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 | 109.2 | ||
Root | \(-4.67933 + 4.67933i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.109 |
Dual form | 117.5.j.b.73.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.67933 | + | 4.67933i | −1.16983 | + | 1.16983i | −0.187584 | + | 0.982249i | \(0.560066\pi\) |
−0.982249 | + | 0.187584i | \(0.939934\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 27.7923i | − | 1.73702i | ||||||
\(5\) | −13.1418 | + | 13.1418i | −0.525671 | + | 0.525671i | −0.919279 | − | 0.393608i | \(-0.871227\pi\) |
0.393608 | + | 0.919279i | \(0.371227\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −30.2175 | − | 30.2175i | −0.616684 | − | 0.616684i | 0.327996 | − | 0.944679i | \(-0.393627\pi\) |
−0.944679 | + | 0.327996i | \(0.893627\pi\) | |||||||
\(8\) | 55.1800 | + | 55.1800i | 0.862187 | + | 0.862187i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 122.989i | − | 1.22989i | ||||||
\(11\) | −58.8012 | − | 58.8012i | −0.485960 | − | 0.485960i | 0.421069 | − | 0.907029i | \(-0.361655\pi\) |
−0.907029 | + | 0.421069i | \(0.861655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 120.640 | + | 118.351i | 0.713846 | + | 0.700303i | ||||
\(14\) | 282.795 | 1.44283 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.7343 | −0.280212 | ||||||||
\(17\) | − | 257.703i | − | 0.891706i | −0.895106 | − | 0.445853i | \(-0.852900\pi\) | ||
0.895106 | − | 0.445853i | \(-0.147100\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 336.208 | − | 336.208i | 0.931323 | − | 0.931323i | −0.0664659 | − | 0.997789i | \(-0.521172\pi\) |
0.997789 | + | 0.0664659i | \(0.0211724\pi\) | |||||||
\(20\) | 365.240 | + | 365.240i | 0.913100 | + | 0.913100i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 550.300 | 1.13698 | ||||||||
\(23\) | 486.231i | 0.919151i | 0.888139 | + | 0.459576i | \(0.151999\pi\) | ||||
−0.888139 | + | 0.459576i | \(0.848001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 279.587i | 0.447340i | ||||||||
\(26\) | −1118.32 | + | 10.7102i | −1.65432 | + | 0.0158436i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −839.813 | + | 839.813i | −1.07119 | + | 1.07119i | ||||
\(29\) | 771.373 | 0.917209 | 0.458604 | − | 0.888641i | \(-0.348350\pi\) | ||||
0.458604 | + | 0.888641i | \(0.348350\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1304.18 | + | 1304.18i | −1.35711 | + | 1.35711i | −0.479654 | + | 0.877458i | \(0.659238\pi\) |
−0.877458 | + | 0.479654i | \(0.840762\pi\) | |||||||
\(32\) | −547.211 | + | 547.211i | −0.534386 | + | 0.534386i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1205.88 | + | 1205.88i | 1.04315 | + | 1.04315i | ||||
\(35\) | 794.223 | 0.648345 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1053.22 | + | 1053.22i | 0.769333 | + | 0.769333i | 0.977989 | − | 0.208656i | \(-0.0669091\pi\) |
−0.208656 | + | 0.977989i | \(0.566909\pi\) | |||||||
\(38\) | 3146.45i | 2.17898i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1450.33 | −0.906454 | ||||||||
\(41\) | 1126.29 | − | 1126.29i | 0.670010 | − | 0.670010i | −0.287708 | − | 0.957718i | \(-0.592893\pi\) |
0.957718 | + | 0.287708i | \(0.0928932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1930.35i | − | 1.04400i | −0.852946 | − | 0.521999i | \(-0.825186\pi\) | ||
0.852946 | − | 0.521999i | \(-0.174814\pi\) | |||||||
\(44\) | −1634.22 | + | 1634.22i | −0.844121 | + | 0.844121i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2275.24 | − | 2275.24i | −1.07525 | − | 1.07525i | ||||
\(47\) | 65.7645 | + | 65.7645i | 0.0297712 | + | 0.0297712i | 0.721836 | − | 0.692064i | \(-0.243299\pi\) |
−0.692064 | + | 0.721836i | \(0.743299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 574.806i | − | 0.239403i | ||||||
