Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(557,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.bk (of order \(6\), degree \(2\), 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: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.329365073333488765586374656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 199x^{12} + 24960x^{8} - 2913559x^{4} + 214358881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 557.4 | ||
Root | \(3.29641 + 0.365632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.557 |
Dual form | 1764.3.bk.g.1745.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | −3.08083 | + | 1.77872i | −0.616166 | + | 0.355744i | −0.775375 | − | 0.631501i | \(-0.782439\pi\) |
0.159209 | + | 0.987245i | \(0.449106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.03119 | + | 4.63681i | 0.730108 | + | 0.421528i | 0.818462 | − | 0.574561i | \(-0.194827\pi\) |
−0.0883536 | + | 0.996089i | \(0.528161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −0.326357 | −0.163178 | − | 0.986597i | \(-0.552175\pi\) | ||||
−0.163178 | + | 0.986597i | \(0.552175\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.11532 | − | 1.22128i | −0.124431 | − | 0.0718400i | 0.436493 | − | 0.899708i | \(-0.356220\pi\) |
−0.560923 | + | 0.827868i | \(0.689554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.3749 | − | 17.9698i | −0.546047 | − | 0.945781i | −0.998540 | − | 0.0540134i | \(-0.982799\pi\) |
0.452493 | − | 0.891768i | \(-0.350535\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.682720 | − | 0.394169i | 0.0296835 | − | 0.0171378i | −0.485085 | − | 0.874467i | \(-0.661211\pi\) |
0.514768 | + | 0.857329i | \(0.327878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.17232 | + | 10.6908i | −0.246893 | + | 0.427631i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.69694i | − | 0.265412i | −0.991155 | − | 0.132706i | \(-0.957633\pi\) | ||
0.991155 | − | 0.132706i | \(-0.0423666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.7891 | + | 20.4193i | −0.380294 | + | 0.658688i | −0.991104 | − | 0.133089i | \(-0.957510\pi\) |
0.610810 | + | 0.791777i | \(0.290844\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6723 | + | 20.2170i | 0.315468 | + | 0.546407i | 0.979537 | − | 0.201265i | \(-0.0645052\pi\) |
−0.664069 | + | 0.747671i | \(0.731172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 51.5574i | − | 1.25750i | −0.777608 | − | 0.628749i | \(-0.783567\pi\) | ||
0.777608 | − | 0.628749i | \(-0.216433\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −49.3446 | −1.14755 | −0.573775 | − | 0.819013i | \(-0.694522\pi\) | ||||
−0.573775 | + | 0.819013i | \(0.694522\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.6574 | − | 7.88512i | 0.290584 | − | 0.167769i | −0.347621 | − | 0.937635i | \(-0.613011\pi\) |
0.638205 | + | 0.769866i | \(0.279677\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 65.1929 | + | 37.6391i | 1.23005 | + | 0.710172i | 0.967041 | − | 0.254620i | \(-0.0819505\pi\) |
0.263013 | + | 0.964792i | \(0.415284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −32.9903 | −0.599824 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.6574 | − | 7.88512i | −0.231482 | − | 0.133646i | 0.379774 | − | 0.925079i | \(-0.376002\pi\) |
−0.611256 | + | 0.791433i | \(0.709335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.01093 | + | 6.94714i | 0.0657530 | + | 0.113888i | 0.897028 | − | 0.441974i | \(-0.145722\pi\) |
−0.831275 | + | 0.555862i | \(0.812388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.0709 | − | 7.54647i | 0.201090 | − | 0.116099i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 43.6723 | − | 75.6427i | 0.651826 | − | 1.12900i | −0.330854 | − | 0.943682i | \(-0.607337\pi\) |
0.982680 | − | 0.185313i | \(-0.0593299\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 40.0614i | − | 0.564245i | −0.959378 | − | 0.282123i | \(-0.908962\pi\) | ||
0.959378 | − | 0.282123i | \(-0.0910385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17.2023 | + | 29.7952i | −0.235648 | + | 0.408154i | −0.959461 | − | 0.281843i | \(-0.909054\pi\) |
0.723813 | + | 0.689996i | \(0.242388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.34463 | − | 7.52512i | −0.0549953 | − | 0.0952547i | 0.837217 | − | 0.546871i | \(-0.184181\pi\) |
−0.892212 | + | 0.451616i | \(0.850848\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 115.115i | − | 1.38693i | −0.720492 | − | 0.693463i | \(-0.756084\pi\) | ||
0.720492 | − | 0.693463i | \(-0.243916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.68926 | 0.102227 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 81.6200 | − | 47.1234i | 0.917079 | − | 0.529476i | 0.0343770 | − | 0.999409i | \(-0.489055\pi\) |
0.882702 | + | 0.469933i | \(0.155722\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 63.9266 | + | 36.9080i | 0.672912 | + | 0.388506i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −154.173 | −1.58941 | −0.794707 | − | 0.606993i | \(-0.792376\pi\) | ||||
−0.794707 | + | 0.606993i | \(0.792376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −165.724 | − | 95.6808i | −1.64083 | − | 0.947335i | −0.980539 | − | 0.196326i | \(-0.937099\pi\) |
−0.660293 | − | 0.751008i | \(-0.729568\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −40.5368 | − | 70.2118i | −0.393561 | − | 0.681668i | 0.599355 | − | 0.800483i | \(-0.295424\pi\) |
