2092i | 0.200470i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 410.772i | − | 0.914860i | −0.889246 | − | 0.457430i | \(-0.848770\pi\) | ||
0.889246 | − | 0.457430i | \(-0.151230\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 227.647i | − | 0.504760i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 25.9117i | − | 0.0569489i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 251.722 | 0.550814 | 0.275407 | − | 0.961328i | \(-0.411187\pi\) | ||||
0.275407 | + | 0.961328i | \(0.411187\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 224.622 | 0.487250 | 0.243625 | − | 0.969870i | \(-0.421663\pi\) | ||||
0.243625 | + | 0.969870i | \(0.421663\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 196.375 | 0.424135 | 0.212068 | − | 0.977255i | \(-0.431980\pi\) | ||||
0.212068 | + | 0.977255i | \(0.431980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −106.381 | −0.227797 | −0.113899 | − | 0.993492i | \(-0.536334\pi\) | ||||
−0.113899 | + | 0.993492i | \(0.536334\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 584.605i | 1.24649i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 473.770 | 1.00163 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −176.474 | − | 407.550i | −0.371525 | − | 0.858000i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 463.154 | 0.966920 | 0.483460 | − | 0.875367i | \(-0.339380\pi\) | ||||
0.483460 | + | 0.875367i | \(0.339380\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 174.708 | 0.363217 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 141.620i | 0.291999i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 248.463i | − | 0.510191i | −0.966916 | − | 0.255095i | \(-0.917893\pi\) | ||
0.966916 | − | 0.255095i | \(-0.0821069\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 305.588 | 0.622379 | 0.311189 | − | 0.950348i | \(-0.399273\pi\) | ||||
0.311189 | + | 0.950348i | \(0.399273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 175.277i | − | 0.355531i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 14.7368i | − | 0.0296514i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −268.918 | −0.538913 | −0.269457 | − | 0.963013i | \(-0.586844\pi\) | ||||
−0.269457 | + | 0.963013i | \(0.586844\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −507.154 | −1.00826 | −0.504130 | − | 0.863628i | \(-0.668187\pi\) | ||||
−0.504130 | + | 0.863628i | \(0.668187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 95.9386 | 0.189977 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 407.256i | 0.800111i | 0.916491 | + | 0.400055i | \(0.131009\pi\) | ||||
−0.916491 | + | 0.400055i | \(0.868991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −159.825 | −0.312769 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 240.289i | 0.466581i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −403.571 | −0.780601 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 607.190i | − | 1.16543i | −0.812676 | − | 0.582716i | \(-0.801990\pi\) | ||
0.812676 | − | 0.582716i | \(-0.198010\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 209.227i | − | 0.400052i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) | ||
0.979791 | − | 0.200026i | \(-0.0641026\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 408.764i | − | 0.775643i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −499.296 | −0.943848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 134.598 | 0.252529 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 10.3808i | − | 0.0194034i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 194.048 | 0.360015 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.6637 | −0.0825576 | −0.0412788 | − | 0.999148i | \(-0.513143\pi\) | ||||
−0.0412788 | + | 0.999148i | \(0.513143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 151.960i | 0.278826i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 595.405i | 1.08849i | 0.838925 | + | 0.544246i | \(0.183184\pi\) | ||||
−0.838925 | + | 0.544246i | \(0.816816\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 149.993 | − | 64.9490i | 0.272220 | − | 0.117875i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 414.248i | − | 0.749092i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 78.4228 | 0.140795 | 0.0703975 | − | 0.997519i | \(-0.477573\pi\) | ||||
0.0703975 | + | 0.997519i | \(0.477573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 280.120i | 0.501110i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 457.825i | 0.813189i | 0.913609 | + | 0.406594i | \(0.133284\pi\) | ||||
