Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,5,Mod(73,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.73");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0942856808\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.9 | ||
Root | \(4.32919 - 4.32919i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.109 |
Dual form | 117.5.j.b.73.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.32919 | − | 4.32919i | 1.08230 | − | 1.08230i | 0.0860014 | − | 0.996295i | \(-0.472591\pi\) |
0.996295 | − | 0.0860014i | \(-0.0274090\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 21.4837i | − | 1.34273i | ||||||
\(5\) | 26.0804 | − | 26.0804i | 1.04322 | − | 1.04322i | 0.0441922 | − | 0.999023i | \(-0.485929\pi\) |
0.999023 | − | 0.0441922i | \(-0.0140714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.9579 | − | 16.9579i | −0.346080 | − | 0.346080i | 0.512567 | − | 0.858647i | \(-0.328694\pi\) |
−0.858647 | + | 0.512567i | \(0.828694\pi\) | |||||||
\(8\) | −23.7399 | − | 23.7399i | −0.370937 | − | 0.370937i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 225.814i | − | 2.25814i | ||||||
\(11\) | 69.5293 | + | 69.5293i | 0.574623 | + | 0.574623i | 0.933417 | − | 0.358794i | \(-0.116812\pi\) |
−0.358794 | + | 0.933417i | \(0.616812\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −93.5895 | − | 140.720i | −0.553784 | − | 0.832660i | ||||
\(14\) | −146.828 | −0.749121 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 138.190 | 0.539804 | ||||||||
\(17\) | − | 166.635i | − | 0.576593i | −0.957541 | − | 0.288296i | \(-0.906911\pi\) | ||
0.957541 | − | 0.288296i | \(-0.0930888\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −468.820 | + | 468.820i | −1.29867 | + | 1.29867i | −0.369401 | + | 0.929270i | \(0.620437\pi\) |
−0.929270 | + | 0.369401i | \(0.879563\pi\) | |||||||
\(20\) | −560.303 | − | 560.303i | −1.40076 | − | 1.40076i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 602.011 | 1.24382 | ||||||||
\(23\) | − | 388.867i | − | 0.735098i | −0.930004 | − | 0.367549i | \(-0.880197\pi\) | ||
0.930004 | − | 0.367549i | \(-0.119803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 735.373i | − | 1.17660i | ||||||
\(26\) | −1014.37 | − | 204.035i | −1.50054 | − | 0.301827i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −364.318 | + | 364.318i | −0.464692 | + | 0.464692i | ||||
\(29\) | 767.891 | 0.913069 | 0.456534 | − | 0.889706i | \(-0.349091\pi\) | ||||
0.456534 | + | 0.889706i | \(0.349091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −66.8738 | + | 66.8738i | −0.0695877 | + | 0.0695877i | −0.741044 | − | 0.671456i | \(-0.765669\pi\) |
0.671456 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(32\) | 978.089 | − | 978.089i | 0.955165 | − | 0.955165i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −721.395 | − | 721.395i | −0.624044 | − | 0.624044i | ||||
\(35\) | −884.537 | −0.722071 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1532.33 | + | 1532.33i | 1.11931 | + | 1.11931i | 0.991843 | + | 0.127465i | \(0.0406841\pi\) |
0.127465 | + | 0.991843i | \(0.459316\pi\) | |||||||
\(38\) | 4059.22i | 2.81109i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1238.29 | −0.773933 | ||||||||
\(41\) | −802.986 | + | 802.986i | −0.477684 | + | 0.477684i | −0.904390 | − | 0.426707i | \(-0.859674\pi\) |
0.426707 | + | 0.904390i | \(0.359674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2798.62i | 1.51358i | 0.653655 | + | 0.756792i | \(0.273235\pi\) | ||||
−0.653655 | + | 0.756792i | \(0.726765\pi\) | |||||||
\(44\) | 1493.75 | − | 1493.75i | 0.771564 | − | 0.771564i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1683.48 | − | 1683.48i | −0.795594 | − | 0.795594i | ||||
\(47\) | −33.8918 | − | 33.8918i | −0.0153426 | − | 0.0153426i | 0.699394 | − | 0.714736i | \(-0.253453\pi\) |
−0.714736 | + | 0.699394i | \(0.753453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1825.86i | − | 0.760458i | ||||||
\(50\) | −3183.56 | − | 3183.56i | −1.27343 | − | 1.27343i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3023.18 | + | 2010.65i | −1.11804 | + | 0.743583i | ||||
\(53\) | 3139.54 | 1.11767 | 0.558836 | − | 0.829278i | \(-0.311248\pi\) | ||||
0.558836 | + | 0.829278i | \(0.311248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3626.70 | 1.19891 | ||||||||
\(56\) | 805.159i | 0.256747i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3324.34 | − | 3324.34i | 0.988211 | − | 0.988211i | ||||
\(59\) | 3959.16 | + | 3959.16i | 1.13736 | + | 1.13736i | 0.988921 | + | 0.148440i | \(0.0474253\pi\) |
0.148440 | + | 0.988921i | \(0.452575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 504.230 | 0.135509 | 0.0677546 | − | 0.997702i | \(-0.478417\pi\) | ||||
0.0677546 | + | 0.997702i | \(0.478417\pi\) | |||||||
\(62\) | 579.018i | 0.150629i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 6257.62i | − | 1.52774i | ||||||
\(65\) | −6110.87 | − | 1229.17i | −1.44636 | − | 0.290928i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4218.53 | − | 4218.53i | 0.939748 | − | 0.939748i | −0.0585372 | − | 0.998285i | \(-0.518644\pi\) |
0.998285 | + | 0.0585372i | \(0.0186436\pi\) | |||||||
\(68\) | −3579.94 | −0.774209 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3829.33 | + | 3829.33i | −0.781495 | + | 0.781495i | ||||
\(71\) | 3025.86 | − | 3025.86i | 0.600249 | − | 0.600249i | −0.340130 | − | 0.940379i | \(-0.610471\pi\) |
0.940379 | + | 0.340130i | \(0.110471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3088.98 | + | 3088.98i | 0.579654 | + | 0.579654i | 0.934808 | − | 0.355154i | \(-0.115571\pi\) |
−0.355154 | + | 0.934808i | \(0.615571\pi\) | |||||||
\(74\) | 13267.5 | 2.42285 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10072.0 | + | 10072.0i | 1.74377 | + | 1.74377i | ||||
\(77\) | − | 2358.14i | − | 0.397730i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9376.55 | −1.50241 | −0.751205 | − | 0.660069i | \(-0.770527\pi\) | ||||
−0.751205 | + | 0.660069i | \(0.770527\pi\) | |||||||
\(80\) | 3604.05 | − | 3604.05i | 0.563132 | − | 0.563132i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6952.55i | 1.03399i | ||||||||
\(83\) | −6229.50 | + | 6229.50i | −0.904267 | + | 0.904267i | −0.995802 | − | 0.0915344i | \(-0.970823\pi\) |
0.0915344 | + | 0.995802i | \(0.470823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4345.91 | − | 4345.91i | −0.601510 | − | 0.601510i | ||||
\(86\) | 12115.7 | + | 12115.7i | 1.63815 | + | 1.63815i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 3301.24i | − | 0.426297i | ||||||
\(89\) | −8558.42 | − | 8558.42i | −1.08047 | − | 1.08047i | −0.996465 | − | 0.0840075i | \(-0.973228\pi\) |
−0.0840075 | − | 0.996465i | \(-0.526772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −799.227 | + | 3973.39i | −0.0965133 | + | 0.479820i | ||||
\(92\) | −8354.30 | −0.987039 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −293.448 | −0.0332105 | ||||||||
\(95\) | 24454.0i | 2.70959i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2882.26 | − | 2882.26i | 0.306330 | − | 0.306330i | −0.537154 | − | 0.843484i | \(-0.680501\pi\) |
0.843484 | + | 0.537154i | \(0.180501\pi\) | |||||||
\(98\) | −7904.48 | − | 7904.48i | −0.823041 | − | 0.823041i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15798.5 | −1.57985 | ||||||||
\(101\) | 5594.65i | 0.548441i | 0.961667 | + | 0.274220i | \(0.0884198\pi\) | ||||
−0.961667 | + | 0.274220i | \(0.911580\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6792.74i | 0.640281i | 0.947370 | + | 0.320140i | \(0.103730\pi\) | ||||
−0.947370 | + | 0.320140i | \(0.896270\pi\) | |||||||
\(104\) | −1118.86 | + | 5562.48i | −0.103445 | + | 0.514283i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13591.7 | − | 13591.7i | 1.20965 | − | 1.20965i | ||||
\(107\) | 8462.24 | 0.739125 | 0.369563 | − | 0.929206i | \(-0.379508\pi\) | ||||
0.369563 | + | 0.929206i | \(0.379508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12077.9 | + | 12077.9i | −1.01657 | + | 1.01657i | −0.0167121 | + | 0.999860i | \(0.505320\pi\) |
−0.999860 | + | 0.0167121i | \(0.994680\pi\) | |||||||
