Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,3,Mod(1711,2736)]
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([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1711");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.m (of order \(2\), degree \(1\), 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: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 2 x^{10} - 28 x^{9} - 400 x^{8} - 520 x^{7} + 17067 x^{6} - 3250 x^{5} + \cdots + 2052928 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 912) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1711.7 | ||
Root | \(4.06962 - 0.767506i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1711 |
Dual form | 2736.3.m.e.1711.8 |
$q$-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 | ||||||||
\(5\) | 4.65777 | 0.931555 | 0.465777 | − | 0.884902i | \(-0.345775\pi\) | ||||
0.465777 | + | 0.884902i | \(0.345775\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.49506i | − 0.642151i | −0.947054 | − | 0.321076i | \(-0.895956\pi\) | ||||
0.947054 | − | 0.321076i | \(-0.104044\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 10.3003i | − 0.936388i | −0.883626 | − | 0.468194i | \(-0.844905\pi\) | ||||
0.883626 | − | 0.468194i | \(-0.155095\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.9629 | 0.843302 | 0.421651 | − | 0.906758i | \(-0.361451\pi\) | ||||
0.421651 | + | 0.906758i | \(0.361451\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.3920 | 0.964237 | 0.482118 | − | 0.876106i | \(-0.339867\pi\) | ||||
0.482118 | + | 0.876106i | \(0.339867\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.35890i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.7559i | 0.989386i | 0.869068 | + | 0.494693i | \(0.164720\pi\) | ||||
−0.869068 | + | 0.494693i | \(0.835280\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30515 | −0.132206 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 55.9066 | 1.92781 | 0.963907 | − | 0.266238i | \(-0.0857806\pi\) | ||||
0.963907 | + | 0.266238i | \(0.0857806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 61.5568i | 1.98570i | 0.119354 | + | 0.992852i | \(0.461918\pi\) | ||||
−0.119354 | + | 0.992852i | \(0.538082\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 20.9370i | − 0.598199i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 38.6211 | 1.04381 | 0.521907 | − | 0.853002i | \(-0.325221\pi\) | ||||
0.521907 | + | 0.853002i | \(0.325221\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.7169 | −1.06627 | −0.533133 | − | 0.846031i | \(-0.678986\pi\) | ||||
−0.533133 | + | 0.846031i | \(0.678986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 39.1687i | 0.910900i | 0.890261 | + | 0.455450i | \(0.150522\pi\) | ||||
−0.890261 | + | 0.455450i | \(0.849478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 30.2344i | − 0.643285i | −0.946861 | − | 0.321642i | \(-0.895765\pi\) | ||||
0.946861 | − | 0.321642i | \(-0.104235\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28.7944 | 0.587642 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −77.4119 | −1.46060 | −0.730301 | − | 0.683126i | \(-0.760620\pi\) | ||||
−0.730301 | + | 0.683126i | \(0.760620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 47.9763i | − 0.872297i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 90.9651i | − 1.54178i | −0.636968 | − | 0.770891i | \(-0.719811\pi\) | ||||
0.636968 | − | 0.770891i | \(-0.280189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 115.683 | 1.89644 | 0.948221 | − | 0.317611i | \(-0.102881\pi\) | ||||
0.948221 | + | 0.317611i | \(0.102881\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 51.0628 | 0.785582 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 37.2160i | − 0.555462i | −0.960659 | − | 0.277731i | \(-0.910418\pi\) | ||||
0.960659 | − | 0.277731i | \(-0.0895824\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 103.972i | − 1.46439i | −0.681096 | − | 0.732194i | \(-0.738497\pi\) | ||||
0.681096 | − | 0.732194i | \(-0.261503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.5741 | −1.02156 | −0.510782 | − | 0.859710i | \(-0.670644\pi\) | ||||
−0.510782 | + | 0.859710i | \(0.670644\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −46.3003 | −0.601303 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 120.050i | 1.51962i | 0.650147 | + | 0.759809i | \(0.274707\pi\) | ||||
−0.650147 | + | 0.759809i | \(0.725293\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 29.4019i | 0.354240i | 0.984189 | + | 0.177120i | \(0.0566781\pi\) | ||||
−0.984189 | + | 0.177120i | \(0.943322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 76.3503 | 0.898239 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 110.359 | 1.23998 | 0.619992 | − | 0.784608i | \(-0.287136\pi\) | ||||
0.619992 | + | 0.784608i | \(0.287136\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 49.2790i | − 0.541527i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 20.3028i | − 0.213713i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1839 | −0.135916 | −0.0679581 | − | 0.997688i | \(-0.521648\pi\) | ||||