−0.913609 | + | 0.406594i | \(0.866716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 250.336i | 0.443073i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 307.833i | − | 0.541007i | −0.962719 | − | 0.270504i | \(-0.912810\pi\) | ||
0.962719 | − | 0.270504i | \(-0.0871902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −589.492 | −1.03238 | −0.516192 | − | 0.856473i | \(-0.672651\pi\) | ||||
−0.516192 | + | 0.856473i | \(0.672651\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −127.395 | −0.221557 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −363.262 | −0.629570 | −0.314785 | − | 0.949163i | \(-0.601932\pi\) | ||||
−0.314785 | + | 0.949163i | \(0.601932\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −575.032 | −0.989727 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 568.280i | − | 0.974751i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 391.625 | 0.667164 | 0.333582 | − | 0.942721i | \(-0.391743\pi\) | ||||
0.333582 | + | 0.942721i | \(0.391743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 349.801 | − | 151.468i | 0.593889 | − | 0.257162i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 212.900 | 0.359022 | 0.179511 | − | 0.983756i | \(-0.442548\pi\) | ||||
0.179511 | + | 0.983756i | \(0.442548\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 122.738 | 0.206283 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 916.888i | 1.53070i | 0.643616 | + | 0.765349i | \(0.277434\pi\) | ||||
−0.643616 | + | 0.765349i | \(0.722566\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 485.078i | − | 0.807118i | −0.914954 | − | 0.403559i | \(-0.867773\pi\) | ||
0.914954 | − | 0.403559i | \(-0.132227\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 86.7907 | 0.143456 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 193.101i | − | 0.318123i | −0.987269 | − | 0.159061i | \(-0.949153\pi\) | ||
0.987269 | − | 0.159061i | \(-0.0508468\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 238.614i | − | 0.390531i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −142.368 | −0.232248 | −0.116124 | − | 0.993235i | \(-0.537047\pi\) | ||||
−0.116124 | + | 0.993235i | \(0.537047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 547.770 | 0.887796 | 0.443898 | − | 0.896077i | \(-0.353595\pi\) | ||||
0.443898 | + | 0.896077i | \(0.353595\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −814.482 | −1.31580 | −0.657901 | − | 0.753104i | \(-0.728556\pi\) | ||||
−0.657901 | + | 0.753104i | \(0.728556\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 330.626i | 0.530700i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 505.736 | 0.809177 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 827.552i | 1.31566i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −641.509 | −1.01665 | −0.508327 | − | 0.861164i | \(-0.669736\pi\) | ||||
−0.508327 | + | 0.861164i | \(0.669736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.4279i | 0.0321699i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 114.733i | 0.180114i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 352.878i | − | 0.550512i | −0.961371 | − | 0.275256i | \(-0.911237\pi\) | ||
0.961371 | − | 0.275256i | \(-0.0887626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 455.757 | 0.708797 | 0.354399 | − | 0.935094i | \(-0.384686\pi\) | ||||
0.354399 | + | 0.935094i | \(0.384686\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 484.368 | 0.748637 | 0.374318 | − | 0.927300i | \(-0.377877\pi\) | ||||
0.374318 | + | 0.927300i | \(0.377877\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 505.696i | 0.779192i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −280.780 | −0.429985 | −0.214992 | − | 0.976616i | \(-0.568973\pi\) | ||||
−0.214992 | + | 0.976616i | \(0.568973\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −211.536 | −0.322955 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 800.259i | 1.21435i | 0.794567 | + | 0.607177i | \(0.207698\pi\) | ||||
−0.794567 | + | 0.607177i | \(0.792302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 812.996i | − | 1.22995i | −0.788547 | − | 0.614975i | \(-0.789166\pi\) | ||
0.788547 | − | 0.614975i | \(-0.210834\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 45.4809 | + | 105.034i | 0.0683923 | + | 0.157945i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 46.8862i | − | 0.0702941i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 44.9244 | 0.0669514 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 79.8930i | − | 0.118712i | −0.998237 | − | 0.0593559i | \(-0.981095\pi\) | ||
