Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(325,1764)]
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, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.325");
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.z (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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.4 | ||
Root | \(-1.60021 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.325 |
Dual form | 1764.3.z.l.901.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | 5.04718 | − | 2.91399i | 1.00944 | − | 0.582798i | 0.0984097 | − | 0.995146i | \(-0.468624\pi\) |
0.911027 | + | 0.412348i | \(0.135291\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.43068 | + | 5.94212i | −0.311880 | + | 0.540193i | −0.978769 | − | 0.204964i | \(-0.934292\pi\) |
0.666889 | + | 0.745157i | \(0.267626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.62063i | 0.278510i | 0.990257 | + | 0.139255i | \(0.0444708\pi\) | ||||
−0.990257 | + | 0.139255i | \(0.955529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.41362 | − | 4.85761i | −0.494919 | − | 0.285742i | 0.231694 | − | 0.972789i | \(-0.425573\pi\) |
−0.726613 | + | 0.687047i | \(0.758907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.2322 | + | 15.1451i | −1.38064 | + | 0.797113i | −0.992235 | − | 0.124376i | \(-0.960307\pi\) |
−0.388405 | + | 0.921489i | \(0.626974\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.07789 | − | 15.7234i | −0.394691 | − | 0.683625i | 0.598371 | − | 0.801219i | \(-0.295815\pi\) |
−0.993062 | + | 0.117595i | \(0.962482\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.48269 | − | 7.76425i | 0.179308 | − | 0.310570i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.4570 | 1.39507 | 0.697534 | − | 0.716552i | \(-0.254281\pi\) | ||||
0.697534 | + | 0.716552i | \(0.254281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −47.8153 | − | 27.6062i | −1.54243 | − | 0.890522i | −0.998685 | − | 0.0512709i | \(-0.983673\pi\) |
−0.543744 | − | 0.839251i | \(-0.682994\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.4873 | − | 47.6093i | −0.742899 | − | 1.28674i | −0.951170 | − | 0.308668i | \(-0.900117\pi\) |
0.208271 | − | 0.978071i | \(-0.433216\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 56.3322i | − | 1.37396i | −0.726678 | − | 0.686978i | \(-0.758937\pi\) | ||
0.726678 | − | 0.686978i | \(-0.241063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −66.0512 | −1.53608 | −0.768038 | − | 0.640405i | \(-0.778767\pi\) | ||||
−0.768038 | + | 0.640405i | \(0.778767\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 42.8003 | − | 24.7108i | 0.910645 | − | 0.525761i | 0.0300061 | − | 0.999550i | \(-0.490447\pi\) |
0.880639 | + | 0.473789i | \(0.157114\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −40.5081 | + | 70.1621i | −0.764303 | + | 1.32381i | 0.176311 | + | 0.984335i | \(0.443584\pi\) |
−0.940614 | + | 0.339478i | \(0.889750\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 39.9879i | 0.727054i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −30.1302 | − | 17.3957i | −0.510682 | − | 0.294842i | 0.222432 | − | 0.974948i | \(-0.428600\pi\) |
−0.733114 | + | 0.680106i | \(0.761934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0331519 | − | 0.0191403i | 0.000543474 | − | 0.000313775i | −0.499728 | − | 0.866182i | \(-0.666567\pi\) |
0.500272 | + | 0.865868i | \(0.333233\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.5505 | + | 18.2740i | 0.162315 | + | 0.281138i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 32.0449 | − | 55.5034i | 0.478282 | − | 0.828409i | −0.521408 | − | 0.853308i | \(-0.674593\pi\) |
0.999690 | + | 0.0248985i | \(0.00792626\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −50.2730 | −0.708070 | −0.354035 | − | 0.935232i | \(-0.615191\pi\) | ||||
−0.354035 | + | 0.935232i | \(0.615191\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 18.4865 | + | 10.6732i | 0.253240 | + | 0.146208i | 0.621247 | − | 0.783615i | \(-0.286626\pi\) |
−0.368007 | + | 0.929823i | \(0.619960\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.7522 | + | 41.1400i | 0.300660 | + | 0.520759i | 0.976286 | − | 0.216486i | \(-0.0694596\pi\) |
−0.675625 | + | 0.737245i | \(0.736126\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 33.6039i | − | 0.404866i | −0.979296 | − | 0.202433i | \(-0.935115\pi\) | ||
0.979296 | − | 0.202433i | \(-0.0648849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −56.6201 | −0.666119 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 135.180 | − | 78.0459i | 1.51887 | − | 0.876920i | 0.519118 | − | 0.854703i | \(-0.326261\pi\) |
0.999753 | − | 0.0222177i | \(-0.00707269\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −88.2656 | + | 152.881i | −0.929112 | + | 1.60927i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 43.7452i | 0.450981i | 0.974245 | + | 0.225491i | \(0.0723985\pi\) | ||||
−0.974245 | + | 0.225491i | \(0.927601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −147.005 | − | 84.8732i | −1.45549 | − | 0.840329i | −0.456708 | − | 0.889617i | \(-0.650972\pi\) |
−0.998785 | + | 0.0492878i | \(0.984305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 51.7204 | − | 29.8608i | 0.502140 | − | 0.289911i | −0.227457 | − | 0.973788i | \(-0.573041\pi\) |
0.729597 | + | 0.683877i | \(0.239708\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −28.8839 | − | 50.0284i | −0.269943 | − | 0.467555i | 0.698904 | − | 0.715216i | \(-0.253671\pi\) |
