Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(683,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("684.683");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.b (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 683.12 | ||
Character | \(\chi\) | \(=\) | 684.683 |
Dual form | 684.3.b.a.683.10 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88680 | + | 0.663313i | −0.943400 | + | 0.331656i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.12003 | − | 2.50308i | 0.780008 | − | 0.625769i | ||||
\(5\) | 0.647124i | 0.129425i | 0.997904 | + | 0.0647124i | \(0.0206130\pi\) | ||||
−0.997904 | + | 0.0647124i | \(0.979387\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.63116i | 0.661595i | 0.943702 | + | 0.330797i | \(0.107318\pi\) | ||||
−0.943702 | + | 0.330797i | \(0.892682\pi\) | |||||||
\(8\) | −4.22656 | + | 6.79236i | −0.528320 | + | 0.849046i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.429246 | − | 1.22099i | −0.0429246 | − | 0.122099i | ||||
\(11\) | 14.8893 | 1.35357 | 0.676787 | − | 0.736179i | \(-0.263372\pi\) | ||||
0.676787 | + | 0.736179i | \(0.263372\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 22.0174i | − | 1.69364i | −0.531877 | − | 0.846822i | \(-0.678513\pi\) | ||
0.531877 | − | 0.846822i | \(-0.321487\pi\) | |||||||
\(14\) | −3.07191 | − | 8.73808i | −0.219422 | − | 0.624149i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.46921 | − | 15.6194i | 0.216826 | − | 0.976210i | ||||
\(17\) | 18.9443i | 1.11437i | 0.830388 | + | 0.557186i | \(0.188119\pi\) | ||||
−0.830388 | + | 0.557186i | \(0.811881\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.76418 | − | 18.9179i | −0.0928516 | − | 0.995680i | ||||
\(20\) | 1.61980 | + | 2.01905i | 0.0809901 | + | 0.100952i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −28.0932 | + | 9.87628i | −1.27696 | + | 0.448922i | ||||
\(23\) | −13.7179 | −0.596431 | −0.298215 | − | 0.954499i | \(-0.596391\pi\) | ||||
−0.298215 | + | 0.954499i | \(0.596391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.5812 | 0.983249 | ||||||||
\(26\) | 14.6044 | + | 41.5424i | 0.561707 | + | 1.59778i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.5922 | + | 14.4494i | 0.414006 | + | 0.516049i | ||||
\(29\) | −21.8371 | −0.753002 | −0.376501 | − | 0.926416i | \(-0.622873\pi\) | ||||
−0.376501 | + | 0.926416i | \(0.622873\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.3751 | 0.625003 | 0.312501 | − | 0.949917i | \(-0.398833\pi\) | ||||
0.312501 | + | 0.949917i | \(0.398833\pi\) | |||||||
\(32\) | 3.81482 | + | 31.7718i | 0.119213 | + | 0.992869i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.5660 | − | 35.7442i | −0.369589 | − | 1.05130i | ||||
\(35\) | −2.99694 | −0.0856268 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 31.3197i | 0.846478i | 0.906018 | + | 0.423239i | \(0.139107\pi\) | ||||
−0.906018 | + | 0.423239i | \(0.860893\pi\) | |||||||
\(38\) | 15.8772 | + | 34.5241i | 0.417820 | + | 0.908530i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.39550 | − | 2.73511i | −0.109888 | − | 0.0683777i | ||||
\(41\) | −38.1704 | −0.930985 | −0.465492 | − | 0.885052i | \(-0.654123\pi\) | ||||
−0.465492 | + | 0.885052i | \(0.654123\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 32.1401i | − | 0.747444i | −0.927541 | − | 0.373722i | \(-0.878081\pi\) | ||
0.927541 | − | 0.373722i | \(-0.121919\pi\) | |||||||
\(44\) | 46.4552 | − | 37.2691i | 1.05580 | − | 0.847026i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25.8830 | − | 9.09926i | 0.562673 | − | 0.197810i | ||||
\(47\) | 75.4122 | 1.60451 | 0.802257 | − | 0.596978i | \(-0.203632\pi\) | ||||
0.802257 | + | 0.596978i | \(0.203632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 27.5523 | 0.562292 | ||||||||
\(50\) | −46.3799 | + | 16.3050i | −0.927598 | + | 0.326101i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −55.1112 | − | 68.6949i | −1.05983 | − | 1.32106i | ||||
\(53\) | 60.7547 | 1.14632 | 0.573158 | − | 0.819445i | \(-0.305718\pi\) | ||||
0.573158 | + | 0.819445i | \(0.305718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.63524i | 0.175186i | ||||||||
\(56\) | −31.4565 | − | 19.5739i | −0.561724 | − | 0.349533i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 41.2022 | − | 14.4848i | 0.710383 | − | 0.249738i | ||||
\(59\) | − | 113.793i | − | 1.92870i | −0.264634 | − | 0.964349i | \(-0.585251\pi\) | ||
0.264634 | − | 0.964349i | \(-0.414749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −106.204 | −1.74105 | −0.870525 | − | 0.492125i | \(-0.836220\pi\) | ||||
−0.870525 | + | 0.492125i | \(0.836220\pi\) | |||||||
\(62\) | −36.5569 | + | 12.8517i | −0.589628 | + | 0.207286i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −28.2724 | − | 57.4166i | −0.441757 | − | 0.897135i | ||||
\(65\) | 14.2480 | 0.219199 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25.0449 | 0.373805 | 0.186903 | − | 0.982378i | \(-0.440155\pi\) | ||||
0.186903 | + | 0.982378i | \(0.440155\pi\) | |||||||
\(68\) | 47.4191 | + | 59.1069i | 0.697340 | + | 0.869219i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.65462 | − | 1.98791i | 0.0807803 | − | 0.0283987i | ||||
\(71\) | 67.2579i | 0.947295i | 0.880715 | + | 0.473647i | \(0.157063\pi\) | ||||
−0.880715 | + | 0.473647i | \(0.842937\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 99.5142 | 1.36321 | 0.681604 | − | 0.731721i | \(-0.261283\pi\) | ||||
0.681604 | + | 0.731721i | \(0.261283\pi\) | |||||||
\(74\) | −20.7747 | − | 59.0940i | −0.280740 | − | 0.798567i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −52.8573 | − | 54.6086i | −0.695491 | − | 0.718535i | ||||
\(77\) | 68.9549i | 0.895518i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 84.4233 | 1.06865 | 0.534324 | − | 0.845279i | \(-0.320566\pi\) | ||||
0.534324 | + | 0.845279i | \(0.320566\pi\) | |||||||
\(80\) | 10.1077 | + | 2.24501i | 0.126346 | + | 0.0280626i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 72.0199 | − | 25.3189i | 0.878291 | − | 0.308767i | ||||
\(83\) | 92.6388 | 1.11613 | 0.558065 | − | 0.829797i | \(-0.311544\pi\) | ||||
0.558065 | + | 0.829797i | \(0.311544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.2593 | −0.144227 | ||||||||
\(86\) | 21.3189 | + | 60.6420i | 0.247895 | + | 0.705139i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −62.9306 | + | 101.134i | −0.715120 | + | 1.14925i | ||||
\(89\) | 120.417 | 1.35300 | 0.676499 | − | 0.736444i | \(-0.263496\pi\) | ||||
0.676499 | + | 0.736444i | \(0.263496\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 101.966 | 1.12051 | ||||||||
\(92\) | −42.8003 | + | 34.3370i | −0.465221 | + | 0.373228i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −142.288 | + | 50.0219i | −1.51370 | + | 0.532147i | ||||
\(95\) | 12.2422 | − | 1.14164i | 0.128866 | − | 0.0120173i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 140.014i | 1.44345i | 0.692182 | + | 0.721723i | \(0.256650\pi\) | ||||
−0.692182 | + | 0.721723i | \(0.743350\pi\) | |||||||
\(98\) | −51.9858 | + | 18.2758i | −0.530467 | + | 0.186488i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 76.6942 | − | 61.5287i | 0.766942 | − | 0.615287i | ||||
\(101\) | 34.2779i | 0.339385i | 0.985497 | + | 0.169692i | \(0.0542774\pi\) | ||||
−0.985497 | + | 0.169692i | \(0.945723\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 185.830 | 1.80418 | 0.902088 | − | 0.431553i | \(-0.142034\pi\) | ||||
0.902088 | + | 0.431553i | \(0.142034\pi\) | |||||||
\(104\) | 149.550 | + | 93.0576i | 1.43798 | + | 0.894785i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −114.632 | + | 40.2994i | −1.08143 | + | 0.380183i | ||||
\(107\) | − | 161.771i | − | 1.51188i | −0.654643 | − | 0.755938i | \(-0.727181\pi\) | ||
0.654643 | − | 0.755938i | \(-0.272819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100.731i | 0.924138i | 0.886844 | + | 0.462069i | \(0.152893\pi\) | ||||
−0.886844 | + | 0.462069i | \(0.847107\pi\) | |||||||
\(110\) | −6.39118 | − | 18.1798i | −0.0581016 | − | 0.165271i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 72.3358 | + | 16.0665i | 0.645856 | + | 0.143451i | ||||
\(113\) | −5.03853 | −0.0445887 | −0.0222944 | − | 0.999751i | \(-0.507097\pi\) | ||||
