Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,5,Mod(73,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.73");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.j (of order \(4\), degree \(2\), 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: | \(12.0942856808\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.4 | ||
Root | \(-1.66937 + 1.66937i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.109 |
Dual form | 117.5.j.b.73.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.66937 | + | 1.66937i | −0.417343 | + | 0.417343i | −0.884287 | − | 0.466944i | \(-0.845355\pi\) |
0.466944 | + | 0.884287i | \(0.345355\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.4264i | 0.651650i | ||||||||
\(5\) | 28.4160 | − | 28.4160i | 1.13664 | − | 1.13664i | 0.147591 | − | 0.989049i | \(-0.452848\pi\) |
0.989049 | − | 0.147591i | \(-0.0471518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −17.1341 | − | 17.1341i | −0.349675 | − | 0.349675i | 0.510314 | − | 0.859988i | \(-0.329529\pi\) |
−0.859988 | + | 0.510314i | \(0.829529\pi\) | |||||||
\(8\) | −44.1155 | − | 44.1155i | −0.689304 | − | 0.689304i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 94.8736i | 0.948736i | ||||||||
\(11\) | −54.2346 | − | 54.2346i | −0.448220 | − | 0.448220i | 0.446542 | − | 0.894762i | \(-0.352655\pi\) |
−0.894762 | + | 0.446542i | \(0.852655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −168.969 | − | 3.22849i | −0.999818 | − | 0.0191035i | ||||
\(14\) | 57.2062 | 0.291868 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.5322 | −0.0762978 | ||||||||
\(17\) | − | 70.4411i | − | 0.243741i | −0.992546 | − | 0.121870i | \(-0.961111\pi\) | ||
0.992546 | − | 0.121870i | \(-0.0388892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 194.123 | − | 194.123i | 0.537736 | − | 0.537736i | −0.385127 | − | 0.922863i | \(-0.625843\pi\) |
0.922863 | + | 0.385127i | \(0.125843\pi\) | |||||||
\(20\) | 296.276 | + | 296.276i | 0.740691 | + | 0.740691i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 181.075 | 0.374123 | ||||||||
\(23\) | − | 716.329i | − | 1.35412i | −0.735928 | − | 0.677059i | \(-0.763254\pi\) | ||
0.735928 | − | 0.677059i | \(-0.236746\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 989.935i | − | 1.58390i | ||||||
\(26\) | 287.462 | − | 276.683i | 0.425239 | − | 0.409294i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 178.647 | − | 178.647i | 0.227866 | − | 0.227866i | ||||
\(29\) | −725.866 | −0.863099 | −0.431550 | − | 0.902089i | \(-0.642033\pi\) | ||||
−0.431550 | + | 0.902089i | \(0.642033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 586.446 | − | 586.446i | 0.610245 | − | 0.610245i | −0.332765 | − | 0.943010i | \(-0.607981\pi\) |
0.943010 | + | 0.332765i | \(0.107981\pi\) | |||||||
\(32\) | 738.454 | − | 738.454i | 0.721147 | − | 0.721147i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 117.592 | + | 117.592i | 0.101723 | + | 0.101723i | ||||
\(35\) | −973.762 | −0.794908 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 575.923 | + | 575.923i | 0.420689 | + | 0.420689i | 0.885441 | − | 0.464752i | \(-0.153856\pi\) |
−0.464752 | + | 0.885441i | \(0.653856\pi\) | |||||||
\(38\) | 648.126i | 0.448840i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2507.17 | −1.56698 | ||||||||
\(41\) | 1810.07 | − | 1810.07i | 1.07678 | − | 1.07678i | 0.0799854 | − | 0.996796i | \(-0.474513\pi\) |
0.996796 | − | 0.0799854i | \(-0.0254874\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2879.48i | 1.55732i | 0.627448 | + | 0.778659i | \(0.284100\pi\) | ||||
−0.627448 | + | 0.778659i | \(0.715900\pi\) | |||||||
\(44\) | 565.472 | − | 565.472i | 0.292083 | − | 0.292083i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1195.82 | + | 1195.82i | 0.565132 | + | 0.565132i | ||||
\(47\) | −1064.86 | − | 1064.86i | −0.482055 | − | 0.482055i | 0.423733 | − | 0.905787i | \(-0.360720\pi\) |
−0.905787 | + | 0.423733i | \(0.860720\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1813.85i | − | 0.755455i | ||||||
\(50\) | 1652.57 | + | 1652.57i | 0.661028 | + | 0.661028i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 33.6615 | − | 1761.74i | 0.0124488 | − | 0.651531i | ||||
\(53\) | −2549.76 | −0.907710 | −0.453855 | − | 0.891076i | \(-0.649952\pi\) | ||||
−0.453855 | + | 0.891076i | \(0.649952\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3082.26 | −1.01893 | ||||||||
\(56\) | 1511.75i | 0.482065i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1211.74 | − | 1211.74i | 0.360208 | − | 0.360208i | ||||
\(59\) | 2264.35 | + | 2264.35i | 0.650487 | + | 0.650487i | 0.953110 | − | 0.302623i | \(-0.0978624\pi\) |
−0.302623 | + | 0.953110i | \(0.597862\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6434.68 | 1.72929 | 0.864644 | − | 0.502386i | \(-0.167544\pi\) | ||||
0.864644 | + | 0.502386i | \(0.167544\pi\) | |||||||
\(62\) | 1957.99i | 0.509363i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2152.99i | 0.525633i | ||||||||
\(65\) | −4893.16 | + | 4709.68i | −1.15815 | + | 1.11472i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5472.27 | + | 5472.27i | −1.21904 | + | 1.21904i | −0.251070 | + | 0.967969i | \(0.580783\pi\) |
−0.967969 | + | 0.251070i | \(0.919217\pi\) | |||||||
\(68\) | 734.447 | 0.158834 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1625.57 | − | 1625.57i | 0.331749 | − | 0.331749i | ||||
\(71\) | −4643.32 | + | 4643.32i | −0.921111 | + | 0.921111i | −0.997108 | − | 0.0759967i | \(-0.975786\pi\) |
0.0759967 | + | 0.997108i | \(0.475786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5605.57 | − | 5605.57i | −1.05190 | − | 1.05190i | −0.998577 | − | 0.0533222i | \(-0.983019\pi\) |
−0.0533222 | − | 0.998577i | \(-0.516981\pi\) | |||||||
\(74\) | −1922.86 | −0.351143 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2024.00 | + | 2024.00i | 0.350416 | + | 0.350416i | ||||
\(77\) | 1858.52i | 0.313462i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6871.05 | −1.10095 | −0.550477 | − | 0.834850i | \(-0.685554\pi\) | ||||
−0.550477 | + | 0.834850i | \(0.685554\pi\) | |||||||
\(80\) | −555.027 | + | 555.027i | −0.0867230 | + | 0.0867230i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6043.36i | 0.898774i | ||||||||
\(83\) | 2647.22 | − | 2647.22i | 0.384267 | − | 0.384267i | −0.488370 | − | 0.872637i | \(-0.662408\pi\) |
0.872637 | + | 0.488370i | \(0.162408\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2001.65 | − | 2001.65i | −0.277045 | − | 0.277045i | ||||
\(86\) | −4806.92 | − | 4806.92i | −0.649935 | − | 0.649935i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4785.17i | 0.617920i | ||||||||
\(89\) | 6804.23 | + | 6804.23i | 0.859012 | + | 0.859012i | 0.991222 | − | 0.132210i | \(-0.0422073\pi\) |
−0.132210 | + | 0.991222i | \(0.542207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2839.81 | + | 2950.45i | 0.342931 | + | 0.356291i | ||||
\(92\) | 7468.73 | 0.882412 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3555.29 | 0.402364 | ||||||||
\(95\) | − | 11032.4i | − | 1.22242i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9498.95 | − | 9498.95i | 1.00956 | − | 1.00956i | 0.00960578 | − | 0.999954i | \(-0.496942\pi\) |
0.999954 | − | 0.00960578i | \(-0.00305766\pi\) | |||||||
\(98\) | 3027.99 | + | 3027.99i | 0.315284 | + | 0.315284i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10321.5 | 1.03215 | ||||||||
\(101\) | − | 16541.4i | − | 1.62155i | −0.585361 | − | 0.810773i | \(-0.699047\pi\) | ||
0.585361 | − | 0.810773i | \(-0.300953\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11148.4i | 1.05084i | 0.850842 | + | 0.525421i | \(0.176092\pi\) | ||||
−0.850842 | + | 0.525421i | \(0.823908\pi\) | |||||||
\(104\) | 7311.73 | + | 7596.58i | 0.676010 | + | 0.702347i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4256.49 | − | 4256.49i | 0.378826 | − | 0.378826i | ||||
\(107\) | −9291.29 | −0.811537 | −0.405769 | − | 0.913976i | \(-0.632996\pi\) | ||||
−0.405769 | + | 0.913976i | \(0.632996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1985.75 | − | 1985.75i | 0.167136 | − | 0.167136i | −0.618583 | − | 0.785719i | \(-0.712293\pi\) |