\(110\) | 15700.7 | − | 15700.7i | 1.29758 | − | 1.29758i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2343.41 | − | 2343.41i | −0.186815 | − | 0.186815i | ||||
\(113\) | −14864.2 | −1.16409 | −0.582043 | − | 0.813158i | \(-0.697746\pi\) | ||||
−0.582043 | + | 0.813158i | \(0.697746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10141.8 | − | 10141.8i | −0.766866 | − | 0.766866i | ||||
\(116\) | − | 16497.1i | − | 1.22601i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 34279.8 | 2.46192 | ||||||||
\(119\) | −2825.78 | + | 2825.78i | −0.199547 | + | 0.199547i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 4972.34i | − | 0.339618i | ||||||
\(122\) | 2182.90 | − | 2182.90i | 0.146661 | − | 0.146661i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1436.70 | + | 1436.70i | 0.0934376 | + | 0.0934376i | ||||
\(125\) | −2878.56 | − | 2878.56i | −0.184228 | − | 0.184228i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10995.6i | 0.681728i | 0.940113 | + | 0.340864i | \(0.110720\pi\) | ||||
−0.940113 | + | 0.340864i | \(0.889280\pi\) | |||||||
\(128\) | −11441.0 | − | 11441.0i | −0.698301 | − | 0.698301i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −31776.4 | + | 21133.8i | −1.88026 | + | 1.25052i | ||||
\(131\) | −14023.3 | −0.817160 | −0.408580 | − | 0.912722i | \(-0.633976\pi\) | ||||
−0.408580 | + | 0.912722i | \(0.633976\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15900.4 | 0.898887 | ||||||||
\(134\) | − | 36525.6i | − | 2.03417i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3955.91 | + | 3955.91i | −0.213879 | + | 0.213879i | ||||
\(137\) | −20682.4 | − | 20682.4i | −1.10194 | − | 1.10194i | −0.994176 | − | 0.107769i | \(-0.965629\pi\) |
−0.107769 | − | 0.994176i | \(-0.534371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12584.1 | −0.651317 | −0.325658 | − | 0.945487i | \(-0.605586\pi\) | ||||
−0.325658 | + | 0.945487i | \(0.605586\pi\) | |||||||
\(140\) | 19003.1i | 0.969547i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 26199.0i | − | 1.29929i | ||||||
\(143\) | 3276.92 | − | 16291.4i | 0.160248 | − | 0.796682i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20026.9 | − | 20026.9i | 0.952527 | − | 0.952527i | ||||
\(146\) | 26745.5 | 1.25472 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32920.2 | − | 32920.2i | 1.50293 | − | 1.50293i | ||||
\(149\) | 1317.22 | − | 1317.22i | 0.0593315 | − | 0.0593315i | −0.676818 | − | 0.736150i | \(-0.736642\pi\) |
0.736150 | + | 0.676818i | \(0.236642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6003.08 | − | 6003.08i | −0.263282 | − | 0.263282i | 0.563104 | − | 0.826386i | \(-0.309607\pi\) |
−0.826386 | + | 0.563104i | \(0.809607\pi\) | |||||||
\(152\) | 22259.5 | 0.963449 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10208.8 | − | 10208.8i | −0.430462 | − | 0.430462i | ||||
\(155\) | 3488.19i | 0.145190i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24232.6 | −0.983107 | −0.491553 | − | 0.870847i | \(-0.663571\pi\) | ||||
−0.491553 | + | 0.870847i | \(0.663571\pi\) | |||||||
\(158\) | −40592.8 | + | 40592.8i | −1.62605 | + | 1.62605i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 51017.9i | − | 1.99289i | ||||||
\(161\) | −6594.37 | + | 6594.37i | −0.254403 | + | 0.254403i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −24239.5 | − | 24239.5i | −0.912322 | − | 0.912322i | 0.0841325 | − | 0.996455i | \(-0.473188\pi\) |
−0.996455 | + | 0.0841325i | \(0.973188\pi\) | |||||||
\(164\) | 17251.1 | + | 17251.1i | 0.641401 | + | 0.641401i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 53937.3i | 1.95737i | ||||||||
\(167\) | 17352.4 | + | 17352.4i | 0.622195 | + | 0.622195i | 0.946092 | − | 0.323897i | \(-0.104993\pi\) |
−0.323897 | + | 0.946092i | \(0.604993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11043.0 | + | 26339.8i | −0.386646 | + | 0.922228i | ||||
\(170\) | −37628.5 | −1.30202 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 60124.7 | 2.03234 | ||||||||
\(173\) | − | 2780.29i | − | 0.0928961i | −0.998921 | − | 0.0464480i | \(-0.985210\pi\) | ||
0.998921 | − | 0.0464480i | \(-0.0147902\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12470.4 | + | 12470.4i | −0.407196 | + | 0.407196i | ||||
\(176\) | 9608.25 | + | 9608.25i | 0.310184 | + | 0.310184i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −74102.0 | −2.33878 | ||||||||
\(179\) | 2972.36i | 0.0927674i | 0.998924 | + | 0.0463837i | \(0.0147697\pi\) | ||||
−0.998924 | + | 0.0463837i | \(0.985230\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 44034.0i | 1.34410i | 0.740507 | + | 0.672049i | \(0.234586\pi\) | ||||
−0.740507 | + | 0.672049i | \(0.765414\pi\) | |||||||
\(182\) | 13741.5 | + | 20661.5i | 0.414852 | + | 0.623764i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9231.68 | + | 9231.68i | −0.272675 | + | 0.272675i | ||||
\(185\) | 79927.7 | 2.33536 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11586.0 | − | 11586.0i | 0.331323 | − | 0.331323i | ||||
\(188\) | −728.122 | + | 728.122i | −0.0206010 | + | 0.0206010i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 105866. | + | 105866.i | 2.93258 | + | 2.93258i | ||||
\(191\) | 3688.96 | 0.101120 | 0.0505601 | − | 0.998721i | \(-0.483899\pi\) | ||||
0.0505601 | + | 0.998721i | \(0.483899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19216.9 | + | 19216.9i | 0.515904 | + | 0.515904i | 0.916329 | − | 0.400426i | \(-0.131138\pi\) |
−0.400426 | + | 0.916329i | \(0.631138\pi\) | |||||||
\(194\) | − | 24955.7i | − | 0.663079i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −39226.2 | −1.02109 | ||||||||
\(197\) | 15917.0 | − | 15917.0i | 0.410136 | − | 0.410136i | −0.471650 | − | 0.881786i | \(-0.656341\pi\) |
0.881786 | + | 0.471650i | \(0.156341\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 23311.0i | − | 0.588646i | −0.955706 | − | 0.294323i | \(-0.904906\pi\) | ||
0.955706 | − | 0.294323i | \(-0.0950941\pi\) | |||||||
\(200\) | −17457.7 | + | 17457.7i | −0.436443 | + | 0.436443i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 24220.3 | + | 24220.3i | 0.593576 | + | 0.593576i | ||||
\(203\) | −13021.8 | − | 13021.8i | −0.315995 | − | 0.315995i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 41884.4i | 0.996654i | ||||||||
\(206\) | 29407.0 | + | 29407.0i | 0.692974 | + | 0.692974i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12933.1 | − | 19446.0i | −0.298935 | − | 0.449474i | ||||
\(209\) | −65193.5 | −1.49249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10045.5 | 0.225636 | 0.112818 | − | 0.993616i | \(-0.464012\pi\) | ||||
0.112818 | + | 0.993616i | \(0.464012\pi\) | |||||||
\(212\) | − | 67448.9i | − | 1.50073i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 36634.6 | − | 36634.6i | 0.799953 | − | 0.799953i | ||||
\(215\) | 72989.0 | + | 72989.0i | 1.57899 | + | 1.57899i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2268.08 | 0.0481658 | ||||||||
\(218\) | 104575.i | 2.20047i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 77915.0i | − | 1.60981i | ||||||
\(221\) | −23448.8 | + | 15595.3i | −0.480106 | + | 0.319308i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24945.0 | − | 24945.0i | 0.501620 | − | 0.501620i | −0.410321 | − | 0.911941i | \(-0.634583\pi\) |
0.911941 | + | 0.410321i | \(0.134583\pi\) | |||||||
\(224\) | −33172.7 | −0.661126 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −64349.9 | + | 64349.9i | −1.25989 | + | 1.25989i | ||||
\(227\) | −15576.9 | + | 15576.9i | −0.302294 | + | 0.302294i | −0.841911 | − | 0.539617i | \(-0.818569\pi\) |
0.539617 | + | 0.841911i | \(0.318569\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24930.7 | − | 24930.7i | −0.475405 | − | 0.475405i | 0.428254 | − | 0.903658i | \(-0.359129\pi\) |
−0.903658 | + | 0.428254i | \(0.859129\pi\) | |||||||
\(230\) | −87811.5 | −1.65995 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18229.7 | − | 18229.7i | −0.338691 | − | 0.338691i | ||||
\(233\) | − | 22434.3i | − | 0.413239i | −0.978421 | − | 0.206619i | \(-0.933754\pi\) | ||
