Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,3,Mod(35,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.35");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.l (of order \(10\), degree \(4\), 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: | \(3.37875527807\) |
Analytic rank: | \(0\) |
Dimension: | \(120\) |
Relative dimension: | \(30\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 35.15 | ||
Character | \(\chi\) | \(=\) | 124.35 |
Dual form | 124.3.l.a.39.15 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.316513 | − | 1.97480i | −0.158257 | − | 0.987398i | ||||
\(3\) | 1.26908 | + | 0.412350i | 0.423028 | + | 0.137450i | 0.512792 | − | 0.858513i | \(-0.328611\pi\) |
−0.0897638 | + | 0.995963i | \(0.528611\pi\) | |||||||
\(4\) | −3.79964 | + | 1.25010i | −0.949910 | + | 0.312525i | ||||
\(5\) | −3.39555 | −0.679110 | −0.339555 | − | 0.940586i | \(-0.610277\pi\) | ||||
−0.339555 | + | 0.940586i | \(0.610277\pi\) | |||||||
\(6\) | 0.412626 | − | 2.63670i | 0.0687710 | − | 0.439449i | ||||
\(7\) | −4.74424 | − | 6.52988i | −0.677748 | − | 0.932840i | 0.322156 | − | 0.946687i | \(-0.395592\pi\) |
−0.999904 | + | 0.0138462i | \(0.995592\pi\) | |||||||
\(8\) | 3.67133 | + | 7.10784i | 0.458916 | + | 0.888480i | ||||
\(9\) | −5.84061 | − | 4.24345i | −0.648957 | − | 0.471495i | ||||
\(10\) | 1.07474 | + | 6.70552i | 0.107474 | + | 0.670552i | ||||
\(11\) | −11.3616 | − | 15.6380i | −1.03288 | − | 1.42163i | −0.902766 | − | 0.430132i | \(-0.858467\pi\) |
−0.130110 | − | 0.991500i | \(-0.541533\pi\) | |||||||
\(12\) | −5.33754 | + | 0.0196984i | −0.444795 | + | 0.00164154i | ||||
\(13\) | −1.03750 | + | 3.19309i | −0.0798076 | + | 0.245623i | −0.982998 | − | 0.183618i | \(-0.941219\pi\) |
0.903190 | + | 0.429241i | \(0.141219\pi\) | |||||||
\(14\) | −11.3936 | + | 11.4357i | −0.813827 | + | 0.816836i | ||||
\(15\) | −4.30924 | − | 1.40016i | −0.287283 | − | 0.0933438i | ||||
\(16\) | 12.8745 | − | 9.49985i | 0.804657 | − | 0.593741i | ||||
\(17\) | 16.9607 | + | 12.3227i | 0.997688 | + | 0.724863i | 0.961591 | − | 0.274485i | \(-0.0885074\pi\) |
0.0360971 | + | 0.999348i | \(0.488507\pi\) | |||||||
\(18\) | −6.53132 | + | 12.8771i | −0.362851 | + | 0.715396i | ||||
\(19\) | 17.3206 | − | 5.62780i | 0.911610 | − | 0.296200i | 0.184590 | − | 0.982816i | \(-0.440904\pi\) |
0.727021 | + | 0.686616i | \(0.240904\pi\) | |||||||
\(20\) | 12.9019 | − | 4.24478i | 0.645093 | − | 0.212239i | ||||
\(21\) | −3.32824 | − | 10.2433i | −0.158487 | − | 0.487774i | ||||
\(22\) | −27.2857 | + | 27.3865i | −1.24026 | + | 1.24484i | ||||
\(23\) | −5.79544 | + | 7.97674i | −0.251976 | + | 0.346815i | −0.916202 | − | 0.400717i | \(-0.868761\pi\) |
0.664226 | + | 0.747532i | \(0.268761\pi\) | |||||||
\(24\) | 1.72830 | + | 10.5343i | 0.0720127 | + | 0.438930i | ||||
\(25\) | −13.4702 | −0.538809 | ||||||||
\(26\) | 6.63409 | + | 1.03819i | 0.255157 | + | 0.0399304i | ||||
\(27\) | −12.7215 | − | 17.5096i | −0.471166 | − | 0.648504i | ||||
\(28\) | 26.1894 | + | 18.8804i | 0.935335 | + | 0.674301i | ||||
\(29\) | 11.5876 | + | 35.6630i | 0.399573 | + | 1.22976i | 0.925343 | + | 0.379132i | \(0.123777\pi\) |
−0.525770 | + | 0.850627i | \(0.676223\pi\) | |||||||
\(30\) | −1.40109 | + | 8.95304i | −0.0467031 | + | 0.298435i | ||||
\(31\) | 8.73751 | − | 29.7432i | 0.281855 | − | 0.959457i | ||||
\(32\) | −22.8352 | − | 22.4177i | −0.713601 | − | 0.700553i | ||||
\(33\) | −7.97056 | − | 24.5309i | −0.241532 | − | 0.743359i | ||||
\(34\) | 18.9665 | − | 37.3942i | 0.557837 | − | 1.09983i | ||||
\(35\) | 16.1093 | + | 22.1726i | 0.460266 | + | 0.633502i | ||||
\(36\) | 27.4969 | + | 8.82224i | 0.763804 | + | 0.245062i | ||||
\(37\) | −2.06373 | −0.0557766 | −0.0278883 | − | 0.999611i | \(-0.508878\pi\) | ||||
−0.0278883 | + | 0.999611i | \(0.508878\pi\) | |||||||
\(38\) | −16.5960 | − | 32.4234i | −0.436736 | − | 0.853246i | ||||
\(39\) | −2.63335 | + | 3.62449i | −0.0675217 | + | 0.0929357i | ||||
\(40\) | −12.4662 | − | 24.1350i | −0.311655 | − | 0.603376i | ||||
\(41\) | −15.8322 | − | 48.7264i | −0.386151 | − | 1.18845i | −0.935642 | − | 0.352950i | \(-0.885178\pi\) |
0.549491 | − | 0.835499i | \(-0.314822\pi\) | |||||||
\(42\) | −19.1749 | + | 9.81472i | −0.456546 | + | 0.233684i | ||||
\(43\) | 75.3810 | − | 24.4928i | 1.75305 | − | 0.569599i | 0.756604 | − | 0.653873i | \(-0.226857\pi\) |
0.996443 | + | 0.0842740i | \(0.0268571\pi\) | |||||||
\(44\) | 62.7191 | + | 45.2154i | 1.42543 | + | 1.02762i | ||||
\(45\) | 19.8321 | + | 14.4089i | 0.440713 | + | 0.320197i | ||||
\(46\) | 17.5868 | + | 8.92007i | 0.382321 | + | 0.193915i | ||||
\(47\) | −19.5843 | − | 6.36333i | −0.416688 | − | 0.135390i | 0.0931671 | − | 0.995650i | \(-0.470301\pi\) |
−0.509855 | + | 0.860260i | \(0.670301\pi\) | |||||||
\(48\) | 20.2561 | − | 6.74730i | 0.422002 | − | 0.140569i | ||||
\(49\) | −4.98975 | + | 15.3569i | −0.101832 | + | 0.313406i | ||||
\(50\) | 4.26351 | + | 26.6010i | 0.0852702 | + | 0.532019i | ||||
\(51\) | 16.4433 | + | 22.6323i | 0.322418 | + | 0.443770i | ||||
\(52\) | −0.0495625 | − | 13.4296i | −0.000953124 | − | 0.258261i | ||||
\(53\) | −43.2730 | − | 31.4397i | −0.816472 | − | 0.593202i | 0.0992274 | − | 0.995065i | \(-0.468363\pi\) |
−0.915700 | + | 0.401863i | \(0.868363\pi\) | |||||||
\(54\) | −30.5514 | + | 30.6643i | −0.565766 | + | 0.567858i | ||||
\(55\) | 38.5790 | + | 53.0995i | 0.701437 | + | 0.965445i | ||||
\(56\) | 28.9957 | − | 57.6946i | 0.517780 | − | 1.03026i | ||||
\(57\) | 24.3019 | 0.426349 | ||||||||
\(58\) | 66.7595 | − | 34.1710i | 1.15103 | − | 0.589155i | ||||
\(59\) | −83.3220 | − | 27.0730i | −1.41224 | − | 0.458864i | −0.499110 | − | 0.866539i | \(-0.666340\pi\) |
−0.913127 | + | 0.407675i | \(0.866340\pi\) | |||||||
\(60\) | 18.1239 | − | 0.0668870i | 0.302065 | − | 0.00111478i | ||||
\(61\) | 59.1013 | 0.968873 | 0.484437 | − | 0.874826i | \(-0.339025\pi\) | ||||
0.484437 | + | 0.874826i | \(0.339025\pi\) | |||||||
\(62\) | −61.5022 | − | 7.84068i | −0.991971 | − | 0.126463i | ||||
\(63\) | 58.2705i | 0.924928i | ||||||||
\(64\) | −37.0427 | + | 52.1904i | −0.578792 | + | 0.815475i | ||||
\(65\) | 3.52288 | − | 10.8423i | 0.0541982 | − | 0.166805i | ||||
\(66\) | −45.9206 | + | 23.5046i | −0.695767 | + | 0.356130i | ||||
\(67\) | − | 53.1994i | − | 0.794021i | −0.917814 | − | 0.397011i | \(-0.870048\pi\) | ||
0.917814 | − | 0.397011i | \(-0.129952\pi\) | |||||||
\(68\) | −79.8491 | − | 25.6191i | −1.17425 | − | 0.376752i | ||||
\(69\) | −10.6441 | + | 7.73340i | −0.154263 | + | 0.112078i | ||||
\(70\) | 38.6875 | − | 38.8305i | 0.552678 | − | 0.554722i | ||||
\(71\) | −55.3694 | + | 76.2095i | −0.779851 | + | 1.07337i | 0.215447 | + | 0.976515i | \(0.430879\pi\) |
−0.995298 | + | 0.0968572i | \(0.969121\pi\) | |||||||
\(72\) | 8.71897 | − | 57.0932i | 0.121097 | − | 0.792961i | ||||
\(73\) | 33.5930 | − | 24.4068i | 0.460179 | − | 0.334339i | −0.333423 | − | 0.942777i | \(-0.608204\pi\) |
0.793601 | + | 0.608438i | \(0.208204\pi\) | |||||||
\(74\) | 0.653200 | + | 4.07545i | 0.00882702 | + | 0.0550737i | ||||
\(75\) | −17.0949 | − | 5.55445i | −0.227931 | − | 0.0740594i | ||||
\(76\) | −58.7767 | + | 43.0361i | −0.773377 | + | 0.566264i | ||||
\(77\) | −48.2117 | + | 148.380i | −0.626126 | + | 1.92702i | ||||
\(78\) | 7.99112 | + | 4.05312i | 0.102450 | + | 0.0519631i | ||||
\(79\) | −57.0857 | + | 78.5717i | −0.722604 | + | 0.994579i | 0.276830 | + | 0.960919i | \(0.410716\pi\) |
−0.999433 | + | 0.0336598i | \(0.989284\pi\) | |||||||
\(80\) | −43.7160 | + | 32.2572i | −0.546451 | + | 0.403215i | ||||
\(81\) | 11.1537 | + | 34.3276i | 0.137700 | + | 0.423797i | ||||
\(82\) | −91.2137 | + | 46.6879i | −1.11236 | + | 0.569365i | ||||
\(83\) | 9.23141 | − | 2.99947i | 0.111222 | − | 0.0361381i | −0.252877 | − | 0.967498i | \(-0.581377\pi\) |
0.364099 | + | 0.931360i | \(0.381377\pi\) | |||||||
\(84\) | 25.4512 | + | 34.7601i | 0.302990 | + | 0.413810i | ||||
\(85\) | −57.5909 | − | 41.8423i | −0.677541 | − | 0.492262i | ||||
\(86\) | −72.2273 | − | 141.110i | −0.839853 | − | 1.64081i | ||||
\(87\) | 50.0375i | 0.575144i | ||||||||
\(88\) | 69.4397 | − | 138.169i | 0.789088 | − | 1.57010i | ||||
\(89\) | 47.7459 | − | 34.6894i | 0.536471 | − | 0.389769i | −0.286302 | − | 0.958140i | \(-0.592426\pi\) |
0.822773 | + | 0.568370i | \(0.192426\pi\) | |||||||
\(90\) | 22.1774 | − | 43.7249i | 0.246416 | − | 0.485833i | ||||
\(91\) | 25.7727 | − | 8.37405i | 0.283216 | − | 0.0920225i | ||||
\(92\) | 12.0489 | − | 37.5536i | 0.130966 | − | 0.408191i | ||||
\(93\) | 23.3532 | − | 34.1437i | 0.251110 | − | 0.367136i | ||||
\(94\) | −6.36758 | + | 40.6891i | −0.0677402 | + | 0.432863i | ||||
\(95\) | −58.8130 | + | 19.1095i | −0.619084 | + | 0.201153i | ||||
\(96\) | −19.7359 | − | 37.8660i | −0.205582 | − | 0.394438i | ||||
\(97\) | −35.2198 | + | 25.5887i | −0.363091 | + | 0.263801i | −0.754340 | − | 0.656484i | \(-0.772043\pi\) |
0.391249 | + | 0.920285i | \(0.372043\pi\) | |||||||
\(98\) | 31.9060 | + | 4.99308i | 0.325572 | + | 0.0509498i | ||||
\(99\) | 139.548i | 1.40957i | ||||||||
\(100\) | 51.1820 | − | 16.8391i | 0.511820 | − | 0.168391i | ||||
\(101\) | 0.937819 | + | 0.681365i | 0.00928534 | + | 0.00674619i | 0.592418 | − | 0.805631i | \(-0.298173\pi\) |
−0.583133 | + | 0.812377i | \(0.698173\pi\) | |||||||
\(102\) | 39.4896 | − | 39.6356i | 0.387153 | − | 0.388584i | ||||
\(103\) | 17.5722 | − | 5.70954i | 0.170604 | − | 0.0554325i | −0.222470 | − | 0.974940i | \(-0.571412\pi\) |
0.393073 | + | 0.919507i | \(0.371412\pi\) | |||||||
\(104\) | −26.5050 | + | 4.34852i | −0.254856 | + | 0.0418127i | ||||
\(105\) | 11.3012 | + | 34.7815i | 0.107630 | + | 0.331253i | ||||
\(106\) | −48.3905 | + | 95.4065i | −0.456514 | + | 0.900061i | ||||
\(107\) | 70.2069 | − | 96.6314i | 0.656139 | − | 0.903098i | −0.343207 | − | 0.939260i | \(-0.611513\pi\) |
0.999346 | + | 0.0361621i | \(0.0115133\pi\) | |||||||
\(108\) | 70.2257 | + | 50.6271i | 0.650238 | + | 0.468769i | ||||
\(109\) | 51.1725 | − | 157.493i | 0.469473 | − | 1.44489i | −0.383796 | − | 0.923418i | \(-0.625383\pi\) |
0.853269 | − | 0.521471i | \(-0.174617\pi\) | |||||||
\(110\) | 92.6499 | − | 92.9924i | 0.842271 | − | 0.845386i | ||||
\(111\) | −2.61905 | − | 0.850982i | −0.0235951 | − | 0.00766650i | ||||
