Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(313,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.313");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.m (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: | \(16.0218395444\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 313.4 | ||
Root | \(-1.60021 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.313 |
Dual form | 588.3.m.e.325.4 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.04718 | + | 2.91399i | 1.00944 | + | 0.582798i | 0.911027 | − | 0.412348i | \(-0.135291\pi\) |
0.0984097 | + | 0.995146i | \(0.468624\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.43068 | + | 5.94212i | 0.311880 | + | 0.540193i | 0.978769 | − | 0.204964i | \(-0.0657078\pi\) |
−0.666889 | + | 0.745157i | \(0.732374\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.62063i | 0.278510i | 0.990257 | + | 0.139255i | \(0.0444708\pi\) | ||||
−0.990257 | + | 0.139255i | \(0.955529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.0944 | −0.672957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.41362 | + | 4.85761i | −0.494919 | + | 0.285742i | −0.726613 | − | 0.687047i | \(-0.758907\pi\) |
0.231694 | + | 0.972789i | \(0.425573\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.2322 | + | 15.1451i | 1.38064 | + | 0.797113i | 0.992235 | − | 0.124376i | \(-0.0396930\pi\) |
0.388405 | + | 0.921489i | \(0.373026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.07789 | − | 15.7234i | 0.394691 | − | 0.683625i | −0.598371 | − | 0.801219i | \(-0.704185\pi\) |
0.993062 | + | 0.117595i | \(0.0375183\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.48269 | + | 7.76425i | 0.179308 | + | 0.310570i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −40.4570 | −1.39507 | −0.697534 | − | 0.716552i | \(-0.745719\pi\) | ||||
−0.697534 | + | 0.716552i | \(0.745719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 47.8153 | − | 27.6062i | 1.54243 | − | 0.890522i | 0.543744 | − | 0.839251i | \(-0.317006\pi\) |
0.998685 | − | 0.0512709i | \(-0.0163272\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.2921 | − | 5.94212i | −0.311880 | − | 0.180064i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.4873 | + | 47.6093i | −0.742899 | + | 1.28674i | 0.208271 | + | 0.978071i | \(0.433216\pi\) |
−0.951170 | + | 0.308668i | \(0.900117\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.13556 | − | 5.43095i | −0.0803989 | − | 0.139255i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 56.3322i | 1.37396i | 0.726678 | + | 0.686978i | \(0.241063\pi\) | ||||
−0.726678 | + | 0.686978i | \(0.758937\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −66.0512 | −1.53608 | −0.768038 | − | 0.640405i | \(-0.778767\pi\) | ||||
−0.768038 | + | 0.640405i | \(0.778767\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.1415 | − | 8.74197i | 0.336479 | − | 0.194266i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 42.8003 | + | 24.7108i | 0.910645 | + | 0.525761i | 0.880639 | − | 0.473789i | \(-0.157114\pi\) |
0.0300061 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.41362 | − | 14.5728i | 0.164973 | − | 0.285742i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 40.5081 | + | 70.1621i | 0.764303 | + | 1.32381i | 0.940614 | + | 0.339478i | \(0.110250\pi\) |
−0.176311 | + | 0.984335i | \(0.556416\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 39.9879i | 0.727054i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −52.4643 | −0.920426 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −30.1302 | + | 17.3957i | −0.510682 | + | 0.294842i | −0.733114 | − | 0.680106i | \(-0.761934\pi\) |
0.222432 | + | 0.974948i | \(0.428600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0331519 | − | 0.0191403i | −0.000543474 | − | 0.000313775i | 0.499728 | − | 0.866182i | \(-0.333433\pi\) |
−0.500272 | + | 0.865868i | \(0.666767\pi\) | |||||||
\(62\) | 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 | 0.999690 | − | 0.0248985i | \(-0.00792626\pi\) |
−0.521408 | + | 0.853308i | \(0.674593\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 31.4467i | 0.455750i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 50.2730 | 0.708070 | 0.354035 | − | 0.935232i | \(-0.384809\pi\) | ||||
0.354035 | + | 0.935232i | \(0.384809\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18.4865 | + | 10.6732i | −0.253240 | + | 0.146208i | −0.621247 | − | 0.783615i | \(-0.713374\pi\) |
0.368007 | + | 0.929823i | \(0.380040\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.4481 | − | 7.76425i | −0.179308 | − | 0.103523i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.7522 | − | 41.1400i | 0.300660 | − | 0.520759i | −0.675625 | − | 0.737245i | \(-0.736126\pi\) |
0.976286 | + | 0.216486i | \(0.0694596\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 33.6039i | 0.404866i | 0.979296 | + | 0.202433i | \(0.0648849\pi\) | ||||
−0.979296 | + | 0.202433i | \(0.935115\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −56.6201 | −0.666119 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 60.6855 | − | 35.0368i | 0.697534 | − | 0.402722i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 135.180 | + | 78.0459i | 1.51887 | + | 0.876920i | 0.999753 | + | 0.0222177i | \(0.00707269\pi\) |
0.519118 | + | 0.854703i | \(0.326261\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −47.8153 | + | 82.8185i | −0.514143 | + | 0.890522i | ||||
\(94\) | 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 | ||||||||
\(99\) | 20.5841 | 0.207920 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −147.005 | + | 84.8732i | −1.45549 | + | 0.840329i | −0.998785 | − | 0.0492878i | \(-0.984305\pi\) |
−0.456708 | + | 0.889617i | \(0.650972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −51.7204 | − | 29.8608i | −0.502140 | − | 0.289911i | 0.227457 | − | 0.973788i | \(-0.426959\pi\) |
−0.729597 | + | 0.683877i | \(0.760292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 28.8839 | − | 50.0284i | 0.269943 | − | 0.467555i | −0.698904 | − | 0.715216i | \(-0.746329\pi\) |