−0.0679581 | + | 0.997688i | \(0.521648\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −25.4992 | −0.252468 | −0.126234 | − | 0.992001i | \(-0.540289\pi\) | ||||
−0.126234 | + | 0.992001i | \(0.540289\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 164.210i | − 1.59427i | −0.603802 | − | 0.797134i | \(-0.706348\pi\) | ||||
0.603802 | − | 0.797134i | \(-0.293652\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.78316i | 0.0353566i | 0.999844 | + | 0.0176783i | \(0.00562747\pi\) | ||||
−0.999844 | + | 0.0176783i | \(0.994373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.83296 | 0.0718620 | 0.0359310 | − | 0.999354i | \(-0.488560\pi\) | ||||
0.0359310 | + | 0.999354i | \(0.488560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.22373 | −0.0639268 | −0.0319634 | − | 0.999489i | \(-0.510176\pi\) | ||||
−0.0319634 | + | 0.999489i | \(0.510176\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 105.992i | 0.921667i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 73.6831i | − 0.619186i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.9044 | 0.123177 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −131.839 | −1.05471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 167.160i | 1.31622i | 0.752920 | + | 0.658112i | \(0.228645\pi\) | ||||
−0.752920 | + | 0.658112i | \(0.771355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 211.318i | − 1.61311i | −0.591157 | − | 0.806557i | \(-0.701328\pi\) | ||||
0.591157 | − | 0.806557i | \(-0.298672\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.5935 | −0.147320 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 195.425 | 1.42646 | 0.713229 | − | 0.700931i | \(-0.247232\pi\) | ||||
0.713229 | + | 0.700931i | \(0.247232\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 62.5804i | − 0.450219i | −0.974334 | − | 0.225109i | \(-0.927726\pi\) | ||||
0.974334 | − | 0.225109i | \(-0.0722739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 112.921i | − 0.789658i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 260.400 | 1.79586 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 166.917 | 1.12025 | 0.560125 | − | 0.828408i | \(-0.310753\pi\) | ||||
0.560125 | + | 0.828408i | \(0.310753\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.43568i | 0.0161303i | 0.999967 | + | 0.00806516i | \(0.00256725\pi\) | ||||
−0.999967 | + | 0.00806516i | \(0.997433\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 286.718i | 1.84979i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 186.584 | 1.18843 | 0.594216 | − | 0.804306i | \(-0.297463\pi\) | ||||
0.594216 | + | 0.804306i | \(0.297463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 102.289 | 0.635336 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 155.612i | − 0.954673i | −0.878721 | − | 0.477336i | \(-0.841602\pi\) | ||||
0.878721 | − | 0.477336i | \(-0.158398\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 112.843i | − 0.675708i | −0.941199 | − | 0.337854i | \(-0.890299\pi\) | ||||
0.941199 | − | 0.337854i | \(-0.109701\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −48.8142 | −0.288842 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −127.897 | −0.739290 | −0.369645 | − | 0.929173i | \(-0.620521\pi\) | ||||
−0.369645 | + | 0.929173i | \(0.620521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.8569i | 0.0848964i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.0432i | 0.0896267i | 0.998995 | + | 0.0448134i | \(0.0142693\pi\) | ||||
−0.998995 | + | 0.0448134i | \(0.985731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −219.288 | −1.21153 | −0.605767 | − | 0.795642i | \(-0.707134\pi\) | ||||
−0.605767 | + | 0.795642i | \(0.707134\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 179.888 | 0.972370 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 168.842i | − 0.902900i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 49.0084i | − 0.256588i | −0.991736 | − | 0.128294i | \(-0.959050\pi\) | ||||
0.991736 | − | 0.128294i | \(-0.0409502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −336.473 | −1.74338 | −0.871691 | − | 0.490056i | \(-0.836976\pi\) | ||||
−0.871691 | + | 0.490056i | \(0.836976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 50.7872 | 0.257803 | 0.128902 | − | 0.991657i | \(-0.458855\pi\) | ||||
0.128902 | + | 0.991657i | \(0.458855\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 262.657i | 1.31989i | 0.751316 | + | 0.659943i | \(0.229420\pi\) | ||||
−0.751316 | + | 0.659943i | \(0.770580\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 251.304i | − 1.23795i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −203.623 | −0.993285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −44.8978 | −0.214822 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 131.345i | 0.622488i | 0.950330 | + | 0.311244i | \(0.100746\pi\) | ||||
−0.950330 | + | 0.311244i | \(0.899254\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 182.439i | 0.848553i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 276.701 | 1.27512 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 179.705 | 0.813143 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 240.108i | 1.07672i | 0.842715 | + | 0.538360i | \(0.180956\pi\) | ||||
