Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,5,Mod(163,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.163");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.d (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: | \(33.4918680392\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 163.9 | ||
Character | \(\chi\) | \(=\) | 324.163 |
Dual form | 324.5.d.e.163.10 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.34653 | − | 3.76654i | −0.336633 | − | 0.941636i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −12.3737 | + | 10.1435i | −0.773357 | + | 0.633971i | ||||
\(5\) | −11.0316 | −0.441263 | −0.220632 | − | 0.975357i | \(-0.570812\pi\) | ||||
−0.220632 | + | 0.975357i | \(0.570812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.9152i | 0.243167i | 0.992581 | + | 0.121583i | \(0.0387972\pi\) | ||||
−0.992581 | + | 0.121583i | \(0.961203\pi\) | |||||||
\(8\) | 54.8676 | + | 32.9476i | 0.857307 | + | 0.514806i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 14.8544 | + | 41.5509i | 0.148544 | + | 0.415509i | ||||
\(11\) | − | 219.387i | − | 1.81312i | −0.422080 | − | 0.906559i | \(-0.638700\pi\) | ||
0.422080 | − | 0.906559i | \(-0.361300\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.0701 | −0.219349 | −0.109675 | − | 0.993968i | \(-0.534981\pi\) | ||||
−0.109675 | + | 0.993968i | \(0.534981\pi\) | |||||||
\(14\) | 44.8790 | − | 16.0441i | 0.228975 | − | 0.0818579i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 50.2175 | − | 251.026i | 0.196162 | − | 0.980571i | ||||
\(17\) | −284.021 | −0.982771 | −0.491386 | − | 0.870942i | \(-0.663509\pi\) | ||||
−0.491386 | + | 0.870942i | \(0.663509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 45.4901i | − | 0.126011i | −0.998013 | − | 0.0630057i | \(-0.979931\pi\) | ||
0.998013 | − | 0.0630057i | \(-0.0200686\pi\) | |||||||
\(20\) | 136.502 | − | 111.899i | 0.341254 | − | 0.279748i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −826.332 | + | 295.412i | −1.70730 | + | 0.610354i | ||||
\(23\) | 201.286i | 0.380503i | 0.981735 | + | 0.190252i | \(0.0609304\pi\) | ||||
−0.981735 | + | 0.190252i | \(0.939070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −503.304 | −0.805287 | ||||||||
\(26\) | 49.9160 | + | 139.626i | 0.0738402 | + | 0.206547i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −120.862 | − | 147.435i | −0.154161 | − | 0.188055i | ||||
\(29\) | 1228.31 | 1.46053 | 0.730265 | − | 0.683164i | \(-0.239397\pi\) | ||||
0.730265 | + | 0.683164i | \(0.239397\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1514.77i | 1.57624i | 0.615520 | + | 0.788121i | \(0.288946\pi\) | ||||
−0.615520 | + | 0.788121i | \(0.711054\pi\) | |||||||
\(32\) | −1013.12 | + | 148.868i | −0.989376 | + | 0.145379i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 382.443 | + | 1069.78i | 0.330833 | + | 0.925413i | ||||
\(35\) | − | 131.443i | − | 0.107301i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1521.29 | −1.11124 | −0.555622 | − | 0.831435i | \(-0.687520\pi\) | ||||
−0.555622 | + | 0.831435i | \(0.687520\pi\) | |||||||
\(38\) | −171.340 | + | 61.2538i | −0.118657 | + | 0.0424195i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −605.277 | − | 363.464i | −0.378298 | − | 0.227165i | ||||
\(41\) | 2633.95 | 1.56689 | 0.783447 | − | 0.621459i | \(-0.213460\pi\) | ||||
0.783447 | + | 0.621459i | \(0.213460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 39.9593i | − | 0.0216113i | −0.999942 | − | 0.0108056i | \(-0.996560\pi\) | ||
0.999942 | − | 0.0108056i | \(-0.00343961\pi\) | |||||||
\(44\) | 2225.36 | + | 2714.63i | 1.14946 | + | 1.40219i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 758.153 | − | 271.038i | 0.358295 | − | 0.128090i | ||||
\(47\) | 2884.86i | 1.30596i | 0.757377 | + | 0.652978i | \(0.226481\pi\) | ||||
−0.757377 | + | 0.652978i | \(0.773519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2259.03 | 0.940870 | ||||||||
\(50\) | 677.714 | + | 1895.72i | 0.271086 | + | 0.758287i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 458.694 | − | 376.021i | 0.169635 | − | 0.139061i | ||||
\(53\) | −1415.13 | −0.503783 | −0.251892 | − | 0.967755i | \(-0.581053\pi\) | ||||
−0.251892 | + | 0.967755i | \(0.581053\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2420.19i | 0.800062i | ||||||||
\(56\) | −392.576 | + | 653.757i | −0.125184 | + | 0.208469i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1653.95 | − | 4626.47i | −0.491662 | − | 1.37529i | ||||
\(59\) | 2832.86i | 0.813808i | 0.913471 | + | 0.406904i | \(0.133392\pi\) | ||||
−0.913471 | + | 0.406904i | \(0.866608\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5257.27 | −1.41287 | −0.706433 | − | 0.707780i | \(-0.749697\pi\) | ||||
−0.706433 | + | 0.707780i | \(0.749697\pi\) | |||||||
\(62\) | 5705.44 | − | 2039.68i | 1.48425 | − | 0.530614i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1924.92 | + | 3615.51i | 0.469950 | + | 0.882693i | ||||
\(65\) | 408.941 | 0.0967909 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 930.592i | − | 0.207305i | −0.994614 | − | 0.103653i | \(-0.966947\pi\) | ||
0.994614 | − | 0.103653i | \(-0.0330530\pi\) | |||||||
\(68\) | 3514.39 | − | 2880.97i | 0.760033 | − | 0.623048i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −495.087 | + | 176.992i | −0.101038 | + | 0.0361209i | ||||
\(71\) | 1162.75i | 0.230659i | 0.993327 | + | 0.115329i | \(0.0367923\pi\) | ||||
−0.993327 | + | 0.115329i | \(0.963208\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2162.87 | −0.405867 | −0.202934 | − | 0.979192i | \(-0.565048\pi\) | ||||
−0.202934 | + | 0.979192i | \(0.565048\pi\) | |||||||
\(74\) | 2048.47 | + | 5730.02i | 0.374081 | + | 1.04639i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 461.430 | + | 562.881i | 0.0798875 | + | 0.0974518i | ||||
\(77\) | 2614.04 | 0.440890 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7485.40i | 1.19939i | 0.800229 | + | 0.599695i | \(0.204711\pi\) | ||||
−0.800229 | + | 0.599695i | \(0.795289\pi\) | |||||||
\(80\) | −553.978 | + | 2769.22i | −0.0865591 | + | 0.432690i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3546.69 | − | 9920.88i | −0.527467 | − | 1.47544i | ||||
\(83\) | 1116.31i | 0.162043i | 0.996712 | + | 0.0810215i | \(0.0258182\pi\) | ||||
−0.996712 | + | 0.0810215i | \(0.974182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3133.20 | 0.433661 | ||||||||
\(86\) | −150.508 | + | 53.8064i | −0.0203500 | + | 0.00727506i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7228.27 | − | 12037.3i | 0.933403 | − | 1.55440i | ||||
\(89\) | 6739.71 | 0.850866 | 0.425433 | − | 0.904990i | \(-0.360122\pi\) | ||||
0.425433 | + | 0.904990i | \(0.360122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 441.696i | − | 0.0533385i | ||||||
\(92\) | −2041.75 | − | 2490.66i | −0.241228 | − | 0.294265i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10865.9 | − | 3884.55i | 1.22974 | − | 0.439627i | ||||
\(95\) | 501.828i | 0.0556042i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12046.6 | 1.28032 | 0.640161 | − | 0.768240i | \(-0.278867\pi\) | ||||
0.640161 | + | 0.768240i | \(0.278867\pi\) | |||||||
\(98\) | −3041.85 | − | 8508.73i | −0.316727 | − | 0.885957i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6227.74 | − | 5105.28i | 0.622774 | − | 0.510528i | ||||
\(101\) | 9555.20 | 0.936692 | 0.468346 | − | 0.883545i | \(-0.344850\pi\) | ||||
0.468346 | + | 0.883545i | \(0.344850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11503.4i | 1.08431i | 0.840279 | + | 0.542154i | \(0.182391\pi\) | ||||
−0.840279 | + | 0.542154i | \(0.817609\pi\) | |||||||
\(104\) | −2033.95 | − | 1221.37i | −0.188050 | − | 0.112922i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1905.51 | + | 5330.14i | 0.169590 | + | 0.474380i | ||||
\(107\) | 6602.72i | 0.576707i | 0.957524 | + | 0.288353i | \(0.0931078\pi\) | ||||
−0.957524 | + | 0.288353i | \(0.906892\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12045.3 | 1.01383 | 0.506913 | − | 0.861997i | \(-0.330786\pi\) | ||||
0.506913 | + | 0.861997i | \(0.330786\pi\) | |||||||
