Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 21.7 | ||
Character | \(\chi\) | \(=\) | 76.21 |
Dual form | 76.5.j.a.29.7 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{18}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 10.9995 | − | 13.1087i | 1.22217 | − | 1.45652i | 0.373472 | − | 0.927642i | \(-0.378167\pi\) |
0.848696 | − | 0.528881i | \(-0.177388\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −41.8937 | + | 15.2481i | −1.67575 | + | 0.609922i | −0.992717 | − | 0.120468i | \(-0.961561\pi\) |
−0.683030 | + | 0.730390i | \(0.739338\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.2709 | − | 45.5025i | −0.536141 | − | 0.928623i | −0.999107 | − | 0.0422474i | \(-0.986548\pi\) |
0.462966 | − | 0.886376i | \(-0.346785\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −36.7834 | − | 208.609i | −0.454116 | − | 2.57542i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −55.1598 | + | 95.5395i | −0.455866 | + | 0.789583i | −0.998738 | − | 0.0502329i | \(-0.984004\pi\) |
0.542872 | + | 0.839816i | \(0.317337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 31.8438 | + | 37.9500i | 0.188425 | + | 0.224556i | 0.851984 | − | 0.523568i | \(-0.175399\pi\) |
−0.663559 | + | 0.748124i | \(0.730955\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −260.928 | + | 716.893i | −1.15968 | + | 3.18619i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 62.4554 | − | 354.202i | 0.216109 | − | 1.22561i | −0.662863 | − | 0.748740i | \(-0.730659\pi\) |
0.878972 | − | 0.476873i | \(-0.158230\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 346.709 | − | 100.566i | 0.960414 | − | 0.278577i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −885.446 | − | 156.128i | −2.00781 | − | 0.354032i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −253.544 | − | 92.2824i | −0.479289 | − | 0.174447i | 0.0910666 | − | 0.995845i | \(-0.470972\pi\) |
−0.570356 | + | 0.821398i | \(0.693195\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1043.80 | − | 875.852i | 1.67008 | − | 1.40136i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1938.81 | − | 1119.37i | −2.65955 | − | 1.53549i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −563.593 | + | 99.3766i | −0.670146 | + | 0.118165i | −0.498361 | − | 0.866970i | \(-0.666065\pi\) |
−0.171785 | + | 0.985134i | \(0.554953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 910.085 | − | 525.438i | 0.947019 | − | 0.546762i | 0.0548653 | − | 0.998494i | \(-0.482527\pi\) |
0.892154 | + | 0.451732i | \(0.149194\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 645.669 | + | 1773.96i | 0.592901 | + | 1.62898i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1794.41 | + | 1505.69i | 1.46482 | + | 1.22913i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 527.558i | − | 0.385360i | −0.981262 | − | 0.192680i | \(-0.938282\pi\) | ||
0.981262 | − | 0.192680i | \(-0.0617180\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 847.742 | 0.557358 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 407.245 | − | 485.336i | 0.242264 | − | 0.288719i | −0.631188 | − | 0.775630i | \(-0.717432\pi\) |
0.873451 | + | 0.486912i | \(0.161877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −910.710 | + | 331.471i | −0.492542 | + | 0.179271i | −0.576337 | − | 0.817212i | \(-0.695518\pi\) |
0.0837945 | + | 0.996483i | \(0.473296\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4721.88 | + | 8178.53i | 2.33179 | + | 4.03878i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22.9255 | − | 130.017i | −0.0103782 | − | 0.0588578i | 0.979179 | − | 0.203000i | \(-0.0650690\pi\) |
−0.989557 | + | 0.144142i | \(0.953958\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −179.821 | + | 311.459i | −0.0748941 | + | 0.129720i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3956.15 | − | 4714.76i | −1.52101 | − | 1.81267i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −203.387 | + | 558.802i | −0.0724056 | + | 0.198933i | −0.970616 | − | 0.240632i | \(-0.922645\pi\) |
0.898211 | + | 0.439565i | \(0.144867\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 854.054 | − | 4843.58i | 0.282332 | − | 1.60118i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2495.34 | − | 5651.09i | 0.768032 | − | 1.73933i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3752.63 | + | 661.690i | 1.07803 | + | 0.190086i | 0.684345 | − | 0.729159i | \(-0.260088\pi\) |
0.393687 | + | 0.919245i | \(0.371199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1592.89 | + | 579.765i | 0.428081 | + | 0.155809i | 0.547070 | − | 0.837087i | \(-0.315743\pi\) |
−0.118989 | + | 0.992896i | \(0.537965\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8525.91 | + | 7154.09i | −2.14813 | + | 1.80249i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1912.72 | − | 1104.31i | −0.452715 | − | 0.261375i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2494.24 | − | 439.803i | 0.555635 | − | 0.0979734i | 0.111222 | − | 0.993796i | \(-0.464524\pi\) |
0.444413 | + | 0.895822i | \(0.353412\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3998.56 | + | 2308.57i | −0.839858 | + | 0.484892i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1828.11 | + | 5022.70i | 0.362649 | + | 0.996371i | 0.978089 | + | 0.208187i | \(0.0667562\pi\) |
−0.615440 | + | 0.788184i | \(0.711022\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 500.371 | + | 419.861i | 0.0938959 | + | 0.0787880i | 0.688527 | − | 0.725210i | \(-0.258258\pi\) |
−0.594631 | + | 0.803998i | \(0.702702\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 23316.8i | − | 4.14521i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5796.39 | 0.977633 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −53.2273 | + | 63.4339i | −0.00852866 | + | 0.0101641i | −0.770292 | − | 0.637691i | \(-0.779889\pi\) |
0.761763 | + | 0.647855i | \(0.224334\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −19876.2 | + | 7234.34i | −3.02945 | + | 1.10263i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3329.40 | − | 5766.69i | −0.483292 | − | 0.837086i | 0.516524 | − | 0.856273i | \(-0.327226\pi\) |
−0.999816 | + | 0.0191865i | \(0.993892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2784.41 | + | 15791.2i | 0.385385 | + | 2.18563i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4896.54 | + | 8481.06i | −0.646921 | + | 1.12050i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3754.44 | + | 4474.37i | 0.473986 | + | 0.564874i | 0.949070 | − | 0.315066i | \(-0.102027\pi\) |
−0.475084 | + | 0.879940i | \(0.657582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 890.255 | − | 2445.96i | 0.107506 | − | 0.295370i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3122.68 | − | 17709.6i | 0.361045 | − | 2.04759i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12991.5 | + | 9499.74i | −1.43950 | + | 1.05260i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14207.9 | − | 2505.23i | −1.51003 | − | 0.266259i | −0.643525 | − | 0.765425i | \(-0.722529\pi\) |
−0.866506 | + | 0.499166i | \(0.833640\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 21959.4 | + | 7992.56i | 2.24052 | + | 0.815484i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8269.68 | − | 6939.09i | 0.810674 | − | 0.680236i | −0.140095 | − | 0.990138i | \(-0.544741\pi\) |
0.950768 | + | 0.309902i | \(0.100296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17589.1 | − | 10155.0i | −1.65794 | − | 0.957211i | −0.973665 | − | 0.227984i | \(-0.926787\pi\) |
−0.684273 | − | 0.729226i | \(-0.739880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 39475.3 | − | 6960.55i | 3.58052 | − | 0.631343i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12395.5 | + | 7156.56i | −1.08267 | + | 0.625082i | −0.931616 | − | 0.363443i | \(-0.881601\pi\) |
−0.151057 | + | 0.988525i | \(0.548268\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1122.64 | − | 3084.44i | −0.0944906 | − | 0.259611i | 0.883439 | − | 0.468547i | \(-0.155222\pi\) |
−0.977929 | + | 0.208936i | \(0.933000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6915.61 | − | 5802.88i | −0.561286 | − | 0.470975i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14029.8i | − | 1.09874i | −0.835578 | − | 0.549371i | \(-0.814867\pi\) | ||