0.785719 | + | 0.618583i | \(0.212293\pi\) | |||||||
\(110\) | 5145.43 | − | 5145.43i | 0.425243 | − | 0.425243i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 334.666 | + | 334.666i | 0.0266794 | + | 0.0266794i | ||||
\(113\) | 1799.10 | 0.140896 | 0.0704478 | − | 0.997515i | \(-0.477557\pi\) | ||||
0.0704478 | + | 0.997515i | \(0.477557\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20355.2 | − | 20355.2i | −1.53914 | − | 1.53914i | ||||
\(116\) | − | 7568.17i | − | 0.562439i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7560.07 | −0.542952 | ||||||||
\(119\) | −1206.94 | + | 1206.94i | −0.0852300 | + | 0.0852300i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 8758.21i | − | 0.598198i | ||||||
\(122\) | −10741.9 | + | 10741.9i | −0.721706 | + | 0.721706i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6114.52 | + | 6114.52i | 0.397666 | + | 0.397666i | ||||
\(125\) | −10370.0 | − | 10370.0i | −0.663680 | − | 0.663680i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7557.96i | 0.468594i | 0.972165 | + | 0.234297i | \(0.0752789\pi\) | ||||
−0.972165 | + | 0.234297i | \(0.924721\pi\) | |||||||
\(128\) | 8221.12 | + | 8221.12i | 0.501777 | + | 0.501777i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 306.299 | − | 16030.7i | 0.0181242 | − | 0.948563i | ||||
\(131\) | −9705.21 | −0.565539 | −0.282769 | − | 0.959188i | \(-0.591253\pi\) | ||||
−0.282769 | + | 0.959188i | \(0.591253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6652.22 | −0.376065 | ||||||||
\(134\) | − | 18270.5i | − | 1.01751i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3107.54 | + | 3107.54i | −0.168012 | + | 0.168012i | ||||
\(137\) | 7306.03 | + | 7306.03i | 0.389261 | + | 0.389261i | 0.874424 | − | 0.485163i | \(-0.161240\pi\) |
−0.485163 | + | 0.874424i | \(0.661240\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14508.5 | 0.750921 | 0.375460 | − | 0.926838i | \(-0.377485\pi\) | ||||
0.375460 | + | 0.926838i | \(0.377485\pi\) | |||||||
\(140\) | − | 10152.8i | − | 0.518002i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 15502.9i | − | 0.768838i | ||||||
\(143\) | 8988.88 | + | 9339.07i | 0.439576 | + | 0.456701i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20626.2 | + | 20626.2i | −0.981032 | + | 0.981032i | ||||
\(146\) | 18715.6 | 0.878005 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6004.81 | + | 6004.81i | −0.274142 | + | 0.274142i | ||||
\(149\) | −6209.08 | + | 6209.08i | −0.279675 | + | 0.279675i | −0.832979 | − | 0.553304i | \(-0.813367\pi\) |
0.553304 | + | 0.832979i | \(0.313367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6322.22 | + | 6322.22i | 0.277278 | + | 0.277278i | 0.832021 | − | 0.554743i | \(-0.187184\pi\) |
−0.554743 | + | 0.832021i | \(0.687184\pi\) | |||||||
\(152\) | −17127.6 | −0.741327 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3102.56 | − | 3102.56i | −0.130821 | − | 0.130821i | ||||
\(155\) | − | 33328.9i | − | 1.38726i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26942.7 | 1.09305 | 0.546526 | − | 0.837442i | \(-0.315950\pi\) | ||||
0.546526 | + | 0.837442i | \(0.315950\pi\) | |||||||
\(158\) | 11470.3 | − | 11470.3i | 0.459475 | − | 0.459475i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 41967.8i | − | 1.63937i | ||||||
\(161\) | −12273.6 | + | 12273.6i | −0.473501 | + | 0.473501i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22832.2 | + | 22832.2i | 0.859355 | + | 0.859355i | 0.991262 | − | 0.131907i | \(-0.0421101\pi\) |
−0.131907 | + | 0.991262i | \(0.542110\pi\) | |||||||
\(164\) | 18872.5 | + | 18872.5i | 0.701685 | + | 0.701685i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8838.37i | 0.320742i | ||||||||
\(167\) | −7664.75 | − | 7664.75i | −0.274831 | − | 0.274831i | 0.556211 | − | 0.831041i | \(-0.312255\pi\) |
−0.831041 | + | 0.556211i | \(0.812255\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28540.2 | + | 1091.03i | 0.999270 | + | 0.0382000i | ||||
\(170\) | 6683.00 | 0.231246 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −30022.6 | −1.01483 | ||||||||
\(173\) | 9382.63i | 0.313496i | 0.987639 | + | 0.156748i | \(0.0501011\pi\) | ||||
−0.987639 | + | 0.156748i | \(0.949899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16961.6 | + | 16961.6i | −0.553849 | + | 0.553849i | ||||
\(176\) | 1059.32 | + | 1059.32i | 0.0341982 | + | 0.0341982i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22717.6 | −0.717005 | ||||||||
\(179\) | − | 322.023i | − | 0.0100503i | −0.999987 | − | 0.00502517i | \(-0.998400\pi\) | ||
0.999987 | − | 0.00502517i | \(-0.00159957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 28479.3i | 0.869306i | 0.900598 | + | 0.434653i | \(0.143129\pi\) | ||||
−0.900598 | + | 0.434653i | \(0.856871\pi\) | |||||||
\(182\) | −9666.09 | − | 184.690i | −0.291815 | − | 0.00557571i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −31601.2 | + | 31601.2i | −0.933400 | + | 0.933400i | ||||
\(185\) | 32730.8 | 0.956343 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3820.35 | + | 3820.35i | −0.109249 | + | 0.109249i | ||||
\(188\) | 11102.6 | − | 11102.6i | 0.314131 | − | 0.314131i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18417.1 | + | 18417.1i | 0.510170 | + | 0.510170i | ||||
\(191\) | −39049.7 | −1.07041 | −0.535206 | − | 0.844722i | \(-0.679766\pi\) | ||||
−0.535206 | + | 0.844722i | \(0.679766\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −34849.0 | − | 34849.0i | −0.935570 | − | 0.935570i | 0.0624768 | − | 0.998046i | \(-0.480100\pi\) |
−0.998046 | + | 0.0624768i | \(0.980100\pi\) | |||||||
\(194\) | 31714.5i | 0.842665i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18911.9 | 0.492292 | ||||||||
\(197\) | −33755.4 | + | 33755.4i | −0.869784 | + | 0.869784i | −0.992448 | − | 0.122664i | \(-0.960856\pi\) |
0.122664 | + | 0.992448i | \(0.460856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12091.0i | 0.305322i | 0.988279 | + | 0.152661i | \(0.0487842\pi\) | ||||
−0.988279 | + | 0.152661i | \(0.951216\pi\) | |||||||
\(200\) | −43671.5 | + | 43671.5i | −1.09179 | + | 1.09179i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 27613.7 | + | 27613.7i | 0.676740 | + | 0.676740i | ||||
\(203\) | 12437.0 | + | 12437.0i | 0.301804 | + | 0.301804i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 102870.i | − | 2.44782i | ||||||
\(206\) | −18610.8 | − | 18610.8i | −0.438561 | − | 0.438561i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3300.34 | + | 63.0596i | 0.0762838 | + | 0.00145755i | ||||
\(209\) | −21056.3 | −0.482048 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 51063.6 | 1.14695 | 0.573477 | − | 0.819221i | \(-0.305594\pi\) | ||||
0.573477 | + | 0.819221i | \(0.305594\pi\) | |||||||
\(212\) | − | 26584.8i | − | 0.591509i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15510.6 | − | 15510.6i | 0.338689 | − | 0.338689i | ||||
\(215\) | 81823.2 | + | 81823.2i | 1.77011 | + | 1.77011i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20096.4 | −0.426775 | ||||||||
\(218\) | 6629.90i | 0.139506i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 32136.9i | − | 0.663985i | ||||||
\(221\) | −227.418 | + | 11902.4i | −0.00465630 | + | 0.243696i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7861.80 | − | 7861.80i | 0.158093 | − | 0.158093i | −0.623628 | − | 0.781721i | \(-0.714342\pi\) |
0.781721 | + | 0.623628i | \(0.214342\pi\) | |||||||
\(224\) | −25305.4 | −0.504333 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3003.36 | + | 3003.36i | −0.0588018 | + | 0.0588018i | ||||
\(227\) | 9642.38 | − | 9642.38i | 0.187125 | − | 0.187125i | −0.607327 | − | 0.794452i | \(-0.707758\pi\) |
0.794452 | + | 0.607327i | \(0.207758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 36285.4 | + | 36285.4i | 0.691928 | + | 0.691928i | 0.962656 | − | 0.270728i | \(-0.0872643\pi\) |
−0.270728 | + | 0.962656i | \(0.587264\pi\) | |||||||
\(230\) | 67960.7 | 1.28470 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 32021.9 | + | 32021.9i | 0.594938 | + | 0.594938i | ||||
\(233\) | 2365.03i | 0.0435637i | 0.999763 | + | 0.0217819i | \(0.00693393\pi\) | ||||