−0.992916 | + | 0.118815i | \(0.962090\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −143.879 | + | 83.0684i | −1.34466 | + | 0.776340i | −0.987487 | − | 0.157698i | \(-0.949593\pi\) |
−0.357173 | + | 0.934038i | \(0.616259\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 64.3446 | − | 111.448i | 0.590318 | − | 1.02246i | −0.403872 | − | 0.914816i | \(-0.632336\pi\) |
0.994189 | − | 0.107645i | \(-0.0343309\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 188.138i | − | 1.66494i | −0.554069 | − | 0.832471i | \(-0.686926\pi\) | ||
0.554069 | − | 0.832471i | \(-0.313074\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.40223 | + | 2.42873i | −0.0121933 | + | 0.0211194i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.5000 | − | 30.3109i | −0.144628 | − | 0.250503i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 132.851i | − | 1.06281i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −40.6554 | −0.320121 | −0.160061 | − | 0.987107i | \(-0.551169\pi\) | ||||
−0.160061 | + | 0.987107i | \(0.551169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 83.1384 | − | 48.0000i | 0.634645 | − | 0.366412i | −0.147904 | − | 0.989002i | \(-0.547253\pi\) |
0.782549 | + | 0.622590i | \(0.213919\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 100.830 | + | 58.2145i | 0.735988 | + | 0.424923i | 0.820609 | − | 0.571490i | \(-0.193634\pi\) |
−0.0846205 | + | 0.996413i | \(0.526968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −99.9218 | −0.718862 | −0.359431 | − | 0.933172i | \(-0.617029\pi\) | ||||
−0.359431 | + | 0.933172i | \(0.617029\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −34.0735 | − | 19.6723i | −0.238276 | − | 0.137569i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.6907 | + | 23.7130i | 0.0944186 | + | 0.163538i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 94.0655 | − | 54.3087i | 0.631312 | − | 0.364488i | −0.149948 | − | 0.988694i | \(-0.547911\pi\) |
0.781260 | + | 0.624206i | \(0.214577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 112.017 | − | 194.019i | 0.741834 | − | 1.28489i | −0.209825 | − | 0.977739i | \(-0.567290\pi\) |
0.951659 | − | 0.307155i | \(-0.0993771\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 83.8780i | − | 0.541149i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −52.5576 | + | 91.0325i | −0.334762 | + | 0.579825i | −0.983439 | − | 0.181239i | \(-0.941989\pi\) |
0.648677 | + | 0.761064i | \(0.275323\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.9831 | + | 19.0232i | 0.0673807 | + | 0.116707i | 0.897748 | − | 0.440510i | \(-0.145202\pi\) |
−0.830367 | + | 0.557217i | \(0.811869\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 311.838i | − | 1.86729i | −0.358195 | − | 0.933647i | \(-0.616608\pi\) | ||
0.358195 | − | 0.933647i | \(-0.383392\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −151.000 | −0.893491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 56.0079 | − | 32.3362i | 0.323745 | − | 0.186914i | −0.329316 | − | 0.944220i | \(-0.606818\pi\) |
0.653061 | + | 0.757306i | \(0.273485\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 289.483 | + | 167.133i | 1.61722 | + | 0.933703i | 0.987635 | + | 0.156773i | \(0.0501091\pi\) |
0.629587 | + | 0.776930i | \(0.283224\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −229.590 | −1.26845 | −0.634226 | − | 0.773147i | \(-0.718681\pi\) | ||||
−0.634226 | + | 0.773147i | \(0.718681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −71.9209 | − | 41.5235i | −0.388762 | − | 0.224452i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.3257 | − | 19.6167i | −0.0605652 | − | 0.104902i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −65.4535 | + | 37.7896i | −0.342688 | + | 0.197851i | −0.661460 | − | 0.749980i | \(-0.730063\pi\) |
0.318772 | + | 0.947832i | \(0.396730\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.68926 | + | 8.12204i | −0.0242967 | + | 0.0420831i | −0.877918 | − | 0.478811i | \(-0.841068\pi\) |
0.853621 | + | 0.520894i | \(0.174401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 38.5566i | 0.195719i | 0.995200 | + | 0.0978594i | \(0.0311996\pi\) | ||||
−0.995200 | + | 0.0978594i | \(0.968800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −32.5509 | + | 56.3798i | −0.163572 | + | 0.283315i | −0.936147 | − | 0.351608i | \(-0.885635\pi\) |
0.772575 | + | 0.634923i | \(0.218968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 91.7062 | + | 158.840i | 0.447347 | + | 0.774828i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 192.426i | − | 0.920697i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −176.068 | −0.834444 | −0.417222 | − | 0.908804i | \(-0.636996\pi\) | ||||
−0.417222 | + | 0.908804i | \(0.636996\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 152.023 | − | 87.7702i | 0.707082 | − | 0.408234i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.97454 | + | 5.18146i | 0.0406088 | + | 0.0234455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 146.199 | 0.655602 | 0.327801 | − | 0.944747i | \(-0.393692\pi\) | ||||
0.327801 | + | 0.944747i | \(0.393692\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.3815 | − | 12.3446i | −0.0941918 | − | 0.0543816i | 0.452164 | − | 0.891935i | \(-0.350652\pi\) |
−0.546356 | + | 0.837553i | \(0.683985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −104.919 | − | 181.726i | −0.458164 | − | 0.793563i | 0.540700 | − | 0.841215i | \(-0.318159\pi\) |