0.835578 | − | 0.549371i | \(-0.185133\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12029.0 | 0.909567 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6745.39 | − | 8038.85i | 0.492760 | − | 0.587249i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17757.9 | + | 6463.33i | −1.25400 | + | 0.456418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1235.30 | + | 2139.61i | 0.0843728 | + | 0.146138i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1882.63 | − | 10676.9i | −0.124438 | − | 0.705725i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −16441.6 | + | 28477.7i | −1.05226 | + | 1.82257i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8633.73 | + | 10289.3i | 0.535292 | + | 0.637936i | 0.964125 | − | 0.265447i | \(-0.0855197\pi\) |
−0.428833 | + | 0.903384i | \(0.641075\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5672.21 | + | 15584.3i | −0.340857 | + | 0.936498i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4716.15 | + | 26746.6i | −0.274818 | + | 1.55857i | 0.464722 | + | 0.885457i | \(0.346154\pi\) |
−0.739539 | + | 0.673113i | \(0.764957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13684.4 | − | 13134.2i | −0.773611 | − | 0.742506i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 98292.1 | + | 17331.5i | 5.39326 | + | 0.950976i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5504.69 | + | 2003.54i | 0.293286 | + | 0.106747i | 0.484473 | − | 0.874806i | \(-0.339011\pi\) |
−0.191187 | + | 0.981554i | \(0.561234\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12225.2 | − | 10258.2i | 0.632742 | − | 0.530934i | −0.269038 | − | 0.963130i | \(-0.586706\pi\) |
0.901780 | + | 0.432196i | \(0.142261\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1956.52 | − | 1129.60i | −0.0984116 | − | 0.0568180i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5382.22 | + | 949.031i | −0.263202 | + | 0.0464097i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22095.7 | − | 12756.9i | 1.05092 | − | 0.606751i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2104.88 | + | 5783.11i | 0.0974075 | + | 0.267625i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 29156.7 | + | 24465.3i | 1.31330 | + | 1.10199i | 0.987679 | + | 0.156494i | \(0.0500192\pi\) |
0.325625 | + | 0.945499i | \(0.394425\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9506.58i | − | 0.416937i | −0.978029 | − | 0.208468i | \(-0.933152\pi\) | ||
0.978029 | − | 0.208468i | \(-0.0668479\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −76187.2 | −3.25461 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30114.9 | + | 35889.6i | −1.25348 | + | 1.49384i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3899.48 | − | 1419.29i | 0.158200 | − | 0.0575802i | −0.261706 | − | 0.965148i | \(-0.584285\pi\) |
0.419906 | + | 0.907567i | \(0.362063\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5088.01 | + | 8812.69i | 0.201258 | + | 0.348589i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2461.74 | + | 13961.2i | 0.0949710 | + | 0.538607i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16062.6 | − | 27821.3i | 0.604563 | − | 1.04713i | −0.387558 | − | 0.921846i | \(-0.626681\pi\) |
0.992120 | − | 0.125288i | \(-0.0399855\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −54098.9 | − | 64472.6i | −1.98710 | − | 2.36814i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2073.67 | − | 5697.35i | 0.0743543 | − | 0.204287i | −0.896948 | − | 0.442137i | \(-0.854221\pi\) |
0.971302 | + | 0.237850i | \(0.0764427\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4533.39 | − | 25710.1i | 0.158727 | − | 0.900184i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −33732.2 | − | 68627.6i | −1.15359 | − | 2.34696i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −31337.6 | − | 5525.66i | −1.04706 | − | 0.184626i | −0.376454 | − | 0.926435i | \(-0.622857\pi\) |
−0.670610 | + | 0.741810i | \(0.733968\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −67275.1 | − | 24486.1i | −2.19674 | − | 0.799547i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 49951.0 | − | 41913.8i | 1.59440 | − | 1.33786i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22968.8 | + | 13261.0i | 0.716856 | + | 0.413877i | 0.813594 | − | 0.581433i | \(-0.197508\pi\) |
−0.0967384 | + | 0.995310i | \(0.530841\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10942.8 | − | 1929.51i | 0.334018 | − | 0.0588965i | −0.00412374 | − | 0.999991i | \(-0.501313\pi\) |
0.338142 | + | 0.941095i | \(0.390202\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25121.0 | − | 14503.6i | 0.750127 | − | 0.433086i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8044.24 | + | 22101.4i | 0.235040 | + | 0.645767i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30395.3 | + | 25504.7i | 0.869207 | + | 0.729351i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 117628.i | 3.29295i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −29302.4 | −0.803223 | −0.401612 | − | 0.915810i | \(-0.631550\pi\) | ||||
−0.401612 | + | 0.915810i | \(0.631550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −38939.0 | + | 46405.6i | −1.04537 | + | 1.24582i | −0.0768082 | + | 0.997046i | \(0.524473\pi\) |
−0.968561 | + | 0.248777i | \(0.919972\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −35515.0 | + | 12926.4i | −0.933992 | + | 0.339945i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20192.4 | − | 34974.2i | −0.520302 | − | 0.901189i | −0.999721 | − | 0.0236031i | \(-0.992486\pi\) |
0.479420 | − | 0.877586i | \(-0.340847\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4759.75 | − | 26993.9i | −0.120193 | − | 0.681647i | −0.984048 | − | 0.177906i | \(-0.943068\pi\) |
0.863855 | − | 0.503741i | \(-0.168043\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21670.2 | − | 37533.9i | 0.536378 | − | 0.929034i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 19328.0 | + | 23034.2i | 0.469023 | + | 0.558960i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9660.58 | + | 26542.2i | −0.229877 | + | 0.631582i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9924.75 | + | 56286.1i | −0.231622 | + | 1.31359i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9516.34 | + | 38671.7i | −0.217860 | + | 0.885320i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2493.73 | + | 439.712i | 0.0560124 | + | 0.00987650i | 0.201584 | − | 0.979471i | \(-0.435391\pi\) |
−0.145572 | + | 0.989348i | \(0.546502\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 85949.5 | + | 31283.1i | 1.89445 | + | 0.689525i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33098.7 | − | 27773.1i | 0.716035 | − | 0.600825i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −47817.5 | − | 27607.5i | −1.01547 | − | 0.586283i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11007.7 | − | 1940.95i | 0.229513 | − | 0.0404693i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15430.8 | − | 8908.98i | 0.315939 | − | 0.182408i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13104.1 | + | 36003.2i | 0.263510 | + | 0.723989i | 0.998924 | + | 0.0463706i | \(0.0147655\pi\) |
−0.735414 | + | 0.677618i | \(0.763012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −221105. | − | 185529.i | −4.36751 | − | 3.66478i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15193.9i | 0.294861i | 0.989072 | + | 0.147430i | \(0.0471002\pi\) | ||||
−0.989072 | + | 0.147430i | \(0.952900\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 102554. | 1.95560 | 0.977801 | − | 0.209538i | \(-0.0671959\pi\) | ||||
0.977801 | + | 0.209538i | \(0.0671959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 63757.4 | − | 75983.1i | 1.19483 | − | 1.42394i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 62891.4 | − | 22890.6i | 1.15846 | − | 0.421643i | 0.309910 | − | 0.950766i | \(-0.399701\pi\) |
0.848546 | + | 0.529122i | \(0.177479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2942.94 | + | 5097.32i | 0.0532899 | + | 0.0923009i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 246.061 | + | 1395.48i | 0.00438073 | + | 0.0248444i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26990.1 | − | 46748.2i | 0.472508 | − | 0.818407i | −0.526997 | − | 0.849867i | \(-0.676682\pi\) |