\(112\) | −123.113 | − | 38.9995i | −1.09922 | − | 0.348210i | ||||
\(113\) | −44.8104 | + | 32.5567i | −0.396552 | + | 0.288112i | −0.768135 | − | 0.640288i | \(-0.778815\pi\) |
0.371583 | + | 0.928400i | \(0.378815\pi\) | |||||||
\(114\) | −7.69189 | − | 47.9913i | −0.0674727 | − | 0.420977i | ||||
\(115\) | 19.6787 | − | 27.0854i | 0.171119 | − | 0.235526i | ||||
\(116\) | −88.6110 | − | 121.021i | −0.763888 | − | 1.04328i | ||||
\(117\) | 19.6094 | − | 14.2470i | 0.167601 | − | 0.121770i | ||||
\(118\) | −27.0910 | + | 173.113i | −0.229585 | + | 1.46706i | ||||
\(119\) | − | 169.213i | − | 1.42196i | ||||||
\(120\) | −5.86855 | − | 35.7698i | −0.0489045 | − | 0.298082i | ||||
\(121\) | −78.0677 | + | 240.268i | −0.645188 | + | 1.98568i | ||||
\(122\) | −18.7063 | − | 116.713i | −0.153331 | − | 0.956663i | ||||
\(123\) | − | 68.3664i | − | 0.555824i | ||||||
\(124\) | 3.98254 | + | 123.936i | 0.0321173 | + | 0.999484i | ||||
\(125\) | 130.628 | 1.04502 | ||||||||
\(126\) | 115.072 | − | 18.4434i | 0.913272 | − | 0.146376i | ||||
\(127\) | −29.0431 | − | 9.43669i | −0.228686 | − | 0.0743047i | 0.192432 | − | 0.981310i | \(-0.438362\pi\) |
−0.421119 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(128\) | 114.790 | + | 56.6328i | 0.896796 | + | 0.442444i | ||||
\(129\) | 105.764 | 0.819879 | ||||||||
\(130\) | −22.5264 | − | 3.52523i | −0.173280 | − | 0.0271172i | ||||
\(131\) | −10.7868 | − | 14.8467i | −0.0823417 | − | 0.113334i | 0.765859 | − | 0.643008i | \(-0.222314\pi\) |
−0.848201 | + | 0.529675i | \(0.822314\pi\) | |||||||
\(132\) | 60.9512 | + | 83.2444i | 0.461752 | + | 0.630639i | ||||
\(133\) | −118.922 | − | 86.4018i | −0.894150 | − | 0.649638i | ||||
\(134\) | −105.058 | + | 16.8383i | −0.784015 | + | 0.125659i | ||||
\(135\) | 43.1964 | + | 59.4548i | 0.319973 | + | 0.440406i | ||||
\(136\) | −25.3193 | + | 165.794i | −0.186171 | + | 1.21908i | ||||
\(137\) | 3.04768 | − | 9.37980i | 0.0222458 | − | 0.0684657i | −0.939317 | − | 0.343050i | \(-0.888540\pi\) |
0.961563 | + | 0.274584i | \(0.0885401\pi\) | |||||||
\(138\) | 18.6409 | + | 18.5722i | 0.135079 | + | 0.134581i | ||||
\(139\) | 151.000 | + | 49.0629i | 1.08633 | + | 0.352971i | 0.796828 | − | 0.604206i | \(-0.206510\pi\) |
0.289504 | + | 0.957177i | \(0.406510\pi\) | |||||||
\(140\) | −88.9274 | − | 64.1095i | −0.635196 | − | 0.457925i | ||||
\(141\) | −22.2302 | − | 16.1512i | −0.157661 | − | 0.114548i | ||||
\(142\) | 168.023 | + | 85.2220i | 1.18326 | + | 0.600155i | ||||
\(143\) | 61.7211 | − | 20.0544i | 0.431616 | − | 0.140241i | ||||
\(144\) | −115.507 | + | 0.852580i | −0.802133 | + | 0.00592070i | ||||
\(145\) | −39.3463 | − | 121.096i | −0.271354 | − | 0.835142i | ||||
\(146\) | −58.8310 | − | 58.6143i | −0.402952 | − | 0.401468i | ||||
\(147\) | −12.6648 | + | 17.4316i | −0.0861553 | + | 0.118583i | ||||
\(148\) | 7.84144 | − | 2.57987i | 0.0529827 | − | 0.0174316i | ||||
\(149\) | −162.013 | −1.08734 | −0.543669 | − | 0.839300i | \(-0.682965\pi\) | ||||
−0.543669 | + | 0.839300i | \(0.682965\pi\) | |||||||
\(150\) | −5.55816 | + | 35.5169i | −0.0370544 | + | 0.236779i | ||||
\(151\) | −12.4297 | − | 17.1080i | −0.0823158 | − | 0.113298i | 0.765873 | − | 0.642991i | \(-0.222307\pi\) |
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(152\) | 103.591 | + | 102.450i | 0.681520 | + | 0.674016i | ||||
\(153\) | −46.7702 | − | 143.944i | −0.305688 | − | 0.940810i | ||||
\(154\) | 308.281 | + | 48.2439i | 2.00182 | + | 0.313272i | ||||
\(155\) | −29.6687 | + | 100.994i | −0.191411 | + | 0.651577i | ||||
\(156\) | 5.47479 | − | 17.0637i | 0.0350948 | − | 0.109383i | ||||
\(157\) | −43.9915 | − | 135.392i | −0.280201 | − | 0.862369i | −0.987796 | − | 0.155751i | \(-0.950220\pi\) |
0.707596 | − | 0.706618i | \(-0.249780\pi\) | |||||||
\(158\) | 173.232 | + | 87.8636i | 1.09640 | + | 0.556099i | ||||
\(159\) | −41.9530 | − | 57.7433i | −0.263855 | − | 0.363165i | ||||
\(160\) | 77.5382 | + | 76.1204i | 0.484614 | + | 0.475753i | ||||
\(161\) | 79.5821 | 0.494299 | ||||||||
\(162\) | 64.2597 | − | 32.8914i | 0.396665 | − | 0.203034i | ||||
\(163\) | 94.6893 | − | 130.329i | 0.580916 | − | 0.799562i | −0.412879 | − | 0.910786i | \(-0.635477\pi\) |
0.993795 | + | 0.111223i | \(0.0354769\pi\) | |||||||
\(164\) | 121.069 | + | 165.351i | 0.738228 | + | 1.00824i | ||||
\(165\) | 27.0644 | + | 83.2958i | 0.164027 | + | 0.504823i | ||||
\(166\) | −8.84520 | − | 17.2808i | −0.0532843 | − | 0.104101i | ||||
\(167\) | −87.1507 | + | 28.3170i | −0.521860 | + | 0.169563i | −0.558089 | − | 0.829781i | \(-0.688465\pi\) |
0.0362290 | + | 0.999344i | \(0.488465\pi\) | |||||||
\(168\) | 60.5884 | − | 61.2629i | 0.360645 | − | 0.364660i | ||||
\(169\) | 127.604 | + | 92.7100i | 0.755056 | + | 0.548580i | ||||
\(170\) | −64.4016 | + | 126.974i | −0.378833 | + | 0.746906i | ||||
\(171\) | −125.044 | − | 40.6293i | −0.731252 | − | 0.237598i | ||||
\(172\) | −255.802 | + | 187.297i | −1.48722 | + | 1.08894i | ||||
\(173\) | −59.8985 | + | 184.349i | −0.346234 | + | 1.06560i | 0.614686 | + | 0.788772i | \(0.289283\pi\) |
−0.960920 | + | 0.276827i | \(0.910717\pi\) | |||||||
\(174\) | 98.8138 | − | 15.8375i | 0.567896 | − | 0.0910204i | ||||
\(175\) | 63.9060 | + | 87.9590i | 0.365177 | + | 0.502623i | ||||
\(176\) | −294.834 | − | 93.3970i | −1.67519 | − | 0.530665i | ||||
\(177\) | −94.5791 | − | 68.7157i | −0.534345 | − | 0.388224i | ||||
\(178\) | −83.6168 | − | 83.3088i | −0.469757 | − | 0.468027i | ||||
\(179\) | 15.6768 | + | 21.5773i | 0.0875800 | + | 0.120544i | 0.850559 | − | 0.525880i | \(-0.176264\pi\) |
−0.762979 | + | 0.646424i | \(0.776264\pi\) | |||||||
\(180\) | −93.3673 | − | 29.9564i | −0.518707 | − | 0.166424i | ||||
\(181\) | 324.182 | 1.79106 | 0.895529 | − | 0.445002i | \(-0.146797\pi\) | ||||
0.895529 | + | 0.445002i | \(0.146797\pi\) | |||||||
\(182\) | −24.6944 | − | 48.2453i | −0.135684 | − | 0.265084i | ||||
\(183\) | 75.0045 | + | 24.3704i | 0.409861 | + | 0.133172i | ||||
\(184\) | −77.9743 | − | 11.9078i | −0.423774 | − | 0.0647165i | ||||
\(185\) | 7.00752 | 0.0378785 | ||||||||
\(186\) | −74.8184 | − | 35.3110i | −0.402249 | − | 0.189844i | ||||
\(187\) | − | 405.236i | − | 2.16704i | ||||||
\(188\) | 82.3681 | − | 0.303983i | 0.438128 | − | 0.00161693i | ||||
\(189\) | −53.9820 | + | 166.139i | −0.285619 | + | 0.879045i | ||||
\(190\) | 56.3525 | + | 110.095i | 0.296592 | + | 0.579449i | ||||
\(191\) | 59.5868i | 0.311973i | 0.987759 | + | 0.155987i | \(0.0498556\pi\) | ||||
−0.987759 | + | 0.155987i | \(0.950144\pi\) | |||||||
\(192\) | −68.5311 | + | 50.9594i | −0.356933 | + | 0.265414i | ||||
\(193\) | −30.2314 | + | 21.9644i | −0.156640 | + | 0.113805i | −0.663344 | − | 0.748314i | \(-0.730863\pi\) |
0.506705 | + | 0.862120i | \(0.330863\pi\) | |||||||
\(194\) | 61.6800 | + | 61.4528i | 0.317938 | + | 0.316767i | ||||
\(195\) | 8.94167 | − | 12.3071i | 0.0458547 | − | 0.0631136i | ||||
\(196\) | −0.238366 | − | 64.5882i | −0.00121615 | − | 0.329532i | ||||
\(197\) | 116.581 | − | 84.7013i | 0.591783 | − | 0.429956i | −0.251170 | − | 0.967943i | \(-0.580815\pi\) |
0.842953 | + | 0.537987i | \(0.180815\pi\) | |||||||
\(198\) | 275.578 | − | 44.1687i | 1.39181 | − | 0.223074i | ||||
\(199\) | −231.474 | − | 75.2104i | −1.16319 | − | 0.377942i | −0.337090 | − | 0.941472i | \(-0.609443\pi\) |
−0.826095 | + | 0.563531i | \(0.809443\pi\) | |||||||
\(200\) | −49.4536 | − | 95.7442i | −0.247268 | − | 0.478721i | ||||
\(201\) | 21.9368 | − | 67.5145i | 0.109138 | − | 0.335893i | ||||
\(202\) | 1.04873 | − | 2.06766i | 0.00519171 | − | 0.0102360i | ||||
\(203\) | 177.901 | − | 244.859i | 0.876359 | − | 1.20620i | ||||
\(204\) | −90.7712 | − | 65.4387i | −0.444957 | − | 0.320778i | ||||
\(205\) | 53.7590 | + | 165.453i | 0.262239 | + | 0.807088i | ||||
\(206\) | −16.8370 | − | 32.8943i | −0.0817331 | − | 0.159681i | ||||
\(207\) | 67.6978 | − | 21.9964i | 0.327043 | − | 0.106263i | ||||
\(208\) | 16.9766 | + | 50.9656i | 0.0816184 | + | 0.245027i | ||||
\(209\) | −284.798 | − | 206.918i | −1.36267 | − | 0.990036i | ||||
\(210\) | 65.1094 | − | 33.3264i | 0.310045 | − | 0.158697i | ||||
\(211\) | − | 290.791i | − | 1.37816i | −0.724687 | − | 0.689078i | \(-0.758016\pi\) | ||
0.724687 | − | 0.689078i | \(-0.241984\pi\) | |||||||
\(212\) | 203.725 | + | 65.3639i | 0.960965 | + | 0.308320i | ||||
\(213\) | −101.693 | + | 73.8846i | −0.477434 | + | 0.346876i | ||||
\(214\) | −213.049 | − | 108.059i | −0.995555 | − | 0.504949i | ||||
\(215\) | −255.960 | + | 83.1665i | −1.19051 | + | 0.386821i | ||||
\(216\) | 77.7507 | − | 154.706i | 0.359957 | − | 0.716230i | ||||
\(217\) | −235.672 | + | 84.0538i | −1.08605 | + | 0.387345i | ||||
\(218\) | −327.213 | − | 51.2067i | −1.50098 | − | 0.234893i | ||||
\(219\) | 52.6965 | − | 17.1221i | 0.240623 | − | 0.0781833i | ||||
\(220\) | −212.966 | − | 153.531i | −0.968027 | − | 0.697869i | ||||
\(221\) | −56.9442 | + | 41.3724i | −0.257666 | + | 0.187205i | ||||
\(222\) | −0.851550 | + | 5.44144i | −0.00383581 | + | 0.0245110i | ||||
\(223\) | − | 8.78854i | − | 0.0394105i | −0.999806 | − | 0.0197052i | \(-0.993727\pi\) | ||
0.999806 | − | 0.0197052i | \(-0.00627278\pi\) | |||||||
\(224\) | −38.0492 | + | 255.466i | −0.169862 | + | 1.14047i | ||||
\(225\) | 78.6744 | + | 57.1603i | 0.349664 | + | 0.254046i | ||||
\(226\) | 78.4759 | + | 78.1868i | 0.347238 | + | 0.345959i | ||||
\(227\) | −122.718 | + | 39.8736i | −0.540609 | + | 0.175654i | −0.566578 | − | 0.824008i | \(-0.691733\pi\) |
0.0259689 | + | 0.999663i | \(0.491733\pi\) | |||||||
\(228\) | −92.3385 | + | 30.3798i | −0.404993 | + | 0.133245i | ||||
\(229\) | 33.7541 | + | 103.884i | 0.147398 | + | 0.453644i | 0.997312 | − | 0.0732780i | \(-0.0233460\pi\) |
−0.849914 | + | 0.526922i | \(0.823346\pi\) | |||||||
\(230\) | −59.7168 | − | 30.2886i | −0.259638 | − | 0.131689i | ||||
\(231\) | −122.369 | + | 168.427i | −0.529738 | + | 0.729121i | ||||
\(232\) | −210.945 | + | 213.293i | −0.909245 | + | 0.919368i | ||||
\(233\) | 125.302 | − | 385.640i | 0.537776 | − | 1.65511i | −0.199796 | − | 0.979837i | \(-0.564028\pi\) |
0.737573 | − | 0.675268i | \(-0.235972\pi\) | |||||||
\(234\) | −34.3416 | − | 34.2151i | −0.146759 | − | 0.146218i | ||||
\(235\) | 66.4996 | + | 21.6070i | 0.282977 | + | 0.0919448i | ||||
\(236\) | 350.437 | − | 1.29330i | 1.48490 | − | 0.00548010i | ||||