−0.968847 | + | 0.247661i | \(0.920338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −89.9228 | + | 155.751i | −0.824980 | + | 1.42891i | 0.0769549 | + | 0.997035i | \(0.475480\pi\) |
−0.901935 | + | 0.431872i | \(0.857853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −96.6900 | −0.855664 | −0.427832 | − | 0.903858i | \(-0.640722\pi\) | ||||
−0.427832 | + | 0.903858i | \(0.640722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −91.6355 | − | 52.9058i | −0.796831 | − | 0.460050i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 36.9608 | + | 64.0180i | 0.305461 | + | 0.529074i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 93.4495i | 0.747596i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −136.454 | −1.07444 | −0.537221 | − | 0.843441i | \(-0.680526\pi\) | ||||
−0.537221 | + | 0.843441i | \(0.680526\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.9812 | + | 13.2682i | −0.175429 | + | 0.101284i | −0.585143 | − | 0.810930i | \(-0.698962\pi\) |
0.409714 | + | 0.912214i | \(0.365628\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 105.433 | − | 182.615i | 0.769583 | − | 1.33296i | −0.168206 | − | 0.985752i | \(-0.553797\pi\) |
0.937789 | − | 0.347206i | \(-0.112869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 83.7490i | − | 0.602511i | −0.953543 | − | 0.301256i | \(-0.902594\pi\) | ||
0.953543 | − | 0.301256i | \(-0.0974057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.5142 | − | 12.4212i | −0.150449 | − | 0.0868619i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 204.194 | − | 117.891i | 1.40823 | − | 0.813043i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.99740 | + | 6.92371i | 0.0268282 | + | 0.0464678i | 0.879128 | − | 0.476586i | \(-0.158126\pi\) |
−0.852300 | + | 0.523054i | \(0.824793\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −30.4415 | + | 52.7263i | −0.201600 | + | 0.349181i | −0.949044 | − | 0.315144i | \(-0.897947\pi\) |
0.747444 | + | 0.664324i | \(0.231281\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −321.777 | −2.07598 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25.2670 | + | 14.5879i | 0.160936 | + | 0.0929166i | 0.578305 | − | 0.815821i | \(-0.303714\pi\) |
−0.417369 | + | 0.908737i | \(0.637048\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31.2278 | + | 54.0881i | 0.191582 | + | 0.331829i | 0.945775 | − | 0.324824i | \(-0.105305\pi\) |
−0.754193 | + | 0.656653i | \(0.771972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 141.404i | 0.846730i | 0.905959 | + | 0.423365i | \(0.139151\pi\) | ||||
−0.905959 | + | 0.423365i | \(0.860849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 155.891 | 0.922432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 211.178 | − | 121.924i | 1.22068 | − | 0.704763i | 0.255621 | − | 0.966777i | \(-0.417720\pi\) |
0.965064 | + | 0.262015i | \(0.0843868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −143.321 | + | 248.239i | −0.800676 | + | 1.38681i | 0.118496 | + | 0.992954i | \(0.462193\pi\) |
−0.919172 | + | 0.393856i | \(0.871141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 214.838i | − | 1.18695i | −0.804852 | − | 0.593475i | \(-0.797755\pi\) | ||
0.804852 | − | 0.593475i | \(-0.202245\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −277.466 | − | 160.195i | −1.49982 | − | 0.865921i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 57.7290 | − | 33.3298i | 0.308711 | − | 0.178234i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.6624 | − | 39.2525i | −0.118652 | − | 0.205511i | 0.800582 | − | 0.599223i | \(-0.204524\pi\) |
−0.919234 | + | 0.393713i | \(0.871190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −157.015 | + | 271.958i | −0.813551 | + | 1.40911i | 0.0968130 | + | 0.995303i | \(0.469135\pi\) |
−0.910364 | + | 0.413809i | \(0.864198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −259.231 | −1.31590 | −0.657948 | − | 0.753063i | \(-0.728575\pi\) | ||||
−0.657948 | + | 0.753063i | \(0.728575\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −63.6749 | − | 36.7627i | −0.319975 | − | 0.184737i | 0.331407 | − | 0.943488i | \(-0.392477\pi\) |
−0.651381 | + | 0.758751i | \(0.725810\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −164.151 | − | 284.319i | −0.800739 | − | 1.38692i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 207.833i | − | 0.994415i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 263.537 | 1.24899 | 0.624496 | − | 0.781028i | \(-0.285304\pi\) | ||||
0.624496 | + | 0.781028i | \(0.285304\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −333.372 | + | 192.473i | −1.55057 | + | 0.895222i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.5876 | − | 30.4626i | 0.0795819 | − | 0.137840i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 191.042i | − | 0.856689i | −0.903616 | − | 0.428344i | \(-0.859097\pi\) | ||
0.903616 | − | 0.428344i | \(-0.140903\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −373.608 | − | 215.702i | −1.64585 | − | 0.950231i | −0.978697 | − | 0.205308i | \(-0.934180\pi\) |
−0.667151 | − | 0.744923i | \(-0.732486\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.1973 | − | 17.4344i | 0.131866 | − | 0.0761329i | −0.432616 | − | 0.901578i | \(-0.642409\pi\) |
0.564482 | + | 0.825445i | \(0.309076\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −175.386 | − | 303.777i | −0.752728 | − | 1.30376i | −0.946496 | − | 0.322715i | \(-0.895404\pi\) |