0.968847 | + | 0.247661i | \(0.0796618\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −89.9228 | − | 155.751i | −0.824980 | − | 1.42891i | −0.901935 | − | 0.431872i | \(-0.857853\pi\) |
0.0769549 | − | 0.997035i | \(-0.475480\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 95.2187i | − | 0.857826i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 96.6900 | 0.855664 | 0.427832 | − | 0.903858i | \(-0.359278\pi\) | ||||
0.427832 | + | 0.903858i | \(0.359278\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 91.6355 | − | 52.9058i | 0.796831 | − | 0.460050i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.40668 | + | 5.43095i | 0.0803989 | + | 0.0464183i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 36.9608 | − | 64.0180i | 0.305461 | − | 0.529074i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −48.7851 | − | 84.4983i | −0.396627 | − | 0.686978i | ||||
\(124\) | 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 | ||||||||
\(129\) | 99.0768 | − | 57.2020i | 0.768038 | − | 0.443427i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.9812 | − | 13.2682i | −0.175429 | − | 0.101284i | 0.409714 | − | 0.912214i | \(-0.365628\pi\) |
−0.585143 | + | 0.810930i | \(0.698962\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.1415 | + | 26.2259i | −0.112160 | + | 0.194266i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −105.433 | − | 182.615i | −0.769583 | − | 1.33296i | −0.937789 | − | 0.347206i | \(-0.887131\pi\) |
0.168206 | − | 0.985752i | \(-0.446203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 83.7490i | − | 0.602511i | −0.953543 | − | 0.301256i | \(-0.902594\pi\) | ||
0.953543 | − | 0.301256i | \(-0.0974057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −85.6006 | −0.607096 | ||||||||
\(142\) | 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 | \(-0.841874\pi\) |
0.852300 | + | 0.523054i | \(0.175207\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −30.4415 | − | 52.7263i | −0.201600 | − | 0.349181i | 0.747444 | − | 0.664324i | \(-0.231281\pi\) |
−0.949044 | + | 0.315144i | \(0.897947\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.1456i | 0.190494i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 321.777 | 2.07598 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −25.2670 | + | 14.5879i | −0.160936 | + | 0.0929166i | −0.578305 | − | 0.815821i | \(-0.696286\pi\) |
0.417369 | + | 0.908737i | \(0.362952\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −121.524 | − | 70.1621i | −0.764303 | − | 0.441271i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31.2278 | − | 54.0881i | 0.191582 | − | 0.331829i | −0.754193 | − | 0.656653i | \(-0.771972\pi\) |
0.945775 | + | 0.324824i | \(0.105305\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −34.6306 | − | 59.9819i | −0.209882 | − | 0.363527i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 141.404i | − | 0.846730i | −0.905959 | − | 0.423365i | \(-0.860849\pi\) | ||
0.905959 | − | 0.423365i | \(-0.139151\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 155.891 | 0.922432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 78.6965 | − | 45.4354i | 0.460213 | − | 0.265704i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 211.178 | + | 121.924i | 1.22068 | + | 0.704763i | 0.965064 | − | 0.262015i | \(-0.0843868\pi\) |
0.255621 | + | 0.966777i | \(0.417720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.1302 | − | 52.1871i | 0.170227 | − | 0.294842i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 143.321 | + | 248.239i | 0.800676 | + | 1.38681i | 0.919172 | + | 0.393856i | \(0.128859\pi\) |
−0.118496 | + | 0.992954i | \(0.537807\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 214.838i | − | 1.18695i | −0.804852 | − | 0.593475i | \(-0.797755\pi\) | ||
0.804852 | − | 0.593475i | \(-0.202245\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0663038 | 0.000362316 | ||||||||
\(184\) | 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 | \(-0.795476\pi\) |
0.919234 | + | 0.393713i | \(0.128810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −157.015 | − | 271.958i | −0.813551 | − | 1.40911i | −0.910364 | − | 0.413809i | \(-0.864198\pi\) |
0.0968130 | − | 0.995303i | \(-0.469135\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 36.5480i | − | 0.187425i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 259.231 | 1.31590 | 0.657948 | − | 0.753063i | \(-0.271425\pi\) | ||||
0.657948 | + | 0.753063i | \(0.271425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 63.6749 | − | 36.7627i | 0.319975 | − | 0.184737i | −0.331407 | − | 0.943488i | \(-0.607523\pi\) |
0.651381 | + | 0.758751i | \(0.274190\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −96.1347 | − | 55.5034i | −0.478282 | − | 0.276136i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −164.151 | + | 284.319i | −0.800739 | + | 1.38692i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27.2337 | − | 47.1701i | −0.131564 | − | 0.227875i | ||||
\(208\) | 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 | ||||||||
\(213\) | −75.4095 | + | 43.5377i | −0.354035 | + | 0.204402i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −333.372 | − | 192.473i | −1.55057 | − | 0.895222i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.4865 | − | 32.0196i | 0.0844133 | − | 0.146208i | ||||
\(220\) | 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 | ||||||||
\(225\) | 26.8961 | 0.119538 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −373.608 | + | 215.702i | −1.64585 | + | 0.950231i | −0.667151 | + | 0.744923i | \(0.732486\pi\) |
−0.978697 | + | 0.205308i | \(0.934180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −30.1973 | − | 17.4344i | −0.131866 | − | 0.0761329i | 0.432616 | − | 0.901578i | \(-0.357591\pi\) |
−0.564482 | + | 0.825445i | \(0.690924\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 175.386 | − | 303.777i | 0.752728 | − | 1.30376i | −0.193768 | − | 0.981047i | \(-0.562071\pi\) |
