Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,3,Mod(2177,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.2177");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.h (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: | \(62.7794529086\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 1152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2177.3 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.2177 |
Dual form | 2304.3.h.i.2177.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2304\mathbb{Z}\right)^\times\).
\(n\) | \(1279\) | \(1793\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.04989 | −0.409978 | −0.204989 | − | 0.978764i | \(-0.565716\pi\) | ||||
−0.204989 | + | 0.978764i | \(0.565716\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.79796 | 1.11399 | 0.556997 | − | 0.830514i | \(-0.311953\pi\) | ||||
0.556997 | + | 0.830514i | \(0.311953\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.09978 | −0.372707 | −0.186353 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186353 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.69694i | − 0.515149i | −0.966258 | − | 0.257575i | \(-0.917077\pi\) | ||||
0.966258 | − | 0.257575i | \(-0.0829233\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.3704i | 1.13944i | 0.821841 | + | 0.569718i | \(0.192947\pi\) | ||||
−0.821841 | + | 0.569718i | \(0.807053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.79796i | − 0.0946294i | −0.998880 | − | 0.0473147i | \(-0.984934\pi\) | ||||
0.998880 | − | 0.0473147i | \(-0.0150664\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.1421i | 0.614875i | 0.951568 | + | 0.307438i | \(0.0994716\pi\) | ||||
−0.951568 | + | 0.307438i | \(0.900528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.7980 | −0.831918 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28.4914 | −0.982460 | −0.491230 | − | 0.871030i | \(-0.663453\pi\) | ||||
−0.491230 | + | 0.871030i | \(0.663453\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.2020 | −0.651679 | −0.325839 | − | 0.945425i | \(-0.605647\pi\) | ||||
−0.325839 | + | 0.945425i | \(0.605647\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.9849 | −0.456713 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 41.5959i | − 1.12421i | −0.827065 | − | 0.562107i | \(-0.809991\pi\) | ||||
0.827065 | − | 0.562107i | \(-0.190009\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.94253i | 0.120550i | 0.998182 | + | 0.0602748i | \(0.0191977\pi\) | ||||
−0.998182 | + | 0.0602748i | \(0.980802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 75.1918i | − 1.74865i | −0.485343 | − | 0.874324i | \(-0.661305\pi\) | ||||
0.485343 | − | 0.874324i | \(-0.338695\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.5707i | 0.288738i | 0.989524 | + | 0.144369i | \(0.0461152\pi\) | ||||
−0.989524 | + | 0.144369i | \(0.953885\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.8082 | 0.240983 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 20.8633 | 0.393646 | 0.196823 | − | 0.980439i | \(-0.436938\pi\) | ||||
0.196823 | + | 0.980439i | \(0.436938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.40408 | 0.152801 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.8542 | 0.929732 | 0.464866 | − | 0.885381i | \(-0.346103\pi\) | ||||
0.464866 | + | 0.885381i | \(0.346103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 89.1918i | 1.46216i | 0.682291 | + | 0.731081i | \(0.260984\pi\) | ||||
−0.682291 | + | 0.731081i | \(0.739016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.7280i | 0.211200i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 37.7980i | 0.564149i | 0.959393 | + | 0.282074i | \(0.0910225\pi\) | ||||
−0.959393 | + | 0.282074i | \(0.908978\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 117.937i | 1.66108i | 0.556958 | + | 0.830541i | \(0.311968\pi\) | ||||
−0.556958 | + | 0.830541i | \(0.688032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48.4041 | −0.663070 | −0.331535 | − | 0.943443i | \(-0.607566\pi\) | ||||
−0.331535 | + | 0.943443i | \(0.607566\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −31.9699 | −0.415193 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −92.6061 | −1.17223 | −0.586115 | − | 0.810228i | \(-0.699343\pi\) | ||||
−0.586115 | + | 0.810228i | \(0.699343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −158.806 | −1.91333 | −0.956663 | − | 0.291197i | \(-0.905947\pi\) | ||||
−0.956663 | + | 0.291197i | \(0.905947\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 39.7071i | − 0.467143i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 121.036i | − 1.35996i | −0.733230 | − | 0.679980i | \(-0.761988\pi\) | ||||
0.733230 | − | 0.679980i | \(-0.238012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 52.2225i | − 0.573873i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.68561i | 0.0387959i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 167.373 | 1.72550 | 0.862750 | − | 0.505631i | \(-0.168740\pi\) | ||||
0.862750 | + | 0.505631i | \(0.168740\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 91.7024 | 0.907944 | 0.453972 | − | 0.891016i | \(-0.350007\pi\) | ||||
0.453972 | + | 0.891016i | \(0.350007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 58.9898 | 0.572716 | 0.286358 | − | 0.958123i | \(-0.407555\pi\) | ||||