0.999505 | + | 0.0314597i | \(0.0100156\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29546.6 | + | 35212.3i | 0.508714 | + | 0.606261i | 0.957874 | − | 0.287190i | \(-0.0927211\pi\) |
−0.449160 | + | 0.893451i | \(0.648277\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −61774.2 | + | 169723.i | −1.04615 | + | 2.87428i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2784.21 | − | 15790.1i | 0.0463842 | − | 0.263058i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14857.1 | + | 9955.20i | 0.243522 | + | 0.163176i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −112216. | − | 19786.6i | −1.80990 | − | 0.319134i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −85519.4 | − | 31126.5i | −1.35743 | − | 0.494064i | −0.442171 | − | 0.896931i | \(-0.645792\pi\) |
−0.915259 | + | 0.402867i | \(0.868014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22802.0 | − | 19133.2i | 0.356232 | − | 0.298914i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 237629. | + | 137195.i | 3.65442 | + | 2.10988i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 124558. | − | 21963.0i | 1.88584 | − | 0.332525i | 0.892818 | − | 0.450418i | \(-0.148725\pi\) |
0.993026 | + | 0.117893i | \(0.0376139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24005.2 | + | 13859.4i | −0.357855 | + | 0.206607i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41461.7 | + | 113915.i | 0.608648 | + | 1.67225i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −78177.9 | − | 65599.1i | −1.13025 | − | 0.948388i | −0.131169 | − | 0.991360i | \(-0.541873\pi\) |
−0.999076 | + | 0.0429718i | \(0.986317\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 26511.5i | − | 0.377523i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 99950.1 | 1.40204 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12170.1 | + | 14503.8i | −0.168186 | + | 0.200436i | −0.843554 | − | 0.537045i | \(-0.819541\pi\) |
0.675368 | + | 0.737481i | \(0.263985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 39181.9 | − | 14261.1i | 0.533516 | − | 0.194184i | −0.0611917 | − | 0.998126i | \(-0.519490\pi\) |
0.594707 | + | 0.803942i | \(0.297268\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22270.9 | − | 38574.4i | −0.298823 | − | 0.517576i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26102.7 | + | 148036.i | 0.345160 | + | 1.95750i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 69589.1 | − | 120532.i | 0.906946 | − | 1.57088i | 0.0886635 | − | 0.996062i | \(-0.471740\pi\) |
0.818283 | − | 0.574816i | \(-0.194926\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −143087. | − | 170525.i | −1.83820 | − | 2.19068i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 37180.7 | − | 102153.i | 0.470875 | − | 1.29372i | −0.446176 | − | 0.894945i | \(-0.647214\pi\) |
0.917050 | − | 0.398772i | \(-0.130563\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21903.0 | + | 124218.i | −0.273484 | + | 1.55100i | 0.470254 | + | 0.882531i | \(0.344162\pi\) |
−0.743738 | + | 0.668471i | \(0.766949\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18370.7 | + | 274794.i | −0.226171 | + | 3.38312i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32782.7 | − | 5780.48i | −0.397998 | − | 0.0701778i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −43074.5 | − | 15677.8i | −0.515733 | − | 0.187711i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −189120. | + | 158691.i | −2.23332 | + | 1.87398i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 104194. | + | 60156.7i | 1.21369 | + | 0.700727i | 0.963562 | − | 0.267485i | \(-0.0861924\pi\) |
0.250133 | + | 0.968212i | \(0.419526\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −167301. | + | 29499.7i | −1.92245 | + | 0.338979i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 213888. | − | 123489.i | 2.42479 | − | 1.39995i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4571.69 | − | 12560.6i | −0.0511369 | − | 0.140498i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39008.0 | + | 32731.6i | 0.430547 | + | 0.361272i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 184731.i | − | 2.01213i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −75572.4 | −0.812388 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 55205.7 | − | 65791.6i | 0.585743 | − | 0.698062i | −0.389038 | − | 0.921222i | \(-0.627193\pi\) |
0.974782 | + | 0.223160i | \(0.0716371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −326591. | + | 118869.i | −3.42048 | + | 1.24495i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25459.7 | + | 44097.5i | 0.263229 | + | 0.455925i | 0.967098 | − | 0.254404i | \(-0.0818793\pi\) |
−0.703869 | + | 0.710329i | \(0.748546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5380.77 | − | 30515.9i | −0.0549232 | − | 0.311485i | 0.944953 | − | 0.327205i | \(-0.106107\pi\) |
−0.999876 | + | 0.0157205i | \(0.994996\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 248096. | − | 429715.i | 2.50034 | − | 4.33071i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −48597.9 | − | 57916.7i | −0.483614 | − | 0.576348i | 0.467968 | − | 0.883746i | \(-0.344986\pi\) |
−0.951581 | + | 0.307397i | \(0.900542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21593.2 | − | 59327.0i | 0.212196 | − | 0.583003i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42531.5 | + | 241208.i | −0.412763 | + | 2.34089i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13967.0 | − | 129086.i | −0.133874 | − | 1.23730i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 66477.2 | + | 11721.7i | 0.629370 | + | 0.110975i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −52781.5 | − | 19210.9i | −0.493612 | − | 0.179660i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5313.82 | + | 4458.83i | −0.0490925 | + | 0.0411935i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −61581.7 | − | 35554.2i | −0.562077 | − | 0.324515i | 0.191902 | − | 0.981414i | \(-0.438534\pi\) |
−0.753979 | + | 0.656899i | \(0.771868\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −110054. | + | 19405.4i | −0.992466 | + | 0.174998i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −97787.0 | + | 56457.3i | −0.871347 | + | 0.503073i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 52702.3 | + | 144798.i | 0.464055 | + | 1.27498i | 0.922410 | + | 0.386212i | \(0.126217\pi\) |
−0.458355 | + | 0.888769i | \(0.651561\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −183913. | − | 154321.i | −1.60034 | − | 1.34285i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 115932.i | 0.997000i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −107257. | −0.911667 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 132313. | − | 157685.i | 1.11164 | − | 1.32480i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 142072. | − | 51710.0i | 1.17991 | − | 0.429453i | 0.323742 | − | 0.946145i | \(-0.395059\pi\) |
0.856171 | + | 0.516692i | \(0.172837\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11647.2 | + | 20173.6i | 0.0956250 | + | 0.165627i | 0.909869 | − | 0.414895i | \(-0.136182\pi\) |
−0.814244 | + | 0.580522i | \(0.802848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19258.9 | − | 109223.i | −0.156321 | − | 0.886542i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28616.5 | + | 49565.3i | −0.229650 | + | 0.397766i | −0.957705 | − | 0.287753i | \(-0.907092\pi\) |
0.728054 | + | 0.685520i | \(0.240425\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −153173. | − | 182544.i | −1.21542 | − | 1.44848i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −110602. | + | 303876.i | −0.867813 | + | 2.38430i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3682.01 | − | 20881.7i | 0.0285691 | − | 0.162023i | −0.967185 | − | 0.254071i | \(-0.918230\pi\) |