0.978421 | − | 0.206619i | \(-0.0662462\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1767.82 | −0.0320113 | ||||||||
\(236\) | 85057.3 | − | 85057.3i | 1.52717 | − | 1.52717i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24466.7i | 0.431938i | ||||||||
\(239\) | 66829.7 | − | 66829.7i | 1.16997 | − | 1.16997i | 0.187751 | − | 0.982217i | \(-0.439880\pi\) |
0.982217 | − | 0.187751i | \(-0.0601199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −34827.1 | − | 34827.1i | −0.599629 | − | 0.599629i | 0.340585 | − | 0.940214i | \(-0.389375\pi\) |
−0.940214 | + | 0.340585i | \(0.889375\pi\) | |||||||
\(242\) | −21526.2 | − | 21526.2i | −0.367567 | − | 0.367567i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 10832.7i | − | 0.181952i | ||||||
\(245\) | −47619.1 | − | 47619.1i | −0.793321 | − | 0.793321i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 109849. | + | 22095.5i | 1.80054 | + | 0.362168i | ||||
\(248\) | 3175.16 | 0.0516253 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −24923.6 | −0.398778 | ||||||||
\(251\) | 4768.38i | 0.0756873i | 0.999284 | + | 0.0378437i | \(0.0120489\pi\) | ||||
−0.999284 | + | 0.0378437i | \(0.987951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27037.7 | − | 27037.7i | 0.422404 | − | 0.422404i | ||||
\(254\) | 47601.9 | + | 47601.9i | 0.737832 | + | 0.737832i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1061.74 | 0.0162008 | ||||||||
\(257\) | − | 62743.6i | − | 0.949956i | −0.879998 | − | 0.474978i | \(-0.842456\pi\) | ||
0.879998 | − | 0.474978i | \(-0.157544\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 51970.3i | − | 0.774740i | ||||||
\(260\) | −26407.1 | + | 131284.i | −0.390638 | + | 1.94207i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −60709.4 | + | 60709.4i | −0.884409 | + | 0.884409i | ||||
\(263\) | −45421.0 | −0.656667 | −0.328333 | − | 0.944562i | \(-0.606487\pi\) | ||||
−0.328333 | + | 0.944562i | \(0.606487\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 81880.4 | − | 81880.4i | 1.16597 | − | 1.16597i | ||||
\(266\) | 68835.8 | − | 68835.8i | 0.972862 | − | 0.972862i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −90629.6 | − | 90629.6i | −1.26183 | − | 1.26183i | ||||
\(269\) | −79205.8 | −1.09459 | −0.547296 | − | 0.836939i | \(-0.684343\pi\) | ||||
−0.547296 | + | 0.836939i | \(0.684343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16180.5 | − | 16180.5i | −0.220320 | − | 0.220320i | 0.588313 | − | 0.808633i | \(-0.299792\pi\) |
−0.808633 | + | 0.588313i | \(0.799792\pi\) | |||||||
\(272\) | − | 23027.3i | − | 0.311247i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −179076. | −2.38526 | ||||||||
\(275\) | 51130.0 | − | 51130.0i | 0.676099 | − | 0.676099i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2884.24i | − | 0.0375899i | −0.999823 | − | 0.0187950i | \(-0.994017\pi\) | ||
0.999823 | − | 0.0187950i | \(-0.00598298\pi\) | |||||||
\(278\) | −54478.9 | + | 54478.9i | −0.704918 | + | 0.704918i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 20998.9 | + | 20998.9i | 0.267843 | + | 0.267843i | ||||
\(281\) | 103231. | + | 103231.i | 1.30736 | + | 1.30736i | 0.923311 | + | 0.384052i | \(0.125472\pi\) |
0.384052 | + | 0.923311i | \(0.374528\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 78581.6i | 0.981178i | 0.871391 | + | 0.490589i | \(0.163218\pi\) | ||||
−0.871391 | + | 0.490589i | \(0.836782\pi\) | |||||||
\(284\) | −65006.6 | − | 65006.6i | −0.805973 | − | 0.805973i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −56341.9 | − | 84714.7i | −0.688810 | − | 1.03568i | ||||
\(287\) | 27233.9 | 0.330633 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 55753.7 | 0.667541 | ||||||||
\(290\) | − | 173400.i | − | 2.06183i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 66362.7 | − | 66362.7i | 0.778320 | − | 0.778320i | ||||
\(293\) | 5490.45 | + | 5490.45i | 0.0639547 | + | 0.0639547i | 0.738361 | − | 0.674406i | \(-0.235600\pi\) |
−0.674406 | + | 0.738361i | \(0.735600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 206513. | 2.37303 | ||||||||
\(296\) | − | 72755.0i | − | 0.830385i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 11405.0i | − | 0.128429i | ||||||
\(299\) | −54721.2 | + | 36393.9i | −0.612087 | + | 0.407086i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47458.7 | − | 47458.7i | 0.523821 | − | 0.523821i | ||||
\(302\) | −51976.9 | −0.569897 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −64786.2 | + | 64786.2i | −0.701028 | + | 0.701028i | ||||
\(305\) | 13150.5 | − | 13150.5i | 0.141365 | − | 0.141365i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 36642.5 | + | 36642.5i | 0.388784 | + | 0.388784i | 0.874254 | − | 0.485469i | \(-0.161351\pi\) |
−0.485469 | + | 0.874254i | \(0.661351\pi\) | |||||||
\(308\) | −50661.6 | −0.534045 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15101.0 | + | 15101.0i | 0.157139 | + | 0.157139i | ||||
\(311\) | 57004.6i | 0.589371i | 0.955594 | + | 0.294686i | \(0.0952149\pi\) | ||||
−0.955594 | + | 0.294686i | \(0.904785\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −168911. | −1.72413 | −0.862064 | − | 0.506799i | \(-0.830829\pi\) | ||||
−0.862064 | + | 0.506799i | \(0.830829\pi\) | |||||||
\(314\) | −104907. | + | 104907.i | −1.06401 | + | 1.06401i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 201443.i | 2.01733i | ||||||||
\(317\) | 57585.7 | − | 57585.7i | 0.573055 | − | 0.573055i | −0.359926 | − | 0.932981i | \(-0.617198\pi\) |
0.932981 | + | 0.359926i | \(0.117198\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 53390.9 | + | 53390.9i | 0.524670 | + | 0.524670i | ||||
\(320\) | −163201. | − | 163201.i | −1.59376 | − | 1.59376i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 57096.5i | 0.550678i | ||||||||
\(323\) | 78122.0 | + | 78122.0i | 0.748804 | + | 0.748804i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −103481. | + | 68823.2i | −0.979705 | + | 0.651580i | ||||
\(326\) | −209874. | −1.97481 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 38125.7 | 0.354381 | ||||||||
\(329\) | 1149.47i | 0.0106195i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −134787. | + | 134787.i | −1.23025 | + | 1.23025i | −0.266382 | + | 0.963868i | \(0.585828\pi\) |
−0.963868 | + | 0.266382i | \(0.914172\pi\) | |||||||
\(332\) | 133833. | + | 133833.i | 1.21419 | + | 1.21419i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 150243. | 1.34680 | ||||||||
\(335\) | − | 220042.i | − | 1.96072i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 56729.9i | 0.499520i | 0.968308 | + | 0.249760i | \(0.0803517\pi\) | ||||
−0.968308 | + | 0.249760i | \(0.919648\pi\) | |||||||
\(338\) | 66222.5 | + | 161837.i | 0.579659 | + | 1.41659i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −93366.3 | + | 93366.3i | −0.807667 | + | 0.807667i | ||||
\(341\) | −9299.38 | −0.0799734 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −71678.7 | + | 71678.7i | −0.609259 | + | 0.609259i | ||||
\(344\) | 66439.0 | − | 66439.0i | 0.561444 | − | 0.561444i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12036.4 | − | 12036.4i | −0.100541 | − | 0.100541i | ||||
\(347\) | 183864. | 1.52699 | 0.763497 | − | 0.645811i | \(-0.223481\pi\) | ||||
0.763497 | + | 0.645811i | \(0.223481\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −72786.9 | − | 72786.9i | −0.597588 | − | 0.597588i | 0.342082 | − | 0.939670i | \(-0.388868\pi\) |
−0.939670 | + | 0.342082i | \(0.888868\pi\) | |||||||
\(350\) | 107973.i | 0.881413i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 136012. | 1.09772 | ||||||||
\(353\) | −106752. | + | 106752.i | −0.856695 | + | 0.856695i | −0.990947 | − | 0.134252i | \(-0.957137\pi\) |
0.134252 | + | 0.990947i | \(0.457137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 157831.i | − | 1.25238i | ||||||
\(356\) | −183867. | + | 183867.i | −1.45078 | + | 1.45078i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12867.9 | + | 12867.9i | 0.100402 | + | 0.100402i | ||||
\(359\) | 26893.9 | + | 26893.9i | 0.208672 | + | 0.208672i | 0.803703 | − | 0.595031i | \(-0.202860\pi\) |
−0.595031 | + | 0.803703i | \(0.702860\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 309264.i | − | 2.37309i | ||||||