\(110\) | 9115.74 | − | 3258.86i | 0.753367 | − | 0.269327i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2991.02 | + | 598.350i | 0.238442 | + | 0.0477001i | ||||
\(113\) | −3730.69 | −0.292168 | −0.146084 | − | 0.989272i | \(-0.546667\pi\) | ||||
−0.146084 | + | 0.989272i | \(0.546667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 2220.50i | − | 0.167902i | ||||||
\(116\) | −15198.7 | + | 12459.4i | −1.12951 | + | 0.925933i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10670.1 | − | 3814.54i | 0.766311 | − | 0.273954i | ||||
\(119\) | − | 3384.16i | − | 0.238977i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −33489.7 | −2.28739 | ||||||||
\(122\) | 7079.08 | + | 19801.7i | 0.475617 | + | 1.33041i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15365.1 | − | 18743.3i | −0.999291 | − | 1.21900i | ||||
\(125\) | 12447.0 | 0.796607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26549.7i | 1.64608i | 0.567980 | + | 0.823042i | \(0.307725\pi\) | ||||
−0.567980 | + | 0.823042i | \(0.692275\pi\) | |||||||
\(128\) | 11026.0 | − | 12118.7i | 0.672975 | − | 0.739665i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −550.652 | − | 1540.30i | −0.0325830 | − | 0.0911418i | ||||
\(131\) | − | 1319.64i | − | 0.0768978i | −0.999261 | − | 0.0384489i | \(-0.987758\pi\) | ||
0.999261 | − | 0.0384489i | \(-0.0122417\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 542.022 | 0.0306418 | ||||||||
\(134\) | −3505.12 | + | 1253.07i | −0.195206 | + | 0.0697856i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15583.6 | − | 9357.79i | −0.842537 | − | 0.505936i | ||||
\(137\) | −25812.9 | −1.37530 | −0.687648 | − | 0.726044i | \(-0.741357\pi\) | ||||
−0.687648 | + | 0.726044i | \(0.741357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13138.0i | 0.679985i | 0.940428 | + | 0.339993i | \(0.110425\pi\) | ||||
−0.940428 | + | 0.339993i | \(0.889575\pi\) | |||||||
\(140\) | 1333.30 | + | 1626.44i | 0.0680254 | + | 0.0829816i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4379.55 | − | 1565.68i | 0.217197 | − | 0.0776472i | ||||
\(143\) | 8132.70i | 0.397706i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13550.2 | −0.644478 | ||||||||
\(146\) | 2912.37 | + | 8146.54i | 0.136628 | + | 0.382179i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18824.0 | − | 15431.3i | 0.859388 | − | 0.704496i | ||||
\(149\) | −25936.4 | −1.16826 | −0.584128 | − | 0.811662i | \(-0.698563\pi\) | ||||
−0.584128 | + | 0.811662i | \(0.698563\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 28395.5i | 1.24536i | 0.782475 | + | 0.622681i | \(0.213957\pi\) | ||||
−0.782475 | + | 0.622681i | \(0.786043\pi\) | |||||||
\(152\) | 1498.79 | − | 2495.93i | 0.0648714 | − | 0.108030i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3519.88 | − | 9845.88i | −0.148418 | − | 0.415158i | ||||
\(155\) | − | 16710.3i | − | 0.695538i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5520.37 | −0.223959 | −0.111980 | − | 0.993711i | \(-0.535719\pi\) | ||||
−0.111980 | + | 0.993711i | \(0.535719\pi\) | |||||||
\(158\) | 28194.1 | − | 10079.3i | 1.12939 | − | 0.403754i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 11176.3 | − | 1642.25i | 0.436575 | − | 0.0641504i | ||||
\(161\) | −2398.36 | −0.0925257 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 407.281i | − | 0.0153292i | −0.999971 | − | 0.00766459i | \(-0.997560\pi\) | ||
0.999971 | − | 0.00766459i | \(-0.00243974\pi\) | |||||||
\(164\) | −32591.7 | + | 26717.5i | −1.21177 | + | 0.993365i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4204.65 | − | 1503.15i | 0.152586 | − | 0.0545490i | ||||
\(167\) | − | 23742.9i | − | 0.851334i | −0.904880 | − | 0.425667i | \(-0.860040\pi\) | ||
0.904880 | − | 0.425667i | \(-0.139960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27186.8 | −0.951886 | ||||||||
\(170\) | −4218.95 | − | 11801.3i | −0.145984 | − | 0.408351i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 405.328 | + | 494.444i | 0.0137009 | + | 0.0167132i | ||||
\(173\) | 2826.49 | 0.0944400 | 0.0472200 | − | 0.998885i | \(-0.484964\pi\) | ||||
0.0472200 | + | 0.998885i | \(0.484964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 5996.96i | − | 0.195819i | ||||||
\(176\) | −55072.0 | − | 11017.1i | −1.77789 | − | 0.355665i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9075.23 | − | 25385.4i | −0.286429 | − | 0.801206i | ||||
\(179\) | − | 45743.4i | − | 1.42765i | −0.700323 | − | 0.713826i | \(-0.746961\pi\) | ||
0.700323 | − | 0.713826i | \(-0.253039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24226.2 | −0.739483 | −0.369742 | − | 0.929135i | \(-0.620554\pi\) | ||||
−0.369742 | + | 0.929135i | \(0.620554\pi\) | |||||||
\(182\) | −1663.67 | + | 594.757i | −0.0502255 | + | 0.0179555i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6631.89 | + | 11044.1i | −0.195885 | + | 0.326208i | ||||
\(185\) | 16782.3 | 0.490351 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 62310.5i | 1.78188i | ||||||||
\(188\) | −29262.6 | − | 35696.4i | −0.827938 | − | 1.00997i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1890.16 | − | 675.726i | 0.0523589 | − | 0.0187182i | ||||
\(191\) | 22522.0i | 0.617362i | 0.951166 | + | 0.308681i | \(0.0998875\pi\) | ||||
−0.951166 | + | 0.308681i | \(0.900112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18288.7 | 0.490985 | 0.245493 | − | 0.969398i | \(-0.421050\pi\) | ||||
0.245493 | + | 0.969398i | \(0.421050\pi\) | |||||||
\(194\) | −16221.1 | − | 45373.9i | −0.430998 | − | 1.20560i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −27952.6 | + | 22914.5i | −0.727628 | + | 0.596484i | ||||
\(197\) | −36300.2 | −0.935356 | −0.467678 | − | 0.883899i | \(-0.654909\pi\) | ||||
−0.467678 | + | 0.883899i | \(0.654909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 47336.5i | 1.19533i | 0.801744 | + | 0.597667i | \(0.203906\pi\) | ||||
−0.801744 | + | 0.597667i | \(0.796094\pi\) | |||||||
\(200\) | −27615.1 | − | 16582.6i | −0.690378 | − | 0.414566i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12866.4 | − | 35990.1i | −0.315321 | − | 0.882023i | ||||
\(203\) | 14635.5i | 0.355152i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29056.6 | −0.691412 | ||||||||
\(206\) | 43328.2 | − | 15489.7i | 1.02102 | − | 0.365014i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1861.57 | + | 9305.56i | −0.0430280 | + | 0.215088i | ||||
\(209\) | −9979.95 | −0.228473 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 46490.2i | 1.04423i | 0.852875 | + | 0.522115i | \(0.174857\pi\) | ||||
−0.852875 | + | 0.522115i | \(0.825143\pi\) | |||||||
\(212\) | 17510.4 | − | 14354.4i | 0.389604 | − | 0.319384i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 24869.4 | − | 8890.76i | 0.543048 | − | 0.194138i | ||||
\(215\) | 440.814i | 0.00953626i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18048.7 | −0.383290 | ||||||||
\(218\) | −16219.3 | − | 45369.1i | −0.341287 | − | 0.954656i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −24549.3 | − | 29946.7i | −0.507216 | − | 0.618734i | ||||
\(221\) | 10528.7 | 0.215570 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 82597.9i | − | 1.66096i | −0.557048 | − | 0.830480i | \(-0.688066\pi\) | ||
0.557048 | − | 0.830480i | \(-0.311934\pi\) | |||||||
\(224\) | −1773.79 | − | 12071.5i | −0.0353514 | − | 0.240583i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5023.49 | + | 14051.8i | 0.0983533 | + | 0.275116i | ||||
\(227\) | − | 29701.6i | − | 0.576405i | −0.957569 | − | 0.288203i | \(-0.906942\pi\) | ||
0.957569 | − | 0.288203i | \(-0.0930577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 45335.9 | 0.864512 | 0.432256 | − | 0.901751i | \(-0.357718\pi\) | ||||
0.432256 | + | 0.901751i | \(0.357718\pi\) | |||||||
\(230\) | −8363.63 | + | 2989.98i | −0.158103 | + | 0.0565213i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 67394.2 | + | 40469.7i | 1.25212 | + | 0.751889i | ||||
\(233\) | −50931.3 | −0.938151 | −0.469075 | − | 0.883158i | \(-0.655413\pi\) | ||||
−0.469075 | + | 0.883158i | \(0.655413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 31824.5i | − | 0.576270i | ||||||
\(236\) | −28735.3 | − | 35053.1i | −0.515930 | − | 0.629364i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12746.6 | + | 4556.87i | −0.225030 | + | 0.0804475i | ||||