−0.0222944 | + | 0.999751i | \(0.507097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 8.87719i | − | 0.0771929i | ||||||
\(116\) | −68.1324 | + | 54.6599i | −0.587348 | + | 0.471206i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 75.4804 | + | 214.705i | 0.639665 | + | 1.81953i | ||||
\(119\) | −87.7343 | −0.737263 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 100.692 | 0.832165 | ||||||||
\(122\) | 200.386 | − | 70.4465i | 1.64251 | − | 0.577430i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 60.4509 | − | 48.4973i | 0.487507 | − | 0.391107i | ||||
\(125\) | 32.0852i | 0.256682i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −31.2889 | −0.246369 | −0.123185 | − | 0.992384i | \(-0.539311\pi\) | ||||
−0.123185 | + | 0.992384i | \(0.539311\pi\) | |||||||
\(128\) | 91.4296 | + | 89.5803i | 0.714294 | + | 0.699846i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −26.8831 | + | 9.45085i | −0.206793 | + | 0.0726989i | ||||
\(131\) | −18.9095 | −0.144347 | −0.0721736 | − | 0.997392i | \(-0.522994\pi\) | ||||
−0.0721736 | + | 0.997392i | \(0.522994\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 87.6120 | − | 8.17021i | 0.658737 | − | 0.0614301i | ||||
\(134\) | −47.2548 | + | 16.6126i | −0.352648 | + | 0.123975i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −128.677 | − | 80.0693i | −0.946153 | − | 0.588745i | ||||
\(137\) | 140.158i | 1.02305i | 0.859269 | + | 0.511524i | \(0.170919\pi\) | ||||
−0.859269 | + | 0.511524i | \(0.829081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 155.210i | − | 1.11662i | −0.829633 | − | 0.558309i | \(-0.811450\pi\) | ||
0.829633 | − | 0.558309i | \(-0.188550\pi\) | |||||||
\(140\) | −9.35054 | + | 7.50156i | −0.0667896 | + | 0.0535826i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −44.6130 | − | 126.902i | −0.314176 | − | 0.893678i | ||||
\(143\) | − | 327.824i | − | 2.29247i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 14.1313i | − | 0.0974572i | ||||||
\(146\) | −187.764 | + | 66.0091i | −1.28605 | + | 0.452117i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 78.3956 | + | 97.7184i | 0.529700 | + | 0.660260i | ||||
\(149\) | − | 204.301i | − | 1.37115i | −0.728002 | − | 0.685575i | \(-0.759551\pi\) | ||
0.728002 | − | 0.685575i | \(-0.240449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 194.202 | 1.28610 | 0.643052 | − | 0.765823i | \(-0.277668\pi\) | ||||
0.643052 | + | 0.765823i | \(0.277668\pi\) | |||||||
\(152\) | 135.954 | + | 67.9747i | 0.894433 | + | 0.447202i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −45.7386 | − | 130.104i | −0.297004 | − | 0.844832i | ||||
\(155\) | 12.5381i | 0.0808909i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −124.358 | −0.792087 | −0.396043 | − | 0.918232i | \(-0.629617\pi\) | ||||
−0.396043 | + | 0.918232i | \(0.629617\pi\) | |||||||
\(158\) | −159.290 | + | 55.9990i | −1.00816 | + | 0.354424i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20.5603 | + | 2.46866i | −0.128502 | + | 0.0154291i | ||||
\(161\) | − | 63.5299i | − | 0.394595i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 194.930i | 1.19589i | 0.801538 | + | 0.597944i | \(0.204016\pi\) | ||||
−0.801538 | + | 0.597944i | \(0.795984\pi\) | |||||||
\(164\) | −119.093 | + | 95.5434i | −0.726176 | + | 0.582582i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −174.791 | + | 61.4485i | −1.05296 | + | 0.370171i | ||||
\(167\) | 6.41401i | 0.0384073i | 0.999816 | + | 0.0192036i | \(0.00611308\pi\) | ||||
−0.999816 | + | 0.0192036i | \(0.993887\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −315.764 | −1.86843 | ||||||||
\(170\) | 23.1309 | − | 8.13177i | 0.136064 | − | 0.0478339i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −80.4492 | − | 100.278i | −0.467728 | − | 0.583013i | ||||
\(173\) | −99.2301 | −0.573585 | −0.286792 | − | 0.957993i | \(-0.592589\pi\) | ||||
−0.286792 | + | 0.957993i | \(0.592589\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 113.840i | 0.650512i | ||||||||
\(176\) | 51.6542 | − | 232.562i | 0.293490 | − | 1.32137i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −227.202 | + | 79.8740i | −1.27642 | + | 0.448730i | ||||
\(179\) | 127.149i | 0.710330i | 0.934804 | + | 0.355165i | \(0.115575\pi\) | ||||
−0.934804 | + | 0.355165i | \(0.884425\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.33163i | 0.0184068i | 0.999958 | + | 0.00920341i | \(0.00292958\pi\) | ||||
−0.999958 | + | 0.00920341i | \(0.997070\pi\) | |||||||
\(182\) | −192.389 | + | 67.6353i | −1.05709 | + | 0.371623i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 57.9795 | − | 93.1770i | 0.315106 | − | 0.506397i | ||||
\(185\) | −20.2677 | −0.109555 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 282.068i | 1.50839i | ||||||||
\(188\) | 235.288 | − | 188.763i | 1.25153 | − | 1.00406i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −22.3414 | + | 10.2745i | −0.117586 | + | 0.0540762i | ||||
\(191\) | −99.7437 | −0.522219 | −0.261109 | − | 0.965309i | \(-0.584088\pi\) | ||||
−0.261109 | + | 0.965309i | \(0.584088\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 55.1904i | − | 0.285961i | −0.989726 | − | 0.142980i | \(-0.954331\pi\) | ||
0.989726 | − | 0.142980i | \(-0.0456686\pi\) | |||||||
\(194\) | −92.8733 | − | 264.179i | −0.478728 | − | 1.36175i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 85.9642 | − | 68.9656i | 0.438593 | − | 0.351865i | ||||
\(197\) | − | 148.744i | − | 0.755043i | −0.926001 | − | 0.377522i | \(-0.876776\pi\) | ||
0.926001 | − | 0.377522i | \(-0.123224\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 119.642i | − | 0.601216i | −0.953748 | − | 0.300608i | \(-0.902810\pi\) | ||
0.953748 | − | 0.300608i | \(-0.0971897\pi\) | |||||||
\(200\) | −103.894 | + | 166.965i | −0.519470 | + | 0.834823i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −22.7369 | − | 64.6755i | −0.112559 | − | 0.320176i | ||||
\(203\) | − | 101.131i | − | 0.498182i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 24.7010i | − | 0.120493i | ||||||
\(206\) | −350.624 | + | 123.263i | −1.70206 | + | 0.598366i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −343.897 | − | 76.3828i | −1.65335 | − | 0.367225i | ||||
\(209\) | −26.2674 | − | 281.675i | −0.125682 | − | 1.34773i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 273.915 | 1.29817 | 0.649087 | − | 0.760714i | \(-0.275151\pi\) | ||||
0.649087 | + | 0.760714i | \(0.275151\pi\) | |||||||
\(212\) | 189.557 | − | 152.074i | 0.894135 | − | 0.717329i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 107.305 | + | 305.229i | 0.501423 | + | 1.42630i | ||||
\(215\) | 20.7986 | 0.0967378 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 89.7292i | 0.413498i | ||||||||
\(218\) | −66.8162 | − | 190.059i | −0.306496 | − | 0.871832i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 24.1177 | + | 30.0623i | 0.109626 | + | 0.136647i | ||||
\(221\) | 417.104 | 1.88735 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −208.529 | −0.935108 | −0.467554 | − | 0.883965i | \(-0.654865\pi\) | ||||
−0.467554 | + | 0.883965i | \(0.654865\pi\) | |||||||
\(224\) | −147.140 | + | 17.6670i | −0.656877 | + | 0.0788707i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.50669 | − | 3.34212i | 0.0420650 | − | 0.0147881i | ||||
\(227\) | 218.093i | 0.960762i | 0.877060 | + | 0.480381i | \(0.159502\pi\) | ||||
−0.877060 | + | 0.480381i | \(0.840498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 104.878 | 0.457983 | 0.228991 | − | 0.973428i | \(-0.426457\pi\) | ||||
0.228991 | + | 0.973428i | \(0.426457\pi\) | |||||||
\(230\) | 5.88835 | + | 16.7495i | 0.0256015 | + | 0.0728238i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 92.2956 | − | 148.325i | 0.397826 | − | 0.639333i | ||||
\(233\) | 85.0991i | 0.365232i | 0.983184 | + | 0.182616i | \(0.0584566\pi\) | ||||
−0.983184 | + | 0.182616i | \(0.941543\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 48.8010i | 0.207664i | ||||||||
\(236\) | −284.833 | − | 355.038i | −1.20692 | − | 1.50440i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 165.537 | − | 58.1952i | 0.695534 | − | 0.244518i | ||||