−0.842715 | + | 0.538360i | \(0.819044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 129.300i | 0.569605i | 0.958586 | + | 0.284802i | \(0.0919280\pi\) | ||||
−0.958586 | + | 0.284802i | \(0.908072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.2842 | −0.101678 | −0.0508389 | − | 0.998707i | \(-0.516189\pi\) | ||||
−0.0508389 | + | 0.998707i | \(0.516189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 141.563 | 0.607568 | 0.303784 | − | 0.952741i | \(-0.401750\pi\) | ||||
0.303784 | + | 0.952741i | \(0.401750\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 140.825i | − 0.599255i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 47.6515i | 0.199379i | 0.995019 | + | 0.0996893i | \(0.0317849\pi\) | ||||
−0.995019 | + | 0.0996893i | \(0.968215\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −164.728 | −0.683519 | −0.341759 | − | 0.939788i | \(-0.611023\pi\) | ||||
−0.341759 | + | 0.939788i | \(0.611023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 134.118 | 0.547420 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 47.7863i | − 0.193467i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 158.643i | − 0.632045i | −0.948752 | − | 0.316022i | \(-0.897653\pi\) | ||||
0.948752 | − | 0.316022i | \(-0.102347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 234.392 | 0.926450 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 399.158 | 1.55314 | 0.776571 | − | 0.630029i | \(-0.216957\pi\) | ||||
0.776571 | + | 0.630029i | \(0.216957\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 173.604i | − 0.670287i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 12.2067i | − 0.0464134i | −0.999731 | − | 0.0232067i | \(-0.992612\pi\) | ||||
0.999731 | − | 0.0232067i | \(-0.00738758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −360.567 | −1.36063 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 348.721 | 1.29636 | 0.648180 | − | 0.761487i | \(-0.275530\pi\) | ||||
0.648180 | + | 0.761487i | \(0.275530\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 314.514i | − 1.16057i | −0.814413 | − | 0.580285i | \(-0.802941\pi\) | ||||
0.814413 | − | 0.580285i | \(-0.197059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 34.0440i | 0.123796i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 360.287 | 1.30068 | 0.650338 | − | 0.759645i | \(-0.274627\pi\) | ||||
0.650338 | + | 0.759645i | \(0.274627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −404.603 | −1.43987 | −0.719935 | − | 0.694042i | \(-0.755828\pi\) | ||||
−0.719935 | + | 0.694042i | \(0.755828\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 109.783i | − 0.387925i | −0.981009 | − | 0.193962i | \(-0.937866\pi\) | ||||
0.981009 | − | 0.193962i | \(-0.0621339\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 196.510i | 0.684704i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.3014 | −0.0702472 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 51.7076 | 0.176476 | 0.0882382 | − | 0.996099i | \(-0.471876\pi\) | ||||
0.0882382 | + | 0.996099i | \(0.471876\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 423.695i | − 1.43625i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 249.471i | 0.834352i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 176.066 | 0.584935 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 538.825 | 1.76664 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 43.7081i | 0.142372i | 0.997463 | + | 0.0711858i | \(0.0226783\pi\) | ||||
−0.997463 | + | 0.0711858i | \(0.977322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 350.883i | 1.12824i | 0.825692 | + | 0.564121i | \(0.190785\pi\) | ||||
−0.825692 | + | 0.564121i | \(0.809215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 130.501 | 0.416936 | 0.208468 | − | 0.978029i | \(-0.433152\pi\) | ||||
0.208468 | + | 0.978029i | \(0.433152\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −214.564 | −0.676858 | −0.338429 | − | 0.940992i | \(-0.609895\pi\) | ||||
−0.338429 | + | 0.940992i | \(0.609895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 575.853i | − 1.80518i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 71.4512i | − 0.221211i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −36.2342 | −0.111490 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −135.905 | −0.413086 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 261.592i | − 0.790308i | −0.918615 | − | 0.395154i | \(-0.870691\pi\) | ||||
0.918615 | − | 0.395154i | \(-0.129309\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 173.344i | − 0.517443i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 485.821 | 1.44160 | 0.720802 | − | 0.693141i | \(-0.243774\pi\) | ||||
0.720802 | + | 0.693141i | \(0.243774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 634.052 | 1.85939 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 349.691i | − 1.01951i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 106.505i | − 0.306931i | −0.988154 | − | 0.153465i | \(-0.950957\pi\) | ||||