0.193768 | − | 0.981047i | \(-0.437929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 144.014 | − | 249.439i | 0.612825 | − | 1.06144i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −167.400 | −0.700419 | −0.350209 | − | 0.936671i | \(-0.613890\pi\) | ||||
−0.350209 | + | 0.936671i | \(0.613890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −71.0711 | − | 41.0329i | −0.294901 | − | 0.170261i | 0.345249 | − | 0.938511i | \(-0.387794\pi\) |
−0.640150 | + | 0.768250i | \(0.721128\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −54.8350 | − | 94.9770i | −0.222004 | − | 0.384522i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 232.918i | 0.927959i | 0.885846 | + | 0.463979i | \(0.153579\pi\) | ||||
−0.885846 | + | 0.463979i | \(0.846421\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 124.574 | 0.492385 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 32.3538 | − | 18.6795i | 0.125890 | − | 0.0726827i | −0.435732 | − | 0.900076i | \(-0.643511\pi\) |
0.561623 | + | 0.827394i | \(0.310177\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.68631 | − | 2.92077i | 0.00641181 | − | 0.0111056i | −0.862802 | − | 0.505543i | \(-0.831292\pi\) |
0.869214 | + | 0.494437i | \(0.164626\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 472.161i | 1.78174i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 75.5768 | + | 43.6343i | 0.280955 | + | 0.162209i | 0.633856 | − | 0.773451i | \(-0.281471\pi\) |
−0.352901 | + | 0.935661i | \(0.614805\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −79.6808 | + | 46.0037i | −0.294025 | + | 0.169756i | −0.639756 | − | 0.768578i | \(-0.720964\pi\) |
0.345731 | + | 0.938334i | \(0.387631\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.7574 | + | 53.2734i | 0.111845 | + | 0.193721i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −76.2406 | + | 132.053i | −0.275237 | + | 0.476724i | −0.970195 | − | 0.242326i | \(-0.922090\pi\) |
0.694958 | + | 0.719050i | \(0.255423\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 219.880 | 0.782491 | 0.391245 | − | 0.920286i | \(-0.372044\pi\) | ||||
0.391245 | + | 0.920286i | \(0.372044\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −335.489 | − | 193.695i | −1.18547 | − | 0.684433i | −0.228199 | − | 0.973615i | \(-0.573284\pi\) |
−0.957274 | + | 0.289181i | \(0.906617\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −97.3073 | − | 168.541i | −0.336704 | − | 0.583188i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.8794i | 0.0507828i | 0.999678 | + | 0.0253914i | \(0.00808320\pi\) | ||||
−0.999678 | + | 0.0253914i | \(0.991917\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −202.764 | −0.687335 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56.9285 | − | 32.8677i | 0.190396 | − | 0.109925i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.111549 | − | 0.193209i | 0.000365735 | − | 0.000633471i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 453.211i | − | 1.47626i | −0.674660 | − | 0.738128i | \(-0.735710\pi\) | ||
0.674660 | − | 0.738128i | \(-0.264290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 376.934 | + | 217.623i | 1.21201 | + | 0.699752i | 0.963196 | − | 0.268801i | \(-0.0866273\pi\) |
0.248810 | + | 0.968552i | \(0.419961\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 47.5799 | − | 27.4703i | 0.152012 | − | 0.0877644i | −0.422064 | − | 0.906566i | \(-0.638694\pi\) |
0.574077 | + | 0.818801i | \(0.305361\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 216.846 | + | 375.587i | 0.684055 | + | 1.18482i | 0.973733 | + | 0.227694i | \(0.0731186\pi\) |
−0.289677 | + | 0.957124i | \(0.593548\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −138.795 | + | 240.400i | −0.435095 | + | 0.753606i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 294.277 | 0.911073 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.1115 | + | 16.2302i | 0.0864968 | + | 0.0499390i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 288.274 | + | 499.305i | 0.870919 | + | 1.50848i | 0.861048 | + | 0.508524i | \(0.169809\pi\) |
0.00987084 | + | 0.999951i | \(0.496858\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 373.514i | − | 1.11497i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −301.108 | −0.893495 | −0.446747 | − | 0.894660i | \(-0.647418\pi\) | ||||
−0.446747 | + | 0.894660i | \(0.647418\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 328.078 | − | 189.416i | 0.962107 | − | 0.555473i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −126.056 | + | 218.335i | −0.363273 | + | 0.629208i | −0.988497 | − | 0.151237i | \(-0.951674\pi\) |
0.625224 | + | 0.780445i | \(0.285008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 406.452i | 1.16462i | 0.812967 | + | 0.582309i | \(0.197851\pi\) | ||||
−0.812967 | + | 0.582309i | \(0.802149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −116.419 | − | 67.2146i | −0.329799 | − | 0.190410i | 0.325953 | − | 0.945386i | \(-0.394315\pi\) |
−0.655752 | + | 0.754976i | \(0.727648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −253.737 | + | 146.495i | −0.714752 | + | 0.412662i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −58.3380 | − | 101.044i | −0.162501 | − | 0.281461i | 0.773264 | − | 0.634084i | \(-0.218623\pi\) |