−0.998864 | + | 0.0476526i | \(0.984826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 34.6942 | − | 20.0307i | 0.148902 | − | 0.0859687i | −0.423698 | − | 0.905804i | \(-0.639268\pi\) |
0.572600 | + | 0.819835i | \(0.305935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.0508 | + | 48.5855i | −0.119365 | + | 0.206747i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 229.662i | − | 0.960928i | −0.877014 | − | 0.480464i | \(-0.840468\pi\) | ||
0.877014 | − | 0.480464i | \(-0.159532\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −190.711 | + | 330.321i | −0.791332 | + | 1.37063i | 0.133810 | + | 0.991007i | \(0.457279\pi\) |
−0.925142 | + | 0.379621i | \(0.876054\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.0169 | + | 76.2396i | 0.178206 | + | 0.308662i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 72.2636i | 0.287903i | 0.989585 | + | 0.143951i | \(0.0459809\pi\) | ||||
−0.989585 | + | 0.143951i | \(0.954019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.31074 | 0.0288962 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −192.899 | + | 111.370i | −0.750578 | + | 0.433347i | −0.825903 | − | 0.563813i | \(-0.809334\pi\) |
0.0753246 | + | 0.997159i | \(0.476001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 278.882 | + | 161.013i | 1.06039 | + | 0.612215i | 0.925540 | − | 0.378651i | \(-0.123612\pi\) |
0.134848 | + | 0.990866i | \(0.456945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −267.798 | −1.01056 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −266.382 | − | 153.796i | −0.990267 | − | 0.571731i | −0.0849131 | − | 0.996388i | \(-0.527061\pi\) |
−0.905354 | + | 0.424657i | \(0.860395\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −181.055 | − | 313.597i | −0.668101 | − | 1.15718i | −0.978435 | − | 0.206557i | \(-0.933774\pi\) |
0.310334 | − | 0.950628i | \(-0.399559\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −99.1421 | + | 57.2397i | −0.360517 | + | 0.208144i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3446 | + | 24.8456i | −0.0517857 | + | 0.0896954i | −0.890756 | − | 0.454481i | \(-0.849825\pi\) |
0.838971 | + | 0.544177i | \(0.183158\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 89.7693i | 0.319464i | 0.987160 | + | 0.159732i | \(0.0510629\pi\) | ||||
−0.987160 | + | 0.159732i | \(0.948937\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 150.869 | − | 261.313i | 0.533107 | − | 0.923369i | −0.466145 | − | 0.884708i | \(-0.654357\pi\) |
0.999252 | − | 0.0386609i | \(-0.0123092\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −141.517 | − | 245.115i | −0.489678 | − | 0.848147i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 235.855i | − | 0.804966i | −0.915428 | − | 0.402483i | \(-0.868147\pi\) | ||
0.915428 | − | 0.402483i | \(-0.131853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 56.1017 | 0.190175 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.89654 | + | 1.67232i | −0.00968741 | + | 0.00559303i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.7140 | − | 14.2686i | −0.0810296 | − | 0.0467824i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −68.8810 | −0.224368 | −0.112184 | − | 0.993687i | \(-0.535785\pi\) | ||||
−0.112184 | + | 0.993687i | \(0.535785\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 432.931 | + | 249.953i | 1.39206 | + | 0.803707i | 0.993543 | − | 0.113453i | \(-0.0361912\pi\) |
0.398518 | + | 0.917160i | \(0.369525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 144.006 | + | 249.426i | 0.460083 | + | 0.796888i | 0.998965 | − | 0.0454940i | \(-0.0144862\pi\) |
−0.538881 | + | 0.842382i | \(0.681153\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 142.972 | − | 82.5451i | 0.451017 | − | 0.260395i | −0.257243 | − | 0.966347i | \(-0.582814\pi\) |
0.708259 | + | 0.705952i | \(0.249481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.6893 | − | 61.8156i | 0.111879 | − | 0.193779i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 50.6826i | 0.156912i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.1869 | − | 45.3571i | 0.0805751 | − | 0.139560i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 132.655 | + | 229.766i | 0.400772 | + | 0.694157i | 0.993819 | − | 0.111011i | \(-0.0354088\pi\) |
−0.593048 | + | 0.805167i | \(0.702075\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 310.723i | 0.927532i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 220.655 | 0.654764 | 0.327382 | − | 0.944892i | \(-0.393834\pi\) | ||||
0.327382 | + | 0.944892i | \(0.393834\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −189.361 | + | 109.328i | −0.555311 | + | 0.320609i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −162.151 | − | 93.6177i | −0.467293 | − | 0.269792i | 0.247813 | − | 0.968808i | \(-0.420288\pi\) |
−0.715106 | + | 0.699016i | \(0.753622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 318.270 | 0.911948 | 0.455974 | − | 0.889993i | \(-0.349291\pi\) | ||||
0.455974 | + | 0.889993i | \(0.349291\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −146.502 | − | 84.5829i | −0.415019 | − | 0.239611i | 0.277925 | − | 0.960603i | \(-0.410353\pi\) |
−0.692944 | + | 0.720991i | \(0.743687\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 71.2580 | + | 123.422i | 0.200727 | + | 0.347669i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −96.2128 | + | 55.5485i | −0.268002 | + | 0.154731i | −0.627979 | − | 0.778230i | \(-0.716118\pi\) |