\(237\) | −104.846 | + | 76.1748i | −0.442387 | + | 0.321413i | ||||
\(238\) | −334.161 | + | 53.5582i | −1.40404 | + | 0.225035i | ||||
\(239\) | −107.352 | + | 147.757i | −0.449170 | + | 0.618229i | −0.972219 | − | 0.234073i | \(-0.924794\pi\) |
0.523049 | + | 0.852302i | \(0.324794\pi\) | |||||||
\(240\) | −68.7806 | + | 22.9108i | −0.286586 | + | 0.0954617i | ||||
\(241\) | −221.566 | + | 160.977i | −0.919360 | + | 0.667954i | −0.943365 | − | 0.331757i | \(-0.892358\pi\) |
0.0240043 | + | 0.999712i | \(0.492358\pi\) | |||||||
\(242\) | 499.189 | + | 78.1198i | 2.06276 | + | 0.322809i | ||||
\(243\) | 242.951i | 0.999800i | ||||||||
\(244\) | −224.563 | + | 73.8824i | −0.920342 | + | 0.302797i | ||||
\(245\) | 16.9430 | − | 52.1451i | 0.0691549 | − | 0.212837i | ||||
\(246\) | −135.010 | + | 21.6389i | −0.548820 | + | 0.0879629i | ||||
\(247\) | 61.1451i | 0.247551i | ||||||||
\(248\) | 243.488 | − | 47.0921i | 0.981806 | − | 0.189888i | ||||
\(249\) | 12.9523 | 0.0520171 | ||||||||
\(250\) | −41.3454 | − | 257.963i | −0.165382 | − | 1.03185i | ||||
\(251\) | −23.9280 | − | 7.77469i | −0.0953309 | − | 0.0309749i | 0.260963 | − | 0.965349i | \(-0.415960\pi\) |
−0.356294 | + | 0.934374i | \(0.615960\pi\) | |||||||
\(252\) | −72.8438 | − | 221.407i | −0.289063 | − | 0.878598i | ||||
\(253\) | 190.586 | 0.753303 | ||||||||
\(254\) | −9.44299 | + | 60.3411i | −0.0371771 | + | 0.237564i | ||||
\(255\) | −55.8341 | − | 76.8490i | −0.218957 | − | 0.301369i | ||||
\(256\) | 75.5057 | − | 244.612i | 0.294944 | − | 0.955514i | ||||
\(257\) | 375.690 | + | 272.955i | 1.46183 | + | 1.06208i | 0.982882 | + | 0.184237i | \(0.0589812\pi\) |
0.478947 | + | 0.877844i | \(0.341019\pi\) | |||||||
\(258\) | −33.4759 | − | 208.863i | −0.129751 | − | 0.809547i | ||||
\(259\) | 9.79085 | + | 13.4759i | 0.0378025 | + | 0.0520307i | ||||
\(260\) | 0.168292 | + | 45.6008i | 0.000647277 | + | 0.175388i | ||||
\(261\) | 83.6555 | − | 257.465i | 0.320519 | − | 0.986456i | ||||
\(262\) | −25.9051 | + | 26.0008i | −0.0988743 | + | 0.0992399i | ||||
\(263\) | 308.301 | + | 100.173i | 1.17225 | + | 0.380886i | 0.829481 | − | 0.558535i | \(-0.188636\pi\) |
0.342765 | + | 0.939421i | \(0.388636\pi\) | |||||||
\(264\) | 145.099 | − | 146.714i | 0.549617 | − | 0.555736i | ||||
\(265\) | 146.936 | + | 106.755i | 0.554475 | + | 0.402850i | ||||
\(266\) | −132.986 | + | 262.194i | −0.499946 | + | 0.985691i | ||||
\(267\) | 74.8978 | − | 24.3358i | 0.280516 | − | 0.0911452i | ||||
\(268\) | 66.5045 | + | 202.139i | 0.248151 | + | 0.754248i | ||||
\(269\) | −106.144 | − | 326.678i | −0.394588 | − | 1.21442i | −0.929282 | − | 0.369371i | \(-0.879573\pi\) |
0.534694 | − | 0.845046i | \(-0.320427\pi\) | |||||||
\(270\) | 103.739 | − | 104.122i | 0.384218 | − | 0.385638i | ||||
\(271\) | −177.854 | + | 244.795i | −0.656287 | + | 0.903302i | −0.999351 | − | 0.0360102i | \(-0.988535\pi\) |
0.343064 | + | 0.939312i | \(0.388535\pi\) | |||||||
\(272\) | 335.424 | − | 2.47583i | 1.23318 | − | 0.00910231i | ||||
\(273\) | 36.1607 | 0.132457 | ||||||||
\(274\) | −19.4878 | − | 3.04972i | −0.0711234 | − | 0.0111303i | ||||
\(275\) | 153.044 | + | 210.647i | 0.556523 | + | 0.765988i | ||||
\(276\) | 30.7763 | − | 42.6903i | 0.111508 | − | 0.154675i | ||||
\(277\) | −31.0948 | − | 95.6999i | −0.112255 | − | 0.345487i | 0.879109 | − | 0.476620i | \(-0.158138\pi\) |
−0.991365 | + | 0.131133i | \(0.958138\pi\) | |||||||
\(278\) | 49.0957 | − | 313.724i | 0.176603 | − | 1.12850i | ||||
\(279\) | −177.246 | + | 136.641i | −0.635291 | + | 0.489753i | ||||
\(280\) | −98.4564 | + | 195.905i | −0.351630 | + | 0.699661i | ||||
\(281\) | −8.35541 | − | 25.7153i | −0.0297346 | − | 0.0915135i | 0.935088 | − | 0.354416i | \(-0.115320\pi\) |
−0.964822 | + | 0.262902i | \(0.915320\pi\) | |||||||
\(282\) | −24.8592 | + | 49.0123i | −0.0881531 | + | 0.173802i | ||||
\(283\) | 27.7630 | + | 38.2125i | 0.0981024 | + | 0.135026i | 0.855246 | − | 0.518222i | \(-0.173406\pi\) |
−0.757144 | + | 0.653248i | \(0.773406\pi\) | |||||||
\(284\) | 115.114 | − | 358.786i | 0.405332 | − | 1.26333i | ||||
\(285\) | −82.5184 | −0.289538 | ||||||||
\(286\) | −59.1389 | − | 115.539i | −0.206780 | − | 0.403983i | ||||
\(287\) | −243.066 | + | 334.552i | −0.846921 | + | 1.16569i | ||||
\(288\) | 38.2432 | + | 227.833i | 0.132789 | + | 0.791087i | ||||
\(289\) | 46.5113 | + | 143.147i | 0.160939 | + | 0.495318i | ||||
\(290\) | −226.685 | + | 116.029i | −0.781674 | + | 0.400101i | ||||
\(291\) | −55.2484 | + | 17.9513i | −0.189857 | + | 0.0616883i | ||||
\(292\) | −97.1305 | + | 134.732i | −0.332639 | + | 0.461409i | ||||
\(293\) | 370.466 | + | 269.159i | 1.26439 | + | 0.918633i | 0.998964 | − | 0.0454989i | \(-0.0144877\pi\) |
0.265425 | + | 0.964132i | \(0.414488\pi\) | |||||||
\(294\) | 38.4325 | + | 19.4931i | 0.130723 | + | 0.0663031i | ||||
\(295\) | 282.924 | + | 91.9276i | 0.959065 | + | 0.311619i | ||||
\(296\) | −7.57664 | − | 14.6687i | −0.0255968 | − | 0.0495564i | ||||
\(297\) | −129.278 | + | 397.876i | −0.435278 | + | 1.33965i | ||||
\(298\) | 51.2794 | + | 319.943i | 0.172078 | + | 1.07363i | ||||
\(299\) | −19.4577 | − | 26.7812i | −0.0650760 | − | 0.0895694i | ||||
\(300\) | 71.8979 | − | 0.265342i | 0.239660 | − | 0.000884475i | ||||
\(301\) | −517.560 | − | 376.030i | −1.71947 | − | 1.24927i | ||||
\(302\) | −29.8506 | + | 29.9610i | −0.0988431 | + | 0.0992086i | ||||
\(303\) | 0.909210 | + | 1.25142i | 0.00300069 | + | 0.00413010i | ||||
\(304\) | 169.531 | − | 236.998i | 0.557667 | − | 0.779599i | ||||
\(305\) | −200.681 | −0.657972 | ||||||||
\(306\) | −269.456 | + | 137.922i | −0.880576 | + | 0.450725i | ||||
\(307\) | 168.115 | + | 54.6239i | 0.547606 | + | 0.177928i | 0.569737 | − | 0.821827i | \(-0.307045\pi\) |
−0.0221311 | + | 0.999755i | \(0.507045\pi\) | |||||||
\(308\) | −2.30313 | − | 624.061i | −0.00747768 | − | 2.02617i | ||||
\(309\) | 24.6549 | 0.0797893 | ||||||||
\(310\) | 208.834 | + | 26.6234i | 0.673658 | + | 0.0858820i | ||||
\(311\) | 601.514i | 1.93413i | 0.254531 | + | 0.967065i | \(0.418079\pi\) | ||||
−0.254531 | + | 0.967065i | \(0.581921\pi\) | |||||||
\(312\) | −35.4302 | − | 5.41071i | −0.113558 | − | 0.0173420i | ||||
\(313\) | 107.138 | − | 329.735i | 0.342292 | − | 1.05347i | −0.620725 | − | 0.784028i | \(-0.713162\pi\) |
0.963017 | − | 0.269439i | \(-0.0868383\pi\) | |||||||
\(314\) | −253.448 | + | 129.728i | −0.807158 | + | 0.413145i | ||||
\(315\) | − | 197.860i | − | 0.628128i | ||||||
\(316\) | 118.683 | − | 369.907i | 0.375578 | − | 1.17059i | ||||
\(317\) | 363.102 | − | 263.809i | 1.14543 | − | 0.832206i | 0.157566 | − | 0.987508i | \(-0.449635\pi\) |
0.987867 | + | 0.155302i | \(0.0496352\pi\) | |||||||
\(318\) | −100.753 | + | 101.125i | −0.316832 | + | 0.318003i | ||||
\(319\) | 426.042 | − | 586.396i | 1.33555 | − | 1.83823i | ||||
\(320\) | 125.780 | − | 177.215i | 0.393064 | − | 0.553798i | ||||
\(321\) | 128.944 | − | 93.6836i | 0.401696 | − | 0.291849i | ||||
\(322\) | −25.1888 | − | 157.158i | −0.0782261 | − | 0.488070i | ||||
\(323\) | 363.119 | + | 117.985i | 1.12421 | + | 0.365277i | ||||
\(324\) | −85.2929 | − | 116.489i | −0.263250 | − | 0.359534i | ||||
\(325\) | 13.9753 | − | 43.0117i | 0.0430011 | − | 0.132344i | ||||
\(326\) | −287.343 | − | 145.741i | −0.881420 | − | 0.447059i | ||||
\(327\) | 129.885 | − | 178.771i | 0.397200 | − | 0.546699i | ||||
\(328\) | 288.214 | − | 291.423i | 0.878703 | − | 0.888486i | ||||
\(329\) | 51.3609 | + | 158.073i | 0.156112 | + | 0.480464i | ||||
\(330\) | 155.926 | − | 79.8110i | 0.472503 | − | 0.241852i | ||||
\(331\) | −156.879 | + | 50.9731i | −0.473955 | + | 0.153997i | −0.536248 | − | 0.844061i | \(-0.680159\pi\) |
0.0622928 | + | 0.998058i | \(0.480159\pi\) | |||||||
\(332\) | −31.3264 | + | 22.9371i | −0.0943566 | + | 0.0690875i | ||||
\(333\) | 12.0535 | + | 8.75736i | 0.0361966 | + | 0.0262984i | ||||
\(334\) | 83.5046 | + | 163.142i | 0.250014 | + | 0.488450i | ||||
\(335\) | 180.641i | 0.539228i | ||||||||
\(336\) | −140.159 | − | 100.259i | −0.417139 | − | 0.298390i | ||||
\(337\) | 45.0078 | − | 32.7001i | 0.133554 | − | 0.0970330i | −0.519002 | − | 0.854773i | \(-0.673696\pi\) |
0.652557 | + | 0.757740i | \(0.273696\pi\) | |||||||
\(338\) | 142.695 | − | 281.337i | 0.422174 | − | 0.832357i | ||||
\(339\) | −70.2929 | + | 22.8396i | −0.207354 | + | 0.0673733i | ||||
\(340\) | 271.132 | + | 86.9911i | 0.797446 | + | 0.255856i | ||||
\(341\) | −564.395 | + | 201.294i | −1.65512 | + | 0.590306i | ||||
\(342\) | −40.6564 | + | 259.796i | −0.118878 | + | 0.759639i | ||||
\(343\) | −252.189 | + | 81.9413i | −0.735246 | + | 0.238896i | ||||
\(344\) | 450.839 | + | 445.875i | 1.31058 | + | 1.29615i | ||||
\(345\) | 36.1426 | − | 26.2592i | 0.104761 | − | 0.0761135i | ||||
\(346\) | 383.009 | + | 59.9385i | 1.10696 | + | 0.173233i | ||||
\(347\) | − | 300.110i | − | 0.864872i | −0.901665 | − | 0.432436i | \(-0.857654\pi\) | ||
0.901665 | − | 0.432436i | \(-0.142346\pi\) | |||||||
\(348\) | −62.5518 | − | 190.124i | −0.179747 | − | 0.546334i | ||||
\(349\) | −99.8351 | − | 72.5345i | −0.286060 | − | 0.207835i | 0.435496 | − | 0.900191i | \(-0.356573\pi\) |
−0.721557 | + | 0.692356i | \(0.756573\pi\) | |||||||
\(350\) | 153.474 | − | 154.041i | 0.438497 | − | 0.440118i | ||||
\(351\) | 69.1083 | − | 22.4547i | 0.196890 | − | 0.0639734i | ||||
\(352\) | −91.1213 | + | 611.798i | −0.258867 | + | 1.73806i | ||||
\(353\) | 68.8064 | + | 211.764i | 0.194919 | + | 0.599899i | 0.999978 | + | 0.00670372i | \(0.00213388\pi\) |
−0.805058 | + | 0.593195i | \(0.797866\pi\) | |||||||
\(354\) | −105.764 | + | 208.524i | −0.298768 | + | 0.589050i | ||||
\(355\) | 188.010 | − | 258.773i | 0.529605 | − | 0.728939i | ||||
\(356\) | −138.052 | + | 191.494i | −0.387787 | + | 0.537906i | ||||
\(357\) | 69.7751 | − | 214.746i | 0.195448 | − | 0.601529i | ||||
\(358\) | 37.6488 | − | 37.7880i | 0.105164 | − | 0.105553i | ||||
\(359\) | 105.336 | + | 34.2258i | 0.293416 | + | 0.0953366i | 0.452026 | − | 0.892005i | \(-0.350701\pi\) |
−0.158610 | + | 0.987341i | \(0.550701\pi\) | |||||||
\(360\) | −29.6057 | + | 193.863i | −0.0822381 | + | 0.538508i | ||||
\(361\) | −23.7243 | + | 17.2367i | −0.0657183 | + | 0.0477472i | ||||
\(362\) | −102.608 | − | 640.193i | −0.283447 | − | 1.76849i | ||||