\(239\) | − | 36888.3i | − | 0.645792i | −0.946434 | − | 0.322896i | \(-0.895344\pi\) | ||
0.946434 | − | 0.322896i | \(-0.104656\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8387.27 | 0.144407 | 0.0722033 | − | 0.997390i | \(-0.476997\pi\) | ||||
0.0722033 | + | 0.997390i | \(0.476997\pi\) | |||||||
\(242\) | 45094.9 | + | 126141.i | 0.770011 | + | 2.15389i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 65052.0 | − | 53327.3i | 1.09265 | − | 0.895715i | ||||
\(245\) | −24920.7 | −0.415171 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1686.32i | 0.0276405i | ||||||||
\(248\) | −49907.9 | + | 83111.8i | −0.811458 | + | 1.35132i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16760.2 | − | 46882.1i | −0.268164 | − | 0.750114i | ||||
\(251\) | − | 1475.47i | − | 0.0234198i | −0.999931 | − | 0.0117099i | \(-0.996273\pi\) | ||
0.999931 | − | 0.0117099i | \(-0.00372746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44159.6 | 0.689897 | ||||||||
\(254\) | 100001. | − | 35750.0i | 1.55001 | − | 0.554126i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −60492.4 | − | 25211.8i | −0.923041 | − | 0.384702i | ||||
\(257\) | −34673.1 | −0.524960 | −0.262480 | − | 0.964937i | \(-0.584540\pi\) | ||||
−0.262480 | + | 0.964937i | \(0.584540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 18126.5i | − | 0.270218i | ||||||
\(260\) | −5060.12 | + | 4148.11i | −0.0748539 | + | 0.0613626i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4970.49 | + | 1776.94i | −0.0724097 | + | 0.0258863i | ||||
\(263\) | 19032.4i | 0.275158i | 0.990491 | + | 0.137579i | \(0.0439321\pi\) | ||||
−0.990491 | + | 0.137579i | \(0.956068\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15611.1 | 0.222301 | ||||||||
\(266\) | −729.850 | − | 2041.55i | −0.0103150 | − | 0.0288534i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9439.50 | + | 11514.9i | 0.131425 | + | 0.160321i | ||||
\(269\) | −58724.1 | −0.811544 | −0.405772 | − | 0.913974i | \(-0.632997\pi\) | ||||
−0.405772 | + | 0.913974i | \(0.632997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31474.1i | − | 0.428563i | −0.976772 | − | 0.214281i | \(-0.931259\pi\) | ||
0.976772 | − | 0.214281i | \(-0.0687409\pi\) | |||||||
\(272\) | −14262.8 | + | 71296.7i | −0.192782 | + | 0.963677i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 34757.9 | + | 97225.5i | 0.462969 | + | 1.29503i | ||||
\(275\) | 110418.i | 1.46008i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 66531.5 | 0.867098 | 0.433549 | − | 0.901130i | \(-0.357261\pi\) | ||||
0.433549 | + | 0.901130i | \(0.357261\pi\) | |||||||
\(278\) | 49484.8 | − | 17690.7i | 0.640299 | − | 0.228905i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4330.73 | − | 7211.98i | 0.0552389 | − | 0.0919895i | ||||
\(281\) | 123720. | 1.56685 | 0.783424 | − | 0.621488i | \(-0.213471\pi\) | ||||
0.783424 | + | 0.621488i | \(0.213471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 54735.0i | 0.683427i | 0.939804 | + | 0.341713i | \(0.111007\pi\) | ||||
−0.939804 | + | 0.341713i | \(0.888993\pi\) | |||||||
\(284\) | −11794.4 | − | 14387.5i | −0.146231 | − | 0.178382i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 30632.2 | − | 10950.9i | 0.374495 | − | 0.133881i | ||||
\(287\) | 31383.9i | 0.381016i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2853.15 | −0.0341609 | ||||||||
\(290\) | 18245.7 | + | 51037.2i | 0.216952 | + | 0.606864i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26762.7 | − | 21939.1i | 0.313880 | − | 0.257308i | ||||
\(293\) | 88617.9 | 1.03225 | 0.516127 | − | 0.856512i | \(-0.327373\pi\) | ||||
0.516127 | + | 0.856512i | \(0.327373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 31251.0i | − | 0.359103i | ||||||
\(296\) | −83469.8 | − | 50122.9i | −0.952677 | − | 0.572075i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 34924.2 | + | 97690.7i | 0.393273 | + | 1.10007i | ||||
\(299\) | − | 7461.69i | − | 0.0834632i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 476.121 | 0.00525514 | ||||||||
\(302\) | 106953. | − | 38235.4i | 1.17268 | − | 0.419230i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11419.2 | − | 2284.40i | −0.123563 | − | 0.0247186i | ||||
\(305\) | 57996.0 | 0.623446 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 123447.i | − | 1.30980i | −0.755716 | − | 0.654900i | \(-0.772711\pi\) | ||
0.755716 | − | 0.654900i | \(-0.227289\pi\) | |||||||
\(308\) | −32345.3 | + | 26515.6i | −0.340965 | + | 0.279511i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −62940.1 | + | 22500.9i | −0.654943 | + | 0.234141i | ||||
\(311\) | − | 60543.1i | − | 0.625956i | −0.949760 | − | 0.312978i | \(-0.898673\pi\) | ||
0.949760 | − | 0.312978i | \(-0.101327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −52386.2 | −0.534722 | −0.267361 | − | 0.963596i | \(-0.586152\pi\) | ||||
−0.267361 | + | 0.963596i | \(0.586152\pi\) | |||||||
\(314\) | 7433.35 | + | 20792.7i | 0.0753920 | + | 0.210888i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −75928.4 | − | 92622.1i | −0.760378 | − | 0.927557i | ||||
\(317\) | 25997.4 | 0.258708 | 0.129354 | − | 0.991598i | \(-0.458710\pi\) | ||||
0.129354 | + | 0.991598i | \(0.458710\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 269474.i | − | 2.64811i | ||||||
\(320\) | −21234.9 | − | 39884.8i | −0.207372 | − | 0.389500i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3229.46 | + | 9033.52i | 0.0311472 | + | 0.0871255i | ||||
\(323\) | 12920.1i | 0.123840i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18657.5 | 0.176639 | ||||||||
\(326\) | −1534.04 | + | 548.416i | −0.0144345 | + | 0.00516030i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 144518. | + | 86782.1i | 1.34331 | + | 0.806645i | ||||
\(329\) | −34373.6 | −0.317565 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 43231.1i | 0.394584i | 0.980345 | + | 0.197292i | \(0.0632148\pi\) | ||||
−0.980345 | + | 0.197292i | \(0.936785\pi\) | |||||||
\(332\) | −11323.4 | − | 13812.9i | −0.102731 | − | 0.125317i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −89428.5 | + | 31970.5i | −0.801647 | + | 0.286587i | ||||
\(335\) | 10265.9i | 0.0914761i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11852.8 | 0.104366 | 0.0521831 | − | 0.998638i | \(-0.483382\pi\) | ||||
0.0521831 | + | 0.998638i | \(0.483382\pi\) | |||||||
\(338\) | 36607.9 | + | 102400.i | 0.320436 | + | 0.896330i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −38769.3 | + | 31781.7i | −0.335375 | + | 0.274928i | ||||
\(341\) | 332321. | 2.85791 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 55525.0i | 0.471955i | ||||||||
\(344\) | 1316.56 | − | 2192.47i | 0.0111256 | − | 0.0185275i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3805.96 | − | 10646.1i | −0.0317916 | − | 0.0889281i | ||||
\(347\) | 29124.4i | 0.241879i | 0.992660 | + | 0.120940i | \(0.0385907\pi\) | ||||
−0.992660 | + | 0.120940i | \(0.961409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 119977. | 0.985023 | 0.492512 | − | 0.870306i | \(-0.336079\pi\) | ||||
0.492512 | + | 0.870306i | \(0.336079\pi\) | |||||||
\(350\) | −22587.8 | + | 8075.08i | −0.184390 | + | 0.0659191i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 32659.8 | + | 222266.i | 0.263589 | + | 1.79385i | ||||
\(353\) | −154758. | −1.24195 | −0.620975 | − | 0.783831i | \(-0.713263\pi\) | ||||
−0.620975 | + | 0.783831i | \(0.713263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 12827.0i | − | 0.101781i | ||||||
\(356\) | −83395.3 | + | 68364.5i | −0.658023 | + | 0.539424i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −172294. | + | 61594.9i | −1.34433 | + | 0.480594i | ||||
\(359\) | 66839.6i | 0.518615i | 0.965795 | + | 0.259307i | \(0.0834942\pi\) | ||||
−0.965795 | + | 0.259307i | \(0.916506\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 128252. | 0.984121 | ||||||||
\(362\) | 32621.3 | + | 91249.1i | 0.248934 | + | 0.696324i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4480.36 | + | 5465.42i | 0.0338151 | + | 0.0412497i | ||||