−0.999763 | + | 0.0217819i | \(0.993066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −60518.0 | −1.09584 | ||||||||
\(236\) | −23609.0 | + | 23609.0i | −0.423890 | + | 0.423890i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 4029.67i | − | 0.0711402i | ||||||
\(239\) | 18841.4 | − | 18841.4i | 0.329850 | − | 0.329850i | −0.522679 | − | 0.852529i | \(-0.675067\pi\) |
0.852529 | + | 0.522679i | \(0.175067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27569.6 | − | 27569.6i | −0.474676 | − | 0.474676i | 0.428748 | − | 0.903424i | \(-0.358955\pi\) |
−0.903424 | + | 0.428748i | \(0.858955\pi\) | |||||||
\(242\) | 14620.7 | + | 14620.7i | 0.249653 | + | 0.249653i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 67090.5i | 1.12689i | ||||||||
\(245\) | −51542.3 | − | 51542.3i | −0.858680 | − | 0.858680i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −33427.5 | + | 32174.0i | −0.547910 | + | 0.527365i | ||||
\(248\) | −51742.7 | −0.841289 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 34622.8 | 0.553964 | ||||||||
\(251\) | − | 52279.9i | − | 0.829826i | −0.909861 | − | 0.414913i | \(-0.863812\pi\) | ||
0.909861 | − | 0.414913i | \(-0.136188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38849.8 | + | 38849.8i | −0.606943 | + | 0.606943i | ||||
\(254\) | −12617.0 | − | 12617.0i | −0.195564 | − | 0.195564i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −61896.1 | −0.944459 | ||||||||
\(257\) | − | 87118.8i | − | 1.31900i | −0.751703 | − | 0.659501i | \(-0.770768\pi\) | ||
0.751703 | − | 0.659501i | \(-0.229232\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19735.8i | − | 0.294209i | ||||||
\(260\) | −49105.0 | − | 51018.1i | −0.726406 | − | 0.754705i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16201.6 | − | 16201.6i | 0.236023 | − | 0.236023i | ||||
\(263\) | 92681.2 | 1.33992 | 0.669962 | − | 0.742395i | \(-0.266310\pi\) | ||||
0.669962 | + | 0.742395i | \(0.266310\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −72453.8 | + | 72453.8i | −1.03174 | + | 1.03174i | ||||
\(266\) | 11105.0 | − | 11105.0i | 0.156948 | − | 0.156948i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −57056.0 | − | 57056.0i | −0.794387 | − | 0.794387i | ||||
\(269\) | 123465. | 1.70624 | 0.853118 | − | 0.521717i | \(-0.174708\pi\) | ||||
0.853118 | + | 0.521717i | \(0.174708\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 60295.3 | + | 60295.3i | 0.821003 | + | 0.821003i | 0.986252 | − | 0.165249i | \(-0.0528428\pi\) |
−0.165249 | + | 0.986252i | \(0.552843\pi\) | |||||||
\(272\) | 1375.87i | 0.0185969i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24393.0 | −0.324910 | ||||||||
\(275\) | −53688.8 | + | 53688.8i | −0.709934 | + | 0.709934i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 62673.2i | − | 0.816812i | −0.912800 | − | 0.408406i | \(-0.866085\pi\) | ||
0.912800 | − | 0.408406i | \(-0.133915\pi\) | |||||||
\(278\) | −24220.1 | + | 24220.1i | −0.313391 | + | 0.313391i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 42958.0 | + | 42958.0i | 0.547933 | + | 0.547933i | ||||
\(281\) | −17050.4 | − | 17050.4i | −0.215934 | − | 0.215934i | 0.590848 | − | 0.806783i | \(-0.298793\pi\) |
−0.806783 | + | 0.590848i | \(0.798793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 135558.i | − | 1.69259i | −0.532716 | − | 0.846294i | \(-0.678829\pi\) | ||
0.532716 | − | 0.846294i | \(-0.321171\pi\) | |||||||
\(284\) | −48413.1 | − | 48413.1i | −0.600242 | − | 0.600242i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −30596.2 | − | 584.600i | −0.374054 | − | 0.00714705i | ||||
\(287\) | −62027.7 | −0.753047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 78559.1 | 0.940590 | ||||||||
\(290\) | − | 68865.6i | − | 0.818854i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 58445.9 | − | 58445.9i | 0.685470 | − | 0.685470i | ||||
\(293\) | 33642.1 | + | 33642.1i | 0.391876 | + | 0.391876i | 0.875356 | − | 0.483480i | \(-0.160627\pi\) |
−0.483480 | + | 0.875356i | \(0.660627\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 128687. | 1.47874 | ||||||||
\(296\) | − | 50814.3i | − | 0.579966i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 20730.5i | − | 0.233441i | ||||||
\(299\) | −2312.66 | + | 121037.i | −0.0258684 | + | 1.35387i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 49337.2 | − | 49337.2i | 0.544555 | − | 0.544555i | ||||
\(302\) | −21108.2 | −0.231440 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3791.65 | + | 3791.65i | −0.0410281 | + | 0.0410281i | ||||
\(305\) | 182848. | − | 182848.i | 1.96558 | − | 1.96558i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −121981. | − | 121981.i | −1.29425 | − | 1.29425i | −0.932135 | − | 0.362112i | \(-0.882056\pi\) |
−0.362112 | − | 0.932135i | \(-0.617944\pi\) | |||||||
\(308\) | −19377.7 | −0.204268 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 55638.2 | + | 55638.2i | 0.578962 | + | 0.578962i | ||||
\(311\) | 1370.53i | 0.0141699i | 0.999975 | + | 0.00708495i | \(0.00225523\pi\) | ||||
−0.999975 | + | 0.00708495i | \(0.997745\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 52462.0 | 0.535495 | 0.267748 | − | 0.963489i | \(-0.413721\pi\) | ||||
0.267748 | + | 0.963489i | \(0.413721\pi\) | |||||||
\(314\) | −44977.3 | + | 44977.3i | −0.456178 | + | 0.456178i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 71640.4i | − | 0.717437i | ||||||
\(317\) | 101779. | − | 101779.i | 1.01284 | − | 1.01284i | 0.0129239 | − | 0.999916i | \(-0.495886\pi\) |
0.999916 | − | 0.0129239i | \(-0.00411392\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39367.1 | + | 39367.1i | 0.386858 | + | 0.386858i | ||||
\(320\) | 61179.4 | + | 61179.4i | 0.597455 | + | 0.597455i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 40978.5i | − | 0.395225i | ||||||
\(323\) | −13674.2 | − | 13674.2i | −0.131068 | − | 0.131068i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3196.00 | + | 167269.i | −0.0302580 | + | 1.58361i | ||||
\(326\) | −76230.8 | −0.717291 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −159704. | −1.48446 | ||||||||
\(329\) | 36490.7i | 0.337125i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 90476.9 | − | 90476.9i | 0.825813 | − | 0.825813i | −0.161122 | − | 0.986935i | \(-0.551511\pi\) |
0.986935 | + | 0.161122i | \(0.0515112\pi\) | |||||||
\(332\) | 27600.9 | + | 27600.9i | 0.250408 | + | 0.250408i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25590.6 | 0.229397 | ||||||||
\(335\) | 311000.i | 2.77122i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 48432.3i | − | 0.426457i | −0.977002 | − | 0.213228i | \(-0.931602\pi\) | ||
0.977002 | − | 0.213228i | \(-0.0683979\pi\) | |||||||
\(338\) | −49465.4 | + | 45822.8i | −0.432981 | + | 0.401096i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20870.0 | − | 20870.0i | 0.180537 | − | 0.180537i | ||||
\(341\) | −63611.3 | −0.547048 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −72217.5 | + | 72217.5i | −0.613838 | + | 0.613838i | ||||
\(344\) | 127030. | − | 127030.i | 1.07347 | − | 1.07347i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15663.1 | − | 15663.1i | −0.130835 | − | 0.130835i | ||||
\(347\) | −50065.9 | −0.415799 | −0.207899 | − | 0.978150i | \(-0.566663\pi\) | ||||
−0.207899 | + | 0.978150i | \(0.566663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −36678.7 | − | 36678.7i | −0.301137 | − | 0.301137i | 0.540322 | − | 0.841458i | \(-0.318302\pi\) |
−0.841458 | + | 0.540322i | \(0.818302\pi\) | |||||||
\(350\) | − | 56630.5i | − | 0.462290i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −80099.5 | −0.646465 | ||||||||
\(353\) | 91471.6 | − | 91471.6i | 0.734069 | − | 0.734069i | −0.237354 | − | 0.971423i | \(-0.576280\pi\) |
0.971423 | + | 0.237354i | \(0.0762803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 263889.i | 2.09394i | ||||||||
\(356\) | −70943.6 | + | 70943.6i | −0.559775 | + | 0.559775i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 537.576 | + | 537.576i | 0.00419444 | + | 0.00419444i | ||||
\(359\) | −19904.6 | − | 19904.6i | −0.154442 | − | 0.154442i | 0.625657 | − | 0.780098i | \(-0.284831\pi\) |