\(50\) | −1308.28 | − | 1308.28i | −0.523313 | − | 0.523313i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3289.25 | − | 3352.86i | 1.21644 | − | 1.23996i | ||||
\(53\) | 5040.23 | 1.79432 | 0.897158 | − | 0.441710i | \(-0.145628\pi\) | ||||
0.897158 | + | 0.441710i | \(0.145628\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1545.50 | 0.510910 | ||||||||
\(56\) | − | 3334.80i | − | 1.06339i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3609.51 | + | 3609.51i | −1.07298 | + | 1.07298i | ||||
\(59\) | 206.279 | + | 206.279i | 0.0592586 | + | 0.0592586i | 0.736115 | − | 0.676856i | \(-0.236658\pi\) |
−0.676856 | + | 0.736115i | \(0.736658\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6998.83 | 1.88090 | 0.940450 | − | 0.339932i | \(-0.110404\pi\) | ||||
0.940450 | + | 0.339932i | \(0.110404\pi\) | |||||||
\(62\) | − | 12205.4i | − | 3.17519i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 6268.91i | − | 1.53050i | ||||||
\(65\) | −3140.77 | + | 30.0794i | −0.743377 | + | 0.00711939i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −939.648 | + | 939.648i | −0.209322 | + | 0.209322i | −0.803979 | − | 0.594657i | \(-0.797288\pi\) |
0.594657 | + | 0.803979i | \(0.297288\pi\) | |||||||
\(68\) | −7162.15 | −1.54891 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3716.43 | + | 3716.43i | −0.758456 | + | 0.758456i | ||||
\(71\) | 3049.34 | − | 3049.34i | 0.604908 | − | 0.604908i | −0.336703 | − | 0.941611i | \(-0.609312\pi\) |
0.941611 | + | 0.336703i | \(0.109312\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −840.175 | − | 840.175i | −0.157661 | − | 0.157661i | 0.623869 | − | 0.781529i | \(-0.285560\pi\) |
−0.781529 | + | 0.623869i | \(0.785560\pi\) | |||||||
\(74\) | −9856.69 | −1.79998 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9343.97 | − | 9343.97i | −1.61772 | − | 1.61772i | ||||
\(77\) | 3553.65i | 0.599367i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4044.54 | 0.648059 | 0.324030 | − | 0.946047i | \(-0.394962\pi\) | ||||
0.324030 | + | 0.946047i | \(0.394962\pi\) | |||||||
\(80\) | 942.716 | − | 942.716i | 0.147299 | − | 0.147299i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10540.5i | 1.56760i | ||||||||
\(83\) | −2060.82 | + | 2060.82i | −0.299147 | + | 0.299147i | −0.840680 | − | 0.541533i | \(-0.817844\pi\) |
0.541533 | + | 0.840680i | \(0.317844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3386.67 | + | 3386.67i | 0.468744 | + | 0.468744i | ||||
\(86\) | 9032.76 | + | 9032.76i | 1.22130 | + | 1.22130i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 6489.30i | − | 0.837977i | ||||||
\(89\) | −6032.18 | − | 6032.18i | −0.761543 | − | 0.761543i | 0.215059 | − | 0.976601i | \(-0.431006\pi\) |
−0.976601 | + | 0.215059i | \(0.931006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −69.1630 | − | 7221.71i | −0.00835202 | − | 0.872082i | ||||
\(92\) | 13513.5 | 1.59658 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −615.468 | −0.0696546 | ||||||||
\(95\) | 8836.73i | 0.979139i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5575.10 | − | 5575.10i | 0.592528 | − | 0.592528i | −0.345785 | − | 0.938314i | \(-0.612387\pi\) |
0.938314 | + | 0.345785i | \(0.112387\pi\) | |||||||
\(98\) | 2689.71 | + | 2689.71i | 0.280061 | + | 0.280061i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7770.37 | 0.777037 | ||||||||
\(101\) | − | 14591.5i | − | 1.43040i | −0.698920 | − | 0.715200i | \(-0.746335\pi\) | ||
0.698920 | − | 0.715200i | \(-0.253665\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13071.3i | 1.23210i | 0.787708 | + | 0.616048i | \(0.211267\pi\) | ||||
−0.787708 | + | 0.616048i | \(0.788733\pi\) | |||||||