0.359977 | + | 0.932961i | \(0.382784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −34.7768 | + | 60.2353i | −0.0963347 | + | 0.166857i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 122.392i | − | 0.335321i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 40.5248 | − | 70.1910i | 0.110422 | − | 0.191256i | −0.805519 | − | 0.592571i | \(-0.798113\pi\) |
0.915940 | + | 0.401314i | \(0.131446\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −219.723 | − | 380.572i | −0.589070 | − | 1.02030i | −0.994355 | − | 0.106109i | \(-0.966161\pi\) |
0.405284 | − | 0.914191i | \(-0.367172\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.6554i | 0.0866190i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −81.3785 | −0.214719 | −0.107360 | − | 0.994220i | \(-0.534240\pi\) | ||||
−0.107360 | + | 0.994220i | \(0.534240\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 399.226 | − | 230.493i | 1.04237 | − | 0.601810i | 0.121864 | − | 0.992547i | \(-0.461113\pi\) |
0.920503 | + | 0.390736i | \(0.127780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −480.866 | − | 277.628i | −1.23616 | − | 0.713697i | −0.267852 | − | 0.963460i | \(-0.586314\pi\) |
−0.968307 | + | 0.249764i | \(0.919647\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.92556 | −0.00492471 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.7702 | + | 15.4558i | 0.0677726 | + | 0.0391285i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 152.064 | + | 263.382i | 0.383033 | + | 0.663432i | 0.991494 | − | 0.130152i | \(-0.0415464\pi\) |
−0.608462 | + | 0.793583i | \(0.708213\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 213.465 | − | 123.244i | 0.532333 | − | 0.307342i | −0.209633 | − | 0.977780i | \(-0.567227\pi\) |
0.741966 | + | 0.670438i | \(0.233894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 50.0169 | − | 86.6319i | 0.124112 | − | 0.214967i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 216.489i | 0.531915i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.30278 | + | 12.6488i | −0.0178552 | + | 0.0309261i | −0.874815 | − | 0.484457i | \(-0.839017\pi\) |
0.856960 | + | 0.515383i | \(0.172350\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 204.757 | + | 354.650i | 0.493390 | + | 0.854577i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 619.804i | 1.47925i | 0.673021 | + | 0.739623i | \(0.264996\pi\) | ||||
−0.673021 | + | 0.739623i | \(0.735004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −307.379 | −0.730115 | −0.365058 | − | 0.930985i | \(-0.618951\pi\) | ||||
−0.365058 | + | 0.930985i | \(0.618951\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.1128 | − | 15.0763i | 0.0614420 | − | 0.0354736i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −452.837 | − | 261.446i | −1.05067 | − | 0.606603i | −0.127831 | − | 0.991796i | \(-0.540801\pi\) |
−0.922836 | + | 0.385193i | \(0.874135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 547.444 | 1.26431 | 0.632153 | − | 0.774844i | \(-0.282171\pi\) | ||||
0.632153 | + | 0.774844i | \(0.282171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.1663 | − | 8.17891i | −0.0324171 | − | 0.0187161i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 258.386 | + | 447.537i | 0.588578 | + | 1.01945i | 0.994419 | + | 0.105503i | \(0.0336452\pi\) |
−0.405841 | + | 0.913944i | \(0.633021\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −474.560 | + | 273.987i | −1.07124 | + | 0.618481i | −0.928520 | − | 0.371282i | \(-0.878918\pi\) |
−0.142721 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −167.638 | + | 290.358i | −0.376716 | + | 0.652490i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 575.681i | 1.28214i | 0.767482 | + | 0.641070i | \(0.221509\pi\) | ||||
−0.767482 | + | 0.641070i | \(0.778491\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 239.062 | − | 414.068i | 0.530071 | − | 0.918110i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −203.412 | − | 352.321i | −0.445104 | − | 0.770942i | 0.552956 | − | 0.833211i | \(-0.313500\pi\) |
−0.998059 | + | 0.0622683i | \(0.980167\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 209.524i | 0.454498i | 0.973837 | + | 0.227249i | \(0.0729731\pi\) | ||||
−0.973837 | + | 0.227249i | \(0.927027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 870.169 | 1.87942 | 0.939708 | − | 0.341978i | \(-0.111097\pi\) | ||||
0.939708 | + | 0.341978i | \(0.111097\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −201.088 | + | 116.098i | −0.430594 | + | 0.248604i | −0.699600 | − | 0.714535i | \(-0.746638\pi\) |
0.269006 | + | 0.963139i | \(0.413305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −396.296 | − | 228.802i | −0.837835 | − | 0.483724i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 256.148 | 0.539260 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 770.453 | + | 444.821i | 1.60846 | + | 0.928645i | 0.989715 | + | 0.143054i | \(0.0456923\pi\) |
0.618746 | + | 0.785591i | \(0.287641\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.5214 | − | 85.7737i | −0.102955 | − | 0.178324i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 474.982 | − | 274.231i | 0.979344 | − | 0.565425i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.7062 | − | 56.6488i | 0.0671585 | − | 0.116322i | −0.830491 | − | 0.557032i | \(-0.811940\pi\) |
0.897649 | + | 0.440710i | \(0.145273\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 82.4878i | 0.168000i | 0.996466 | + | 0.0839998i | \(0.0267695\pi\) | ||||