0.995755 | + | 0.0920479i | \(0.0293413\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 110094. | − | 69734.7i | 0.844789 | − | 0.535099i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 41635.2 | + | 7341.40i | 0.315971 | + | 0.0557142i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27364.5 | − | 9959.85i | −0.205400 | − | 0.0747596i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9637.00 | − | 8086.40i | 0.0715500 | − | 0.0600376i | −0.606311 | − | 0.795227i | \(-0.707351\pi\) |
0.677861 | + | 0.735190i | \(0.262907\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −116225. | − | 67102.8i | −0.853588 | − | 0.492819i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30770.1 | − | 5425.59i | 0.223553 | − | 0.0394184i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 208217. | − | 120214.i | 1.49658 | − | 0.864049i | 0.496585 | − | 0.867988i | \(-0.334587\pi\) |
0.999992 | + | 0.00393908i | \(0.00125385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 192456. | + | 528769.i | 1.36858 | + | 3.76014i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21718.3 | − | 18223.8i | −0.152807 | − | 0.128220i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 218287.i | 1.51967i | 0.650116 | + | 0.759835i | \(0.274720\pi\) | ||||
−0.650116 | + | 0.759835i | \(0.725280\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 229846. | 1.58339 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9812.87 | − | 11694.5i | 0.0668958 | − | 0.0797233i | −0.731559 | − | 0.681778i | \(-0.761207\pi\) |
0.798455 | + | 0.602055i | \(0.205651\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −242832. | + | 88383.6i | −1.63827 | + | 0.596280i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 102647. | + | 177790.i | 0.685369 | + | 1.18709i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −46356.7 | − | 262902.i | −0.306347 | − | 1.73738i | −0.617096 | − | 0.786888i | \(-0.711691\pi\) |
0.310749 | − | 0.950492i | \(-0.399420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −48521.8 | + | 84042.3i | −0.317383 | + | 0.549724i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 298738. | + | 356022.i | 1.93422 | + | 2.30511i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1262.65 | − | 3469.09i | 0.00809259 | − | 0.0222342i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25111.4 | + | 142414.i | −0.159327 | + | 0.903589i | 0.795395 | + | 0.606091i | \(0.207263\pi\) |
−0.954722 | + | 0.297498i | \(0.903848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −322694. | + | 34915.1i | −2.02696 | + | 0.219315i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 59433.0 | + | 10479.6i | 0.369606 | + | 0.0651715i | 0.355366 | − | 0.934727i | \(-0.384356\pi\) |
0.0142397 | + | 0.999899i | \(0.495467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 48921.0 | + | 17805.8i | 0.301221 | + | 0.109635i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 722377. | − | 606147.i | 4.40407 | − | 3.69545i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 50402.7 | + | 29100.0i | 0.304274 | + | 0.175673i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −224415. | + | 39570.4i | −1.34155 | + | 0.236551i | −0.797913 | − | 0.602773i | \(-0.794062\pi\) |
−0.543632 | + | 0.839323i | \(0.682951\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 86812.7 | − | 50121.3i | 0.513925 | − | 0.296715i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −68476.4 | − | 188137.i | −0.401459 | − | 1.10300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 227412. | + | 190821.i | 1.32043 | + | 1.10797i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 273092.i | − | 1.57049i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 103744. | 0.590930 | 0.295465 | − | 0.955354i | \(-0.404525\pi\) | ||||
0.295465 | + | 0.955354i | \(0.404525\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −185363. | + | 220907.i | −1.04583 | + | 1.24637i | −0.0774170 | + | 0.996999i | \(0.524667\pi\) |
−0.968409 | + | 0.249368i | \(0.919777\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26279.4 | + | 9564.93i | −0.146871 | + | 0.0534566i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −245038. | − | 424418.i | −1.35661 | − | 2.34972i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15465.9 | − | 87711.5i | −0.0848242 | − | 0.481062i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −46761.2 | + | 80992.8i | −0.254081 | + | 0.440080i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −115204. | − | 137295.i | −0.620173 | − | 0.739093i | 0.360927 | − | 0.932594i | \(-0.382460\pi\) |
−0.981100 | + | 0.193501i | \(0.938016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −95452.7 | + | 262254.i | −0.509111 | + | 1.39877i | 0.373045 | + | 0.927813i | \(0.378314\pi\) |
−0.882156 | + | 0.470958i | \(0.843908\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 75814.6 | − | 429966.i | 0.400658 | − | 2.27225i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −97186.6 | − | 6497.18i | −0.508913 | − | 0.0340221i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2077.19 | + | 366.264i | 0.0107782 | + | 0.00190049i | 0.179035 | − | 0.983843i | \(-0.442703\pi\) |
−0.168256 | + | 0.985743i | \(0.553814\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 71587.5 | + | 26055.7i | 0.368095 | + | 0.133976i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −150418. | + | 126215.i | −0.766463 | + | 0.643139i | −0.939801 | − | 0.341723i | \(-0.888989\pi\) |
0.173337 | + | 0.984863i | \(0.444545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −225513. | − | 130200.i | −1.13881 | − | 0.657492i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 641418. | − | 113099.i | 3.21016 | − | 0.566037i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 129237. | − | 74614.8i | 0.641052 | − | 0.370111i | −0.143968 | − | 0.989582i | \(-0.545986\pi\) |
0.785020 | + | 0.619471i | \(0.212653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23905.2 | + | 65679.0i | 0.117528 | + | 0.322904i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −124619. | − | 104568.i | −0.607278 | − | 0.509567i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 116045.i | 0.560535i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −48048.6 | −0.230064 | −0.115032 | − | 0.993362i | \(-0.536697\pi\) | ||||
−0.115032 | + | 0.993362i | \(0.536697\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −517573. | + | 616820.i | −2.45667 | + | 2.92774i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −134980. | + | 49128.5i | −0.635135 | + | 0.231170i | −0.639465 | − | 0.768820i | \(-0.720844\pi\) |
0.00432977 | + | 0.999991i | \(0.498622\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 185533. | + | 321352.i | 0.865483 | + | 1.49906i | 0.866566 | + | 0.499062i | \(0.166322\pi\) |
−0.00108317 | + | 0.999999i | \(0.500345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 139216. | + | 789535.i | 0.643849 | + | 3.65145i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −59097.8 | + | 102360.i | −0.270980 | + | 0.469351i | −0.969113 | − | 0.246617i | \(-0.920681\pi\) |
0.698133 | + | 0.715968i | \(0.254014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −85538.2 | − | 101940.i | −0.388879 | − | 0.463448i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24287.2 | − | 66728.7i | 0.109480 | − | 0.300795i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18565.9 | − | 105293.i | 0.0829841 | − | 0.470626i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 273814. | − | 408638.i | 1.21358 | − | 1.81114i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 124052. | + | 21873.8i | 0.545216 | + | 0.0961363i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 138747. | + | 50499.8i | 0.604718 | + | 0.220099i | 0.626191 | − | 0.779670i | \(-0.284613\pi\) |
−0.0214724 | + | 0.999769i | \(0.506835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20020.8 | − | 16799.5i | 0.0865351 | − | 0.0726116i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 210092. | + | 121296.i | 0.900564 | + | 0.519941i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 633421. | − | 111689.i | 2.69283 | − | 0.474818i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3850.49 | − | 2223.08i | 0.0162352 | − | 0.00937341i | −0.491860 | − | 0.870674i | \(-0.663683\pi\) |