\(104\) | 126.298 | + | 13187.5i | 0.0116770 | + | 1.21926i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23584.9 | + | 23584.9i | −2.09905 | + | 2.09905i | ||||
\(107\) | 14255.0 | 1.24509 | 0.622545 | − | 0.782584i | \(-0.286099\pi\) | ||||
0.622545 | + | 0.782584i | \(0.286099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4886.68 | + | 4886.68i | −0.411302 | + | 0.411302i | −0.882192 | − | 0.470890i | \(-0.843933\pi\) |
0.470890 | + | 0.882192i | \(0.343933\pi\) | |||||||
\(110\) | −7231.92 | + | 7231.92i | −0.597680 | + | 0.597680i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2167.63 | + | 2167.63i | 0.172802 | + | 0.172802i | ||||
\(113\) | 3433.45 | 0.268890 | 0.134445 | − | 0.990921i | \(-0.457075\pi\) | ||||
0.134445 | + | 0.990921i | \(0.457075\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6389.94 | − | 6389.94i | −0.483171 | − | 0.483171i | ||||
\(116\) | − | 21438.2i | − | 1.59321i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1930.50 | −0.138645 | ||||||||
\(119\) | −7787.14 | + | 7787.14i | −0.549900 | + | 0.549900i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 7725.84i | − | 0.527685i | ||||||
\(122\) | −32749.8 | + | 32749.8i | −2.20034 | + | 2.20034i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 36246.3 | + | 36246.3i | 2.35733 | + | 2.35733i | ||||
\(125\) | −11887.9 | − | 11887.9i | −0.760825 | − | 0.760825i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 21948.2i | − | 1.36079i | −0.732846 | − | 0.680395i | \(-0.761808\pi\) | ||
0.732846 | − | 0.680395i | \(-0.238192\pi\) | |||||||
\(128\) | 20578.9 | + | 20578.9i | 1.25604 | + | 1.25604i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14555.9 | − | 14837.4i | 0.861298 | − | 0.877955i | ||||
\(131\) | 1658.15 | 0.0966231 | 0.0483116 | − | 0.998832i | \(-0.484616\pi\) | ||||
0.0483116 | + | 0.998832i | \(0.484616\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20318.7 | −1.14866 | ||||||||
\(134\) | − | 8793.84i | − | 0.489744i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14220.0 | − | 14220.0i | 0.768817 | − | 0.768817i | ||||
\(137\) | 21604.3 | + | 21604.3i | 1.15106 | + | 1.15106i | 0.986340 | + | 0.164724i | \(0.0526732\pi\) |
0.164724 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4658.17 | −0.241094 | −0.120547 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120547 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(140\) | − | 22073.3i | − | 1.12619i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 28537.8i | 1.41528i | ||||||||
\(143\) | −134.587 | − | 14053.0i | −0.00658157 | − | 0.687220i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10137.2 | + | 10137.2i | −0.482150 | + | 0.482150i | ||||
\(146\) | 7862.91 | 0.368874 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 29271.3 | − | 29271.3i | 1.33634 | − | 1.33634i | ||||
\(149\) | −393.889 | + | 393.889i | −0.0177420 | + | 0.0177420i | −0.715922 | − | 0.698180i | \(-0.753993\pi\) |
0.698180 | + | 0.715922i | \(0.253993\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7620.89 | − | 7620.89i | −0.334235 | − | 0.334235i | 0.519957 | − | 0.854192i | \(-0.325948\pi\) |
−0.854192 | + | 0.519957i | \(0.825948\pi\) | |||||||
\(152\) | 37103.8 | 1.60595 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16628.7 | − | 16628.7i | −0.701159 | − | 0.701159i | ||||
\(155\) | − | 34278.6i | − | 1.42679i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 25587.3 | 1.03807 | 0.519034 | − | 0.854754i | \(-0.326292\pi\) | ||||
0.519034 | + | 0.854754i | \(0.326292\pi\) | |||||||
\(158\) | −18925.7 | + | 18925.7i | −0.758121 | + | 0.758121i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 14382.7i | − | 0.561822i | ||||||
