Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(229,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.f (of order \(2\), degree \(1\), 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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.7 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.5 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −3.10921 | + | 3.91571i | −0.621842 | + | 0.783142i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | 3.09410 | 0.442015 | 0.221007 | − | 0.975272i | \(-0.429066\pi\) | ||||
0.221007 | + | 0.975272i | \(0.429066\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −5.53765 | − | 4.39709i | −0.553765 | − | 0.439709i | ||||
\(11\) | 15.9443i | 1.44949i | 0.689019 | + | 0.724743i | \(0.258042\pi\) | ||||
−0.689019 | + | 0.724743i | \(0.741958\pi\) | |||||||
\(12\) | − | 3.46410i | − | 0.288675i | ||||||
\(13\) | 24.8732i | 1.91332i | 0.291208 | + | 0.956660i | \(0.405943\pi\) | ||||
−0.291208 | + | 0.956660i | \(0.594057\pi\) | |||||||
\(14\) | 4.37572i | 0.312551i | ||||||||
\(15\) | −6.78221 | − | 5.38531i | −0.452148 | − | 0.359021i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 12.6980 | 0.746940 | 0.373470 | − | 0.927642i | \(-0.378168\pi\) | ||||
0.373470 | + | 0.927642i | \(0.378168\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | − | 10.4874i | − | 0.551969i | −0.961162 | − | 0.275984i | \(-0.910996\pi\) | ||
0.961162 | − | 0.275984i | \(-0.0890038\pi\) | |||||||
\(20\) | 6.21842 | − | 7.83142i | 0.310921 | − | 0.391571i | ||||
\(21\) | 5.35914i | 0.255197i | ||||||||
\(22\) | −22.5487 | −1.02494 | ||||||||
\(23\) | 22.9821 | + | 0.906621i | 0.999223 | + | 0.0394183i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | −5.66561 | − | 24.3496i | −0.226624 | − | 0.973982i | ||||
\(26\) | −35.1760 | −1.35292 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −6.18820 | −0.221007 | ||||||||
\(29\) | −44.7809 | −1.54417 | −0.772084 | − | 0.635520i | \(-0.780786\pi\) | ||||
−0.772084 | + | 0.635520i | \(0.780786\pi\) | |||||||
\(30\) | 7.61598 | − | 9.59150i | 0.253866 | − | 0.319717i | ||||
\(31\) | −50.0174 | −1.61346 | −0.806732 | − | 0.590917i | \(-0.798766\pi\) | ||||
−0.806732 | + | 0.590917i | \(0.798766\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −27.6164 | −0.836861 | ||||||||
\(34\) | 17.9577i | 0.528167i | ||||||||
\(35\) | −9.62022 | + | 12.1156i | −0.274863 | + | 0.346160i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 39.1282 | 1.05752 | 0.528759 | − | 0.848772i | \(-0.322657\pi\) | ||||
0.528759 | + | 0.848772i | \(0.322657\pi\) | |||||||
\(38\) | 14.8314 | 0.390301 | ||||||||
\(39\) | −43.0816 | −1.10466 | ||||||||
\(40\) | 11.0753 | + | 8.79418i | 0.276883 | + | 0.219854i | ||||
\(41\) | 41.3571 | 1.00871 | 0.504355 | − | 0.863497i | \(-0.331730\pi\) | ||||
0.504355 | + | 0.863497i | \(0.331730\pi\) | |||||||
\(42\) | −7.57897 | −0.180452 | ||||||||
\(43\) | −71.6357 | −1.66595 | −0.832973 | − | 0.553313i | \(-0.813363\pi\) | ||||
−0.832973 | + | 0.553313i | \(0.813363\pi\) | |||||||
\(44\) | − | 31.8887i | − | 0.724743i | ||||||
\(45\) | 9.32763 | − | 11.7471i | 0.207281 | − | 0.261047i | ||||
\(46\) | −1.28216 | + | 32.5016i | −0.0278730 | + | 0.706557i | ||||
\(47\) | − | 17.3085i | − | 0.368266i | −0.982901 | − | 0.184133i | \(-0.941052\pi\) | ||
0.982901 | − | 0.184133i | \(-0.0589477\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −39.4265 | −0.804623 | ||||||||
\(50\) | 34.4355 | − | 8.01238i | 0.688709 | − | 0.160248i | ||||
\(51\) | 21.9936i | 0.431246i | ||||||||
\(52\) | − | 49.7463i | − | 0.956660i | ||||||
\(53\) | 39.6184 | 0.747517 | 0.373758 | − | 0.927526i | \(-0.378069\pi\) | ||||
0.373758 | + | 0.927526i | \(0.378069\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | −62.4335 | − | 49.5744i | −1.13515 | − | 0.901352i | ||||
\(56\) | − | 8.75144i | − | 0.156276i | ||||||
\(57\) | 18.1647 | 0.318679 | ||||||||
\(58\) | − | 63.3298i | − | 1.09189i | ||||||
\(59\) | 24.0107 | 0.406961 | 0.203481 | − | 0.979079i | \(-0.434775\pi\) | ||||
0.203481 | + | 0.979079i | \(0.434775\pi\) | |||||||
\(60\) | 13.5644 | + | 10.7706i | 0.226074 | + | 0.179510i | ||||
\(61\) | − | 76.0777i | − | 1.24717i | −0.781754 | − | 0.623587i | \(-0.785675\pi\) | ||
0.781754 | − | 0.623587i | \(-0.214325\pi\) | |||||||
\(62\) | − | 70.7353i | − | 1.14089i | ||||||
\(63\) | −9.28230 | −0.147338 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −97.3961 | − | 77.3359i | −1.49840 | − | 1.18978i | ||||
\(66\) | − | 39.0555i | − | 0.591750i | ||||||
\(67\) | 76.7774 | 1.14593 | 0.572966 | − | 0.819579i | \(-0.305793\pi\) | ||||
0.572966 | + | 0.819579i | \(0.305793\pi\) | |||||||
\(68\) | −25.3960 | −0.373470 | ||||||||
\(69\) | −1.57031 | + | 39.8062i | −0.0227582 | + | 0.576902i | ||||
\(70\) | −17.1341 | − | 13.6050i | −0.244772 | − | 0.194358i | ||||
\(71\) | 22.9757 | 0.323602 | 0.161801 | − | 0.986823i | \(-0.448270\pi\) | ||||
0.161801 | + | 0.986823i | \(0.448270\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | − | 51.8874i | − | 0.710786i | −0.934717 | − | 0.355393i | \(-0.884347\pi\) | ||
0.934717 | − | 0.355393i | \(-0.115653\pi\) | |||||||
\(74\) | 55.3356i | 0.747779i | ||||||||
\(75\) | 42.1747 | − | 9.81312i | 0.562329 | − | 0.130842i | ||||
\(76\) | 20.9748i | 0.275984i | ||||||||
\(77\) | 49.3334i | 0.640694i | ||||||||
\(78\) | − | 60.9265i | − | 0.781110i | ||||||
\(79\) | − | 25.5241i | − | 0.323090i | −0.986865 | − | 0.161545i | \(-0.948352\pi\) | ||
0.986865 | − | 0.161545i | \(-0.0516478\pi\) | |||||||
\(80\) | −12.4368 | + | 15.6628i | −0.155461 | + | 0.195786i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 58.4877i | 0.713265i | ||||||||
\(83\) | 21.6791 | 0.261194 | 0.130597 | − | 0.991436i | \(-0.458311\pi\) | ||||
0.130597 | + | 0.991436i | \(0.458311\pi\) | |||||||
\(84\) | − | 10.7183i | − | 0.127599i | ||||||
\(85\) | −39.4807 | + | 49.7217i | −0.464479 | + | 0.584961i | ||||
\(86\) | − | 101.308i | − | 1.17800i | ||||||
\(87\) | − | 77.5628i | − | 0.891526i | ||||||
\(88\) | 45.0974 | 0.512471 | ||||||||
\(89\) | 165.958i | 1.86469i | 0.361566 | + | 0.932346i | \(0.382242\pi\) | ||||
−0.361566 | + | 0.932346i | \(0.617758\pi\) | |||||||
\(90\) | 16.6130 | + | 13.1913i | 0.184588 | + | 0.146570i | ||||
\(91\) | 76.9601i | 0.845715i | ||||||||
\(92\) | −45.9642 | − | 1.81324i | −0.499611 | − | 0.0197092i | ||||
\(93\) | − | 86.6327i | − | 0.931534i | ||||||
\(94\) | 24.4779 | 0.260403 | ||||||||
\(95\) | 41.0657 | + | 32.6076i | 0.432270 | + | 0.343237i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 0.580105 | 0.00598047 | 0.00299023 | − | 0.999996i | \(-0.499048\pi\) | ||||
0.00299023 | + | 0.999996i | \(0.499048\pi\) | |||||||
\(98\) | − | 55.7575i | − | 0.568955i | ||||||
\(99\) | − | 47.8330i | − | 0.483162i | ||||||
\(100\) | 11.3312 | + | 48.6991i | 0.113312 | + | 0.486991i | ||||
\(101\) | −164.285 | −1.62658 | −0.813290 | − | 0.581859i | \(-0.802326\pi\) | ||||
−0.813290 | + | 0.581859i | \(0.802326\pi\) | |||||||
\(102\) | −31.1036 | −0.304937 | ||||||||
\(103\) | −160.952 | −1.56264 | −0.781322 | − | 0.624128i | \(-0.785454\pi\) | ||||
−0.781322 | + | 0.624128i | \(0.785454\pi\) | |||||||
\(104\) | 70.3519 | 0.676461 | ||||||||
\(105\) | −20.9849 | − | 16.6627i | −0.199856 | − | 0.158692i | ||||
\(106\) | 56.0288i | 0.528574i | ||||||||
\(107\) | −53.6355 | −0.501266 | −0.250633 | − | 0.968082i | \(-0.580639\pi\) | ||||
−0.250633 | + | 0.968082i | \(0.580639\pi\) | |||||||
\(108\) | 10.3923i | 0.0962250i | ||||||||
\(109\) | 77.5961i | 0.711890i | 0.934507 | + | 0.355945i | \(0.115841\pi\) | ||||
−0.934507 | + | 0.355945i | \(0.884159\pi\) | |||||||
\(110\) | 70.1087 | − | 88.2943i | 0.637352 | − | 0.802675i | ||||
\(111\) | 67.7720i | 0.610559i | ||||||||
\(112\) | 12.3764 | 0.110504 | ||||||||
\(113\) | 61.1674 | 0.541305 | 0.270652 | − | 0.962677i | \(-0.412761\pi\) | ||||
0.270652 | + | 0.962677i | \(0.412761\pi\) | |||||||
\(114\) | 25.6888i | 0.225340i | ||||||||
\(115\) | −75.0064 | + | 87.1725i | −0.652229 | + | 0.758022i | ||||
\(116\) | 89.5618 | 0.772084 | ||||||||
\(117\) | − | 74.6195i | − | 0.637773i | ||||||