0.286358 | + | 0.958123i | \(0.407555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −182.676 | −1.70725 | −0.853626 | − | 0.520886i | \(-0.825602\pi\) | ||||
−0.853626 | + | 0.520886i | \(0.825602\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 62.6969i | 0.575201i | 0.957750 | + | 0.287601i | \(0.0928576\pi\) | ||||
−0.957750 | + | 0.287601i | \(0.907142\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7567i | 0.0951919i | 0.998867 | + | 0.0475959i | \(0.0151560\pi\) | ||||
−0.998867 | + | 0.0475959i | \(0.984844\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 28.9898i | − 0.252085i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 151.050i | 1.26932i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −104.192 | −0.861090 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 93.8807 | 0.751046 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −222.182 | −1.74946 | −0.874731 | − | 0.484609i | \(-0.838962\pi\) | ||||
−0.874731 | + | 0.484609i | \(0.838962\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −111.166 | −0.848594 | −0.424297 | − | 0.905523i | \(-0.639479\pi\) | ||||
−0.424297 | + | 0.905523i | \(0.639479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 14.0204i | − 0.105417i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 76.5104i | − 0.558470i | −0.960223 | − | 0.279235i | \(-0.909919\pi\) | ||||
0.960223 | − | 0.279235i | \(-0.0900809\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 223.778i | − 1.60991i | −0.593336 | − | 0.804955i | \(-0.702189\pi\) | ||||
0.593336 | − | 0.804955i | \(-0.297811\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27.4559i | 0.192000i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 58.4041 | 0.402787 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 121.672 | 0.816592 | 0.408296 | − | 0.912850i | \(-0.366123\pi\) | ||||
0.408296 | + | 0.912850i | \(0.366123\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −82.9898 | −0.549601 | −0.274801 | − | 0.961501i | \(-0.588612\pi\) | ||||
−0.274801 | + | 0.961501i | \(0.588612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 41.4119 | 0.267174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 32.4245i | 0.206525i | 0.994654 | + | 0.103263i | \(0.0329282\pi\) | ||||
−0.994654 | + | 0.103263i | \(0.967072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 110.280i | 0.684968i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.1714i | 0.0808063i | 0.999183 | + | 0.0404031i | \(0.0128642\pi\) | ||||
−0.999183 | + | 0.0404031i | \(0.987136\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 50.6548i | 0.303322i | 0.988433 | + | 0.151661i | \(0.0484622\pi\) | ||||
−0.988433 | + | 0.151661i | \(0.951538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 124.151 | 0.734621 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −294.335 | −1.70136 | −0.850678 | − | 0.525687i | \(-0.823808\pi\) | ||||
−0.850678 | + | 0.525687i | \(0.823808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −162.182 | −0.926752 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −205.047 | −1.14551 | −0.572756 | − | 0.819726i | \(-0.694126\pi\) | ||||
−0.572756 | + | 0.819726i | \(0.694126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 107.464i | − 0.593725i | −0.954920 | − | 0.296863i | \(-0.904060\pi\) | ||||
0.954920 | − | 0.296863i | \(-0.0959404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 85.2670i | 0.460903i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 79.4143i | − 0.424675i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 219.731i | 1.15043i | 0.818004 | + | 0.575213i | \(0.195081\pi\) | ||||
−0.818004 | + | 0.575213i | \(0.804919\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −177.151 | −0.917881 | −0.458940 | − | 0.888467i | \(-0.651771\pi\) | ||||
−0.458940 | + | 0.888467i | \(0.651771\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −182.055 | −0.924136 | −0.462068 | − | 0.886845i | \(-0.652892\pi\) | ||||
−0.462068 | + | 0.886845i | \(0.652892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −267.757 | −1.34551 | −0.672757 | − | 0.739864i | \(-0.734890\pi\) | ||||
−0.672757 | + | 0.739864i | \(0.734890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −222.174 | −1.09446 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 10.1316i | − 0.0494226i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.37123i | 0.0352690i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 40.2225i | − 0.190628i | −0.995447 | − | 0.0953139i | \(-0.969615\pi\) | ||||
0.995447 | − | 0.0953139i | \(-0.0303855\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 154.135i | 0.716906i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −157.535 | −0.725966 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 129.722 | 0.586979 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 44.9694 | 0.201656 | 0.100828 | − | 0.994904i | \(-0.467851\pi\) | ||||
0.100828 | + | 0.994904i | \(0.467851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −180.605 | −0.795618 | −0.397809 | − | 0.917468i | \(-0.630229\pi\) | ||||
−0.397809 | + | 0.917468i | \(0.630229\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 129.666i | − 0.566228i | −0.959086 | − | 0.283114i | \(-0.908632\pi\) | ||||