\(239\) | −208.984 | −0.874411 | −0.437205 | − | 0.899362i | \(-0.644032\pi\) | ||||
−0.437205 | + | 0.899362i | \(0.644032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 291.886i | − | 1.21115i | −0.795790 | − | 0.605573i | \(-0.792944\pi\) | ||
0.795790 | − | 0.605573i | \(-0.207056\pi\) | |||||||
\(242\) | −189.986 | + | 66.7902i | −0.785064 | + | 0.275993i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −331.360 | + | 265.837i | −1.35803 | + | 1.08950i | ||||
\(245\) | 17.8298i | 0.0727746i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −416.523 | + | 38.8426i | −1.68633 | + | 0.157257i | ||||
\(248\) | −81.8899 | + | 131.603i | −0.330201 | + | 0.530656i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.2825 | − | 60.5384i | −0.0851301 | − | 0.242154i | ||||
\(251\) | −234.938 | −0.936006 | −0.468003 | − | 0.883727i | \(-0.655026\pi\) | ||||
−0.468003 | + | 0.883727i | \(0.655026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −204.250 | −0.807313 | ||||||||
\(254\) | 59.0359 | − | 20.7543i | 0.232425 | − | 0.0817099i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −231.929 | − | 108.374i | −0.905973 | − | 0.423335i | ||||
\(257\) | 54.0528 | 0.210322 | 0.105161 | − | 0.994455i | \(-0.466464\pi\) | ||||
0.105161 | + | 0.994455i | \(0.466464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −145.047 | −0.560025 | ||||||||
\(260\) | 44.4541 | − | 35.6638i | 0.170977 | − | 0.137168i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 35.6784 | − | 12.5429i | 0.136177 | − | 0.0478736i | ||||
\(263\) | −482.093 | −1.83305 | −0.916526 | − | 0.399975i | \(-0.869019\pi\) | ||||
−0.916526 | + | 0.399975i | \(0.869019\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.3158i | 0.148362i | ||||||||
\(266\) | −159.887 | + | 73.5297i | −0.601079 | + | 0.276427i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 78.1411 | − | 62.6894i | 0.291571 | − | 0.233916i | ||||
\(269\) | −99.6712 | −0.370525 | −0.185262 | − | 0.982689i | \(-0.559314\pi\) | ||||
−0.185262 | + | 0.982689i | \(0.559314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 78.1924i | 0.288533i | 0.989539 | + | 0.144266i | \(0.0460822\pi\) | ||||
−0.989539 | + | 0.144266i | \(0.953918\pi\) | |||||||
\(272\) | 295.898 | + | 65.7218i | 1.08786 | + | 0.241624i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −92.9684 | − | 264.450i | −0.339301 | − | 0.965145i | ||||
\(275\) | 365.998 | 1.33090 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 87.8522 | 0.317156 | 0.158578 | − | 0.987346i | \(-0.449309\pi\) | ||||
0.158578 | + | 0.987346i | \(0.449309\pi\) | |||||||
\(278\) | 102.953 | + | 292.850i | 0.370333 | + | 1.05342i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.6667 | − | 20.3563i | 0.0452383 | − | 0.0727010i | ||||
\(281\) | −223.682 | −0.796023 | −0.398011 | − | 0.917380i | \(-0.630300\pi\) | ||||
−0.398011 | + | 0.917380i | \(0.630300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 427.937i | − | 1.51214i | −0.654488 | − | 0.756072i | \(-0.727116\pi\) | ||
0.654488 | − | 0.756072i | \(-0.272884\pi\) | |||||||
\(284\) | 168.352 | + | 209.847i | 0.592788 | + | 0.738898i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 217.450 | + | 618.538i | 0.760313 | + | 2.16272i | ||||
\(287\) | − | 176.773i | − | 0.615935i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −69.8875 | −0.241825 | ||||||||
\(290\) | 9.37346 | + | 26.6629i | 0.0323223 | + | 0.0919411i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 310.488 | − | 249.092i | 1.06331 | − | 0.853054i | ||||
\(293\) | −264.532 | −0.902841 | −0.451420 | − | 0.892311i | \(-0.649082\pi\) | ||||
−0.451420 | + | 0.892311i | \(0.649082\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 73.6383 | 0.249621 | ||||||||
\(296\) | −212.735 | − | 132.374i | −0.718698 | − | 0.447211i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 135.516 | + | 385.476i | 0.454751 | + | 1.29354i | ||||
\(299\) | 302.032i | 1.01014i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 148.846 | 0.494505 | ||||||||
\(302\) | −366.420 | + | 128.816i | −1.21331 | + | 0.426544i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −301.606 | − | 38.0748i | −0.992126 | − | 0.125246i | ||||
\(305\) | − | 68.7272i | − | 0.225335i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 567.515 | 1.84858 | 0.924291 | − | 0.381689i | \(-0.124657\pi\) | ||||
0.924291 | + | 0.381689i | \(0.124657\pi\) | |||||||
\(308\) | 172.599 | + | 215.141i | 0.560388 | + | 0.698511i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.31667 | − | 23.6569i | −0.0268280 | − | 0.0763125i | ||||
\(311\) | −121.048 | −0.389222 | −0.194611 | − | 0.980880i | \(-0.562345\pi\) | ||||
−0.194611 | + | 0.980880i | \(0.562345\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 109.296 | 0.349190 | 0.174595 | − | 0.984640i | \(-0.444138\pi\) | ||||
0.174595 | + | 0.984640i | \(0.444138\pi\) | |||||||
\(314\) | 234.638 | − | 82.4880i | 0.747255 | − | 0.262701i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 263.403 | − | 211.318i | 0.833555 | − | 0.668728i | ||||
\(317\) | −494.489 | −1.55990 | −0.779952 | − | 0.625840i | \(-0.784756\pi\) | ||||
−0.779952 | + | 0.625840i | \(0.784756\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −325.139 | −1.01924 | ||||||||
\(320\) | 37.1557 | − | 18.2958i | 0.116112 | − | 0.0571743i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42.1402 | + | 119.868i | 0.130870 | + | 0.372261i | ||||
\(323\) | 358.387 | − | 33.4212i | 1.10956 | − | 0.103471i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 541.214i | − | 1.66527i | ||||||
\(326\) | −129.299 | − | 367.794i | −0.396624 | − | 1.12820i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 161.329 | − | 259.267i | 0.491858 | − | 0.790449i | ||||
\(329\) | 349.246i | 1.06154i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −488.208 | −1.47495 | −0.737475 | − | 0.675375i | \(-0.763982\pi\) | ||||
−0.737475 | + | 0.675375i | \(0.763982\pi\) | |||||||
\(332\) | 289.036 | − | 231.882i | 0.870590 | − | 0.698440i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.25450 | − | 12.1020i | −0.0127380 | − | 0.0362334i | ||||
\(335\) | 16.2072i | 0.0483797i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 322.191i | 0.956056i | 0.878345 | + | 0.478028i | \(0.158648\pi\) | ||||
−0.878345 | + | 0.478028i | \(0.841352\pi\) | |||||||
\(338\) | 595.784 | − | 209.450i | 1.76267 | − | 0.619676i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −38.2495 | + | 30.6860i | −0.112499 | + | 0.0902531i | ||||
\(341\) | 288.482 | 0.845988 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 354.526i | 1.03360i | ||||||||
\(344\) | 218.307 | + | 135.842i | 0.634614 | + | 0.394889i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 187.227 | − | 65.8206i | 0.541120 | − | 0.190233i | ||||
\(347\) | 269.767 | 0.777425 | 0.388713 | − | 0.921359i | \(-0.372920\pi\) | ||||
0.388713 | + | 0.921359i | \(0.372920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 248.416 | 0.711795 | 0.355897 | − | 0.934525i | \(-0.384175\pi\) | ||||
0.355897 | + | 0.934525i | \(0.384175\pi\) | |||||||
\(350\) | −75.5113 | − | 214.793i | −0.215747 | − | 0.613694i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 56.8000 | + | 473.061i | 0.161364 | + | 1.34392i | ||||
\(353\) | − | 318.157i | − | 0.901294i | −0.892702 | − | 0.450647i | \(-0.851193\pi\) | ||
0.892702 | − | 0.450647i | \(-0.148807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.5242 | −0.122603 | ||||||||
\(356\) | 375.704 | − | 301.412i | 1.05535 | − | 0.846664i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −84.3395 | − | 239.905i | −0.235585 | − | 0.670125i | ||||
\(359\) | 203.903 | 0.567976 | 0.283988 | − | 0.958828i | \(-0.408342\pi\) | ||||
0.283988 | + | 0.958828i | \(0.408342\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −354.775 | + | 66.7492i | −0.982757 | + | 0.184901i | ||||
\(362\) | −2.20991 | − | 6.28613i | −0.00610474 | − | 0.0173650i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 318.137 | − | 255.229i | 0.874003 | − | 0.701178i | ||||