0.946496 | − | 0.322715i | \(-0.104596\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 144.014 | + | 249.439i | 0.612825 | + | 1.06144i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 82.2800i | 0.347173i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 167.400 | 0.700419 | 0.350209 | − | 0.936671i | \(-0.386110\pi\) | ||||
0.350209 | + | 0.936671i | \(0.386110\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 71.0711 | − | 41.0329i | 0.294901 | − | 0.170261i | −0.345249 | − | 0.938511i | \(-0.612206\pi\) |
0.640150 | + | 0.768250i | \(0.278872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −54.8350 | + | 94.9770i | −0.222004 | + | 0.384522i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −29.1018 | − | 50.4059i | −0.116875 | − | 0.202433i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 232.918i | − | 0.927959i | −0.885846 | − | 0.463979i | \(-0.846421\pi\) | ||
0.885846 | − | 0.463979i | \(-0.153579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 124.574 | 0.492385 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 84.9301 | − | 49.0344i | 0.333059 | − | 0.192292i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 32.3538 | + | 18.6795i | 0.125890 | + | 0.0726827i | 0.561623 | − | 0.827394i | \(-0.310177\pi\) |
−0.435732 | + | 0.900076i | \(0.643511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −60.6855 | + | 105.110i | −0.232511 | + | 0.402722i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.68631 | − | 2.92077i | −0.00641181 | − | 0.0111056i | 0.862802 | − | 0.505543i | \(-0.168708\pi\) |
−0.869214 | + | 0.494437i | \(0.835374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 472.161i | 1.78174i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −270.359 | −1.01258 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 75.5768 | − | 43.6343i | 0.280955 | − | 0.162209i | −0.352901 | − | 0.935661i | \(-0.614805\pi\) |
0.633856 | + | 0.773451i | \(0.281471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 79.6808 | + | 46.0037i | 0.294025 | + | 0.169756i | 0.639756 | − | 0.768578i | \(-0.279036\pi\) |
−0.345731 | + | 0.938334i | \(0.612369\pi\) | |||||||
\(272\) | 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 | 0.694958 | − | 0.719050i | \(-0.255423\pi\) |
−0.970195 | + | 0.242326i | \(0.922090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 165.637i | − | 0.593681i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −219.880 | −0.782491 | −0.391245 | − | 0.920286i | \(-0.627956\pi\) | ||||
−0.391245 | + | 0.920286i | \(0.627956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 335.489 | − | 193.695i | 1.18547 | − | 0.684433i | 0.228199 | − | 0.973615i | \(-0.426716\pi\) |
0.957274 | + | 0.289181i | \(0.0933831\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −264.797 | − | 152.881i | −0.929112 | − | 0.536423i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −97.3073 | + | 168.541i | −0.336704 | + | 0.583188i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.8845 | − | 65.6178i | −0.130187 | − | 0.225491i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 14.8794i | − | 0.0507828i | −0.999678 | − | 0.0253914i | \(-0.991917\pi\) | ||
0.999678 | − | 0.0253914i | \(-0.00808320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −202.764 | −0.687335 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.8762 | + | 17.8264i | −0.103960 | + | 0.0600214i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 56.9285 | + | 32.8677i | 0.190396 | + | 0.109925i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 147.005 | − | 254.620i | 0.485164 | − | 0.840329i | ||||
\(304\) | 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 | ||||||||
\(309\) | 103.441 | 0.334760 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 376.934 | − | 217.623i | 1.21201 | − | 0.699752i | 0.248810 | − | 0.968552i | \(-0.419961\pi\) |
0.963196 | + | 0.268801i | \(0.0866273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −47.5799 | − | 27.4703i | −0.152012 | − | 0.0877644i | 0.422064 | − | 0.906566i | \(-0.361306\pi\) |
−0.574077 | + | 0.818801i | \(0.694639\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −216.846 | + | 375.587i | −0.684055 | + | 1.18482i | 0.289677 | + | 0.957124i | \(0.406452\pi\) |
−0.973733 | + | 0.227694i | \(0.926881\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −138.795 | − | 240.400i | −0.435095 | − | 0.753606i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 100.057i | 0.311703i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −294.277 | −0.911073 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.1115 | + | 16.2302i | −0.0864968 | + | 0.0499390i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 269.768 | + | 155.751i | 0.824980 | + | 0.476302i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 288.274 | − | 499.305i | 0.870919 | − | 1.50848i | 0.00987084 | − | 0.999951i | \(-0.496858\pi\) |
0.861048 | − | 0.508524i | \(-0.169809\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 82.4618 | + | 142.828i | 0.247633 | + | 0.428913i | ||||
\(334\) | 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 | ||||||||
\(339\) | −145.035 | + | 83.7360i | −0.427832 | + | 0.247009i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 328.078 | + | 189.416i | 0.962107 | + | 0.555473i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −91.6355 | + | 158.717i | −0.265610 | + | 0.460050i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 126.056 | + | 218.335i | 0.363273 | + | 0.629208i | 0.988497 | − | 0.151237i | \(-0.0483258\pi\) |
−0.625224 | + | 0.780445i | \(0.714992\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 406.452i | 1.16462i | 0.812967 | + | 0.582309i | \(0.197851\pi\) | ||||
−0.812967 | + | 0.582309i | \(0.802149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.8134 | −0.0535993 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −116.419 | + | 67.2146i | −0.329799 | + | 0.190410i | −0.655752 | − | 0.754976i | \(-0.727648\pi\) |
0.325953 | + | 0.945386i | \(0.394315\pi\) | |||||||
\(354\) | 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 | \(-0.781377\pi\) |