0.998237 | − | 0.0593559i | \(-0.0189047\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1153.64i | 1.70404i | 0.523506 | + | 0.852022i | \(0.324624\pi\) | ||||
−0.523506 | + | 0.852022i | \(0.675376\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 524.869i | 0.773003i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 382.766i | 0.560419i | 0.959939 | + | 0.280209i | \(0.0904039\pi\) | ||||
−0.959939 | + | 0.280209i | \(0.909596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −254.567 | −0.371631 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 336.000 | 0.487663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −133.330 | −0.192952 | −0.0964759 | − | 0.995335i | \(-0.530757\pi\) | ||||
−0.0964759 | + | 0.995335i | \(0.530757\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −69.5772 | −0.100111 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 637.562i | 0.914723i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 934.042 | 1.33244 | 0.666221 | − | 0.745755i | \(-0.267911\pi\) | ||||
0.666221 | + | 0.745755i | \(0.267911\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −708.179 | + | 306.651i | −1.00737 | + | 0.436203i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 355.566 | 0.502923 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 287.993 | 0.406197 | 0.203098 | − | 0.979158i | \(-0.434899\pi\) | ||||
0.203098 | + | 0.979158i | \(0.434899\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 109.344i | − | 0.153357i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 39.8947i | − | 0.0557968i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 78.0723 | 0.108585 | 0.0542923 | − | 0.998525i | \(-0.482710\pi\) | ||||
0.0542923 | + | 0.998525i | \(0.482710\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 890.556i | 1.23517i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 201.085i | 0.277358i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 320.169 | 0.440397 | 0.220199 | − | 0.975455i | \(-0.429329\pi\) | ||||
0.220199 | + | 0.975455i | \(0.429329\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1326.87 | −1.81514 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −565.781 | −0.771870 | −0.385935 | − | 0.922526i | \(-0.626121\pi\) | ||||
−0.385935 | + | 0.922526i | \(0.626121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 900.080i | 1.22127i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 869.557 | 1.17667 | 0.588334 | − | 0.808618i | \(-0.299784\pi\) | ||||
0.588334 | + | 0.808618i | \(0.299784\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7.74529i | − | 0.0104243i | −0.999986 | − | 0.00521217i | \(-0.998341\pi\) | ||
0.999986 | − | 0.00521217i | \(-0.00165909\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −312.767 | −0.419821 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 38.4733i | − | 0.0513663i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1281.23i | − | 1.70603i | −0.521890 | − | 0.853013i | \(-0.674773\pi\) | ||
0.521890 | − | 0.853013i | \(-0.325227\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 101.098i | − | 0.133904i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −441.172 | −0.582790 | −0.291395 | − | 0.956603i | \(-0.594119\pi\) | ||||
−0.291395 | + | 0.956603i | \(0.594119\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −476.532 | −0.626192 | −0.313096 | − | 0.949721i | \(-0.601366\pi\) | ||||
−0.313096 | + | 0.949721i | \(0.601366\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 563.193i | 0.738129i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −298.997 | −0.389826 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −624.567 | −0.812181 | −0.406091 | − | 0.913833i | \(-0.633108\pi\) | ||||
−0.406091 | + | 0.913833i | \(0.633108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 334.038i | 0.432133i | 0.976379 | + | 0.216066i | \(0.0693227\pi\) | ||||
−0.976379 | + | 0.216066i | \(0.930677\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 468.951i | 0.605098i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −545.595 | + | 236.249i | −0.700378 | + | 0.303273i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 22.6893i | − | 0.0290516i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 68.4601 | 0.0872103 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 479.323i | 0.609051i | 0.952504 | + | 0.304526i | \(0.0984980\pi\) | ||||