\(118\) | 33.9563i | 0.287765i | ||||||||
\(119\) | 39.2889 | 0.330159 | ||||||||
\(120\) | −15.2320 | + | 19.1830i | −0.126933 | + | 0.159858i | ||||
\(121\) | −133.222 | −1.10101 | ||||||||
\(122\) | 107.590 | 0.881886 | ||||||||
\(123\) | 71.6326i | 0.582379i | ||||||||
\(124\) | 100.035 | 0.806732 | ||||||||
\(125\) | 112.961 | + | 53.5230i | 0.903691 | + | 0.428184i | ||||
\(126\) | − | 13.1272i | − | 0.104184i | ||||||
\(127\) | − | 17.0523i | − | 0.134270i | −0.997744 | − | 0.0671350i | \(-0.978614\pi\) | ||
0.997744 | − | 0.0671350i | \(-0.0213858\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | − | 124.077i | − | 0.961835i | ||||||
\(130\) | 109.369 | − | 137.739i | 0.841304 | − | 1.05953i | ||||
\(131\) | 210.657 | 1.60807 | 0.804034 | − | 0.594583i | \(-0.202683\pi\) | ||||
0.804034 | + | 0.594583i | \(0.202683\pi\) | |||||||
\(132\) | 55.2328 | 0.418431 | ||||||||
\(133\) | − | 32.4491i | − | 0.243978i | ||||||
\(134\) | 108.580i | 0.810296i | ||||||||
\(135\) | 20.3466 | + | 16.1559i | 0.150716 | + | 0.119674i | ||||
\(136\) | − | 35.9153i | − | 0.264083i | ||||||
\(137\) | −0.388976 | −0.00283924 | −0.00141962 | − | 0.999999i | \(-0.500452\pi\) | ||||
−0.00141962 | + | 0.999999i | \(0.500452\pi\) | |||||||
\(138\) | −56.2945 | − | 2.22076i | −0.407931 | − | 0.0160925i | ||||
\(139\) | 113.401 | 0.815837 | 0.407918 | − | 0.913018i | \(-0.366255\pi\) | ||||
0.407918 | + | 0.913018i | \(0.366255\pi\) | |||||||
\(140\) | 19.2404 | − | 24.2312i | 0.137432 | − | 0.173080i | ||||
\(141\) | 29.9792 | 0.212618 | ||||||||
\(142\) | 32.4926i | 0.228821i | ||||||||
\(143\) | −396.586 | −2.77333 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 139.233 | − | 175.349i | 0.960230 | − | 1.20930i | ||||
\(146\) | 73.3799 | 0.502602 | ||||||||
\(147\) | − | 68.2888i | − | 0.464549i | ||||||
\(148\) | −78.2564 | −0.528759 | ||||||||
\(149\) | − | 92.8418i | − | 0.623099i | −0.950230 | − | 0.311550i | \(-0.899152\pi\) | ||
0.950230 | − | 0.311550i | \(-0.100848\pi\) | |||||||
\(150\) | 13.8778 | + | 59.6440i | 0.0925190 | + | 0.397627i | ||||
\(151\) | −184.936 | −1.22474 | −0.612372 | − | 0.790570i | \(-0.709784\pi\) | ||||
−0.612372 | + | 0.790570i | \(0.709784\pi\) | |||||||
\(152\) | −29.6629 | −0.195150 | ||||||||
\(153\) | −38.0940 | −0.248980 | ||||||||
\(154\) | −69.7680 | −0.453039 | ||||||||
\(155\) | 155.515 | − | 195.854i | 1.00332 | − | 1.26357i | ||||
\(156\) | 86.1631 | 0.552328 | ||||||||
\(157\) | 176.605 | 1.12488 | 0.562438 | − | 0.826840i | \(-0.309864\pi\) | ||||
0.562438 | + | 0.826840i | \(0.309864\pi\) | |||||||
\(158\) | 36.0966 | 0.228459 | ||||||||
\(159\) | 68.6210i | 0.431579i | ||||||||
\(160\) | −22.1506 | − | 17.5884i | −0.138441 | − | 0.109927i | ||||
\(161\) | 71.1090 | + | 2.80518i | 0.441671 | + | 0.0174235i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | 282.949i | 1.73589i | 0.496664 | + | 0.867943i | \(0.334558\pi\) | ||||
−0.496664 | + | 0.867943i | \(0.665442\pi\) | |||||||
\(164\) | −82.7142 | −0.504355 | ||||||||
\(165\) | 85.8653 | − | 108.138i | 0.520396 | − | 0.655382i | ||||
\(166\) | 30.6588i | 0.184692i | ||||||||
\(167\) | 181.294i | 1.08559i | 0.839864 | + | 0.542797i | \(0.182635\pi\) | ||||
−0.839864 | + | 0.542797i | \(0.817365\pi\) | |||||||
\(168\) | 15.1579 | 0.0902258 | ||||||||
\(169\) | −449.674 | −2.66079 | ||||||||
\(170\) | −70.3171 | − | 55.8342i | −0.413630 | − | 0.328436i | ||||
\(171\) | 31.4622i | 0.183990i | ||||||||
\(172\) | 143.271 | 0.832973 | ||||||||
\(173\) | − | 111.291i | − | 0.643300i | −0.946859 | − | 0.321650i | \(-0.895763\pi\) | ||
0.946859 | − | 0.321650i | \(-0.104237\pi\) | |||||||
\(174\) | 109.690 | 0.630404 | ||||||||
\(175\) | −17.5300 | − | 75.3400i | −0.100171 | − | 0.430514i | ||||
\(176\) | 63.7774i | 0.362372i | ||||||||
\(177\) | 41.5878i | 0.234959i | ||||||||
\(178\) | −234.700 | −1.31854 | ||||||||
\(179\) | 81.4644 | 0.455108 | 0.227554 | − | 0.973765i | \(-0.426927\pi\) | ||||
0.227554 | + | 0.973765i | \(0.426927\pi\) | |||||||
\(180\) | −18.6553 | + | 23.4943i | −0.103640 | + | 0.130524i | ||||
\(181\) | 126.722i | 0.700121i | 0.936727 | + | 0.350061i | \(0.113839\pi\) | ||||
−0.936727 | + | 0.350061i | \(0.886161\pi\) | |||||||
\(182\) | −108.838 | −0.598011 | ||||||||
\(183\) | 131.770 | 0.720057 | ||||||||
\(184\) | 2.56431 | − | 65.0033i | 0.0139365 | − | 0.353279i | ||||
\(185\) | −121.658 | + | 153.215i | −0.657610 | + | 0.828188i | ||||
\(186\) | 122.517 | 0.658694 | ||||||||
\(187\) | 202.461i | 1.08268i | ||||||||
\(188\) | 34.6170i | 0.184133i | ||||||||
\(189\) | − | 16.0774i | − | 0.0850657i | ||||||
\(190\) | −46.1141 | + | 58.0756i | −0.242706 | + | 0.305661i | ||||
\(191\) | − | 111.905i | − | 0.585888i | −0.956130 | − | 0.292944i | \(-0.905365\pi\) | ||
0.956130 | − | 0.292944i | \(-0.0946350\pi\) | |||||||
\(192\) | − | 13.8564i | − | 0.0721688i | ||||||
\(193\) | 162.315i | 0.841011i | 0.907290 | + | 0.420506i | \(0.138147\pi\) | ||||
−0.907290 | + | 0.420506i | \(0.861853\pi\) | |||||||
\(194\) | 0.820393i | 0.00422883i | ||||||||
\(195\) | 133.950 | − | 168.695i | 0.686922 | − | 0.865103i | ||||
\(196\) | 78.8531 | 0.402312 | ||||||||
\(197\) | 351.020i | 1.78183i | 0.454174 | + | 0.890913i | \(0.349934\pi\) | ||||
−0.454174 | + | 0.890913i | \(0.650066\pi\) | |||||||
\(198\) | 67.6461 | 0.341647 | ||||||||
\(199\) | 17.0849i | 0.0858540i | 0.999078 | + | 0.0429270i | \(0.0136683\pi\) | ||||
−0.999078 | + | 0.0429270i | \(0.986332\pi\) | |||||||
\(200\) | −68.8709 | + | 16.0248i | −0.344355 | + | 0.0801238i | ||||
\(201\) | 132.982i | 0.661604i | ||||||||
\(202\) | − | 232.333i | − | 1.15017i | ||||||
\(203\) | −138.557 | −0.682545 | ||||||||
\(204\) | − | 43.9871i | − | 0.215623i | ||||||
\(205\) | −128.588 | + | 161.942i | −0.627258 | + | 0.789963i | ||||
\(206\) | − | 227.621i | − | 1.10496i | ||||||
\(207\) | −68.9464 | − | 2.71986i | −0.333074 | − | 0.0131394i | ||||
\(208\) | 99.4926i | 0.478330i | ||||||||
\(209\) | 167.215 | 0.800071 | ||||||||
\(210\) | 23.5646 | − | 29.6771i | 0.112212 | − | 0.141319i | ||||
\(211\) | −167.474 | −0.793717 | −0.396858 | − | 0.917880i | \(-0.629900\pi\) | ||||
−0.396858 | + | 0.917880i | \(0.629900\pi\) | |||||||
\(212\) | −79.2368 | −0.373758 | ||||||||
\(213\) | 39.7951i | 0.186832i | ||||||||
\(214\) | − | 75.8520i | − | 0.354449i | ||||||
\(215\) | 222.731 | − | 280.505i | 1.03596 | − | 1.30467i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −154.759 | −0.713175 | ||||||||
\(218\) | −109.737 | −0.503383 | ||||||||
\(219\) | 89.8716 | 0.410373 | ||||||||
\(220\) | 124.867 | + | 99.1487i | 0.567577 | + | 0.450676i | ||||
\(221\) | 315.839i | 1.42914i | ||||||||
\(222\) | −95.8441 | −0.431730 | ||||||||
\(223\) | − | 53.1179i | − | 0.238197i | −0.992882 | − | 0.119098i | \(-0.962000\pi\) | ||
0.992882 | − | 0.119098i | \(-0.0380004\pi\) | |||||||
\(224\) | 17.5029i | 0.0781379i | ||||||||
\(225\) | 16.9968 | + | 73.0487i | 0.0755414 | + | 0.324661i | ||||
\(226\) | 86.5038i | 0.382760i | ||||||||
\(227\) | 371.776 | 1.63778 | 0.818889 | − | 0.573951i | \(-0.194590\pi\) | ||||
0.818889 | + | 0.573951i | \(0.194590\pi\) | |||||||
\(228\) | −36.3294 | −0.159340 | ||||||||
\(229\) | 297.261i | 1.29808i | 0.760752 | + | 0.649042i | \(0.224830\pi\) | ||||
−0.760752 | + | 0.649042i | \(0.775170\pi\) | |||||||
\(230\) | −123.281 | − | 106.075i | −0.536002 | − | 0.461196i | ||||
\(231\) | −85.4480 | −0.369905 | ||||||||
\(232\) | 126.660i | 0.545946i | ||||||||
\(233\) | 180.942i | 0.776575i | 0.921538 | + | 0.388287i | \(0.126933\pi\) | ||||
−0.921538 | + | 0.388287i | \(0.873067\pi\) | |||||||
\(234\) | 105.528 | 0.450974 | ||||||||
\(235\) | 67.7751 | + | 53.8158i | 0.288405 | + | 0.229003i | ||||
\(236\) | −48.0214 | −0.203481 | ||||||||
\(237\) | 44.2091 | 0.186536 | ||||||||
\(238\) | 55.5628i | 0.233457i | ||||||||
\(239\) | 339.522 | 1.42059 | 0.710296 | − | 0.703903i | \(-0.248561\pi\) | ||||
0.710296 | + | 0.703903i | \(0.248561\pi\) | |||||||
\(240\) | −27.1289 | − | 21.5412i | −0.113037 | − | 0.0897552i | ||||
\(241\) | − | 33.1123i | − | 0.137395i | −0.997638 | − | 0.0686977i | \(-0.978116\pi\) | ||