0.935765 | + | 0.352624i | \(0.114710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 278.251 | + | 481.944i | 0.770777 | + | 1.33503i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 128.036i | 0.352716i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −124.406 | −0.340839 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −362.993 | + | 209.574i | −0.989081 | + | 0.571046i | −0.905000 | − | 0.425413i | \(-0.860129\pi\) |
−0.0840817 | + | 0.996459i | \(0.526796\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 146.355 | + | 84.4983i | 0.396627 | + | 0.228993i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 63.4962 | − | 109.979i | 0.170231 | − | 0.294849i | −0.768270 | − | 0.640127i | \(-0.778882\pi\) |
0.938501 | + | 0.345278i | \(0.112215\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 80.9296 | + | 140.174i | 0.215812 | + | 0.373798i | ||||
\(376\) | 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 | ||||||||
\(381\) | 204.681 | − | 118.173i | 0.537221 | − | 0.310165i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 223.750 | + | 129.182i | 0.584203 | + | 0.337290i | 0.762802 | − | 0.646632i | \(-0.223823\pi\) |
−0.178599 | + | 0.983922i | \(0.557157\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −99.0768 | + | 171.606i | −0.256013 | + | 0.443427i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −271.198 | − | 469.728i | −0.697166 | − | 1.20753i | −0.969445 | − | 0.245309i | \(-0.921111\pi\) |
0.272279 | − | 0.962218i | \(-0.412223\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 176.387i | 0.451118i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 45.9623 | 0.116953 | ||||||||
\(394\) | 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 | \(-0.163061\pi\) |
0.0113280 | + | 0.999936i | \(0.496394\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 236.718 | − | 410.008i | 0.590319 | − | 1.02246i | −0.403870 | − | 0.914816i | \(-0.632335\pi\) |
0.994189 | − | 0.107646i | \(-0.0343315\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 99.9518 | + | 173.122i | 0.248019 | + | 0.429582i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 52.4518i | − | 0.129511i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −377.201 | −0.926783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −349.578 | + | 201.829i | −0.854714 | + | 0.493469i | −0.862239 | − | 0.506502i | \(-0.830938\pi\) |
0.00752476 | + | 0.999972i | \(0.497605\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 316.299 | + | 182.615i | 0.769583 | + | 0.444319i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −97.9215 | + | 169.605i | −0.235955 | + | 0.408687i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 72.5288 | + | 125.624i | 0.173930 | + | 0.301256i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 454.684i | 1.08517i | 0.840003 | + | 0.542583i | \(0.182553\pi\) | ||||
−0.840003 | + | 0.542583i | \(0.817447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −180.928 | −0.429758 | −0.214879 | − | 0.976641i | \(-0.568936\pi\) | ||||
−0.214879 | + | 0.976641i | \(0.568936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 128.401 | − | 74.1323i | 0.303548 | − | 0.175254i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −75.4313 | − | 43.5503i | −0.177485 | − | 0.102471i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.5142 | − | 37.2637i | 0.0501497 | − | 0.0868619i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 403.946 | + | 699.655i | 0.937229 | + | 1.62333i | 0.770610 | + | 0.637307i | \(0.219952\pi\) |
0.166619 | + | 0.986021i | \(0.446715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 166.000i | 0.383372i | 0.981456 | + | 0.191686i | \(0.0613955\pi\) | ||||
−0.981456 | + | 0.191686i | \(0.938604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 408.387 | 0.938822 | ||||||||
\(436\) | 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 | \(-0.322713\pi\) |
−0.470832 | + | 0.882223i | \(0.656046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −411.376 | + | 712.524i | −0.928613 | + | 1.60841i | −0.142969 | + | 0.989727i | \(0.545665\pi\) |
−0.785645 | + | 0.618678i | \(0.787669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 454.850 | + | 787.824i | 1.02214 | + | 1.77039i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 13.8474i | − | 0.0309786i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −428.131 | −0.953522 | −0.476761 | − | 0.879033i | \(-0.658189\pi\) | ||||
−0.476761 | + | 0.879033i | \(0.658189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −334.733 | + | 193.258i | −0.742201 | + | 0.428510i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 91.3246 | + | 52.7263i | 0.201600 | + | 0.116394i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 93.6555 | − | 162.216i | 0.204935 | − | 0.354959i | −0.745177 | − | 0.666867i | \(-0.767635\pi\) |
0.950112 | + | 0.311908i | \(0.100968\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.2409 | − | 43.7185i | −0.0549910 | − | 0.0952472i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 182.821i | − | 0.396576i | −0.980144 | − | 0.198288i | \(-0.936462\pi\) | ||
0.980144 | − | 0.198288i | \(-0.0635381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 232.389 | 0.501920 | 0.250960 | − | 0.967997i | \(-0.419254\pi\) | ||||
0.250960 | + | 0.967997i | \(0.419254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −482.665 | + | 278.667i | −1.03799 | + | 0.599283i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −388.782 | − | 224.463i | −0.832509 | − | 0.480650i | 0.0222017 | − | 0.999754i | \(-0.492932\pi\) |
−0.854711 | + | 0.519104i | \(0.826266\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.2670 | − | 43.7637i | 0.0536454 | − | 0.0929166i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −226.601 | − | 392.484i | −0.479072 | − | 0.829777i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 271.564i | 0.571713i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 243.049 | 0.509536 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 547.020 | − | 315.822i | 1.14200 | − | 0.659336i | 0.195078 | − | 0.980788i | \(-0.437504\pi\) |