−0.780098 | + | 0.625657i | \(0.784831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 54953.8i | 0.421680i | ||||||||
\(362\) | −47542.6 | − | 47542.6i | −0.362799 | − | 0.362799i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −30762.5 | + | 29609.0i | −0.232177 | + | 0.223471i | ||||
\(365\) | −318576. | −2.39126 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13539.5 | 0.100524 | 0.0502620 | − | 0.998736i | \(-0.483994\pi\) | ||||
0.0502620 | + | 0.998736i | \(0.483994\pi\) | |||||||
\(368\) | 13991.5i | 0.103316i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −54639.9 | + | 54639.9i | −0.399123 | + | 0.399123i | ||||
\(371\) | 43687.7 | + | 43687.7i | 0.317403 | + | 0.317403i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −76501.0 | −0.549857 | −0.274928 | − | 0.961465i | \(-0.588654\pi\) | ||||
−0.274928 | + | 0.961465i | \(0.588654\pi\) | |||||||
\(374\) | − | 12755.1i | − | 0.0911890i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 93953.5i | 0.664565i | ||||||||
\(377\) | 122649. | + | 2343.45i | 0.862942 | + | 0.0164882i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9873.34 | − | 9873.34i | 0.0687362 | − | 0.0687362i | −0.671903 | − | 0.740639i | \(-0.734523\pi\) |
0.740639 | + | 0.671903i | \(0.234523\pi\) | |||||||
\(380\) | 115028. | 0.796592 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 65188.4 | − | 65188.4i | 0.446729 | − | 0.446729i | ||||
\(383\) | −92064.1 | + | 92064.1i | −0.627614 | + | 0.627614i | −0.947467 | − | 0.319853i | \(-0.896366\pi\) |
0.319853 | + | 0.947467i | \(0.396366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 52811.6 | + | 52811.6i | 0.356294 | + | 0.356294i | ||||
\(386\) | 116352. | 0.780906 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 99039.8 | + | 99039.8i | 0.657880 | + | 0.657880i | ||||
\(389\) | − | 35489.2i | − | 0.234529i | −0.993101 | − | 0.117265i | \(-0.962587\pi\) | ||
0.993101 | − | 0.117265i | \(-0.0374125\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50459.0 | −0.330054 | ||||||||
\(392\) | −80018.7 | + | 80018.7i | −0.520738 | + | 0.520738i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 112701.i | − | 0.725996i | ||||||
\(395\) | −195248. | + | 195248.i | −1.25139 | + | 1.25139i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 45764.3 | + | 45764.3i | 0.290366 | + | 0.290366i | 0.837225 | − | 0.546859i | \(-0.184177\pi\) |
−0.546859 | + | 0.837225i | \(0.684177\pi\) | |||||||
\(398\) | −20184.4 | − | 20184.4i | −0.127424 | − | 0.127424i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19335.6i | 0.120848i | ||||||||
\(401\) | −53143.4 | − | 53143.4i | −0.330492 | − | 0.330492i | 0.522281 | − | 0.852773i | \(-0.325081\pi\) |
−0.852773 | + | 0.522281i | \(0.825081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −100985. | + | 97197.9i | −0.621792 | + | 0.598476i | ||||
\(404\) | 172467. | 1.05668 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −41524.1 | −0.251911 | ||||||||
\(407\) | − | 62470.0i | − | 0.377123i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 75294.0 | − | 75294.0i | 0.450105 | − | 0.450105i | −0.445284 | − | 0.895389i | \(-0.646897\pi\) |
0.895389 | + | 0.445284i | \(0.146897\pi\) | |||||||
\(410\) | 171728. | + | 171728.i | 1.02158 | + | 1.02158i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −116237. | −0.684781 | ||||||||
\(413\) | − | 77594.9i | − | 0.454918i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 150447.i | − | 0.873546i | ||||||
\(416\) | −127160. | + | 122392.i | −0.734791 | + | 0.707239i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 35150.8 | − | 35150.8i | 0.201179 | − | 0.201179i | ||||
\(419\) | 264545. | 1.50686 | 0.753429 | − | 0.657530i | \(-0.228399\pi\) | ||||
0.753429 | + | 0.657530i | \(0.228399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30687.4 | − | 30687.4i | 0.173140 | − | 0.173140i | −0.615218 | − | 0.788357i | \(-0.710932\pi\) |
0.788357 | + | 0.615218i | \(0.210932\pi\) | |||||||
\(422\) | −85244.1 | + | 85244.1i | −0.478673 | + | 0.478673i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 112484. | + | 112484.i | 0.625688 | + | 0.625688i | ||||
\(425\) | −69732.1 | −0.386060 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −110252. | − | 110252.i | −0.604688 | − | 0.604688i | ||||
\(428\) | − | 96874.7i | − | 0.528838i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −273187. | −1.47748 | ||||||||
\(431\) | −138755. | + | 138755.i | −0.746956 | + | 0.746956i | −0.973906 | − | 0.226950i | \(-0.927124\pi\) |
0.226950 | + | 0.973906i | \(0.427124\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 192478.i | − | 1.02661i | −0.858206 | − | 0.513305i | \(-0.828421\pi\) | ||
0.858206 | − | 0.513305i | \(-0.171579\pi\) | |||||||
\(434\) | 33548.3 | − | 33548.3i | 0.178111 | − | 0.178111i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20704.2 | + | 20704.2i | 0.108914 | + | 0.108914i | ||||
\(437\) | −139056. | − | 139056.i | −0.728158 | − | 0.728158i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 221370.i | 1.14865i | 0.818626 | + | 0.574327i | \(0.194736\pi\) | ||||
−0.818626 | + | 0.574327i | \(0.805264\pi\) | |||||||
\(440\) | 135975. | + | 135975.i | 0.702352 | + | 0.702352i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19489.8 | − | 20249.1i | −0.0997616 | − | 0.103648i | ||||
\(443\) | −354252. | −1.80511 | −0.902557 | − | 0.430570i | \(-0.858313\pi\) | ||||
−0.902557 | + | 0.430570i | \(0.858313\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 386698. | 1.95277 | ||||||||
\(446\) | 26248.5i | 0.131958i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 36889.5 | − | 36889.5i | 0.183801 | − | 0.183801i | ||||
\(449\) | 187721. | + | 187721.i | 0.931152 | + | 0.931152i | 0.997778 | − | 0.0666259i | \(-0.0212234\pi\) |
−0.0666259 | + | 0.997778i | \(0.521223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −196337. | −0.965270 | ||||||||
\(452\) | 18758.1i | 0.0918147i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 32193.4i | 0.156191i | ||||||||
\(455\) | 164536. | + | 3143.78i | 0.794763 | + | 0.0151855i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −88792.4 | + | 88792.4i | −0.425151 | + | 0.425151i | −0.886973 | − | 0.461822i | \(-0.847196\pi\) |
0.461822 | + | 0.886973i | \(0.347196\pi\) | |||||||
\(458\) | −121148. | −0.577543 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 212231. | − | 212231.i | 1.00298 | − | 1.00298i | ||||
\(461\) | 56596.4 | − | 56596.4i | 0.266310 | − | 0.266310i | −0.561302 | − | 0.827611i | \(-0.689699\pi\) |
0.827611 | + | 0.561302i | \(0.189699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 171067. | + | 171067.i | 0.798003 | + | 0.798003i | 0.982780 | − | 0.184777i | \(-0.0591563\pi\) |
−0.184777 | + | 0.982780i | \(0.559156\pi\) | |||||||
\(464\) | 14177.8 | 0.0658526 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3948.11 | − | 3948.11i | −0.0181810 | − | 0.0181810i | ||||
\(467\) | − | 68140.5i | − | 0.312443i | −0.987722 | − | 0.156222i | \(-0.950069\pi\) | ||
0.987722 | − | 0.156222i | \(-0.0499314\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 187524. | 0.852534 | ||||||||
\(470\) | 101027. | − | 101027.i | 0.457343 | − | 0.457343i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 199785.i | − | 0.896767i | ||||||
\(473\) | 156168. | − | 156168.i | 0.698021 | − | 0.698021i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −192169. | − | 192169.i | −0.851718 | − | 0.851718i | ||||
\(476\) | −12584.1 | − | 12584.1i | −0.0555401 | − | 0.0555401i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 62906.5i | 0.275321i | ||||||||
\(479\) | 113713. | + | 113713.i | 0.495610 | + | 0.495610i | 0.910068 | − | 0.414458i | \(-0.136029\pi\) |
−0.414458 | + | 0.910068i | \(0.636029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −95453.9 | − | 99172.6i | −0.412576 | − | 0.428649i | ||||
\(482\) | 92047.9 | 0.396205 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 91316.6 | 0.389816 | ||||||||