0.959086 | − | 0.283114i | \(-0.0913676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 209.832i | 0.900566i | 0.892886 | + | 0.450283i | \(0.148677\pi\) | ||||
−0.892886 | + | 0.450283i | \(0.851323\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 27.8184i | − 0.118376i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 334.583i | 1.39993i | 0.714178 | + | 0.699964i | \(0.246801\pi\) | ||||
−0.714178 | + | 0.699964i | \(0.753199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −51.8184 | −0.215014 | −0.107507 | − | 0.994204i | \(-0.534287\pi\) | ||||
−0.107507 | + | 0.994204i | \(0.534287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.2054 | −0.0987976 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.0408 | −0.0487483 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −311.541 | −1.24120 | −0.620600 | − | 0.784127i | \(-0.713111\pi\) | ||||
−0.620600 | + | 0.784127i | \(0.713111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 57.9796i | − 0.229168i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 50.0978i | − 0.194933i | −0.995239 | − | 0.0974665i | \(-0.968926\pi\) | ||||
0.995239 | − | 0.0974665i | \(-0.0310739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 324.363i | − 1.25237i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 334.268i | 1.27098i | 0.772108 | + | 0.635491i | \(0.219202\pi\) | ||||
−0.772108 | + | 0.635491i | \(0.780798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42.7673 | −0.161386 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −80.1318 | −0.297888 | −0.148944 | − | 0.988846i | \(-0.547587\pi\) | ||||
−0.148944 | + | 0.988846i | \(0.547587\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 61.7775 | 0.227961 | 0.113981 | − | 0.993483i | \(-0.463640\pi\) | ||||
0.113981 | + | 0.993483i | \(0.463640\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 85.2670 | 0.310062 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 423.242i | 1.52795i | 0.645247 | + | 0.763974i | \(0.276755\pi\) | ||||
−0.645247 | + | 0.763974i | \(0.723245\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 63.6396i | − 0.226475i | −0.993568 | − | 0.113238i | \(-0.963878\pi\) | ||||
0.993568 | − | 0.113238i | \(-0.0361222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 98.4245i | 0.347790i | 0.984764 | + | 0.173895i | \(0.0556353\pi\) | ||||
−0.984764 | + | 0.173895i | \(0.944365\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 38.5417i | 0.134291i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −86.2122 | −0.298312 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −368.888 | −1.25900 | −0.629502 | − | 0.776999i | \(-0.716741\pi\) | ||||
−0.629502 | + | 0.776999i | \(0.716741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −112.445 | −0.381169 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 94.7090 | 0.316753 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 586.343i | − 1.94798i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 182.833i | − 0.599453i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 507.737i | − 1.65387i | −0.562301 | − | 0.826933i | \(-0.690084\pi\) | ||||
0.562301 | − | 0.826933i | \(-0.309916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 36.7984i | − 0.118323i | −0.998248 | − | 0.0591614i | \(-0.981157\pi\) | ||||
0.998248 | − | 0.0591614i | \(-0.0188427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 287.576 | 0.918772 | 0.459386 | − | 0.888237i | \(-0.348070\pi\) | ||||
0.459386 | + | 0.888237i | \(0.348070\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 450.726 | 1.42185 | 0.710925 | − | 0.703268i | \(-0.248277\pi\) | ||||
0.710925 | + | 0.703268i | \(0.248277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 116.808 | 0.366170 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.8272 | 0.107824 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 139.283i | 0.428562i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 105.824i | 0.321652i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 133.798i | 0.404223i | 0.979362 | + | 0.202112i | \(0.0647804\pi\) | ||||
−0.979362 | + | 0.202112i | \(0.935220\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 77.4816i | − 0.231288i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −124.808 | −0.370351 | −0.185175 | − | 0.982706i | \(-0.559285\pi\) | ||||
−0.185175 | + | 0.982706i | \(0.559285\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 82.8238 | 0.242885 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −290.020 | −0.845541 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −571.699 | −1.64755 | −0.823773 | − | 0.566919i | \(-0.808135\pi\) | ||||
−0.823773 | + | 0.566919i | \(0.808135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 499.898i | 1.43237i | 0.697909 | + | 0.716186i | \(0.254114\pi\) | ||||
−0.697909 | + | 0.716186i | \(0.745886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 5.64242i | − 0.0159842i | −0.999968 | − | 0.00799210i | \(-0.997456\pi\) | ||||
0.999968 | − | 0.00799210i | \(-0.00254399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 241.757i | − 0.681006i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 586.769i | − 1.63445i | −0.576316 | − | 0.817227i | \(-0.695510\pi\) | ||||