\(161\) | 14692.7 | − | 14692.7i | 0.566826 | − | 0.566826i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16600.8 | − | 16600.8i | −0.624820 | − | 0.624820i | 0.321940 | − | 0.946760i | \(-0.395665\pi\) |
−0.946760 | + | 0.321940i | \(0.895665\pi\) | |||||||
\(164\) | −31302.1 | − | 31302.1i | −1.16382 | − | 1.16382i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 19286.6i | − | 0.699904i | ||||||
\(167\) | 37894.4 | + | 37894.4i | 1.35876 | + | 1.35876i | 0.875451 | + | 0.483307i | \(0.160565\pi\) |
0.483307 | + | 0.875451i | \(0.339435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 547.013 | + | 28555.8i | 0.0191524 | + | 0.999817i | ||||
\(170\) | −31694.7 | −1.09670 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −53648.9 | −1.81344 | ||||||||
\(173\) | − | 1712.90i | − | 0.0572321i | −0.999590 | − | 0.0286161i | \(-0.990890\pi\) | ||
0.999590 | − | 0.0286161i | \(-0.00911002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8448.43 | − | 8448.43i | 0.275867 | − | 0.275867i | ||||
\(176\) | 4218.06 | + | 4218.06i | 0.136172 | + | 0.136172i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 56453.1 | 1.78176 | ||||||||
\(179\) | 2700.43i | 0.0842803i | 0.999112 | + | 0.0421401i | \(0.0134176\pi\) | ||||
−0.999112 | + | 0.0421401i | \(0.986582\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 31325.6i | 0.956186i | 0.878309 | + | 0.478093i | \(0.158672\pi\) | ||||
−0.878309 | + | 0.478093i | \(0.841328\pi\) | |||||||
\(182\) | 34116.4 | + | 33469.1i | 1.02996 | + | 1.01042i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −26830.2 | + | 26830.2i | −0.792481 | + | 0.792481i | ||||
\(185\) | −27682.3 | −0.808832 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15153.2 | + | 15153.2i | −0.433333 | + | 0.433333i | ||||
\(188\) | 1827.75 | − | 1827.75i | 0.0517131 | − | 0.0517131i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −41350.0 | − | 41350.0i | −1.14543 | − | 1.14543i | ||||
\(191\) | −52778.0 | −1.44672 | −0.723362 | − | 0.690469i | \(-0.757404\pi\) | ||||
−0.723362 | + | 0.690469i | \(0.757404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1405.79 | + | 1405.79i | 0.0377403 | + | 0.0377403i | 0.725725 | − | 0.687985i | \(-0.241504\pi\) |
−0.687985 | + | 0.725725i | \(0.741504\pi\) | |||||||
\(194\) | 52175.5i | 1.38632i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −15975.2 | −0.415847 | ||||||||
\(197\) | −10175.2 | + | 10175.2i | −0.262188 | + | 0.262188i | −0.825942 | − | 0.563755i | \(-0.809356\pi\) |
0.563755 | + | 0.825942i | \(0.309356\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7439.54i | − | 0.187862i | −0.995579 | − | 0.0939312i | \(-0.970057\pi\) | ||
0.995579 | − | 0.0939312i | \(-0.0299434\pi\) | |||||||
\(200\) | −15427.6 | + | 15427.6i | −0.385691 | + | 0.385691i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 68278.5 | + | 68278.5i | 1.67333 | + | 1.67333i | ||||
\(203\) | −23308.9 | − | 23308.9i | −0.565627 | − | 0.565627i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29602.8i | 0.704410i | ||||||||
\(206\) | −61165.0 | − | 61165.0i | −1.44135 | − | 1.44135i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8654.02 | − | 8489.84i | −0.200028 | − | 0.196233i | ||||
\(209\) | −39538.8 | −0.905172 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −45876.3 | −1.03044 | −0.515221 | − | 0.857057i | \(-0.672290\pi\) | ||||
−0.515221 | + | 0.857057i | \(0.672290\pi\) | |||||||
\(212\) | − | 140080.i | − | 3.11676i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −66704.1 | + | 66704.1i | −1.45655 | + | 1.45655i | ||||
\(215\) | 25368.3 | + | 25368.3i | 0.548800 | + | 0.548800i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 78818.4 | 1.67382 | ||||||||
\(218\) | − | 45732.8i | − | 0.962309i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 42953.1i | − | 0.887460i | ||||||