\(363\) | −198.149 | + | 272.729i | −0.545865 | + | 0.751319i | ||||
\(364\) | −87.4584 | + | 64.0367i | −0.240270 | + | 0.175925i | ||||
\(365\) | −114.067 | + | 82.8744i | −0.312512 | + | 0.227053i | ||||
\(366\) | 24.3867 | − | 155.832i | 0.0666303 | − | 0.425771i | ||||
\(367\) | − | 501.450i | − | 1.36635i | −0.730255 | − | 0.683175i | \(-0.760599\pi\) | ||
0.730255 | − | 0.683175i | \(-0.239401\pi\) | |||||||
\(368\) | 1.16440 | + | 157.752i | 0.00316413 | + | 0.428675i | ||||
\(369\) | −114.299 | + | 351.775i | −0.309753 | + | 0.953320i | ||||
\(370\) | −2.21797 | − | 13.8384i | −0.00599452 | − | 0.0374011i | ||||
\(371\) | 431.725i | 1.16368i | ||||||||
\(372\) | −46.0509 | + | 158.927i | −0.123793 | + | 0.427224i | ||||
\(373\) | 252.906 | 0.678032 | 0.339016 | − | 0.940781i | \(-0.389906\pi\) | ||||
0.339016 | + | 0.940781i | \(0.389906\pi\) | |||||||
\(374\) | −800.259 | + | 128.263i | −2.13973 | + | 0.342949i | ||||
\(375\) | 165.777 | + | 53.8644i | 0.442073 | + | 0.143638i | ||||
\(376\) | −26.6709 | − | 162.564i | −0.0709333 | − | 0.432351i | ||||
\(377\) | −125.897 | −0.333945 | ||||||||
\(378\) | 345.178 | + | 54.0180i | 0.913168 | + | 0.142905i | ||||
\(379\) | 287.483 | + | 395.686i | 0.758529 | + | 1.04403i | 0.997335 | + | 0.0729586i | \(0.0232441\pi\) |
−0.238806 | + | 0.971067i | \(0.576756\pi\) | |||||||
\(380\) | 199.579 | − | 146.131i | 0.525209 | − | 0.384556i | ||||
\(381\) | −32.9670 | − | 23.9519i | −0.0865275 | − | 0.0628659i | ||||
\(382\) | 117.672 | − | 18.8600i | 0.308042 | − | 0.0493718i | ||||
\(383\) | −378.977 | − | 521.617i | −0.989496 | − | 1.36192i | −0.931553 | − | 0.363605i | \(-0.881546\pi\) |
−0.0579429 | − | 0.998320i | \(-0.518454\pi\) | |||||||
\(384\) | 122.325 | + | 119.205i | 0.318556 | + | 0.310431i | ||||
\(385\) | 163.705 | − | 503.833i | 0.425209 | − | 1.30866i | ||||
\(386\) | 52.9439 | + | 52.7489i | 0.137160 | + | 0.136655i | ||||
\(387\) | −544.205 | − | 176.823i | −1.40621 | − | 0.456907i | ||||
\(388\) | 101.834 | − | 141.256i | 0.262459 | − | 0.364062i | ||||
\(389\) | 83.9351 | + | 60.9824i | 0.215772 | + | 0.156767i | 0.690421 | − | 0.723408i | \(-0.257425\pi\) |
−0.474650 | + | 0.880175i | \(0.657425\pi\) | |||||||
\(390\) | −27.1343 | − | 13.7626i | −0.0695750 | − | 0.0352887i | ||||
\(391\) | −196.590 | + | 63.8758i | −0.502786 | + | 0.163365i | ||||
\(392\) | −127.473 | + | 20.9138i | −0.325187 | + | 0.0533515i | ||||
\(393\) | −7.56727 | − | 23.2897i | −0.0192551 | − | 0.0592612i | ||||
\(394\) | −204.167 | − | 203.415i | −0.518191 | − | 0.516282i | ||||
\(395\) | 193.837 | − | 266.794i | 0.490728 | − | 0.675429i | ||||
\(396\) | −174.449 | − | 530.231i | −0.440527 | − | 1.33897i | ||||
\(397\) | −106.602 | −0.268519 | −0.134260 | − | 0.990946i | \(-0.542866\pi\) | ||||
−0.134260 | + | 0.990946i | \(0.542866\pi\) | |||||||
\(398\) | −75.2606 | + | 480.919i | −0.189097 | + | 1.20834i | ||||
\(399\) | −115.294 | − | 158.689i | −0.288958 | − | 0.397716i | ||||
\(400\) | −173.423 | + | 127.965i | −0.433556 | + | 0.319913i | ||||
\(401\) | 134.274 | + | 413.254i | 0.334849 | + | 1.03056i | 0.966797 | + | 0.255547i | \(0.0822557\pi\) |
−0.631948 | + | 0.775011i | \(0.717744\pi\) | |||||||
\(402\) | −140.271 | − | 21.9515i | −0.348932 | − | 0.0546056i | ||||
\(403\) | 85.9076 | + | 58.7582i | 0.213170 | + | 0.145802i | ||||
\(404\) | −4.41515 | − | 1.41658i | −0.0109286 | − | 0.00350637i | ||||
\(405\) | −37.8730 | − | 116.561i | −0.0935136 | − | 0.287805i | ||||
\(406\) | −539.855 | − | 273.816i | −1.32969 | − | 0.674425i | ||||
\(407\) | 23.4474 | + | 32.2726i | 0.0576103 | + | 0.0792938i | ||||
\(408\) | −100.498 | + | 199.967i | −0.246318 | + | 0.490115i | ||||
\(409\) | 156.052 | 0.381545 | 0.190772 | − | 0.981634i | \(-0.438901\pi\) | ||||
0.190772 | + | 0.981634i | \(0.438901\pi\) | |||||||
\(410\) | 309.721 | − | 158.531i | 0.755416 | − | 0.386661i | ||||
\(411\) | 7.73553 | − | 10.6470i | 0.0188212 | − | 0.0259052i | ||||
\(412\) | −59.6304 | + | 43.6611i | −0.144734 | + | 0.105974i | ||||
\(413\) | 218.516 | + | 672.523i | 0.529095 | + | 1.62839i | ||||
\(414\) | −64.8656 | − | 126.727i | −0.156680 | − | 0.306105i | ||||
\(415\) | −31.3457 | + | 10.1848i | −0.0755319 | + | 0.0245418i | ||||
\(416\) | 95.2733 | − | 49.6567i | 0.229022 | − | 0.119367i | ||||
\(417\) | 171.401 | + | 124.530i | 0.411033 | + | 0.298633i | ||||
\(418\) | −318.478 | + | 627.909i | −0.761908 | + | 1.50218i | ||||
\(419\) | −696.780 | − | 226.398i | −1.66296 | − | 0.540328i | −0.681471 | − | 0.731846i | \(-0.738659\pi\) |
−0.981489 | + | 0.191517i | \(0.938659\pi\) | |||||||
\(420\) | −86.4208 | − | 118.030i | −0.205764 | − | 0.281023i | ||||
\(421\) | −32.6054 | + | 100.349i | −0.0774475 | + | 0.238359i | −0.982283 | − | 0.187402i | \(-0.939993\pi\) |
0.904836 | + | 0.425761i | \(0.139993\pi\) | |||||||
\(422\) | −574.253 | + | 92.0393i | −1.36079 | + | 0.218103i | ||||
\(423\) | 87.3819 | + | 120.271i | 0.206577 | + | 0.284328i | ||||
\(424\) | 64.5988 | − | 423.003i | 0.152356 | − | 0.997649i | ||||
\(425\) | −228.465 | − | 165.989i | −0.537564 | − | 0.390563i | ||||
\(426\) | 178.094 | + | 177.438i | 0.418062 | + | 0.416522i | ||||
\(427\) | −280.390 | − | 385.924i | −0.656652 | − | 0.903804i | ||||
\(428\) | −145.962 | + | 454.930i | −0.341032 | + | 1.06292i | ||||
\(429\) | 86.5988 | 0.201862 | ||||||||
\(430\) | 245.252 | + | 479.146i | 0.570353 | + | 1.11429i | ||||
\(431\) | 76.9423 | + | 25.0001i | 0.178521 | + | 0.0580048i | 0.396913 | − | 0.917856i | \(-0.370081\pi\) |
−0.218393 | + | 0.975861i | \(0.570081\pi\) | |||||||
\(432\) | −330.121 | − | 104.575i | −0.764170 | − | 0.242073i | ||||
\(433\) | −16.8576 | −0.0389321 | −0.0194661 | − | 0.999811i | \(-0.506197\pi\) | ||||
−0.0194661 | + | 0.999811i | \(0.506197\pi\) | |||||||
\(434\) | 240.582 | + | 438.800i | 0.554338 | + | 1.01106i | ||||
\(435\) | − | 169.905i | − | 0.390586i | ||||||
\(436\) | 2.44457 | + | 662.387i | 0.00560681 | + | 1.51924i | ||||
\(437\) | −55.4890 | + | 170.777i | −0.126977 | + | 0.390795i | ||||
\(438\) | −50.4919 | − | 98.6455i | −0.115278 | − | 0.225218i | ||||
\(439\) | − | 556.353i | − | 1.26732i | −0.773612 | − | 0.633659i | \(-0.781552\pi\) | ||
0.773612 | − | 0.633659i | \(-0.218448\pi\) | |||||||
\(440\) | −235.786 | + | 469.159i | −0.535878 | + | 1.06627i | ||||
\(441\) | 94.3093 | − | 68.5197i | 0.213853 | − | 0.155374i | ||||
\(442\) | 99.7255 | + | 99.3582i | 0.225623 | + | 0.224792i | ||||
\(443\) | −170.321 | + | 234.426i | −0.384471 | + | 0.529179i | −0.956762 | − | 0.290872i | \(-0.906055\pi\) |
0.572291 | + | 0.820051i | \(0.306055\pi\) | |||||||
\(444\) | 11.0153 | − | 0.0406523i | 0.0248092 | − | 9.15593e-5i | ||||
\(445\) | −162.124 | + | 117.790i | −0.364323 | + | 0.264696i | ||||
\(446\) | −17.3556 | + | 2.78169i | −0.0389138 | + | 0.00623697i | ||||
\(447\) | −205.609 | − | 66.8063i | −0.459974 | − | 0.149455i | ||||
\(448\) | 516.537 | − | 5.71911i | 1.15298 | − | 0.0127659i | ||||
\(449\) | 180.770 | − | 556.353i | 0.402606 | − | 1.23909i | −0.520272 | − | 0.854001i | \(-0.674169\pi\) |
0.922878 | − | 0.385093i | \(-0.125831\pi\) | |||||||
\(450\) | 87.9784 | − | 173.458i | 0.195507 | − | 0.385462i | ||||
\(451\) | −582.102 | + | 801.195i | −1.29069 | + | 1.77649i | ||||
\(452\) | 129.564 | − | 179.721i | 0.286647 | − | 0.397613i | ||||
\(453\) | −8.71983 | − | 26.8369i | −0.0192491 | − | 0.0592425i | ||||
\(454\) | 117.584 | + | 229.723i | 0.258996 | + | 0.505998i | ||||
\(455\) | −87.5124 | + | 28.4345i | −0.192335 | + | 0.0624934i | ||||
\(456\) | 89.2203 | + | 172.734i | 0.195659 | + | 0.378803i | ||||
\(457\) | −663.600 | − | 482.133i | −1.45208 | − | 1.05500i | −0.985340 | − | 0.170601i | \(-0.945429\pi\) |
−0.466738 | − | 0.884396i | \(-0.654571\pi\) | |||||||
\(458\) | 194.467 | − | 99.5383i | 0.424600 | − | 0.217333i | ||||
\(459\) | − | 453.738i | − | 0.988535i | ||||||
\(460\) | −40.9125 | + | 127.515i | −0.0889403 | + | 0.277207i | ||||
\(461\) | 301.239 | − | 218.863i | 0.653447 | − | 0.474757i | −0.210997 | − | 0.977487i | \(-0.567671\pi\) |
0.864443 | + | 0.502730i | \(0.167671\pi\) | |||||||
\(462\) | 371.341 | + | 188.345i | 0.803768 | + | 0.407674i | ||||
\(463\) | 752.029 | − | 244.349i | 1.62425 | − | 0.527752i | 0.651313 | − | 0.758809i | \(-0.274218\pi\) |
0.972940 | + | 0.231057i | \(0.0742185\pi\) | |||||||
\(464\) | 487.978 | + | 349.063i | 1.05168 | + | 0.752290i | ||||
\(465\) | −79.2971 | + | 115.937i | −0.170531 | + | 0.249326i | ||||
\(466\) | −801.219 | − | 125.386i | −1.71935 | − | 0.269068i | ||||
\(467\) | 662.756 | − | 215.342i | 1.41918 | − | 0.461118i | 0.503836 | − | 0.863799i | \(-0.331921\pi\) |
0.915341 | + | 0.402681i | \(0.131921\pi\) | |||||||
\(468\) | −56.6983 | + | 78.6473i | −0.121150 | + | 0.168050i | ||||
\(469\) | −347.386 | + | 252.391i | −0.740695 | + | 0.538146i | ||||
\(470\) | 21.6215 | − | 138.162i | 0.0460031 | − | 0.293962i | ||||
\(471\) | − | 189.964i | − | 0.403320i | ||||||
\(472\) | −113.472 | − | 691.633i | −0.240407 | − | 1.46532i | ||||
\(473\) | −1239.47 | − | 900.527i | −2.62044 | − | 1.90386i | ||||
\(474\) | 183.615 | + | 182.938i | 0.387373 | + | 0.385946i | ||||
\(475\) | −233.312 | + | 75.8078i | −0.491184 | + | 0.159595i | ||||
\(476\) | 211.533 | + | 642.949i | 0.444397 | + | 1.35073i | ||||
\(477\) | 119.328 | + | 367.254i | 0.250164 | + | 0.769925i | ||||
\(478\) | 325.768 | + | 165.230i | 0.681522 | + | 0.345670i | ||||
\(479\) | 466.311 | − | 641.822i | 0.973509 | − | 1.33992i | 0.0332553 | − | 0.999447i | \(-0.489413\pi\) |
0.940254 | − | 0.340474i | \(-0.110587\pi\) | |||||||
\(480\) | 67.0142 | + | 128.576i | 0.139613 | + | 0.267867i | ||||
\(481\) | 2.14112 | − | 6.58970i | 0.00445140 | − | 0.0137000i | ||||
\(482\) | 388.025 | + | 386.596i | 0.805032 | + | 0.802066i | ||||
\(483\) | 100.996 | + | 32.8157i | 0.209102 | + | 0.0679415i | ||||
\(484\) | −3.72938 | − | 1010.52i | −0.00770533 | − | 2.08786i | ||||
\(485\) | 119.591 | − | 86.8877i | 0.246579 | − | 0.179150i | ||||
\(486\) | 479.779 | − | 76.8974i | 0.987200 | − | 0.158225i | ||||
\(487\) | 133.384 | − | 183.587i | 0.273889 | − | 0.376976i | −0.649809 | − | 0.760098i | \(-0.725151\pi\) |
0.923698 | + | 0.383122i | \(0.125151\pi\) | |||||||
\(488\) | 216.980 | + | 420.082i | 0.444631 | + | 0.860824i | ||||