0.997638 | − | 0.0686977i | \(-0.0218844\pi\) | |||||||
\(242\) | − | 188.405i | − | 0.778532i | ||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 152.155i | 0.623587i | ||||||||
\(245\) | 122.585 | − | 154.383i | 0.500349 | − | 0.630135i | ||||
\(246\) | −101.304 | −0.411804 | ||||||||
\(247\) | 260.855 | 1.05609 | ||||||||
\(248\) | 141.471i | 0.570446i | ||||||||
\(249\) | 37.5492i | 0.150800i | ||||||||
\(250\) | −75.6930 | + | 159.752i | −0.302772 | + | 0.639006i | ||||
\(251\) | − | 21.2171i | − | 0.0845304i | −0.999106 | − | 0.0422652i | \(-0.986543\pi\) | ||
0.999106 | − | 0.0422652i | \(-0.0134574\pi\) | |||||||
\(252\) | 18.5646 | 0.0736691 | ||||||||
\(253\) | −14.4555 | + | 366.435i | −0.0571363 | + | 1.44836i | ||||
\(254\) | 24.1156 | 0.0949432 | ||||||||
\(255\) | −86.1205 | − | 68.3826i | −0.337727 | − | 0.268167i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 368.667i | − | 1.43450i | −0.696815 | − | 0.717251i | \(-0.745400\pi\) | ||
0.696815 | − | 0.717251i | \(-0.254600\pi\) | |||||||
\(258\) | 175.471 | 0.680120 | ||||||||
\(259\) | 121.067 | 0.467439 | ||||||||
\(260\) | 194.792 | + | 154.672i | 0.749201 | + | 0.594892i | ||||
\(261\) | 134.343 | 0.514723 | ||||||||
\(262\) | 297.914i | 1.13708i | ||||||||
\(263\) | −182.829 | −0.695169 | −0.347584 | − | 0.937649i | \(-0.612998\pi\) | ||||
−0.347584 | + | 0.937649i | \(0.612998\pi\) | |||||||
\(264\) | 78.1110i | 0.295875i | ||||||||
\(265\) | −123.182 | + | 155.134i | −0.464837 | + | 0.585412i | ||||
\(266\) | 45.8900 | 0.172519 | ||||||||
\(267\) | −287.447 | −1.07658 | ||||||||
\(268\) | −153.555 | −0.572966 | ||||||||
\(269\) | −231.329 | −0.859958 | −0.429979 | − | 0.902839i | \(-0.641479\pi\) | ||||
−0.429979 | + | 0.902839i | \(0.641479\pi\) | |||||||
\(270\) | −22.8479 | + | 28.7745i | −0.0846220 | + | 0.106572i | ||||
\(271\) | 241.547 | 0.891318 | 0.445659 | − | 0.895203i | \(-0.352969\pi\) | ||||
0.445659 | + | 0.895203i | \(0.352969\pi\) | |||||||
\(272\) | 50.7919 | 0.186735 | ||||||||
\(273\) | −133.299 | −0.488274 | ||||||||
\(274\) | − | 0.550095i | − | 0.00200765i | ||||||
\(275\) | 388.238 | − | 90.3344i | 1.41177 | − | 0.328489i | ||||
\(276\) | 3.14063 | − | 79.6124i | 0.0113791 | − | 0.288451i | ||||
\(277\) | 217.095i | 0.783737i | 0.920021 | + | 0.391869i | \(0.128171\pi\) | ||||
−0.920021 | + | 0.391869i | \(0.871829\pi\) | |||||||
\(278\) | 160.374i | 0.576884i | ||||||||
\(279\) | 150.052 | 0.537821 | ||||||||
\(280\) | 34.2681 | + | 27.2101i | 0.122386 | + | 0.0971789i | ||||
\(281\) | − | 262.796i | − | 0.935218i | −0.883935 | − | 0.467609i | \(-0.845115\pi\) | ||
0.883935 | − | 0.467609i | \(-0.154885\pi\) | |||||||
\(282\) | 42.3970i | 0.150344i | ||||||||
\(283\) | 71.0126 | 0.250928 | 0.125464 | − | 0.992098i | \(-0.459958\pi\) | ||||
0.125464 | + | 0.992098i | \(0.459958\pi\) | |||||||
\(284\) | −45.9514 | −0.161801 | ||||||||
\(285\) | −56.4780 | + | 71.1278i | −0.198168 | + | 0.249571i | ||||
\(286\) | − | 560.858i | − | 1.96104i | ||||||
\(287\) | 127.963 | 0.445864 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | −127.761 | −0.442080 | ||||||||
\(290\) | 247.981 | + | 196.906i | 0.855107 | + | 0.678985i | ||||
\(291\) | 1.00477i | 0.00345282i | ||||||||
\(292\) | 103.775i | 0.355393i | ||||||||
\(293\) | −491.470 | −1.67737 | −0.838687 | − | 0.544614i | \(-0.816676\pi\) | ||||
−0.838687 | + | 0.544614i | \(0.816676\pi\) | |||||||
\(294\) | 96.5749 | 0.328486 | ||||||||
\(295\) | −74.6544 | + | 94.0190i | −0.253066 | + | 0.318708i | ||||
\(296\) | − | 110.671i | − | 0.373889i | ||||||
\(297\) | 82.8493 | 0.278954 | ||||||||
\(298\) | 131.298 | 0.440598 | ||||||||
\(299\) | −22.5505 | + | 571.638i | −0.0754198 | + | 1.91183i | ||||
\(300\) | −84.3493 | + | 19.6262i | −0.281164 | + | 0.0654208i | ||||
\(301\) | −221.648 | −0.736372 | ||||||||
\(302\) | − | 261.539i | − | 0.866025i | ||||||
\(303\) | − | 284.549i | − | 0.939106i | ||||||
\(304\) | − | 41.9496i | − | 0.137992i | ||||||
\(305\) | 297.898 | + | 236.542i | 0.976715 | + | 0.775546i | ||||
\(306\) | − | 53.8730i | − | 0.176056i | ||||||
\(307\) | − | 357.082i | − | 1.16313i | −0.813498 | − | 0.581567i | \(-0.802440\pi\) | ||
0.813498 | − | 0.581567i | \(-0.197560\pi\) | |||||||
\(308\) | − | 98.6669i | − | 0.320347i | ||||||
\(309\) | − | 278.778i | − | 0.902193i | ||||||
\(310\) | 276.979 | + | 219.931i | 0.893481 | + | 0.709455i | ||||
\(311\) | 137.819 | 0.443149 | 0.221575 | − | 0.975143i | \(-0.428880\pi\) | ||||
0.221575 | + | 0.975143i | \(0.428880\pi\) | |||||||
\(312\) | 121.853i | 0.390555i | ||||||||
\(313\) | −476.224 | −1.52148 | −0.760740 | − | 0.649056i | \(-0.775164\pi\) | ||||
−0.760740 | + | 0.649056i | \(0.775164\pi\) | |||||||
\(314\) | 249.758i | 0.795407i | ||||||||
\(315\) | 28.8606 | − | 36.3468i | 0.0916211 | − | 0.115387i | ||||
\(316\) | 51.0483i | 0.161545i | ||||||||
\(317\) | 290.212i | 0.915495i | 0.889082 | + | 0.457748i | \(0.151344\pi\) | ||||
−0.889082 | + | 0.457748i | \(0.848656\pi\) | |||||||
\(318\) | −97.0448 | −0.305172 | ||||||||
\(319\) | − | 714.002i | − | 2.23825i | ||||||
\(320\) | 24.8737 | − | 31.3257i | 0.0777303 | − | 0.0978928i | ||||
\(321\) | − | 92.8994i | − | 0.289406i | ||||||
\(322\) | −3.96712 | + | 100.563i | −0.0123202 | + | 0.312309i | ||||
\(323\) | − | 133.169i | − | 0.412288i | ||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 605.650 | − | 140.922i | 1.86354 | − | 0.433605i | ||||
\(326\) | −400.151 | −1.22746 | ||||||||
\(327\) | −134.400 | −0.411010 | ||||||||
\(328\) | − | 116.975i | − | 0.356633i | ||||||
\(329\) | − | 53.5542i | − | 0.162779i | ||||||
\(330\) | 152.930 | + | 121.432i | 0.463425 | + | 0.367975i | ||||
\(331\) | 124.642 | 0.376561 | 0.188280 | − | 0.982115i | \(-0.439709\pi\) | ||||
0.188280 | + | 0.982115i | \(0.439709\pi\) | |||||||
\(332\) | −43.3581 | −0.130597 | ||||||||
\(333\) | −117.385 | −0.352506 | ||||||||
\(334\) | −256.389 | −0.767631 | ||||||||
\(335\) | −238.717 | + | 300.638i | −0.712589 | + | 0.897428i | ||||
\(336\) | 21.4366i | 0.0637993i | ||||||||
\(337\) | −281.809 | −0.836228 | −0.418114 | − | 0.908395i | \(-0.637309\pi\) | ||||
−0.418114 | + | 0.908395i | \(0.637309\pi\) | |||||||
\(338\) | − | 635.935i | − | 1.88146i | ||||||
\(339\) | 105.945i | 0.312522i | ||||||||
\(340\) | 78.9615 | − | 99.4433i | 0.232240 | − | 0.292480i | ||||
\(341\) | − | 797.495i | − | 2.33869i | ||||||
\(342\) | −44.4943 | −0.130100 | ||||||||
\(343\) | −273.601 | −0.797670 | ||||||||
\(344\) | 202.616i | 0.589001i | ||||||||
\(345\) | −150.987 | − | 129.915i | −0.437644 | − | 0.376565i | ||||
\(346\) | 157.389 | 0.454882 | ||||||||
\(347\) | 31.0131i | 0.0893749i | 0.999001 | + | 0.0446874i | \(0.0142292\pi\) | ||||
−0.999001 | + | 0.0446874i | \(0.985771\pi\) | |||||||
\(348\) | 155.126i | 0.445763i | ||||||||
\(349\) | 226.092 | 0.647828 | 0.323914 | − | 0.946087i | \(-0.395001\pi\) | ||||
0.323914 | + | 0.946087i | \(0.395001\pi\) | |||||||
\(350\) | 106.547 | − | 24.7911i | 0.304420 | − | 0.0708318i | ||||
\(351\) | 129.245 | 0.368219 | ||||||||
\(352\) | −90.1949 | −0.256235 | ||||||||
\(353\) | 230.573i | 0.653180i | 0.945166 | + | 0.326590i | \(0.105900\pi\) | ||||
−0.945166 | + | 0.326590i | \(0.894100\pi\) | |||||||
\(354\) | −58.8140 | −0.166141 | ||||||||
\(355\) | −71.4364 | + | 89.9663i | −0.201229 | + | 0.253426i | ||||
\(356\) | − | 331.915i | − | 0.932346i | ||||||
\(357\) | 68.0503i | 0.190617i | ||||||||
\(358\) | 115.208i | 0.321810i | ||||||||
\(359\) | 569.575i | 1.58656i | 0.608858 | + | 0.793279i | \(0.291628\pi\) | ||||
−0.608858 | + | 0.793279i | \(0.708372\pi\) | |||||||
\(360\) | −33.2259 | − | 26.3825i | −0.0922942 | − | 0.0732848i | ||||
\(361\) | 251.014 | 0.695331 | ||||||||
\(362\) | −179.212 | −0.495061 | ||||||||
\(363\) | − | 230.748i | − | 0.635669i | ||||||
\(364\) | − | 153.920i | − | 0.422858i | ||||||
\(365\) | 203.176 | + | 161.329i | 0.556647 | + | 0.441997i | ||||
\(366\) | 186.351i | 0.509157i | ||||||||
\(367\) | 707.351 | 1.92739 | 0.963693 | − | 0.267012i | \(-0.0860364\pi\) | ||||