0.508096 | + | 0.861301i | \(0.330350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −188020. | − | 516581.i | −0.786297 | − | 2.16033i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −216765. | − | 181887.i | −0.899138 | − | 0.754466i | 0.0708839 | − | 0.997485i | \(-0.477418\pi\) |
−0.970022 | + | 0.243018i | \(0.921862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 205832.i | 0.846876i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.04183e6 | −4.25194 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 180520. | − | 215135.i | 0.730822 | − | 0.870960i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −157919. | + | 57477.9i | −0.634211 | + | 0.230834i | −0.639063 | − | 0.769154i | \(-0.720678\pi\) |
0.00485227 | + | 0.999988i | \(0.498455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −51875.6 | − | 89851.2i | −0.206675 | − | 0.357971i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38236.5 | + | 216850.i | 0.151127 | + | 0.857085i | 0.962241 | + | 0.272197i | \(0.0877503\pi\) |
−0.811114 | + | 0.584888i | \(0.801139\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −240640. | + | 416801.i | −0.943593 | + | 1.63435i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −287162. | − | 342226.i | −1.11715 | − | 1.33136i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 86482.7 | − | 237609.i | 0.333806 | − | 0.917123i | −0.653307 | − | 0.757094i | \(-0.726619\pi\) |
0.987112 | − | 0.160030i | \(-0.0511591\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5959.55 | − | 33798.3i | 0.0228229 | − | 0.129435i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −784774. | − | 193118.i | −2.98202 | − | 0.733816i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 891715. | + | 157233.i | 3.36211 | + | 0.592830i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13686.3 | + | 4981.41i | 0.0512042 | + | 0.0186368i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −417132. | + | 350016.i | −1.54860 | + | 1.29943i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 66835.3 | + | 38587.4i | 0.246224 | + | 0.142158i | 0.618034 | − | 0.786151i | \(-0.287929\pi\) |
−0.371810 | + | 0.928309i | \(0.621263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35806.7 | − | 6313.68i | 0.130906 | − | 0.0230823i | −0.107811 | − | 0.994171i | \(-0.534384\pi\) |
0.238717 | + | 0.971089i | \(0.423273\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.06097e6 | + | 612554.i | −3.84934 | + | 2.22242i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −129272. | − | 355171.i | −0.465459 | − | 1.27884i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −158602. | − | 133083.i | −0.566758 | − | 0.475567i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 807172.i | − | 2.86271i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31386.8 | 0.110482 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 410171. | − | 488823.i | 1.43304 | − | 1.70783i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 426480. | − | 155226.i | 1.47894 | − | 0.538290i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19837.7 | − | 34360.0i | −0.0682833 | − | 0.118270i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −83380.7 | − | 472876.i | −0.284886 | − | 1.61567i | −0.705692 | − | 0.708519i | \(-0.749364\pi\) |
0.420806 | − | 0.907151i | \(-0.361747\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 95071.8 | − | 164669.i | 0.322442 | − | 0.558487i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 94063.3 | + | 112100.i | 0.316685 | + | 0.377410i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 99395.7 | − | 273088.i | 0.332195 | − | 0.912698i | −0.655345 | − | 0.755330i | \(-0.727477\pi\) |
0.987540 | − | 0.157369i | \(-0.0503011\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 62352.3 | − | 353617.i | 0.206875 | − | 1.17325i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −185409. | + | 91133.3i | −0.610699 | + | 0.300175i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4284.73 | + | 755.514i | 0.0140111 | + | 0.00247054i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 378203. | + | 137655.i | 1.22783 | + | 0.446894i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −164551. | + | 138075.i | −0.530384 | + | 0.445045i | −0.868234 | − | 0.496155i | \(-0.834745\pi\) |
0.337850 | + | 0.941200i | \(0.390300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41579.9 | − | 24006.1i | −0.133064 | − | 0.0768243i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 668666. | − | 117904.i | 2.12463 | − | 0.374630i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −277806. | + | 160391.i | −0.876445 | + | 0.506016i | −0.869485 | − | 0.493960i | \(-0.835549\pi\) |
−0.00696069 | + | 0.999976i | \(0.502216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 213928. | + | 587762.i | 0.670148 | + | 1.84122i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 851347. | + | 714365.i | 2.64814 | + | 2.22205i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11383.3i | − | 0.0351597i | −0.999845 | − | 0.0175798i | \(-0.994404\pi\) | ||
0.999845 | − | 0.0175798i | \(-0.00559613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 386192. | 1.18449 | 0.592244 | − | 0.805759i | \(-0.298242\pi\) | ||||
0.592244 | + | 0.805759i | \(0.298242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −322312. | + | 384116.i | −0.981673 | + | 1.16991i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −345475. | + | 125743.i | −1.04491 | + | 0.380318i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39009.3 | − | 67566.1i | −0.117170 | − | 0.202945i | 0.801475 | − | 0.598028i | \(-0.204049\pi\) |
−0.918645 | + | 0.395084i | \(0.870716\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 180008. | + | 1.02088e6i | 0.536952 | + | 3.04521i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −174933. | + | 302992.i | −0.518225 | + | 0.897592i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42168.9 | − | 50254.9i | −0.124067 | − | 0.147857i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −160013. | + | 439631.i | −0.467566 | + | 1.28463i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −105534. | + | 598511.i | −0.306277 | + | 1.73698i | 0.311155 | + | 0.950359i | \(0.399284\pi\) |
−0.617432 | + | 0.786624i | \(0.711827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 262694. | − | 273698.i | 0.757215 | − | 0.788936i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −680573. | − | 120003.i | −1.94850 | − | 0.343573i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7691.86 | + | 2799.61i | 0.0218737 | + | 0.00796137i | 0.352934 | − | 0.935648i | \(-0.385184\pi\) |
−0.331060 | + | 0.943610i | \(0.607406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 645389. | − | 541546.i | 1.82300 | − | 1.52968i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −406210. | − | 234525.i | −1.13973 | − | 0.658023i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 272306. | − | 48014.8i | 0.758932 | − | 0.133820i | 0.219227 | − | 0.975674i | \(-0.429647\pi\) |
0.539706 | + | 0.841854i | \(0.318536\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 172114. | − | 99370.1i | 0.476505 | − | 0.275110i | −0.242454 | − | 0.970163i | \(-0.577952\pi\) |
0.718959 | + | 0.695053i | \(0.244619\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −183494. | − | 504145.i | −0.504646 | − | 1.38650i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −84376.2 | − | 70800.0i | −0.230520 | − | 0.193429i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 145818.i | 0.395763i | 0.980226 | + | 0.197881i | \(0.0634061\pi\) | ||||
−0.980226 | + | 0.197881i | \(0.936594\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 514547. | 1.38736 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4204.10 | − | 5010.26i | 0.0112614 | − | 0.0134208i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 313010. | − | 113926.i | 0.832985 | − | 0.303182i | 0.109902 | − | 0.993942i | \(-0.464946\pi\) |
0.723083 | + | 0.690761i | \(0.242724\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 241672. | + | 418589.i | 0.638965 | + | 1.10672i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22609.1 | − | 128223.i | −0.0593900 | − | 0.336818i | 0.940606 | − | 0.339499i | \(-0.110258\pi\) |