0.988154 | − | 0.153465i | \(-0.0490434\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 167.989 | 0.481345 | 0.240673 | − | 0.970606i | \(-0.422632\pi\) | ||||
0.240673 | + | 0.970606i | \(0.422632\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 596.666 | 1.69027 | 0.845136 | − | 0.534551i | \(-0.179519\pi\) | ||||
0.845136 | + | 0.534551i | \(0.179519\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 484.276i | − 1.36416i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 212.379i | − 0.591584i | −0.955252 | − | 0.295792i | \(-0.904416\pi\) | ||||
0.955252 | − | 0.295792i | \(-0.0955835\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −347.349 | −0.951642 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 429.659i | − 1.17073i | −0.810768 | − | 0.585367i | \(-0.800950\pi\) | ||||
0.810768 | − | 0.585367i | \(-0.199050\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 347.971i | 0.937927i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 207.539 | 0.556405 | 0.278202 | − | 0.960523i | \(-0.410261\pi\) | ||||
0.278202 | + | 0.960523i | \(0.410261\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 612.900 | 1.62573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 647.875i | 1.70943i | 0.519096 | + | 0.854716i | \(0.326269\pi\) | ||||
−0.519096 | + | 0.854716i | \(0.673731\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 485.111i | − 1.26661i | −0.773903 | − | 0.633304i | \(-0.781698\pi\) | ||||
0.773903 | − | 0.633304i | \(-0.218302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −215.656 | −0.560146 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −419.923 | −1.07949 | −0.539747 | − | 0.841828i | \(-0.681480\pi\) | ||||
−0.539747 | + | 0.841828i | \(0.681480\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 373.015i | 0.954003i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 559.165i | 1.41561i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −544.430 | −1.37136 | −0.685680 | − | 0.727903i | \(-0.740495\pi\) | ||||
−0.685680 | + | 0.727903i | \(0.740495\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 103.777 | 0.258796 | 0.129398 | − | 0.991593i | \(-0.458695\pi\) | ||||
0.129398 | + | 0.991593i | \(0.458695\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 674.843i | 1.67455i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 397.808i | − 0.977416i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −291.937 | −0.713782 | −0.356891 | − | 0.934146i | \(-0.616163\pi\) | ||||
−0.356891 | + | 0.934146i | \(0.616163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −408.893 | −0.990057 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 136.947i | 0.329994i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 153.052i | 0.365280i | 0.983180 | + | 0.182640i | \(0.0584643\pi\) | ||||
−0.983180 | + | 0.182640i | \(0.941536\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 438.962 | 1.04266 | 0.521332 | − | 0.853354i | \(-0.325435\pi\) | ||||
0.521332 | + | 0.853354i | \(0.325435\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −54.1782 | −0.127478 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 520.002i | − 1.21780i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 407.423i | − 0.945296i | −0.881251 | − | 0.472648i | \(-0.843298\pi\) | ||||
0.881251 | − | 0.472648i | \(-0.156702\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 139.799 | 0.322861 | 0.161430 | − | 0.986884i | \(-0.448389\pi\) | ||||
0.161430 | + | 0.986884i | \(0.448389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 99.1906 | 0.226981 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 178.585i | 0.406799i | 0.979096 | + | 0.203400i | \(0.0651990\pi\) | ||||
−0.979096 | + | 0.203400i | \(0.934801\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 354.944i | 0.801227i | 0.916247 | + | 0.400614i | \(0.131203\pi\) | ||||
−0.916247 | + | 0.400614i | \(0.868797\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 514.025 | 1.15511 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.7188 | 0.0639618 | 0.0319809 | − | 0.999488i | \(-0.489818\pi\) | ||||
0.0319809 | + | 0.999488i | \(0.489818\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 450.296i | 0.998439i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 229.530i | − 0.504462i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −344.238 | −0.753256 | −0.376628 | − | 0.926365i | \(-0.622917\pi\) | ||||
−0.376628 | + | 0.926365i | \(0.622917\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 173.337 | 0.376002 | 0.188001 | − | 0.982169i | \(-0.439799\pi\) | ||||
0.188001 | + | 0.982169i | \(0.439799\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 277.141i | − 0.598577i | −0.954163 | − | 0.299289i | \(-0.903251\pi\) | ||||
0.954163 | − | 0.299289i | \(-0.0967493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 191.671i | − 0.410430i | −0.978717 | − | 0.205215i | \(-0.934211\pi\) | ||||
0.978717 | − | 0.205215i | \(-0.0657893\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −167.288 | −0.356691 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 403.448 | 0.852956 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.4068i | 0.0303302i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 245.009i | 0.511501i | 0.966743 | + | 0.255751i | \(0.0823226\pi\) | ||||