−0.952504 | + | 0.304526i | \(0.901502\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 927.792i | 1.17294i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.5619i | 0.0334955i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 126.025i | 0.158125i | 0.996870 | + | 0.0790624i | \(0.0251926\pi\) | ||||
−0.996870 | + | 0.0790624i | \(0.974807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1130.26 | 1.41460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −246.072 | −0.306441 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.8323 | 0.0407854 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −901.825 | −1.11474 | −0.557370 | − | 0.830264i | \(-0.688190\pi\) | ||||
−0.557370 | + | 0.830264i | \(0.688190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 183.776i | 0.226604i | 0.993561 | + | 0.113302i | \(0.0361427\pi\) | ||||
−0.993561 | + | 0.113302i | \(0.963857\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 99.9518 | 0.122640 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −491.674 | − | 1135.47i | −0.601804 | − | 1.38981i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1034.35 | −1.25986 | −0.629932 | − | 0.776650i | \(-0.716917\pi\) | ||||
−0.629932 | + | 0.776650i | \(0.716917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −952.107 | −1.15687 | −0.578437 | − | 0.815727i | \(-0.696337\pi\) | ||||
−0.578437 | + | 0.815727i | \(0.696337\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 970.806i | 1.17389i | 0.809627 | + | 0.586944i | \(0.199669\pi\) | ||||
−0.809627 | + | 0.586944i | \(0.800331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 374.908i | − | 0.452242i | −0.974099 | − | 0.226121i | \(-0.927396\pi\) | ||
0.974099 | − | 0.226121i | \(-0.0726044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −543.463 | −0.652417 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 373.996i | 0.447900i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1282.87i | − | 1.52904i | −0.644597 | − | 0.764522i | \(-0.722975\pi\) | ||
0.644597 | − | 0.764522i | \(-0.277025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 766.993 | 0.912002 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −191.873 | −0.227069 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 321.663 | 0.379767 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 221.369i | 0.260128i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 827.595 | 0.970217 | 0.485108 | − | 0.874454i | \(-0.338780\pi\) | ||||
0.485108 | + | 0.874454i | \(0.338780\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 986.671i | − | 1.15131i | −0.817694 | − | 0.575654i | \(-0.804748\pi\) | ||
0.817694 | − | 0.575654i | \(-0.195252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1382.27 | 1.60916 | 0.804582 | − | 0.593842i | \(-0.202389\pi\) | ||||
0.804582 | + | 0.593842i | \(0.202389\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 485.475i | 0.562543i | 0.959628 | + | 0.281272i | \(0.0907562\pi\) | ||||
−0.959628 | + | 0.281272i | \(0.909244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.3961i | 0.0154868i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 637.792i | − | 0.733938i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −532.179 | −0.610998 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −291.413 | −0.333043 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 266.756i | 0.304169i | 0.988368 | + | 0.152084i | \(0.0485985\pi\) | ||||
−0.988368 | + | 0.152084i | \(0.951401\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 979.248 | 1.11152 | 0.555760 | − | 0.831343i | \(-0.312427\pi\) | ||||
0.555760 | + | 0.831343i | \(0.312427\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1551.91 | −1.75755 | −0.878774 | − | 0.477239i | \(-0.841638\pi\) | ||||
−0.878774 | + | 0.477239i | \(0.841638\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 700.543i | 0.789789i | 0.918727 | + | 0.394894i | \(0.129219\pi\) | ||||
−0.918727 | + | 0.394894i | \(0.870781\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 75.7095i | 0.0851626i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 418.821 | + | 967.227i | 0.469005 | + | 1.08312i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.8244i | 0.0176809i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −172.591 | −0.191982 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1591.56i | 1.76644i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 136.136i | − | 0.150426i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1228.07i | 1.35399i | 0.735987 | + | 0.676996i | \(0.236718\pi\) | ||||