0.963693 | + | 0.267012i | \(0.0860364\pi\) | |||||||
\(368\) | 91.9285 | + | 3.62648i | 0.249806 | + | 0.00985458i | ||||
\(369\) | −124.071 | −0.336236 | ||||||||
\(370\) | −216.678 | − | 172.050i | −0.585617 | − | 0.465000i | ||||
\(371\) | 122.583 | 0.330413 | ||||||||
\(372\) | 173.265i | 0.465767i | ||||||||
\(373\) | 476.230 | 1.27676 | 0.638378 | − | 0.769723i | \(-0.279606\pi\) | ||||
0.638378 | + | 0.769723i | \(0.279606\pi\) | |||||||
\(374\) | −286.323 | −0.765570 | ||||||||
\(375\) | −92.7046 | + | 195.655i | −0.247212 | + | 0.521747i | ||||
\(376\) | −48.9558 | −0.130202 | ||||||||
\(377\) | − | 1113.84i | − | 2.95449i | ||||||
\(378\) | 22.7369 | 0.0601506 | ||||||||
\(379\) | − | 218.771i | − | 0.577232i | −0.957445 | − | 0.288616i | \(-0.906805\pi\) | ||
0.957445 | − | 0.288616i | \(-0.0931950\pi\) | |||||||
\(380\) | −82.1313 | − | 65.2151i | −0.216135 | − | 0.171619i | ||||
\(381\) | 29.5354 | 0.0775208 | ||||||||
\(382\) | 158.257 | 0.414286 | ||||||||
\(383\) | −25.9382 | −0.0677238 | −0.0338619 | − | 0.999427i | \(-0.510781\pi\) | ||||
−0.0338619 | + | 0.999427i | \(0.510781\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | −193.176 | − | 153.388i | −0.501755 | − | 0.398411i | ||||
\(386\) | −229.548 | −0.594685 | ||||||||
\(387\) | 214.907 | 0.555315 | ||||||||
\(388\) | −1.16021 | −0.00299023 | ||||||||
\(389\) | 117.093i | 0.301011i | 0.988609 | + | 0.150505i | \(0.0480901\pi\) | ||||
−0.988609 | + | 0.150505i | \(0.951910\pi\) | |||||||
\(390\) | 238.571 | + | 189.434i | 0.611720 | + | 0.485727i | ||||
\(391\) | 291.827 | + | 11.5123i | 0.746360 | + | 0.0294431i | ||||
\(392\) | 111.515i | 0.284477i | ||||||||
\(393\) | 364.869i | 0.928419i | ||||||||
\(394\) | −496.417 | −1.25994 | ||||||||
\(395\) | 99.9452 | + | 79.3600i | 0.253026 | + | 0.200911i | ||||
\(396\) | 95.6661i | 0.241581i | ||||||||
\(397\) | 184.113i | 0.463760i | 0.972744 | + | 0.231880i | \(0.0744876\pi\) | ||||
−0.972744 | + | 0.231880i | \(0.925512\pi\) | |||||||
\(398\) | −24.1618 | −0.0607079 | ||||||||
\(399\) | 56.2035 | 0.140861 | ||||||||
\(400\) | −22.6624 | − | 97.3982i | −0.0566561 | − | 0.243496i | ||||
\(401\) | 483.910i | 1.20676i | 0.797454 | + | 0.603379i | \(0.206179\pi\) | ||||
−0.797454 | + | 0.603379i | \(0.793821\pi\) | |||||||
\(402\) | −188.066 | −0.467825 | ||||||||
\(403\) | − | 1244.09i | − | 3.08707i | ||||||
\(404\) | 328.569 | 0.813290 | ||||||||
\(405\) | −27.9829 | + | 35.2414i | −0.0690936 | + | 0.0870158i | ||||
\(406\) | − | 195.949i | − | 0.482632i | ||||||
\(407\) | 623.873i | 1.53286i | ||||||||
\(408\) | 62.2072 | 0.152469 | ||||||||
\(409\) | −587.697 | −1.43691 | −0.718457 | − | 0.695572i | \(-0.755151\pi\) | ||||
−0.718457 | + | 0.695572i | \(0.755151\pi\) | |||||||
\(410\) | −229.021 | − | 181.851i | −0.558588 | − | 0.443538i | ||||
\(411\) | − | 0.673726i | − | 0.00163924i | ||||||
\(412\) | 321.905 | 0.781322 | ||||||||
\(413\) | 74.2915 | 0.179883 | ||||||||
\(414\) | 3.84647 | − | 97.5049i | 0.00929098 | − | 0.235519i | ||||
\(415\) | −67.4048 | + | 84.8890i | −0.162421 | + | 0.204552i | ||||
\(416\) | −140.704 | −0.338230 | ||||||||
\(417\) | 196.417i | 0.471024i | ||||||||
\(418\) | 236.477i | 0.565736i | ||||||||
\(419\) | − | 249.476i | − | 0.595408i | −0.954658 | − | 0.297704i | \(-0.903779\pi\) | ||
0.954658 | − | 0.297704i | \(-0.0962208\pi\) | |||||||
\(420\) | 41.9697 | + | 33.3254i | 0.0999279 | + | 0.0793462i | ||||
\(421\) | 297.570i | 0.706816i | 0.935469 | + | 0.353408i | \(0.114977\pi\) | ||||
−0.935469 | + | 0.353408i | \(0.885023\pi\) | |||||||
\(422\) | − | 236.844i | − | 0.561243i | ||||||
\(423\) | 51.9255i | 0.122755i | ||||||||
\(424\) | − | 112.058i | − | 0.264287i | ||||||
\(425\) | −71.9418 | − | 309.190i | −0.169275 | − | 0.727507i | ||||
\(426\) | −56.2788 | −0.132110 | ||||||||
\(427\) | − | 235.392i | − | 0.551269i | ||||||
\(428\) | 107.271 | 0.250633 | ||||||||
\(429\) | − | 686.908i | − | 1.60118i | ||||||
\(430\) | 396.694 | + | 314.989i | 0.922543 | + | 0.732531i | ||||
\(431\) | 83.3118i | 0.193299i | 0.995318 | + | 0.0966495i | \(0.0308126\pi\) | ||||
−0.995318 | + | 0.0966495i | \(0.969187\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | −574.608 | −1.32704 | −0.663520 | − | 0.748159i | \(-0.730938\pi\) | ||||
−0.663520 | + | 0.748159i | \(0.730938\pi\) | |||||||
\(434\) | − | 218.862i | − | 0.504291i | ||||||
\(435\) | 303.714 | + | 241.159i | 0.698192 | + | 0.554389i | ||||
\(436\) | − | 155.192i | − | 0.355945i | ||||||
\(437\) | 9.50810 | − | 241.023i | 0.0217577 | − | 0.551540i | ||||
\(438\) | 127.098i | 0.290177i | ||||||||
\(439\) | −196.774 | −0.448231 | −0.224116 | − | 0.974563i | \(-0.571949\pi\) | ||||
−0.224116 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(440\) | −140.217 | + | 176.589i | −0.318676 | + | 0.401338i | ||||
\(441\) | 118.280 | 0.268208 | ||||||||
\(442\) | −446.664 | −1.01055 | ||||||||
\(443\) | 13.1466i | 0.0296764i | 0.999890 | + | 0.0148382i | \(0.00472332\pi\) | ||||
−0.999890 | + | 0.0148382i | \(0.995277\pi\) | |||||||
\(444\) | − | 135.544i | − | 0.305279i | ||||||
\(445\) | −649.842 | − | 515.997i | −1.46032 | − | 1.15954i | ||||
\(446\) | 75.1201 | 0.168431 | ||||||||
\(447\) | 160.807 | 0.359747 | ||||||||
\(448\) | −24.7528 | −0.0552518 | ||||||||
\(449\) | 7.26549 | 0.0161815 | 0.00809074 | − | 0.999967i | \(-0.497425\pi\) | ||||
0.00809074 | + | 0.999967i | \(0.497425\pi\) | |||||||
\(450\) | −103.306 | + | 24.0371i | −0.229570 | + | 0.0534159i | ||||
\(451\) | 659.412i | 1.46211i | ||||||||
\(452\) | −122.335 | −0.270652 | ||||||||
\(453\) | − | 320.319i | − | 0.707106i | ||||||
\(454\) | 525.770i | 1.15808i | ||||||||
\(455\) | −301.354 | − | 239.285i | −0.662315 | − | 0.525901i | ||||
\(456\) | − | 51.3776i | − | 0.112670i | ||||||
\(457\) | 635.868 | 1.39140 | 0.695698 | − | 0.718334i | \(-0.255095\pi\) | ||||
0.695698 | + | 0.718334i | \(0.255095\pi\) | |||||||
\(458\) | −420.391 | −0.917885 | ||||||||
\(459\) | − | 65.9807i | − | 0.143749i | ||||||
\(460\) | 150.013 | − | 174.345i | 0.326115 | − | 0.379011i | ||||
\(461\) | −638.029 | −1.38401 | −0.692006 | − | 0.721892i | \(-0.743273\pi\) | ||||
−0.692006 | + | 0.721892i | \(0.743273\pi\) | |||||||
\(462\) | − | 120.842i | − | 0.261562i | ||||||
\(463\) | − | 593.754i | − | 1.28241i | −0.767371 | − | 0.641203i | \(-0.778436\pi\) | ||
0.767371 | − | 0.641203i | \(-0.221564\pi\) | |||||||
\(464\) | −179.124 | −0.386042 | ||||||||
\(465\) | 339.229 | + | 269.359i | 0.729524 | + | 0.579267i | ||||
\(466\) | −255.891 | −0.549121 | ||||||||
\(467\) | −596.261 | −1.27679 | −0.638395 | − | 0.769709i | \(-0.720401\pi\) | ||||
−0.638395 | + | 0.769709i | \(0.720401\pi\) | |||||||
\(468\) | 149.239i | 0.318887i | ||||||||
\(469\) | 237.557 | 0.506519 | ||||||||
\(470\) | −76.1070 | + | 95.8484i | −0.161930 | + | 0.203933i | ||||
\(471\) | 305.890i | 0.649447i | ||||||||
\(472\) | − | 67.9125i | − | 0.143882i | ||||||
\(473\) | − | 1142.18i | − | 2.41477i | ||||||
\(474\) | 62.5211i | 0.131901i | ||||||||
\(475\) | −255.364 | + | 59.4175i | −0.537608 | + | 0.125090i | ||||
\(476\) | −78.5777 | −0.165079 | ||||||||
\(477\) | −118.855 | −0.249172 | ||||||||
\(478\) | 480.156i | 1.00451i | ||||||||
\(479\) | − | 203.911i | − | 0.425702i | −0.977085 | − | 0.212851i | \(-0.931725\pi\) | ||
0.977085 | − | 0.212851i | \(-0.0682750\pi\) | |||||||
\(480\) | 30.4639 | − | 38.3660i | 0.0634665 | − | 0.0799291i | ||||
\(481\) | 973.242i | 2.02337i | ||||||||
\(482\) | 46.8279 | 0.0971533 | ||||||||
\(483\) | −4.85871 | + | 123.164i | −0.0100594 | + | 0.254999i | ||||
\(484\) | 266.444 | 0.550505 | ||||||||
\(485\) | −1.80367 | + | 2.27153i | −0.00371891 | + | 0.00468356i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | − | 390.999i | − | 0.802873i | −0.915887 | − | 0.401436i | \(-0.868511\pi\) | ||
0.915887 | − | 0.401436i | \(-0.131489\pi\) | |||||||
\(488\) | −215.180 | −0.440943 | ||||||||
\(489\) | −490.083 | −1.00221 | ||||||||
\(490\) | 218.330 | + | 173.362i | 0.445572 | + | 0.353800i | ||||
\(491\) | 449.372 | 0.915217 | 0.457609 | − | 0.889154i | \(-0.348706\pi\) | ||||
0.457609 | + | 0.889154i | \(0.348706\pi\) | |||||||