\(489\) | 173.910 | − | 126.353i | 0.355644 | − | 0.258390i | ||||
\(490\) | −108.339 | − | 16.9543i | −0.221099 | − | 0.0346005i | ||||
\(491\) | 248.654i | 0.506425i | 0.967411 | + | 0.253212i | \(0.0814871\pi\) | ||||
−0.967411 | + | 0.253212i | \(0.918513\pi\) | |||||||
\(492\) | 85.4647 | + | 259.767i | 0.173709 | + | 0.527983i | ||||
\(493\) | −242.929 | + | 747.660i | −0.492757 | + | 1.51655i | ||||
\(494\) | 120.749 | − | 19.3533i | 0.244431 | − | 0.0391766i | ||||
\(495\) | − | 473.842i | − | 0.957256i | ||||||
\(496\) | −170.065 | − | 465.934i | −0.342872 | − | 0.939382i | ||||
\(497\) | 760.325 | 1.52983 | ||||||||
\(498\) | −4.09957 | − | 25.5781i | −0.00823206 | − | 0.0513616i | ||||
\(499\) | −84.6319 | − | 27.4986i | −0.169603 | − | 0.0551074i | 0.222985 | − | 0.974822i | \(-0.428420\pi\) |
−0.392588 | + | 0.919715i | \(0.628420\pi\) | |||||||
\(500\) | −496.338 | + | 163.298i | −0.992676 | + | 0.326595i | ||||
\(501\) | −122.278 | −0.244068 | ||||||||
\(502\) | −7.77989 | + | 49.7138i | −0.0154978 | + | 0.0990315i | ||||
\(503\) | −80.8438 | − | 111.272i | −0.160723 | − | 0.221216i | 0.721059 | − | 0.692874i | \(-0.243656\pi\) |
−0.881782 | + | 0.471658i | \(0.843656\pi\) | |||||||
\(504\) | −414.177 | + | 213.930i | −0.821780 | + | 0.424464i | ||||
\(505\) | −3.18441 | − | 2.31361i | −0.00630577 | − | 0.00458141i | ||||
\(506\) | −60.3229 | − | 376.368i | −0.119215 | − | 0.743810i | ||||
\(507\) | 123.712 | + | 170.275i | 0.244007 | + | 0.335847i | ||||
\(508\) | 122.150 | − | 0.450801i | 0.240453 | − | 0.000887404i | ||||
\(509\) | 247.049 | − | 760.338i | 0.485361 | − | 1.49379i | −0.346097 | − | 0.938199i | \(-0.612493\pi\) |
0.831457 | − | 0.555588i | \(-0.187507\pi\) | |||||||
\(510\) | −134.089 | + | 134.585i | −0.262919 | + | 0.263892i | ||||
\(511\) | −318.747 | − | 103.567i | −0.623770 | − | 0.202675i | ||||
\(512\) | −506.957 | − | 71.6855i | −0.990150 | − | 0.140011i | ||||
\(513\) | −318.884 | − | 231.683i | −0.621606 | − | 0.451623i | ||||
\(514\) | 420.119 | − | 828.305i | 0.817352 | − | 1.61149i | ||||
\(515\) | −59.6672 | + | 19.3870i | −0.115859 | + | 0.0376448i | ||||
\(516\) | −401.867 | + | 132.216i | −0.778811 | + | 0.256233i | ||||
\(517\) | 123.000 | + | 378.557i | 0.237912 | + | 0.732218i | ||||
\(518\) | 23.5133 | − | 23.6002i | 0.0453925 | − | 0.0455603i | ||||
\(519\) | −152.032 | + | 209.255i | −0.292933 | + | 0.403188i | ||||
\(520\) | 89.9991 | − | 14.7656i | 0.173075 | − | 0.0283954i | ||||
\(521\) | 566.494 | 1.08732 | 0.543660 | − | 0.839306i | \(-0.317038\pi\) | ||||
0.543660 | + | 0.839306i | \(0.317038\pi\) | |||||||
\(522\) | −534.919 | − | 83.7113i | −1.02475 | − | 0.160367i | ||||
\(523\) | −102.918 | − | 141.654i | −0.196783 | − | 0.270849i | 0.699210 | − | 0.714916i | \(-0.253535\pi\) |
−0.895993 | + | 0.444067i | \(0.853535\pi\) | |||||||
\(524\) | 59.5457 | + | 42.9276i | 0.113637 | + | 0.0819229i | ||||
\(525\) | 44.8321 | + | 137.979i | 0.0853945 | + | 0.262817i | ||||
\(526\) | 100.240 | − | 640.537i | 0.190570 | − | 1.21775i | ||||
\(527\) | 514.710 | − | 396.796i | 0.976678 | − | 0.752933i | ||||
\(528\) | −335.656 | − | 240.104i | −0.635713 | − | 0.454741i | ||||
\(529\) | 133.429 | + | 410.651i | 0.252228 | + | 0.776279i | ||||
\(530\) | 164.312 | − | 323.958i | 0.310024 | − | 0.611241i | ||||
\(531\) | 371.768 | + | 511.695i | 0.700129 | + | 0.963645i | ||||
\(532\) | 559.871 | + | 179.632i | 1.05239 | + | 0.337653i | ||||
\(533\) | 172.014 | 0.322728 | ||||||||
\(534\) | −71.7644 | − | 140.205i | −0.134390 | − | 0.262557i | ||||
\(535\) | −238.391 | + | 328.117i | −0.445591 | + | 0.613303i | ||||
\(536\) | 378.133 | − | 195.312i | 0.705472 | − | 0.364389i | ||||
\(537\) | 10.9978 | + | 33.8478i | 0.0204801 | + | 0.0630312i | ||||
\(538\) | −611.526 | + | 313.011i | −1.13667 | + | 0.581805i | ||||
\(539\) | 296.842 | − | 96.4497i | 0.550727 | − | 0.178942i | ||||
\(540\) | −238.455 | − | 171.907i | −0.441584 | − | 0.318346i | ||||
\(541\) | 662.911 | + | 481.633i | 1.22534 | + | 0.890264i | 0.996532 | − | 0.0832069i | \(-0.0265162\pi\) |
0.228811 | + | 0.973471i | \(0.426516\pi\) | |||||||
\(542\) | 539.713 | + | 273.744i | 0.995780 | + | 0.505063i | ||||
\(543\) | 411.414 | + | 133.676i | 0.757668 | + | 0.246181i | ||||
\(544\) | −111.056 | − | 661.611i | −0.204146 | − | 1.21620i | ||||
\(545\) | −173.759 | + | 534.775i | −0.318824 | + | 0.981239i | ||||
\(546\) | −11.4454 | − | 71.4101i | −0.0209622 | − | 0.130788i | ||||
\(547\) | 80.9626 | + | 111.435i | 0.148012 | + | 0.203721i | 0.876585 | − | 0.481247i | \(-0.159816\pi\) |
−0.728573 | + | 0.684968i | \(0.759816\pi\) | |||||||
\(548\) | 0.145591 | + | 39.4497i | 0.000265677 | + | 0.0719886i | ||||
\(549\) | −345.188 | − | 250.793i | −0.628757 | − | 0.456819i | ||||
\(550\) | 367.544 | − | 368.903i | 0.668262 | − | 0.670733i | ||||
\(551\) | 401.408 | + | 552.491i | 0.728509 | + | 1.00271i | ||||
\(552\) | −94.0458 | − | 47.2648i | −0.170373 | − | 0.0856246i | ||||
\(553\) | 783.892 | 1.41753 | ||||||||
\(554\) | −179.146 | + | 91.6961i | −0.323368 | + | 0.165516i | ||||
\(555\) | 8.89313 | + | 2.88955i | 0.0160237 | + | 0.00520640i | ||||
\(556\) | −635.079 | + | 2.34379i | −1.14223 | + | 0.00421545i | ||||
\(557\) | −597.655 | −1.07299 | −0.536495 | − | 0.843904i | \(-0.680252\pi\) | ||||
−0.536495 | + | 0.843904i | \(0.680252\pi\) | |||||||
\(558\) | 325.939 | + | 306.776i | 0.584120 | + | 0.549778i | ||||
\(559\) | 266.110i | 0.476046i | ||||||||
\(560\) | 418.035 | + | 132.425i | 0.746492 | + | 0.236473i | ||||
\(561\) | 167.099 | − | 514.279i | 0.297860 | − | 0.916719i | ||||
\(562\) | −48.1379 | + | 24.6395i | −0.0856546 | + | 0.0438425i | ||||
\(563\) | 804.116i | 1.42827i | 0.700008 | + | 0.714135i | \(0.253180\pi\) | ||||
−0.700008 | + | 0.714135i | \(0.746820\pi\) | |||||||
\(564\) | 104.657 | + | 33.5788i | 0.185563 | + | 0.0595368i | ||||
\(565\) | 152.156 | − | 110.548i | 0.269303 | − | 0.195660i | ||||
\(566\) | 66.6745 | − | 66.9210i | 0.117799 | − | 0.118235i | ||||
\(567\) | 171.239 | − | 235.691i | 0.302009 | − | 0.415680i | ||||
\(568\) | −744.964 | − | 113.767i | −1.31156 | − | 0.200294i | ||||
\(569\) | −774.798 | + | 562.924i | −1.36168 | + | 0.989321i | −0.363348 | + | 0.931654i | \(0.618366\pi\) |
−0.998336 | + | 0.0576675i | \(0.981634\pi\) | |||||||
\(570\) | 26.1182 | + | 162.957i | 0.0458214 | + | 0.285890i | ||||
\(571\) | −88.0958 | − | 28.6240i | −0.154283 | − | 0.0501297i | 0.230857 | − | 0.972988i | \(-0.425847\pi\) |
−0.385140 | + | 0.922858i | \(0.625847\pi\) | |||||||
\(572\) | −209.448 | + | 153.357i | −0.366168 | + | 0.268107i | ||||
\(573\) | −24.5707 | + | 75.6207i | −0.0428807 | + | 0.131973i | ||||
\(574\) | 737.606 | + | 374.116i | 1.28503 | + | 0.651770i | ||||
\(575\) | 78.0659 | − | 107.449i | 0.135767 | − | 0.186867i | ||||
\(576\) | 437.820 | − | 147.635i | 0.760103 | − | 0.256311i | ||||
\(577\) | −182.117 | − | 560.500i | −0.315628 | − | 0.971403i | −0.975495 | − | 0.220021i | \(-0.929387\pi\) |
0.659867 | − | 0.751382i | \(-0.270613\pi\) | |||||||
\(578\) | 267.965 | − | 137.158i | 0.463607 | − | 0.237298i | ||||
\(579\) | −47.4233 | + | 15.4088i | −0.0819055 | + | 0.0266127i | ||||
\(580\) | 300.883 | + | 410.932i | 0.518764 | + | 0.708504i | ||||
\(581\) | −63.3822 | − | 46.0498i | −0.109091 | − | 0.0792596i | ||||
\(582\) | 52.9370 | + | 103.423i | 0.0909571 | + | 0.177702i | ||||
\(583\) | 1033.91i | 1.77343i | ||||||||
\(584\) | 296.810 | + | 149.169i | 0.508237 | + | 0.255426i | ||||
\(585\) | −66.5846 | + | 48.3766i | −0.113820 | + | 0.0826950i | ||||
\(586\) | 414.277 | − | 816.788i | 0.706958 | − | 1.39384i | ||||
\(587\) | −642.960 | + | 208.910i | −1.09533 | + | 0.355895i | −0.800304 | − | 0.599594i | \(-0.795329\pi\) |
−0.295027 | + | 0.955489i | \(0.595329\pi\) | |||||||
\(588\) | 26.3305 | − | 82.0662i | 0.0447797 | − | 0.139568i | ||||
\(589\) | −16.0499 | − | 564.342i | −0.0272493 | − | 0.958136i | ||||
\(590\) | 91.9890 | − | 587.814i | 0.155914 | − | 0.996294i | ||||
\(591\) | 182.878 | − | 59.4207i | 0.309438 | − | 0.100543i | ||||
\(592\) | −26.5696 | + | 19.6052i | −0.0448810 | + | 0.0331168i | ||||
\(593\) | 78.5153 | − | 57.0447i | 0.132403 | − | 0.0961968i | −0.519612 | − | 0.854402i | \(-0.673924\pi\) |
0.652016 | + | 0.758205i | \(0.273924\pi\) | |||||||
\(594\) | 826.641 | + | 129.364i | 1.39165 | + | 0.217784i | ||||
\(595\) | 574.572i | 0.965667i | ||||||||
\(596\) | 615.592 | − | 202.533i | 1.03287 | − | 0.339820i | ||||
\(597\) | −262.747 | − | 190.897i | −0.440112 | − | 0.319760i | ||||
\(598\) | −46.7289 | + | 46.9016i | −0.0781419 | + | 0.0784308i | ||||
\(599\) | 388.249 | − | 126.150i | 0.648162 | − | 0.210601i | 0.0335584 | − | 0.999437i | \(-0.489316\pi\) |
0.614604 | + | 0.788836i | \(0.289316\pi\) | |||||||
\(600\) | −23.2806 | − | 141.900i | −0.0388011 | − | 0.236499i | ||||
\(601\) | 185.310 | + | 570.325i | 0.308336 | + | 0.948960i | 0.978411 | + | 0.206667i | \(0.0662617\pi\) |
−0.670076 | + | 0.742293i | \(0.733738\pi\) | |||||||
\(602\) | −578.767 | + | 1141.09i | −0.961407 | + | 1.89551i | ||||
\(603\) | −225.749 | + | 310.717i | −0.374377 | + | 0.515285i | ||||
\(604\) | 68.6150 | + | 49.4658i | 0.113601 | + | 0.0818971i | ||||
\(605\) | 265.083 | − | 815.841i | 0.438154 | − | 1.34850i | ||||
\(606\) | 2.18352 | − | 2.19160i | 0.00360317 | − | 0.00361649i | ||||
\(607\) | −1011.86 | − | 328.773i | −1.66698 | − | 0.541635i | −0.684665 | − | 0.728858i | \(-0.740051\pi\) |
−0.982318 | + | 0.187222i | \(0.940051\pi\) | |||||||
\(608\) | −521.682 | − | 259.776i | −0.858029 | − | 0.427263i | ||||
\(609\) | 326.739 | − | 237.390i | 0.536517 | − | 0.389803i | ||||
\(610\) | 63.5184 | + | 396.305i | 0.104128 | + | 0.649680i | ||||
\(611\) | 40.6374 | − | 55.9326i | 0.0665097 | − | 0.0915428i | ||||
\(612\) | 357.654 | + | 488.467i | 0.584402 | + | 0.798149i | ||||
\(613\) | −74.3019 | + | 53.9835i | −0.121210 | + | 0.0880645i | −0.646739 | − | 0.762712i | \(-0.723868\pi\) |
0.525528 | + | 0.850776i | \(0.323868\pi\) | |||||||
\(614\) | 54.6603 | − | 349.282i | 0.0890234 | − | 0.568863i | ||||
\(615\) | 232.142i | 0.377466i | ||||||||
\(616\) | −1231.66 | + | 202.072i | −1.99945 | + | 0.328039i | ||||
\(617\) | −99.0609 | + | 304.878i | −0.160553 | + | 0.494130i | −0.998681 | − | 0.0513429i | \(-0.983650\pi\) |