\(362\) | 190631. | + | 190631.i | 1.45471 | + | 1.45471i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 85363.1 | + | 17170.3i | 0.644269 | + | 0.129591i | ||||
\(365\) | 161123. | 1.20941 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6492.32 | 0.0482023 | 0.0241012 | − | 0.999710i | \(-0.492328\pi\) | ||||
0.0241012 | + | 0.999710i | \(0.492328\pi\) | |||||||
\(368\) | − | 53737.5i | − | 0.396809i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 346022. | − | 346022.i | 2.52755 | − | 2.52755i | ||||
\(371\) | −53240.0 | − | 53240.0i | −0.386804 | − | 0.386804i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −53286.9 | −0.383004 | −0.191502 | − | 0.981492i | \(-0.561336\pi\) | ||||
−0.191502 | + | 0.981492i | \(0.561336\pi\) | |||||||
\(374\) | − | 100316.i | − | 0.717180i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1609.18i | 0.0113823i | ||||||||
\(377\) | −71866.5 | − | 108057.i | −0.505643 | − | 0.760276i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −92136.8 | + | 92136.8i | −0.641438 | + | 0.641438i | −0.950909 | − | 0.309471i | \(-0.899848\pi\) |
0.309471 | + | 0.950909i | \(0.399848\pi\) | |||||||
\(380\) | 525363. | 3.63825 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15970.2 | − | 15970.2i | 0.109442 | − | 0.109442i | ||||
\(383\) | 15911.5 | − | 15911.5i | 0.108471 | − | 0.108471i | −0.650788 | − | 0.759259i | \(-0.725561\pi\) |
0.759259 | + | 0.650788i | \(0.225561\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −61501.3 | − | 61501.3i | −0.414918 | − | 0.414918i | ||||
\(386\) | 166387. | 1.11672 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −61921.5 | − | 61921.5i | −0.411319 | − | 0.411319i | ||||
\(389\) | − | 215552.i | − | 1.42447i | −0.701941 | − | 0.712236i | \(-0.747683\pi\) | ||
0.701941 | − | 0.712236i | \(-0.252317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −64799.0 | −0.423852 | ||||||||
\(392\) | −43345.8 | + | 43345.8i | −0.282082 | + | 0.282082i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 137815.i | − | 0.887778i | ||||||
\(395\) | −244544. | + | 244544.i | −1.56734 | + | 1.56734i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 81274.7 | + | 81274.7i | 0.515673 | + | 0.515673i | 0.916259 | − | 0.400586i | \(-0.131194\pi\) |
−0.400586 | + | 0.916259i | \(0.631194\pi\) | |||||||
\(398\) | −100917. | − | 100917.i | −0.637089 | − | 0.637089i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 101621.i | − | 0.635132i | ||||||
\(401\) | −170564. | − | 170564.i | −1.06072 | − | 1.06072i | −0.998034 | − | 0.0626817i | \(-0.980035\pi\) |
−0.0626817 | − | 0.998034i | \(-0.519965\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15669.1 | + | 3151.77i | 0.0964795 | + | 0.0194063i | ||||
\(404\) | 120194. | 0.736409 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −112748. | −0.683999 | ||||||||
\(407\) | 213084.i | 1.28636i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −92288.1 | + | 92288.1i | −0.551695 | + | 0.551695i | −0.926930 | − | 0.375235i | \(-0.877562\pi\) |
0.375235 | + | 0.926930i | \(0.377562\pi\) | |||||||
\(410\) | 181325. | + | 181325.i | 1.07867 | + | 1.07867i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 145933. | 0.859725 | ||||||||
\(413\) | − | 134278.i | − | 0.787235i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 324935.i | 1.88669i | ||||||||
\(416\) | −229175. | − | 46097.4i | −1.32428 | − | 0.266373i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −282235. | + | 282235.i | −1.61532 | + | 1.61532i | ||||
\(419\) | 20127.4 | 0.114646 | 0.0573232 | − | 0.998356i | \(-0.481743\pi\) | ||||
0.0573232 | + | 0.998356i | \(0.481743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 171209. | − | 171209.i | 0.965965 | − | 0.965965i | −0.0334748 | − | 0.999440i | \(-0.510657\pi\) |
0.999440 | + | 0.0334748i | \(0.0106573\pi\) | |||||||
\(422\) | 43489.0 | − | 43489.0i | 0.244205 | − | 0.244205i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −74532.5 | − | 74532.5i | −0.414586 | − | 0.414586i | ||||
\(425\) | −122539. | −0.678417 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8550.68 | − | 8550.68i | −0.0468970 | − | 0.0468970i | ||||
\(428\) | − | 181800.i | − | 0.992446i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 631966. | 3.41788 | ||||||||
\(431\) | −127549. | + | 127549.i | −0.686630 | + | 0.686630i | −0.961485 | − | 0.274856i | \(-0.911370\pi\) |
0.274856 | + | 0.961485i | \(0.411370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 68957.0i | 0.367792i | 0.982946 | + | 0.183896i | \(0.0588710\pi\) | ||||
−0.982946 | + | 0.183896i | \(0.941129\pi\) | |||||||
\(434\) | 9818.93 | − | 9818.93i | 0.0521297 | − | 0.0521297i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 259478. | + | 259478.i | 1.36498 | + | 1.36498i | ||||
\(437\) | 182309. | + | 182309.i | 0.954651 | + | 0.954651i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 113397.i | − | 0.588400i | −0.955744 | − | 0.294200i | \(-0.904947\pi\) | ||
0.955744 | − | 0.294200i | \(-0.0950531\pi\) | |||||||
\(440\) | −86097.7 | − | 86097.7i | −0.444720 | − | 0.444720i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −33999.4 | + | 169029.i | −0.174031 | + | 0.865203i | ||||
\(443\) | −92267.8 | −0.470157 | −0.235079 | − | 0.971976i | \(-0.575535\pi\) | ||||
−0.235079 | + | 0.971976i | \(0.575535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −446414. | −2.25433 | ||||||||
\(446\) | − | 215984.i | − | 1.08580i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −106116. | + | 106116.i | −0.528719 | + | 0.528719i | ||||
\(449\) | 17542.3 | + | 17542.3i | 0.0870148 | + | 0.0870148i | 0.749274 | − | 0.662260i | \(-0.230402\pi\) |
−0.662260 | + | 0.749274i | \(0.730402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −111662. | −0.548976 | ||||||||
\(452\) | 319338.i | 1.56305i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 134871.i | 0.654343i | ||||||||
\(455\) | 82783.4 | + | 124472.i | 0.399872 | + | 0.601240i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 104731. | − | 104731.i | 0.501466 | − | 0.501466i | −0.410428 | − | 0.911893i | \(-0.634621\pi\) |
0.911893 | + | 0.410428i | \(0.134621\pi\) | |||||||
\(458\) | −215859. | −1.02906 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −217883. | + | 217883.i | −1.02969 | + | 1.02969i | ||||
\(461\) | 12382.8 | − | 12382.8i | 0.0582663 | − | 0.0582663i | −0.677373 | − | 0.735640i | \(-0.736882\pi\) |
0.735640 | + | 0.677373i | \(0.236882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 156318. | + | 156318.i | 0.729199 | + | 0.729199i | 0.970460 | − | 0.241261i | \(-0.0775611\pi\) |
−0.241261 | + | 0.970460i | \(0.577561\pi\) | |||||||
\(464\) | 106115. | 0.492878 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −97122.3 | − | 97122.3i | −0.447247 | − | 0.447247i | ||||
\(467\) | − | 3880.03i | − | 0.0177911i | −0.999960 | − | 0.00889553i | \(-0.997168\pi\) | ||
0.999960 | − | 0.00889553i | \(-0.00283157\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −143075. | −0.650455 | ||||||||
\(470\) | −7653.24 | + | 7653.24i | −0.0346457 | + | 0.0346457i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 187980.i | − | 0.843778i | ||||||
\(473\) | −194586. | + | 194586.i | −0.869740 | + | 0.869740i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 344758. | + | 344758.i | 1.52801 | + | 1.52801i | ||||
\(476\) | 60708.3 | + | 60708.3i | 0.267938 | + | 0.267938i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 578637.i | − | 2.53250i | ||||||
\(479\) | −53446.0 | − | 53446.0i | −0.232940 | − | 0.232940i | 0.580979 | − | 0.813919i | \(-0.302670\pi\) |
−0.813919 | + | 0.580979i | \(0.802670\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 72218.9 | − | 359040.i | 0.312148 | − | 1.55186i | ||||
\(482\) | −301546. | −1.29795 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −106824. | −0.456015 | ||||||||
\(485\) | − | 150341.i | − | 0.639136i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39739.5 | + | 39739.5i | −0.167558 | + | 0.167558i | −0.785905 | − | 0.618347i | \(-0.787803\pi\) |