\(485\) | − | 539844.i | − | 2.29501i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30988.8 | − | 30988.8i | 0.130661 | − | 0.130661i | −0.638752 | − | 0.769413i | \(-0.720549\pi\) |
0.769413 | + | 0.638752i | \(0.220549\pi\) | |||||||
\(488\) | −283869. | − | 283869.i | −1.19201 | − | 1.19201i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 172086. | 0.716728 | ||||||||
\(491\) | − | 229476.i | − | 0.951861i | −0.879483 | − | 0.475931i | \(-0.842111\pi\) | ||
0.879483 | − | 0.475931i | \(-0.157889\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51130.8i | 0.210372i | ||||||||
\(494\) | 2092.47 | − | 109513.i | 0.00857442 | − | 0.448759i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11454.6 | + | 11454.6i | −0.0465604 | + | 0.0465604i | ||||
\(497\) | 159118. | 0.644179 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29259.2 | − | 29259.2i | 0.117506 | − | 0.117506i | −0.645909 | − | 0.763415i | \(-0.723521\pi\) |
0.763415 | + | 0.645909i | \(0.223521\pi\) | |||||||
\(500\) | 108122. | − | 108122.i | 0.432487 | − | 0.432487i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 87274.5 | + | 87274.5i | 0.346322 | + | 0.346322i | ||||
\(503\) | −432230. | −1.70836 | −0.854180 | − | 0.519978i | \(-0.825940\pi\) | ||||
−0.854180 | + | 0.519978i | \(0.825940\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −470040. | − | 470040.i | −1.84311 | − | 1.84311i | ||||
\(506\) | − | 129710.i | − | 0.506607i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −78802.3 | −0.305360 | ||||||||
\(509\) | 150630. | − | 150630.i | 0.581402 | − | 0.581402i | −0.353886 | − | 0.935289i | \(-0.615140\pi\) |
0.935289 | + | 0.353886i | \(0.115140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 192092.i | 0.735645i | ||||||||
\(512\) | −28210.4 | + | 28210.4i | −0.107614 | + | 0.107614i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 145434. | + | 145434.i | 0.550476 | + | 0.550476i | ||||
\(515\) | 316792. | + | 316792.i | 1.19443 | + | 1.19443i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 115504.i | 0.432133i | ||||||||
\(518\) | 32946.4 | + | 32946.4i | 0.122786 | + | 0.122786i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 423634. | + | 8094.37i | 1.56669 | + | 0.0299348i | ||||
\(521\) | 152305. | 0.561096 | 0.280548 | − | 0.959840i | \(-0.409484\pi\) | ||||
0.280548 | + | 0.959840i | \(0.409484\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 78780.8 | 0.288016 | 0.144008 | − | 0.989577i | \(-0.454001\pi\) | ||||
0.144008 | + | 0.989577i | \(0.454001\pi\) | |||||||
\(524\) | − | 101190.i | − | 0.368533i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −154719. | + | 154719.i | −0.559208 | + | 0.559208i | ||||
\(527\) | −41309.9 | − | 41309.9i | −0.148742 | − | 0.148742i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −233286. | −0.833638 | ||||||||
\(530\) | − | 241905.i | − | 0.861177i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 69358.7i | − | 0.245063i | ||||||
\(533\) | −311690. | + | 300002.i | −1.09716 | + | 1.05601i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −264021. | + | 264021.i | −0.922425 | + | 0.922425i | ||||
\(536\) | 482823. | 1.68058 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −206109. | + | 206109.i | −0.712086 | + | 0.712086i | ||||
\(539\) | −98373.3 | + | 98373.3i | −0.338610 | + | 0.338610i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35408.4 | − | 35408.4i | −0.120979 | − | 0.120979i | 0.644025 | − | 0.765004i | \(-0.277263\pi\) |
−0.765004 | + | 0.644025i | \(0.777263\pi\) | |||||||
\(542\) | −201310. | −0.685279 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −52017.5 | − | 52017.5i | −0.175773 | − | 0.175773i | ||||
\(545\) | − | 112854.i | − | 0.379947i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10939.9 | 0.0365628 | 0.0182814 | − | 0.999833i | \(-0.494181\pi\) | ||||
0.0182814 | + | 0.999833i | \(0.494181\pi\) | |||||||
\(548\) | −76175.6 | + | 76175.6i | −0.253662 | + | 0.253662i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 179253.i | − | 0.592572i | ||||||
\(551\) | −140907. | + | 140907.i | −0.464120 | + | 0.464120i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 117729. | + | 117729.i | 0.384976 | + | 0.384976i | ||||
\(554\) | 104625. | + | 104625.i | 0.340891 | + | 0.340891i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 151272.i | 0.489338i | ||||||||
\(557\) | −32717.3 | − | 32717.3i | −0.105455 | − | 0.105455i | 0.652411 | − | 0.757866i | \(-0.273758\pi\) |
−0.757866 | + | 0.652411i | \(0.773758\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9296.38 | − | 486543.i | 0.0297502 | − | 1.55703i | ||||
\(560\) | 19019.7 | 0.0606497 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 56926.8 | 0.180237 | ||||||||
\(563\) | − | 180795.i | − | 0.570388i | −0.958470 | − | 0.285194i | \(-0.907942\pi\) | ||
0.958470 | − | 0.285194i | \(-0.0920580\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 51123.1 | − | 51123.1i | 0.160148 | − | 0.160148i | ||||
\(566\) | 226296. | + | 226296.i | 0.706390 | + | 0.706390i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 409685. | 1.26985 | ||||||||
\(569\) | 500901.i | 1.54713i | 0.633715 | + | 0.773566i | \(0.281529\pi\) | ||||
−0.633715 | + | 0.773566i | \(0.718471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 246396.i | − | 0.755722i | −0.925862 | − | 0.377861i | \(-0.876660\pi\) | ||
0.925862 | − | 0.377861i | \(-0.123340\pi\) | |||||||
\(572\) | −97372.9 | + | 93721.7i | −0.297609 | + | 0.286449i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 103547. | − | 103547.i | 0.314279 | − | 0.314279i | ||||
\(575\) | −709119. | −2.14478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −184815. | + | 184815.i | −0.555119 | + | 0.555119i | −0.927914 | − | 0.372794i | \(-0.878400\pi\) |
0.372794 | + | 0.927914i | \(0.378400\pi\) | |||||||
\(578\) | −131144. | + | 131144.i | −0.392549 | + | 0.392549i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −215057. | − | 215057.i | −0.639290 | − | 0.639290i | ||||
\(581\) | −90715.2 | −0.268737 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 138285. | + | 138285.i | 0.406854 | + | 0.406854i | ||||
\(584\) | 494585.i | 1.45016i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −112322. | −0.327093 | ||||||||
\(587\) | 402989. | − | 402989.i | 1.16954 | − | 1.16954i | 0.187227 | − | 0.982317i | \(-0.440050\pi\) |
0.982317 | − | 0.187227i | \(-0.0599501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 227685.i | − | 0.656302i | ||||||
\(590\) | −214827. | + | 214827.i | −0.617141 | + | 0.617141i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11249.1 | − | 11249.1i | −0.0320976 | − | 0.0320976i | ||||
\(593\) | −180607. | − | 180607.i | −0.513601 | − | 0.513601i | 0.402027 | − | 0.915628i | \(-0.368306\pi\) |
−0.915628 | + | 0.402027i | \(0.868306\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 68592.9i | 0.193751i | ||||||||
\(596\) | −64738.3 | − | 64738.3i | −0.182251 | − | 0.182251i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −198196. | − | 205917.i | −0.554233 | − | 0.575825i | ||||
\(599\) | 461474. | 1.28615 | 0.643077 | − | 0.765801i | \(-0.277657\pi\) | ||||
0.643077 | + | 0.765801i | \(0.277657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −482801. | −1.33666 | −0.668328 | − | 0.743867i | \(-0.732990\pi\) | ||||
−0.668328 | + | 0.743867i | \(0.732990\pi\) | |||||||
\(602\) | 164724.i | 0.454532i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −65918.0 | + | 65918.0i | −0.180688 | + | 0.180688i | ||||
\(605\) | −248873. | − | 248873.i | −0.679935 | − | 0.679935i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 219694. | 0.596266 | 0.298133 | − | 0.954524i | \(-0.403636\pi\) | ||||
0.298133 | + | 0.954524i | \(0.403636\pi\) | |||||||
\(608\) | − | 286701.i | − | 0.775573i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 610481.i | 1.64064i | ||||||||
\(611\) | 176490. | + | 183366.i | 0.472758 | + | 0.491176i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 193600. | − | 193600.i | 0.515209 | − | 0.515209i | −0.400909 | − | 0.916118i | \(-0.631306\pi\) |
0.916118 | + | 0.400909i | \(0.131306\pi\) | |||||||