\(365\) | 23859.8 | 0.179094 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 94571.4i | − | 0.702147i | −0.936348 | − | 0.351073i | \(-0.885817\pi\) | ||
0.936348 | − | 0.351073i | \(-0.114183\pi\) | |||||||
\(368\) | 50528.1 | + | 10108.1i | 0.373110 | + | 0.0746403i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22597.8 | − | 63211.2i | −0.165068 | − | 0.461732i | ||||
\(371\) | − | 16861.5i | − | 0.122503i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −181061. | −1.30139 | −0.650694 | − | 0.759340i | \(-0.725522\pi\) | ||||
−0.650694 | + | 0.759340i | \(0.725522\pi\) | |||||||
\(374\) | 234695. | − | 83903.0i | 1.67788 | − | 0.599839i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −95049.0 | + | 158285.i | −0.672313 | + | 1.11960i | ||||
\(377\) | −45533.4 | −0.320366 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 51191.3i | 0.356384i | 0.983996 | + | 0.178192i | \(0.0570248\pi\) | ||||
−0.983996 | + | 0.178192i | \(0.942975\pi\) | |||||||
\(380\) | −5090.31 | − | 6209.47i | −0.0352514 | − | 0.0430019i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 84830.0 | − | 30326.5i | 0.581330 | − | 0.207824i | ||||
\(383\) | − | 152568.i | − | 1.04008i | −0.854143 | − | 0.520039i | \(-0.825917\pi\) | ||
0.854143 | − | 0.520039i | \(-0.174083\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28836.9 | −0.194548 | ||||||||
\(386\) | −24626.3 | − | 68885.2i | −0.165282 | − | 0.462329i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −149061. | + | 122195.i | −0.990147 | + | 0.811687i | ||||
\(389\) | −67896.8 | −0.448694 | −0.224347 | − | 0.974509i | \(-0.572025\pi\) | ||||
−0.224347 | + | 0.974509i | \(0.572025\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 57169.5i | − | 0.373947i | ||||||
\(392\) | 123948. | + | 74429.5i | 0.806614 | + | 0.484365i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 48879.4 | + | 136726.i | 0.314871 | + | 0.880765i | ||||
\(395\) | − | 82575.7i | − | 0.529247i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −126087. | −0.799998 | −0.399999 | − | 0.916516i | \(-0.630990\pi\) | ||||
−0.399999 | + | 0.916516i | \(0.630990\pi\) | |||||||
\(398\) | 178295. | − | 63740.0i | 1.12557 | − | 0.402389i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −25274.7 | + | 126343.i | −0.157967 | + | 0.789641i | ||||
\(401\) | −70890.8 | −0.440860 | −0.220430 | − | 0.975403i | \(-0.570746\pi\) | ||||
−0.220430 | + | 0.975403i | \(0.570746\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 56152.6i | − | 0.345748i | ||||||
\(404\) | −118233. | + | 96923.5i | −0.724398 | + | 0.593836i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 55125.1 | − | 19707.1i | 0.334424 | − | 0.119556i | ||||
\(407\) | 333752.i | 2.01482i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 43544.2 | 0.260306 | 0.130153 | − | 0.991494i | \(-0.458453\pi\) | ||||
0.130153 | + | 0.991494i | \(0.458453\pi\) | |||||||
\(410\) | 39125.6 | + | 109443.i | 0.232752 | + | 0.651059i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −116685. | − | 142340.i | −0.687420 | − | 0.838557i | ||||
\(413\) | −33754.1 | −0.197891 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12314.7i | − | 0.0715036i | ||||||
\(416\) | 37556.5 | − | 5518.55i | 0.217019 | − | 0.0318888i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13438.3 | + | 37589.9i | 0.0769116 | + | 0.215139i | ||||
\(419\) | 210600.i | 1.19958i | 0.800156 | + | 0.599792i | \(0.204750\pi\) | ||||
−0.800156 | + | 0.599792i | \(0.795250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 84126.0 | 0.474642 | 0.237321 | − | 0.971431i | \(-0.423731\pi\) | ||||
0.237321 | + | 0.971431i | \(0.423731\pi\) | |||||||
\(422\) | 175107. | − | 62600.4i | 0.983285 | − | 0.351522i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −77644.7 | − | 46625.0i | −0.431897 | − | 0.259350i | ||||
\(425\) | 142949. | 0.791413 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 62641.3i | − | 0.343562i | ||||||
\(428\) | −66974.9 | − | 81700.1i | −0.365615 | − | 0.446000i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1660.34 | − | 593.569i | 0.00897969 | − | 0.00321022i | ||||
\(431\) | 150083.i | 0.807933i | 0.914774 | + | 0.403967i | \(0.132369\pi\) | ||||
−0.914774 | + | 0.403967i | \(0.867631\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 71221.5 | 0.379871 | 0.189935 | − | 0.981797i | \(-0.439172\pi\) | ||||
0.189935 | + | 0.981797i | \(0.439172\pi\) | |||||||
\(434\) | 24303.2 | + | 67981.3i | 0.129028 | + | 0.360919i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −149045. | + | 122182.i | −0.784050 | + | 0.642736i | ||||
\(437\) | 9156.53 | 0.0479477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 109245.i | − | 0.566858i | −0.958993 | − | 0.283429i | \(-0.908528\pi\) | ||
0.958993 | − | 0.283429i | \(-0.0914720\pi\) | |||||||
\(440\) | −79739.3 | + | 132790.i | −0.411876 | + | 0.685899i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14177.2 | − | 39656.7i | −0.0725680 | − | 0.202989i | ||||
\(443\) | − | 230658.i | − | 1.17533i | −0.809103 | − | 0.587666i | \(-0.800047\pi\) | ||
0.809103 | − | 0.587666i | \(-0.199953\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −74349.7 | −0.375456 | ||||||||
\(446\) | −311109. | + | 111221.i | −1.56402 | + | 0.559133i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −43079.4 | + | 22935.7i | −0.214642 | + | 0.114276i | ||||
\(449\) | 9751.64 | 0.0483710 | 0.0241855 | − | 0.999707i | \(-0.492301\pi\) | ||||
0.0241855 | + | 0.999707i | \(0.492301\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 577854.i | − | 2.84096i | ||||||
\(452\) | 46162.5 | − | 37842.4i | 0.225950 | − | 0.185226i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −111872. | + | 39994.1i | −0.542764 | + | 0.194037i | ||||
\(455\) | 4872.61i | 0.0235363i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 66139.1 | 0.316684 | 0.158342 | − | 0.987384i | \(-0.449385\pi\) | ||||
0.158342 | + | 0.987384i | \(0.449385\pi\) | |||||||
\(458\) | −61046.1 | − | 170760.i | −0.291023 | − | 0.814056i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 22523.8 | + | 27475.9i | 0.106445 | + | 0.129848i | ||||
\(461\) | 173989. | 0.818692 | 0.409346 | − | 0.912379i | \(-0.365757\pi\) | ||||
0.409346 | + | 0.912379i | \(0.365757\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 173993.i | 0.811650i | 0.913951 | + | 0.405825i | \(0.133016\pi\) | ||||
−0.913951 | + | 0.405825i | \(0.866984\pi\) | |||||||
\(464\) | 61682.4 | − | 308337.i | 0.286500 | − | 1.43215i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 68580.5 | + | 191835.i | 0.315812 | + | 0.883397i | ||||
\(467\) | 172090.i | 0.789080i | 0.918879 | + | 0.394540i | \(0.129096\pi\) | ||||
−0.918879 | + | 0.394540i | \(0.870904\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11088.2 | 0.0504097 | ||||||||
\(470\) | −119868. | + | 42852.7i | −0.542637 | + | 0.193991i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −93336.0 | + | 155433.i | −0.418953 | + | 0.697683i | ||||
\(473\) | −8766.55 | −0.0391838 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22895.4i | 0.101475i | ||||||||
\(476\) | 34327.3 | + | 41874.6i | 0.151505 | + | 0.184815i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −138941. | + | 49671.2i | −0.608101 | + | 0.217395i | ||||
\(479\) | − | 218398.i | − | 0.951869i | −0.879481 | − | 0.475935i | \(-0.842110\pi\) | ||
0.879481 | − | 0.475935i | \(-0.157890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56394.4 | 0.243751 | ||||||||
\(482\) | −11293.7 | − | 31591.0i | −0.0486119 | − | 0.135978i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 414392. | − | 339704.i | 1.76897 | − | 1.45014i | ||||
\(485\) | −132893. | −0.564959 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 392112.i | 1.65330i | 0.562716 | + | 0.826650i | \(0.309757\pi\) | ||||
−0.562716 | + | 0.826650i | \(0.690243\pi\) | |||||||
\(488\) | −288454. | − | 173214.i | −1.21126 | − | 0.727351i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 33556.4 | + | 93864.8i | 0.139760 | + | 0.390940i | ||||
\(491\) | 209717.i | 0.869903i | 0.900454 | + | 0.434951i | \(0.143234\pi\) | ||||
−0.900454 | + | 0.434951i | \(0.856766\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −348864. | −1.43537 | ||||||||