\(221\) | 30499.4 | − | 31089.3i | 0.624464 | − | 0.636541i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26187.3 | − | 26187.3i | 0.526601 | − | 0.526601i | −0.392956 | − | 0.919557i | \(-0.628548\pi\) |
0.919557 | + | 0.392956i | \(0.128548\pi\) | |||||||
\(224\) | 33070.7 | 0.659094 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16066.3 | + | 16066.3i | −0.314556 | + | 0.314556i | ||||
\(227\) | 20418.0 | − | 20418.0i | 0.396244 | − | 0.396244i | −0.480662 | − | 0.876906i | \(-0.659604\pi\) |
0.876906 | + | 0.480662i | \(0.159604\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −52109.2 | − | 52109.2i | −0.993672 | − | 0.993672i | 0.00630803 | − | 0.999980i | \(-0.497992\pi\) |
−0.999980 | + | 0.00630803i | \(0.997992\pi\) | |||||||
\(230\) | 59801.3 | 1.13046 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 42564.3 | + | 42564.3i | 0.790806 | + | 0.790806i | ||||
\(233\) | 45782.3i | 0.843308i | 0.906757 | + | 0.421654i | \(0.138550\pi\) | ||||
−0.906757 | + | 0.421654i | \(0.861450\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1728.53 | −0.0312997 | ||||||||
\(236\) | 5732.97 | − | 5732.97i | 0.102933 | − | 0.102933i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 72877.2i | − | 1.28658i | ||||||
\(239\) | 54954.6 | − | 54954.6i | 0.962073 | − | 0.962073i | −0.0372339 | − | 0.999307i | \(-0.511855\pi\) |
0.999307 | + | 0.0372339i | \(0.0118546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23474.0 | + | 23474.0i | 0.404159 | + | 0.404159i | 0.879696 | − | 0.475537i | \(-0.157746\pi\) |
−0.475537 | + | 0.879696i | \(0.657746\pi\) | |||||||
\(242\) | 36151.8 | + | 36151.8i | 0.617304 | + | 0.617304i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 194513.i | − | 3.26716i | ||||||
\(245\) | 7553.98 | + | 7553.98i | 0.125847 | + | 0.125847i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 80350.6 | − | 769.526i | 1.31703 | − | 0.0126133i | ||||
\(248\) | −143930. | −2.34017 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 111255. | 1.78008 | ||||||||
\(251\) | 51668.4i | 0.820120i | 0.912059 | + | 0.410060i | \(0.134492\pi\) | ||||
−0.912059 | + | 0.410060i | \(0.865508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28591.0 | − | 28591.0i | 0.446671 | − | 0.446671i | ||||
\(254\) | 102703. | + | 102703.i | 1.59190 | + | 1.59190i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −92288.7 | −1.40821 | ||||||||
\(257\) | 87980.2i | 1.33204i | 0.745932 | + | 0.666022i | \(0.232004\pi\) | ||||
−0.745932 | + | 0.666022i | \(0.767996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 63651.1i | − | 0.948869i | ||||||
\(260\) | 835.976 | + | 87289.1i | 0.0123665 | + | 1.29126i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7759.03 | + | 7759.03i | −0.113033 | + | 0.113033i | ||||
\(263\) | −113585. | −1.64214 | −0.821068 | − | 0.570831i | \(-0.806621\pi\) | ||||
−0.821068 | + | 0.570831i | \(0.806621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −66237.6 | + | 66237.6i | −0.943220 | + | 0.943220i | ||||
\(266\) | 95077.9 | − | 95077.9i | 1.34374 | − | 1.34374i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26114.9 | + | 26114.9i | 0.363596 | + | 0.363596i | ||||
\(269\) | −5647.94 | −0.0780523 | −0.0390262 | − | 0.999238i | \(-0.512426\pi\) | ||||
−0.0390262 | + | 0.999238i | \(0.512426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3722.39 | − | 3722.39i | −0.0506854 | − | 0.0506854i | 0.681310 | − | 0.731995i | \(-0.261411\pi\) |
−0.731995 | + | 0.681310i | \(0.761411\pi\) | |||||||
\(272\) | 18486.1i | 0.249867i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −202187. | −2.69310 | ||||||||
\(275\) | 16440.1 | − | 16440.1i | 0.217389 | − | 0.217389i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31673.1i | 0.412792i | 0.978469 | + | 0.206396i | \(0.0661736\pi\) | ||||