−0.966743 | + | 0.255751i | \(0.917677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 423.401 | 0.880251 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −61.4075 | −0.126613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 944.321i | − 1.93906i | −0.244978 | − | 0.969529i | \(-0.578781\pi\) | ||||
0.244978 | − | 0.969529i | \(-0.421219\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 844.187i | − 1.71932i | −0.510866 | − | 0.859660i | \(-0.670675\pi\) | ||||
0.510866 | − | 0.859660i | \(-0.329325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 916.423 | 1.85887 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −467.358 | −0.940358 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 662.375i | 1.32741i | 0.747997 | + | 0.663703i | \(0.231016\pi\) | ||||
−0.747997 | + | 0.663703i | \(0.768984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 772.361i | − 1.53551i | −0.640744 | − | 0.767755i | \(-0.721374\pi\) | ||||
0.640744 | − | 0.767755i | \(-0.278626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −118.770 | −0.235187 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −278.829 | −0.547797 | −0.273899 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273899 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 335.215i | 0.655998i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 764.851i | − 1.48515i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −311.422 | −0.602364 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −746.210 | −1.43226 | −0.716132 | − | 0.697965i | \(-0.754089\pi\) | ||||
−0.716132 | + | 0.697965i | \(0.754089\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 523.892i | 1.00171i | 0.865532 | + | 0.500853i | \(0.166980\pi\) | ||||
−0.865532 | + | 0.500853i | \(0.833020\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1009.04i | 1.91469i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1696 | 0.0211145 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −479.265 | −0.899185 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.6211i | 0.0329366i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 296.591i | − 0.550261i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −738.463 | −1.36500 | −0.682498 | − | 0.730888i | \(-0.739106\pi\) | ||||
−0.682498 | + | 0.730888i | \(0.739106\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.4841 | 0.0669433 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 715.442i | 1.30794i | 0.756521 | + | 0.653969i | \(0.226897\pi\) | ||||
−0.756521 | + | 0.653969i | \(0.773103\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 243.691i | − 0.442271i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 539.631 | 0.975824 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −142.896 | −0.256546 | −0.128273 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128273 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 429.403i | 0.768164i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1004.23i | 1.78372i | 0.452315 | + | 0.891858i | \(0.350598\pi\) | ||||
−0.452315 | + | 0.891858i | \(0.649402\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.6465 | −0.0595513 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 672.894 | 1.18259 | 0.591295 | − | 0.806455i | \(-0.298617\pi\) | ||||
0.591295 | + | 0.806455i | \(0.298617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 401.764i | − 0.703614i | −0.936073 | − | 0.351807i | \(-0.885567\pi\) | ||||
0.936073 | − | 0.351807i | \(-0.114433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 75.2117i | − 0.130803i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1128.20 | −1.95528 | −0.977640 | − | 0.210284i | \(-0.932561\pi\) | ||||
−0.977640 | + | 0.210284i | \(0.932561\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 132.163 | 0.227476 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 797.363i | 1.36769i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 118.129i | 0.201241i | 0.994925 | + | 0.100621i | \(0.0320828\pi\) | ||||
−0.994925 | + | 0.100621i | \(0.967917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 268.320 | 0.455552 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −64.5109 | −0.108787 | −0.0543937 | − | 0.998520i | \(-0.517323\pi\) | ||||
−0.0543937 | + | 0.998520i | \(0.517323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 343.199i | − 0.576805i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 759.072i | 1.26723i | 0.773647 | + | 0.633616i | \(0.218430\pi\) | ||||
−0.773647 | + | 0.633616i | \(0.781570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −609.382 | −1.01395 | −0.506974 | − | 0.861962i | \(-0.669236\pi\) | ||||
−0.506974 | + | 0.861962i | \(0.669236\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 69.4214 | 0.114746 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 106.361i | − 0.175224i | −0.996155 | − | 0.0876122i | \(-0.972076\pi\) | ||||