0.946926 | + | 0.321452i | \(0.104171\pi\) | |||||||
\(480\) | 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 | −0.960895 | − | 0.276914i | \(-0.910688\pi\) |
0.240633 | − | 0.970616i | \(-0.422645\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 108.176i | 0.221219i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −414.789 | −0.844785 | −0.422392 | − | 0.906413i | \(-0.638810\pi\) | ||||
−0.422392 | + | 0.906413i | \(0.638810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 340.390 | − | 196.524i | 0.690446 | − | 0.398629i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 103.892 | + | 59.9819i | 0.209882 | + | 0.121176i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 306.170 | − | 530.302i | 0.613567 | − | 1.06273i | −0.377067 | − | 0.926186i | \(-0.623067\pi\) |
0.990634 | − | 0.136543i | \(-0.0435992\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 122.459 | + | 212.106i | 0.244430 | + | 0.423365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 467.449i | 0.929323i | 0.885488 | + | 0.464661i | \(0.153824\pi\) | ||||
−0.885488 | + | 0.464661i | \(0.846176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −989.279 | −1.95897 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −233.837 | + | 135.006i | −0.461216 | + | 0.266283i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 54.1843 | + | 31.2833i | 0.106452 | + | 0.0614603i | 0.552281 | − | 0.833658i | \(-0.313758\pi\) |
−0.445829 | + | 0.895118i | \(0.647091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −78.6965 | + | 136.306i | −0.153404 | + | 0.265704i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −174.028 | − | 301.426i | −0.337919 | − | 0.585293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 339.099i | 0.655898i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −422.357 | −0.813790 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 617.108 | − | 356.288i | 1.18447 | − | 0.683853i | 0.227425 | − | 0.973796i | \(-0.426969\pi\) |
0.957044 | + | 0.289942i | \(0.0936362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −242.586 | − | 140.057i | −0.463835 | − | 0.267795i | 0.249821 | − | 0.968292i | \(-0.419628\pi\) |
−0.713655 | + | 0.700497i | \(0.752962\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | 104.374i | 0.196562i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −203.958 | −0.382660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 291.564 | − | 168.335i | 0.544980 | − | 0.314645i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −429.963 | − | 248.239i | −0.800676 | − | 0.462270i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −316.501 | + | 548.196i | −0.585030 | + | 1.01330i | 0.409842 | + | 0.912157i | \(0.365584\pi\) |
−0.994872 | + | 0.101145i | \(0.967749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 186.055 | + | 322.257i | 0.342643 | + | 0.593475i | ||||
\(544\) | 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 | ||||||||
\(549\) | −0.0994557 | + | 0.0574208i | −0.000181158 | + | 0.000104592i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1061.27 | − | 612.727i | −1.92609 | − | 1.11203i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 277.466 | − | 480.586i | 0.499940 | − | 0.865921i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −340.866 | − | 590.397i | −0.611967 | − | 1.05996i | −0.990908 | − | 0.134538i | \(-0.957045\pi\) |
0.378941 | − | 0.925421i | \(-0.376288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 239.147i | − | 0.427812i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 115.458 | 0.205807 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −174.581 | + | 100.794i | −0.310090 | + | 0.179031i | −0.646967 | − | 0.762518i | \(-0.723963\pi\) |
0.336877 | + | 0.941549i | \(0.390629\pi\) | |||||||
\(564\) | 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 | −0.390797 | − | 0.920477i | \(-0.627801\pi\) |
0.992555 | − | 0.121798i | \(-0.0388660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5301 | + | 21.7028i | 0.0219442 | + | 0.0380084i | 0.876789 | − | 0.480875i | \(-0.159681\pi\) |
−0.854845 | + | 0.518884i | \(0.826348\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 78.5050i | 0.137007i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 162.773 | 0.283084 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −883.312 | + | 509.981i | −1.53087 | + | 0.883849i | −0.531549 | + | 0.847028i | \(0.678390\pi\) |
−0.999322 | + | 0.0368210i | \(0.988277\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 471.046 | + | 271.958i | 0.813551 | + | 0.469704i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −277.941 | + | 481.408i | −0.476743 | + | 0.825742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 31.6515 | + | 54.8219i | 0.0541051 | + | 0.0937127i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 581.810i | 0.991158i | 0.868563 | + | 0.495579i | \(0.165044\pi\) | ||||
−0.868563 | + | 0.495579i | \(0.834956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1672.40 | 2.83939 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −388.847 | + | 224.501i | −0.657948 | + | 0.379866i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −124.589 | − | 71.9314i | −0.210099 | − | 0.121301i | 0.391258 | − | 0.920281i | \(-0.372040\pi\) |
−0.601358 | + | 0.798980i | \(0.705373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −63.6749 | + | 110.288i | −0.106658 | + | 0.184737i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −355.368 | − | 615.515i | −0.593269 | − | 1.02757i | −0.993789 | − | 0.111283i | \(-0.964504\pi\) |
0.400520 | − | 0.916288i | \(-0.368829\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 914.930i | − | 1.52235i | −0.648549 | − | 0.761173i | \(-0.724624\pi\) | ||
0.648549 | − | 0.761173i | \(-0.275376\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 192.269 | 0.318855 | ||||||||
\(604\) | 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 | \(-0.161959\pi\) |
0.0147875 | + | 0.999891i | \(0.495293\pi\) | |||||||
\(608\) | 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 | 0.971734 | − | 0.236077i | \(-0.0758618\pi\) |