0.576316 | − | 0.817227i | \(-0.304490\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 357.767 | 0.991045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 99.2229 | 0.271844 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.6265 | 0.0725519 | 0.0362759 | − | 0.999342i | \(-0.488450\pi\) | ||||
0.0362759 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 162.691 | 0.438520 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 226.041i | 0.606008i | 0.952989 | + | 0.303004i | \(0.0979895\pi\) | ||||
−0.952989 | + | 0.303004i | \(0.902011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 190.805i | 0.506114i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 343.292i | − 0.905783i | −0.891566 | − | 0.452892i | \(-0.850392\pi\) | ||||
0.891566 | − | 0.452892i | \(-0.149608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 654.680i | 1.70935i | 0.519166 | + | 0.854673i | \(0.326243\pi\) | ||||
−0.519166 | + | 0.854673i | \(0.673757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 65.5347 | 0.170220 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 298.948 | 0.768504 | 0.384252 | − | 0.923228i | \(-0.374459\pi\) | ||||
0.384252 | + | 0.923228i | \(0.374459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −273.939 | −0.700611 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 189.832 | 0.480588 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 529.596i | − 1.33399i | −0.745060 | − | 0.666997i | \(-0.767579\pi\) | ||||
0.745060 | − | 0.666997i | \(-0.232421\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 447.034i | − 1.11480i | −0.830244 | − | 0.557399i | \(-0.811799\pi\) | ||||
0.830244 | − | 0.557399i | \(-0.188201\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 135.292i | 0.335712i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 170.534i | 0.419002i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 503.292 | 1.23054 | 0.615271 | − | 0.788316i | \(-0.289047\pi\) | ||||
0.615271 | + | 0.788316i | \(0.289047\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 427.751 | 1.03572 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 325.535 | 0.784421 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 142.722 | 0.340624 | 0.170312 | − | 0.985390i | \(-0.445522\pi\) | ||||
0.170312 | + | 0.985390i | \(0.445522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 41.3031i | 0.0981070i | 0.998796 | + | 0.0490535i | \(0.0156205\pi\) | ||||
−0.998796 | + | 0.0490535i | \(0.984380\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 402.865i | − 0.947917i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 695.514i | 1.62884i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 441.719i | 1.02487i | 0.858726 | + | 0.512436i | \(0.171257\pi\) | ||||
−0.858726 | + | 0.512436i | \(0.828743\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −460.343 | −1.06315 | −0.531574 | − | 0.847012i | \(-0.678399\pi\) | ||||
−0.531574 | + | 0.847012i | \(0.678399\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.4270 | 0.0581853 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −219.353 | −0.499665 | −0.249833 | − | 0.968289i | \(-0.580376\pi\) | ||||
−0.249833 | + | 0.968289i | \(0.580376\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.2982 | −0.0435626 | −0.0217813 | − | 0.999763i | \(-0.506934\pi\) | ||||
−0.0217813 | + | 0.999763i | \(0.506934\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 248.111i | 0.557553i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 573.627i | − 1.27756i | −0.769387 | − | 0.638782i | \(-0.779438\pi\) | ||||
0.769387 | − | 0.638782i | \(-0.220562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 20.2633i | − 0.0449296i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 107.050i | 0.235275i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 71.0102 | 0.155383 | 0.0776917 | − | 0.996977i | \(-0.475245\pi\) | ||||
0.0776917 | + | 0.996977i | \(0.475245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −751.869 | −1.63095 | −0.815476 | − | 0.578791i | \(-0.803525\pi\) | ||||
−0.815476 | + | 0.578791i | \(0.803525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 638.182 | 1.37836 | 0.689181 | − | 0.724589i | \(-0.257970\pi\) | ||||
0.689181 | + | 0.724589i | \(0.257970\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 225.032 | 0.481867 | 0.240933 | − | 0.970542i | \(-0.422547\pi\) | ||||
0.240933 | + | 0.970542i | \(0.422547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 294.747i | 0.628458i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 308.270i | 0.651733i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.3939i | 0.0787240i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 757.675i | − 1.58178i | −0.611955 | − | 0.790892i | \(-0.709617\pi\) | ||||
0.611955 | − | 0.790892i | \(-0.290383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −278.565 | −0.579138 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −343.097 | −0.707416 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 266.100 | 0.546407 | 0.273203 | − | 0.961956i | \(-0.411917\pi\) | ||||
0.273203 | + | 0.961956i | \(0.411917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3701 | 0.0292671 | 0.0146335 | − | 0.999893i | \(-0.495342\pi\) | ||||