−0.978469 | + | 0.206396i | \(0.933826\pi\) | |||||||
\(278\) | 21797.1 | − | 21797.1i | 0.282039 | − | 0.282039i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 43825.2 | + | 43825.2i | 0.558995 | + | 0.558995i | ||||
\(281\) | 10897.2 | + | 10897.2i | 0.138007 | + | 0.138007i | 0.772736 | − | 0.634728i | \(-0.218888\pi\) |
−0.634728 | + | 0.772736i | \(0.718888\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30994.4i | 0.387000i | 0.981100 | + | 0.193500i | \(0.0619839\pi\) | ||||
−0.981100 | + | 0.193500i | \(0.938016\pi\) | |||||||
\(284\) | −84748.2 | − | 84748.2i | −1.05074 | − | 1.05074i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 66388.2 | + | 65128.7i | 0.811632 | + | 0.796233i | ||||
\(287\) | −68067.2 | −0.826369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17110.2 | 0.204861 | ||||||||
\(290\) | − | 94870.7i | − | 1.12807i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −23350.4 | + | 23350.4i | −0.273860 | + | 0.273860i | ||||
\(293\) | 113536. | + | 113536.i | 1.32251 | + | 1.32251i | 0.911741 | + | 0.410765i | \(0.134738\pi\) |
0.410765 | + | 0.911741i | \(0.365262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5421.75 | −0.0623011 | ||||||||
\(296\) | 116233.i | 1.32662i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 3686.28i | − | 0.0415103i | ||||||
\(299\) | −57546.0 | + | 58658.9i | −0.643684 | + | 0.656133i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −58330.4 | + | 58330.4i | −0.643817 | + | 0.643817i | ||||
\(302\) | 71321.3 | 0.781998 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24117.6 | + | 24117.6i | −0.260968 | + | 0.260968i | ||||
\(305\) | −91977.0 | + | 91977.0i | −0.988735 | + | 0.988735i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 75222.4 | + | 75222.4i | 0.798124 | + | 0.798124i | 0.982800 | − | 0.184675i | \(-0.0591233\pi\) |
−0.184675 | + | 0.982800i | \(0.559123\pi\) | |||||||
\(308\) | 98764.0 | 1.04111 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 160401. | + | 160401.i | 1.66910 | + | 1.66910i | ||||
\(311\) | − | 150426.i | − | 1.55525i | −0.628726 | − | 0.777627i | \(-0.716423\pi\) | ||
0.628726 | − | 0.777627i | \(-0.283577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 126604. | 1.29229 | 0.646144 | − | 0.763216i | \(-0.276381\pi\) | ||||
0.646144 | + | 0.763216i | \(0.276381\pi\) | |||||||
\(314\) | −119732. | + | 119732.i | −1.21437 | + | 1.21437i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 112407.i | − | 1.12569i | ||||||
\(317\) | 42350.8 | − | 42350.8i | 0.421447 | − | 0.421447i | −0.464255 | − | 0.885702i | \(-0.653678\pi\) |
0.885702 | + | 0.464255i | \(0.153678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45357.6 | − | 45357.6i | −0.445727 | − | 0.445727i | ||||
\(320\) | 82384.6 | + | 82384.6i | 0.804537 | + | 0.804537i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 137504.i | 1.32618i | ||||||||
\(323\) | −86641.7 | − | 86641.7i | −0.830466 | − | 0.830466i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −33089.5 | + | 33729.4i | −0.313273 | + | 0.319332i | ||||
\(326\) | 155362. | 1.46187 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 124297. | 1.15535 | ||||||||
\(329\) | − | 3974.48i | − | 0.0367188i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23593.9 | − | 23593.9i | 0.215349 | − | 0.215349i | −0.591186 | − | 0.806535i | \(-0.701340\pi\) |
0.806535 | + | 0.591186i | \(0.201340\pi\) | |||||||
\(332\) | 57275.0 | + | 57275.0i | 0.519624 | + | 0.519624i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −354641. | −3.17904 | ||||||||