−0.690316 | + | 0.723508i | \(0.742528\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 568.637i | − | 0.924614i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −854.311 | −1.38462 | −0.692310 | − | 0.721600i | \(-0.743407\pi\) | ||||
−0.692310 | + | 0.721600i | \(0.743407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.6240 | + | 24.6090i | −0.0688595 | + | 0.0397561i | −0.534034 | − | 0.845463i | \(-0.679325\pi\) |
0.465175 | + | 0.885219i | \(0.345991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 81.7010 | + | 47.1701i | 0.131564 | + | 0.0759583i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 384.378 | − | 665.763i | 0.615005 | − | 1.06522i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −179.989 | − | 311.749i | −0.287063 | − | 0.497208i | ||||
\(628\) | 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 | ||||||||
\(633\) | −395.306 | + | 228.230i | −0.624496 | + | 0.360553i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −688.709 | − | 397.626i | −1.08458 | − | 0.626183i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 75.4095 | − | 130.613i | 0.118012 | − | 0.204402i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 161.966 | + | 280.533i | 0.252677 | + | 0.437649i | 0.964262 | − | 0.264951i | \(-0.0853558\pi\) |
−0.711585 | + | 0.702600i | \(0.752022\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 117.018i | 0.181987i | 0.995851 | + | 0.0909935i | \(0.0290043\pi\) | ||||
−0.995851 | + | 0.0909935i | \(0.970996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 666.745 | 1.03371 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −467.002 | + | 269.624i | −0.721796 | + | 0.416729i | −0.815413 | − | 0.578879i | \(-0.803490\pi\) |
0.0936176 | + | 0.995608i | \(0.470157\pi\) | |||||||
\(648\) | 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 | −0.380126 | − | 0.924935i | \(-0.624119\pi\) |
0.991080 | − | 0.133268i | \(-0.0425472\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −77.3268 | − | 133.934i | −0.118056 | − | 0.204479i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 64.0391i | 0.0974720i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 295.186 | 0.447929 | 0.223965 | − | 0.974597i | \(-0.428100\pi\) | ||||
0.223965 | + | 0.974597i | \(0.428100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 893.947 | − | 516.120i | 1.35242 | − | 0.780817i | 0.363828 | − | 0.931466i | \(-0.381470\pi\) |
0.988587 | + | 0.150649i | \(0.0481362\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 52.7628 | + | 30.4626i | 0.0795819 | + | 0.0459466i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −367.264 | + | 636.120i | −0.550621 | + | 0.953703i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 165.447 | + | 286.562i | 0.247305 | + | 0.428344i | ||||
\(670\) | 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 | ||||||||
\(675\) | −40.3442 | + | 23.2927i | −0.0597692 | + | 0.0345078i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 403.100 | + | 232.730i | 0.595422 | + | 0.343767i | 0.767238 | − | 0.641362i | \(-0.221630\pi\) |
−0.171817 | + | 0.985129i | \(0.554964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 373.608 | − | 647.107i | 0.548616 | − | 0.950231i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −629.705 | − | 1090.68i | −0.921969 | − | 1.59690i | −0.796364 | − | 0.604817i | \(-0.793246\pi\) |
−0.125605 | − | 0.992080i | \(-0.540087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1228.92i | − | 1.79405i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 60.3947 | 0.0879107 | ||||||||
\(688\) | 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 | \(-0.225598\pi\) |
−0.184081 | + | 0.982911i | \(0.558931\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 607.553i | 0.869175i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 822.907 | 1.17390 | 0.586952 | − | 0.809622i | \(-0.300328\pi\) | ||||
0.586952 | + | 0.809622i | \(0.300328\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1442.10 | + | 832.597i | −2.05135 | + | 1.18435i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −432.042 | − | 249.439i | −0.612825 | − | 0.353815i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −142.954 | + | 247.603i | −0.201627 | + | 0.349229i | −0.949053 | − | 0.315117i | \(-0.897956\pi\) |
0.747426 | + | 0.664346i | \(0.231290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −71.2565 | − | 123.420i | −0.100220 | − | 0.173586i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1002.42i | − | 1.40592i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −144.782 | −0.202492 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −251.100 | + | 144.973i | −0.350209 | + | 0.202193i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −605.561 | − | 349.621i | −0.842227 | − | 0.486260i | 0.0157934 | − | 0.999875i | \(-0.494973\pi\) |
−0.858021 | + | 0.513615i | \(0.828306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −71.0711 | + | 123.099i | −0.0983002 | + | 0.170261i | ||||
\(724\) | 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 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 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 | \(-0.498545\pi\) |
−0.863730 | + | 0.503954i | \(0.831878\pi\) | |||||||
\(734\) | 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 | 0.700191 | − | 0.713956i | \(-0.253098\pi\) |
−0.968399 | + | 0.249405i | \(0.919765\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 189.954i | − | 0.256348i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 739.481 | 0.995263 | 0.497632 | − | 0.867388i | \(-0.334203\pi\) | ||||
0.497632 | + | 0.867388i | \(0.334203\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.3512 | + | 23.2968i | −0.0541627 | + | 0.0312709i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 87.3055 | + | 50.4059i | 0.116875 | + | 0.0674777i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 374.166 | − | 648.075i | 0.498224 | − | 0.862949i | −0.501774 | − | 0.864999i | \(-0.667319\pi\) |