\(492\) | − | 143.265i | − | 0.291189i | ||||||
\(493\) | −568.627 | −1.15340 | ||||||||
\(494\) | 368.905i | 0.746770i | ||||||||
\(495\) | 187.300 | + | 148.723i | 0.378385 | + | 0.300451i | ||||
\(496\) | −200.070 | −0.403366 | ||||||||
\(497\) | 71.0892 | 0.143037 | ||||||||
\(498\) | −53.1027 | −0.106632 | ||||||||
\(499\) | 770.506 | 1.54410 | 0.772050 | − | 0.635561i | \(-0.219231\pi\) | ||||
0.772050 | + | 0.635561i | \(0.219231\pi\) | |||||||
\(500\) | −225.923 | − | 107.046i | −0.451846 | − | 0.214092i | ||||
\(501\) | −314.011 | −0.626768 | ||||||||
\(502\) | 30.0055 | 0.0597720 | ||||||||
\(503\) | 185.848 | 0.369480 | 0.184740 | − | 0.982787i | \(-0.440856\pi\) | ||||
0.184740 | + | 0.982787i | \(0.440856\pi\) | |||||||
\(504\) | 26.2543i | 0.0520919i | ||||||||
\(505\) | 510.795 | − | 643.291i | 1.01148 | − | 1.27384i | ||||
\(506\) | −518.217 | − | 20.4431i | −1.02414 | − | 0.0404015i | ||||
\(507\) | − | 778.858i | − | 1.53621i | ||||||
\(508\) | 34.1046i | 0.0671350i | ||||||||
\(509\) | −110.051 | −0.216210 | −0.108105 | − | 0.994139i | \(-0.534478\pi\) | ||||
−0.108105 | + | 0.994139i | \(0.534478\pi\) | |||||||
\(510\) | 96.7076 | − | 121.793i | 0.189623 | − | 0.238809i | ||||
\(511\) | − | 160.545i | − | 0.314178i | ||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −54.4942 | −0.106226 | ||||||||
\(514\) | 521.374 | 1.01435 | ||||||||
\(515\) | 500.435 | − | 630.243i | 0.971718 | − | 1.22377i | ||||
\(516\) | 248.153i | 0.480917i | ||||||||
\(517\) | 275.973 | 0.533796 | ||||||||
\(518\) | 171.214i | 0.330529i | ||||||||
\(519\) | 192.761 | 0.371409 | ||||||||
\(520\) | −218.739 | + | 275.478i | −0.420652 | + | 0.529765i | ||||
\(521\) | 39.4422i | 0.0757049i | 0.999283 | + | 0.0378524i | \(0.0120517\pi\) | ||||
−0.999283 | + | 0.0378524i | \(0.987948\pi\) | |||||||
\(522\) | 189.989i | 0.363964i | ||||||||
\(523\) | 288.174 | 0.551003 | 0.275501 | − | 0.961301i | \(-0.411156\pi\) | ||||
0.275501 | + | 0.961301i | \(0.411156\pi\) | |||||||
\(524\) | −421.314 | −0.804034 | ||||||||
\(525\) | 130.493 | − | 30.3628i | 0.248558 | − | 0.0578339i | ||||
\(526\) | − | 258.560i | − | 0.491558i | ||||||
\(527\) | −635.120 | −1.20516 | ||||||||
\(528\) | −110.466 | −0.209215 | ||||||||
\(529\) | 527.356 | + | 41.6722i | 0.996892 | + | 0.0787753i | ||||
\(530\) | −219.393 | − | 174.206i | −0.413949 | − | 0.328690i | ||||
\(531\) | −72.0321 | −0.135654 | ||||||||
\(532\) | 64.8982i | 0.121989i | ||||||||
\(533\) | 1028.68i | 1.92998i | ||||||||
\(534\) | − | 406.512i | − | 0.761258i | ||||||
\(535\) | 166.764 | − | 210.021i | 0.311709 | − | 0.392563i | ||||
\(536\) | − | 217.159i | − | 0.405148i | ||||||
\(537\) | 141.100i | 0.262757i | ||||||||
\(538\) | − | 327.148i | − | 0.608082i | ||||||
\(539\) | − | 628.630i | − | 1.16629i | ||||||
\(540\) | −40.6933 | − | 32.3119i | −0.0753579 | − | 0.0598368i | ||||
\(541\) | −153.598 | −0.283915 | −0.141958 | − | 0.989873i | \(-0.545340\pi\) | ||||
−0.141958 | + | 0.989873i | \(0.545340\pi\) | |||||||
\(542\) | 341.599i | 0.630257i | ||||||||
\(543\) | −219.489 | −0.404215 | ||||||||
\(544\) | 71.8307i | 0.132042i | ||||||||
\(545\) | −303.844 | − | 241.263i | −0.557512 | − | 0.442684i | ||||
\(546\) | − | 188.513i | − | 0.345262i | ||||||
\(547\) | − | 756.260i | − | 1.38256i | −0.722588 | − | 0.691279i | \(-0.757047\pi\) | ||
0.722588 | − | 0.691279i | \(-0.242953\pi\) | |||||||
\(548\) | 0.777952 | 0.00141962 | ||||||||
\(549\) | 228.233i | 0.415725i | ||||||||
\(550\) | 127.752 | + | 549.051i | 0.232277 | + | 0.998275i | ||||
\(551\) | 469.635i | 0.852333i | ||||||||
\(552\) | 112.589 | + | 4.44152i | 0.203965 | + | 0.00804623i | ||||
\(553\) | − | 78.9743i | − | 0.142811i | ||||||
\(554\) | −307.019 | −0.554186 | ||||||||
\(555\) | −265.376 | − | 210.718i | −0.478154 | − | 0.379671i | ||||
\(556\) | −226.803 | −0.407918 | ||||||||
\(557\) | −276.554 | −0.496506 | −0.248253 | − | 0.968695i | \(-0.579856\pi\) | ||||
−0.248253 | + | 0.968695i | \(0.579856\pi\) | |||||||
\(558\) | 212.206i | 0.380297i | ||||||||
\(559\) | − | 1781.81i | − | 3.18749i | ||||||
\(560\) | −38.4809 | + | 48.4624i | −0.0687158 | + | 0.0865401i | ||||
\(561\) | −350.673 | −0.625086 | ||||||||
\(562\) | 371.650 | 0.661299 | ||||||||
\(563\) | 535.076 | 0.950401 | 0.475201 | − | 0.879878i | \(-0.342376\pi\) | ||||
0.475201 | + | 0.879878i | \(0.342376\pi\) | |||||||
\(564\) | −59.9584 | −0.106309 | ||||||||
\(565\) | −190.183 | + | 239.514i | −0.336606 | + | 0.423919i | ||||
\(566\) | 100.427i | 0.177433i | ||||||||
\(567\) | 27.8469 | 0.0491127 | ||||||||
\(568\) | − | 64.9851i | − | 0.114410i | ||||||
\(569\) | 94.4406i | 0.165976i | 0.996551 | + | 0.0829882i | \(0.0264464\pi\) | ||||
−0.996551 | + | 0.0829882i | \(0.973554\pi\) | |||||||
\(570\) | −100.590 | − | 79.8719i | −0.176474 | − | 0.140126i | ||||
\(571\) | 594.892i | 1.04184i | 0.853605 | + | 0.520921i | \(0.174411\pi\) | ||||
−0.853605 | + | 0.520921i | \(0.825589\pi\) | |||||||
\(572\) | 793.173 | 1.38667 | ||||||||
\(573\) | 193.825 | 0.338263 | ||||||||
\(574\) | 180.967i | 0.315274i | ||||||||
\(575\) | −108.132 | − | 564.741i | −0.188055 | − | 0.982158i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 511.175i | 0.885919i | 0.896542 | + | 0.442960i | \(0.146071\pi\) | ||||
−0.896542 | + | 0.442960i | \(0.853929\pi\) | |||||||
\(578\) | − | 180.682i | − | 0.312598i | ||||||
\(579\) | −281.138 | −0.485558 | ||||||||
\(580\) | −278.467 | + | 350.698i | −0.480115 | + | 0.604652i | ||||
\(581\) | 67.0772 | 0.115451 | ||||||||
\(582\) | −1.42096 | −0.00244152 | ||||||||
\(583\) | 631.689i | 1.08351i | ||||||||
\(584\) | −146.760 | −0.251301 | ||||||||
\(585\) | 292.188 | + | 232.008i | 0.499467 | + | 0.396594i | ||||
\(586\) | − | 695.044i | − | 1.18608i | ||||||
\(587\) | 492.563i | 0.839119i | 0.907728 | + | 0.419560i | \(0.137815\pi\) | ||||
−0.907728 | + | 0.419560i | \(0.862185\pi\) | |||||||
\(588\) | 136.578i | 0.232275i | ||||||||
\(589\) | 524.553i | 0.890582i | ||||||||
\(590\) | −132.963 | − | 105.577i | −0.225361 | − | 0.178944i | ||||
\(591\) | −607.984 | −1.02874 | ||||||||
\(592\) | 156.513 | 0.264380 | ||||||||
\(593\) | 535.477i | 0.902996i | 0.892272 | + | 0.451498i | \(0.149110\pi\) | ||||
−0.892272 | + | 0.451498i | \(0.850890\pi\) | |||||||
\(594\) | 117.167i | 0.197250i | ||||||||
\(595\) | −122.157 | + | 153.844i | −0.205307 | + | 0.258561i | ||||
\(596\) | 185.684i | 0.311550i | ||||||||
\(597\) | −29.5920 | −0.0495678 | ||||||||
\(598\) | −808.418 | − | 31.8913i | −1.35187 | − | 0.0533299i | ||||
\(599\) | −522.025 | −0.871495 | −0.435747 | − | 0.900069i | \(-0.643516\pi\) | ||||
−0.435747 | + | 0.900069i | \(0.643516\pi\) | |||||||
\(600\) | −27.7557 | − | 119.288i | −0.0462595 | − | 0.198813i | ||||
\(601\) | 500.049 | 0.832028 | 0.416014 | − | 0.909358i | \(-0.363427\pi\) | ||||
0.416014 | + | 0.909358i | \(0.363427\pi\) | |||||||
\(602\) | − | 313.458i | − | 0.520694i | ||||||
\(603\) | −230.332 | −0.381977 | ||||||||
\(604\) | 369.873 | 0.612372 | ||||||||
\(605\) | 414.216 | − | 521.660i | 0.684655 | − | 0.862248i | ||||
\(606\) | 402.413 | 0.664048 | ||||||||
\(607\) | 232.429i | 0.382915i | 0.981501 | + | 0.191457i | \(0.0613214\pi\) | ||||
−0.981501 | + | 0.191457i | \(0.938679\pi\) | |||||||
\(608\) | 59.3257 | 0.0975752 | ||||||||
\(609\) | − | 239.987i | − | 0.394068i | ||||||
\(610\) | −334.520 | + | 421.292i | −0.548394 | + | 0.690642i | ||||
\(611\) | 430.517 | 0.704610 | ||||||||
\(612\) | 76.1879 | 0.124490 | ||||||||
\(613\) | −654.378 | −1.06750 | −0.533751 | − | 0.845642i | \(-0.679218\pi\) | ||||
−0.533751 | + | 0.845642i | \(0.679218\pi\) | |||||||
\(614\) | 504.991 | 0.822460 | ||||||||
\(615\) | −280.493 | − | 222.721i | −0.456085 | − | 0.362148i | ||||
\(616\) | 139.536 | 0.226520 | ||||||||
\(617\) | 675.896 | 1.09546 | 0.547728 | − | 0.836657i | \(-0.315493\pi\) | ||||
0.547728 | + | 0.836657i | \(0.315493\pi\) | |||||||
\(618\) | 394.251 | 0.637947 | ||||||||
\(619\) | − | 1153.52i | − | 1.86352i | −0.363075 | − | 0.931760i | \(-0.618273\pi\) | ||
0.363075 | − | 0.931760i | \(-0.381727\pi\) | |||||||