\(335\) | − | 24697.3i | − | 0.220069i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 114863.i | − | 1.01139i | −0.862711 | − | 0.505697i | \(-0.831235\pi\) | ||
0.862711 | − | 0.505697i | \(-0.168765\pi\) | |||||||
\(338\) | −136182. | − | 131062.i | −1.19202 | − | 1.14721i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 94123.4 | − | 94123.4i | 0.814216 | − | 0.814216i | ||||
\(341\) | 153375. | 1.31900 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −89921.4 | + | 89921.4i | −0.764319 | + | 0.764319i | ||||
\(344\) | 106517. | − | 106517.i | 0.900122 | − | 0.900122i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8015.22 | + | 8015.22i | 0.0669520 | + | 0.0669520i | ||||
\(347\) | −93409.6 | −0.775769 | −0.387885 | − | 0.921708i | \(-0.626794\pi\) | ||||
−0.387885 | + | 0.921708i | \(0.626794\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14479.3 | − | 14479.3i | −0.118877 | − | 0.118877i | 0.645166 | − | 0.764043i | \(-0.276788\pi\) |
−0.764043 | + | 0.645166i | \(0.776788\pi\) | |||||||
\(350\) | 79066.0i | 0.645437i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 64353.3 | 0.519380 | ||||||||
\(353\) | −127078. | + | 127078.i | −1.01981 | + | 1.01981i | −0.0200140 | + | 0.999800i | \(0.506371\pi\) |
−0.999800 | + | 0.0200140i | \(0.993629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 80147.6i | 0.635966i | ||||||||
\(356\) | −167648. | + | 167648.i | −1.32281 | + | 1.32281i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12636.2 | − | 12636.2i | −0.0985939 | − | 0.0985939i | ||||
\(359\) | −40565.6 | − | 40565.6i | −0.314752 | − | 0.314752i | 0.531995 | − | 0.846747i | \(-0.321442\pi\) |
−0.846747 | + | 0.531995i | \(0.821442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 95750.0i | − | 0.734724i | ||||||
\(362\) | −146583. | − | 146583.i | −1.11858 | − | 1.11858i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −200708. | + | 1922.20i | −1.51482 | + | 0.0145076i | ||||
\(365\) | 22082.8 | 0.165755 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −40747.7 | −0.302532 | −0.151266 | − | 0.988493i | \(-0.548335\pi\) | ||||
−0.151266 | + | 0.988493i | \(0.548335\pi\) | |||||||
\(368\) | − | 34879.4i | − | 0.257557i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 129534. | − | 129534.i | 0.946198 | − | 0.946198i | ||||
\(371\) | −152303. | − | 152303.i | −1.10652 | − | 1.10652i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −44353.1 | −0.318791 | −0.159396 | − | 0.987215i | \(-0.550955\pi\) | ||||
−0.159396 | + | 0.987215i | \(0.550955\pi\) | |||||||
\(374\) | − | 141814.i | − | 1.01386i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7257.77i | 0.0513367i | ||||||||
\(377\) | 93058.4 | + | 91292.8i | 0.654746 | + | 0.642324i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27066.7 | + | 27066.7i | −0.188433 | + | 0.188433i | −0.795018 | − | 0.606585i | \(-0.792539\pi\) |
0.606585 | + | 0.795018i | \(0.292539\pi\) | |||||||
\(380\) | 245593. | 1.70078 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 246966. | − | 246966.i | 1.69243 | − | 1.69243i | ||||
\(383\) | 166419. | − | 166419.i | 1.13451 | − | 1.13451i | 0.145087 | − | 0.989419i | \(-0.453654\pi\) |
0.989419 | − | 0.145087i | \(-0.0463461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −46701.2 | − | 46701.2i | −0.315070 | − | 0.315070i | ||||
\(386\) | −13156.3 | −0.0882997 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −154945. | − | 154945.i | −1.02923 | − | 1.02923i | ||||
\(389\) | − | 16474.9i | − | 0.108874i | −0.998517 | − | 0.0544371i | \(-0.982664\pi\) | ||
0.998517 | − | 0.0544371i | \(-0.0173364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 125303. | 0.819613 | ||||||||
\(392\) | 31717.8 | − | 31717.8i | 0.206410 | − | 0.206410i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 95226.6i | − | 0.613431i | ||||||