\(365\) | 64.3981i | 0.176433i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 411.595i | 1.12151i | 0.827981 | + | 0.560756i | \(0.189489\pi\) | ||||
−0.827981 | + | 0.560756i | \(0.810511\pi\) | |||||||
\(368\) | −47.5903 | + | 214.265i | −0.129321 | + | 0.582242i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 38.2411 | − | 13.4438i | 0.103354 | − | 0.0363347i | ||||
\(371\) | 281.365i | 0.758396i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 455.722i | 1.22177i | 0.791718 | + | 0.610887i | \(0.209187\pi\) | ||||
−0.791718 | + | 0.610887i | \(0.790813\pi\) | |||||||
\(374\) | −187.099 | − | 532.206i | −0.500266 | − | 1.42301i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −318.734 | + | 512.227i | −0.847697 | + | 1.36231i | ||||
\(377\) | 480.795i | 1.27532i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −326.021 | −0.860213 | −0.430106 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430106 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(380\) | 35.3386 | − | 34.2052i | 0.0929962 | − | 0.0900138i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 188.197 | − | 66.1613i | 0.492661 | − | 0.173197i | ||||
\(383\) | 239.458i | 0.625217i | 0.949882 | + | 0.312609i | \(0.101203\pi\) | ||||
−0.949882 | + | 0.312609i | \(0.898797\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −44.6224 | −0.115902 | ||||||||
\(386\) | 36.6085 | + | 104.133i | 0.0948407 | + | 0.269776i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 350.467 | + | 436.849i | 0.903265 | + | 1.12590i | ||||
\(389\) | − | 381.887i | − | 0.981714i | −0.871240 | − | 0.490857i | \(-0.836684\pi\) | ||
0.871240 | − | 0.490857i | \(-0.163316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 259.876i | − | 0.664646i | ||||||
\(392\) | −116.451 | + | 187.145i | −0.297070 | + | 0.477412i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 98.6635 | + | 280.649i | 0.250415 | + | 0.712308i | ||||
\(395\) | 54.6323i | 0.138310i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 67.7120 | 0.170559 | 0.0852796 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852796 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(398\) | 79.3601 | + | 225.741i | 0.199397 | + | 0.567188i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 85.2774 | − | 383.943i | 0.213194 | − | 0.959858i | ||||
\(401\) | 393.401 | 0.981050 | 0.490525 | − | 0.871427i | \(-0.336805\pi\) | ||||
0.490525 | + | 0.871427i | \(0.336805\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 426.588i | − | 1.05853i | ||||||
\(404\) | 85.8001 | + | 106.948i | 0.212377 | + | 0.264723i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 67.0815 | + | 190.814i | 0.165225 | + | 0.469985i | ||||
\(407\) | 466.329i | 1.14577i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 497.707i | − | 1.21689i | −0.793597 | − | 0.608443i | \(-0.791794\pi\) | ||
0.793597 | − | 0.608443i | \(-0.208206\pi\) | |||||||
\(410\) | 16.3845 | + | 46.6058i | 0.0399621 | + | 0.113673i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 579.796 | − | 465.147i | 1.40727 | − | 1.12900i | ||||
\(413\) | 526.995 | 1.27602 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 59.9488i | 0.144455i | ||||||||
\(416\) | 699.531 | − | 83.9922i | 1.68157 | − | 0.201904i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 236.400 | + | 514.041i | 0.565550 | + | 1.22976i | ||||
\(419\) | −328.054 | −0.782946 | −0.391473 | − | 0.920190i | \(-0.628034\pi\) | ||||
−0.391473 | + | 0.920190i | \(0.628034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 194.786i | 0.462675i | 0.972874 | + | 0.231338i | \(0.0743102\pi\) | ||||
−0.972874 | + | 0.231338i | \(0.925690\pi\) | |||||||
\(422\) | −516.822 | + | 181.691i | −1.22470 | + | 0.430547i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −256.783 | + | 412.668i | −0.605621 | + | 0.973274i | ||||
\(425\) | 465.675i | 1.09571i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 491.848i | − | 1.15187i | ||||||
\(428\) | −404.925 | − | 504.730i | −0.946085 | − | 1.17928i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −39.2429 | + | 13.7960i | −0.0912625 | + | 0.0320837i | ||||
\(431\) | − | 314.574i | − | 0.729870i | −0.931033 | − | 0.364935i | \(-0.881091\pi\) | ||
0.931033 | − | 0.364935i | \(-0.118909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 234.253i | − | 0.540999i | −0.962720 | − | 0.270500i | \(-0.912811\pi\) | ||
0.962720 | − | 0.270500i | \(-0.0871889\pi\) | |||||||
\(434\) | −59.5185 | − | 169.301i | −0.137139 | − | 0.390095i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 252.138 | + | 314.284i | 0.578297 | + | 0.720836i | ||||
\(437\) | 24.2009 | + | 259.514i | 0.0553795 | + | 0.593854i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 239.334 | 0.545181 | 0.272590 | − | 0.962130i | \(-0.412120\pi\) | ||||
0.272590 | + | 0.962130i | \(0.412120\pi\) | |||||||
\(440\) | −65.4461 | − | 40.7239i | −0.148741 | − | 0.0925543i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −786.992 | + | 276.670i | −1.78053 | + | 0.625951i | ||||
\(443\) | 253.331 | 0.571854 | 0.285927 | − | 0.958251i | \(-0.407699\pi\) | ||||
0.285927 | + | 0.958251i | \(0.407699\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 77.9246i | 0.175111i | ||||||||
\(446\) | 393.453 | − | 138.320i | 0.882181 | − | 0.310134i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 265.906 | − | 130.934i | 0.593540 | − | 0.292264i | ||||
\(449\) | −352.503 | −0.785085 | −0.392543 | − | 0.919734i | \(-0.628404\pi\) | ||||
−0.392543 | + | 0.919734i | \(0.628404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −568.331 | −1.26016 | ||||||||
\(452\) | −15.7204 | + | 12.6118i | −0.0347796 | + | 0.0279023i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −144.664 | − | 411.498i | −0.318643 | − | 0.906383i | ||||
\(455\) | 65.9846i | 0.145021i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.8092 | −0.0739807 | −0.0369903 | − | 0.999316i | \(-0.511777\pi\) | ||||
−0.0369903 | + | 0.999316i | \(0.511777\pi\) | |||||||
\(458\) | −197.884 | + | 69.5670i | −0.432061 | + | 0.151893i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.2203 | − | 27.6971i | −0.0483050 | − | 0.0602111i | ||||
\(461\) | − | 159.193i | − | 0.345321i | −0.984981 | − | 0.172660i | \(-0.944764\pi\) | ||
0.984981 | − | 0.172660i | \(-0.0552363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 383.183i | − | 0.827610i | −0.910366 | − | 0.413805i | \(-0.864200\pi\) | ||
0.910366 | − | 0.413805i | \(-0.135800\pi\) | |||||||
\(464\) | −75.7573 | + | 341.081i | −0.163270 | + | 0.735089i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −56.4473 | − | 160.565i | −0.121132 | − | 0.344560i | ||||
\(467\) | −136.387 | −0.292049 | −0.146025 | − | 0.989281i | \(-0.546648\pi\) | ||||
−0.146025 | + | 0.989281i | \(0.546648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 115.987i | 0.247308i | ||||||||
\(470\) | −32.3703 | − | 92.0778i | −0.0688731 | − | 0.195910i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 772.925 | + | 480.953i | 1.63755 | + | 1.01897i | ||||
\(473\) | − | 478.544i | − | 1.01172i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −43.3657 | − | 465.026i | −0.0912962 | − | 0.979002i | ||||
\(476\) | −273.734 | + | 219.606i | −0.575071 | + | 0.461356i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 394.312 | − | 138.622i | 0.824920 | − | 0.290004i | ||||
\(479\) | 31.4695 | 0.0656982 | 0.0328491 | − | 0.999460i | \(-0.489542\pi\) | ||||
0.0328491 | + | 0.999460i | \(0.489542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 689.577 | 1.43363 | ||||||||
\(482\) | 193.612 | + | 550.731i | 0.401684 | + | 1.14260i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 314.162 | − | 252.040i | 0.649095 | − | 0.520743i | ||||
\(485\) | −90.6067 | −0.186818 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −707.449 | −1.45267 | −0.726333 | − | 0.687343i | \(-0.758777\pi\) | ||||
−0.726333 | + | 0.687343i | \(0.758777\pi\) | |||||||
\(488\) | 448.877 | − | 721.376i | 0.919830 | − | 1.47823i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.8267 | − | 33.6412i | −0.0241362 | − | 0.0686556i | ||||
\(491\) | 549.851 | 1.11986 | 0.559930 | − | 0.828540i | \(-0.310828\pi\) | ||||