\(620\) | −311.029 | + | 391.707i | −0.501660 | + | 0.631786i | ||||
\(621\) | 4.71094 | − | 119.419i | 0.00758606 | − | 0.192301i | ||||
\(622\) | 194.906i | 0.313354i | ||||||||
\(623\) | 513.490i | 0.824221i | ||||||||
\(624\) | −172.326 | −0.276164 | ||||||||
\(625\) | −560.802 | + | 275.910i | −0.897283 | + | 0.441456i | ||||
\(626\) | − | 673.482i | − | 1.07585i | ||||||
\(627\) | 289.625i | 0.461921i | ||||||||
\(628\) | −353.211 | −0.562438 | ||||||||
\(629\) | 496.849 | 0.789903 | ||||||||
\(630\) | 51.4022 | + | 40.8151i | 0.0815908 | + | 0.0647859i | ||||
\(631\) | − | 210.863i | − | 0.334173i | −0.985942 | − | 0.167086i | \(-0.946564\pi\) | ||
0.985942 | − | 0.167086i | \(-0.0534359\pi\) | |||||||
\(632\) | −72.1932 | −0.114230 | ||||||||
\(633\) | − | 290.074i | − | 0.458253i | ||||||
\(634\) | −410.422 | −0.647353 | ||||||||
\(635\) | 66.7719 | + | 53.0192i | 0.105153 | + | 0.0834947i | ||||
\(636\) | − | 137.242i | − | 0.215789i | ||||||
\(637\) | − | 980.662i | − | 1.53950i | ||||||
\(638\) | 1009.75 | 1.58268 | ||||||||
\(639\) | −68.9272 | −0.107867 | ||||||||
\(640\) | 44.3012 | + | 35.1767i | 0.0692207 | + | 0.0549636i | ||||
\(641\) | 358.037i | 0.558560i | 0.960210 | + | 0.279280i | \(0.0900958\pi\) | ||||
−0.960210 | + | 0.279280i | \(0.909904\pi\) | |||||||
\(642\) | 131.380 | 0.204641 | ||||||||
\(643\) | 1177.59 | 1.83141 | 0.915703 | − | 0.401855i | \(-0.131634\pi\) | ||||
0.915703 | + | 0.401855i | \(0.131634\pi\) | |||||||
\(644\) | −142.218 | − | 5.61036i | −0.220835 | − | 0.00871173i | ||||
\(645\) | 485.848 | + | 385.781i | 0.753253 | + | 0.598109i | ||||
\(646\) | 188.329 | 0.291531 | ||||||||
\(647\) | − | 556.482i | − | 0.860096i | −0.902806 | − | 0.430048i | \(-0.858497\pi\) | ||
0.902806 | − | 0.430048i | \(-0.141503\pi\) | |||||||
\(648\) | − | 25.4558i | − | 0.0392837i | ||||||
\(649\) | 382.835i | 0.589884i | ||||||||
\(650\) | 199.293 | + | 856.519i | 0.306605 | + | 1.31772i | ||||
\(651\) | − | 268.050i | − | 0.411752i | ||||||
\(652\) | − | 565.899i | − | 0.867943i | ||||||
\(653\) | 1076.49i | 1.64853i | 0.566204 | + | 0.824265i | \(0.308412\pi\) | ||||
−0.566204 | + | 0.824265i | \(0.691588\pi\) | |||||||
\(654\) | − | 190.071i | − | 0.290628i | ||||||
\(655\) | −654.977 | + | 824.872i | −0.999965 | + | 1.25935i | ||||
\(656\) | 165.428 | 0.252177 | ||||||||
\(657\) | 155.662i | 0.236929i | ||||||||
\(658\) | 75.7371 | 0.115102 | ||||||||
\(659\) | 1142.54i | 1.73375i | 0.498526 | + | 0.866875i | \(0.333875\pi\) | ||||
−0.498526 | + | 0.866875i | \(0.666125\pi\) | |||||||
\(660\) | −171.731 | + | 216.276i | −0.260198 | + | 0.327691i | ||||
\(661\) | − | 1194.32i | − | 1.80684i | −0.428754 | − | 0.903421i | \(-0.641047\pi\) | ||
0.428754 | − | 0.903421i | \(-0.358953\pi\) | |||||||
\(662\) | 176.270i | 0.266269i | ||||||||
\(663\) | −547.049 | −0.825112 | ||||||||
\(664\) | − | 61.3177i | − | 0.0923459i | ||||||
\(665\) | 127.061 | + | 100.891i | 0.191070 | + | 0.151716i | ||||
\(666\) | − | 166.007i | − | 0.249260i | ||||||
\(667\) | −1029.16 | − | 40.5993i | −1.54297 | − | 0.0608685i | ||||
\(668\) | − | 362.588i | − | 0.542797i | ||||||
\(669\) | 92.0029 | 0.137523 | ||||||||
\(670\) | −425.167 | − | 337.597i | −0.634577 | − | 0.503877i | ||||
\(671\) | 1213.01 | 1.80776 | ||||||||
\(672\) | −30.3159 | −0.0451129 | ||||||||
\(673\) | − | 481.936i | − | 0.716100i | −0.933702 | − | 0.358050i | \(-0.883442\pi\) | ||
0.933702 | − | 0.358050i | \(-0.116558\pi\) | |||||||
\(674\) | − | 398.538i | − | 0.591302i | ||||||
\(675\) | −126.524 | + | 29.4394i | −0.187443 | + | 0.0436139i | ||||
\(676\) | 899.348 | 1.33040 | ||||||||
\(677\) | 180.841 | 0.267121 | 0.133560 | − | 0.991041i | \(-0.457359\pi\) | ||||
0.133560 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(678\) | −149.829 | −0.220987 | ||||||||
\(679\) | 1.79490 | 0.00264345 | ||||||||
\(680\) | 140.634 | + | 111.668i | 0.206815 | + | 0.164218i | ||||
\(681\) | 643.935i | 0.945572i | ||||||||
\(682\) | 1127.83 | 1.65371 | ||||||||
\(683\) | − | 18.5491i | − | 0.0271582i | −0.999908 | − | 0.0135791i | \(-0.995678\pi\) | ||
0.999908 | − | 0.0135791i | \(-0.00432250\pi\) | |||||||
\(684\) | − | 62.9244i | − | 0.0919948i | ||||||
\(685\) | 1.20941 | − | 1.52312i | 0.00176556 | − | 0.00222353i | ||||
\(686\) | − | 386.930i | − | 0.564038i | ||||||
\(687\) | −514.872 | −0.749450 | ||||||||
\(688\) | −286.543 | −0.416487 | ||||||||
\(689\) | 985.434i | 1.43024i | ||||||||
\(690\) | 183.727 | − | 213.528i | 0.266271 | − | 0.309461i | ||||
\(691\) | −502.845 | −0.727706 | −0.363853 | − | 0.931456i | \(-0.618539\pi\) | ||||
−0.363853 | + | 0.931456i | \(0.618539\pi\) | |||||||
\(692\) | 222.582i | 0.321650i | ||||||||
\(693\) | − | 148.000i | − | 0.213565i | ||||||
\(694\) | −43.8591 | −0.0631976 | ||||||||
\(695\) | −352.589 | + | 444.047i | −0.507322 | + | 0.638916i | ||||
\(696\) | −219.381 | −0.315202 | ||||||||
\(697\) | 525.152 | 0.753446 | ||||||||
\(698\) | 319.742i | 0.458084i | ||||||||
\(699\) | −313.401 | −0.448356 | ||||||||
\(700\) | 35.0599 | + | 150.680i | 0.0500856 | + | 0.215257i | ||||
\(701\) | 183.664i | 0.262002i | 0.991382 | + | 0.131001i | \(0.0418192\pi\) | ||||
−0.991382 | + | 0.131001i | \(0.958181\pi\) | |||||||
\(702\) | 182.780i | 0.260370i | ||||||||
\(703\) | − | 410.353i | − | 0.583717i | ||||||
\(704\) | − | 127.555i | − | 0.181186i | ||||||
\(705\) | −93.2116 | + | 117.390i | −0.132215 | + | 0.166510i | ||||
\(706\) | −326.079 | −0.461868 | ||||||||
\(707\) | −508.313 | −0.718972 | ||||||||
\(708\) | − | 83.1755i | − | 0.117480i | ||||||
\(709\) | − | 39.2008i | − | 0.0552903i | −0.999618 | − | 0.0276452i | \(-0.991199\pi\) | ||
0.999618 | − | 0.0276452i | \(-0.00880085\pi\) | |||||||
\(710\) | −127.232 | − | 101.026i | −0.179199 | − | 0.142291i | ||||
\(711\) | 76.5724i | 0.107697i | ||||||||
\(712\) | 469.399 | 0.659268 | ||||||||
\(713\) | −1149.51 | − | 45.3468i | −1.61221 | − | 0.0636000i | ||||
\(714\) | −96.2377 | −0.134787 | ||||||||
\(715\) | 1233.07 | − | 1552.92i | 1.72457 | − | 2.17191i | ||||
\(716\) | −162.929 | −0.227554 | ||||||||
\(717\) | 588.069i | 0.820179i | ||||||||
\(718\) | −805.500 | −1.12187 | ||||||||
\(719\) | −44.6052 | −0.0620378 | −0.0310189 | − | 0.999519i | \(-0.509875\pi\) | ||||
−0.0310189 | + | 0.999519i | \(0.509875\pi\) | |||||||
\(720\) | 37.3105 | − | 46.9885i | 0.0518202 | − | 0.0652619i | ||||
\(721\) | −498.003 | −0.690711 | ||||||||
\(722\) | 354.988i | 0.491673i | ||||||||
\(723\) | 57.3522 | 0.0793253 | ||||||||
\(724\) | − | 253.444i | − | 0.350061i | ||||||
\(725\) | 253.711 | + | 1090.39i | 0.349946 | + | 1.50399i | ||||
\(726\) | 326.327 | 0.449486 | ||||||||
\(727\) | 966.099 | 1.32889 | 0.664443 | − | 0.747339i | \(-0.268669\pi\) | ||||
0.664443 | + | 0.747339i | \(0.268669\pi\) | |||||||
\(728\) | 217.676 | 0.299005 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −228.153 | + | 287.334i | −0.312539 | + | 0.393609i | ||||
\(731\) | −909.629 | −1.24436 | ||||||||
\(732\) | −263.541 | −0.360028 | ||||||||
\(733\) | −58.5900 | −0.0799317 | −0.0399659 | − | 0.999201i | \(-0.512725\pi\) | ||||
−0.0399659 | + | 0.999201i | \(0.512725\pi\) | |||||||
\(734\) | 1000.35i | 1.36287i | ||||||||
\(735\) | 267.399 | + | 212.324i | 0.363808 | + | 0.288876i | ||||
\(736\) | −5.12862 | + | 130.007i | −0.00696824 | + | 0.176639i | ||||
\(737\) | 1224.17i | 1.66101i | ||||||||
\(738\) | − | 175.463i | − | 0.237755i | ||||||
\(739\) | −513.758 | −0.695207 | −0.347603 | − | 0.937642i | \(-0.613004\pi\) | ||||
−0.347603 | + | 0.937642i | \(0.613004\pi\) | |||||||
\(740\) | 243.316 | − | 306.429i | 0.328805 | − | 0.414094i | ||||
\(741\) | 451.814i | 0.609735i | ||||||||
\(742\) | 173.359i | 0.233637i | ||||||||
\(743\) | 474.006 | 0.637962 | 0.318981 | − | 0.947761i | \(-0.396659\pi\) | ||||
0.318981 | + | 0.947761i | \(0.396659\pi\) | |||||||
\(744\) | −245.034 | −0.329347 | ||||||||
\(745\) | 363.542 | + | 288.665i | 0.487976 | + | 0.387470i | ||||
\(746\) | 673.491i | 0.902803i | ||||||||
\(747\) | −65.0372 | −0.0870645 | ||||||||
\(748\) | − | 404.922i | − | 0.541340i | ||||||