\(494\) | 6351.60 | − | 2270.68i | 0.0260273 | − | 0.00930470i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 380247. | + | 76067.9i | 1.54562 | + | 0.309199i | ||||
\(497\) | −13854.4 | −0.0560885 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 135886.i | − | 0.545725i | −0.962053 | − | 0.272862i | \(-0.912030\pi\) | ||
0.962053 | − | 0.272862i | \(-0.0879704\pi\) | |||||||
\(500\) | −154015. | + | 126256.i | −0.616061 | + | 0.505025i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5557.42 | + | 1986.76i | −0.0220529 | + | 0.00788385i | ||||
\(503\) | − | 232332.i | − | 0.918275i | −0.888365 | − | 0.459137i | \(-0.848159\pi\) | ||
0.888365 | − | 0.459137i | \(-0.151841\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −105409. | −0.413328 | ||||||||
\(506\) | −59462.2 | − | 166329.i | −0.232242 | − | 0.649632i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −269308. | − | 328518.i | −1.04357 | − | 1.27301i | ||||
\(509\) | 145319. | 0.560901 | 0.280451 | − | 0.959868i | \(-0.409516\pi\) | ||||
0.280451 | + | 0.959868i | \(0.409516\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 25770.9i | − | 0.0986935i | ||||||
\(512\) | −13506.6 | + | 261796.i | −0.0515234 | + | 0.998672i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 46688.3 | + | 130598.i | 0.176719 | + | 0.494321i | ||||
\(515\) | − | 126901.i | − | 0.478465i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 632900. | 2.36785 | ||||||||
\(518\) | −68274.1 | + | 24407.8i | −0.254447 | + | 0.0909641i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22437.7 | + | 13473.6i | 0.0829795 | + | 0.0498285i | ||||
\(521\) | −443088. | −1.63235 | −0.816177 | − | 0.577803i | \(-0.803910\pi\) | ||||
−0.816177 | + | 0.577803i | \(0.803910\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 73202.4i | − | 0.267622i | −0.991007 | − | 0.133811i | \(-0.957278\pi\) | ||
0.991007 | − | 0.133811i | \(-0.0427215\pi\) | |||||||
\(524\) | 13385.8 | + | 16328.9i | 0.0487509 | + | 0.0594694i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 71686.3 | − | 25627.7i | 0.259098 | − | 0.0926271i | ||||
\(527\) | − | 430226.i | − | 1.54909i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 239325. | 0.855217 | ||||||||
\(530\) | −21020.8 | − | 58799.9i | −0.0748338 | − | 0.209327i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6706.83 | + | 5498.02i | −0.0236970 | + | 0.0194260i | ||||
\(533\) | −97640.6 | −0.343697 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 72838.4i | − | 0.254480i | ||||||
\(536\) | 30660.7 | − | 51059.4i | 0.106722 | − | 0.177724i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 79073.8 | + | 221187.i | 0.273192 | + | 0.764179i | ||||
\(539\) | − | 495602.i | − | 1.70591i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 438165. | 1.49707 | 0.748536 | − | 0.663094i | \(-0.230757\pi\) | ||||
0.748536 | + | 0.663094i | \(0.230757\pi\) | |||||||
\(542\) | −118548. | + | 42380.8i | −0.403550 | + | 0.144268i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 287748. | − | 42281.7i | 0.972330 | − | 0.142874i | ||||
\(545\) | −132878. | −0.447364 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 312024.i | − | 1.04283i | −0.853303 | − | 0.521416i | \(-0.825404\pi\) | ||
0.853303 | − | 0.521416i | \(-0.174596\pi\) | |||||||
\(548\) | 319402. | − | 261834.i | 1.06359 | − | 0.871898i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 415896. | − | 148682.i | 1.37486 | − | 0.491510i | ||||
\(551\) | − | 55875.7i | − | 0.184043i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −89189.8 | −0.291652 | ||||||||
\(554\) | −89586.7 | − | 250594.i | −0.291893 | − | 0.816490i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −133266. | − | 162566.i | −0.431091 | − | 0.525871i | ||||
\(557\) | −312549. | −1.00741 | −0.503707 | − | 0.863874i | \(-0.668031\pi\) | ||||
−0.503707 | + | 0.863874i | \(0.668031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1481.29i | 0.00474042i | ||||||||
\(560\) | −32995.7 | − | 6600.75i | −0.105216 | − | 0.0210483i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −166593. | − | 465996.i | −0.527452 | − | 1.47540i | ||||
\(563\) | − | 86349.2i | − | 0.272422i | −0.990680 | − | 0.136211i | \(-0.956508\pi\) | ||
0.990680 | − | 0.136211i | \(-0.0434925\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 41155.5 | 0.128923 | ||||||||
\(566\) | 206162. | − | 73702.3i | 0.643539 | − | 0.230064i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −38309.8 | + | 63797.4i | −0.118744 | + | 0.197745i | ||||
\(569\) | −554958. | −1.71410 | −0.857049 | − | 0.515235i | \(-0.827705\pi\) | ||||
−0.857049 | + | 0.515235i | \(0.827705\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 303511.i | 0.930898i | 0.885075 | + | 0.465449i | \(0.154107\pi\) | ||||
−0.885075 | + | 0.465449i | \(0.845893\pi\) | |||||||
\(572\) | −82494.3 | − | 100632.i | −0.252134 | − | 0.307569i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 118209. | − | 42259.4i | 0.358779 | − | 0.128263i | ||||
\(575\) | − | 101308.i | − | 0.306414i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −500884. | −1.50448 | −0.752238 | − | 0.658892i | \(-0.771026\pi\) | ||||
−0.752238 | + | 0.658892i | \(0.771026\pi\) | |||||||
\(578\) | 3841.86 | + | 10746.5i | 0.0114997 | + | 0.0321671i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 167666. | − | 137446.i | 0.498412 | − | 0.408580i | ||||
\(581\) | −13301.1 | −0.0394035 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 310461.i | 0.913418i | ||||||||
\(584\) | −118671. | − | 71261.2i | −0.347953 | − | 0.208943i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −119327. | − | 333783.i | −0.347490 | − | 0.972007i | ||||
\(587\) | 575710.i | 1.67081i | 0.549633 | + | 0.835406i | \(0.314767\pi\) | ||||
−0.549633 | + | 0.835406i | \(0.685233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 68907.0 | 0.198624 | ||||||||
\(590\) | −117708. | + | 42080.4i | −0.338145 | + | 0.120886i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −76395.5 | + | 381885.i | −0.217984 | + | 1.08965i | ||||
\(593\) | 138143. | 0.392843 | 0.196421 | − | 0.980520i | \(-0.437068\pi\) | ||||
0.196421 | + | 0.980520i | \(0.437068\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 37332.6i | 0.105452i | ||||||||
\(596\) | 320930. | − | 263087.i | 0.903478 | − | 0.740640i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28104.8 | + | 10047.4i | −0.0785919 | + | 0.0280964i | ||||
\(599\) | − | 191294.i | − | 0.533147i | −0.963815 | − | 0.266574i | \(-0.914108\pi\) | ||
0.963815 | − | 0.266574i | \(-0.0858916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −406240. | −1.12469 | −0.562346 | − | 0.826902i | \(-0.690101\pi\) | ||||
−0.562346 | + | 0.826902i | \(0.690101\pi\) | |||||||
\(602\) | −641.112 | − | 1793.33i | −0.00176905 | − | 0.00494843i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −288031. | − | 351358.i | −0.789524 | − | 0.963110i | ||||
\(605\) | 369445. | 1.00934 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 68666.5i | − | 0.186366i | −0.995649 | − | 0.0931831i | \(-0.970296\pi\) | ||
0.995649 | − | 0.0931831i | \(-0.0297042\pi\) | |||||||
\(608\) | 6772.03 | + | 46087.0i | 0.0183194 | + | 0.124673i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −78093.4 | − | 218445.i | −0.209872 | − | 0.587059i | ||||
\(611\) | − | 106942.i | − | 0.286461i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −572114. | −1.52252 | −0.761258 | − | 0.648450i | \(-0.775418\pi\) | ||||
−0.761258 | + | 0.648450i | \(0.775418\pi\) | |||||||
\(614\) | −464970. | + | 166225.i | −1.23335 | + | 0.440921i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 143426. | + | 86126.1i | 0.377978 | + | 0.226973i | ||||
\(617\) | −20380.8 | −0.0535367 | −0.0267684 | − | 0.999642i | \(-0.508522\pi\) | ||||
−0.0267684 | + | 0.999642i | \(0.508522\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 448721.i | 1.17110i | 0.810635 | + | 0.585552i | \(0.199122\pi\) | ||||
−0.810635 | + | 0.585552i | \(0.800878\pi\) | |||||||
\(620\) | 169501. | + | 206768.i | 0.440951 | + | 0.537899i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −228038. | + | 81523.2i | −0.589423 | + | 0.210717i | ||||