0.559930 | + | 0.828540i | \(0.310828\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 413.689i | − | 0.839125i | ||||||
\(494\) | 760.130 | − | 349.573i | 1.53873 | − | 0.707638i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 67.2162 | − | 302.627i | 0.135517 | − | 0.610134i | ||||
\(497\) | −311.482 | −0.626725 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 92.5348i | 0.185440i | 0.995692 | + | 0.0927202i | \(0.0295562\pi\) | ||||
−0.995692 | + | 0.0927202i | \(0.970444\pi\) | |||||||
\(500\) | 80.3117 | + | 100.107i | 0.160623 | + | 0.200214i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 443.280 | − | 155.837i | 0.883029 | − | 0.310432i | ||||
\(503\) | 29.7026 | 0.0590510 | 0.0295255 | − | 0.999564i | \(-0.490600\pi\) | ||||
0.0295255 | + | 0.999564i | \(0.490600\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.1820 | −0.0439248 | ||||||||
\(506\) | 385.380 | − | 135.482i | 0.761620 | − | 0.267751i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −97.6223 | + | 78.3185i | −0.192170 | + | 0.154170i | ||||
\(509\) | −573.572 | −1.12686 | −0.563431 | − | 0.826163i | \(-0.690519\pi\) | ||||
−0.563431 | + | 0.826163i | \(0.690519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 460.867i | 0.901892i | ||||||||
\(512\) | 509.490 | + | 50.6380i | 0.995097 | + | 0.0989023i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −101.987 | + | 35.8539i | −0.198418 | + | 0.0697547i | ||||
\(515\) | 120.255i | 0.233505i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1122.84 | 2.17183 | ||||||||
\(518\) | 273.674 | − | 96.2112i | 0.528328 | − | 0.185736i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −60.2198 | + | 96.7774i | −0.115807 | + | 0.186110i | ||||
\(521\) | 546.984 | 1.04987 | 0.524937 | − | 0.851141i | \(-0.324089\pi\) | ||||
0.524937 | + | 0.851141i | \(0.324089\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −144.876 | −0.277009 | −0.138504 | − | 0.990362i | \(-0.544229\pi\) | ||||
−0.138504 | + | 0.990362i | \(0.544229\pi\) | |||||||
\(524\) | −58.9982 | + | 47.3319i | −0.112592 | + | 0.0903280i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 909.613 | − | 319.778i | 1.72930 | − | 0.607943i | ||||
\(527\) | 367.048i | 0.696486i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −340.819 | −0.644271 | ||||||||
\(530\) | −26.0787 | − | 74.1811i | −0.0492051 | − | 0.139964i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 252.902 | − | 244.791i | 0.475379 | − | 0.460133i | ||||
\(533\) | 840.411i | 1.57676i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 104.686 | 0.195674 | ||||||||
\(536\) | −105.854 | + | 170.114i | −0.197489 | + | 0.317378i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 188.060 | − | 66.1132i | 0.349553 | − | 0.122887i | ||||
\(539\) | 410.236 | 0.761105 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −933.960 | −1.72636 | −0.863179 | − | 0.504898i | \(-0.831530\pi\) | ||||
−0.863179 | + | 0.504898i | \(0.831530\pi\) | |||||||
\(542\) | −51.8660 | − | 147.534i | −0.0956938 | − | 0.272202i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −601.895 | + | 72.2691i | −1.10643 | + | 0.132848i | ||||
\(545\) | −65.1855 | −0.119606 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −670.814 | −1.22635 | −0.613176 | − | 0.789947i | \(-0.710108\pi\) | ||||
−0.613176 | + | 0.789947i | \(0.710108\pi\) | |||||||
\(548\) | 350.826 | + | 437.297i | 0.640193 | + | 0.797987i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −690.565 | + | 242.771i | −1.25557 | + | 0.441402i | ||||
\(551\) | 38.5245 | + | 413.112i | 0.0699175 | + | 0.749749i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 390.978i | 0.707013i | ||||||||
\(554\) | −165.760 | + | 58.2735i | −0.299205 | + | 0.105187i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −388.502 | − | 484.260i | −0.698745 | − | 0.870971i | ||||
\(557\) | 29.7179i | 0.0533535i | 0.999644 | + | 0.0266767i | \(0.00849248\pi\) | ||||
−0.999644 | + | 0.0266767i | \(0.991508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −707.640 | −1.26590 | ||||||||
\(560\) | −10.3970 | + | 46.8103i | −0.0185661 | + | 0.0835897i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 422.044 | − | 148.371i | 0.750968 | − | 0.264006i | ||||
\(563\) | 909.252i | 1.61501i | 0.589859 | + | 0.807506i | \(0.299183\pi\) | ||||
−0.589859 | + | 0.807506i | \(0.700817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3.26055i | − | 0.00577089i | ||||||
\(566\) | 283.856 | + | 807.432i | 0.501512 | + | 1.42656i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −456.840 | − | 284.269i | −0.804296 | − | 0.500474i | ||||
\(569\) | −808.539 | −1.42098 | −0.710491 | − | 0.703706i | \(-0.751527\pi\) | ||||
−0.710491 | + | 0.703706i | \(0.751527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 384.360i | − | 0.673135i | −0.941659 | − | 0.336567i | \(-0.890734\pi\) | ||
0.941659 | − | 0.336567i | \(-0.109266\pi\) | |||||||
\(572\) | −820.568 | − | 1022.82i | −1.43456 | − | 1.78815i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 117.256 | + | 333.536i | 0.204279 | + | 0.581073i | ||||
\(575\) | −337.203 | −0.586440 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −197.780 | −0.342773 | −0.171387 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171387 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(578\) | 131.864 | − | 46.3573i | 0.228138 | − | 0.0802029i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −35.3717 | − | 44.0901i | −0.0609857 | − | 0.0760174i | ||||
\(581\) | 429.025i | 0.738426i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 904.596 | 1.55162 | ||||||||
\(584\) | −420.603 | + | 675.937i | −0.720210 | + | 1.15743i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 499.120 | − | 175.468i | 0.851740 | − | 0.299433i | ||||
\(587\) | 779.727 | 1.32833 | 0.664163 | − | 0.747588i | \(-0.268788\pi\) | ||||
0.664163 | + | 0.747588i | \(0.268788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.1811 | − | 366.536i | −0.0580325 | − | 0.622303i | ||||
\(590\) | −138.941 | + | 48.8452i | −0.235493 | + | 0.0827885i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 489.193 | + | 108.655i | 0.826340 | + | 0.183538i | ||||
\(593\) | 118.684i | 0.200142i | 0.994980 | + | 0.100071i | \(0.0319069\pi\) | ||||
−0.994980 | + | 0.100071i | \(0.968093\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 56.7750i | − | 0.0954201i | ||||||
\(596\) | −511.382 | − | 637.427i | −0.858024 | − | 1.06951i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −200.342 | − | 569.874i | −0.335020 | − | 0.952967i | ||||
\(599\) | 278.133i | 0.464329i | 0.972677 | + | 0.232164i | \(0.0745808\pi\) | ||||
−0.972677 | + | 0.232164i | \(0.925419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 769.770i | 1.28082i | 0.768035 | + | 0.640408i | \(0.221235\pi\) | ||||
−0.768035 | + | 0.640408i | \(0.778765\pi\) | |||||||
\(602\) | −280.843 | + | 98.7315i | −0.466516 | + | 0.164006i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 605.916 | − | 486.102i | 1.00317 | − | 0.804804i | ||||
\(605\) | 65.1602i | 0.107703i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −341.395 | −0.562430 | −0.281215 | − | 0.959645i | \(-0.590737\pi\) | ||||
−0.281215 | + | 0.959645i | \(0.590737\pi\) | |||||||
\(608\) | 594.326 | − | 128.220i | 0.977510 | − | 0.210887i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 45.5876 | + | 129.674i | 0.0747338 | + | 0.212581i | ||||
\(611\) | − | 1660.38i | − | 2.71748i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 192.021 | 0.313247 | 0.156624 | − | 0.987658i | \(-0.449939\pi\) | ||||
0.156624 | + | 0.987658i | \(0.449939\pi\) | |||||||
\(614\) | −1070.79 | + | 376.440i | −1.74395 | + | 0.613094i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −468.367 | − | 291.442i | −0.760336 | − | 0.473120i | ||||
\(617\) | − | 607.759i | − | 0.985023i | −0.870306 | − | 0.492511i | \(-0.836079\pi\) | ||
0.870306 | − | 0.492511i | \(-0.163921\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 118.381i | − | 0.191246i | −0.995418 | − | 0.0956231i | \(-0.969516\pi\) | ||
0.995418 | − | 0.0956231i | \(-0.0304844\pi\) | |||||||