\(749\) | −165.954 | −0.221567 | ||||||||
\(750\) | −276.698 | − | 131.104i | −0.368930 | − | 0.174805i | ||||
\(751\) | 870.368i | 1.15894i | 0.814992 | + | 0.579472i | \(0.196741\pi\) | ||||
−0.814992 | + | 0.579472i | \(0.803259\pi\) | |||||||
\(752\) | − | 69.2340i | − | 0.0920665i | ||||||
\(753\) | 36.7491 | 0.0488036 | ||||||||
\(754\) | 1575.21 | 2.08914 | ||||||||
\(755\) | 575.006 | − | 724.157i | 0.761597 | − | 0.959149i | ||||
\(756\) | 32.1548i | 0.0425329i | ||||||||
\(757\) | −439.359 | −0.580395 | −0.290197 | − | 0.956967i | \(-0.593721\pi\) | ||||
−0.290197 | + | 0.956967i | \(0.593721\pi\) | |||||||
\(758\) | 309.389 | 0.408164 | ||||||||
\(759\) | −634.684 | − | 25.0376i | −0.836211 | − | 0.0329877i | ||||
\(760\) | 92.2281 | − | 116.151i | 0.121353 | − | 0.152831i | ||||
\(761\) | −814.037 | −1.06969 | −0.534847 | − | 0.844949i | \(-0.679631\pi\) | ||||
−0.534847 | + | 0.844949i | \(0.679631\pi\) | |||||||
\(762\) | 41.7694i | 0.0548155i | ||||||||
\(763\) | 240.090i | 0.314666i | ||||||||
\(764\) | 223.809i | 0.292944i | ||||||||
\(765\) | 118.442 | − | 149.165i | 0.154826 | − | 0.194987i | ||||
\(766\) | − | 36.6822i | − | 0.0478880i | ||||||
\(767\) | 597.222i | 0.778647i | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | − | 1396.26i | − | 1.81568i | −0.419320 | − | 0.907838i | \(-0.637731\pi\) | ||
0.419320 | − | 0.907838i | \(-0.362269\pi\) | |||||||
\(770\) | 216.923 | − | 273.191i | 0.281719 | − | 0.354794i | ||||
\(771\) | 638.550 | 0.828210 | ||||||||
\(772\) | − | 324.630i | − | 0.420506i | ||||||
\(773\) | −60.6538 | −0.0784654 | −0.0392327 | − | 0.999230i | \(-0.512491\pi\) | ||||
−0.0392327 | + | 0.999230i | \(0.512491\pi\) | |||||||
\(774\) | 303.924i | 0.392667i | ||||||||
\(775\) | 283.379 | + | 1217.90i | 0.365650 | + | 1.57149i | ||||
\(776\) | − | 1.64079i | − | 0.00211441i | ||||||
\(777\) | 209.693i | 0.269876i | ||||||||
\(778\) | −165.595 | −0.212847 | ||||||||
\(779\) | − | 433.728i | − | 0.556776i | ||||||
\(780\) | −267.899 | + | 337.390i | −0.343461 | + | 0.432551i | ||||
\(781\) | 366.333i | 0.469056i | ||||||||
\(782\) | −16.2808 | + | 412.705i | −0.0208194 | + | 0.527756i | ||||
\(783\) | 232.688i | 0.297175i | ||||||||
\(784\) | −157.706 | −0.201156 | ||||||||
\(785\) | −549.104 | + | 691.536i | −0.699495 | + | 0.880938i | ||||
\(786\) | −516.002 | −0.656491 | ||||||||
\(787\) | −910.682 | −1.15716 | −0.578578 | − | 0.815627i | \(-0.696392\pi\) | ||||
−0.578578 | + | 0.815627i | \(0.696392\pi\) | |||||||
\(788\) | − | 702.039i | − | 0.890913i | ||||||
\(789\) | − | 316.670i | − | 0.401356i | ||||||
\(790\) | −112.232 | + | 141.344i | −0.142066 | + | 0.178916i | ||||
\(791\) | 189.258 | 0.239265 | ||||||||
\(792\) | −135.292 | −0.170824 | ||||||||
\(793\) | 1892.29 | 2.38624 | ||||||||
\(794\) | −260.374 | −0.327928 | ||||||||
\(795\) | −268.700 | − | 213.357i | −0.337988 | − | 0.268374i | ||||
\(796\) | − | 34.1699i | − | 0.0429270i | ||||||
\(797\) | −554.031 | −0.695146 | −0.347573 | − | 0.937653i | \(-0.612994\pi\) | ||||
−0.347573 | + | 0.937653i | \(0.612994\pi\) | |||||||
\(798\) | 79.4837i | 0.0996037i | ||||||||
\(799\) | − | 219.783i | − | 0.275073i | ||||||
\(800\) | 137.742 | − | 32.0495i | 0.172177 | − | 0.0400619i | ||||
\(801\) | − | 497.873i | − | 0.621564i | ||||||
\(802\) | −684.352 | −0.853307 | ||||||||
\(803\) | 827.311 | 1.03027 | ||||||||
\(804\) | − | 265.965i | − | 0.330802i | ||||||
\(805\) | −232.077 | + | 269.721i | −0.288295 | + | 0.335057i | ||||
\(806\) | 1759.41 | 2.18289 | ||||||||
\(807\) | − | 400.673i | − | 0.496497i | ||||||
\(808\) | 464.667i | 0.575083i | ||||||||
\(809\) | 91.9575 | 0.113668 | 0.0568341 | − | 0.998384i | \(-0.481899\pi\) | ||||
0.0568341 | + | 0.998384i | \(0.481899\pi\) | |||||||
\(810\) | −49.8389 | − | 39.5738i | −0.0615295 | − | 0.0488565i | ||||
\(811\) | 11.1806 | 0.0137862 | 0.00689311 | − | 0.999976i | \(-0.497806\pi\) | ||||
0.00689311 | + | 0.999976i | \(0.497806\pi\) | |||||||
\(812\) | 277.113 | 0.341273 | ||||||||
\(813\) | 418.372i | 0.514602i | ||||||||
\(814\) | −882.290 | −1.08389 | ||||||||
\(815\) | −1107.95 | − | 879.749i | −1.35945 | − | 1.07945i | ||||
\(816\) | 87.9742i | 0.107812i | ||||||||
\(817\) | 751.272i | 0.919550i | ||||||||
\(818\) | − | 831.130i | − | 1.01605i | ||||||
\(819\) | − | 230.880i | − | 0.281905i | ||||||
\(820\) | 257.176 | − | 323.885i | 0.313629 | − | 0.394982i | ||||
\(821\) | −1163.60 | −1.41730 | −0.708651 | − | 0.705559i | \(-0.750696\pi\) | ||||
−0.708651 | + | 0.705559i | \(0.750696\pi\) | |||||||
\(822\) | 0.952793 | 0.00115912 | ||||||||
\(823\) | − | 261.580i | − | 0.317837i | −0.987292 | − | 0.158918i | \(-0.949199\pi\) | ||
0.987292 | − | 0.158918i | \(-0.0508007\pi\) | |||||||
\(824\) | 455.242i | 0.552478i | ||||||||
\(825\) | 156.464 | + | 672.448i | 0.189653 | + | 0.815088i | ||||
\(826\) | 105.064i | 0.127196i | ||||||||
\(827\) | 773.865 | 0.935750 | 0.467875 | − | 0.883795i | \(-0.345020\pi\) | ||||
0.467875 | + | 0.883795i | \(0.345020\pi\) | |||||||
\(828\) | 137.893 | + | 5.43973i | 0.166537 | + | 0.00656972i | ||||
\(829\) | 1240.96 | 1.49693 | 0.748466 | − | 0.663173i | \(-0.230791\pi\) | ||||
0.748466 | + | 0.663173i | \(0.230791\pi\) | |||||||
\(830\) | −120.051 | − | 95.3248i | −0.144640 | − | 0.114849i | ||||
\(831\) | −376.020 | −0.452491 | ||||||||
\(832\) | − | 198.985i | − | 0.239165i | ||||||
\(833\) | −500.638 | −0.601006 | ||||||||
\(834\) | −277.775 | −0.333064 | ||||||||
\(835\) | −709.896 | − | 563.682i | −0.850175 | − | 0.675068i | ||||
\(836\) | −334.430 | −0.400036 | ||||||||
\(837\) | 259.898i | 0.310511i | ||||||||
\(838\) | 352.812 | 0.421017 | ||||||||
\(839\) | 634.862i | 0.756689i | 0.925665 | + | 0.378344i | \(0.123507\pi\) | ||||
−0.925665 | + | 0.378344i | \(0.876493\pi\) | |||||||
\(840\) | −47.1292 | + | 59.3541i | −0.0561062 | + | 0.0706597i | ||||
\(841\) | 1164.33 | 1.38446 | ||||||||
\(842\) | −420.827 | −0.499795 | ||||||||
\(843\) | 455.177 | 0.539948 | ||||||||
\(844\) | 334.949 | 0.396858 | ||||||||
\(845\) | 1398.13 | − | 1760.79i | 1.65459 | − | 2.08378i | ||||
\(846\) | −73.4337 | −0.0868011 | ||||||||
\(847\) | −412.203 | −0.486663 | ||||||||
\(848\) | 158.474 | 0.186879 | ||||||||
\(849\) | 122.997i | 0.144873i | ||||||||
\(850\) | 437.261 | − | 101.741i | 0.514425 | − | 0.119695i | ||||
\(851\) | 899.249 | + | 35.4744i | 1.05670 | + | 0.0416856i | ||||
\(852\) | − | 79.5902i | − | 0.0934158i | ||||||
\(853\) | 228.755i | 0.268177i | 0.990969 | + | 0.134089i | \(0.0428107\pi\) | ||||
−0.990969 | + | 0.134089i | \(0.957189\pi\) | |||||||
\(854\) | 332.895 | 0.389806 | ||||||||
\(855\) | −123.197 | − | 97.8227i | −0.144090 | − | 0.114412i | ||||
\(856\) | 151.704i | 0.177224i | ||||||||
\(857\) | − | 820.109i | − | 0.956953i | −0.878100 | − | 0.478477i | \(-0.841189\pi\) | ||
0.878100 | − | 0.478477i | \(-0.158811\pi\) | |||||||
\(858\) | 971.434 | 1.13221 | ||||||||
\(859\) | 1282.12 | 1.49257 | 0.746286 | − | 0.665626i | \(-0.231835\pi\) | ||||
0.746286 | + | 0.665626i | \(0.231835\pi\) | |||||||
\(860\) | −445.461 | + | 561.010i | −0.517978 | + | 0.652337i | ||||
\(861\) | 221.638i | 0.257420i | ||||||||
\(862\) | −117.821 | −0.136683 | ||||||||
\(863\) | 216.368i | 0.250717i | 0.992112 | + | 0.125358i | \(0.0400080\pi\) | ||||
−0.992112 | + | 0.125358i | \(0.959992\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | 435.783 | + | 346.027i | 0.503795 | + | 0.400031i | ||||
\(866\) | − | 812.619i | − | 0.938359i | ||||||
\(867\) | − | 221.289i | − | 0.255235i | ||||||
\(868\) | 309.518 | 0.356587 | ||||||||
\(869\) | 406.966 | 0.468315 | ||||||||
\(870\) | −341.050 | + | 429.516i | −0.392012 | + | 0.493696i | ||||
\(871\) | 1909.70i | 2.19253i | ||||||||
\(872\) | 219.475 | 0.251691 | ||||||||
\(873\) | −1.74032 | −0.00199349 | ||||||||
\(874\) | 340.858 | + | 13.4465i | 0.389997 | + | 0.0153850i | ||||
\(875\) | 349.514 | + | 165.606i | 0.399445 | + | 0.189264i | ||||
\(876\) | −179.743 | −0.205186 | ||||||||
\(877\) | 957.335i | 1.09160i | 0.837915 | + | 0.545801i | \(0.183774\pi\) | ||||
−0.837915 | + | 0.545801i | \(0.816226\pi\) | |||||||