−0.999996 | + | 0.00268147i | \(0.999146\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −215279. | + | 372875.i | −0.561851 | + | 0.973155i | 0.435484 | + | 0.900196i | \(0.356577\pi\) |
−0.997335 | + | 0.0729581i | \(0.976756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 388275. | + | 462728.i | 1.00683 | + | 1.19989i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 104963. | − | 288382.i | 0.270432 | − | 0.743006i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 106689. | − | 605062.i | 0.273123 | − | 1.54896i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 402260. | + | 550116.i | 1.02323 | + | 1.39933i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −186862. | − | 32948.9i | −0.472303 | − | 0.0832797i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −292661. | − | 106520.i | −0.735031 | − | 0.267530i | −0.0527384 | − | 0.998608i | \(-0.516795\pi\) |
−0.682293 | + | 0.731079i | \(0.739017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33193.8 | − | 27852.9i | 0.0828419 | − | 0.0695126i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −518590. | − | 299408.i | −1.28611 | − | 0.742534i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17546.0 | + | 3093.84i | −0.0432414 | + | 0.00762463i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 980538. | − | 566114.i | 2.40139 | − | 1.38644i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 103019. | + | 283042.i | 0.250726 | + | 0.688865i | 0.999656 | + | 0.0262160i | \(0.00834577\pi\) |
−0.748930 | + | 0.662649i | \(0.769432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 138701. | + | 116384.i | 0.335473 | + | 0.281496i | 0.794926 | − | 0.606707i | \(-0.207510\pi\) |
−0.459452 | + | 0.888202i | \(0.651954\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 739372.i | − | 1.77723i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 67772.6 | 0.161900 | 0.0809498 | − | 0.996718i | \(-0.474205\pi\) | ||||
0.0809498 | + | 0.996718i | \(0.474205\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −270212. | + | 322026.i | −0.641526 | + | 0.764541i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −887867. | + | 323157.i | −2.09501 | + | 0.762521i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −320652. | − | 555385.i | −0.751981 | − | 1.30247i | −0.946861 | − | 0.321643i | \(-0.895765\pi\) |
0.194880 | − | 0.980827i | \(-0.437568\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −210257. | − | 1.19243e6i | −0.490081 | − | 2.77939i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 69181.5 | − | 119826.i | 0.160273 | − | 0.277600i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 498145. | + | 593666.i | 1.14706 | + | 1.36701i | 0.919427 | + | 0.393262i | \(0.128653\pi\) |
0.227631 | + | 0.973748i | \(0.426902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −275464. | + | 756832.i | −0.630468 | + | 1.73220i | 0.0493168 | + | 0.998783i | \(0.484296\pi\) |
−0.679784 | + | 0.733412i | \(0.737927\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 52946.1 | − | 300272.i | 0.120450 | − | 0.683106i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 773561. | + | 341579.i | 1.74925 | + | 0.772410i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 152066. | + | 26813.4i | 0.341807 | + | 0.0602698i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 616094. | + | 224240.i | 1.37656 | + | 0.501027i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −143254. | + | 120204.i | −0.318172 | + | 0.266978i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −245414. | − | 141690.i | −0.541838 | − | 0.312830i | 0.203986 | − | 0.978974i | \(-0.434610\pi\) |
−0.745823 | + | 0.666144i | \(0.767944\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.00413e6 | + | 529710.i | −6.59343 | + | 1.16260i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 411346. | − | 237491.i | 0.897491 | − | 0.518167i | 0.0211057 | − | 0.999777i | \(-0.493281\pi\) |
0.876385 | + | 0.481611i | \(0.159948\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 259259. | + | 712310.i | 0.562335 | + | 1.54500i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 199172. | + | 167125.i | 0.429471 | + | 0.360369i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 274079.i | 0.587535i | 0.955877 | + | 0.293768i | \(0.0949092\pi\) | ||||
−0.955877 | + | 0.293768i | \(0.905091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −261162. | −0.556581 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.12804e6 | − | 1.34435e6i | 2.39007 | − | 2.84838i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27683.2 | + | 10075.8i | −0.0583146 | + | 0.0212248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 134489. | + | 232942.i | 0.281664 | + | 0.487856i | 0.971795 | − | 0.235828i | \(-0.0757803\pi\) |
−0.690131 | + | 0.723685i | \(0.742447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −213211. | − | 1.20918e6i | −0.443959 | − | 2.51782i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −355742. | + | 616163.i | −0.736488 | + | 1.27563i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −146472. | − | 174559.i | −0.301502 | − | 0.359316i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 391708. | − | 1.07621e6i | 0.801694 | − | 2.20264i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14474.6 | + | 82089.7i | −0.0294558 | + | 0.167052i | −0.995987 | − | 0.0894963i | \(-0.971474\pi\) |
0.966531 | + | 0.256549i | \(0.0825854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53054.7 | − | 182909.i | −0.107353 | − | 0.370105i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 99190.1 | + | 17489.9i | 0.199568 | + | 0.0351891i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −532998. | − | 193995.i | −1.06632 | − | 0.388108i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −402160. | + | 337452.i | −0.800029 | + | 0.671304i | −0.948206 | − | 0.317657i | \(-0.897104\pi\) |
0.148176 | + | 0.988961i | \(0.452660\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15190.8 | + | 8770.40i | 0.0300497 | + | 0.0173492i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −279235. | + | 49236.7i | −0.549277 | + | 0.0968523i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 211010. | − | 121827.i | 0.412754 | − | 0.238304i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −315931. | − | 868013.i | −0.614545 | − | 1.68845i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −264994. | − | 222356.i | −0.512600 | − | 0.430122i | 0.349443 | − | 0.936958i | \(-0.386371\pi\) |
−0.862043 | + | 0.506835i | \(0.830815\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.06713e6i | 2.05280i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 786585. | 1.50477 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −501239. | + | 597353.i | −0.953606 | + | 1.13646i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −297089. | + | 108132.i | −0.562106 | + | 0.204590i | −0.607417 | − | 0.794383i | \(-0.707794\pi\) |
0.0453112 | + | 0.998973i | \(0.485572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 688717. | + | 1.19289e6i | 1.29594 | + | 2.24464i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 60529.2 | + | 343278.i | 0.113274 | + | 0.642408i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 289215. | − | 500934.i | 0.538285 | − | 0.932337i | −0.460712 | − | 0.887550i | \(-0.652406\pi\) |
0.998997 | − | 0.0447870i | \(-0.0142609\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −176362. | − | 210180.i | −0.326461 | − | 0.389061i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −95563.4 | + | 262558.i | −0.175937 | + | 0.483382i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36043.3 | + | 204412.i | −0.0659988 | + | 0.374298i | 0.933862 | + | 0.357633i | \(0.116416\pi\) |
−0.999861 | + | 0.0166650i | \(0.994695\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 293920. | − | 85254.4i | 0.535295 | − | 0.155267i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −817496. | − | 144147.i | −1.48084 | − | 0.261112i | −0.625926 | − | 0.779882i | \(-0.715279\pi\) |