0.999998 | + | 0.00204963i | \(0.000652418\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 201.713 | + | 349.377i | 0.267879 | + | 0.463979i | ||||
\(754\) | 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 | ||||||||
\(759\) | −186.860 | + | 107.884i | −0.246193 | + | 0.142139i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −849.966 | − | 490.728i | −1.11691 | − | 0.644846i | −0.176297 | − | 0.984337i | \(-0.556412\pi\) |
−0.940609 | + | 0.339491i | \(0.889745\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −84.9301 | + | 147.103i | −0.111020 | + | 0.192292i | ||||
\(766\) | 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 | ||||||||
\(771\) | −64.7075 | −0.0839268 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1216.68 | − | 702.449i | 1.57397 | − | 0.908731i | 0.578293 | − | 0.815829i | \(-0.303719\pi\) |
0.995675 | − | 0.0929015i | \(-0.0296142\pi\) | |||||||
\(774\) | 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 | ||||||||
\(783\) | − | 210.221i | − | 0.268481i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −170.036 | −0.216607 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 221.541 | − | 127.907i | 0.281501 | − | 0.162525i | −0.352602 | − | 0.935773i | \(-0.614703\pi\) |
0.634103 | + | 0.773249i | \(0.281370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.05892 | + | 2.92077i | 0.00641181 | + | 0.00370186i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0692998 | − | 0.120031i | 8.73894e−5 | − | 0.000151363i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −408.903 | − | 708.241i | −0.514344 | − | 0.890869i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 474.641i | 0.595534i | 0.954639 | + | 0.297767i | \(0.0962418\pi\) | ||||
−0.954639 | + | 0.297767i | \(0.903758\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −480.141 | −0.600927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 405.539 | − | 234.138i | 0.506290 | − | 0.292307i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −126.843 | − | 73.2327i | −0.157961 | − | 0.0911989i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −75.5768 | + | 130.903i | −0.0936516 | + | 0.162209i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −233.864 | − | 405.064i | −0.289077 | − | 0.500697i | 0.684512 | − | 0.729001i | \(-0.260015\pi\) |
−0.973590 | + | 0.228304i | \(0.926682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1567.70i | − | 1.93305i | −0.256571 | − | 0.966525i | \(-0.582593\pi\) | ||
0.256571 | − | 0.966525i | \(-0.417407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −159.362 | −0.196017 | ||||||||
\(814\) | 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 | \(-0.747334\pi\) |
0.968060 | + | 0.250720i | \(0.0806672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −468.606 | − | 811.650i | −0.569388 | − | 0.986209i | −0.996627 | − | 0.0820702i | \(-0.973847\pi\) |
0.427238 | − | 0.904139i | \(-0.359487\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 106.547i | − | 0.129148i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1160.31 | −1.40303 | −0.701516 | − | 0.712654i | \(-0.747493\pi\) | ||||
−0.701516 | + | 0.712654i | \(0.747493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 220.489 | − | 127.300i | 0.265970 | − | 0.153558i | −0.361085 | − | 0.932533i | \(-0.617594\pi\) |
0.627055 | + | 0.778975i | \(0.284260\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 228.722 | + | 132.053i | 0.275237 | + | 0.158908i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 412.050 | − | 713.691i | 0.493473 | − | 0.854720i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 143.446 | + | 248.456i | 0.171381 | + | 0.296841i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 129.902i | 0.154829i | 0.996999 | + | 0.0774146i | \(0.0246665\pi\) | ||||
−0.996999 | + | 0.0774146i | \(0.975333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 795.767 | 0.946215 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 329.820 | − | 190.422i | 0.391245 | − | 0.225886i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 786.810 | + | 454.265i | 0.931136 | + | 0.537592i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −335.489 | + | 581.084i | −0.395158 | + | 0.684433i | ||||
\(850\) | 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 | ||||||||
\(855\) | 529.594 | 0.619408 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −578.670 | + | 334.095i | −0.675227 | + | 0.389843i | −0.798054 | − | 0.602585i | \(-0.794137\pi\) |
0.122827 | + | 0.992428i | \(0.460804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7929 | − | 9.69537i | −0.0195493 | − | 0.0112868i | 0.490193 | − | 0.871614i | \(-0.336926\pi\) |
−0.509743 | + | 0.860327i | \(0.670259\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.4856 | + | 80.5154i | −0.0538651 | + | 0.0932971i | −0.891701 | − | 0.452626i | \(-0.850487\pi\) |
0.837836 | + | 0.545923i | \(0.183821\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 710.571 | + | 1230.74i | 0.821469 | + | 1.42283i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 337.082i | − | 0.388792i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 325.945 | 0.375080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −200.957 | + | 116.023i | −0.230720 | + | 0.133206i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 113.653 | + | 65.6178i | 0.130187 | + | 0.0751636i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −156.154 | + | 270.467i | −0.178055 | + | 0.308400i | −0.941214 | − | 0.337810i | \(-0.890314\pi\) |
0.763159 | + | 0.646210i | \(0.223647\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.8859 | + | 22.3190i | 0.0146597 | + | 0.0253914i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 772.018i | 0.876298i | 0.898902 | + | 0.438149i | \(0.144366\pi\) | ||||
−0.898902 | + | 0.438149i | \(0.855634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −959.154 | −1.08624 | −0.543122 | − | 0.839654i | \(-0.682758\pi\) | ||||
−0.543122 | + | 0.839654i | \(0.682758\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 304.146 | − | 175.599i | 0.343667 | − | 0.198416i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 480.613 | + | 277.482i | 0.541841 | + | 0.312832i | 0.745825 | − | 0.666142i | \(-0.232056\pi\) |