0.618347 | + | 0.785905i | \(0.287803\pi\) | |||||||
\(488\) | −11970.4 | − | 11970.4i | −0.0502653 | − | 0.0502653i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −412304. | −1.71722 | ||||||||
\(491\) | − | 183063.i | − | 0.759342i | −0.925122 | − | 0.379671i | \(-0.876037\pi\) | ||
0.925122 | − | 0.379671i | \(-0.123963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 127958.i | − | 0.526469i | ||||||
\(494\) | 571212. | − | 379900.i | 2.34069 | − | 1.55674i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9241.28 | + | 9241.28i | −0.0375638 | + | 0.0375638i | ||||
\(497\) | −102624. | −0.415468 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −57389.5 | + | 57389.5i | −0.230479 | + | 0.230479i | −0.812893 | − | 0.582414i | \(-0.802108\pi\) |
0.582414 | + | 0.812893i | \(0.302108\pi\) | |||||||
\(500\) | −61842.1 | + | 61842.1i | −0.247368 | + | 0.247368i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20643.2 | + | 20643.2i | 0.0819161 | + | 0.0819161i | ||||
\(503\) | 192555. | 0.761061 | 0.380530 | − | 0.924768i | \(-0.375741\pi\) | ||||
0.380530 | + | 0.924768i | \(0.375741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 145910. | + | 145910.i | 0.572142 | + | 0.572142i | ||||
\(506\) | − | 234102.i | − | 0.914333i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 236226. | 0.915377 | ||||||||
\(509\) | 84764.7 | − | 84764.7i | 0.327175 | − | 0.327175i | −0.524336 | − | 0.851511i | \(-0.675687\pi\) |
0.851511 | + | 0.524336i | \(0.175687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 104765.i | − | 0.401213i | ||||||
\(512\) | 187652. | − | 187652.i | 0.715835 | − | 0.715835i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −271629. | − | 271629.i | −1.02813 | − | 1.02813i | ||||
\(515\) | 177157. | + | 177157.i | 0.667951 | + | 0.667951i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4712.95i | − | 0.0176324i | ||||||
\(518\) | −224989. | − | 224989.i | −0.838498 | − | 0.838498i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 115891. | + | 174252.i | 0.428592 | + | 0.644424i | ||||
\(521\) | −314076. | −1.15707 | −0.578534 | − | 0.815658i | \(-0.696375\pi\) | ||||
−0.578534 | + | 0.815658i | \(0.696375\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37022.8 | −0.135352 | −0.0676762 | − | 0.997707i | \(-0.521558\pi\) | ||||
−0.0676762 | + | 0.997707i | \(0.521558\pi\) | |||||||
\(524\) | 301272.i | 1.09723i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −196636. | + | 196636.i | −0.710708 | + | 0.710708i | ||||
\(527\) | 11143.5 | + | 11143.5i | 0.0401238 | + | 0.0401238i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 128624. | 0.459631 | ||||||||
\(530\) | − | 708951.i | − | 2.52386i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 341600.i | − | 1.20696i | ||||||
\(533\) | 188147. | + | 37844.8i | 0.662282 | + | 0.133214i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 220699. | − | 220699.i | 0.771067 | − | 0.771067i | ||||
\(536\) | −200295. | −0.697174 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −342897. | + | 342897.i | −1.18467 | + | 1.18467i | ||||
\(539\) | 126951. | − | 126951.i | 0.436976 | − | 0.436976i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38918.2 | − | 38918.2i | −0.132971 | − | 0.132971i | 0.637489 | − | 0.770460i | \(-0.279973\pi\) |
−0.770460 | + | 0.637489i | \(0.779973\pi\) | |||||||
\(542\) | −140097. | −0.476903 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −162984. | − | 162984.i | −0.550741 | − | 0.550741i | ||||
\(545\) | 629992.i | 2.12101i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −383774. | −1.28263 | −0.641314 | − | 0.767279i | \(-0.721610\pi\) | ||||
−0.641314 | + | 0.767279i | \(0.721610\pi\) | |||||||
\(548\) | −444334. | + | 444334.i | −1.47962 | + | 1.47962i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 442702.i | − | 1.46348i | ||||||
\(551\) | −360003. | + | 360003.i | −1.18578 | + | 1.18578i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 159007. | + | 159007.i | 0.519954 | + | 0.519954i | ||||
\(554\) | −12486.4 | − | 12486.4i | −0.0406835 | − | 0.0406835i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 270353.i | 0.874543i | ||||||||
\(557\) | −280053. | − | 280053.i | −0.902672 | − | 0.902672i | 0.0929944 | − | 0.995667i | \(-0.470356\pi\) |
−0.995667 | + | 0.0929944i | \(0.970356\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 393820. | − | 261921.i | 1.26030 | − | 0.838199i | ||||
\(560\) | −122234. | −0.389777 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 893810. | 2.82991 | ||||||||
\(563\) | − | 50493.5i | − | 0.159301i | −0.996823 | − | 0.0796505i | \(-0.974620\pi\) | ||
0.996823 | − | 0.0796505i | \(-0.0253804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −387664. | + | 387664.i | −1.21439 | + | 1.21439i | ||||
\(566\) | 340194. | + | 340194.i | 1.06193 | + | 1.06193i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −143667. | −0.445309 | ||||||||
\(569\) | 301875.i | 0.932400i | 0.884679 | + | 0.466200i | \(0.154377\pi\) | ||||
−0.884679 | + | 0.466200i | \(0.845623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 290046.i | − | 0.889601i | −0.895630 | − | 0.444800i | \(-0.853275\pi\) | ||
0.895630 | − | 0.444800i | \(-0.146725\pi\) | |||||||
\(572\) | −349999. | − | 70400.4i | −1.06973 | − | 0.215171i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 117901. | − | 117901.i | 0.357843 | − | 0.357843i | ||||
\(575\) | −285962. | −0.864914 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 127765. | − | 127765.i | 0.383760 | − | 0.383760i | −0.488695 | − | 0.872455i | \(-0.662527\pi\) |
0.872455 | + | 0.488695i | \(0.162527\pi\) | |||||||
\(578\) | 241368. | − | 241368.i | 0.722477 | − | 0.722477i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −430252. | − | 430252.i | −1.27899 | − | 1.27899i | ||||
\(581\) | 211278. | 0.625897 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 218290. | + | 218290.i | 0.642240 | + | 0.642240i | ||||
\(584\) | − | 146664.i | − | 0.430030i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 47538.4 | 0.138436 | ||||||||
\(587\) | 432681. | − | 432681.i | 1.25572 | − | 1.25572i | 0.302598 | − | 0.953118i | \(-0.402146\pi\) |
0.953118 | − | 0.302598i | \(-0.0978541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 62703.6i | − | 0.180743i | ||||||
\(590\) | 894031. | − | 894031.i | 2.56832 | − | 2.56832i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 211753. | + | 211753.i | 0.604207 | + | 0.604207i | ||||
\(593\) | −351836. | − | 351836.i | −1.00053 | − | 1.00053i | −1.00000 | 0.000531251i | \(-0.999831\pi\) | |
−0.000531251 | − | 1.00000i | \(-0.500169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 147395.i | 0.416341i | ||||||||
\(596\) | −28298.7 | − | 28298.7i | −0.0796663 | − | 0.0796663i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −79342.4 | + | 394454.i | −0.221872 | + | 1.10305i | ||||
\(599\) | 484810. | 1.35119 | 0.675597 | − | 0.737271i | \(-0.263886\pi\) | ||||
0.675597 | + | 0.737271i | \(0.263886\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 214570. | 0.594046 | 0.297023 | − | 0.954870i | \(-0.404006\pi\) | ||||
0.297023 | + | 0.954870i | \(0.404006\pi\) | |||||||
\(602\) | − | 410915.i | − | 1.13386i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −128968. | + | 128968.i | −0.353516 | + | 0.353516i | ||||
\(605\) | −129681. | − | 129681.i | −0.354294 | − | 0.354294i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2800.08 | −0.00759964 | −0.00379982 | − | 0.999993i | \(-0.501210\pi\) | ||||
−0.00379982 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(608\) | 917096.i | 2.48089i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 113862.i | − | 0.305998i | ||||||
\(611\) | −1597.32 | + | 7941.17i | −0.00427869 | + | 0.0212717i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −92722.6 | + | 92722.6i | −0.246754 | + | 0.246754i | −0.819637 | − | 0.572883i | \(-0.805825\pi\) |
0.572883 | + | 0.819637i | \(0.305825\pi\) | |||||||
\(614\) | 317265. | 0.841560 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −55982.2 | + | 55982.2i | −0.147533 | + | 0.147533i | ||||