\(614\) | 407265. | 1.08029 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 81989.4 | − | 81989.4i | 0.216071 | − | 0.216071i | ||||
\(617\) | −234942. | + | 234942.i | −0.617149 | + | 0.617149i | −0.944799 | − | 0.327650i | \(-0.893743\pi\) |
0.327650 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 518107. | + | 518107.i | 1.35219 | + | 1.35219i | 0.883206 | + | 0.468984i | \(0.155380\pi\) |
0.468984 | + | 0.883206i | \(0.344620\pi\) | |||||||
\(620\) | 347500. | 0.904006 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2287.92 | − | 2287.92i | −0.00591371 | − | 0.00591371i | ||||
\(623\) | − | 233168.i | − | 0.600749i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29362.4 | 0.0751678 | ||||||||
\(626\) | −87578.5 | + | 87578.5i | −0.223485 | + | 0.223485i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 280915.i | 0.712288i | ||||||||
\(629\) | 40568.7 | − | 40568.7i | 0.102539 | − | 0.102539i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −335596. | − | 335596.i | −0.842866 | − | 0.842866i | 0.146365 | − | 0.989231i | \(-0.453243\pi\) |
−0.989231 | + | 0.146365i | \(0.953243\pi\) | |||||||
\(632\) | 303120. | + | 303120.i | 0.758892 | + | 0.758892i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 339815.i | 0.845403i | ||||||||
\(635\) | 214767. | + | 214767.i | 0.532623 | + | 0.532623i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5855.99 | + | 306484.i | −0.0144318 | + | 0.755317i | ||||
\(638\) | −131437. | −0.322905 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 467222. | 1.14068 | ||||||||
\(641\) | 555098.i | 1.35099i | 0.737362 | + | 0.675497i | \(0.236071\pi\) | ||||
−0.737362 | + | 0.675497i | \(0.763929\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 263449. | − | 263449.i | 0.637197 | − | 0.637197i | −0.312666 | − | 0.949863i | \(-0.601222\pi\) |
0.949863 | + | 0.312666i | \(0.101222\pi\) | |||||||
\(644\) | −127970. | − | 127970.i | −0.308557 | − | 0.308557i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 45654.7 | 0.109401 | ||||||||
\(647\) | − | 396185.i | − | 0.946433i | −0.880946 | − | 0.473216i | \(-0.843093\pi\) | ||
0.880946 | − | 0.473216i | \(-0.156907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 245612.i | − | 0.583123i | ||||||
\(650\) | −273898. | − | 284569.i | −0.648279 | − | 0.673535i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −238058. | + | 238058.i | −0.559999 | + | 0.559999i | ||||
\(653\) | −825533. | −1.93601 | −0.968006 | − | 0.250929i | \(-0.919264\pi\) | ||||
−0.968006 | + | 0.250929i | \(0.919264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −275783. | + | 275783.i | −0.642813 | + | 0.642813i | ||||
\(656\) | −35354.7 | + | 35354.7i | −0.0821560 | + | 0.0821560i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −60916.5 | − | 60916.5i | −0.140697 | − | 0.140697i | ||||
\(659\) | −123474. | −0.284317 | −0.142159 | − | 0.989844i | \(-0.545404\pi\) | ||||
−0.142159 | + | 0.989844i | \(0.545404\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 121255. | + | 121255.i | 0.277522 | + | 0.277522i | 0.832119 | − | 0.554597i | \(-0.187128\pi\) |
−0.554597 | + | 0.832119i | \(0.687128\pi\) | |||||||
\(662\) | 302079.i | 0.689294i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −233566. | −0.529754 | ||||||||
\(665\) | −189029. | + | 189029.i | −0.427451 | + | 0.427451i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 519959.i | 1.16874i | ||||||||
\(668\) | 79915.8 | − | 79915.8i | 0.179093 | − | 0.179093i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −519174. | − | 519174.i | −1.15655 | − | 1.15655i | ||||
\(671\) | −348982. | − | 348982.i | −0.775101 | − | 0.775101i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 140601.i | − | 0.310425i | −0.987881 | − | 0.155213i | \(-0.950394\pi\) | ||
0.987881 | − | 0.155213i | \(-0.0496062\pi\) | |||||||
\(674\) | 80851.5 | + | 80851.5i | 0.177979 | + | 0.177979i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11375.5 | + | 297571.i | −0.0248930 | + | 0.651174i | ||||
\(677\) | 543307. | 1.18541 | 0.592704 | − | 0.805420i | \(-0.298060\pi\) | ||||
0.592704 | + | 0.805420i | \(0.298060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −325511. | −0.706035 | ||||||||
\(680\) | 176608.i | 0.381937i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 106191. | − | 106191.i | 0.228307 | − | 0.228307i | ||||
\(683\) | 475365. | + | 475365.i | 1.01903 | + | 1.01903i | 0.999815 | + | 0.0192116i | \(0.00611561\pi\) |
0.0192116 | + | 0.999815i | \(0.493884\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 415216. | 0.884898 | ||||||||
\(686\) | − | 241115.i | − | 0.512362i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 56242.7i | − | 0.118820i | ||||||
\(689\) | 430830. | + | 8231.87i | 0.907544 | + | 0.0173404i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −212706. | + | 212706.i | −0.445476 | + | 0.445476i | −0.893847 | − | 0.448371i | \(-0.852004\pi\) |
0.448371 | + | 0.893847i | \(0.352004\pi\) | |||||||
\(692\) | −97827.1 | −0.204290 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 83578.6 | − | 83578.6i | 0.173531 | − | 0.173531i | ||||
\(695\) | 412274. | − | 412274.i | 0.853526 | − | 0.853526i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −127503. | − | 127503.i | −0.262456 | − | 0.262456i | ||||
\(698\) | 122461. | 0.251354 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −176849. | − | 176849.i | −0.360916 | − | 0.360916i | ||||
\(701\) | − | 56550.4i | − | 0.115080i | −0.998343 | − | 0.0575400i | \(-0.981674\pi\) | ||
0.998343 | − | 0.0575400i | \(-0.0183257\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 223600. | 0.452439 | ||||||||
\(704\) | 116767. | − | 116767.i | 0.235599 | − | 0.235599i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 305400.i | 0.612716i | ||||||||
\(707\) | −283421. | + | 283421.i | −0.567013 | + | 0.567013i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 284754. | + | 284754.i | 0.566470 | + | 0.566470i | 0.931138 | − | 0.364668i | \(-0.118818\pi\) |
−0.364668 | + | 0.931138i | \(0.618818\pi\) | |||||||
\(710\) | −440529. | − | 440529.i | −0.873892 | − | 0.873892i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 600344.i | − | 1.18424i | ||||||
\(713\) | −420088. | − | 420088.i | −0.826345 | − | 0.826345i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 520807. | + | 9951.05i | 1.01874 | + | 0.0194651i | ||||
\(716\) | 3357.54 | 0.00654931 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 66456.3 | 0.128910 | ||||||||
\(719\) | 513980.i | 0.994234i | 0.867684 | + | 0.497117i | \(0.165608\pi\) | ||||
−0.867684 | + | 0.497117i | \(0.834392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 191017. | − | 191017.i | 0.367453 | − | 0.367453i | ||||
\(722\) | −91738.2 | − | 91738.2i | −0.175985 | − | 0.175985i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −296937. | −0.566483 | ||||||||
\(725\) | 718561.i | 1.36706i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5325.23i | 0.0100756i | 0.999987 | + | 0.00503779i | \(0.00160358\pi\) | ||||
−0.999987 | + | 0.00503779i | \(0.998396\pi\) | |||||||
\(728\) | 4880.69 | − | 255440.i | 0.00920912 | − | 0.481977i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 531821. | − | 531821.i | 0.997975 | − | 0.997975i | ||||
\(731\) | 202834. | 0.379582 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 471793. | − | 471793.i | 0.878100 | − | 0.878100i | −0.115238 | − | 0.993338i | \(-0.536763\pi\) |
0.993338 | + | 0.115238i | \(0.0367631\pi\) | |||||||
\(734\) | −22602.4 | + | 22602.4i | −0.0419530 | + | 0.0419530i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −528976. | − | 528976.i | −0.976518 | − | 0.976518i | ||||
\(737\) | 593573. | 1.09280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 383237. | + | 383237.i | 0.701745 | + | 0.701745i | 0.964785 | − | 0.263040i | \(-0.0847252\pi\) |
−0.263040 | + | 0.964785i | \(0.584725\pi\) | |||||||
\(740\) | 341265.i | 0.623201i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −145862. | −0.264932 | ||||||||
\(743\) | −77467.3 | + | 77467.3i | −0.140327 | + | 0.140327i | −0.773781 | − | 0.633454i | \(-0.781637\pi\) |