\(623\) | 80304.8i | 0.206902i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 177255. | 0.453773 | ||||||||
\(626\) | 70539.6 | + | 197315.i | 0.180005 | + | 0.503514i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 68307.5 | − | 55996.1i | 0.173200 | − | 0.141984i | ||||
\(629\) | 432079. | 1.09210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 402529.i | 1.01097i | 0.862835 | + | 0.505486i | \(0.168687\pi\) | ||||
−0.862835 | + | 0.505486i | \(0.831313\pi\) | |||||||
\(632\) | −246625. | + | 410706.i | −0.617453 | + | 1.02825i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −35006.2 | − | 97920.2i | −0.0870897 | − | 0.243609i | ||||
\(635\) | − | 292885.i | − | 0.726357i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −83742.3 | −0.206379 | ||||||||
\(638\) | −1.01499e6 | + | 362856.i | −2.49356 | + | 0.891441i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −121634. | + | 133688.i | −0.296959 | + | 0.326387i | ||||
\(641\) | −353813. | −0.861108 | −0.430554 | − | 0.902565i | \(-0.641682\pi\) | ||||
−0.430554 | + | 0.902565i | \(0.641682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 263141.i | 0.636452i | 0.948015 | + | 0.318226i | \(0.103087\pi\) | ||||
−0.948015 | + | 0.318226i | \(0.896913\pi\) | |||||||
\(644\) | 29676.6 | − | 24327.8i | 0.0715554 | − | 0.0586586i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 48664.3 | − | 17397.4i | 0.116613 | − | 0.0416887i | ||||
\(647\) | 265174.i | 0.633464i | 0.948515 | + | 0.316732i | \(0.102586\pi\) | ||||
−0.948515 | + | 0.316732i | \(0.897414\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 621494. | 1.47553 | ||||||||
\(650\) | −25122.9 | − | 70274.4i | −0.0594625 | − | 0.166330i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4131.27 | + | 5039.58i | 0.00971825 | + | 0.0118549i | ||||
\(653\) | 5877.92 | 0.0137847 | 0.00689235 | − | 0.999976i | \(-0.497806\pi\) | ||||
0.00689235 | + | 0.999976i | \(0.497806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14557.7i | 0.0339322i | ||||||||
\(656\) | 132270. | − | 661190.i | 0.307365 | − | 1.53645i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 46285.0 | + | 129470.i | 0.106903 | + | 0.299031i | ||||
\(659\) | − | 554642.i | − | 1.27715i | −0.769560 | − | 0.638575i | \(-0.779524\pi\) | ||
0.769560 | − | 0.638575i | \(-0.220476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −821227. | −1.87958 | −0.939789 | − | 0.341755i | \(-0.888979\pi\) | ||||
−0.939789 | + | 0.341755i | \(0.888979\pi\) | |||||||
\(662\) | 162832. | − | 58212.0i | 0.371555 | − | 0.132830i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36779.8 | + | 61249.5i | −0.0834206 | + | 0.138921i | ||||
\(665\) | −5979.36 | −0.0135211 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 247241.i | 0.555736i | ||||||||
\(668\) | 240836. | + | 293787.i | 0.539721 | + | 0.658385i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 38667.0 | − | 13823.4i | 0.0861372 | − | 0.0307938i | ||||
\(671\) | 1.15338e6i | 2.56169i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 516865. | 1.14116 | 0.570580 | − | 0.821242i | \(-0.306718\pi\) | ||||
0.570580 | + | 0.821242i | \(0.306718\pi\) | |||||||
\(674\) | −15960.1 | − | 44643.9i | −0.0351330 | − | 0.0982749i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 336402. | − | 275770.i | 0.736148 | − | 0.603468i | ||||
\(677\) | 690686. | 1.50697 | 0.753483 | − | 0.657468i | \(-0.228372\pi\) | ||||
0.753483 | + | 0.657468i | \(0.228372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 143537.i | 0.311332i | ||||||||
\(680\) | 171911. | + | 103231.i | 0.371780 | + | 0.223251i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −447480. | − | 1.25170e6i | −0.962066 | − | 2.69111i | ||||
\(683\) | 764551.i | 1.63895i | 0.573117 | + | 0.819474i | \(0.305734\pi\) | ||||
−0.573117 | + | 0.819474i | \(0.694266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 284757. | 0.606868 | ||||||||
\(686\) | 209138. | − | 74766.2i | 0.444410 | − | 0.158875i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10030.8 | − | 2006.65i | −0.0211914 | − | 0.00423931i | ||||
\(689\) | 52458.9 | 0.110505 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 321130.i | 0.672550i | 0.941764 | + | 0.336275i | \(0.109167\pi\) | ||||
−0.941764 | + | 0.336275i | \(0.890833\pi\) | |||||||
\(692\) | −34974.2 | + | 28670.6i | −0.0730358 | + | 0.0598722i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 109698. | − | 39216.9i | 0.227762 | − | 0.0814244i | ||||
\(695\) | − | 144933.i | − | 0.300053i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −748096. | −1.53990 | ||||||||
\(698\) | −161552. | − | 451898.i | −0.331591 | − | 0.927534i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 60830.3 | + | 74204.6i | 0.124144 | + | 0.151438i | ||||
\(701\) | 621799. | 1.26536 | 0.632680 | − | 0.774413i | \(-0.281955\pi\) | ||||
0.632680 | + | 0.774413i | \(0.281955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 69203.8i | 0.140029i | ||||||||
\(704\) | 793196. | − | 422302.i | 1.60043 | − | 0.852075i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 208386. | + | 582903.i | 0.418081 | + | 1.16946i | ||||
\(707\) | 113852.i | 0.227772i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −524870. | −1.04414 | −0.522070 | − | 0.852903i | \(-0.674840\pi\) | ||||
−0.522070 | + | 0.852903i | \(0.674840\pi\) | |||||||
\(710\) | −48313.4 | + | 17271.9i | −0.0958409 | + | 0.0342629i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 369792. | + | 222057.i | 0.729454 | + | 0.438031i | ||||
\(713\) | −304902. | −0.599765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 89716.5i | − | 0.175493i | ||||||
\(716\) | 463999. | + | 566015.i | 0.905089 | + | 1.10408i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 251754. | − | 90001.5i | 0.488346 | − | 0.174583i | ||||
\(719\) | 348658.i | 0.674438i | 0.941426 | + | 0.337219i | \(0.109486\pi\) | ||||
−0.941426 | + | 0.337219i | \(0.890514\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −137065. | −0.263668 | ||||||||
\(722\) | −172695. | − | 483066.i | −0.331287 | − | 0.926684i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 299768. | − | 245739.i | 0.571885 | − | 0.468811i | ||||
\(725\) | −618211. | −1.17615 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 604820.i | 1.14435i | 0.820133 | + | 0.572173i | \(0.193899\pi\) | ||||
−0.820133 | + | 0.572173i | \(0.806101\pi\) | |||||||
\(728\) | 14552.8 | − | 24234.8i | 0.0274590 | − | 0.0457275i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −32128.0 | − | 89869.2i | −0.0602890 | − | 0.168642i | ||||
\(731\) | 11349.3i | 0.0212389i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −475610. | −0.885204 | −0.442602 | − | 0.896718i | \(-0.645945\pi\) | ||||
−0.442602 | + | 0.896718i | \(0.645945\pi\) | |||||||
\(734\) | −356208. | + | 127343.i | −0.661167 | + | 0.236365i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29965.1 | − | 203927.i | −0.0553172 | − | 0.376461i | ||||
\(737\) | −204160. | −0.375868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 844449.i | 1.54627i | 0.634244 | + | 0.773133i | \(0.281312\pi\) | ||||
−0.634244 | + | 0.773133i | \(0.718688\pi\) | |||||||
\(740\) | −207659. | + | 170231.i | −0.379216 | + | 0.310868i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −63509.5 | + | 22704.5i | −0.115354 | + | 0.0412386i | ||||
\(743\) | − | 620323.i | − | 1.12367i | −0.827248 | − | 0.561837i | \(-0.810095\pi\) | ||
0.827248 | − | 0.561837i | \(-0.189905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 286120. | 0.515508 | ||||||||
\(746\) | 243804. | + | 681974.i | 0.438090 | + | 1.22543i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −632049. | − | 771013.i | −1.12966 | − | 1.37803i | ||||
\(749\) | −78672.5 | −0.140236 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 730748.i | 1.29565i | 0.761789 | + | 0.647825i | \(0.224321\pi\) | ||||
−0.761789 | + | 0.647825i | \(0.775679\pi\) | |||||||
\(752\) | 724175. | + | 144870.i | 1.28058 | + | 0.256179i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 61312.0 | + | 171503.i | 0.107846 | + | 0.301669i | ||||