−0.935765 | + | 0.352624i | \(0.885290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 278.251 | − | 481.944i | 0.770777 | − | 1.33503i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 124.406 | 0.340839 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 362.993 | + | 209.574i | 0.989081 | + | 0.571046i | 0.905000 | − | 0.425413i | \(-0.139871\pi\) |
0.0840817 | + | 0.996459i | \(0.473204\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 63.4962 | + | 109.979i | 0.170231 | + | 0.294849i | 0.938501 | − | 0.345278i | \(-0.112215\pi\) |
−0.768270 | + | 0.640127i | \(0.778882\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 146.480i | 0.388541i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −366.675 | −0.967479 | −0.483740 | − | 0.875212i | \(-0.660722\pi\) | ||||
−0.483740 | + | 0.875212i | \(0.660722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 223.750 | − | 129.182i | 0.584203 | − | 0.337290i | −0.178599 | − | 0.983922i | \(-0.557157\pi\) |
0.762802 | + | 0.646632i | \(0.223823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 271.198 | − | 469.728i | 0.697166 | − | 1.20753i | −0.272279 | − | 0.962218i | \(-0.587777\pi\) |
0.969445 | − | 0.245309i | \(-0.0788893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 176.387i | 0.451118i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 239.763 | + | 138.427i | 0.606995 | + | 0.350449i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −350.536 | + | 202.382i | −0.882962 | + | 0.509778i | −0.871634 | − | 0.490158i | \(-0.836939\pi\) |
−0.0113280 | + | 0.999936i | \(0.503606\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −236.718 | − | 410.008i | −0.590319 | − | 1.02246i | −0.994189 | − | 0.107646i | \(-0.965669\pi\) |
0.403870 | − | 0.914816i | \(-0.367665\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 99.9518 | − | 173.122i | 0.248019 | − | 0.429582i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 377.201 | 0.926783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 349.578 | + | 201.829i | 0.854714 | + | 0.493469i | 0.862239 | − | 0.506502i | \(-0.169062\pi\) |
−0.00752476 | + | 0.999972i | \(0.502395\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −97.9215 | − | 169.605i | −0.235955 | − | 0.408687i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 454.684i | − | 1.08517i | −0.840003 | − | 0.542583i | \(-0.817447\pi\) | ||
0.840003 | − | 0.542583i | \(-0.182553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −180.928 | −0.429758 | −0.214879 | − | 0.976641i | \(-0.568936\pi\) | ||||
−0.214879 | + | 0.976641i | \(0.568936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −75.4313 | + | 43.5503i | −0.177485 | + | 0.102471i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −403.946 | + | 699.655i | −0.937229 | + | 1.62333i | −0.166619 | + | 0.986021i | \(0.553285\pi\) |
−0.770610 | + | 0.637307i | \(0.780048\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 166.000i | 0.383372i | 0.981456 | + | 0.191686i | \(0.0613955\pi\) | ||||
−0.981456 | + | 0.191686i | \(0.938604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 476.265 | + | 274.972i | 1.08985 | + | 0.629226i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.3654 | + | 14.6447i | −0.0577800 | + | 0.0333593i | −0.528612 | − | 0.848864i | \(-0.677287\pi\) |
0.470832 | + | 0.882223i | \(0.343954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 411.376 | + | 712.524i | 0.928613 | + | 1.60841i | 0.785645 | + | 0.618678i | \(0.212331\pi\) |
0.142969 | + | 0.989727i | \(0.454335\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 454.850 | − | 787.824i | 1.02214 | − | 1.77039i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 428.131 | 0.953522 | 0.476761 | − | 0.879033i | \(-0.341811\pi\) | ||||
0.476761 | + | 0.879033i | \(0.341811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 334.733 | + | 193.258i | 0.742201 | + | 0.428510i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 93.6555 | + | 162.216i | 0.204935 | + | 0.354959i | 0.950112 | − | 0.311908i | \(-0.100968\pi\) |
−0.745177 | + | 0.666867i | \(0.767635\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 182.821i | 0.396576i | 0.980144 | + | 0.198288i | \(0.0635381\pi\) | ||||
−0.980144 | + | 0.198288i | \(0.936462\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 232.389 | 0.501920 | 0.250960 | − | 0.967997i | \(-0.419254\pi\) | ||||
0.250960 | + | 0.967997i | \(0.419254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −388.782 | + | 224.463i | −0.832509 | + | 0.480650i | −0.854711 | − | 0.519104i | \(-0.826266\pi\) |
0.0222017 | + | 0.999754i | \(0.492932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 226.601 | − | 392.484i | 0.479072 | − | 0.829777i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 271.564i | 0.571713i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 547.020 | + | 315.822i | 1.14200 | + | 0.659336i | 0.946926 | − | 0.321452i | \(-0.104171\pi\) |
0.195078 | + | 0.980788i | \(0.437504\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 172.376 | − | 99.5213i | 0.358370 | − | 0.206905i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 127.473 | + | 220.790i | 0.262831 | + | 0.455237i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −350.767 | + | 607.547i | −0.720262 | + | 1.24753i | 0.240633 | + | 0.970616i | \(0.422645\pi\) |
−0.960895 | + | 0.276914i | \(0.910688\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 414.789 | 0.844785 | 0.422392 | − | 0.906413i | \(-0.361190\pi\) | ||||