0.838129 | + | 0.545473i | \(0.183650\pi\) | |||||||
\(618\) | −7.80361 | − | 48.6884i | −0.0126272 | − | 0.0787838i | ||||
\(619\) | 186.724i | 0.301654i | 0.988560 | + | 0.150827i | \(0.0481936\pi\) | ||||
−0.988560 | + | 0.150827i | \(0.951806\pi\) | |||||||
\(620\) | −13.5229 | − | 420.831i | −0.0218112 | − | 0.678760i | ||||
\(621\) | 213.396 | 0.343633 | ||||||||
\(622\) | 1187.87 | − | 190.387i | 1.90976 | − | 0.306089i | ||||
\(623\) | −453.036 | − | 147.200i | −0.727185 | − | 0.236277i | ||||
\(624\) | 0.529083 | + | 71.6799i | 0.000847890 | + | 0.114872i | ||||
\(625\) | −106.797 | −0.170876 | ||||||||
\(626\) | −685.070 | − | 107.209i | −1.09436 | − | 0.171260i | ||||
\(627\) | −276.110 | − | 380.032i | −0.440366 | − | 0.606112i | ||||
\(628\) | 336.405 | + | 459.447i | 0.535677 | + | 0.731603i | ||||
\(629\) | −35.0024 | − | 25.4307i | −0.0556477 | − | 0.0404304i | ||||
\(630\) | −390.734 | + | 62.6255i | −0.620212 | + | 0.0994055i | ||||
\(631\) | 629.251 | + | 866.089i | 0.997228 | + | 1.37257i | 0.927011 | + | 0.375035i | \(0.122369\pi\) |
0.0702170 | + | 0.997532i | \(0.477631\pi\) | |||||||
\(632\) | −768.055 | − | 117.293i | −1.21528 | − | 0.185591i | ||||
\(633\) | 119.908 | − | 369.038i | 0.189428 | − | 0.582999i | ||||
\(634\) | −635.896 | − | 633.554i | −1.00299 | − | 0.999296i | ||||
\(635\) | 98.6175 | + | 32.0428i | 0.155303 | + | 0.0504611i | ||||
\(636\) | 231.591 | + | 166.958i | 0.364137 | + | 0.262513i | ||||
\(637\) | −43.8591 | − | 31.8655i | −0.0688525 | − | 0.0500243i | ||||
\(638\) | −1292.86 | − | 655.744i | −2.02643 | − | 1.02781i | ||||
\(639\) | 646.782 | − | 210.152i | 1.01218 | − | 0.328877i | ||||
\(640\) | −389.775 | − | 192.300i | −0.609024 | − | 0.300468i | ||||
\(641\) | 259.106 | + | 797.448i | 0.404222 | + | 1.24407i | 0.921543 | + | 0.388277i | \(0.126929\pi\) |
−0.517321 | + | 0.855792i | \(0.673071\pi\) | |||||||
\(642\) | −225.819 | − | 224.987i | −0.351743 | − | 0.350447i | ||||
\(643\) | −174.595 | + | 240.310i | −0.271533 | + | 0.373732i | −0.922906 | − | 0.385024i | \(-0.874193\pi\) |
0.651374 | + | 0.758757i | \(0.274193\pi\) | |||||||
\(644\) | −302.383 | + | 99.4856i | −0.469539 | + | 0.154481i | ||||
\(645\) | −359.129 | −0.556789 | ||||||||
\(646\) | 118.063 | − | 754.430i | 0.182761 | − | 1.16785i | ||||
\(647\) | −73.6604 | − | 101.385i | −0.113849 | − | 0.156700i | 0.748290 | − | 0.663372i | \(-0.230875\pi\) |
−0.862139 | + | 0.506672i | \(0.830875\pi\) | |||||||
\(648\) | −203.046 | + | 205.307i | −0.313343 | + | 0.316831i | ||||
\(649\) | 523.309 | + | 1610.58i | 0.806331 | + | 2.48163i | ||||
\(650\) | −89.3627 | − | 13.9847i | −0.137481 | − | 0.0215149i | ||||
\(651\) | −333.748 | + | 9.49176i | −0.512669 | + | 0.0145803i | ||||
\(652\) | −196.861 | + | 613.573i | −0.301935 | + | 0.941063i | ||||
\(653\) | 29.0527 | + | 89.4151i | 0.0444912 | + | 0.136930i | 0.970835 | − | 0.239750i | \(-0.0770656\pi\) |
−0.926343 | + | 0.376680i | \(0.877066\pi\) | |||||||
\(654\) | −394.146 | − | 199.912i | −0.602670 | − | 0.305676i | ||||
\(655\) | 36.6270 | + | 50.4128i | 0.0559191 | + | 0.0769661i | ||||
\(656\) | −666.725 | − | 476.925i | −1.01635 | − | 0.727020i | ||||
\(657\) | −299.773 | −0.456275 | ||||||||
\(658\) | 295.905 | − | 151.459i | 0.449703 | − | 0.230181i | ||||
\(659\) | −46.2771 | + | 63.6949i | −0.0702232 | + | 0.0966539i | −0.842684 | − | 0.538409i | \(-0.819026\pi\) |
0.772461 | + | 0.635063i | \(0.219026\pi\) | |||||||
\(660\) | −206.963 | − | 282.661i | −0.313580 | − | 0.428274i | ||||
\(661\) | 38.9223 | + | 119.791i | 0.0588840 | + | 0.181226i | 0.976172 | − | 0.216998i | \(-0.0696266\pi\) |
−0.917288 | + | 0.398224i | \(0.869627\pi\) | |||||||
\(662\) | 150.316 | + | 293.670i | 0.227063 | + | 0.443611i | ||||
\(663\) | −89.3268 | + | 29.0240i | −0.134731 | + | 0.0437768i | ||||
\(664\) | 55.2112 | + | 54.6033i | 0.0831495 | + | 0.0822339i | ||||
\(665\) | 403.806 | + | 293.382i | 0.607226 | + | 0.441176i | ||||
\(666\) | 13.4789 | − | 26.5750i | 0.0202386 | − | 0.0399023i | ||||
\(667\) | −351.630 | − | 114.251i | −0.527181 | − | 0.171291i | ||||
\(668\) | 295.742 | − | 216.541i | 0.442728 | − | 0.324164i | ||||
\(669\) | 3.62396 | − | 11.1534i | 0.00541698 | − | 0.0166717i | ||||
\(670\) | 356.730 | − | 57.1754i | 0.532433 | − | 0.0853365i | ||||
\(671\) | −671.487 | − | 924.223i | −1.00073 | − | 1.37738i | ||||
\(672\) | −153.629 | + | 308.518i | −0.228615 | + | 0.459105i | ||||
\(673\) | −1038.52 | − | 754.531i | −1.54312 | − | 1.12115i | −0.948338 | − | 0.317263i | \(-0.897236\pi\) |
−0.594787 | − | 0.803883i | \(-0.702764\pi\) | |||||||
\(674\) | −78.8216 | − | 78.5313i | −0.116946 | − | 0.116515i | ||||
\(675\) | 171.361 | + | 235.858i | 0.253868 | + | 0.349420i | ||||
\(676\) | −600.747 | − | 192.746i | −0.888680 | − | 0.285128i | ||||
\(677\) | −513.431 | −0.758392 | −0.379196 | − | 0.925316i | \(-0.623799\pi\) | ||||
−0.379196 | + | 0.925316i | \(0.623799\pi\) | |||||||
\(678\) | 67.3521 | + | 131.585i | 0.0993394 | + | 0.194078i | ||||
\(679\) | 334.182 | + | 108.582i | 0.492168 | + | 0.159915i | ||||
\(680\) | 85.9728 | − | 562.964i | 0.126431 | − | 0.827888i | ||||
\(681\) | −172.182 | −0.252836 | ||||||||
\(682\) | 576.154 | + | 1050.85i | 0.844800 | + | 1.54084i | ||||
\(683\) | − | 1151.65i | − | 1.68616i | −0.537791 | − | 0.843078i | \(-0.680741\pi\) | ||
0.537791 | − | 0.843078i | \(-0.319259\pi\) | |||||||
\(684\) | 525.913 | − | 1.94091i | 0.768879 | − | 0.00283758i | ||||
\(685\) | −10.3486 | + | 31.8496i | −0.0151074 | + | 0.0464957i | ||||
\(686\) | 241.639 | + | 472.087i | 0.352243 | + | 0.688174i | ||||
\(687\) | 145.757i | 0.212164i | ||||||||
\(688\) | 737.815 | − | 1031.44i | 1.07241 | − | 1.49919i | ||||
\(689\) | 145.286 | − | 105.556i | 0.210865 | − | 0.153202i | ||||
\(690\) | −63.2961 | − | 63.0630i | −0.0917335 | − | 0.0913956i | ||||
\(691\) | −713.489 | + | 982.033i | −1.03255 | + | 1.42118i | −0.129527 | + | 0.991576i | \(0.541346\pi\) |
−0.903019 | + | 0.429601i | \(0.858654\pi\) | |||||||
\(692\) | −2.86142 | − | 775.337i | −0.00413499 | − | 1.12043i | ||||
\(693\) | 911.231 | − | 662.048i | 1.31491 | − | 0.955336i | ||||
\(694\) | −592.657 | + | 94.9890i | −0.853973 | + | 0.136872i | ||||
\(695\) | −512.729 | − | 166.596i | −0.737739 | − | 0.239706i | ||||
\(696\) | −355.658 | + | 183.704i | −0.511003 | + | 0.263943i | ||||
\(697\) | 331.915 | − | 1021.53i | 0.476205 | − | 1.46561i | ||||
\(698\) | −111.642 | + | 220.112i | −0.159945 | + | 0.315347i | ||||
\(699\) | 318.037 | − | 437.741i | 0.454989 | − | 0.626239i | ||||
\(700\) | −352.777 | − | 254.324i | −0.503967 | − | 0.363320i | ||||
\(701\) | −32.2430 | − | 99.2337i | −0.0459957 | − | 0.141560i | 0.925421 | − | 0.378940i | \(-0.123711\pi\) |
−0.971417 | + | 0.237380i | \(0.923711\pi\) | |||||||
\(702\) | −66.2171 | − | 129.368i | −0.0943263 | − | 0.184284i | ||||
\(703\) | −35.7451 | + | 11.6143i | −0.0508465 | + | 0.0165210i | ||||
\(704\) | 1237.02 | − | 13.6963i | 1.75713 | − | 0.0194550i | ||||
\(705\) | 75.4839 | + | 54.8423i | 0.107069 | + | 0.0777905i | ||||
\(706\) | 396.413 | − | 202.905i | 0.561492 | − | 0.287401i | ||||
\(707\) | − | 9.35641i | − | 0.0132340i | ||||||
\(708\) | 445.268 | + | 142.862i | 0.628909 | + | 0.201782i | ||||
\(709\) | 208.334 | − | 151.363i | 0.293842 | − | 0.213489i | −0.431090 | − | 0.902309i | \(-0.641871\pi\) |
0.724932 | + | 0.688820i | \(0.241871\pi\) | |||||||
\(710\) | −570.532 | − | 289.376i | −0.803566 | − | 0.407571i | ||||
\(711\) | 666.831 | − | 216.666i | 0.937877 | − | 0.304735i | ||||
\(712\) | 421.858 | + | 212.014i | 0.592497 | + | 0.297772i | ||||
\(713\) | 186.616 | + | 242.072i | 0.261733 | + | 0.339511i | ||||
\(714\) | −446.164 | − | 69.8217i | −0.624879 | − | 0.0977895i | ||||
\(715\) | −209.577 | + | 68.0958i | −0.293115 | + | 0.0952389i | ||||
\(716\) | −86.5400 | − | 62.3883i | −0.120866 | − | 0.0871346i | ||||
\(717\) | −197.166 | + | 143.249i | −0.274987 | + | 0.199790i | ||||
\(718\) | 34.2487 | − | 218.851i | 0.0477001 | − | 0.304806i | ||||
\(719\) | − | 404.409i | − | 0.562461i | −0.959640 | − | 0.281230i | \(-0.909258\pi\) | ||
0.959640 | − | 0.281230i | \(-0.0907425\pi\) | |||||||
\(720\) | 392.210 | − | 2.89498i | 0.544737 | − | 0.00402081i | ||||
\(721\) | −120.649 | − | 87.6568i | −0.167336 | − | 0.121577i | ||||
\(722\) | 41.5481 | + | 41.3950i | 0.0575458 | + | 0.0573338i | ||||
\(723\) | −347.565 | + | 112.931i | −0.480726 | + | 0.156197i | ||||
\(724\) | −1231.77 | + | 405.259i | −1.70134 | + | 0.559750i | ||||
\(725\) | −156.088 | − | 480.389i | −0.215293 | − | 0.662605i | ||||
\(726\) | 601.300 | + | 304.981i | 0.828237 | + | 0.420085i | ||||
\(727\) | −382.717 | + | 526.765i | −0.526433 | + | 0.724573i | −0.986582 | − | 0.163269i | \(-0.947796\pi\) |
0.460148 | + | 0.887842i | \(0.347796\pi\) | |||||||
\(728\) | 154.141 | + | 152.444i | 0.211733 | + | 0.209401i | ||||
\(729\) | 0.202247 | − | 0.622451i | 0.000277430 | − | 0.000853843i | ||||
\(730\) | 199.764 | + | 199.028i | 0.273649 | + | 0.272641i | ||||
\(731\) | 1580.33 | + | 513.481i | 2.16188 | + | 0.702436i | ||||
\(732\) | −315.455 | + | 1.16420i | −0.430950 | + | 0.00159044i | ||||
\(733\) | −1.55060 | + | 1.12658i | −0.00211542 | + | 0.00153694i | −0.588842 | − | 0.808248i | \(-0.700416\pi\) |
0.586727 | + | 0.809785i | \(0.300416\pi\) | |||||||
\(734\) | −990.262 | + | 158.716i | −1.34913 | + | 0.216234i | ||||
\(735\) | 43.0041 | − | 59.1900i | 0.0585089 | − | 0.0805307i | ||||
\(736\) | 311.160 | − | 52.2302i | 0.422772 | − | 0.0709650i | ||||
\(737\) | −831.930 | + | 604.433i | −1.12881 | + | 0.820126i | ||||
\(738\) | 730.861 | + | 114.375i | 0.990327 | + | 0.154980i | ||||
\(739\) | 868.687i | 1.17549i | 0.809046 | + | 0.587745i | \(0.199984\pi\) | ||||
−0.809046 | + | 0.587745i | \(0.800016\pi\) | |||||||
\(740\) | −26.6260 | + | 8.76009i | −0.0359811 | + | 0.0118380i | ||||
\(741\) | −25.2132 | + | 77.5983i | −0.0340259 | + | 0.104721i | ||||
\(742\) | 852.569 | − | 136.647i | 1.14902 | − | 0.184160i | ||||
\(743\) | − | 819.871i | − | 1.10346i | −0.834023 | − | 0.551730i | \(-0.813968\pi\) | ||
0.834023 | − | 0.551730i | \(-0.186032\pi\) | |||||||
\(744\) | 328.425 | + | 40.6384i | 0.441432 | + | 0.0546216i | ||||
\(745\) | 550.125 | 0.738422 | ||||||||
\(746\) | −80.0482 | − | 499.438i | −0.107303 | − | 0.669488i | ||||