−0.996466 | + | 0.0839998i | \(0.973230\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.40013 | + | 16.2815i | −0.0190672 | + | 0.0330254i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.3277 | + | 57.7252i | 0.0667889 | + | 0.115682i | 0.897486 | − | 0.441043i | \(-0.145391\pi\) |
−0.830697 | + | 0.556724i | \(0.812058\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 592.885i | 1.17870i | 0.807879 | + | 0.589349i | \(0.200616\pi\) | ||||
−0.807879 | + | 0.589349i | \(0.799384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 680.757 | 1.34803 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −673.701 | + | 388.961i | −1.32358 | + | 0.764168i | −0.984297 | − | 0.176518i | \(-0.943517\pi\) |
−0.339280 | + | 0.940685i | \(0.610183\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 249.774 | + | 144.207i | 0.484998 | + | 0.280014i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 146.247 | 0.282877 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −375.133 | − | 216.583i | −0.720024 | − | 0.415706i | 0.0947375 | − | 0.995502i | \(-0.469799\pi\) |
−0.814762 | + | 0.579796i | \(0.803132\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −138.617 | − | 240.092i | −0.265042 | − | 0.459066i | 0.702533 | − | 0.711651i | \(-0.252052\pi\) |
−0.967575 | + | 0.252585i | \(0.918719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 49.8755 | − | 28.7956i | 0.0946404 | − | 0.0546406i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −264.189 | + | 457.589i | −0.499413 | + | 0.865008i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 218.740i | 0.410393i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 295.511 | − | 511.840i | 0.552356 | − | 0.956709i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −360.379 | − | 624.194i | −0.666134 | − | 1.15378i | −0.978977 | − | 0.203973i | \(-0.934615\pi\) |
0.312842 | − | 0.949805i | \(-0.398719\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 457.804i | 0.840008i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −744.825 | −1.36165 | −0.680827 | − | 0.732444i | \(-0.738379\pi\) | ||||
−0.680827 | + | 0.732444i | \(0.738379\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −138.313 | + | 79.8550i | −0.251022 | + | 0.144927i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −620.101 | − | 358.016i | −1.11329 | − | 0.642757i | −0.173609 | − | 0.984815i | \(-0.555543\pi\) |
−0.939679 | + | 0.342057i | \(0.888876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 209.352 | 0.374511 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 650.256 | + | 375.426i | 1.15498 | + | 0.666831i | 0.950097 | − | 0.311955i | \(-0.100984\pi\) |
0.204888 | + | 0.978786i | \(0.434317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 334.645 | + | 579.623i | 0.592293 | + | 1.02588i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 147.006 | − | 84.8741i | 0.258359 | − | 0.149164i | −0.365227 | − | 0.930919i | \(-0.619009\pi\) |
0.623586 | + | 0.781755i | \(0.285675\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −313.757 | + | 543.443i | −0.549487 | + | 0.951739i | 0.448823 | + | 0.893621i | \(0.351843\pi\) |
−0.998310 | + | 0.0581185i | \(0.981490\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.73173i | 0.0169247i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −82.3160 | + | 142.576i | −0.142662 | + | 0.247098i | −0.928498 | − | 0.371337i | \(-0.878900\pi\) |
0.785836 | + | 0.618435i | \(0.212233\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 349.051 | + | 604.574i | 0.598715 | + | 1.03700i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1040.76i | 1.77301i | 0.462719 | + | 0.886505i | \(0.346874\pi\) | ||||
−0.462719 | + | 0.886505i | \(0.653126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 489.243 | 0.830633 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −543.797 | + | 313.961i | −0.917027 | + | 0.529446i | −0.882685 | − | 0.469964i | \(-0.844267\pi\) |
−0.0343417 | + | 0.999410i | \(0.510933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −228.485 | − | 131.916i | −0.381445 | − | 0.220227i | 0.297002 | − | 0.954877i | \(-0.404013\pi\) |
−0.678447 | + | 0.734650i | \(0.737347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 502.094 | 0.835431 | 0.417715 | − | 0.908578i | \(-0.362831\pi\) | ||||
0.417715 | + | 0.908578i | \(0.362831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 107.829 | + | 62.2552i | 0.178230 | + | 0.102901i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −499.801 | − | 865.680i | −0.823395 | − | 1.42616i | −0.903140 | − | 0.429346i | \(-0.858744\pi\) |
0.0797451 | − | 0.996815i | \(-0.474589\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −57.9436 | + | 33.4537i | −0.0948340 | + | 0.0547524i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −460.085 | + | 796.890i | −0.750546 | + | 1.29998i | 0.197012 | + | 0.980401i | \(0.436876\pi\) |
−0.947558 | + | 0.319583i | \(0.896457\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 520.713i | 0.843943i | 0.906609 | + | 0.421972i | \(0.138662\pi\) | ||||
−0.906609 | + | 0.421972i | \(0.861338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 119.305 | − | 206.643i | 0.192739 | − | 0.333833i | −0.753418 | − | 0.657542i | \(-0.771596\pi\) |