\(617\) | −260927. | + | 260927.i | −0.685407 | + | 0.685407i | −0.961213 | − | 0.275806i | \(-0.911055\pi\) |
0.275806 | + | 0.961213i | \(0.411055\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 103595. | + | 103595.i | 0.270369 | + | 0.270369i | 0.829249 | − | 0.558880i | \(-0.188769\pi\) |
−0.558880 | + | 0.829249i | \(0.688769\pi\) | |||||||
\(620\) | 74939.2 | 0.194951 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 246783. | + | 246783.i | 0.637874 | + | 0.637874i | ||||
\(623\) | 290266.i | 0.747859i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 309460. | 0.792218 | ||||||||
\(626\) | −731248. | + | 731248.i | −1.86602 | + | 1.86602i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 520606.i | 1.32005i | ||||||||
\(629\) | 255341. | − | 255341.i | 0.645385 | − | 0.645385i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −300176. | − | 300176.i | −0.753907 | − | 0.753907i | 0.221299 | − | 0.975206i | \(-0.428970\pi\) |
−0.975206 | + | 0.221299i | \(0.928970\pi\) | |||||||
\(632\) | 222599. | + | 222599.i | 0.557299 | + | 0.557299i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 498599.i | − | 1.24043i | ||||||
\(635\) | 286769. | + | 286769.i | 0.711189 | + | 0.711189i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −256934. | + | 170881.i | −0.633203 | + | 0.421130i | ||||
\(638\) | 462279. | 1.13570 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −596770. | −1.45696 | ||||||||
\(641\) | − | 466494.i | − | 1.13535i | −0.823253 | − | 0.567675i | \(-0.807843\pi\) | ||
0.823253 | − | 0.567675i | \(-0.192157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 439463. | − | 439463.i | 1.06292 | − | 1.06292i | 0.0650372 | − | 0.997883i | \(-0.479283\pi\) |
0.997883 | − | 0.0650372i | \(-0.0207166\pi\) | |||||||
\(644\) | 141671. | + | 141671.i | 0.341594 | + | 0.341594i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 676409. | 1.62086 | ||||||||
\(647\) | 562437.i | 1.34358i | 0.740740 | + | 0.671792i | \(0.234475\pi\) | ||||
−0.740740 | + | 0.671792i | \(0.765525\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 550555.i | 1.30711i | ||||||||
\(650\) | −150042. | + | 745938.i | −0.355128 | + | 1.76553i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −520754. | + | 520754.i | −1.22500 | + | 1.22500i | ||||
\(653\) | −37629.2 | −0.0882467 | −0.0441234 | − | 0.999026i | \(-0.514049\pi\) | ||||
−0.0441234 | + | 0.999026i | \(0.514049\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −365733. | + | 365733.i | −0.852474 | + | 0.852474i | ||||
\(656\) | −110965. | + | 110965.i | −0.257856 | + | 0.257856i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4976.27 | + | 4976.27i | 0.0114935 | + | 0.0114935i | ||||
\(659\) | −18033.4 | −0.0415248 | −0.0207624 | − | 0.999784i | \(-0.506609\pi\) | ||||
−0.0207624 | + | 0.999784i | \(0.506609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 536607. | + | 536607.i | 1.22816 | + | 1.22816i | 0.964661 | + | 0.263495i | \(0.0848754\pi\) |
0.263495 | + | 0.964661i | \(0.415125\pi\) | |||||||
\(662\) | 1.16704e6i | 2.66299i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 295776. | 0.670852 | ||||||||
\(665\) | 414689. | − | 414689.i | 0.937733 | − | 0.937733i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 298607.i | − | 0.671195i | ||||||
\(668\) | 372794. | − | 372794.i | 0.835440 | − | 0.835440i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −952601. | − | 952601.i | −2.12208 | − | 2.12208i | ||||
\(671\) | 35058.7 | + | 35058.7i | 0.0778666 | + | 0.0778666i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 75975.6i | 0.167743i | 0.996477 | + | 0.0838715i | \(0.0267285\pi\) | ||||
−0.996477 | + | 0.0838715i | \(0.973271\pi\) | |||||||
\(674\) | 245594. | + | 245594.i | 0.540628 | + | 0.540628i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 565875. | + | 237244.i | 1.23830 | + | 0.519162i | ||||
\(677\) | −438381. | −0.956478 | −0.478239 | − | 0.878230i | \(-0.658725\pi\) | ||||
−0.478239 | + | 0.878230i | \(0.658725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −97754.1 | −0.212029 | ||||||||
\(680\) | 206343.i | 0.446244i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −40258.7 | + | 40258.7i | −0.0865549 | + | 0.0865549i | ||||
\(683\) | 14323.9 | + | 14323.9i | 0.0307057 | + | 0.0307057i | 0.722293 | − | 0.691587i | \(-0.243088\pi\) |
−0.691587 | + | 0.722293i | \(0.743088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.07881e6 | −2.29913 | ||||||||
\(686\) | 620620.i | 1.31880i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 386741.i | 0.817039i | ||||||||
\(689\) | −293828. | − | 441795.i | −0.618949 | − | 0.930641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 64315.1 | − | 64315.1i | 0.134697 | − | 0.134697i | −0.636544 | − | 0.771241i | \(-0.719637\pi\) |
0.771241 | + | 0.636544i | \(0.219637\pi\) | |||||||
\(692\) | −59730.8 | −0.124734 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 795981. | − | 795981.i | 1.65266 | − | 1.65266i | ||||
\(695\) | −328198. | + | 328198.i | −0.679464 | + | 0.679464i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 133806. | + | 133806.i | 0.275429 | + | 0.275429i | ||||
\(698\) | −630216. | −1.29354 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 267910. | + | 267910.i | 0.546755 | + | 0.546755i | ||||
\(701\) | − | 77204.1i | − | 0.157110i | −0.996910 | − | 0.0785551i | \(-0.974969\pi\) | ||
0.996910 | − | 0.0785551i | \(-0.0250307\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.43678e6 | −2.90723 | ||||||||
\(704\) | 435088. | − | 435088.i | 0.877873 | − | 0.877873i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 924298.i | 1.85440i | ||||||||
\(707\) | 94873.4 | − | 94873.4i | 0.189804 | − | 0.189804i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 561910. | + | 561910.i | 1.11783 | + | 1.11783i | 0.992060 | + | 0.125766i | \(0.0401389\pi\) |
0.125766 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(710\) | −683279. | − | 683279.i | −1.35544 | − | 1.35544i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 406353.i | 0.801574i | ||||||||
\(713\) | 26005.0 | + | 26005.0i | 0.0511538 | + | 0.0511538i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −339421. | − | 510348.i | −0.663937 | − | 0.998285i | ||||
\(716\) | 63857.3 | 0.124562 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 232857. | 0.451690 | ||||||||
\(719\) | 324777.i | 0.628243i | 0.949383 | + | 0.314121i | \(0.101710\pi\) | ||||
−0.949383 | + | 0.314121i | \(0.898290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 115191. | − | 115191.i | 0.221588 | − | 0.221588i | ||||
\(722\) | −1.33886e6 | − | 1.33886e6i | −2.56839 | − | 2.56839i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 946013. | 1.80476 | ||||||||
\(725\) | − | 564686.i | − | 1.07431i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 922269.i | − | 1.74497i | −0.488638 | − | 0.872487i | \(-0.662506\pi\) | ||
0.488638 | − | 0.872487i | \(-0.337494\pi\) | |||||||
\(728\) | 113302. | − | 75354.5i | 0.213783 | − | 0.142183i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 697533. | − | 697533.i | 1.30894 | − | 1.30894i | ||||
\(731\) | 466348. | 0.872722 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 295621. | − | 295621.i | 0.550209 | − | 0.550209i | −0.376292 | − | 0.926501i | \(-0.622801\pi\) |
0.926501 | + | 0.376292i | \(0.122801\pi\) | |||||||
\(734\) | 28106.5 | − | 28106.5i | 0.0521692 | − | 0.0521692i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −380346. | − | 380346.i | −0.702140 | − | 0.702140i | ||||
\(737\) | 586623. | 1.08000 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 369186. | + | 369186.i | 0.676015 | + | 0.676015i | 0.959096 | − | 0.283081i | \(-0.0913566\pi\) |
−0.283081 | + | 0.959096i | \(0.591357\pi\) | |||||||
\(740\) | − | 1.71714e6i | − | 3.13576i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −460972. | −0.837272 | ||||||||
\(743\) | 671107. | − | 671107.i | 1.21567 | − | 1.21567i | 0.246530 | − | 0.969135i | \(-0.420710\pi\) |