\(747\) | −66.6452 | − | 21.6543i | −0.0892171 | − | 0.0289884i | ||||
\(748\) | 506.586 | + | 1539.75i | 0.677254 | + | 2.05849i | ||||
\(749\) | −964.070 | −1.28714 | ||||||||
\(750\) | 53.9003 | − | 344.426i | 0.0718671 | − | 0.459234i | ||||
\(751\) | −275.787 | − | 379.588i | −0.367226 | − | 0.505443i | 0.584918 | − | 0.811092i | \(-0.301127\pi\) |
−0.952144 | + | 0.305649i | \(0.901127\pi\) | |||||||
\(752\) | −312.589 | + | 104.123i | −0.415677 | + | 0.138462i | ||||
\(753\) | −27.1608 | − | 19.7335i | −0.0360701 | − | 0.0262065i | ||||
\(754\) | 39.8482 | + | 248.622i | 0.0528491 | + | 0.329737i | ||||
\(755\) | 42.2056 | + | 58.0911i | 0.0559015 | + | 0.0769418i | ||||
\(756\) | −2.57878 | − | 698.753i | −0.00341108 | − | 0.924276i | ||||
\(757\) | 4.86327 | − | 14.9676i | 0.00642440 | − | 0.0197723i | −0.947793 | − | 0.318886i | \(-0.896691\pi\) |
0.954217 | + | 0.299114i | \(0.0966911\pi\) | |||||||
\(758\) | 690.407 | − | 692.959i | 0.910827 | − | 0.914194i | ||||
\(759\) | 241.869 | + | 78.5881i | 0.318668 | + | 0.103542i | ||||
\(760\) | −351.749 | − | 347.876i | −0.462827 | − | 0.457731i | ||||
\(761\) | 98.1508 | + | 71.3107i | 0.128976 | + | 0.0937066i | 0.650403 | − | 0.759589i | \(-0.274600\pi\) |
−0.521427 | + | 0.853296i | \(0.674600\pi\) | |||||||
\(762\) | −36.8656 | + | 72.6842i | −0.0483801 | + | 0.0953860i | ||||
\(763\) | −1271.18 | + | 413.033i | −1.66604 | + | 0.541328i | ||||
\(764\) | −74.4895 | − | 226.408i | −0.0974993 | − | 0.296346i | ||||
\(765\) | 158.811 | + | 488.769i | 0.207596 | + | 0.638914i | ||||
\(766\) | −910.136 | + | 913.501i | −1.18817 | + | 1.19256i | ||||
\(767\) | 172.893 | − | 237.967i | 0.225415 | − | 0.310256i | ||||
\(768\) | 196.689 | − | 279.298i | 0.256105 | − | 0.363669i | ||||
\(769\) | −1133.84 | −1.47443 | −0.737216 | − | 0.675658i | \(-0.763860\pi\) | ||||
−0.737216 | + | 0.675658i | \(0.763860\pi\) | |||||||
\(770\) | −1046.78 | − | 163.815i | −1.35946 | − | 0.212746i | ||||
\(771\) | 364.229 | + | 501.318i | 0.472411 | + | 0.650218i | ||||
\(772\) | 87.4108 | − | 121.249i | 0.113226 | − | 0.157058i | ||||
\(773\) | 145.151 | + | 446.728i | 0.187776 | + | 0.577915i | 0.999985 | − | 0.00545140i | \(-0.00173524\pi\) |
−0.812209 | + | 0.583366i | \(0.801735\pi\) | |||||||
\(774\) | −176.941 | + | 1130.66i | −0.228606 | + | 1.46080i | ||||
\(775\) | −117.696 | + | 400.647i | −0.151866 | + | 0.516964i | ||||
\(776\) | −311.184 | − | 156.392i | −0.401010 | − | 0.201536i | ||||
\(777\) | 6.86860 | + | 21.1394i | 0.00883989 | + | 0.0272064i | ||||
\(778\) | 93.8613 | − | 185.057i | 0.120644 | − | 0.237862i | ||||
\(779\) | −548.445 | − | 754.870i | −0.704038 | − | 0.969025i | ||||
\(780\) | −18.5899 | + | 57.9407i | −0.0238333 | + | 0.0742829i | ||||
\(781\) | 1820.85 | 2.33143 | ||||||||
\(782\) | 188.365 | + | 368.007i | 0.240876 | + | 0.470597i | ||||
\(783\) | 477.033 | − | 656.580i | 0.609238 | − | 0.838544i | ||||
\(784\) | 81.6474 | + | 245.114i | 0.104142 | + | 0.312645i | ||||
\(785\) | 149.375 | + | 459.730i | 0.190287 | + | 0.585644i | ||||
\(786\) | −43.5972 | + | 22.3153i | −0.0554671 | + | 0.0283910i | ||||
\(787\) | 847.027 | − | 275.216i | 1.07627 | − | 0.349703i | 0.283346 | − | 0.959018i | \(-0.408556\pi\) |
0.792928 | + | 0.609315i | \(0.208556\pi\) | |||||||
\(788\) | −337.082 | + | 467.572i | −0.427769 | + | 0.593366i | ||||
\(789\) | 349.953 | + | 254.256i | 0.443540 | + | 0.322251i | ||||
\(790\) | −588.217 | − | 298.345i | −0.744578 | − | 0.377652i | ||||
\(791\) | 425.182 | + | 138.150i | 0.537525 | + | 0.174653i | ||||
\(792\) | −991.883 | + | 512.326i | −1.25238 | + | 0.646876i | ||||
\(793\) | −61.3175 | + | 188.716i | −0.0773235 | + | 0.237977i | ||||
\(794\) | 33.7410 | + | 210.518i | 0.0424950 | + | 0.265136i | ||||
\(795\) | 142.453 | + | 196.070i | 0.179187 | + | 0.246629i | ||||
\(796\) | 973.538 | − | 3.59288i | 1.22304 | − | 0.00451367i | ||||
\(797\) | −49.7487 | − | 36.1445i | −0.0624199 | − | 0.0453507i | 0.556138 | − | 0.831090i | \(-0.312283\pi\) |
−0.618558 | + | 0.785739i | \(0.712283\pi\) | |||||||
\(798\) | −276.886 | + | 277.909i | −0.346975 | + | 0.348257i | ||||
\(799\) | −253.751 | − | 349.258i | −0.317585 | − | 0.437119i | ||||
\(800\) | 307.596 | + | 301.971i | 0.384494 | + | 0.377464i | ||||
\(801\) | −426.068 | −0.531921 | ||||||||
\(802\) | 773.592 | − | 395.965i | 0.964579 | − | 0.493722i | ||||
\(803\) | −763.344 | − | 248.025i | −0.950615 | − | 0.308874i | ||||
\(804\) | 1.04795 | + | 283.954i | 0.00130341 | + | 0.353177i | ||||
\(805\) | −270.225 | −0.335684 | ||||||||
\(806\) | 88.8445 | − | 188.248i | 0.110229 | − | 0.233558i | ||||
\(807\) | − | 458.350i | − | 0.567968i | ||||||
\(808\) | −1.39999 | + | 9.16738i | −0.00173267 | + | 0.0113458i | ||||
\(809\) | 93.7547 | − | 288.547i | 0.115890 | − | 0.356672i | −0.876242 | − | 0.481872i | \(-0.839957\pi\) |
0.992132 | + | 0.125200i | \(0.0399572\pi\) | |||||||
\(810\) | −218.197 | + | 111.685i | −0.269379 | + | 0.137882i | ||||
\(811\) | − | 287.487i | − | 0.354484i | −0.984167 | − | 0.177242i | \(-0.943282\pi\) | ||
0.984167 | − | 0.177242i | \(-0.0567176\pi\) | |||||||
\(812\) | −369.860 | + | 1152.77i | −0.455493 | + | 1.41967i | ||||
\(813\) | −326.653 | + | 237.327i | −0.401787 | + | 0.291915i | ||||
\(814\) | 56.3103 | − | 56.5185i | 0.0691773 | − | 0.0694331i | ||||
\(815\) | −321.523 | + | 442.538i | −0.394506 | + | 0.542991i | ||||
\(816\) | 426.702 | + | 135.170i | 0.522920 | + | 0.165650i | ||||
\(817\) | 1167.80 | − | 848.459i | 1.42938 | − | 1.03851i | ||||
\(818\) | −49.3925 | − | 308.170i | −0.0603820 | − | 0.376736i | ||||
\(819\) | −186.063 | − | 60.4555i | −0.227183 | − | 0.0738163i | ||||
\(820\) | −411.098 | − | 561.458i | −0.501338 | − | 0.684705i | ||||
\(821\) | 269.145 | − | 828.342i | 0.327825 | − | 1.00894i | −0.642324 | − | 0.766434i | \(-0.722029\pi\) |
0.970149 | − | 0.242510i | \(-0.0779706\pi\) | |||||||
\(822\) | −23.4741 | − | 11.9062i | −0.0285573 | − | 0.0144844i | ||||
\(823\) | 574.273 | − | 790.420i | 0.697781 | − | 0.960413i | −0.302194 | − | 0.953247i | \(-0.597719\pi\) |
0.999974 | − | 0.00716608i | \(-0.00228105\pi\) | |||||||
\(824\) | 105.096 | + | 103.938i | 0.127543 | + | 0.126139i | ||||
\(825\) | 107.365 | + | 330.436i | 0.130140 | + | 0.400529i | ||||
\(826\) | 1258.93 | − | 644.387i | 1.52413 | − | 0.780130i | ||||
\(827\) | 1140.54 | − | 370.583i | 1.37913 | − | 0.448105i | 0.476744 | − | 0.879042i | \(-0.341817\pi\) |
0.902382 | + | 0.430937i | \(0.141817\pi\) | |||||||
\(828\) | −229.730 | + | 168.207i | −0.277451 | + | 0.203149i | ||||
\(829\) | −587.618 | − | 426.930i | −0.708828 | − | 0.514993i | 0.173968 | − | 0.984751i | \(-0.444341\pi\) |
−0.882795 | + | 0.469758i | \(0.844341\pi\) | |||||||
\(830\) | 30.0343 | + | 58.6778i | 0.0361859 | + | 0.0706961i | ||||
\(831\) | − | 134.273i | − | 0.161580i | ||||||
\(832\) | −128.217 | − | 172.428i | −0.154107 | − | 0.207246i | ||||
\(833\) | −273.867 | + | 198.976i | −0.328772 | + | 0.238867i | ||||
\(834\) | 191.671 | − | 377.897i | 0.229821 | − | 0.453114i | ||||
\(835\) | 295.925 | − | 96.1518i | 0.354401 | − | 0.115152i | ||||
\(836\) | 1340.80 | + | 430.187i | 1.60382 | + | 0.514577i | ||||
\(837\) | −631.945 | + | 225.387i | −0.755012 | + | 0.269279i | ||||
\(838\) | −226.549 | + | 1447.66i | −0.270345 | + | 1.72751i | ||||
\(839\) | −1476.64 | + | 479.789i | −1.76000 | + | 0.571858i | −0.997200 | − | 0.0747808i | \(-0.976174\pi\) |
−0.762797 | + | 0.646638i | \(0.776174\pi\) | |||||||
\(840\) | −205.731 | + | 208.021i | −0.244918 | + | 0.247645i | ||||
\(841\) | −457.193 | + | 332.170i | −0.543630 | + | 0.394970i | ||||
\(842\) | 208.489 | + | 32.6272i | 0.247612 | + | 0.0387496i | ||||
\(843\) | − | 36.0802i | − | 0.0427998i | ||||||
\(844\) | 363.518 | + | 1104.90i | 0.430708 | + | 1.30912i | ||||
\(845\) | −433.287 | − | 314.802i | −0.512766 | − | 0.372546i | ||||
\(846\) | 209.853 | − | 210.629i | 0.248053 | − | 0.248970i | ||||
\(847\) | 1939.29 | − | 630.114i | 2.28960 | − | 0.743936i | ||||
\(848\) | −855.791 | + | 6.31676i | −1.00919 | + | 0.00744901i | ||||
\(849\) | 19.4766 | + | 59.9429i | 0.0229407 | + | 0.0706042i | ||||
\(850\) | −255.483 | + | 503.709i | −0.300568 | + | 0.592598i | ||||
\(851\) | 11.9603 | − | 16.4619i | 0.0140543 | − | 0.0193442i | ||||
\(852\) | 294.035 | − | 407.862i | 0.345112 | − | 0.478711i | ||||
\(853\) | −415.732 | + | 1279.49i | −0.487377 | + | 1.49999i | 0.341132 | + | 0.940015i | \(0.389190\pi\) |
−0.828509 | + | 0.559976i | \(0.810810\pi\) | |||||||
\(854\) | −673.375 | + | 675.864i | −0.788495 | + | 0.791410i | ||||
\(855\) | 424.594 | + | 137.959i | 0.496601 | + | 0.161355i | ||||
\(856\) | 944.593 | + | 144.253i | 1.10350 | + | 0.168520i | ||||
\(857\) | 894.050 | − | 649.566i | 1.04323 | − | 0.757953i | 0.0723186 | − | 0.997382i | \(-0.476960\pi\) |
0.970914 | + | 0.239429i | \(0.0769601\pi\) | |||||||
\(858\) | −27.4097 | − | 171.015i | −0.0319460 | − | 0.199318i | ||||
\(859\) | −437.193 | + | 601.745i | −0.508956 | + | 0.700518i | −0.983743 | − | 0.179583i | \(-0.942525\pi\) |
0.474787 | + | 0.880101i | \(0.342525\pi\) | |||||||
\(860\) | 868.590 | − | 635.978i | 1.00999 | − | 0.739509i | ||||
\(861\) | −446.424 | + | 324.346i | −0.518495 | + | 0.376709i | ||||
\(862\) | 25.0168 | − | 159.858i | 0.0290218 | − | 0.185450i | ||||
\(863\) | − | 1109.84i | − | 1.28602i | −0.765857 | − | 0.643011i | \(-0.777685\pi\) | ||
0.765857 | − | 0.643011i | \(-0.222315\pi\) | |||||||
\(864\) | −102.027 | + | 685.022i | −0.118087 | + | 0.792849i | ||||
\(865\) | 203.388 | − | 625.965i | 0.235131 | − | 0.723659i | ||||
\(866\) | 5.33566 | + | 33.2904i | 0.00616127 | + | 0.0384415i | ||||
\(867\) | 200.845i | 0.231655i | ||||||||
\(868\) | 790.394 | − | 613.988i | 0.910592 | − | 0.707359i | ||||
\(869\) | 1877.29 | 2.16029 | ||||||||
\(870\) | −335.528 | + | 53.7772i | −0.385664 | + | 0.0618129i | ||||
\(871\) | 169.871 | + | 55.1943i | 0.195030 | + | 0.0633689i | ||||
\(872\) | 1307.31 | − | 214.482i | 1.49920 | − | 0.245965i | ||||
\(873\) | 314.290 | 0.360011 | ||||||||
\(874\) | 354.814 | + | 55.5260i | 0.405965 | + | 0.0635309i | ||||
\(875\) | −619.729 | − | 852.983i | −0.708261 | − | 0.974838i | ||||
\(876\) | −178.823 | + | 130.934i | −0.204136 | + | 0.149468i | ||||