−0.854914 | + | 0.518770i | \(0.826390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.59453e6 | − | 580361.i | −2.87290 | − | 1.04565i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.08052e6 | + | 906662.i | −1.93638 | + | 1.62482i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 651283. | + | 376019.i | 1.16093 | + | 0.670264i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −616937. | + | 108783.i | −1.09386 | + | 0.192877i | −0.691336 | − | 0.722534i | \(-0.742977\pi\) |
−0.402522 | + | 0.915410i | \(0.631866\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.34870e6 | + | 778673.i | −2.37862 | + | 1.37330i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 144957. | + | 398266.i | 0.254299 | + | 0.698681i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 820428. | + | 688421.i | 1.43169 | + | 1.20133i | 0.944706 | + | 0.327918i | \(0.106347\pi\) |
0.486982 | + | 0.873412i | \(0.338098\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 509361.i | − | 0.884183i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 499722. | 0.862898 | 0.431449 | − | 0.902137i | \(-0.358002\pi\) | ||||
0.431449 | + | 0.902137i | \(0.358002\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −110857. | + | 132114.i | −0.190420 | + | 0.226934i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.19176e6 | − | 1.16171e6i | 5.45391 | − | 1.98506i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 94387.0 | + | 163483.i | 0.160443 | + | 0.277896i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1847.28 | − | 10476.5i | −0.00312378 | − | 0.0177158i | 0.983206 | − | 0.182499i | \(-0.0584187\pi\) |
−0.986330 | + | 0.164783i | \(0.947308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.08217e6 | − | 1.87438e6i | 1.82049 | − | 3.15318i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −530184. | − | 631849.i | −0.887294 | − | 1.05744i | −0.997977 | − | 0.0635803i | \(-0.979748\pi\) |
0.110682 | − | 0.993856i | \(-0.464696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 489741. | − | 1.34555e6i | 0.815386 | − | 2.24025i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −82366.7 | + | 467125.i | −0.136430 | + | 0.773732i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 92387.2 | − | 209226.i | 0.152243 | − | 0.344779i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −580705. | − | 102394.i | −0.952036 | − | 0.167870i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.20394e6 | + | 438197.i | 1.96372 | + | 0.714737i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −141722. | + | 118919.i | −0.229984 | + | 0.192980i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −548575. | − | 316720.i | −0.885700 | − | 0.511359i | −0.0131663 | − | 0.999913i | \(-0.504191\pi\) |
−0.872533 | + | 0.488554i | \(0.837524\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.71984e6 | + | 303254.i | −2.76270 | + | 0.487138i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −638394. | + | 368577.i | −1.02032 | + | 0.589081i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28721.7 | + | 78912.2i | 0.0456734 | + | 0.125487i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −347532. | − | 291614.i | −0.549870 | − | 0.461396i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 166005.i | − | 0.261339i | −0.991426 | − | 0.130669i | \(-0.958287\pi\) | ||
0.991426 | − | 0.130669i | \(-0.0417127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47484.1 | −0.0743797 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 795293. | − | 947793.i | 1.23954 | − | 1.47723i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −67713.7 | + | 24645.8i | −0.105014 | + | 0.0382218i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −316013. | − | 547351.i | −0.487656 | − | 0.844645i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 56260.4 | + | 319069.i | 0.0863885 | + | 0.489933i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 54503.9 | − | 94403.6i | 0.0832781 | − | 0.144242i | −0.821378 | − | 0.570384i | \(-0.806794\pi\) |
0.904656 | + | 0.426142i | \(0.140128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 764460. | + | 911047.i | 1.16229 | + | 1.38516i | 0.908493 | + | 0.417899i | \(0.137233\pi\) |
0.253792 | + | 0.967259i | \(0.418322\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 244038. | − | 670489.i | 0.369213 | − | 1.01440i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −248702. | + | 1.41046e6i | −0.374425 | + | 2.12347i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −282417. | + | 206511.i | −0.423103 | + | 0.309385i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −542996. | − | 95744.8i | −0.809522 | − | 0.142741i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −300804. | − | 109484.i | −0.446270 | − | 0.162429i | 0.109103 | − | 0.994030i | \(-0.465202\pi\) |
−0.555373 | + | 0.831601i | \(0.687424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −211259. | + | 177267.i | −0.311900 | + | 0.261715i | −0.785277 | − | 0.619145i | \(-0.787479\pi\) |
0.473377 | + | 0.880860i | \(0.343035\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.22768e6 | + | 1.28615e6i | 3.27299 | + | 1.88966i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.13395e6 | − | 199947.i | 1.65800 | − | 0.292350i | 0.735263 | − | 0.677782i | \(-0.237059\pi\) |
0.922736 | + | 0.385432i | \(0.125948\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.02004e6 | − | 588921.i | 1.48426 | − | 0.856935i | 0.484416 | − | 0.874838i | \(-0.339032\pi\) |
0.999840 | + | 0.0179028i | \(0.00569896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −814570. | − | 2.23801e6i | −1.17958 | − | 3.24086i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 99088.5 | + | 83145.2i | 0.142802 | + | 0.119825i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 270303.i | 0.387683i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.35264e6 | −3.35819 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −168297. | + | 200568.i | −0.239085 | + | 0.284930i | −0.872223 | − | 0.489109i | \(-0.837322\pi\) |
0.633138 | + | 0.774039i | \(0.281767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −356866. | + | 129889.i | −0.504560 | + | 0.183645i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −930126. | − | 1.61103e6i | −1.30884 | − | 2.26698i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 202109. | + | 1.14622e6i | 0.283056 | + | 1.60529i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 64905.0 | − | 112419.i | 0.0904714 | − | 0.156701i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.38742e6 | + | 1.65346e6i | 1.92483 | + | 2.29392i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48684.4 | + | 133759.i | −0.0672249 | + | 0.184699i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35555.7 | + | 201647.i | −0.0488665 | + | 0.277136i | −0.999444 | − | 0.0333527i | \(-0.989382\pi\) |
0.950577 | + | 0.310489i | \(0.100493\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.45961e6 | + | 2.36071e6i | 3.36460 | + | 3.22932i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −598777. | − | 105581.i | −0.815274 | − | 0.143755i | −0.249563 | − | 0.968359i | \(-0.580287\pi\) |
−0.565711 | + | 0.824604i | \(0.691398\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 482388. | + | 175575.i | 0.653747 | + | 0.237944i | 0.647534 | − | 0.762036i | \(-0.275800\pi\) |
0.00621270 | + | 0.999981i | \(0.498022\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −436368. | + | 366157.i | −0.588636 | + | 0.493924i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 267501. | + | 154442.i | 0.359173 | + | 0.207368i | 0.668718 | − | 0.743516i | \(-0.266843\pi\) |
−0.309545 | + | 0.950885i | \(0.600177\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.39710e6 | − | 246347.i | 1.86722 | − | 0.329242i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −679315. | + | 392203.i | −0.903718 | + | 0.521762i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3124.43 | − | 8584.31i | −0.00413744 | − | 0.0113675i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 96116.8 | + | 80651.6i | 0.126696 | + | 0.106311i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.05605e6i | 4.00988i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.72774e6 | 2.25665 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 692582. | − | 825387.i | 0.900476 | − | 1.07315i | −0.0964920 | − | 0.995334i | \(-0.530762\pi\) |