−0.735987 | + | 0.676996i | \(0.763282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1077.26i | 1.18250i | 0.806487 | + | 0.591252i | \(0.201366\pi\) | ||||
−0.806487 | + | 0.591252i | \(0.798634\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −885.341 | −0.969705 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −783.991 | −0.854952 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 348.488 | 0.379204 | 0.189602 | − | 0.981861i | \(-0.439280\pi\) | ||||
0.189602 | + | 0.981861i | \(0.439280\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.4152 | 0.0145344 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 949.403i | − | 1.02638i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1506.48 | 1.62162 | 0.810808 | − | 0.585312i | \(-0.199028\pi\) | ||||
0.810808 | + | 0.585312i | \(0.199028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −201.381 | − | 465.070i | −0.216306 | − | 0.499538i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 188.973 | 0.202110 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −145.777 | −0.155578 | −0.0777890 | − | 0.996970i | \(-0.524786\pi\) | ||||
−0.0777890 | + | 0.996970i | \(0.524786\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1501.75i | 1.59590i | 0.602721 | + | 0.797952i | \(0.294083\pi\) | ||||
−0.602721 | + | 0.797952i | \(0.705917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 170.547i | 0.180855i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 765.794 | 0.808653 | 0.404326 | − | 0.914615i | \(-0.367506\pi\) | ||||
0.404326 | + | 0.914615i | \(0.367506\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 145.492i | − | 0.153311i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1308.88i | − | 1.37344i | −0.726924 | − | 0.686718i | \(-0.759051\pi\) | ||
0.726924 | − | 0.686718i | \(-0.240949\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.2584 | 0.0254014 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −943.474 | −0.983810 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 558.498 | 0.581164 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 140.739i | − | 0.145844i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −587.704 | −0.607760 | −0.303880 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303880 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 653.823i | − | 0.673351i | −0.941621 | − | 0.336675i | \(-0.890698\pi\) | ||
0.941621 | − | 0.336675i | \(-0.109302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −257.866 | −0.265022 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 101.034i | − | 0.103413i | −0.998662 | − | 0.0517064i | \(-0.983534\pi\) | ||
0.998662 | − | 0.0517064i | \(-0.0164660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 509.045i | 0.519964i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 888.065i | 0.903423i | 0.892164 | + | 0.451711i | \(0.149186\pi\) | ||||
−0.892164 | + | 0.451711i | \(0.850814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 419.128 | 0.425511 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −354.935 | −0.358883 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1782.19i | 1.79838i | 0.437562 | + | 0.899188i | \(0.355842\pi\) | ||||
−0.437562 | + | 0.899188i | \(0.644158\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −340.368 | −0.342078 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 891.200 | 0.893882 | 0.446941 | − | 0.894563i | \(-0.352513\pi\) | ||||
0.446941 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2736.3.o.l.721.1 | 4 | ||
3.2 | odd | 2 | 912.3.o.b.721.4 | 4 | |||
4.3 | odd | 2 | 171.3.c.f.37.2 | 4 | |||
12.11 | even | 2 | 57.3.c.b.37.3 | yes | 4 | ||
19.18 | odd | 2 | inner | 2736.3.o.l.721.2 | 4 | ||
57.56 | even | 2 | 912.3.o.b.721.2 | 4 | |||
76.75 | even | 2 | 171.3.c.f.37.3 | 4 | |||
228.227 | odd | 2 | 57.3.c.b.37.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.c.b.37.2 | ✓ | 4 | 228.227 | odd | 2 | ||
57.3.c.b.37.3 | yes | 4 | 12.11 | even | 2 | ||
171.3.c.f.37.2 | 4 | 4.3 | odd | 2 | |||
171.3.c.f.37.3 | 4 | 76.75 | even | 2 | |||
912.3.o.b.721.2 | 4 | 57.56 | even | 2 | |||
912.3.o.b.721.4 | 4 | 3.2 | odd | 2 | |||
2736.3.o.l.721.1 | 4 | 1.1 | even | 1 | trivial | ||
2736.3.o.l.721.2 | 4 | 19.18 | odd | 2 | inner |