\(877\) | −347.368 | − | 252.378i | −0.396087 | − | 0.287774i | 0.371858 | − | 0.928289i | \(-0.378721\pi\) |
−0.767945 | + | 0.640516i | \(0.778721\pi\) | |||||||
\(878\) | −1098.68 | + | 176.093i | −1.25135 | + | 0.200562i | ||||
\(879\) | 359.165 | + | 494.348i | 0.408606 | + | 0.562398i | ||||
\(880\) | 1001.12 | + | 317.134i | 1.13764 | + | 0.360380i | ||||
\(881\) | 220.040 | − | 677.215i | 0.249762 | − | 0.768689i | −0.745054 | − | 0.667004i | \(-0.767577\pi\) |
0.994817 | − | 0.101685i | \(-0.0324235\pi\) | |||||||
\(882\) | −165.163 | − | 164.554i | −0.187259 | − | 0.186569i | ||||
\(883\) | 31.7991 | + | 10.3322i | 0.0360126 | + | 0.0117012i | 0.326968 | − | 0.945035i | \(-0.393973\pi\) |
−0.290955 | + | 0.956737i | \(0.593973\pi\) | |||||||
\(884\) | 164.648 | − | 228.386i | 0.186253 | − | 0.258355i | ||||
\(885\) | 321.148 | + | 233.328i | 0.362879 | + | 0.263647i | ||||
\(886\) | 516.853 | + | 262.149i | 0.583355 | + | 0.295880i | ||||
\(887\) | 159.980 | − | 51.9807i | 0.180361 | − | 0.0586029i | −0.217444 | − | 0.976073i | \(-0.569772\pi\) |
0.397805 | + | 0.917470i | \(0.369772\pi\) | |||||||
\(888\) | −3.56676 | − | 21.7400i | −0.00401662 | − | 0.0244820i | ||||
\(889\) | 76.1671 | + | 234.418i | 0.0856773 | + | 0.263688i | ||||
\(890\) | 283.925 | + | 282.879i | 0.319017 | + | 0.317842i | ||||
\(891\) | 410.089 | − | 564.439i | 0.460257 | − | 0.633489i | ||||
\(892\) | 10.9865 | + | 33.3933i | 0.0123168 | + | 0.0374364i | ||||
\(893\) | −375.024 | −0.419959 | ||||||||
\(894\) | −66.8509 | + | 427.180i | −0.0747772 | + | 0.477830i | ||||
\(895\) | −53.2315 | − | 73.2668i | −0.0594765 | − | 0.0818624i | ||||
\(896\) | −174.785 | − | 1018.24i | −0.195072 | − | 1.13643i | ||||
\(897\) | −13.6502 | − | 42.0111i | −0.0152176 | − | 0.0468351i | ||||
\(898\) | −1155.90 | − | 180.891i | −1.28719 | − | 0.201437i | ||||
\(899\) | 1161.98 | − | 33.0466i | 1.29252 | − | 0.0367592i | ||||
\(900\) | −370.390 | − | 118.838i | −0.411545 | − | 0.132042i | ||||
\(901\) | −346.520 | − | 1066.48i | −0.384595 | − | 1.18366i | ||||
\(902\) | 1766.44 | + | 895.944i | 1.95836 | + | 0.993286i | ||||
\(903\) | −501.772 | − | 690.630i | −0.555672 | − | 0.764817i | ||||
\(904\) | −395.921 | − | 198.979i | −0.437966 | − | 0.220109i | ||||
\(905\) | −1100.78 | −1.21633 | ||||||||
\(906\) | −50.2374 | + | 25.7141i | −0.0554497 | + | 0.0283820i | ||||
\(907\) | 171.296 | − | 235.769i | 0.188860 | − | 0.259944i | −0.704078 | − | 0.710122i | \(-0.748640\pi\) |
0.892939 | + | 0.450178i | \(0.148640\pi\) | |||||||
\(908\) | 416.439 | − | 304.915i | 0.458633 | − | 0.335810i | ||||
\(909\) | −2.58609 | − | 7.95918i | −0.00284499 | − | 0.00875597i | ||||
\(910\) | 83.8512 | + | 163.819i | 0.0921442 | + | 0.180021i | ||||
\(911\) | −865.996 | + | 281.379i | −0.950599 | + | 0.308868i | −0.742959 | − | 0.669337i | \(-0.766578\pi\) |
−0.207640 | + | 0.978205i | \(0.566578\pi\) | |||||||
\(912\) | 312.875 | − | 230.865i | 0.343065 | − | 0.253141i | ||||
\(913\) | −151.789 | − | 110.281i | −0.166253 | − | 0.120790i | ||||
\(914\) | −742.077 | + | 1463.08i | −0.811900 | + | 1.60074i | ||||
\(915\) | −254.682 | − | 82.7511i | −0.278341 | − | 0.0904383i | ||||
\(916\) | −258.119 | − | 352.527i | −0.281790 | − | 0.384855i | ||||
\(917\) | −45.7723 | + | 140.873i | −0.0499153 | + | 0.153623i | ||||
\(918\) | −896.039 | + | 143.614i | −0.976078 | + | 0.156442i | ||||
\(919\) | −269.693 | − | 371.200i | −0.293463 | − | 0.403918i | 0.636672 | − | 0.771135i | \(-0.280311\pi\) |
−0.930135 | + | 0.367217i | \(0.880311\pi\) | |||||||
\(920\) | 264.766 | + | 40.4336i | 0.287789 | + | 0.0439496i | ||||
\(921\) | 190.828 | + | 138.645i | 0.207196 | + | 0.150537i | ||||
\(922\) | −527.556 | − | 525.612i | −0.572186 | − | 0.570078i | ||||
\(923\) | −185.898 | − | 255.867i | −0.201407 | − | 0.277212i | ||||
\(924\) | 254.409 | − | 792.936i | 0.275334 | − | 0.858156i | ||||
\(925\) | 27.7990 | 0.0300529 | ||||||||
\(926\) | −720.567 | − | 1407.76i | −0.778150 | − | 1.52026i | ||||
\(927\) | −126.860 | − | 41.2194i | −0.136850 | − | 0.0444654i | ||||
\(928\) | 534.876 | − | 1074.14i | 0.576375 | − | 1.15748i | ||||
\(929\) | −1534.96 | −1.65227 | −0.826137 | − | 0.563469i | \(-0.809467\pi\) | ||||
−0.826137 | + | 0.563469i | \(0.809467\pi\) | |||||||
\(930\) | 254.050 | + | 119.900i | 0.273172 | + | 0.128925i | ||||
\(931\) | 294.071i | 0.315866i | ||||||||
\(932\) | 5.98581 | + | 1621.93i | 0.00642254 | + | 1.74027i | ||||
\(933\) | −248.035 | + | 763.372i | −0.265846 | + | 0.818191i | ||||
\(934\) | −635.028 | − | 1240.65i | −0.679902 | − | 1.32832i | ||||
\(935\) | 1376.00i | 1.47166i | ||||||||
\(936\) | 173.258 | + | 87.0747i | 0.185105 | + | 0.0930285i | ||||
\(937\) | −464.604 | + | 337.554i | −0.495842 | + | 0.360250i | −0.807426 | − | 0.589968i | \(-0.799140\pi\) |
0.311585 | + | 0.950218i | \(0.399140\pi\) | |||||||
\(938\) | 608.373 | + | 606.131i | 0.648585 | + | 0.646196i | ||||
\(939\) | 271.933 | − | 374.284i | 0.289599 | − | 0.398598i | ||||
\(940\) | −279.685 | + | 1.03219i | −0.297538 | + | 0.00109808i | ||||
\(941\) | 638.412 | − | 463.833i | 0.678440 | − | 0.492915i | −0.194400 | − | 0.980922i | \(-0.562276\pi\) |
0.872840 | + | 0.488007i | \(0.162276\pi\) | |||||||
\(942\) | −375.140 | + | 60.1261i | −0.398237 | + | 0.0638281i | ||||
\(943\) | 480.433 | + | 156.102i | 0.509473 | + | 0.165538i | ||||
\(944\) | −1329.92 | + | 442.995i | −1.40881 | + | 0.469275i | ||||
\(945\) | 183.299 | − | 564.135i | 0.193967 | − | 0.596968i | ||||
\(946\) | −1386.05 | + | 2732.73i | −1.46517 | + | 2.88872i | ||||
\(947\) | −504.439 | + | 694.300i | −0.532670 | + | 0.733158i | −0.987534 | − | 0.157403i | \(-0.949688\pi\) |
0.454864 | + | 0.890561i | \(0.349688\pi\) | |||||||
\(948\) | 303.149 | − | 420.504i | 0.319778 | − | 0.443570i | ||||
\(949\) | 43.0804 | + | 132.588i | 0.0453955 | + | 0.139713i | ||||
\(950\) | 223.551 | + | 436.750i | 0.235317 | + | 0.459737i | ||||
\(951\) | 569.589 | − | 185.071i | 0.598937 | − | 0.194607i | ||||
\(952\) | 1202.74 | − | 621.237i | 1.26338 | − | 0.652560i | ||||
\(953\) | 812.977 | + | 590.662i | 0.853071 | + | 0.619793i | 0.925991 | − | 0.377545i | \(-0.123232\pi\) |
−0.0729199 | + | 0.997338i | \(0.523232\pi\) | |||||||
\(954\) | 687.483 | − | 351.890i | 0.720632 | − | 0.368857i | ||||
\(955\) | − | 202.330i | − | 0.211864i | ||||||
\(956\) | 223.187 | − | 695.622i | 0.233459 | − | 0.727638i | ||||
\(957\) | 782.484 | − | 568.508i | 0.817643 | − | 0.594052i | ||||
\(958\) | −1415.06 | − | 717.724i | −1.47710 | − | 0.749190i | ||||
\(959\) | −75.7079 | + | 24.5990i | −0.0789446 | + | 0.0256507i | ||||
\(960\) | 232.701 | − | 173.035i | 0.242397 | − | 0.180245i | ||||
\(961\) | −808.312 | − | 519.762i | −0.841115 | − | 0.540856i | ||||
\(962\) | −13.6910 | − | 2.14255i | −0.0142318 | − | 0.00222718i | ||||
\(963\) | −820.102 | + | 266.467i | −0.851612 | + | 0.276705i | ||||
\(964\) | 640.633 | − | 888.634i | 0.664557 | − | 0.921819i | ||||
\(965\) | 102.652 | − | 74.5813i | 0.106376 | − | 0.0772864i | ||||
\(966\) | 32.8376 | − | 209.834i | 0.0339934 | − | 0.217219i | ||||
\(967\) | 507.531i | 0.524851i | 0.964952 | + | 0.262425i | \(0.0845224\pi\) | ||||
−0.964952 | + | 0.262425i | \(0.915478\pi\) | |||||||
\(968\) | −1994.40 | + | 327.209i | −2.06033 | + | 0.338026i | ||||
\(969\) | 412.178 | + | 299.465i | 0.425364 | + | 0.309045i | ||||
\(970\) | −209.438 | − | 208.666i | −0.215915 | − | 0.215120i | ||||
\(971\) | −392.109 | + | 127.404i | −0.403819 | + | 0.131209i | −0.503882 | − | 0.863772i | \(-0.668096\pi\) |
0.100063 | + | 0.994981i | \(0.468096\pi\) | |||||||
\(972\) | −303.713 | − | 923.127i | −0.312462 | − | 0.949720i | ||||
\(973\) | −396.005 | − | 1218.78i | −0.406994 | − | 1.25260i | ||||
\(974\) | −404.765 | − | 205.298i | −0.415570 | − | 0.210778i | ||||
\(975\) | 35.4718 | − | 48.8227i | 0.0363813 | − | 0.0500746i | ||||
\(976\) | 760.899 | − | 561.453i | 0.779610 | − | 0.575259i | ||||
\(977\) | 38.1628 | − | 117.453i | 0.0390612 | − | 0.120218i | −0.929624 | − | 0.368508i | \(-0.879869\pi\) |
0.968686 | + | 0.248290i | \(0.0798686\pi\) | |||||||
\(978\) | −304.566 | − | 303.444i | −0.311417 | − | 0.310270i | ||||
\(979\) | −1084.94 | − | 352.520i | −1.10822 | − | 0.360081i | ||||
\(980\) | 0.809383 | + | 219.313i | 0.000825901 | + | 0.223789i | ||||
\(981\) | −967.192 | + | 702.706i | −0.985925 | + | 0.716316i | ||||
\(982\) | 491.042 | − | 78.7025i | 0.500043 | − | 0.0801451i | ||||
\(983\) | 264.202 | − | 363.643i | 0.268771 | − | 0.369932i | −0.653203 | − | 0.757183i | \(-0.726575\pi\) |
0.921974 | + | 0.387251i | \(0.126575\pi\) | |||||||
\(984\) | 485.937 | − | 250.995i | 0.493838 | − | 0.255077i | ||||
\(985\) | −395.858 | + | 287.608i | −0.401886 | + | 0.291987i | ||||
\(986\) | 1553.37 | + | 243.092i | 1.57542 | + | 0.246543i | ||||
\(987\) | 221.786i | 0.224707i | ||||||||
\(988\) | −76.4375 | − | 232.329i | −0.0773658 | − | 0.235151i | ||||
\(989\) | −241.494 | + | 743.241i | −0.244180 | + | 0.751508i | ||||
\(990\) | −935.741 | + | 149.977i | −0.945193 | + | 0.151492i | ||||
\(991\) | 804.782i | 0.812091i | 0.913853 | + | 0.406045i | \(0.133092\pi\) | ||||
−0.913853 | + | 0.406045i | \(0.866908\pi\) | |||||||
\(992\) | −866.296 | + | 483.317i | −0.873282 | + | 0.487215i | ||||
\(993\) | −220.112 | −0.221663 | ||||||||
\(994\) | −240.653 | − | 1501.49i | −0.242106 | − | 1.51055i | ||||
\(995\) | 785.982 | + | 255.381i | 0.789931 | + | 0.256664i | ||||
\(996\) | −49.2139 | + | 16.1916i | −0.0494116 | + | 0.0162566i | ||||
\(997\) | 777.454 | 0.779793 | 0.389897 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389897 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(998\) | −27.5169 | + | 175.834i | −0.0275721 | + | 0.176187i | ||||
\(999\) | 26.2537 | + | 36.1352i | 0.0262800 | + | 0.0361713i |
(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 | 124.3.l.a.35.15 | yes | 120 | |
4.3 | odd | 2 | inner | 124.3.l.a.35.11 | ✓ | 120 | |
31.8 | even | 5 | inner | 124.3.l.a.39.11 | yes | 120 | |
124.39 | odd | 10 | inner | 124.3.l.a.39.15 | yes | 120 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.3.l.a.35.11 | ✓ | 120 | 4.3 | odd | 2 | inner | |
124.3.l.a.35.15 | yes | 120 | 1.1 | even | 1 | trivial | |
124.3.l.a.39.11 | yes | 120 | 31.8 | even | 5 | inner | |
124.3.l.a.39.15 | yes | 120 | 124.39 | odd | 10 | inner |