0.996155 | − | 0.0876122i | \(-0.0279236\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 331.457i | − 0.542484i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 470.099 | 0.766882 | 0.383441 | − | 0.923565i | \(-0.374739\pi\) | ||||
0.383441 | + | 0.923565i | \(0.374739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1173.48 | −1.90191 | −0.950955 | − | 0.309330i | \(-0.899895\pi\) | ||||
−0.950955 | + | 0.309330i | \(0.899895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 655.252i | − 1.05857i | −0.848446 | − | 0.529283i | \(-0.822461\pi\) | ||||
0.848446 | − | 0.529283i | \(-0.177539\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 496.068i | − 0.796257i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −531.447 | −0.850315 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 633.079 | 1.00648 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 488.854i | 0.774729i | 0.921927 | + | 0.387364i | \(0.126614\pi\) | ||||
−0.921927 | + | 0.387364i | \(0.873386\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 778.596i | 1.22613i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 315.671 | 0.495560 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −181.853 | −0.283702 | −0.141851 | − | 0.989888i | \(-0.545305\pi\) | ||||
−0.141851 | + | 0.989888i | \(0.545305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 340.140i | 0.528990i | 0.964387 | + | 0.264495i | \(0.0852052\pi\) | ||||
−0.964387 | + | 0.264495i | \(0.914795\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 638.906i | − 0.987490i | −0.869607 | − | 0.493745i | \(-0.835628\pi\) | ||||
0.869607 | − | 0.493745i | \(-0.164372\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −936.965 | −1.44371 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −420.515 | −0.643975 | −0.321987 | − | 0.946744i | \(-0.604351\pi\) | ||||
−0.321987 | + | 0.946744i | \(0.604351\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 984.271i | − 1.50270i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 549.294i | 0.833527i | 0.909015 | + | 0.416763i | \(0.136836\pi\) | ||||
−0.909015 | + | 0.416763i | \(0.863164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −621.536 | −0.940297 | −0.470148 | − | 0.882587i | \(-0.655800\pi\) | ||||
−0.470148 | + | 0.882587i | \(0.655800\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −91.2621 | −0.137236 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1272.20i | 1.90735i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 1191.57i | − 1.77581i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 782.350 | 1.16248 | 0.581241 | − | 0.813732i | \(-0.302568\pi\) | ||||
0.581241 | + | 0.813732i | \(0.302568\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1007.37 | −1.48798 | −0.743992 | − | 0.668189i | \(-0.767070\pi\) | ||||
−0.743992 | + | 0.668189i | \(0.767070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 59.2623i | 0.0872788i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 217.854i | 0.318966i | 0.987201 | + | 0.159483i | \(0.0509827\pi\) | ||||
−0.987201 | + | 0.159483i | \(0.949017\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 910.244 | 1.32882 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −848.661 | −1.23173 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 569.606i | 0.824321i | 0.911111 | + | 0.412160i | \(0.135226\pi\) | ||||
−0.911111 | + | 0.412160i | \(0.864774\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 291.485i | − 0.419403i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −716.609 | −1.02813 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 98.9249 | 0.141120 | 0.0705598 | − | 0.997508i | \(-0.477521\pi\) | ||||
0.0705598 | + | 0.997508i | \(0.477521\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 168.346i | − 0.239467i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 114.621i | 0.162122i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 878.241 | 1.23870 | 0.619352 | − | 0.785113i | \(-0.287395\pi\) | ||||
0.619352 | + | 0.785113i | \(0.287395\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1400.78 | −1.96463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 525.961i | − 0.735610i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 295.797i | 0.411401i | 0.978615 | + | 0.205701i | \(0.0659473\pi\) | ||||
−0.978615 | + | 0.205701i | \(0.934053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −738.132 | −1.02376 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −184.780 | −0.254869 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 702.264i | 0.965975i | 0.875627 | + | 0.482988i | \(0.160448\pi\) | ||||
−0.875627 | + | 0.482988i | \(0.839552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 642.054i | 0.878323i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1118.98 | −1.52657 | −0.763285 | − | 0.646062i | \(-0.776415\pi\) | ||||
−0.763285 | + | 0.646062i | \(0.776415\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −383.335 | −0.520128 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 437.441i | 0.591936i | 0.955198 | + | 0.295968i | \(0.0956422\pi\) | ||||