0.0146335 | + | 0.999893i | \(0.495342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 551.889i | − 1.11945i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 919.666i | 1.85043i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 603.151i | 1.20872i | 0.796712 | + | 0.604360i | \(0.206571\pi\) | ||||
−0.796712 | + | 0.604360i | \(0.793429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 781.388i | − 1.55345i | −0.629837 | − | 0.776727i | \(-0.716878\pi\) | ||||
0.629837 | − | 0.776727i | \(-0.283122\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −187.980 | −0.372237 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 930.002 | 1.82712 | 0.913558 | − | 0.406709i | \(-0.133324\pi\) | ||||
0.913558 | + | 0.406709i | \(0.133324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −377.453 | −0.738656 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −120.922 | −0.234801 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 55.6367i | − 0.107615i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 463.947i | 0.890494i | 0.895408 | + | 0.445247i | \(0.146884\pi\) | ||||
−0.895408 | + | 0.445247i | \(0.853116\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 426.524i | 0.815534i | 0.913086 | + | 0.407767i | \(0.133693\pi\) | ||||
−0.913086 | + | 0.407767i | \(0.866307\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 391.322i | − 0.742546i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 329.000 | 0.621928 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.0998 | 0.0621010 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 374.465 | 0.699935 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −48.4108 | −0.0898160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 281.930i | 0.521127i | 0.965457 | + | 0.260563i | \(0.0839083\pi\) | ||||
−0.965457 | + | 0.260563i | \(0.916092\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 128.522i | − 0.235820i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 204.727i | − 0.374272i | −0.982334 | − | 0.187136i | \(-0.940080\pi\) | ||||
0.982334 | − | 0.187136i | \(-0.0599204\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.2263i | 0.0929697i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −722.139 | −1.30586 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −813.465 | −1.46044 | −0.730220 | − | 0.683212i | \(-0.760582\pi\) | ||||
−0.730220 | + | 0.683212i | \(0.760582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −503.555 | −0.900814 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 666.523 | 1.18388 | 0.591939 | − | 0.805983i | \(-0.298363\pi\) | ||||
0.591939 | + | 0.805983i | \(0.298363\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 22.0500i | − 0.0390265i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 308.756i | − 0.542629i | −0.962491 | − | 0.271315i | \(-0.912542\pi\) | ||||
0.962491 | − | 0.271315i | \(-0.0874584\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 534.747i | 0.936510i | 0.883594 | + | 0.468255i | \(0.155117\pi\) | ||||
−0.883594 | + | 0.468255i | \(0.844883\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 294.128i | − 0.511526i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 158.000 | 0.273830 | 0.136915 | − | 0.990583i | \(-0.456281\pi\) | ||||
0.136915 | + | 0.990583i | \(0.456281\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1238.36 | −2.13143 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −85.5347 | −0.146715 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 783.503 | 1.33476 | 0.667379 | − | 0.744718i | \(-0.267416\pi\) | ||||
0.667379 | + | 0.744718i | \(0.267416\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.3224i | 0.0616680i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 26.1283i | − 0.0440613i | −0.999757 | − | 0.0220306i | \(-0.992987\pi\) | ||||
0.999757 | − | 0.0220306i | \(-0.00701313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 309.635i | − 0.520394i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 440.063i | − 0.734663i | −0.930090 | − | 0.367331i | \(-0.880272\pi\) | ||||
0.930090 | − | 0.367331i | \(-0.119728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −66.0000 | −0.109817 | −0.0549085 | − | 0.998491i | \(-0.517487\pi\) | ||||
−0.0549085 | + | 0.998491i | \(0.517487\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 213.582 | 0.353027 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 465.373 | 0.766678 | 0.383339 | − | 0.923608i | \(-0.374774\pi\) | ||||
0.383339 | + | 0.923608i | \(0.374774\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 90.8820 | 0.148743 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 580.706i | − 0.947318i | −0.880708 | − | 0.473659i | \(-0.842933\pi\) | ||||
0.880708 | − | 0.473659i | \(-0.157067\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 43.8118i | − 0.0710077i | −0.999370 | − | 0.0355039i | \(-0.988696\pi\) | ||||
0.999370 | − | 0.0355039i | \(-0.0113036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 401.980i | − 0.649402i | −0.945817 | − | 0.324701i | \(-0.894736\pi\) | ||||
0.945817 | − | 0.324701i | \(-0.105264\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 943.837i | − 1.51499i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 327.504 | 0.524007 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 805.729 | 1.28097 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 94.5857 | 0.149898 | 0.0749491 | − | 0.997187i | \(-0.476121\pi\) | ||||