\(620\) | 31.3838 | + | 39.1192i | 0.0506190 | + | 0.0630955i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 228.394 | − | 80.2928i | 0.367193 | − | 0.129088i | ||||
\(623\) | 557.670i | 0.895136i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 593.768 | 0.950028 | ||||||||
\(626\) | −206.221 | + | 72.4977i | −0.329426 | + | 0.115811i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −388.000 | + | 311.277i | −0.617834 | + | 0.495664i | ||||
\(629\) | −593.330 | −0.943291 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1215.14i | 1.92574i | 0.269960 | + | 0.962871i | \(0.412989\pi\) | ||||
−0.269960 | + | 0.962871i | \(0.587011\pi\) | |||||||
\(632\) | −356.820 | + | 573.434i | −0.564588 | + | 0.907332i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 933.003 | − | 328.001i | 1.47161 | − | 0.517352i | ||||
\(635\) | − | 20.2478i | − | 0.0318863i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 606.630i | − | 0.952323i | ||||||
\(638\) | 613.473 | − | 215.669i | 0.961556 | − | 0.338039i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −57.9695 | + | 59.1663i | −0.0905774 | + | 0.0924473i | ||||
\(641\) | 507.836 | 0.792255 | 0.396128 | − | 0.918195i | \(-0.370354\pi\) | ||||
0.396128 | + | 0.918195i | \(0.370354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 517.738i | − | 0.805191i | −0.915378 | − | 0.402596i | \(-0.868108\pi\) | ||
0.915378 | − | 0.402596i | \(-0.131892\pi\) | |||||||
\(644\) | −159.020 | − | 198.215i | −0.246926 | − | 0.307788i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −654.037 | + | 300.782i | −1.01244 | + | 0.465607i | ||||
\(647\) | −174.389 | −0.269535 | −0.134768 | − | 0.990877i | \(-0.543029\pi\) | ||||
−0.134768 | + | 0.990877i | \(0.543029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1694.30i | − | 2.61064i | ||||||
\(650\) | 358.994 | + | 1021.16i | 0.552298 | + | 1.57102i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 487.924 | + | 608.188i | 0.748350 | + | 0.932803i | ||||
\(653\) | 1222.16i | 1.87161i | 0.352513 | + | 0.935807i | \(0.385327\pi\) | ||||
−0.352513 | + | 0.935807i | \(0.614673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 12.2368i | − | 0.0186821i | ||||||
\(656\) | −132.421 | + | 596.197i | −0.201861 | + | 0.908837i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −231.659 | − | 658.958i | −0.352066 | − | 1.00146i | ||||
\(659\) | 289.924i | 0.439945i | 0.975506 | + | 0.219973i | \(0.0705968\pi\) | ||||
−0.975506 | + | 0.219973i | \(0.929403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 116.537i | − | 0.176304i | −0.996107 | − | 0.0881520i | \(-0.971904\pi\) | ||
0.996107 | − | 0.0881520i | \(-0.0280961\pi\) | |||||||
\(662\) | 921.152 | − | 323.835i | 1.39147 | − | 0.489176i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −391.543 | + | 629.236i | −0.589673 | + | 0.947645i | ||||
\(665\) | 5.28714 | + | 56.6958i | 0.00795058 | + | 0.0852569i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 299.559 | 0.449114 | ||||||||
\(668\) | 16.0548 | + | 20.0119i | 0.0240341 | + | 0.0299580i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.7504 | − | 30.5797i | −0.0160454 | − | 0.0456414i | ||||
\(671\) | −1581.31 | −2.35664 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 436.189i | − | 0.648126i | −0.946035 | − | 0.324063i | \(-0.894951\pi\) | ||
0.946035 | − | 0.324063i | \(-0.105049\pi\) | |||||||
\(674\) | −213.713 | − | 607.910i | −0.317082 | − | 0.901944i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −985.195 | + | 790.382i | −1.45739 | + | 1.16920i | ||||
\(677\) | 384.501 | 0.567949 | 0.283974 | − | 0.958832i | \(-0.408347\pi\) | ||||
0.283974 | + | 0.958832i | \(0.408347\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −648.429 | −0.954977 | ||||||||
\(680\) | 51.8148 | − | 83.2698i | 0.0761982 | − | 0.122456i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −544.308 | + | 191.354i | −0.798105 | + | 0.280577i | ||||
\(683\) | − | 670.786i | − | 0.982116i | −0.871127 | − | 0.491058i | \(-0.836610\pi\) | ||
0.871127 | − | 0.491058i | \(-0.163390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −90.6994 | −0.132408 | ||||||||
\(686\) | −235.162 | − | 668.920i | −0.342801 | − | 0.975103i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −502.008 | − | 111.501i | −0.729663 | − | 0.162065i | ||||
\(689\) | − | 1337.66i | − | 1.94145i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 710.048i | 1.02757i | 0.857920 | + | 0.513783i | \(0.171756\pi\) | ||||
−0.857920 | + | 0.513783i | \(0.828244\pi\) | |||||||
\(692\) | −309.601 | + | 248.381i | −0.447401 | + | 0.358932i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −508.996 | + | 178.940i | −0.733423 | + | 0.257838i | ||||
\(695\) | 100.440 | 0.144518 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 723.112i | − | 1.03746i | ||||||
\(698\) | −468.712 | + | 164.778i | −0.671508 | + | 0.236071i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 284.950 | + | 355.184i | 0.407071 | + | 0.507405i | ||||
\(701\) | − | 1318.94i | − | 1.88152i | −0.339078 | − | 0.940758i | \(-0.610115\pi\) | ||
0.339078 | − | 0.940758i | \(-0.389885\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 592.503 | − | 55.2535i | 0.842821 | − | 0.0785968i | ||||
\(704\) | −420.957 | − | 854.895i | −0.597951 | − | 1.21434i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 211.037 | + | 600.298i | 0.298920 | + | 0.850281i | ||||
\(707\) | −158.746 | −0.224535 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 352.865 | 0.497694 | 0.248847 | − | 0.968543i | \(-0.419948\pi\) | ||||
0.248847 | + | 0.968543i | \(0.419948\pi\) | |||||||
\(710\) | 82.1215 | − | 28.8702i | 0.115664 | − | 0.0406622i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −508.948 | + | 817.914i | −0.714815 | + | 1.14876i | ||||
\(713\) | −265.786 | −0.372771 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 212.143 | 0.296703 | ||||||||
\(716\) | 318.264 | + | 396.709i | 0.444502 | + | 0.554063i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −384.725 | + | 135.252i | −0.535829 | + | 0.188373i | ||||
\(719\) | −123.090 | −0.171196 | −0.0855979 | − | 0.996330i | \(-0.527280\pi\) | ||||
−0.0855979 | + | 0.996330i | \(0.527280\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 860.609i | 1.19363i | ||||||||
\(722\) | 625.115 | − | 361.269i | 0.865810 | − | 0.500373i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.33934 | + | 10.3948i | 0.0115184 | + | 0.0143575i | ||||
\(725\) | −536.782 | −0.740389 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 668.993i | − | 0.920211i | −0.887864 | − | 0.460105i | \(-0.847812\pi\) | ||
0.887864 | − | 0.460105i | \(-0.152188\pi\) | |||||||
\(728\) | −430.965 | + | 692.590i | −0.591985 | + | 0.951360i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −42.7160 | − | 121.506i | −0.0585151 | − | 0.166447i | ||||
\(731\) | 608.873 | 0.832931 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −954.382 | −1.30202 | −0.651011 | − | 0.759068i | \(-0.725655\pi\) | ||||
−0.651011 | + | 0.759068i | \(0.725655\pi\) | |||||||
\(734\) | −273.016 | − | 776.597i | −0.371956 | − | 1.05803i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −52.3313 | − | 435.842i | −0.0711023 | − | 0.592177i | ||||
\(737\) | 372.902 | 0.505973 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 387.814i | − | 0.524782i | −0.964962 | − | 0.262391i | \(-0.915489\pi\) | ||
0.964962 | − | 0.262391i | \(-0.0845110\pi\) | |||||||
\(740\) | −63.2359 | + | 50.7317i | −0.0854540 | + | 0.0685563i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −186.633 | − | 530.880i | −0.251527 | − | 0.715471i | ||||
\(743\) | − | 478.165i | − | 0.643560i | −0.946815 | − | 0.321780i | \(-0.895719\pi\) | ||
0.946815 | − | 0.321780i | \(-0.104281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 132.208 | 0.177461 | ||||||||
\(746\) | −302.286 | − | 859.856i | −0.405209 | − | 1.15262i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 706.038 | + | 880.062i | 0.943902 | + | 1.17655i | ||||
\(749\) | 749.186 | 1.00025 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 938.092 | 1.24912 | 0.624562 | − | 0.780975i | \(-0.285277\pi\) | ||||
0.624562 | + | 0.780975i | \(0.285277\pi\) | |||||||