0.996968 | − | 0.0778118i | \(-0.0247933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.93466e6 | − | 704160.i | 2.50396 | − | 0.911368i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 75496.4 | + | 130764.i | 0.0972690 | + | 0.168475i | 0.910553 | − | 0.413392i | \(-0.135656\pi\) |
−0.813284 | + | 0.581866i | \(0.802323\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13623.0 | + | 77259.7i | 0.0174723 | + | 0.0990904i | 0.992297 | − | 0.123883i | \(-0.0395348\pi\) |
−0.974825 | + | 0.222973i | \(0.928424\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.45353e6 | + | 2.51758e6i | −1.85582 | + | 3.21438i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −849061. | − | 1.01187e6i | −1.07917 | − | 1.28611i | −0.955886 | − | 0.293739i | \(-0.905100\pi\) |
−0.123289 | − | 0.992371i | \(-0.539344\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 241372. | − | 663165.i | 0.305410 | − | 0.839108i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 405201. | − | 2.29801e6i | 0.510405 | − | 2.89465i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21023.8 | − | 42772.5i | −0.0263638 | − | 0.0536367i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.16445e6 | − | 205324.i | −1.45370 | − | 0.256327i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −214940. | − | 78231.7i | −0.267136 | − | 0.0972295i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −460701. | + | 386574.i | −0.570033 | + | 0.478314i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 185226. | + | 106940.i | 0.228167 | + | 0.131732i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 858137. | − | 151313.i | 1.05240 | − | 0.185567i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −429012. | + | 247690.i | −0.523808 | + | 0.302421i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9681.06 | + | 26598.5i | 0.0117682 | + | 0.0323327i | 0.945438 | − | 0.325803i | \(-0.105635\pi\) |
−0.933669 | + | 0.358136i | \(0.883412\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.75174e6 | − | 1.46989e6i | −2.12003 | − | 1.77892i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 55248.4i | − | 0.0665707i | −0.999446 | − | 0.0332854i | \(-0.989403\pi\) | ||
0.999446 | − | 0.0332854i | \(-0.0105970\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 734595. | 0.881265 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −831259. | + | 990656.i | −0.992874 | + | 1.18326i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.34094e6 | − | 488061.i | 1.59467 | − | 0.580411i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −717339. | − | 1.24247e6i | −0.849363 | − | 1.47114i | −0.881778 | − | 0.471665i | \(-0.843653\pi\) |
0.0324146 | − | 0.999475i | \(-0.489680\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −255207. | − | 1.44735e6i | −0.300866 | − | 1.70630i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −132397. | + | 229319.i | −0.155409 | + | 0.269176i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −462063. | − | 550666.i | −0.540030 | − | 0.643583i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.47145e6 | + | 4.04278e6i | −1.71232 | + | 4.70457i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 101467. | − | 575448.i | 0.117569 | − | 0.666768i | −0.867877 | − | 0.496779i | \(-0.834516\pi\) |
0.985446 | − | 0.169989i | \(-0.0543731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31023.2 | + | 126070.i | −0.0357921 | + | 0.145449i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 858106. | + | 151307.i | 0.985775 | + | 0.173819i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.66227e6 | − | 605016.i | −1.90142 | − | 0.692060i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.19616e6 | − | 1.00370e6i | 1.36242 | − | 1.14320i | 0.387189 | − | 0.922000i | \(-0.373446\pi\) |
0.975228 | − | 0.221203i | \(-0.0709984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −459209. | − | 265125.i | −0.520810 | − | 0.300690i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −179523. | + | 31654.7i | −0.202741 | + | 0.0357486i | −0.274096 | − | 0.961702i | \(-0.588379\pi\) |
0.0713555 | + | 0.997451i | \(0.477268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −148043. | + | 85472.4i | −0.166480 | + | 0.0961175i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.79359e6 | − | 4.92785e6i | −2.00845 | − | 5.51816i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −132026. | − | 110783.i | −0.147218 | − | 0.123530i | 0.566204 | − | 0.824265i | \(-0.308411\pi\) |
−0.713422 | + | 0.700735i | \(0.752856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32359.1i | 0.0359305i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.29377e6 | −1.43052 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −246554. | + | 293832.i | −0.271473 | + | 0.323529i | −0.884506 | − | 0.466528i | \(-0.845505\pi\) |
0.613033 | + | 0.790057i | \(0.289949\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.22758e6 | − | 446804.i | 1.34600 | − | 0.489904i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −540184. | − | 935627.i | −0.589818 | − | 1.02160i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −53446.8 | − | 303112.i | −0.0581145 | − | 0.329584i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 90409.6 | − | 156594.i | 0.0978966 | − | 0.169562i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.94887e6 | + | 2.32258e6i | 2.10151 | + | 2.50448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 923701. | − | 2.53785e6i | 0.991920 | − | 2.72528i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −219463. | + | 1.24464e6i | −0.234697 | + | 1.33103i | 0.608553 | + | 0.793513i | \(0.291750\pi\) |
−0.843251 | + | 0.537521i | \(0.819361\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.84578e6 | − | 1.23680e6i | −1.96577 | − | 1.31720i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −989071. | − | 174400.i | −1.04903 | − | 0.184973i | −0.377547 | − | 0.925990i | \(-0.623232\pi\) |
−0.671486 | + | 0.741018i | \(0.734344\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −787940. | − | 286787.i | −0.832276 | − | 0.302924i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 884873. | − | 742497.i | 0.930833 | − | 0.781062i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −222265. | − | 128324.i | −0.232853 | − | 0.134438i | 0.379035 | − | 0.925382i | \(-0.376256\pi\) |
−0.611887 | + | 0.790945i | \(0.709589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −634573. | + | 111892.i | −0.662088 | + | 0.116744i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −602147. | + | 347650.i | −0.625698 | + | 0.361247i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 519865. | + | 1.42832e6i | 0.538001 | + | 1.47815i | 0.849339 | + | 0.527847i | \(0.177001\pi\) |
−0.311338 | + | 0.950299i | \(0.600777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.37922e6 | + | 1.15731e6i | 1.42155 | + | 1.19282i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 118702.i | 0.121850i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 261494. | 0.267343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −671040. | + | 799714.i | −0.683284 | + | 0.814306i | −0.990526 | − | 0.137325i | \(-0.956149\pi\) |
0.307242 | + | 0.951631i | \(0.400594\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.14344e6 | + | 416177.i | −1.15962 | + | 0.422066i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 611008. | + | 1.05830e6i | 0.617164 | + | 1.06896i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 228944. | + | 1.29841e6i | 0.230324 | + | 1.30623i | 0.852241 | + | 0.523149i | \(0.175243\pi\) |
−0.621917 | + | 0.783083i | \(0.713646\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −590534. | + | 1.02283e6i | −0.591717 | + | 1.02488i |
(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 | 76.5.j.a.21.7 | ✓ | 42 | |
19.10 | odd | 18 | inner | 76.5.j.a.29.7 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.21.7 | ✓ | 42 | 1.1 | even | 1 | trivial | |
76.5.j.a.29.7 | yes | 42 | 19.10 | odd | 18 | inner |