0.0749491 | + | 0.997187i | \(0.476121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 455.447 | 0.717240 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 79.0785i | − 0.124142i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 866.698i | 1.35210i | 0.736854 | + | 0.676051i | \(0.236310\pi\) | ||||
−0.736854 | + | 0.676051i | \(0.763690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 802.020i | 1.24731i | 0.781700 | + | 0.623655i | \(0.214353\pi\) | ||||
−0.781700 | + | 0.623655i | \(0.785647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 109.223i | − 0.168815i | −0.996431 | − | 0.0844076i | \(-0.973100\pi\) | ||||
0.996431 | − | 0.0844076i | \(-0.0268998\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −224.890 | −0.346517 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −976.727 | −1.49575 | −0.747877 | − | 0.663837i | \(-0.768927\pi\) | ||||
−0.747877 | + | 0.663837i | \(0.768927\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 227.878 | 0.347905 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −528.887 | −0.802560 | −0.401280 | − | 0.915955i | \(-0.631435\pi\) | ||||
−0.401280 | + | 0.915955i | \(0.631435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 287.535i | − 0.435000i | −0.976060 | − | 0.217500i | \(-0.930210\pi\) | ||||
0.976060 | − | 0.217500i | \(-0.0697901\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.7403i | 0.0432185i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 402.929i | − 0.604091i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 365.667i | − 0.544958i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −597.029 | −0.887115 | −0.443558 | − | 0.896246i | \(-0.646284\pi\) | ||||
−0.443558 | + | 0.896246i | \(0.646284\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 652.630 | 0.964003 | 0.482001 | − | 0.876170i | \(-0.339910\pi\) | ||||
0.482001 | + | 0.876170i | \(0.339910\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1305.17 | 1.92220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 288.971 | 0.423091 | 0.211546 | − | 0.977368i | \(-0.432150\pi\) | ||||
0.211546 | + | 0.977368i | \(0.432150\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 156.838i | 0.228960i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 139.720i | − 0.202787i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 752.241i | 1.08863i | 0.838882 | + | 0.544313i | \(0.183210\pi\) | ||||
−0.838882 | + | 0.544313i | \(0.816790\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 458.719i | 0.660027i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −95.7388 | −0.137358 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 808.152 | 1.15286 | 0.576428 | − | 0.817148i | \(-0.304446\pi\) | ||||
0.576428 | + | 0.817148i | \(0.304446\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −74.7878 | −0.106384 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 715.091 | 1.01144 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 737.748i | − 1.04055i | −0.854000 | − | 0.520274i | \(-0.825830\pi\) | ||||
0.854000 | − | 0.520274i | \(-0.174170\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 285.700i | − 0.400701i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 56.2816i | − 0.0787156i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 236.275i | − 0.328616i | −0.986409 | − | 0.164308i | \(-0.947461\pi\) | ||||
0.986409 | − | 0.164308i | \(-0.0525390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 460.000 | 0.638003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 592.562 | 0.817327 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 444.606 | 0.611563 | 0.305781 | − | 0.952102i | \(-0.401082\pi\) | ||||
0.305781 | + | 0.952102i | \(0.401082\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1456.50 | 1.99247 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1196.74i | 1.63265i | 0.577590 | + | 0.816327i | \(0.303993\pi\) | ||||
−0.577590 | + | 0.816327i | \(0.696007\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 154.963i | − 0.210262i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1437.78i | 1.94557i | 0.231712 | + | 0.972784i | \(0.425567\pi\) | ||||
−0.231712 | + | 0.972784i | \(0.574433\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 1265.05i | − 1.70262i | −0.524661 | − | 0.851311i | \(-0.675808\pi\) | ||||
0.524661 | − | 0.851311i | \(-0.324192\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −249.414 | −0.334784 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1424.50 | −1.90187 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 578.990 | 0.770958 | 0.385479 | − | 0.922717i | \(-0.374036\pi\) | ||||
0.385479 | + | 0.922717i | \(0.374036\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 170.120 | 0.225324 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 82.6561i | 0.109189i | 0.998509 | + | 0.0545945i | \(0.0173866\pi\) | ||||
−0.998509 | + | 0.0545945i | \(0.982613\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 512.088i | 0.672915i | 0.941699 | + | 0.336457i | \(0.109229\pi\) | ||||