\(755\) | − | 313247.i | − | 0.549533i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −769023. | −1.34198 | −0.670992 | − | 0.741465i | \(-0.734132\pi\) | ||||
−0.670992 | + | 0.741465i | \(0.734132\pi\) | |||||||
\(758\) | 192814. | − | 68930.6i | 0.335584 | − | 0.119970i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16534.0 | + | 27534.1i | −0.0286253 | + | 0.0476699i | ||||
\(761\) | −275394. | −0.475538 | −0.237769 | − | 0.971322i | \(-0.576416\pi\) | ||||
−0.237769 | + | 0.971322i | \(0.576416\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 143522.i | 0.246529i | ||||||||
\(764\) | −228452. | − | 278680.i | −0.391389 | − | 0.477441i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −574654. | + | 205437.i | −0.979375 | + | 0.350124i | ||||
\(767\) | − | 105014.i | − | 0.178508i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52842.1 | −0.0893568 | −0.0446784 | − | 0.999001i | \(-0.514226\pi\) | ||||
−0.0446784 | + | 0.999001i | \(0.514226\pi\) | |||||||
\(770\) | 38829.8 | + | 108616.i | 0.0654914 | + | 0.183194i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −226299. | + | 185512.i | −0.379707 | + | 0.311270i | ||||
\(773\) | 195309. | 0.326861 | 0.163430 | − | 0.986555i | \(-0.447744\pi\) | ||||
0.163430 | + | 0.986555i | \(0.447744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 762389.i | − | 1.26933i | ||||||
\(776\) | 660966. | + | 396905.i | 1.09763 | + | 0.659117i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 91425.1 | + | 255736.i | 0.151045 | + | 0.422506i | ||||
\(779\) | − | 119819.i | − | 0.197446i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 255093. | 0.418211 | ||||||||
\(782\) | −215331. | + | 76980.4i | −0.352122 | + | 0.125883i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 113443. | − | 567076.i | 0.184563 | − | 0.922590i | ||||
\(785\) | 60898.4 | 0.0988250 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 782238.i | 1.26296i | 0.775393 | + | 0.631480i | \(0.217552\pi\) | ||||
−0.775393 | + | 0.631480i | \(0.782448\pi\) | |||||||
\(788\) | 449169. | − | 368213.i | 0.723364 | − | 0.592989i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −311025. | + | 111191.i | −0.498358 | + | 0.178162i | ||||
\(791\) | − | 44451.9i | − | 0.0710456i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 194887. | 0.309911 | ||||||||
\(794\) | 169780. | + | 474912.i | 0.269305 | + | 0.753307i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −480159. | − | 585728.i | −0.757807 | − | 0.924421i | ||||
\(797\) | 1.17343e6 | 1.84731 | 0.923655 | − | 0.383226i | \(-0.125187\pi\) | ||||
0.923655 | + | 0.383226i | \(0.125187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 819359.i | − | 1.28346i | ||||||
\(800\) | 509908. | − | 74926.0i | 0.796731 | − | 0.117072i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 95456.6 | + | 267013.i | 0.148408 | + | 0.415130i | ||||
\(803\) | 474505.i | 0.735885i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26457.7 | 0.0408282 | ||||||||
\(806\) | −211501. | + | 75611.1i | −0.325569 | + | 0.116390i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 524271. | + | 314820.i | 0.803033 | + | 0.482214i | ||||
\(809\) | 421614. | 0.644196 | 0.322098 | − | 0.946706i | \(-0.395612\pi\) | ||||
0.322098 | + | 0.946706i | \(0.395612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 504037.i | 0.766339i | 0.923678 | + | 0.383169i | \(0.125167\pi\) | ||||
−0.923678 | + | 0.383169i | \(0.874833\pi\) | |||||||
\(812\) | −148455. | − | 181095.i | −0.225156 | − | 0.274659i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.25709e6 | − | 449407.i | 1.89722 | − | 0.678253i | ||||
\(815\) | 4492.95i | 0.00676420i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1817.75 | −0.00272327 | ||||||||
\(818\) | −58633.6 | − | 164011.i | −0.0876275 | − | 0.245113i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 359538. | − | 294737.i | 0.534709 | − | 0.438335i | ||||
\(821\) | 71554.1 | 0.106157 | 0.0530785 | − | 0.998590i | \(-0.483097\pi\) | ||||
0.0530785 | + | 0.998590i | \(0.483097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 812709.i | − | 1.19987i | −0.800048 | − | 0.599936i | \(-0.795193\pi\) | ||
0.800048 | − | 0.599936i | \(-0.204807\pi\) | |||||||
\(824\) | −379010. | + | 631166.i | −0.558208 | + | 0.929585i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 45450.9 | + | 127136.i | 0.0666166 | + | 0.186341i | ||||
\(827\) | − | 375951.i | − | 0.549693i | −0.961488 | − | 0.274847i | \(-0.911373\pi\) | ||
0.961488 | − | 0.274847i | \(-0.0886271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 423699. | 0.616522 | 0.308261 | − | 0.951302i | \(-0.400253\pi\) | ||||
0.308261 | + | 0.951302i | \(0.400253\pi\) | |||||||
\(830\) | −46383.9 | + | 16582.1i | −0.0673304 | + | 0.0240704i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −71356.8 | − | 134027.i | −0.103083 | − | 0.193618i | ||||
\(833\) | −641611. | −0.924660 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 261921.i | 0.375662i | ||||||||
\(836\) | 123489. | − | 101232.i | 0.176691 | − | 0.144845i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 793234. | − | 283579.i | 1.12957 | − | 0.403819i | ||||
\(839\) | 1.10840e6i | 1.57460i | 0.616568 | + | 0.787302i | \(0.288523\pi\) | ||||
−0.616568 | + | 0.787302i | \(0.711477\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 801453. | 1.13315 | ||||||||
\(842\) | −113278. | − | 316864.i | −0.159780 | − | 0.446940i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −471575. | − | 575256.i | −0.662012 | − | 0.807563i | ||||
\(845\) | 299914. | 0.420032 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 399036.i | − | 0.556218i | ||||||
\(848\) | −71064.1 | + | 355234.i | −0.0988231 | + | 0.493995i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −192485. | − | 538423.i | −0.266415 | − | 0.745223i | ||||
\(851\) | − | 306215.i | − | 0.422832i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −509319. | −0.699989 | −0.349995 | − | 0.936752i | \(-0.613817\pi\) | ||||
−0.349995 | + | 0.936752i | \(0.613817\pi\) | |||||||
\(854\) | −235941. | + | 84348.4i | −0.323510 | + | 0.115654i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −217543. | + | 362276.i | −0.296892 | + | 0.494415i | ||||
\(857\) | 656788. | 0.894260 | 0.447130 | − | 0.894469i | \(-0.352446\pi\) | ||||
0.447130 | + | 0.894469i | \(0.352446\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.05866e6i | − | 1.43474i | −0.696694 | − | 0.717368i | \(-0.745347\pi\) | ||
0.696694 | − | 0.717368i | \(-0.254653\pi\) | |||||||
\(860\) | −4471.41 | − | 5454.50i | −0.00604571 | − | 0.00737494i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 565292. | − | 202091.i | 0.760779 | − | 0.271977i | ||||
\(863\) | − | 676878.i | − | 0.908844i | −0.890787 | − | 0.454422i | \(-0.849846\pi\) | ||
0.890787 | − | 0.454422i | \(-0.150154\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31180.7 | −0.0416729 | ||||||||
\(866\) | −95902.0 | − | 268259.i | −0.127877 | − | 0.357700i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 223330. | − | 183078.i | 0.296420 | − | 0.242994i | ||||
\(869\) | 1.64220e6 | 2.17464 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34497.1i | 0.0454723i | ||||||||
\(872\) | 660896. | + | 396862.i | 0.869161 | + | 0.521924i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12329.5 | − | 34488.5i | −0.0161408 | − | 0.0451493i | ||||
\(875\) | 148308.i | 0.193708i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.47583e6 | 1.91883 | 0.959415 | − | 0.281998i | \(-0.0909973\pi\) | ||||
0.959415 | + | 0.281998i | \(0.0909973\pi\) | |||||||
\(878\) | −411478. | + | 147102.i | −0.533774 | + | 0.190823i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 607531. | + | 121536.i | 0.784518 | + | 0.156942i | ||||
\(881\) | −599513. | −0.772408 | −0.386204 | − | 0.922413i | \(-0.626214\pi\) | ||||
−0.386204 | + | 0.922413i | \(0.626214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 729187.i | 0.935229i | 0.883933 | + | 0.467614i | \(0.154886\pi\) | ||||
−0.883933 | + | 0.467614i | \(0.845114\pi\) | |||||||