0.422392 | + | 0.906413i | \(0.361190\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −340.390 | − | 196.524i | −0.690446 | − | 0.398629i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 306.170 | + | 530.302i | 0.613567 | + | 1.06273i | 0.990634 | + | 0.136543i | \(0.0435992\pi\) |
−0.377067 | + | 0.926186i | \(0.623067\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 467.449i | − | 0.929323i | −0.885488 | − | 0.464661i | \(-0.846176\pi\) | ||
0.885488 | − | 0.464661i | \(-0.153824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −989.279 | −1.95897 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 54.1843 | − | 31.2833i | 0.106452 | − | 0.0614603i | −0.445829 | − | 0.895118i | \(-0.647091\pi\) |
0.552281 | + | 0.833658i | \(0.313758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 174.028 | − | 301.426i | 0.337919 | − | 0.585293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 339.099i | 0.655898i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 617.108 | + | 356.288i | 1.18447 | + | 0.683853i | 0.957044 | − | 0.289942i | \(-0.0936362\pi\) |
0.227425 | + | 0.973796i | \(0.426969\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 242.586 | − | 140.057i | 0.463835 | − | 0.267795i | −0.249821 | − | 0.968292i | \(-0.580372\pi\) |
0.713655 | + | 0.700497i | \(0.247038\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 268.200 | + | 464.536i | 0.508918 | + | 0.881472i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 99.6838 | − | 172.657i | 0.188438 | − | 0.326385i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 203.958 | 0.382660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −291.564 | − | 168.335i | −0.544980 | − | 0.314645i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −316.501 | − | 548.196i | −0.585030 | − | 1.01330i | −0.994872 | − | 0.101145i | \(-0.967749\pi\) |
0.409842 | − | 0.912157i | \(-0.365584\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1048.14i | 1.92319i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1047.16 | 1.91438 | 0.957189 | − | 0.289465i | \(-0.0934773\pi\) | ||||
0.957189 | + | 0.289465i | \(0.0934773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1061.27 | + | 612.727i | −1.92609 | + | 1.11203i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 340.866 | − | 590.397i | 0.611967 | − | 1.05996i | −0.378941 | − | 0.925421i | \(-0.623712\pi\) |
0.990908 | − | 0.134538i | \(-0.0429550\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 239.147i | − | 0.427812i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −174.581 | − | 100.794i | −0.310090 | − | 0.179031i | 0.336877 | − | 0.941549i | \(-0.390629\pi\) |
−0.646967 | + | 0.762518i | \(0.723963\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −488.012 | + | 281.754i | −0.863738 | + | 0.498679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −342.400 | − | 593.054i | −0.601758 | − | 1.04227i | −0.992555 | − | 0.121798i | \(-0.961134\pi\) |
0.390797 | − | 0.920477i | \(-0.372199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5301 | − | 21.7028i | 0.0219442 | − | 0.0380084i | −0.854845 | − | 0.518884i | \(-0.826348\pi\) |
0.876789 | + | 0.480875i | \(0.159681\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −162.773 | −0.283084 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 883.312 | + | 509.981i | 1.53087 | + | 0.883849i | 0.999322 | + | 0.0368210i | \(0.0117231\pi\) |
0.531549 | + | 0.847028i | \(0.321610\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −277.941 | − | 481.408i | −0.476743 | − | 0.825742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 581.810i | − | 0.991158i | −0.868563 | − | 0.495579i | \(-0.834956\pi\) | ||
0.868563 | − | 0.495579i | \(-0.165044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1672.40 | 2.83939 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −124.589 | + | 71.9314i | −0.210099 | + | 0.121301i | −0.601358 | − | 0.798980i | \(-0.705373\pi\) |
0.391258 | + | 0.920281i | \(0.372040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 355.368 | − | 615.515i | 0.593269 | − | 1.02757i | −0.400520 | − | 0.916288i | \(-0.631171\pi\) |
0.993789 | − | 0.111283i | \(-0.0354961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 914.930i | − | 1.52235i | −0.648549 | − | 0.761173i | \(-0.724624\pi\) | ||
0.648549 | − | 0.761173i | \(-0.275376\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 373.096 | + | 215.407i | 0.616687 | + | 0.356044i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −539.084 | + | 311.240i | −0.888112 | + | 0.512752i | −0.873324 | − | 0.487139i | \(-0.838041\pi\) |
−0.0147875 | + | 0.999891i | \(0.504707\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 89.4686 | + | 154.964i | 0.146430 | + | 0.253624i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 172.510 | − | 298.795i | 0.281419 | − | 0.487431i | −0.690316 | − | 0.723508i | \(-0.742528\pi\) |
0.971734 | + | 0.236077i | \(0.0758618\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 854.311 | 1.38462 | 0.692310 | − | 0.721600i | \(-0.256593\pi\) | ||||
0.692310 | + | 0.721600i | \(0.256593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.6240 | + | 24.6090i | 0.0688595 | + | 0.0397561i | 0.534034 | − | 0.845463i | \(-0.320675\pi\) |