0.969135 | − | 0.246530i | \(-0.0792905\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 68707.2i | − | 0.123791i | ||||||
\(746\) | −230689. | + | 230689.i | −0.414523 | + | 0.414523i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −248911. | − | 248911.i | −0.444878 | − | 0.444878i | ||||
\(749\) | −143502. | − | 143502.i | −0.255796 | − | 0.255796i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 167627.i | 0.297210i | 0.988897 | + | 0.148605i | \(0.0474784\pi\) | ||||
−0.988897 | + | 0.148605i | \(0.952522\pi\) | |||||||
\(752\) | −4683.51 | − | 4683.51i | −0.00828201 | − | 0.00828201i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −778924. | − | 156676.i | −1.37010 | − | 0.275588i | ||||
\(755\) | −313125. | −0.549319 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −578076. | −1.00877 | −0.504386 | − | 0.863478i | \(-0.668281\pi\) | ||||
−0.504386 | + | 0.863478i | \(0.668281\pi\) | |||||||
\(758\) | 797754.i | 1.38845i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 580537. | − | 580537.i | 1.00508 | − | 1.00508i | ||||
\(761\) | 762616. | + | 762616.i | 1.31685 | + | 1.31685i | 0.916254 | + | 0.400597i | \(0.131197\pi\) |
0.400597 | + | 0.916254i | \(0.368803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 409632. | 0.703630 | ||||||||
\(764\) | − | 79252.6i | − | 0.135777i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 137768.i | − | 0.234795i | ||||||
\(767\) | 186595. | − | 927666.i | 0.317183 | − | 1.57689i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 698760. | − | 698760.i | 1.18161 | − | 1.18161i | 0.202287 | − | 0.979326i | \(-0.435163\pi\) |
0.979326 | − | 0.202287i | \(-0.0648374\pi\) | |||||||
\(770\) | −532501. | −0.898129 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 412850. | − | 412850.i | 0.692720 | − | 0.692720i | ||||
\(773\) | 311294. | − | 311294.i | 0.520968 | − | 0.520968i | −0.396895 | − | 0.917864i | \(-0.629912\pi\) |
0.917864 | + | 0.396895i | \(0.129912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49177.2 | + | 49177.2i | 0.0818766 | + | 0.0818766i | ||||
\(776\) | −136849. | −0.227258 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −933166. | − | 933166.i | −1.54170 | − | 1.54170i | ||||
\(779\) | − | 752912.i | − | 1.24071i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 420771. | 0.689833 | ||||||||
\(782\) | −280527. | + | 280527.i | −0.458734 | + | 0.458734i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 252315.i | − | 0.410498i | ||||||
\(785\) | −631996. | + | 631996.i | −1.02559 | + | 1.02559i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −528223. | − | 528223.i | −0.852841 | − | 0.852841i | 0.137642 | − | 0.990482i | \(-0.456048\pi\) |
−0.990482 | + | 0.137642i | \(0.956048\pi\) | |||||||
\(788\) | −341955. | − | 341955.i | −0.550702 | − | 0.550702i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.11735e6i | 3.39265i | ||||||||
\(791\) | 252066. | + | 252066.i | 0.402866 | + | 0.402866i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47190.6 | − | 70955.0i | −0.0750428 | − | 0.112833i | ||||
\(794\) | 703706. | 1.11622 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −500805. | −0.790393 | ||||||||
\(797\) | 550495.i | 0.866636i | 0.901241 | + | 0.433318i | \(0.142657\pi\) | ||||
−0.901241 | + | 0.433318i | \(0.857343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5647.58 | + | 5647.58i | −0.00884644 | + | 0.00884644i | ||||
\(800\) | −719260. | − | 719260.i | −1.12384 | − | 1.12384i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.47681e6 | −2.29602 | ||||||||
\(803\) | 429549.i | 0.666165i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 343967.i | 0.530793i | ||||||||
\(806\) | 81479.2 | − | 54190.0i | 0.125423 | − | 0.0834160i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 132817. | − | 132817.i | 0.203437 | − | 0.203437i | ||||
\(809\) | −705446. | −1.07787 | −0.538936 | − | 0.842347i | \(-0.681173\pi\) | ||||
−0.538936 | + | 0.842347i | \(0.681173\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 476089. | − | 476089.i | 0.723846 | − | 0.723846i | −0.245540 | − | 0.969386i | \(-0.578965\pi\) |
0.969386 | + | 0.245540i | \(0.0789654\pi\) | |||||||
\(812\) | −279757. | + | 279757.i | −0.424296 | + | 0.424296i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 922481. | + | 922481.i | 1.39222 | + | 1.39222i | ||||
\(815\) | −1.26435e6 | −1.90350 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.31205e6 | − | 1.31205e6i | −1.96565 | − | 1.96565i | ||||
\(818\) | 799064.i | 1.19419i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 899831. | 1.33824 | ||||||||
\(821\) | −162224. | + | 162224.i | −0.240675 | + | 0.240675i | −0.817129 | − | 0.576455i | \(-0.804436\pi\) |
0.576455 | + | 0.817129i | \(0.304436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.34448e6i | 1.98497i | 0.122378 | + | 0.992484i | \(0.460948\pi\) | ||||
−0.122378 | + | 0.992484i | \(0.539052\pi\) | |||||||
\(824\) | 161259. | − | 161259.i | 0.237504 | − | 0.237504i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −581314. | − | 581314.i | −0.852022 | − | 0.852022i | ||||
\(827\) | 542193. | + | 542193.i | 0.792762 | + | 0.792762i | 0.981942 | − | 0.189180i | \(-0.0605830\pi\) |
−0.189180 | + | 0.981942i | \(0.560583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 485612.i | 0.706611i | 0.935508 | + | 0.353305i | \(0.114942\pi\) | ||||
−0.935508 | + | 0.353305i | \(0.885058\pi\) | |||||||
\(830\) | 1.40671e6 | + | 1.40671e6i | 2.04196 | + | 2.04196i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −880569. | + | 585648.i | −1.27209 | + | 0.846038i | ||||
\(833\) | −304253. | −0.438474 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 905114. | 1.29817 | ||||||||
\(836\) | 1.40060e6i | 2.00401i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 87135.4 | − | 87135.4i | 0.124081 | − | 0.124081i | ||||
\(839\) | −702797. | − | 702797.i | −0.998404 | − | 0.998404i | 0.00159522 | − | 0.999999i | \(-0.499492\pi\) |
−0.999999 | + | 0.00159522i | \(0.999492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −117625. | −0.166305 | ||||||||
\(842\) | − | 1.48239e6i | − | 2.09092i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 215815.i | − | 0.302969i | ||||||
\(845\) | 398945. | + | 974957.i | 0.558727 | + | 1.36544i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −84320.5 | + | 84320.5i | −0.117535 | + | 0.117535i | ||||
\(848\) | 433853. | 0.603324 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −530494. | + | 530494.i | −0.734248 | + | 0.734248i | ||||
\(851\) | 595874. | − | 595874.i | 0.822801 | − | 0.822801i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 528758. | + | 528758.i | 0.726706 | + | 0.726706i | 0.969962 | − | 0.243256i | \(-0.0782154\pi\) |
−0.243256 | + | 0.969962i | \(0.578215\pi\) | |||||||
\(854\) | −74034.9 | −0.101513 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −200893. | − | 200893.i | −0.274169 | − | 0.274169i | ||||
\(857\) | − | 427769.i | − | 0.582435i | −0.956657 | − | 0.291217i | \(-0.905940\pi\) | ||
0.956657 | − | 0.291217i | \(-0.0940603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −110526. | −0.149788 | −0.0748941 | − | 0.997191i | \(-0.523862\pi\) | ||||
−0.0748941 | + | 0.997191i | \(0.523862\pi\) | |||||||
\(860\) | 1.56807e6 | − | 1.56807e6i | 2.12016 | − | 2.12016i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.10437e6i | 1.48627i | ||||||||
\(863\) | −115225. | + | 115225.i | −0.154713 | + | 0.154713i | −0.780219 | − | 0.625506i | \(-0.784892\pi\) |
0.625506 | + | 0.780219i | \(0.284892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72510.9 | − | 72510.9i | −0.0969106 | − | 0.0969106i | ||||
\(866\) | 298528. | + | 298528.i | 0.398060 | + | 0.398060i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 48726.7i | − | 0.0646737i | ||||||
\(869\) | −651945. | − | 651945.i | −0.863319 | − | 0.863319i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −988440. | − | 198819.i | −1.30291 | − | 0.262073i | ||||
\(872\) | 573457. | 0.754168 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.57850e6 | 2.06643 | ||||||||