0.946157 | + | 0.323708i | \(0.104930\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 81.9972 | + | 142.023i | 0.131195 | + | 0.227237i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 57.0207i | − | 0.0906529i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 534.034 | 0.846329 | 0.423165 | − | 0.906053i | \(-0.360919\pi\) | ||||
0.423165 | + | 0.906053i | \(0.360919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 125.252 | − | 72.3145i | 0.197248 | − | 0.113881i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −868.646 | − | 501.513i | −1.35514 | − | 0.782392i | −0.366178 | − | 0.930545i | \(-0.619334\pi\) |
−0.988964 | + | 0.148153i | \(0.952667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 744.923 | 1.15851 | 0.579256 | − | 0.815146i | \(-0.303343\pi\) | ||||
0.579256 | + | 0.815146i | \(0.303343\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 772.015 | + | 445.723i | 1.19322 | + | 0.688908i | 0.959036 | − | 0.283284i | \(-0.0914239\pi\) |
0.234187 | + | 0.972192i | \(0.424757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −73.1236 | − | 126.654i | −0.112671 | − | 0.195152i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 70.5924 | − | 40.7565i | 0.108105 | − | 0.0624143i | −0.444973 | − | 0.895544i | \(-0.646787\pi\) |
0.553078 | + | 0.833130i | \(0.313453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −170.757 | + | 295.760i | −0.260698 | + | 0.451542i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 185.430i | 0.281380i | 0.990054 | + | 0.140690i | \(0.0449322\pi\) | ||||
−0.990054 | + | 0.140690i | \(0.955068\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −272.783 | + | 472.475i | −0.412683 | + | 0.714788i | −0.995182 | − | 0.0980435i | \(-0.968742\pi\) |
0.582499 | + | 0.812831i | \(0.302075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.03389 | − | 5.25486i | −0.00454857 | − | 0.00787835i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 74.3917i | 0.110867i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −994.136 | −1.47717 | −0.738585 | − | 0.674160i | \(-0.764506\pi\) | ||||
−0.738585 | + | 0.674160i | \(0.764506\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −181.821 | + | 104.975i | −0.268569 | + | 0.155058i | −0.628237 | − | 0.778022i | \(-0.716223\pi\) |
0.359668 | + | 0.933080i | \(0.382890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 355.619 | + | 205.317i | 0.520672 | + | 0.300610i | 0.737209 | − | 0.675664i | \(-0.236143\pi\) |
−0.216538 | + | 0.976274i | \(0.569476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −414.189 | −0.604655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −276.590 | − | 159.689i | −0.401437 | − | 0.231770i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 662.339 | + | 1147.21i | 0.958523 | + | 1.66021i | 0.726092 | + | 0.687597i | \(0.241335\pi\) |
0.232431 | + | 0.972613i | \(0.425332\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 307.842 | − | 177.733i | 0.442938 | − | 0.255731i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −62.9661 | + | 109.060i | −0.0903387 | + | 0.156471i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 580.339i | 0.827873i | 0.910306 | + | 0.413936i | \(0.135846\pi\) | ||||
−0.910306 | + | 0.413936i | \(0.864154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 242.198 | − | 419.499i | 0.344521 | − | 0.596727i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 163.689 | + | 283.518i | 0.230873 | + | 0.399885i | 0.958065 | − | 0.286550i | \(-0.0925083\pi\) |
−0.727192 | + | 0.686434i | \(0.759175\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.5876i | 0.0260695i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 139.966 | 0.195757 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 339.821 | − | 196.196i | 0.472630 | − | 0.272873i | −0.244710 | − | 0.969596i | \(-0.578693\pi\) |
0.717340 | + | 0.696723i | \(0.245359\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 82.2862 | + | 47.5080i | 0.113498 | + | 0.0655282i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1340.99 | 1.84455 | 0.922274 | − | 0.386537i | \(-0.126329\pi\) | ||||
0.922274 | + | 0.386537i | \(0.126329\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 104.380 | + | 60.2636i | 0.142790 | + | 0.0824400i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −65.2016 | − | 112.933i | −0.0889518 | − | 0.154069i | 0.818117 | − | 0.575052i | \(-0.195018\pi\) |
−0.907068 | + | 0.420983i | \(0.861685\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 701.481 | − | 405.000i | 0.951806 | − | 0.549526i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 101.017 | − | 174.966i | 0.136694 | − | 0.236761i | −0.789549 | − | 0.613687i | \(-0.789686\pi\) |
0.926243 | + | 0.376926i | \(0.123019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 821.453i | 1.10559i | 0.833317 | + | 0.552795i | \(0.186439\pi\) | ||||
−0.833317 | + | 0.552795i | \(0.813561\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −193.200 | + | 334.632i | −0.259329 | + | 0.449171i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −402.068 | − | 696.402i | −0.535377 | − | 0.927299i | −0.999145 | − | 0.0413429i | \(-0.986836\pi\) |
0.463768 | − | 0.885956i | \(-0.346497\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 796.987i | 1.05561i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 518.000 | 0.684280 | 0.342140 | − | 0.939649i | \(-0.388848\pi\) | ||||
0.342140 | + | 0.939649i | \(0.388848\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −583.576 | + | 336.927i | −0.766854 | + | 0.442743i | −0.831751 | − | 0.555149i | \(-0.812661\pi\) |