−0.465175 | + | 0.885219i | \(0.654009\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 384.378 | + | 665.763i | 0.615005 | + | 1.06522i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 534.089i | 0.849109i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 457.699 | 0.725355 | 0.362677 | − | 0.931915i | \(-0.381863\pi\) | ||||
0.362677 | + | 0.931915i | \(0.381863\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −688.709 | + | 397.626i | −1.08458 | + | 0.626183i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −161.966 | + | 280.533i | −0.252677 | + | 0.437649i | −0.964262 | − | 0.264951i | \(-0.914644\pi\) |
0.711585 | + | 0.702600i | \(0.247978\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 117.018i | 0.181987i | 0.995851 | + | 0.0909935i | \(0.0290043\pi\) | ||||
−0.995851 | + | 0.0909935i | \(0.970996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −467.002 | − | 269.624i | −0.721796 | − | 0.416729i | 0.0936176 | − | 0.995608i | \(-0.470157\pi\) |
−0.815413 | + | 0.578879i | \(0.803490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 206.735 | − | 119.358i | 0.318543 | − | 0.183911i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −398.953 | − | 691.007i | −0.610954 | − | 1.05820i | −0.991080 | − | 0.133268i | \(-0.957453\pi\) |
0.380126 | − | 0.924935i | \(-0.375881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −77.3268 | + | 133.934i | −0.118056 | + | 0.204479i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −295.186 | −0.447929 | −0.223965 | − | 0.974597i | \(-0.571900\pi\) | ||||
−0.223965 | + | 0.974597i | \(0.571900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −893.947 | − | 516.120i | −1.35242 | − | 0.780817i | −0.363828 | − | 0.931466i | \(-0.618530\pi\) |
−0.988587 | + | 0.150649i | \(0.951864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −367.264 | − | 636.120i | −0.550621 | − | 0.953703i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.262657i | 0.000391441i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 418.188 | 0.621379 | 0.310689 | − | 0.950512i | \(-0.399440\pi\) | ||||
0.310689 | + | 0.950512i | \(0.399440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 403.100 | − | 232.730i | 0.595422 | − | 0.343767i | −0.171817 | − | 0.985129i | \(-0.554964\pi\) |
0.767238 | + | 0.641362i | \(0.221630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 629.705 | − | 1090.68i | 0.921969 | − | 1.59690i | 0.125605 | − | 0.992080i | \(-0.459913\pi\) |
0.796364 | − | 0.604817i | \(-0.206754\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1228.92i | − | 1.79405i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −254.031 | − | 146.665i | −0.368695 | − | 0.212866i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −397.397 | + | 229.437i | −0.575104 | + | 0.332036i | −0.759185 | − | 0.650875i | \(-0.774402\pi\) |
0.184081 | + | 0.982911i | \(0.441069\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −244.044 | − | 422.697i | −0.351142 | − | 0.608196i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −273.640 | + | 473.958i | −0.392596 | + | 0.679997i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −822.907 | −1.17390 | −0.586952 | − | 0.809622i | \(-0.699672\pi\) | ||||
−0.586952 | + | 0.809622i | \(0.699672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1442.10 | + | 832.597i | 2.05135 | + | 1.18435i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −142.954 | − | 247.603i | −0.201627 | − | 0.349229i | 0.747426 | − | 0.664346i | \(-0.231290\pi\) |
−0.949053 | + | 0.315117i | \(0.897956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1002.42i | 1.40592i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −144.782 | −0.202492 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −605.561 | + | 349.621i | −0.842227 | + | 0.486260i | −0.858021 | − | 0.513615i | \(-0.828306\pi\) |
0.0157934 | + | 0.999875i | \(0.494973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 181.356 | − | 314.118i | 0.250146 | − | 0.433266i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 216.138i | 0.297302i | 0.988890 | + | 0.148651i | \(0.0474930\pi\) | ||||
−0.988890 | + | 0.148651i | \(0.952507\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 555.730 | + | 320.851i | 0.760233 | + | 0.438920i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 629.763 | − | 363.594i | 0.859159 | − | 0.496035i | −0.00457181 | − | 0.999990i | \(-0.501455\pi\) |
0.863730 | + | 0.503954i | \(0.168122\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 219.872 | + | 380.829i | 0.298334 | + | 0.516729i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −198.206 | + | 343.303i | −0.268209 | + | 0.464551i | −0.968399 | − | 0.249405i | \(-0.919765\pi\) |
0.700191 | + | 0.713956i | \(0.253098\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −739.481 | −0.995263 | −0.497632 | − | 0.867388i | \(-0.665797\pi\) | ||||
−0.497632 | + | 0.867388i | \(0.665797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.3512 | + | 23.2968i | 0.0541627 | + | 0.0312709i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 374.166 | + | 648.075i | 0.498224 | + | 0.862949i | 0.999998 | − | 0.00204963i | \(-0.000652418\pi\) |
−0.501774 | + | 0.864999i | \(0.667319\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 354.825i | 0.469967i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 199.145 | 0.263071 | 0.131536 | − | 0.991311i | \(-0.458009\pi\) | ||||
0.131536 | + | 0.991311i | \(0.458009\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −849.966 | + | 490.728i | −1.11691 | + | 0.644846i | −0.940609 | − | 0.339491i | \(-0.889745\pi\) |