−0.203984 | + | 0.978974i | \(0.565389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.8762 | − | 53.4791i | 0.0346534 | − | 0.0600214i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 748.496 | + | 1296.43i | 0.838181 | + | 1.45177i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1670.54i | 1.86653i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −113.857 | −0.126931 | ||||||||
\(898\) | 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 | 0.663697 | − | 0.748002i | \(-0.268987\pi\) |
−0.979637 | + | 0.200777i | \(0.935653\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 509.239i | 0.560219i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 726.088 | 0.797023 | 0.398511 | − | 0.917163i | \(-0.369527\pi\) | ||||
0.398511 | + | 0.917163i | \(0.369527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −199.679 | + | 115.284i | −0.218706 | + | 0.126270i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.334647 | + | 0.193209i | 0.000365735 | + | 0.000211157i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −392.266 | + | 679.425i | −0.426840 | + | 0.739309i | −0.996590 | − | 0.0825089i | \(-0.973707\pi\) |
0.569750 | + | 0.821818i | \(0.307040\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 392.492 | + | 679.816i | 0.426159 | + | 0.738128i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 182.020i | 0.197205i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −492.868 | −0.532830 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −155.161 | + | 89.5824i | −0.167380 | + | 0.0966369i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 137.793 | + | 79.5547i | 0.148324 | + | 0.0856347i | 0.572325 | − | 0.820027i | \(-0.306042\pi\) |
−0.424001 | + | 0.905662i | \(0.639375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −376.934 | + | 652.868i | −0.404002 | + | 0.699752i | ||||
\(934\) | 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 | ||||||||
\(939\) | 95.1597 | 0.101342 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 279.939 | − | 161.623i | 0.297491 | − | 0.171756i | −0.343824 | − | 0.939034i | \(-0.611722\pi\) |
0.641315 | + | 0.767278i | \(0.278389\pi\) | |||||||
\(942\) | 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 | \(-0.948975\pi\) |
0.631821 | + | 0.775115i | \(0.282308\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.6437 | − | 66.9328i | −0.0407204 | − | 0.0705298i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 751.175i | − | 0.789879i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −195.034 | −0.204653 | −0.102326 | − | 0.994751i | \(-0.532629\pi\) | ||||
−0.102326 | + | 0.994751i | \(0.532629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 228.763 | − | 132.076i | 0.239542 | − | 0.138300i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 416.385 | + | 240.400i | 0.435095 | + | 0.251202i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1043.70 | − | 1807.75i | 1.08606 | − | 1.88111i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −86.6517 | − | 150.085i | −0.0899810 | − | 0.155852i | ||||
\(964\) | 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 | ||||||||
\(969\) | 441.415 | − | 254.851i | 0.455536 | − | 0.263004i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 431.992 | + | 249.411i | 0.444894 | + | 0.256860i | 0.705672 | − | 0.708539i | \(-0.250645\pi\) |
−0.260777 | + | 0.965399i | \(0.583979\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.1115 | − | 48.6905i | 0.0288323 | − | 0.0499390i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 90.3523 | + | 156.495i | 0.0924794 | + | 0.160179i | 0.908554 | − | 0.417768i | \(-0.137187\pi\) |
−0.816074 | + | 0.577947i | \(0.803854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1071.00i | 1.09398i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −539.537 | −0.549987 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 282.894 | − | 163.329i | 0.287786 | − | 0.166153i | −0.349157 | − | 0.937064i | \(-0.613532\pi\) |
0.636943 | + | 0.770911i | \(0.280199\pi\) | |||||||
\(984\) | 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 | 0.897362 | + | 0.441295i | \(0.145481\pi\) |
−0.0665084 | + | 0.997786i | \(0.521186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 998.611i | 1.00565i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 428.505 | 0.430659 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −121.381 | + | 70.0792i | −0.121746 | + | 0.0702900i | −0.559636 | − | 0.828738i | \(-0.689059\pi\) |
0.437890 | + | 0.899028i | \(0.355726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −247.385 | − | 142.828i | −0.247633 | − | 0.142971i |
(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 | 588.3.m.e.313.4 | 8 | ||
3.2 | odd | 2 | 1764.3.z.m.901.1 | 8 | |||
7.2 | even | 3 | 588.3.d.c.97.1 | ✓ | 8 | ||
7.3 | odd | 6 | inner | 588.3.m.e.325.4 | 8 | ||
7.4 | even | 3 | 588.3.m.f.325.1 | 8 | |||
7.5 | odd | 6 | 588.3.d.c.97.8 | yes | 8 | ||
7.6 | odd | 2 | 588.3.m.f.313.1 | 8 | |||
21.2 | odd | 6 | 1764.3.d.h.685.8 | 8 | |||
21.5 | even | 6 | 1764.3.d.h.685.1 | 8 | |||
21.11 | odd | 6 | 1764.3.z.l.325.4 | 8 | |||
21.17 | even | 6 | 1764.3.z.m.325.1 | 8 | |||
21.20 | even | 2 | 1764.3.z.l.901.4 | 8 | |||
28.19 | even | 6 | 2352.3.f.j.97.4 | 8 | |||
28.23 | odd | 6 | 2352.3.f.j.97.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.1 | ✓ | 8 | 7.2 | even | 3 | ||
588.3.d.c.97.8 | yes | 8 | 7.5 | odd | 6 | ||
588.3.m.e.313.4 | 8 | 1.1 | even | 1 | trivial | ||
588.3.m.e.325.4 | 8 | 7.3 | odd | 6 | inner | ||
588.3.m.f.313.1 | 8 | 7.6 | odd | 2 | |||
588.3.m.f.325.1 | 8 | 7.4 | even | 3 | |||
1764.3.d.h.685.1 | 8 | 21.5 | even | 6 | |||
1764.3.d.h.685.8 | 8 | 21.2 | odd | 6 | |||
1764.3.z.l.325.4 | 8 | 21.11 | odd | 6 | |||
1764.3.z.l.901.4 | 8 | 21.20 | even | 2 | |||
1764.3.z.m.325.1 | 8 | 21.17 | even | 6 | |||
1764.3.z.m.901.1 | 8 | 3.2 | odd | 2 | |||
2352.3.f.j.97.4 | 8 | 28.19 | even | 6 | |||
2352.3.f.j.97.5 | 8 | 28.23 | odd | 6 |