\(878\) | − | 278.280i | − | 0.316947i | ||||||
\(879\) | − | 851.252i | − | 0.968432i | ||||||
\(880\) | −249.734 | − | 198.297i | −0.283789 | − | 0.225338i | ||||
\(881\) | − | 802.836i | − | 0.911278i | −0.890165 | − | 0.455639i | \(-0.849411\pi\) | ||
0.890165 | − | 0.455639i | \(-0.150589\pi\) | |||||||
\(882\) | 167.273i | 0.189652i | ||||||||
\(883\) | 188.170i | 0.213103i | 0.994307 | + | 0.106552i | \(0.0339809\pi\) | ||||
−0.994307 | + | 0.106552i | \(0.966019\pi\) | |||||||
\(884\) | − | 631.678i | − | 0.714568i | ||||||
\(885\) | −162.846 | − | 129.305i | −0.184006 | − | 0.146107i | ||||
\(886\) | −18.5922 | −0.0209844 | ||||||||
\(887\) | 1228.23i | 1.38470i | 0.721564 | + | 0.692348i | \(0.243424\pi\) | ||||
−0.721564 | + | 0.692348i | \(0.756576\pi\) | |||||||
\(888\) | 191.688 | 0.215865 | ||||||||
\(889\) | − | 52.7615i | − | 0.0593493i | ||||||
\(890\) | 729.731 | − | 919.016i | 0.819922 | − | 1.03260i | ||||
\(891\) | 143.499i | 0.161054i | ||||||||
\(892\) | 106.236i | 0.119098i | ||||||||
\(893\) | −181.521 | −0.203271 | ||||||||
\(894\) | 227.415i | 0.254379i | ||||||||
\(895\) | −253.290 | + | 318.991i | −0.283006 | + | 0.356415i | ||||
\(896\) | − | 35.0058i | − | 0.0390689i | ||||||
\(897\) | −990.106 | − | 39.0587i | −1.10380 | − | 0.0435437i | ||||
\(898\) | 10.2749i | 0.0114420i | ||||||||
\(899\) | 2239.82 | 2.49146 | ||||||||
\(900\) | −33.9936 | − | 146.097i | −0.0377707 | − | 0.162330i | ||||
\(901\) | 503.074 | 0.558350 | ||||||||
\(902\) | −932.549 | −1.03387 | ||||||||
\(903\) | − | 383.906i | − | 0.425145i | ||||||
\(904\) | − | 173.008i | − | 0.191380i | ||||||
\(905\) | −496.207 | − | 394.005i | −0.548295 | − | 0.435365i | ||||
\(906\) | 453.000 | 0.499999 | ||||||||
\(907\) | −969.640 | −1.06906 | −0.534531 | − | 0.845149i | \(-0.679512\pi\) | ||||
−0.534531 | + | 0.845149i | \(0.679512\pi\) | |||||||
\(908\) | −743.552 | −0.818889 | ||||||||
\(909\) | 492.854 | 0.542193 | ||||||||
\(910\) | 338.400 | − | 426.178i | 0.371868 | − | 0.468328i | ||||
\(911\) | − | 82.3091i | − | 0.0903503i | −0.998979 | − | 0.0451751i | \(-0.985615\pi\) | ||
0.998979 | − | 0.0451751i | \(-0.0143846\pi\) | |||||||
\(912\) | 72.6589 | 0.0796698 | ||||||||
\(913\) | 345.659i | 0.378596i | ||||||||
\(914\) | 899.254i | 0.983866i | ||||||||
\(915\) | −409.702 | + | 515.975i | −0.447762 | + | 0.563907i | ||||
\(916\) | − | 594.523i | − | 0.649042i | ||||||
\(917\) | 651.794 | 0.710790 | ||||||||
\(918\) | 93.3108 | 0.101646 | ||||||||
\(919\) | 1404.90i | 1.52872i | 0.644788 | + | 0.764362i | \(0.276946\pi\) | ||||
−0.644788 | + | 0.764362i | \(0.723054\pi\) | |||||||
\(920\) | 246.561 | + | 212.150i | 0.268001 | + | 0.230598i | ||||
\(921\) | 618.485 | 0.671536 | ||||||||
\(922\) | − | 902.310i | − | 0.978644i | ||||||
\(923\) | 571.479i | 0.619153i | ||||||||
\(924\) | 170.896 | 0.184952 | ||||||||
\(925\) | −221.685 | − | 952.754i | −0.239659 | − | 1.03000i | ||||
\(926\) | 839.695 | 0.906798 | ||||||||
\(927\) | 482.857 | 0.520881 | ||||||||
\(928\) | − | 253.319i | − | 0.272973i | ||||||
\(929\) | −1680.30 | −1.80872 | −0.904361 | − | 0.426769i | \(-0.859652\pi\) | ||||
−0.904361 | + | 0.426769i | \(0.859652\pi\) | |||||||
\(930\) | −380.932 | + | 479.742i | −0.409604 | + | 0.515851i | ||||
\(931\) | 413.482i | 0.444127i | ||||||||
\(932\) | − | 361.884i | − | 0.388287i | ||||||
\(933\) | 238.710i | 0.255852i | ||||||||
\(934\) | − | 843.240i | − | 0.902827i | ||||||
\(935\) | −792.780 | − | 629.494i | −0.847893 | − | 0.673256i | ||||
\(936\) | −211.056 | −0.225487 | ||||||||
\(937\) | −283.310 | −0.302359 | −0.151180 | − | 0.988506i | \(-0.548307\pi\) | ||||
−0.151180 | + | 0.988506i | \(0.548307\pi\) | |||||||
\(938\) | 335.957i | 0.358163i | ||||||||
\(939\) | − | 824.843i | − | 0.878427i | ||||||
\(940\) | −135.550 | − | 107.632i | −0.144202 | − | 0.114502i | ||||
\(941\) | 1715.42i | 1.82297i | 0.411328 | + | 0.911487i | \(0.365065\pi\) | ||||
−0.411328 | + | 0.911487i | \(0.634935\pi\) | |||||||
\(942\) | −432.593 | −0.459228 | ||||||||
\(943\) | 950.474 | + | 37.4952i | 1.00793 | + | 0.0397616i | ||||
\(944\) | 96.0428 | 0.101740 | ||||||||
\(945\) | 62.9546 | + | 49.9881i | 0.0666186 | + | 0.0528975i | ||||
\(946\) | 1615.29 | 1.70750 | ||||||||
\(947\) | 451.702i | 0.476982i | 0.971145 | + | 0.238491i | \(0.0766528\pi\) | ||||
−0.971145 | + | 0.238491i | \(0.923347\pi\) | |||||||
\(948\) | −88.4182 | −0.0932682 | ||||||||
\(949\) | 1290.60 | 1.35996 | ||||||||
\(950\) | −84.0291 | − | 361.139i | −0.0884516 | − | 0.380146i | ||||
\(951\) | −502.662 | −0.528562 | ||||||||
\(952\) | − | 111.126i | − | 0.116729i | ||||||
\(953\) | 844.626 | 0.886281 | 0.443141 | − | 0.896452i | \(-0.353864\pi\) | ||||
0.443141 | + | 0.896452i | \(0.353864\pi\) | |||||||
\(954\) | − | 168.087i | − | 0.176191i | ||||||
\(955\) | 438.187 | + | 347.935i | 0.458834 | + | 0.364330i | ||||
\(956\) | −679.043 | −0.710296 | ||||||||
\(957\) | 1236.69 | 1.29226 | ||||||||
\(958\) | 288.374 | 0.301017 | ||||||||
\(959\) | −1.20353 | −0.00125499 | ||||||||
\(960\) | 54.2577 | + | 43.0825i | 0.0565184 | + | 0.0448776i | ||||
\(961\) | 1540.74 | 1.60327 | ||||||||
\(962\) | −1376.37 | −1.43074 | ||||||||
\(963\) | 160.906 | 0.167089 | ||||||||
\(964\) | 66.2246i | 0.0686977i | ||||||||
\(965\) | −635.580 | − | 504.672i | −0.658632 | − | 0.522976i | ||||
\(966\) | −174.181 | − | 6.87125i | −0.180311 | − | 0.00711310i | ||||
\(967\) | − | 910.755i | − | 0.941836i | −0.882177 | − | 0.470918i | \(-0.843923\pi\) | ||
0.882177 | − | 0.470918i | \(-0.156077\pi\) | |||||||
\(968\) | 376.809i | 0.389266i | ||||||||
\(969\) | 230.655 | 0.238034 | ||||||||
\(970\) | −3.21242 | − | 2.55077i | −0.00331178 | − | 0.00262966i | ||||
\(971\) | 1833.23i | 1.88798i | 0.329979 | + | 0.943988i | \(0.392958\pi\) | ||||
−0.329979 | + | 0.943988i | \(0.607042\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | 350.875 | 0.360612 | ||||||||
\(974\) | 552.956 | 0.567717 | ||||||||
\(975\) | 244.083 | + | 1049.02i | 0.250342 | + | 1.07592i | ||||
\(976\) | − | 304.311i | − | 0.311794i | ||||||
\(977\) | 494.521 | 0.506163 | 0.253082 | − | 0.967445i | \(-0.418556\pi\) | ||||
0.253082 | + | 0.967445i | \(0.418556\pi\) | |||||||
\(978\) | − | 693.081i | − | 0.708672i | ||||||
\(979\) | −2646.09 | −2.70285 | ||||||||
\(980\) | −245.171 | + | 308.766i | −0.250174 | + | 0.315067i | ||||
\(981\) | − | 232.788i | − | 0.237297i | ||||||
\(982\) | 635.507i | 0.647156i | ||||||||
\(983\) | 484.584 | 0.492965 | 0.246482 | − | 0.969147i | \(-0.420725\pi\) | ||||
0.246482 | + | 0.969147i | \(0.420725\pi\) | |||||||
\(984\) | 202.607 | 0.205902 | ||||||||
\(985\) | −1374.49 | − | 1091.39i | −1.39542 | − | 1.10801i | ||||
\(986\) | − | 804.160i | − | 0.815579i | ||||||
\(987\) | 92.7587 | 0.0939804 | ||||||||
\(988\) | −521.710 | −0.528046 | ||||||||
\(989\) | −1646.34 | − | 64.9464i | −1.66465 | − | 0.0656688i | ||||
\(990\) | −210.326 | + | 264.883i | −0.212451 | + | 0.267558i | ||||
\(991\) | −517.471 | −0.522171 | −0.261085 | − | 0.965316i | \(-0.584080\pi\) | ||||
−0.261085 | + | 0.965316i | \(0.584080\pi\) | |||||||
\(992\) | − | 282.941i | − | 0.285223i | ||||||
\(993\) | 215.886i | 0.217408i | ||||||||
\(994\) | 100.535i | 0.101142i | ||||||||
\(995\) | −66.8997 | − | 53.1207i | −0.0672359 | − | 0.0533876i | ||||
\(996\) | − | 75.0985i | − | 0.0754001i | ||||||
\(997\) | − | 21.9492i | − | 0.0220152i | −0.999939 | − | 0.0110076i | \(-0.996496\pi\) | ||
0.999939 | − | 0.0110076i | \(-0.00350391\pi\) | |||||||
\(998\) | 1089.66i | 1.09184i | ||||||||
\(999\) | − | 203.316i | − | 0.203520i |
(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 | 690.3.f.a.229.7 | yes | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.6 | yes | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.8 | yes | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.5 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.5 | ✓ | 48 | 115.114 | odd | 2 | inner | |
690.3.f.a.229.6 | yes | 48 | 5.4 | even | 2 | inner | |
690.3.f.a.229.7 | yes | 48 | 1.1 | even | 1 | trivial | |
690.3.f.a.229.8 | yes | 48 | 23.22 | odd | 2 | inner |