−0.941699 | + | 0.336457i | \(0.890771\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 488.908i | 0.640771i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 367.355i | − 0.478950i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1267.49 | 1.64824 | 0.824118 | − | 0.566418i | \(-0.191671\pi\) | ||||
0.824118 | + | 0.566418i | \(0.191671\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −437.342 | −0.565772 | −0.282886 | − | 0.959154i | \(-0.591292\pi\) | ||||
−0.282886 | + | 0.959154i | \(0.591292\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 420.161 | 0.542144 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.88647 | 0.0114075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 483.514i | − 0.619096i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 66.4666i | − 0.0846708i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 965.031i | 1.22621i | 0.790000 | + | 0.613107i | \(0.210081\pi\) | ||||
−0.790000 | + | 0.613107i | \(0.789919\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 83.8802i | 0.106043i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 597.312 | 0.753231 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 996.513 | 1.25033 | 0.625165 | − | 0.780492i | \(-0.285032\pi\) | ||||
0.625165 | + | 0.780492i | \(0.285032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −262.869 | −0.328998 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 198.446 | 0.247131 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 226.061i | − 0.280821i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 1530.32i | − 1.89162i | −0.324723 | − | 0.945809i | \(-0.605271\pi\) | ||||
0.324723 | − | 0.945809i | \(-0.394729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 833.716i | − 1.02801i | −0.857787 | − | 0.514005i | \(-0.828161\pi\) | ||||
0.857787 | − | 0.514005i | \(-0.171839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 26.9999i | − 0.0331288i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −135.192 | −0.165473 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1414.40 | 1.72278 | 0.861391 | − | 0.507942i | \(-0.169593\pi\) | ||||
0.861391 | + | 0.507942i | \(0.169593\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1168.16 | 1.41939 | 0.709697 | − | 0.704507i | \(-0.248832\pi\) | ||||
0.709697 | + | 0.704507i | \(0.248832\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 624.110 | 0.754667 | 0.377334 | − | 0.926077i | \(-0.376841\pi\) | ||||
0.377334 | + | 0.926077i | \(0.376841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1531.46i | 1.84736i | 0.383161 | + | 0.923682i | \(0.374836\pi\) | ||||
−0.383161 | + | 0.923682i | \(0.625164\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 228.729i | 0.274584i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 103.837i | − 0.124355i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1013.95i | 1.20852i | 0.796787 | + | 0.604260i | \(0.206531\pi\) | ||||
−0.796787 | + | 0.604260i | \(0.793469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.2429 | −0.0347715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −254.496 | −0.301178 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −812.484 | −0.959249 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 588.255 | 0.691252 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 258.808i | 0.303409i | 0.988426 | + | 0.151705i | \(0.0484763\pi\) | ||||
−0.988426 | + | 0.151705i | \(0.951524\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1453.90i | − 1.69650i | −0.529600 | − | 0.848248i | \(-0.677658\pi\) | ||||
0.529600 | − | 0.848248i | \(-0.322342\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 740.645i | 0.862218i | 0.902300 | + | 0.431109i | \(0.141877\pi\) | ||||
−0.902300 | + | 0.431109i | \(0.858123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 675.593i | − 0.782842i | −0.920212 | − | 0.391421i | \(-0.871984\pi\) | ||||
0.920212 | − | 0.391421i | \(-0.128016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 603.353 | 0.697518 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 379.664 | 0.436898 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 253.131 | 0.290621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 732.078 | 0.836660 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 321.678i | − 0.366793i | −0.983039 | − | 0.183397i | \(-0.941291\pi\) | ||||
0.983039 | − | 0.183397i | \(-0.0587092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 586.899i | 0.666173i | 0.942896 | + | 0.333087i | \(0.108090\pi\) | ||||
−0.942896 | + | 0.333087i | \(0.891910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1186.95i | − 1.34422i | −0.740451 | − | 0.672110i | \(-0.765388\pi\) | ||||
0.740451 | − | 0.672110i | \(-0.234612\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 682.707i | − 0.769681i | −0.922983 | − | 0.384841i | \(-0.874256\pi\) | ||||
0.922983 | − | 0.384841i | \(-0.125744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1732.56 | −1.94889 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.3995 | 0.0273231 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 420.322 | 0.469634 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 575.583 | 0.640249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 404.130i | 0.448534i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 220.290i | 0.243414i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 803.837i | − 0.886259i | −0.896458 | − | 0.443129i | \(-0.853868\pi\) | ||||