−0.176297 | + | 0.984337i | \(0.556412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 62.9834 | − | 109.090i | 0.0821166 | − | 0.142230i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 724.214i | 0.941760i | 0.882197 | + | 0.470880i | \(0.156064\pi\) | ||||
−0.882197 | + | 0.470880i | \(0.843936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1216.68 | + | 702.449i | 1.57397 | + | 0.908731i | 0.995675 | + | 0.0929015i | \(0.0296142\pi\) |
0.578293 | + | 0.815829i | \(0.303719\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −428.682 | + | 247.500i | −0.553139 | + | 0.319355i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 853.159 | + | 1477.71i | 1.09520 | + | 1.89694i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 172.471 | − | 298.728i | 0.220833 | − | 0.382495i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 170.036 | 0.216607 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −221.541 | − | 127.907i | −0.281501 | − | 0.162525i | 0.352602 | − | 0.935773i | \(-0.385297\pi\) |
−0.634103 | + | 0.773249i | \(0.718630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0692998 | + | 0.120031i | 8.73894e−5 | + | 0.000151363i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 474.641i | − | 0.595534i | −0.954639 | − | 0.297767i | \(-0.903758\pi\) | ||
0.954639 | − | 0.297767i | \(-0.0962418\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −480.141 | −0.600927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −126.843 | + | 73.2327i | −0.157961 | + | 0.0911989i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 233.864 | − | 405.064i | 0.289077 | − | 0.500697i | −0.684512 | − | 0.729001i | \(-0.739985\pi\) |
0.973590 | + | 0.228304i | \(0.0733182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1567.70i | − | 1.93305i | −0.256571 | − | 0.966525i | \(-0.582593\pi\) | ||
0.256571 | − | 0.966525i | \(-0.417407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 315.225 | + | 181.995i | 0.386779 | + | 0.223307i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1732.67 | − | 1000.36i | 2.12077 | − | 1.22442i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −219.125 | − | 379.536i | −0.266900 | − | 0.462285i | 0.701159 | − | 0.713005i | \(-0.252666\pi\) |
−0.968060 | + | 0.250720i | \(0.919333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −468.606 | + | 811.650i | −0.569388 | + | 0.986209i | 0.427238 | + | 0.904139i | \(0.359487\pi\) |
−0.996627 | + | 0.0820702i | \(0.973847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1160.31 | 1.40303 | 0.701516 | − | 0.712654i | \(-0.252507\pi\) | ||||
0.701516 | + | 0.712654i | \(0.252507\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −220.489 | − | 127.300i | −0.265970 | − | 0.153558i | 0.361085 | − | 0.932533i | \(-0.382406\pi\) |
−0.627055 | + | 0.778975i | \(0.715740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 412.050 | + | 713.691i | 0.493473 | + | 0.854720i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 129.902i | − | 0.154829i | −0.996999 | − | 0.0774146i | \(-0.975333\pi\) | ||
0.996999 | − | 0.0774146i | \(-0.0246665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 795.767 | 0.946215 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 786.810 | − | 454.265i | 0.931136 | − | 0.537592i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −499.053 | + | 864.385i | −0.586431 | + | 1.01573i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1229.45i | 1.44133i | 0.693284 | + | 0.720665i | \(0.256163\pi\) | ||||
−0.693284 | + | 0.720665i | \(0.743837\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −578.670 | − | 334.095i | −0.675227 | − | 0.389843i | 0.122827 | − | 0.992428i | \(-0.460804\pi\) |
−0.798054 | + | 0.602585i | \(0.794137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.7929 | − | 9.69537i | 0.0195493 | − | 0.0112868i | −0.490193 | − | 0.871614i | \(-0.663074\pi\) |
0.509743 | + | 0.860327i | \(0.329741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4856 | + | 80.5154i | 0.0538651 | + | 0.0932971i | 0.891701 | − | 0.452626i | \(-0.149513\pi\) |
−0.837836 | + | 0.545923i | \(0.816179\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 710.571 | − | 1230.74i | 0.821469 | − | 1.42283i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −325.945 | −0.375080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 200.957 | + | 116.023i | 0.230720 | + | 0.133206i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −156.154 | − | 270.467i | −0.178055 | − | 0.308400i | 0.763159 | − | 0.646210i | \(-0.223647\pi\) |
−0.941214 | + | 0.337810i | \(0.890314\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 772.018i | − | 0.876298i | −0.898902 | − | 0.438149i | \(-0.855634\pi\) | ||
0.898902 | − | 0.438149i | \(-0.144366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −959.154 | −1.08624 | −0.543122 | − | 0.839654i | \(-0.682758\pi\) | ||||
−0.543122 | + | 0.839654i | \(0.682758\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 480.613 | − | 277.482i | 0.541841 | − | 0.312832i | −0.203984 | − | 0.978974i | \(-0.565389\pi\) |