0.633454 | + | 0.773781i | \(0.281637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 352874.i | 0.635780i | ||||||||
\(746\) | 127709. | − | 127709.i | 0.229479 | − | 0.229479i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −39832.4 | − | 39832.4i | −0.0711924 | − | 0.0711924i | ||||
\(749\) | 159198. | + | 159198.i | 0.283774 | + | 0.283774i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 287709.i | − | 0.510121i | −0.966925 | − | 0.255061i | \(-0.917905\pi\) | ||
0.966925 | − | 0.255061i | \(-0.0820954\pi\) | |||||||
\(752\) | 20799.1 | + | 20799.1i | 0.0367797 | + | 0.0367797i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −208659. | + | 200835.i | −0.367024 | + | 0.353261i | ||||
\(755\) | 359304. | 0.630330 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −962044. | −1.67882 | −0.839408 | − | 0.543502i | \(-0.817098\pi\) | ||||
−0.839408 | + | 0.543502i | \(0.817098\pi\) | |||||||
\(758\) | 32964.5i | 0.0573731i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −486698. | + | 486698.i | −0.842622 | + | 0.842622i | ||||
\(761\) | −496273. | − | 496273.i | −0.856943 | − | 0.856943i | 0.134034 | − | 0.990977i | \(-0.457207\pi\) |
−0.990977 | + | 0.134034i | \(0.957207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −68047.8 | −0.116887 | ||||||||
\(764\) | − | 407148.i | − | 0.697534i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 307378.i | − | 0.523860i | ||||||
\(767\) | −375294. | − | 389915.i | −0.637942 | − | 0.662795i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 326544. | − | 326544.i | 0.552191 | − | 0.552191i | −0.374882 | − | 0.927073i | \(-0.622317\pi\) |
0.927073 | + | 0.374882i | \(0.122317\pi\) | |||||||
\(770\) | −176324. | −0.297393 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 363350. | − | 363350.i | 0.609664 | − | 0.609664i | ||||
\(773\) | −213799. | + | 213799.i | −0.357804 | + | 0.357804i | −0.863003 | − | 0.505199i | \(-0.831419\pi\) |
0.505199 | + | 0.863003i | \(0.331419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −580544. | − | 580544.i | −0.966566 | − | 0.966566i | ||||
\(776\) | −838101. | −1.39179 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 59244.6 | + | 59244.6i | 0.0978790 | + | 0.0978790i | ||||
\(779\) | − | 702751.i | − | 1.15805i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 503658. | 0.825721 | ||||||||
\(782\) | 84234.8 | − | 84234.8i | 0.137746 | − | 0.137746i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 35428.5i | 0.0576395i | ||||||||
\(785\) | 765602. | − | 765602.i | 1.24241 | − | 1.24241i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 642953. | + | 642953.i | 1.03808 | + | 1.03808i | 0.999246 | + | 0.0388320i | \(0.0123637\pi\) |
0.0388320 | + | 0.999246i | \(0.487636\pi\) | |||||||
\(788\) | −351948. | − | 351948.i | −0.566795 | − | 0.566795i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 651882.i | − | 1.04452i | ||||||
\(791\) | −30825.8 | − | 30825.8i | −0.0492677 | − | 0.0492677i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.08726e6 | − | 20774.3i | −1.72897 | − | 0.0330354i | ||||
\(794\) | −152795. | −0.242364 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −126066. | −0.198963 | ||||||||
\(797\) | 735073.i | 1.15721i | 0.815606 | + | 0.578607i | \(0.196404\pi\) | ||||
−0.815606 | + | 0.578607i | \(0.803596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −75009.8 | + | 75009.8i | −0.117496 | + | 0.117496i | ||||
\(800\) | −731022. | − | 731022.i | −1.14222 | − | 1.14222i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 177432. | 0.275857 | ||||||||
\(803\) | 608032.i | 0.942965i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 697534.i | 1.07640i | ||||||||
\(806\) | 6321.36 | − | 330840.i | 0.00973062 | − | 0.509270i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −729731. | + | 729731.i | −1.11774 | + | 1.11774i | ||||
\(809\) | 388192. | 0.593130 | 0.296565 | − | 0.955013i | \(-0.404159\pi\) | ||||
0.296565 | + | 0.955013i | \(0.404159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −163285. | + | 163285.i | −0.248259 | + | 0.248259i | −0.820256 | − | 0.571997i | \(-0.806169\pi\) |
0.571997 | + | 0.820256i | \(0.306169\pi\) | |||||||
\(812\) | −129674. | + | 129674.i | −0.196671 | + | 0.196671i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 104286. | + | 104286.i | 0.157389 | + | 0.157389i | ||||
\(815\) | 1.29760e6 | 1.95355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 558972. | + | 558972.i | 0.837426 | + | 0.837426i | ||||
\(818\) | 251387.i | 0.375696i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.07256e6 | 1.59512 | ||||||||
\(821\) | 401933. | − | 401933.i | 0.596303 | − | 0.596303i | −0.343024 | − | 0.939327i | \(-0.611451\pi\) |
0.939327 | + | 0.343024i | \(0.111451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 129326.i | 0.190935i | 0.995433 | + | 0.0954674i | \(0.0304346\pi\) | ||||
−0.995433 | + | 0.0954674i | \(0.969565\pi\) | |||||||
\(824\) | 491816. | − | 491816.i | 0.724350 | − | 0.724350i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 129535. | + | 129535.i | 0.189857 | + | 0.189857i | ||||
\(827\) | −51675.4 | − | 51675.4i | −0.0755567 | − | 0.0755567i | 0.668319 | − | 0.743875i | \(-0.267014\pi\) |
−0.743875 | + | 0.668319i | \(0.767014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 984088.i | − | 1.43194i | −0.698131 | − | 0.715970i | \(-0.745985\pi\) | ||
0.698131 | − | 0.715970i | \(-0.254015\pi\) | |||||||
\(830\) | 251151. | + | 251151.i | 0.364568 | + | 0.364568i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6950.92 | − | 363789.i | 0.0100414 | − | 0.525537i | ||||
\(833\) | −127769. | −0.184135 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −435603. | −0.624767 | ||||||||
\(836\) | − | 219542.i | − | 0.314127i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −441624. | + | 441624.i | −0.628876 | + | 0.628876i | ||||
\(839\) | −378169. | − | 378169.i | −0.537232 | − | 0.537232i | 0.385483 | − | 0.922715i | \(-0.374035\pi\) |
−0.922715 | + | 0.385483i | \(0.874035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −180399. | −0.255060 | ||||||||
\(842\) | 102457.i | 0.144517i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 532409.i | 0.747413i | ||||||||
\(845\) | 841999. | − | 779994.i | 1.17923 | − | 1.09239i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −150064. | + | 150064.i | −0.209175 | + | 0.209175i | ||||
\(848\) | 49802.4 | 0.0692562 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 116409. | − | 116409.i | 0.161119 | − | 0.161119i | ||||
\(851\) | 412551. | − | 412551.i | 0.569663 | − | 0.569663i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −296254. | − | 296254.i | −0.407161 | − | 0.407161i | 0.473586 | − | 0.880747i | \(-0.342959\pi\) |
−0.880747 | + | 0.473586i | \(0.842959\pi\) | |||||||
\(854\) | 368104. | 0.504724 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 409890. | + | 409890.i | 0.559396 | + | 0.559396i | ||||
\(857\) | 1.04442e6i | 1.42205i | 0.703168 | + | 0.711023i | \(0.251768\pi\) | ||||
−0.703168 | + | 0.711023i | \(0.748232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 503818. | 0.682790 | 0.341395 | − | 0.939920i | \(-0.389101\pi\) | ||||
0.341395 | + | 0.939920i | \(0.389101\pi\) | |||||||
\(860\) | −853122. | + | 853122.i | −1.15349 | + | 1.15349i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 463268.i | − | 0.623473i | ||||||
\(863\) | 283034. | − | 283034.i | 0.380029 | − | 0.380029i | −0.491083 | − | 0.871113i | \(-0.663399\pi\) |
0.871113 | + | 0.491083i | \(0.163399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 266617. | + | 266617.i | 0.356332 | + | 0.356332i | ||||
\(866\) | 321318. | + | 321318.i | 0.428449 | + | 0.428449i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 209533.i | − | 0.278108i | ||||||
\(869\) | 372649. | + | 372649.i | 0.493470 | + | 0.493470i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 942311. | − | 906977.i | 1.24210 | − | 1.19553i | ||||
\(872\) | −175204. | −0.230416 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 464271. | 0.607783 | ||||||||