0.896458 | − | 0.443129i | \(-0.146132\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1090.77i | − 1.19733i | −0.800998 | − | 0.598667i | \(-0.795697\pi\) | ||||
0.800998 | − | 0.598667i | \(-0.204303\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 651.069 | 0.713110 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −866.867 | −0.945329 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 362.141 | 0.394060 | 0.197030 | − | 0.980397i | \(-0.436870\pi\) | ||||
0.197030 | + | 0.980397i | \(0.436870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 789.815 | 0.855704 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 865.110i | 0.935254i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 421.437i | 0.453646i | 0.973936 | + | 0.226823i | \(0.0728339\pi\) | ||||
−0.973936 | + | 0.226823i | \(0.927166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 21.2306i | − 0.0228041i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 162.790i | 0.174107i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.23266 | −0.00985342 | −0.00492671 | − | 0.999988i | \(-0.501568\pi\) | ||||
−0.00492671 | + | 0.999988i | \(0.501568\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −175.499 | −0.186503 | −0.0932513 | − | 0.995643i | \(-0.529726\pi\) | ||||
−0.0932513 | + | 0.995643i | \(0.529726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −69.8979 | −0.0741230 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1185.99 | −1.25237 | −0.626185 | − | 0.779675i | \(-0.715384\pi\) | ||||
−0.626185 | + | 0.779675i | \(0.715384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 324.159i | 0.341580i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 929.581i | 0.975426i | 0.873004 | + | 0.487713i | \(0.162169\pi\) | ||||
−0.873004 | + | 0.487713i | \(0.837831\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 450.424i | − 0.471649i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 596.625i | − 0.622132i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −552.878 | −0.575315 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 363.140 | 0.376311 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 272.284 | 0.281576 | 0.140788 | − | 0.990040i | \(-0.455036\pi\) | ||||
0.140788 | + | 0.990040i | \(0.455036\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1439.00 | −1.48197 | −0.740986 | − | 0.671520i | \(-0.765642\pi\) | ||||
−0.740986 | + | 0.671520i | \(0.765642\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1745.01i | − 1.79343i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1448.98i | − 1.48309i | −0.670902 | − | 0.741546i | \(-0.734093\pi\) | ||||
0.670902 | − | 0.741546i | \(-0.265907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 496.222i | 0.506867i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 289.013i | − 0.294011i | −0.989136 | − | 0.147006i | \(-0.953036\pi\) | ||||
0.989136 | − | 0.147006i | \(-0.0469636\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 373.192 | 0.378875 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1063.37 | 1.07520 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −340.202 | −0.343292 | −0.171646 | − | 0.985159i | \(-0.554908\pi\) | ||||
−0.171646 | + | 0.985159i | \(0.554908\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 548.872 | 0.551630 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1664.06i | − 1.66906i | −0.550959 | − | 0.834532i | \(-0.685738\pi\) | ||||
0.550959 | − | 0.834532i | \(-0.314262\pi\) | |||||||
\(998\) | 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 | 2304.3.h.i.2177.3 | 8 | ||
3.2 | odd | 2 | inner | 2304.3.h.i.2177.5 | 8 | ||
4.3 | odd | 2 | 2304.3.h.k.2177.3 | 8 | |||
8.3 | odd | 2 | 2304.3.h.k.2177.6 | 8 | |||
8.5 | even | 2 | inner | 2304.3.h.i.2177.6 | 8 | ||
12.11 | even | 2 | 2304.3.h.k.2177.5 | 8 | |||
16.3 | odd | 4 | 1152.3.e.b.1025.3 | yes | 4 | ||
16.5 | even | 4 | 1152.3.e.h.1025.2 | yes | 4 | ||
16.11 | odd | 4 | 1152.3.e.d.1025.2 | yes | 4 | ||
16.13 | even | 4 | 1152.3.e.f.1025.3 | yes | 4 | ||
24.5 | odd | 2 | inner | 2304.3.h.i.2177.4 | 8 | ||
24.11 | even | 2 | 2304.3.h.k.2177.4 | 8 | |||
48.5 | odd | 4 | 1152.3.e.h.1025.3 | yes | 4 | ||
48.11 | even | 4 | 1152.3.e.d.1025.3 | yes | 4 | ||
48.29 | odd | 4 | 1152.3.e.f.1025.2 | yes | 4 | ||
48.35 | even | 4 | 1152.3.e.b.1025.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.3.e.b.1025.2 | ✓ | 4 | 48.35 | even | 4 | ||
1152.3.e.b.1025.3 | yes | 4 | 16.3 | odd | 4 | ||
1152.3.e.d.1025.2 | yes | 4 | 16.11 | odd | 4 | ||
1152.3.e.d.1025.3 | yes | 4 | 48.11 | even | 4 | ||
1152.3.e.f.1025.2 | yes | 4 | 48.29 | odd | 4 | ||
1152.3.e.f.1025.3 | yes | 4 | 16.13 | even | 4 | ||
1152.3.e.h.1025.2 | yes | 4 | 16.5 | even | 4 | ||
1152.3.e.h.1025.3 | yes | 4 | 48.5 | odd | 4 | ||
2304.3.h.i.2177.3 | 8 | 1.1 | even | 1 | trivial | ||
2304.3.h.i.2177.4 | 8 | 24.5 | odd | 2 | inner | ||
2304.3.h.i.2177.5 | 8 | 3.2 | odd | 2 | inner | ||
2304.3.h.i.2177.6 | 8 | 8.5 | even | 2 | inner | ||
2304.3.h.k.2177.3 | 8 | 4.3 | odd | 2 | |||
2304.3.h.k.2177.4 | 8 | 24.11 | even | 2 | |||
2304.3.h.k.2177.5 | 8 | 12.11 | even | 2 | |||
2304.3.h.k.2177.6 | 8 | 8.3 | odd | 2 |