\(752\) | 261.621 | − | 1177.89i | 0.347900 | − | 1.56634i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −318.917 | − | 907.163i | −0.422967 | − | 1.20313i | ||||
\(755\) | 125.673i | 0.166454i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −710.155 | −0.938117 | −0.469059 | − | 0.883167i | \(-0.655407\pi\) | ||||
−0.469059 | + | 0.883167i | \(0.655407\pi\) | |||||||
\(758\) | 615.136 | − | 216.254i | 0.811525 | − | 0.285295i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −43.9881 | + | 87.9790i | −0.0578790 | + | 0.115762i | ||||
\(761\) | − | 1234.32i | − | 1.62197i | −0.585065 | − | 0.810986i | \(-0.698931\pi\) | ||
0.585065 | − | 0.810986i | \(-0.301069\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −466.502 | −0.611405 | ||||||||
\(764\) | −311.204 | + | 249.666i | −0.407335 | + | 0.326788i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −158.836 | − | 451.810i | −0.207357 | − | 0.589830i | ||||
\(767\) | −2505.43 | −3.26653 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −343.803 | −0.447078 | −0.223539 | − | 0.974695i | \(-0.571761\pi\) | ||||
−0.223539 | + | 0.974695i | \(0.571761\pi\) | |||||||
\(770\) | 84.1935 | − | 29.5986i | 0.109342 | − | 0.0384397i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −138.146 | − | 172.196i | −0.178945 | − | 0.223052i | ||||
\(773\) | −172.010 | −0.222522 | −0.111261 | − | 0.993791i | \(-0.535489\pi\) | ||||
−0.111261 | + | 0.993791i | \(0.535489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 476.263 | 0.614533 | ||||||||
\(776\) | −951.029 | − | 591.779i | −1.22555 | − | 0.762601i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 253.310 | + | 720.544i | 0.325592 | + | 0.926149i | ||||
\(779\) | 67.3394 | + | 722.104i | 0.0864434 | + | 0.926963i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1001.43i | 1.28223i | ||||||||
\(782\) | 172.379 | + | 490.335i | 0.220434 | + | 0.627027i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 95.5848 | − | 430.350i | 0.121919 | − | 0.548916i | ||||
\(785\) | − | 80.4748i | − | 0.102516i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 783.490 | 0.995540 | 0.497770 | − | 0.867309i | \(-0.334152\pi\) | ||||
0.497770 | + | 0.867309i | \(0.334152\pi\) | |||||||
\(788\) | −372.317 | − | 464.085i | −0.472483 | − | 0.588940i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −36.2383 | − | 103.080i | −0.0458713 | − | 0.130481i | ||||
\(791\) | − | 23.3342i | − | 0.0294997i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2338.33i | 2.94872i | ||||||||
\(794\) | −127.759 | + | 44.9142i | −0.160906 | + | 0.0565670i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −299.473 | − | 373.287i | −0.376223 | − | 0.468954i | ||||
\(797\) | 699.849 | 0.878104 | 0.439052 | − | 0.898462i | \(-0.355314\pi\) | ||||
0.439052 | + | 0.898462i | \(0.355314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1428.63i | 1.78803i | ||||||||
\(800\) | 93.7729 | + | 780.990i | 0.117216 | + | 0.976237i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −742.269 | + | 260.948i | −0.925523 | + | 0.325371i | ||||
\(803\) | 1481.70 | 1.84521 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.1117 | 0.0510704 | ||||||||
\(806\) | 282.961 | + | 804.887i | 0.351069 | + | 0.998619i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −232.828 | − | 144.877i | −0.288153 | − | 0.179304i | ||||
\(809\) | 361.258i | 0.446549i | 0.974756 | + | 0.223275i | \(0.0716747\pi\) | ||||
−0.974756 | + | 0.223275i | \(0.928325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1441.11 | 1.77695 | 0.888475 | − | 0.458925i | \(-0.151765\pi\) | ||||
0.888475 | + | 0.458925i | \(0.151765\pi\) | |||||||
\(812\) | −253.139 | − | 315.532i | −0.311747 | − | 0.388586i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −309.322 | − | 879.869i | −0.380002 | − | 1.08092i | ||||
\(815\) | −126.144 | −0.154778 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −608.024 | + | 56.7009i | −0.744215 | + | 0.0694014i | ||||
\(818\) | 330.135 | + | 939.073i | 0.403588 | + | 1.14801i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −61.8284 | − | 77.0678i | −0.0754005 | − | 0.0939852i | ||||
\(821\) | 179.449i | 0.218574i | 0.994010 | + | 0.109287i | \(0.0348567\pi\) | ||||
−0.994010 | + | 0.109287i | \(0.965143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 941.294i | 1.14373i | 0.820346 | + | 0.571867i | \(0.193781\pi\) | ||||
−0.820346 | + | 0.571867i | \(0.806219\pi\) | |||||||
\(824\) | −785.421 | + | 1262.23i | −0.953181 | + | 1.53183i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −994.334 | + | 349.562i | −1.20379 | + | 0.423199i | ||||
\(827\) | − | 533.837i | − | 0.645510i | −0.946482 | − | 0.322755i | \(-0.895391\pi\) | ||
0.946482 | − | 0.322755i | \(-0.104609\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 639.861i | 0.771846i | 0.922531 | + | 0.385923i | \(0.126117\pi\) | ||||
−0.922531 | + | 0.385923i | \(0.873883\pi\) | |||||||
\(830\) | −39.7648 | − | 113.111i | −0.0479094 | − | 0.136279i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1264.16 | + | 622.484i | −1.51943 | + | 0.748178i | ||||
\(833\) | 521.960i | 0.626603i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.15066 | −0.00497085 | ||||||||
\(836\) | −787.010 | − | 813.086i | −0.941399 | − | 0.972591i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 618.973 | − | 217.603i | 0.738631 | − | 0.259669i | ||||
\(839\) | − | 1332.64i | − | 1.58836i | −0.607680 | − | 0.794182i | \(-0.707900\pi\) | ||
0.607680 | − | 0.794182i | \(-0.292100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −364.143 | −0.432988 | ||||||||
\(842\) | −129.204 | − | 367.523i | −0.153449 | − | 0.436488i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 854.623 | − | 685.629i | 1.01259 | − | 0.812357i | ||||
\(845\) | − | 204.339i | − | 0.241821i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 466.321i | 0.550556i | ||||||||
\(848\) | 210.771 | − | 948.950i | 0.248550 | − | 1.11904i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −308.888 | − | 878.636i | −0.363398 | − | 1.03369i | ||||
\(851\) | − | 429.640i | − | 0.504865i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −683.872 | −0.801726 | −0.400863 | − | 0.916138i | \(-0.631290\pi\) | ||||
−0.400863 | + | 0.916138i | \(0.631290\pi\) | |||||||
\(854\) | 326.249 | + | 928.019i | 0.382025 | + | 1.08667i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1098.81 | + | 683.733i | 1.28365 | + | 0.798754i | ||||
\(857\) | 301.501 | 0.351810 | 0.175905 | − | 0.984407i | \(-0.443715\pi\) | ||||
0.175905 | + | 0.984407i | \(0.443715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.82960i | − | 0.00212992i | −0.999999 | − | 0.00106496i | \(-0.999661\pi\) | ||
0.999999 | − | 0.00106496i | \(-0.000338987\pi\) | |||||||
\(860\) | 64.8924 | − | 52.0606i | 0.0754563 | − | 0.0605356i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 208.661 | + | 593.539i | 0.242066 | + | 0.688560i | ||||
\(863\) | − | 1323.69i | − | 1.53382i | −0.641754 | − | 0.766911i | \(-0.721793\pi\) | ||
0.641754 | − | 0.766911i | \(-0.278207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 64.2142i | − | 0.0742361i | ||||||
\(866\) | 155.383 | + | 441.988i | 0.179426 | + | 0.510379i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 224.599 | + | 279.958i | 0.258755 | + | 0.322532i | ||||
\(869\) | 1257.01 | 1.44650 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 551.424i | − | 0.633093i | ||||||
\(872\) | −684.202 | − | 425.746i | −0.784636 | − | 0.488240i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −217.801 | − | 473.599i | −0.249200 | − | 0.541875i | ||||
\(875\) | −148.592 | −0.169819 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 452.958i | 0.516485i | 0.966080 | + | 0.258243i | \(0.0831434\pi\) | ||||
−0.966080 | + | 0.258243i | \(0.916857\pi\) | |||||||
\(878\) | −451.576 | + | 158.753i | −0.514324 | + | 0.180813i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 150.496 | + | 33.4267i | 0.171019 | + | 0.0379848i | ||||
\(881\) | 553.999i | 0.628830i | 0.949286 | + | 0.314415i | \(0.101808\pi\) | ||||