0.0648975 | + | 0.997892i | \(0.479328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 57.9436 | + | 33.4537i | 0.0755457 | + | 0.0436164i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −653.023 | −0.849185 | −0.424592 | − | 0.905385i | \(-0.639583\pi\) | ||||
−0.424592 | + | 0.905385i | \(0.639583\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 399.499 | + | 230.651i | 0.516816 | + | 0.298384i | 0.735631 | − | 0.677383i | \(-0.236886\pi\) |
−0.218815 | + | 0.975766i | \(0.570219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −145.532 | − | 252.069i | −0.187783 | − | 0.325250i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −926.479 | + | 534.903i | −1.18932 | + | 0.686653i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 185.757 | − | 321.741i | 0.237845 | − | 0.411960i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 373.941i | − | 0.476358i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 396.563 | − | 686.867i | 0.503892 | − | 0.872767i | −0.496098 | − | 0.868267i | \(-0.665234\pi\) |
0.999990 | − | 0.00450000i | \(-0.00143240\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.0169 | − | 29.4742i | −0.0214589 | − | 0.0371680i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 435.599i | 0.546548i | 0.961936 | + | 0.273274i | \(0.0881066\pi\) | ||||
−0.961936 | + | 0.273274i | \(0.911893\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.5198 | −0.0482100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −276.309 | + | 159.527i | −0.344096 | + | 0.198664i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −499.721 | − | 288.514i | −0.617702 | − | 0.356631i | 0.158272 | − | 0.987396i | \(-0.449408\pi\) |
−0.775974 | + | 0.630765i | \(0.782741\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.5274 | −0.0475060 | −0.0237530 | − | 0.999718i | \(-0.507562\pi\) | ||||
−0.0237530 | + | 0.999718i | \(0.507562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −67.6739 | − | 39.0715i | −0.0830354 | − | 0.0479405i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 511.945 | + | 886.715i | 0.626616 | + | 1.08533i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 394.707 | − | 227.884i | 0.480764 | − | 0.277569i | −0.239971 | − | 0.970780i | \(-0.577138\pi\) |
0.720735 | + | 0.693211i | \(0.243805\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 199.791 | − | 346.048i | 0.242759 | − | 0.420472i | −0.718740 | − | 0.695279i | \(-0.755281\pi\) |
0.961499 | + | 0.274808i | \(0.0886141\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1182.94i | − | 1.43040i | −0.698922 | − | 0.715198i | \(-0.746336\pi\) | ||
0.698922 | − | 0.715198i | \(-0.253664\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −81.7807 | + | 141.648i | −0.0986498 | + | 0.170866i | −0.911126 | − | 0.412128i | \(-0.864786\pi\) |
0.812476 | + | 0.582994i | \(0.198119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 554.672 | + | 960.721i | 0.664278 | + | 1.15056i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 980.535i | − | 1.16869i | −0.811504 | − | 0.584347i | \(-0.801351\pi\) | ||
0.811504 | − | 0.584347i | \(-0.198649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 781.757 | 0.929557 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 465.206 | − | 268.587i | 0.550539 | − | 0.317854i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.9378 | + | 9.20172i | 0.0187284 | + | 0.0108128i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −184.455 | −0.216243 | −0.108121 | − | 0.994138i | \(-0.534483\pi\) | ||||
−0.108121 | + | 0.994138i | \(0.534483\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −992.826 | − | 573.208i | −1.15849 | − | 0.668854i | −0.207548 | − | 0.978225i | \(-0.566548\pi\) |
−0.950942 | + | 0.309371i | \(0.899882\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −445.537 | − | 771.693i | −0.518670 | − | 0.898362i | −0.999765 | − | 0.0216937i | \(-0.993094\pi\) |
0.481095 | − | 0.876668i | \(-0.340239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1239.05 | + | 715.366i | −1.43575 | + | 0.828929i | −0.997550 | − | 0.0699503i | \(-0.977716\pi\) |
−0.438197 | + | 0.898879i | \(0.644383\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −115.034 | + | 199.245i | −0.132987 | + | 0.230341i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 80.5809i | − | 0.0927283i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −185.286 | + | 320.925i | −0.212728 | + | 0.368455i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −707.429 | − | 1225.30i | −0.806647 | − | 1.39715i | −0.915174 | − | 0.403060i | \(-0.867947\pi\) |
0.108527 | − | 0.994094i | \(-0.465387\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 407.260i | − | 0.462270i | −0.972922 | − | 0.231135i | \(-0.925756\pi\) | ||
0.972922 | − | 0.231135i | \(-0.0742439\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −386.723 | −0.437965 | −0.218983 | − | 0.975729i | \(-0.570274\pi\) | ||||
−0.218983 | + | 0.975729i | \(0.570274\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 999.171 | − | 576.872i | 1.12646 | − | 0.650363i | 0.183419 | − | 0.983035i | \(-0.441283\pi\) |