−0.955198 | + | 0.295968i | \(0.904358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 296.960i | 0.399677i | 0.979829 | + | 0.199839i | \(0.0640418\pi\) | ||||
−0.979829 | + | 0.199839i | \(0.935958\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 777.463 | 1.04357 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.0055 | 0.0227043 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 978.482i | 1.30291i | 0.758689 | + | 0.651453i | \(0.225840\pi\) | ||||
−0.758689 | + | 0.651453i | \(0.774160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.3448i | 0.0150263i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1303.36 | −1.72175 | −0.860874 | − | 0.508819i | \(-0.830082\pi\) | ||||
−0.860874 | + | 0.508819i | \(0.830082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 368.703 | 0.484498 | 0.242249 | − | 0.970214i | \(-0.422115\pi\) | ||||
0.242249 | + | 0.970214i | \(0.422115\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 35.2096i | − 0.0461463i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 997.244i | − 1.30019i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 723.932 | 0.941393 | 0.470697 | − | 0.882295i | \(-0.344003\pi\) | ||||
0.470697 | + | 0.882295i | \(0.344003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1172.19 | 1.51642 | 0.758208 | − | 0.652013i | \(-0.226075\pi\) | ||||
0.758208 | + | 0.652013i | \(0.226075\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 203.455i | − 0.262522i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 190.558i | 0.244618i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1070.93 | −1.37124 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 869.064 | 1.10709 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 896.417i | 1.13903i | 0.821981 | + | 0.569515i | \(0.192869\pi\) | ||||
−0.821981 | + | 0.569515i | \(0.807131\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.4711i | 0.0410507i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1268.22 | 1.59927 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −200.885 | −0.252052 | −0.126026 | − | 0.992027i | \(-0.540222\pi\) | ||||
−0.126026 | + | 0.992027i | \(0.540222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 495.603i | − 0.620279i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 768.134i | 0.956580i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 476.439 | 0.591850 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1204.46 | −1.48883 | −0.744415 | − | 0.667717i | \(-0.767272\pi\) | ||||
−0.744415 | + | 0.667717i | \(0.767272\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 324.831i | 0.400531i | 0.979742 | + | 0.200265i | \(0.0641805\pi\) | ||||
−0.979742 | + | 0.200265i | \(0.935820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 724.804i | − 0.889330i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 170.732 | 0.208975 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1525.76 | −1.85841 | −0.929206 | − | 0.369562i | \(-0.879508\pi\) | ||||
−0.929206 | + | 0.369562i | \(0.879508\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 632.977i | 0.769110i | 0.923102 | + | 0.384555i | \(0.125645\pi\) | ||||
−0.923102 | + | 0.384555i | \(0.874355\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 75.0303i | 0.0907258i | 0.998971 | + | 0.0453629i | \(0.0144444\pi\) | ||||
−0.998971 | + | 0.0453629i | \(0.985556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 912.657 | 1.10091 | 0.550457 | − | 0.834864i | \(-0.314454\pi\) | ||||
0.550457 | + | 0.834864i | \(0.314454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 471.999 | 0.566626 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 525.598i | − 0.629458i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 927.103i | 1.10501i | 0.833510 | + | 0.552505i | \(0.186328\pi\) | ||||
−0.833510 | + | 0.552505i | \(0.813672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2284.55 | 2.71647 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −227.366 | −0.269072 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 66.9963i | − 0.0790983i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 878.858i | 1.03274i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1383.56 | −1.62199 | −0.810997 | − | 0.585051i | \(-0.801074\pi\) | ||||
−0.810997 | + | 0.585051i | \(0.801074\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −405.494 | −0.473155 | −0.236577 | − | 0.971613i | \(-0.576026\pi\) | ||||
−0.236577 | + | 0.971613i | \(0.576026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 442.450i | − 0.515076i | −0.966268 | − | 0.257538i | \(-0.917089\pi\) | ||||
0.966268 | − | 0.257538i | \(-0.0829113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 703.125i | − 0.814745i | −0.913262 | − | 0.407373i | \(-0.866445\pi\) | ||||
0.913262 | − | 0.407373i | \(-0.133555\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −595.716 | −0.688689 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1236.55 | 1.42295 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 407.996i | − 0.468422i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 592.624i | 0.677284i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1034.99 | 1.18015 | 0.590074 | − | 0.807349i | \(-0.299099\pi\) | ||||