\(884\) | −130279. | + | 106798.i | −0.166713 | + | 0.136665i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −868783. | + | 310588.i | −1.10674 | + | 0.395655i | ||||
\(887\) | 1.45744e6i | 1.85244i | 0.376981 | + | 0.926221i | \(0.376962\pi\) | ||||
−0.376981 | + | 0.926221i | \(0.623038\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −316344. | −0.400273 | ||||||||
\(890\) | 100114. | + | 280041.i | 0.126391 | + | 0.353543i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 837834. | + | 1.02204e6i | 1.05300 | + | 1.28452i | ||||
\(893\) | 131232. | 0.164565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 504622.i | 0.629970i | ||||||||
\(896\) | 144396. | + | 131377.i | 0.179862 | + | 0.163645i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13130.9 | − | 36730.0i | −0.0162833 | − | 0.0455479i | ||||
\(899\) | 1.86060e6i | 2.30215i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 401926. | 0.495104 | ||||||||
\(902\) | −2.17651e6 | + | 778098.i | −2.67515 | + | 0.956360i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −204694. | − | 122917.i | −0.250478 | − | 0.150410i | ||||
\(905\) | 267253. | 0.326307 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3476.53i | 0.00422602i | 0.999998 | + | 0.00211301i | \(0.000672593\pi\) | ||||
−0.999998 | + | 0.00211301i | \(0.999327\pi\) | |||||||
\(908\) | 301279. | + | 367519.i | 0.365424 | + | 0.445767i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18352.9 | − | 6561.11i | 0.0221627 | − | 0.00792309i | ||||
\(911\) | − | 822935.i | − | 0.991583i | −0.868442 | − | 0.495791i | \(-0.834878\pi\) | ||
0.868442 | − | 0.495791i | \(-0.165122\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 244905. | 0.293803 | ||||||||
\(914\) | −89058.3 | − | 249116.i | −0.106606 | − | 0.298201i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −560973. | + | 459866.i | −0.668577 | + | 0.548076i | ||||
\(917\) | 15723.8 | 0.0186990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 873279.i | − | 1.03400i | −0.855984 | − | 0.517002i | \(-0.827048\pi\) | ||
0.855984 | − | 0.517002i | \(-0.172952\pi\) | |||||||
\(920\) | 73160.2 | − | 121834.i | 0.0864369 | − | 0.143944i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −234282. | − | 655338.i | −0.275598 | − | 0.770910i | ||||
\(923\) | − | 43103.2i | − | 0.0505949i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 765673. | 0.894870 | ||||||||
\(926\) | 655351. | − | 234286.i | 0.764279 | − | 0.273228i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.24442e6 | + | 182856.i | −1.44501 | + | 0.212330i | ||||
\(929\) | −345961. | −0.400863 | −0.200431 | − | 0.979708i | \(-0.564234\pi\) | ||||
−0.200431 | + | 0.979708i | \(0.564234\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 102763.i | − | 0.118560i | ||||||
\(932\) | 630209. | − | 516623.i | 0.725526 | − | 0.594760i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 648183. | − | 231724.i | 0.743026 | − | 0.265630i | ||||
\(935\) | − | 687384.i | − | 0.786278i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.10958e6 | −1.26380 | −0.631901 | − | 0.775049i | \(-0.717725\pi\) | ||||
−0.631901 | + | 0.775049i | \(0.717725\pi\) | |||||||
\(938\) | −14930.6 | − | 41764.1i | −0.0169696 | − | 0.0474676i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 322813. | + | 393788.i | 0.365339 | + | 0.445663i | ||||
\(941\) | −322543. | −0.364257 | −0.182129 | − | 0.983275i | \(-0.558299\pi\) | ||||
−0.182129 | + | 0.983275i | \(0.558299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 530177.i | 0.596208i | ||||||||
\(944\) | 711124. | + | 142259.i | 0.797997 | + | 0.159638i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11804.4 | + | 33019.6i | 0.0131905 | + | 0.0368969i | ||||
\(947\) | − | 139420.i | − | 0.155463i | −0.996974 | − | 0.0777314i | \(-0.975232\pi\) | ||
0.996974 | − | 0.0777314i | \(-0.0247676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 80177.6 | 0.0890268 | ||||||||
\(950\) | 86236.4 | − | 30829.3i | 0.0955528 | − | 0.0341599i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 111500. | − | 185681.i | 0.123027 | − | 0.204877i | ||||
\(953\) | −1.68438e6 | −1.85462 | −0.927308 | − | 0.374300i | \(-0.877883\pi\) | ||||
−0.927308 | + | 0.374300i | \(0.877883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 248453.i | − | 0.272419i | ||||||
\(956\) | 374178. | + | 456445.i | 0.409413 | + | 0.499428i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −822605. | + | 294079.i | −0.896314 | + | 0.320430i | ||||
\(959\) | − | 307566.i | − | 0.334426i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.37100e6 | −1.48454 | ||||||||
\(962\) | −75936.8 | − | 212412.i | −0.0820545 | − | 0.229525i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −103782. | + | 85076.6i | −0.111678 | + | 0.0915495i | ||||
\(965\) | −201753. | −0.216654 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45357.5i | − | 0.0485061i | −0.999706 | − | 0.0242530i | \(-0.992279\pi\) | ||
0.999706 | − | 0.0242530i | \(-0.00772074\pi\) | |||||||
\(968\) | −1.83750e6 | − | 1.10340e6i | −1.96100 | − | 1.17756i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 178944. | + | 500546.i | 0.190184 | + | 0.531986i | ||||
\(971\) | − | 1.18319e6i | − | 1.25492i | −0.778648 | − | 0.627461i | \(-0.784094\pi\) | ||
0.778648 | − | 0.627461i | \(-0.215906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −156541. | −0.165350 | ||||||||
\(974\) | 1.47691e6 | − | 527990.i | 1.55681 | − | 0.556555i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −264007. | + | 1.31971e6i | −0.277151 | + | 1.38542i | ||||
\(977\) | −1.12593e6 | −1.17957 | −0.589783 | − | 0.807562i | \(-0.700787\pi\) | ||||
−0.589783 | + | 0.807562i | \(0.700787\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.47861e6i | − | 1.54272i | ||||||
\(980\) | 308361. | − | 252784.i | 0.321076 | − | 0.263206i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 789909. | − | 282390.i | 0.819132 | − | 0.292838i | ||||
\(983\) | − | 1.35328e6i | − | 1.40049i | −0.713904 | − | 0.700243i | \(-0.753075\pi\) | ||
0.713904 | − | 0.700243i | \(-0.246925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 400449. | 0.412738 | ||||||||
\(986\) | 469756. | + | 1.31401e6i | 0.483191 | + | 1.35159i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17105.3 | − | 20866.0i | −0.0175233 | − | 0.0213760i | ||||
\(989\) | 8043.24 | 0.00822316 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.02847e6i | − | 1.04724i | −0.851953 | − | 0.523619i | \(-0.824582\pi\) | ||
0.851953 | − | 0.523619i | \(-0.175418\pi\) | |||||||
\(992\) | −225501. | − | 1.53464e6i | −0.229153 | − | 1.55950i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18655.3 | + | 52183.1i | 0.0188812 | + | 0.0528150i | ||||
\(995\) | − | 522196.i | − | 0.527457i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.12806e6 | 1.13486 | 0.567430 | − | 0.823422i | \(-0.307938\pi\) | ||||
0.567430 | + | 0.823422i | \(0.307938\pi\) | |||||||
\(998\) | −511821. | + | 182975.i | −0.513874 | + | 0.183709i | ||||
\(999\) | 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 | 324.5.d.e.163.9 | 22 | ||
3.2 | odd | 2 | 324.5.d.f.163.14 | 22 | |||
4.3 | odd | 2 | inner | 324.5.d.e.163.10 | 22 | ||
9.2 | odd | 6 | 36.5.f.a.31.16 | yes | 44 | ||
9.4 | even | 3 | 108.5.f.a.19.21 | 44 | |||
9.5 | odd | 6 | 36.5.f.a.7.2 | ✓ | 44 | ||
9.7 | even | 3 | 108.5.f.a.91.7 | 44 | |||
12.11 | even | 2 | 324.5.d.f.163.13 | 22 | |||
36.7 | odd | 6 | 108.5.f.a.91.21 | 44 | |||
36.11 | even | 6 | 36.5.f.a.31.2 | yes | 44 | ||
36.23 | even | 6 | 36.5.f.a.7.16 | yes | 44 | ||
36.31 | odd | 6 | 108.5.f.a.19.7 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.5.f.a.7.2 | ✓ | 44 | 9.5 | odd | 6 | ||
36.5.f.a.7.16 | yes | 44 | 36.23 | even | 6 | ||
36.5.f.a.31.2 | yes | 44 | 36.11 | even | 6 | ||
36.5.f.a.31.16 | yes | 44 | 9.2 | odd | 6 | ||
108.5.f.a.19.7 | 44 | 36.31 | odd | 6 | |||
108.5.f.a.19.21 | 44 | 9.4 | even | 3 | |||
108.5.f.a.91.7 | 44 | 9.7 | even | 3 | |||
108.5.f.a.91.21 | 44 | 36.7 | odd | 6 | |||
324.5.d.e.163.9 | 22 | 1.1 | even | 1 | trivial | ||
324.5.d.e.163.10 | 22 | 4.3 | odd | 2 | inner | ||
324.5.d.f.163.13 | 22 | 12.11 | even | 2 | |||
324.5.d.f.163.14 | 22 | 3.2 | odd | 2 |