0.943043 | + | 0.332672i | \(0.107950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −283.389 | − | 163.615i | −0.317345 | − | 0.183219i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1189.13 | −1.32864 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 157.166 | + | 90.7401i | 0.174824 | + | 0.100934i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −91.9359 | − | 159.238i | −0.102038 | − | 0.176734i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 707.328 | − | 408.376i | 0.781578 | − | 0.451244i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 284.085 | − | 492.049i | 0.313214 | − | 0.542502i | −0.665843 | − | 0.746092i | \(-0.731928\pi\) |
0.979056 | + | 0.203590i | \(0.0652611\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 78.5035i | − | 0.0861729i | −0.999071 | − | 0.0430864i | \(-0.986281\pi\) | ||
0.999071 | − | 0.0430864i | \(-0.0137191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 533.766 | − | 924.509i | 0.584628 | − | 1.01261i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −271.463 | − | 470.188i | −0.295390 | − | 0.511630i | 0.679686 | − | 0.733504i | \(-0.262116\pi\) |
−0.975076 | + | 0.221873i | \(0.928783\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 169.966i | 0.184145i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −288.181 | −0.311547 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 158.773 | − | 91.6676i | 0.170907 | − | 0.0986734i | −0.412106 | − | 0.911136i | \(-0.635207\pi\) |
0.583014 | + | 0.812462i | \(0.301873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 69.7851 | + | 40.2905i | 0.0746365 | + | 0.0430914i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −532.184 | −0.567966 | −0.283983 | − | 0.958829i | \(-0.591656\pi\) | ||||
−0.283983 | + | 0.958829i | \(0.591656\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1442.91 | − | 833.063i | −1.53338 | − | 0.885295i | −0.999203 | − | 0.0399209i | \(-0.987289\pi\) |
−0.534174 | − | 0.845375i | \(-0.679377\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.3223 | − | 35.1993i | −0.0215507 | − | 0.0373269i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −466.690 | + | 269.444i | −0.492809 | + | 0.284523i | −0.725739 | − | 0.687970i | \(-0.758502\pi\) |
0.232930 | + | 0.972493i | \(0.425169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72.9831 | − | 126.410i | 0.0769052 | − | 0.133204i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1047.62i | − | 1.09928i | −0.835400 | − | 0.549642i | \(-0.814764\pi\) | ||
0.835400 | − | 0.549642i | \(-0.185236\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 134.434 | − | 232.847i | 0.140769 | − | 0.243819i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 202.534 | + | 350.799i | 0.210753 | + | 0.365035i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 33.3635i | − | 0.0345736i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 347.209 | 0.359058 | 0.179529 | − | 0.983753i | \(-0.442543\pi\) | ||||
0.179529 | + | 0.983753i | \(0.442543\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −388.746 | + | 224.443i | −0.400356 | + | 0.231146i | −0.686638 | − | 0.727000i | \(-0.740914\pi\) |
0.286281 | + | 0.958146i | \(0.407581\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 818.821 | + | 472.747i | 0.838098 | + | 0.483876i | 0.856617 | − | 0.515953i | \(-0.172562\pi\) |
−0.0185194 | + | 0.999829i | \(0.505895\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 874.008 | 0.892756 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 934.658 | + | 539.625i | 0.950822 | + | 0.548958i | 0.893336 | − | 0.449389i | \(-0.148358\pi\) |
0.0574860 | + | 0.998346i | \(0.481692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −68.5814 | − | 118.786i | −0.0696258 | − | 0.120595i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.6886 | + | 19.4501i | −0.0340633 | + | 0.0196664i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 393.429 | − | 681.440i | 0.397002 | − | 0.687628i | −0.596352 | − | 0.802723i | \(-0.703384\pi\) |
0.993355 | + | 0.115095i | \(0.0367171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 231.595i | − | 0.232759i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −937.999 | + | 1624.66i | −0.940822 | + | 1.62955i | −0.176913 | + | 0.984227i | \(0.556611\pi\) |
−0.763909 | + | 0.645324i | \(0.776722\pi\) | |||||||
\(998\) | 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 | 1764.3.bk.g.557.4 | 16 | ||
3.2 | odd | 2 | inner | 1764.3.bk.g.557.5 | 16 | ||
7.2 | even | 3 | inner | 1764.3.bk.g.1745.5 | 16 | ||
7.3 | odd | 6 | 1764.3.c.h.197.5 | yes | 8 | ||
7.4 | even | 3 | 1764.3.c.h.197.3 | ✓ | 8 | ||
7.5 | odd | 6 | inner | 1764.3.bk.g.1745.3 | 16 | ||
7.6 | odd | 2 | inner | 1764.3.bk.g.557.6 | 16 | ||
21.2 | odd | 6 | inner | 1764.3.bk.g.1745.4 | 16 | ||
21.5 | even | 6 | inner | 1764.3.bk.g.1745.6 | 16 | ||
21.11 | odd | 6 | 1764.3.c.h.197.6 | yes | 8 | ||
21.17 | even | 6 | 1764.3.c.h.197.4 | yes | 8 | ||
21.20 | even | 2 | inner | 1764.3.bk.g.557.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.3.c.h.197.3 | ✓ | 8 | 7.4 | even | 3 | ||
1764.3.c.h.197.4 | yes | 8 | 21.17 | even | 6 | ||
1764.3.c.h.197.5 | yes | 8 | 7.3 | odd | 6 | ||
1764.3.c.h.197.6 | yes | 8 | 21.11 | odd | 6 | ||
1764.3.bk.g.557.3 | 16 | 21.20 | even | 2 | inner | ||
1764.3.bk.g.557.4 | 16 | 1.1 | even | 1 | trivial | ||
1764.3.bk.g.557.5 | 16 | 3.2 | odd | 2 | inner | ||
1764.3.bk.g.557.6 | 16 | 7.6 | odd | 2 | inner | ||
1764.3.bk.g.1745.3 | 16 | 7.5 | odd | 6 | inner | ||
1764.3.bk.g.1745.4 | 16 | 21.2 | odd | 6 | inner | ||
1764.3.bk.g.1745.5 | 16 | 7.2 | even | 3 | inner | ||
1764.3.bk.g.1745.6 | 16 | 21.5 | even | 6 | inner |