0.590074 | + | 0.807349i | \(0.299099\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 222.517 | 0.252573 | 0.126287 | − | 0.991994i | \(-0.459694\pi\) | ||||
0.126287 | + | 0.991994i | \(0.459694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 616.520i | 0.698211i | 0.937084 | + | 0.349105i | \(0.113514\pi\) | ||||
−0.937084 | + | 0.349105i | \(0.886486\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 603.814i | 0.680737i | 0.940292 | + | 0.340368i | \(0.110552\pi\) | ||||
−0.940292 | + | 0.340368i | \(0.889448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 751.396 | 0.845215 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −131.789 | −0.147580 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 74.7255i | 0.0834922i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3441.43i | 3.82807i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1268.94 | −1.40837 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1021.39 | −1.12861 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 685.479i | 0.755765i | 0.925854 | + | 0.377882i | \(0.123348\pi\) | ||||
−0.925854 | + | 0.377882i | \(0.876652\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 937.378i | 1.02895i | 0.857504 | + | 0.514477i | \(0.172014\pi\) | ||||
−0.857504 | + | 0.514477i | \(0.827986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 302.848 | 0.331706 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −949.886 | −1.03586 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 251.118i | − 0.273252i | −0.990623 | − | 0.136626i | \(-0.956374\pi\) | ||||
0.990623 | − | 0.136626i | \(-0.0436258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 1139.83i | − 1.23492i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −127.649 | −0.137999 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 119.382 | 0.128506 | 0.0642531 | − | 0.997934i | \(-0.479534\pi\) | ||||
0.0642531 | + | 0.997934i | \(0.479534\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 125.512i | − 0.134814i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 786.429i | − 0.841101i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1028.78 | −1.09795 | −0.548973 | − | 0.835840i | \(-0.684981\pi\) | ||||
−0.548973 | + | 0.835840i | \(0.684981\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 789.816 | 0.839337 | 0.419669 | − | 0.907677i | \(-0.362146\pi\) | ||||
0.419669 | + | 0.907677i | \(0.362146\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 994.817i | − 1.05495i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1386.53i | − 1.46413i | −0.681237 | − | 0.732063i | \(-0.738558\pi\) | ||||
0.681237 | − | 0.732063i | \(-0.261442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −817.551 | −0.861487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1433.00 | −1.50368 | −0.751838 | − | 0.659348i | \(-0.770832\pi\) | ||||
−0.751838 | + | 0.659348i | \(0.770832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 228.270i | − 0.239026i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 878.446i | − 0.916002i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2828.24 | −2.94302 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1567.21 | −1.62406 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 987.717i | − 1.02142i | −0.859752 | − | 0.510712i | \(-0.829382\pi\) | ||||
0.859752 | − | 0.510712i | \(-0.170618\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 871.164i | 0.897182i | 0.893737 | + | 0.448591i | \(0.148074\pi\) | ||||
−0.893737 | + | 0.448591i | \(0.851926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −281.302 | −0.289108 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 395.790 | 0.405108 | 0.202554 | − | 0.979271i | \(-0.435076\pi\) | ||||
0.202554 | + | 0.979271i | \(0.435076\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1136.72i | − 1.16111i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 189.551i | − 0.192830i | −0.995341 | − | 0.0964148i | \(-0.969262\pi\) | ||||
0.995341 | − | 0.0964148i | \(-0.0307375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 236.555 | 0.240158 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −891.318 | −0.901232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1028.23i | − 1.03757i | −0.854905 | − | 0.518784i | \(-0.826385\pi\) | ||||
0.854905 | − | 0.518784i | \(-0.173615\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1223.40i | 1.22955i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −788.638 | −0.791011 | −0.395505 | − | 0.918464i | \(-0.629431\pi\) | ||||
−0.395505 | + | 0.918464i | \(0.629431\pi\) | |||||||
\(998\) | 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.m.e.1711.7 | 12 | ||
3.2 | odd | 2 | 912.3.m.b.799.3 | ✓ | 12 | ||
4.3 | odd | 2 | inner | 2736.3.m.e.1711.8 | 12 | ||
12.11 | even | 2 | 912.3.m.b.799.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
912.3.m.b.799.3 | ✓ | 12 | 3.2 | odd | 2 | ||
912.3.m.b.799.9 | yes | 12 | 12.11 | even | 2 | ||
2736.3.m.e.1711.7 | 12 | 1.1 | even | 1 | trivial | ||
2736.3.m.e.1711.8 | 12 | 4.3 | odd | 2 | inner |