\(875\) | 355360.i | 0.464144i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 86669.2 | − | 86669.2i | 0.112685 | − | 0.112685i | −0.648516 | − | 0.761201i | \(-0.724610\pi\) |
0.761201 | + | 0.648516i | \(0.224610\pi\) | |||||||
\(878\) | −369548. | − | 369548.i | −0.479383 | − | 0.479383i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 60203.4 | 0.0777420 | ||||||||
\(881\) | − | 346696.i | − | 0.446681i | −0.974741 | − | 0.223340i | \(-0.928304\pi\) | ||
0.974741 | − | 0.223340i | \(-0.0716961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 570534.i | − | 0.731746i | −0.930665 | − | 0.365873i | \(-0.880770\pi\) | ||
0.930665 | − | 0.365873i | \(-0.119230\pi\) | |||||||
\(884\) | −124099. | − | 2371.16i | −0.158805 | − | 0.00303428i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 591378. | − | 591378.i | 0.753352 | − | 0.753352i | ||||
\(887\) | −988202. | −1.25603 | −0.628013 | − | 0.778203i | \(-0.716131\pi\) | ||||
−0.628013 | + | 0.778203i | \(0.716131\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 129499. | − | 129499.i | 0.163856 | − | 0.163856i | ||||
\(890\) | −645542. | + | 645542.i | −0.814976 | + | 0.814976i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 81970.3 | + | 81970.3i | 0.103021 | + | 0.103021i | ||||
\(893\) | −413427. | −0.518436 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9150.60 | − | 9150.60i | −0.0114236 | − | 0.0114236i | ||||
\(896\) | − | 281722.i | − | 0.350918i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −626753. | −0.777219 | ||||||||
\(899\) | −425681. | + | 425681.i | −0.526702 | + | 0.526702i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 179608.i | 0.221246i | ||||||||
\(902\) | 327759. | − | 327759.i | 0.402848 | − | 0.402848i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −79368.0 | − | 79368.0i | −0.0971200 | − | 0.0971200i | ||||
\(905\) | 809268. | + | 809268.i | 0.988088 | + | 0.988088i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 720192.i | 0.875455i | 0.899108 | + | 0.437728i | \(0.144217\pi\) | ||||
−0.899108 | + | 0.437728i | \(0.855783\pi\) | |||||||
\(908\) | 100535. | + | 100535.i | 0.121940 | + | 0.121940i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −279919. | + | 269423.i | −0.338026 | + | 0.325351i | ||||
\(911\) | −963155. | −1.16054 | −0.580269 | − | 0.814425i | \(-0.697053\pi\) | ||||
−0.580269 | + | 0.814425i | \(0.697053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −287142. | −0.344473 | ||||||||
\(914\) | − | 296455.i | − | 0.354867i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −378326. | + | 378326.i | −0.450895 | + | 0.450895i | ||||
\(917\) | 166290. | + | 166290.i | 0.197755 | + | 0.197755i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.29069e6 | −1.52823 | −0.764117 | − | 0.645077i | \(-0.776825\pi\) | ||||
−0.764117 | + | 0.645077i | \(0.776825\pi\) | |||||||
\(920\) | 1.79596e6i | 2.12188i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 188961.i | 0.222285i | ||||||||
\(923\) | 799569. | − | 769587.i | 0.938540 | − | 0.903347i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 570127. | − | 570127.i | 0.666328 | − | 0.666328i | ||||
\(926\) | −571149. | −0.666082 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −536019. | + | 536019.i | −0.622421 | + | 0.622421i | ||||
\(929\) | −620998. | + | 620998.i | −0.719546 | + | 0.719546i | −0.968512 | − | 0.248966i | \(-0.919909\pi\) |
0.248966 | + | 0.968512i | \(0.419909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −352109. | − | 352109.i | −0.406235 | − | 0.406235i | ||||
\(932\) | −24658.8 | −0.0283883 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 113752. | + | 113752.i | 0.130396 | + | 0.130396i | ||||
\(935\) | 217118.i | 0.248354i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.00082e6 | 1.13992 | 0.569960 | − | 0.821672i | \(-0.306959\pi\) | ||||
0.569960 | + | 0.821672i | \(0.306959\pi\) | |||||||
\(938\) | −313048. | + | 313048.i | −0.355799 | + | 0.355799i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 630985.i | − | 0.714107i | ||||||
\(941\) | −902091. | + | 902091.i | −1.01876 | + | 1.01876i | −0.0189381 | + | 0.999821i | \(0.506029\pi\) |
−0.999821 | + | 0.0189381i | \(0.993971\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.29661e6 | − | 1.29661e6i | −1.45809 | − | 1.45809i | ||||
\(944\) | −44227.7 | − | 44227.7i | −0.0496307 | − | 0.0496307i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 521403.i | 0.582628i | ||||||||
\(947\) | 64662.8 | + | 64662.8i | 0.0721032 | + | 0.0721032i | 0.742239 | − | 0.670136i | \(-0.233764\pi\) |
−0.670136 | + | 0.742239i | \(0.733764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 929071. | + | 965266.i | 1.03161 | + | 1.07180i | ||||
\(950\) | 641603. | 0.710917 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 106490. | 0.117499 | ||||||||
\(953\) | 1.57625e6i | 1.73556i | 0.496948 | + | 0.867781i | \(0.334454\pi\) | ||||
−0.496948 | + | 0.867781i | \(0.665546\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.10963e6 | + | 1.10963e6i | −1.21667 | + | 1.21667i | ||||
\(956\) | 196448. | + | 196448.i | 0.214947 | + | 0.214947i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −379659. | −0.413679 | ||||||||
\(959\) | − | 250364.i | − | 0.272229i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 235683.i | 0.255201i | ||||||||
\(962\) | 324904. | + | 6207.93i | 0.351079 | + | 0.00670806i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 287452. | − | 287452.i | 0.309322 | − | 0.309322i | ||||
\(965\) | −1.98054e6 | −2.12681 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −561644. | + | 561644.i | −0.600632 | + | 0.600632i | −0.940480 | − | 0.339849i | \(-0.889624\pi\) |
0.339849 | + | 0.940480i | \(0.389624\pi\) | |||||||
\(968\) | −386373. | + | 386373.i | −0.412340 | + | 0.412340i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 901199. | + | 901199.i | 0.957806 | + | 0.957806i | ||||
\(971\) | 70845.6 | 0.0751405 | 0.0375703 | − | 0.999294i | \(-0.488038\pi\) | ||||
0.0375703 | + | 0.999294i | \(0.488038\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −248590. | − | 248590.i | −0.262578 | − | 0.262578i | ||||
\(974\) | 103464.i | 0.109061i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −125684. | −0.131941 | ||||||||
\(977\) | 617175. | − | 617175.i | 0.646576 | − | 0.646576i | −0.305588 | − | 0.952164i | \(-0.598853\pi\) |
0.952164 | + | 0.305588i | \(0.0988531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 738050.i | − | 0.770052i | ||||||
\(980\) | 537400. | − | 537400.i | 0.559559 | − | 0.559559i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 383080. | + | 383080.i | 0.397252 | + | 0.397252i | ||||
\(983\) | −665135. | − | 665135.i | −0.688339 | − | 0.688339i | 0.273526 | − | 0.961865i | \(-0.411810\pi\) |
−0.961865 | + | 0.273526i | \(0.911810\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.91839e6i | 1.97726i | ||||||||
\(986\) | −85356.3 | − | 85356.3i | −0.0877974 | − | 0.0877974i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −335459. | − | 348528.i | −0.343658 | − | 0.357046i | ||||
\(989\) | 2.06265e6 | 2.10879 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 250003. | 0.254565 | 0.127282 | − | 0.991867i | \(-0.459375\pi\) | ||||
0.127282 | + | 0.991867i | \(0.459375\pi\) | |||||||
\(992\) | − | 866127.i | − | 0.880153i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −265627. | + | 265627.i | −0.268843 | + | 0.268843i | ||||
\(995\) | 343579. | + | 343579.i | 0.347041 | + | 0.347041i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.47712e6 | −1.48602 | −0.743011 | − | 0.669279i | \(-0.766603\pi\) | ||||
−0.743011 | + | 0.669279i | \(0.766603\pi\) | |||||||
\(998\) | 97688.8i | 0.0980808i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 117.5.j.b.109.4 | 20 | ||
3.2 | odd | 2 | 39.5.g.a.31.7 | ✓ | 20 | ||
13.8 | odd | 4 | inner | 117.5.j.b.73.4 | 20 | ||
39.8 | even | 4 | 39.5.g.a.34.7 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.7 | ✓ | 20 | 3.2 | odd | 2 | ||
39.5.g.a.34.7 | yes | 20 | 39.8 | even | 4 | ||
117.5.j.b.73.4 | 20 | 13.8 | odd | 4 | inner | ||
117.5.j.b.109.4 | 20 | 1.1 | even | 1 | trivial |