−0.949286 | + | 0.314415i | \(0.898192\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 319.684i | 0.362043i | 0.983479 | + | 0.181022i | \(0.0579404\pi\) | ||||
−0.983479 | + | 0.181022i | \(0.942060\pi\) | |||||||
\(884\) | 1301.38 | − | 1044.04i | 1.47215 | − | 1.18105i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −477.986 | + | 168.038i | −0.539487 | + | 0.189659i | ||||
\(887\) | − | 807.771i | − | 0.910678i | −0.890318 | − | 0.455339i | \(-0.849518\pi\) | ||
0.890318 | − | 0.455339i | \(-0.150482\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 144.904i | − | 0.162996i | ||||||
\(890\) | −51.6884 | − | 147.028i | −0.0580768 | − | 0.165200i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −650.617 | + | 521.964i | −0.729392 | + | 0.585162i | ||||
\(893\) | −133.041 | − | 1426.64i | −0.148982 | − | 1.59758i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −82.2812 | −0.0919343 | ||||||||
\(896\) | −414.861 | + | 423.425i | −0.463014 | + | 0.472573i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 665.103 | − | 233.820i | 0.740650 | − | 0.260378i | ||||
\(899\) | −423.095 | −0.470628 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1150.96i | 1.27742i | ||||||||
\(902\) | 1072.33 | − | 376.981i | 1.18883 | − | 0.417939i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.2956 | − | 34.2235i | 0.0235571 | − | 0.0378579i | ||||
\(905\) | −2.15598 | −0.00238230 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −298.229 | −0.328808 | −0.164404 | − | 0.986393i | \(-0.552570\pi\) | ||||
−0.164404 | + | 0.986393i | \(0.552570\pi\) | |||||||
\(908\) | 545.903 | + | 680.457i | 0.601215 | + | 0.749402i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −43.7684 | − | 124.500i | −0.0480972 | − | 0.136813i | ||||
\(911\) | 92.4614i | 0.101494i | 0.998712 | + | 0.0507472i | \(0.0161603\pi\) | ||||
−0.998712 | + | 0.0507472i | \(0.983840\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1379.33 | 1.51077 | ||||||||
\(914\) | 63.7912 | − | 22.4261i | 0.0697934 | − | 0.0245362i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 327.223 | − | 262.518i | 0.357230 | − | 0.286592i | ||||
\(917\) | − | 87.5728i | − | 0.0954993i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1375.18i | 1.49638i | 0.663483 | + | 0.748191i | \(0.269078\pi\) | ||||
−0.663483 | + | 0.748191i | \(0.730922\pi\) | |||||||
\(920\) | 60.2971 | + | 37.5199i | 0.0655403 | + | 0.0407825i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 105.595 | + | 300.365i | 0.114528 | + | 0.325775i | ||||
\(923\) | 1480.84 | 1.60438 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 769.876i | 0.832299i | ||||||||
\(926\) | 254.170 | + | 722.990i | 0.274482 | + | 0.780767i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −83.3044 | − | 693.803i | −0.0897677 | − | 0.747632i | ||||
\(929\) | 1131.43i | 1.21790i | 0.793209 | + | 0.608950i | \(0.208409\pi\) | ||||
−0.793209 | + | 0.608950i | \(0.791591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.6073 | − | 521.233i | −0.0522097 | − | 0.559863i | ||||
\(932\) | 213.010 | + | 265.512i | 0.228551 | + | 0.284884i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 257.335 | − | 90.4673i | 0.275520 | − | 0.0968600i | ||||
\(935\) | −182.533 | −0.195223 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 891.424 | 0.951359 | 0.475680 | − | 0.879619i | \(-0.342202\pi\) | ||||
0.475680 | + | 0.879619i | \(0.342202\pi\) | |||||||
\(938\) | −76.9358 | − | 218.845i | −0.0820211 | − | 0.233310i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 122.153 | + | 152.261i | 0.129950 | + | 0.161980i | ||||
\(941\) | −1384.39 | −1.47119 | −0.735594 | − | 0.677423i | \(-0.763097\pi\) | ||||
−0.735594 | + | 0.677423i | \(0.763097\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 523.618 | 0.555268 | ||||||||
\(944\) | −1777.38 | − | 394.772i | −1.88281 | − | 0.418191i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 317.425 | + | 902.918i | 0.335544 | + | 0.954459i | ||||
\(947\) | −743.814 | −0.785442 | −0.392721 | − | 0.919658i | \(-0.628466\pi\) | ||||
−0.392721 | + | 0.919658i | \(0.628466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2191.04i | − | 2.30879i | ||||||
\(950\) | 390.280 | + | 848.646i | 0.410821 | + | 0.893311i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 370.814 | − | 595.923i | 0.389510 | − | 0.625970i | ||||
\(953\) | 1024.06 | 1.07457 | 0.537283 | − | 0.843402i | \(-0.319451\pi\) | ||||
0.537283 | + | 0.843402i | \(0.319451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 64.5466i | − | 0.0675880i | ||||||
\(956\) | −652.038 | + | 523.104i | −0.682048 | + | 0.547180i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −59.3766 | + | 20.8741i | −0.0619797 | + | 0.0217892i | ||||
\(959\) | −649.093 | −0.676844 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −585.606 | −0.609372 | ||||||||
\(962\) | −1301.09 | + | 457.405i | −1.35249 | + | 0.475473i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −730.614 | − | 910.695i | −0.757898 | − | 0.944704i | ||||
\(965\) | 35.7151 | 0.0370104 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 635.451i | − | 0.657136i | −0.944480 | − | 0.328568i | \(-0.893434\pi\) | ||
0.944480 | − | 0.328568i | \(-0.106566\pi\) | |||||||
\(968\) | −425.580 | + | 683.936i | −0.439649 | + | 0.706546i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 170.957 | − | 60.1005i | 0.176244 | − | 0.0619593i | ||||
\(971\) | − | 446.440i | − | 0.459773i | −0.973217 | − | 0.229887i | \(-0.926164\pi\) | ||
0.973217 | − | 0.229887i | \(-0.0738355\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 718.802 | 0.738749 | ||||||||
\(974\) | 1334.81 | − | 469.260i | 1.37045 | − | 0.481786i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −368.444 | + | 1658.84i | −0.377504 | + | 1.69963i | ||||
\(977\) | 256.983 | 0.263033 | 0.131516 | − | 0.991314i | \(-0.458015\pi\) | ||||
0.131516 | + | 0.991314i | \(0.458015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1792.92 | 1.83138 | ||||||||
\(980\) | 44.6293 | + | 55.6295i | 0.0455401 | + | 0.0567648i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1037.46 | + | 364.723i | −1.05648 | + | 0.371408i | ||||
\(983\) | 247.488i | 0.251768i | 0.992045 | + | 0.125884i | \(0.0401768\pi\) | ||||
−0.992045 | + | 0.125884i | \(0.959823\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 96.2555 | 0.0977213 | ||||||||
\(986\) | 274.405 | + | 780.548i | 0.278301 | + | 0.791631i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1202.34 | + | 1163.78i | −1.21694 | + | 1.17791i | ||||
\(989\) | 440.895i | 0.445799i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1352.52 | 1.36481 | 0.682404 | − | 0.730976i | \(-0.260935\pi\) | ||||
0.682404 | + | 0.730976i | \(0.260935\pi\) | |||||||
\(992\) | 73.9124 | + | 615.581i | 0.0745085 | + | 0.620546i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 587.705 | − | 206.610i | 0.591253 | − | 0.207857i | ||||
\(995\) | 77.4233 | 0.0778123 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −874.644 | −0.877276 | −0.438638 | − | 0.898664i | \(-0.644539\pi\) | ||||
−0.438638 | + | 0.898664i | \(0.644539\pi\) | |||||||
\(998\) | −61.3795 | − | 174.595i | −0.0615025 | − | 0.174945i | ||||
\(999\) | 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 | 684.3.b.a.683.12 | yes | 80 | |
3.2 | odd | 2 | inner | 684.3.b.a.683.70 | yes | 80 | |
4.3 | odd | 2 | inner | 684.3.b.a.683.9 | ✓ | 80 | |
12.11 | even | 2 | inner | 684.3.b.a.683.71 | yes | 80 | |
19.18 | odd | 2 | inner | 684.3.b.a.683.69 | yes | 80 | |
57.56 | even | 2 | inner | 684.3.b.a.683.11 | yes | 80 | |
76.75 | even | 2 | inner | 684.3.b.a.683.72 | yes | 80 | |
228.227 | odd | 2 | inner | 684.3.b.a.683.10 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.b.a.683.9 | ✓ | 80 | 4.3 | odd | 2 | inner | |
684.3.b.a.683.10 | yes | 80 | 228.227 | odd | 2 | inner | |
684.3.b.a.683.11 | yes | 80 | 57.56 | even | 2 | inner | |
684.3.b.a.683.12 | yes | 80 | 1.1 | even | 1 | trivial | |
684.3.b.a.683.69 | yes | 80 | 19.18 | odd | 2 | inner | |
684.3.b.a.683.70 | yes | 80 | 3.2 | odd | 2 | inner | |
684.3.b.a.683.71 | yes | 80 | 12.11 | even | 2 | inner | |
684.3.b.a.683.72 | yes | 80 | 76.75 | even | 2 | inner |