\(875\) | 97628.6i | 0.127515i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 352595. | − | 352595.i | 0.458435 | − | 0.458435i | −0.439707 | − | 0.898141i | \(-0.644918\pi\) |
0.898141 | + | 0.439707i | \(0.144918\pi\) | |||||||
\(878\) | −490917. | − | 490917.i | −0.636823 | − | 0.636823i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 501174. | 0.647177 | ||||||||
\(881\) | − | 776892.i | − | 1.00094i | −0.865753 | − | 0.500471i | \(-0.833160\pi\) | ||
0.865753 | − | 0.500471i | \(-0.166840\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 990585.i | 1.27049i | 0.772312 | + | 0.635244i | \(0.219100\pi\) | ||||
−0.772312 | + | 0.635244i | \(0.780900\pi\) | |||||||
\(884\) | 335045. | + | 503768.i | 0.428745 | + | 0.644653i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −399445. | + | 399445.i | −0.508849 | + | 0.508849i | ||||
\(887\) | −951592. | −1.20949 | −0.604747 | − | 0.796418i | \(-0.706726\pi\) | ||||
−0.604747 | + | 0.796418i | \(0.706726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 186462. | − | 186462.i | 0.235932 | − | 0.235932i | ||||
\(890\) | −1.93261e6 | + | 1.93261e6i | −2.43985 | + | 2.43985i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −535912. | − | 535912.i | −0.673540 | − | 0.673540i | ||||
\(893\) | 31778.4 | 0.0398500 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 77520.3 | + | 77520.3i | 0.0967764 | + | 0.0967764i | ||||
\(896\) | 388030.i | 0.483336i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 151887. | 0.188352 | ||||||||
\(899\) | −51351.8 | + | 51351.8i | −0.0635384 | + | 0.0635384i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 523158.i | − | 0.644442i | ||||||
\(902\) | −483406. | + | 483406.i | −0.594154 | + | 0.594154i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 352875. | + | 352875.i | 0.431802 | + | 0.431802i | ||||
\(905\) | 1.14842e6 | + | 1.14842e6i | 1.40218 | + | 1.40218i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 122762.i | − | 0.149228i | −0.997212 | − | 0.0746141i | \(-0.976227\pi\) | ||
0.997212 | − | 0.0746141i | \(-0.0237725\pi\) | |||||||
\(908\) | 334650. | + | 334650.i | 0.405900 | + | 0.405900i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 897246. | + | 180476.i | 1.08350 | + | 0.217940i | ||||
\(911\) | −93939.2 | −0.113191 | −0.0565953 | − | 0.998397i | \(-0.518024\pi\) | ||||
−0.0565953 | + | 0.998397i | \(0.518024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −866266. | −1.03923 | ||||||||
\(914\) | − | 906796.i | − | 1.08547i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −535604. | + | 535604.i | −0.638341 | + | 0.638341i | ||||
\(917\) | 237805. | + | 237805.i | 0.282802 | + | 0.282802i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 217922. | 0.258030 | 0.129015 | − | 0.991643i | \(-0.458818\pi\) | ||||
0.129015 | + | 0.991643i | \(0.458818\pi\) | |||||||
\(920\) | 481531.i | 0.568917i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 107215.i | − | 0.126123i | ||||||
\(923\) | −708986. | − | 142609.i | −0.832212 | − | 0.167395i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.12684e6 | − | 1.12684e6i | 1.31697 | − | 1.31697i | ||||
\(926\) | 1.35346e6 | 1.57842 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 751065. | − | 751065.i | 0.872131 | − | 0.872131i | ||||
\(929\) | 489424. | − | 489424.i | 0.567092 | − | 0.567092i | −0.364221 | − | 0.931313i | \(-0.618665\pi\) |
0.931313 | + | 0.364221i | \(0.118665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 856000. | + | 856000.i | 0.987584 | + | 0.987584i | ||||
\(932\) | −481972. | −0.554868 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16797.4 | − | 16797.4i | −0.0192552 | − | 0.0192552i | ||||
\(935\) | − | 604337.i | − | 0.691283i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 74994.8 | 0.0854185 | 0.0427093 | − | 0.999088i | \(-0.486401\pi\) | ||||
0.0427093 | + | 0.999088i | \(0.486401\pi\) | |||||||
\(938\) | −619397. | + | 619397.i | −0.703985 | + | 0.703985i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 37979.4i | 0.0429826i | ||||||||
\(941\) | 746527. | − | 746527.i | 0.843075 | − | 0.843075i | −0.146183 | − | 0.989258i | \(-0.546699\pi\) |
0.989258 | + | 0.146183i | \(0.0466988\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 312255. | + | 312255.i | 0.351144 | + | 0.351144i | ||||
\(944\) | 547115. | + | 547115.i | 0.613953 | + | 0.613953i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.68480e6i | 1.88263i | ||||||||
\(947\) | 392710. | + | 392710.i | 0.437897 | + | 0.437897i | 0.891304 | − | 0.453407i | \(-0.149792\pi\) |
−0.453407 | + | 0.891304i | \(0.649792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 145584. | − | 723776.i | 0.161652 | − | 0.803659i | ||||
\(950\) | 2.98504e6 | 3.30752 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 134168. | 0.148039 | ||||||||
\(953\) | 920738.i | 1.01380i | 0.862006 | + | 0.506898i | \(0.169208\pi\) | ||||
−0.862006 | + | 0.506898i | \(0.830792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 96209.5 | − | 96209.5i | 0.105490 | − | 0.105490i | ||||
\(956\) | −1.43575e6 | − | 1.43575e6i | −1.57095 | − | 1.57095i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −462756. | −0.504221 | ||||||||
\(959\) | 701460.i | 0.762721i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 914577.i | 0.990315i | ||||||||
\(962\) | −1.24170e6 | − | 1.86700e6i | −1.34173 | − | 2.01741i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −748214. | + | 748214.i | −0.805141 | + | 0.805141i | ||||
\(965\) | 1.00237e6 | 1.07640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −683545. | + | 683545.i | −0.730994 | + | 0.730994i | −0.970817 | − | 0.239823i | \(-0.922911\pi\) |
0.239823 | + | 0.970817i | \(0.422911\pi\) | |||||||
\(968\) | −118043. | + | 118043.i | −0.125977 | + | 0.125977i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −650853. | − | 650853.i | −0.691734 | − | 0.691734i | ||||
\(971\) | 107226. | 0.113726 | 0.0568632 | − | 0.998382i | \(-0.481890\pi\) | ||||
0.0568632 | + | 0.998382i | \(0.481890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 213400. | + | 213400.i | 0.225407 | + | 0.225407i | ||||
\(974\) | 344080.i | 0.362695i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 69679.4 | 0.0731484 | ||||||||
\(977\) | 730243. | − | 730243.i | 0.765030 | − | 0.765030i | −0.212197 | − | 0.977227i | \(-0.568062\pi\) |
0.977227 | + | 0.212197i | \(0.0680619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.19012e6i | − | 1.24173i | ||||||
\(980\) | −1.02303e6 | + | 1.02303e6i | −1.06522 | + | 1.06522i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −792514. | − | 792514.i | −0.821833 | − | 0.821833i | ||||
\(983\) | −180212. | − | 180212.i | −0.186500 | − | 0.186500i | 0.607681 | − | 0.794181i | \(-0.292100\pi\) |
−0.794181 | + | 0.607681i | \(0.792100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 830241.i | − | 0.855720i | ||||||
\(986\) | −553953. | − | 553953.i | −0.569795 | − | 0.569795i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 474693. | − | 2.35996e6i | 0.486294 | − | 2.41763i | ||||
\(989\) | 1.08829e6 | 1.11263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −662719. | −0.674811 | −0.337405 | − | 0.941359i | \(-0.609549\pi\) | ||||
−0.337405 | + | 0.941359i | \(0.609549\pi\) | |||||||
\(992\) | 130817.i | 0.132936i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −444280. | + | 444280.i | −0.449659 | + | 0.449659i | ||||
\(995\) | −607959. | − | 607959.i | −0.614084 | − | 0.614084i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 464482. | 0.467281 | 0.233641 | − | 0.972323i | \(-0.424936\pi\) | ||||
0.233641 | + | 0.972323i | \(0.424936\pi\) | |||||||
\(998\) | 496899.i | 0.498893i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 117.5.j.b.109.9 | 20 | ||
3.2 | odd | 2 | 39.5.g.a.31.2 | ✓ | 20 | ||
13.8 | odd | 4 | inner | 117.5.j.b.73.9 | 20 | ||
39.8 | even | 4 | 39.5.g.a.34.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.2 | ✓ | 20 | 3.2 | odd | 2 | ||
39.5.g.a.34.2 | yes | 20 | 39.8 | even | 4 | ||
117.5.j.b.73.9 | 20 | 13.8 | odd | 4 | inner | ||
117.5.j.b.109.9 | 20 | 1.1 | even | 1 | trivial |