0.745825 | + | 0.666142i | \(0.232056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −748.496 | + | 1296.43i | −0.838181 | + | 1.45177i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1670.54i | 1.86653i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1934.46 | − | 1116.86i | −2.15179 | − | 1.24234i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 681.639 | − | 393.545i | 0.756536 | − | 0.436787i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −626.036 | − | 1084.33i | −0.691753 | − | 1.19815i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −286.558 | + | 496.333i | −0.315940 | + | 0.547225i | −0.979637 | − | 0.200777i | \(-0.935653\pi\) |
0.663697 | + | 0.748002i | \(0.268987\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −726.088 | −0.797023 | −0.398511 | − | 0.917163i | \(-0.630473\pi\) | ||||
−0.398511 | + | 0.917163i | \(0.630473\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 199.679 | + | 115.284i | 0.218706 | + | 0.126270i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −392.266 | − | 679.425i | −0.426840 | − | 0.739309i | 0.569750 | − | 0.821818i | \(-0.307040\pi\) |
−0.996590 | + | 0.0825089i | \(0.973707\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 182.020i | − | 0.197205i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −492.868 | −0.532830 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 137.793 | − | 79.5547i | 0.148324 | − | 0.0856347i | −0.424001 | − | 0.905662i | \(-0.639375\pi\) |
0.572325 | + | 0.820027i | \(0.306042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 194.246 | − | 336.443i | 0.207749 | − | 0.359833i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 728.876i | − | 0.777883i | −0.921262 | − | 0.388941i | \(-0.872841\pi\) | ||
0.921262 | − | 0.388941i | \(-0.127159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 279.939 | + | 161.623i | 0.297491 | + | 0.171756i | 0.641315 | − | 0.767278i | \(-0.278389\pi\) |
−0.343824 | + | 0.939034i | \(0.611722\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −885.732 | + | 511.377i | −0.939270 | + | 0.542288i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 336.525 | + | 582.878i | 0.355359 | + | 0.615499i | 0.987179 | − | 0.159615i | \(-0.0510254\pi\) |
−0.631821 | + | 0.775115i | \(0.717692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.6437 | + | 66.9328i | −0.0407204 | + | 0.0705298i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 195.034 | 0.204653 | 0.102326 | − | 0.994751i | \(-0.467371\pi\) | ||||
0.102326 | + | 0.994751i | \(0.467371\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −228.763 | − | 132.076i | −0.239542 | − | 0.138300i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1043.70 | + | 1807.75i | 1.08606 | + | 1.88111i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1830.16i | 1.89654i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −731.573 | −0.756538 | −0.378269 | − | 0.925696i | \(-0.623481\pi\) | ||||
−0.378269 | + | 0.925696i | \(0.623481\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 431.992 | − | 249.411i | 0.444894 | − | 0.256860i | −0.260777 | − | 0.965399i | \(-0.583979\pi\) |
0.705672 | + | 0.708539i | \(0.250645\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −90.3523 | + | 156.495i | −0.0924794 | + | 0.160179i | −0.908554 | − | 0.417768i | \(-0.862813\pi\) |
0.816074 | + | 0.577947i | \(0.196146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1071.00i | 1.09398i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 282.894 | + | 163.329i | 0.287786 | + | 0.166153i | 0.636943 | − | 0.770911i | \(-0.280199\pi\) |
−0.349157 | + | 0.937064i | \(0.613532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1308.39 | + | 755.398i | −1.32831 | + | 0.766902i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 599.606 | + | 1038.55i | 0.606275 | + | 1.05010i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 823.376 | − | 1426.13i | 0.830854 | − | 1.43908i | −0.0665084 | − | 0.997786i | \(-0.521186\pi\) |
0.897362 | − | 0.441295i | \(-0.145481\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −428.505 | −0.430659 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 121.381 | + | 70.0792i | 0.121746 | + | 0.0702900i | 0.559636 | − | 0.828738i | \(-0.310941\pi\) |
−0.437890 | + | 0.899028i | \(0.644274\pi\) | |||||||
\(998\) | 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.z.l.325.4 | 8 | ||
3.2 | odd | 2 | 588.3.m.f.325.1 | 8 | |||
7.2 | even | 3 | 1764.3.z.m.901.1 | 8 | |||
7.3 | odd | 6 | 1764.3.d.h.685.1 | 8 | |||
7.4 | even | 3 | 1764.3.d.h.685.8 | 8 | |||
7.5 | odd | 6 | inner | 1764.3.z.l.901.4 | 8 | ||
7.6 | odd | 2 | 1764.3.z.m.325.1 | 8 | |||
21.2 | odd | 6 | 588.3.m.e.313.4 | 8 | |||
21.5 | even | 6 | 588.3.m.f.313.1 | 8 | |||
21.11 | odd | 6 | 588.3.d.c.97.1 | ✓ | 8 | ||
21.17 | even | 6 | 588.3.d.c.97.8 | yes | 8 | ||
21.20 | even | 2 | 588.3.m.e.325.4 | 8 | |||
84.11 | even | 6 | 2352.3.f.j.97.5 | 8 | |||
84.59 | odd | 6 | 2352.3.f.j.97.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.1 | ✓ | 8 | 21.11 | odd | 6 | ||
588.3.d.c.97.8 | yes | 8 | 21.17 | even | 6 | ||
588.3.m.e.313.4 | 8 | 21.2 | odd | 6 | |||
588.3.m.e.325.4 | 8 | 21.20 | even | 2 | |||
588.3.m.f.313.1 | 8 | 21.5 | even | 6 | |||
588.3.m.f.325.1 | 8 | 3.2 | odd | 2 | |||
1764.3.d.h.685.1 | 8 | 7.3 | odd | 6 | |||
1764.3.d.h.685.8 | 8 | 7.4 | even | 3 | |||
1764.3.z.l.325.4 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.z.l.901.4 | 8 | 7.5 | odd | 6 | inner | ||
1764.3.z.m.325.1 | 8 | 7.6 | odd | 2 | |||
1764.3.z.m.901.1 | 8 | 7.2 | even | 3 | |||
2352.3.f.j.97.4 | 8 | 84.59 | odd | 6 | |||
2352.3.f.j.97.5 | 8 | 84.11 | even | 6 |