\(395\) | −53152.4 | + | 53152.4i | −0.340666 | + | 0.340666i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −155869. | − | 155869.i | −0.988957 | − | 0.988957i | 0.0109822 | − | 0.999940i | \(-0.496504\pi\) |
−0.999940 | + | 0.0109822i | \(0.996504\pi\) | |||||||
\(398\) | 34812.1 | + | 34812.1i | 0.219768 | + | 0.219768i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 20056.0i | − | 0.125350i | ||||||
\(401\) | 142185. | + | 142185.i | 0.884230 | + | 0.884230i | 0.993961 | − | 0.109732i | \(-0.0349991\pi\) |
−0.109732 | + | 0.993961i | \(0.534999\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −311689. | + | 2985.07i | −1.91916 | + | 0.0183800i | ||||
\(404\) | −405531. | −2.48463 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 218141. | 1.32338 | ||||||||
\(407\) | − | 123861.i | − | 0.747730i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9949.25 | − | 9949.25i | 0.0594763 | − | 0.0594763i | −0.676743 | − | 0.736219i | \(-0.736609\pi\) |
0.736219 | + | 0.676743i | \(0.236609\pi\) | |||||||
\(410\) | −138521. | − | 138521.i | −0.824042 | − | 0.824042i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 363282. | 2.14017 | ||||||||
\(413\) | − | 12466.5i | − | 0.0730876i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 54165.8i | − | 0.314506i | ||||||
\(416\) | −130779. | + | 1252.48i | −0.755701 | + | 0.00723742i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 185015. | − | 185015.i | 1.05890 | − | 1.05890i | ||||
\(419\) | 17793.2 | 0.101351 | 0.0506753 | − | 0.998715i | \(-0.483863\pi\) | ||||
0.0506753 | + | 0.998715i | \(0.483863\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −123242. | + | 123242.i | −0.695334 | + | 0.695334i | −0.963400 | − | 0.268066i | \(-0.913615\pi\) |
0.268066 | + | 0.963400i | \(0.413615\pi\) | |||||||
\(422\) | 214671. | − | 214671.i | 1.20545 | − | 1.20545i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 278120. | + | 278120.i | 1.54704 | + | 1.54704i | ||||
\(425\) | 72050.5 | 0.398896 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −211487. | − | 211487.i | −1.15992 | − | 1.15992i | ||||
\(428\) | − | 396180.i | − | 2.16274i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −237413. | −1.28401 | ||||||||
\(431\) | 81585.7 | − | 81585.7i | 0.439197 | − | 0.439197i | −0.452545 | − | 0.891742i | \(-0.649484\pi\) |
0.891742 | + | 0.452545i | \(0.149484\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 60799.1i | − | 0.324281i | −0.986768 | − | 0.162141i | \(-0.948160\pi\) | ||
0.986768 | − | 0.162141i | \(-0.0518398\pi\) | |||||||
\(434\) | −368817. | + | 368817.i | −1.95809 | + | 1.95809i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 135812. | + | 135812.i | 0.714439 | + | 0.714439i | ||||
\(437\) | 163475. | + | 163475.i | 0.856027 | + | 0.856027i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 275044.i | 1.42716i | 0.700572 | + | 0.713581i | \(0.252928\pi\) | ||||
−0.700572 | + | 0.713581i | \(0.747072\pi\) | |||||||
\(440\) | 85280.9 | + | 85280.9i | 0.440500 | + | 0.440500i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2760.06 | + | 288194.i | 0.0141278 | + | 1.47516i | ||||
\(443\) | 8716.50 | 0.0444155 | 0.0222077 | − | 0.999753i | \(-0.492930\pi\) | ||||
0.0222077 | + | 0.999753i | \(0.492930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 158547. | 0.800642 | ||||||||
\(446\) | 245078.i | 1.23207i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −189431. | + | 189431.i | −0.943832 | + | 0.943832i | ||||
\(449\) | −246638. | − | 246638.i | −1.22340 | − | 1.22340i | −0.966416 | − | 0.256982i | \(-0.917272\pi\) |
−0.256982 | − | 0.966416i | \(-0.582728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −132454. | −0.651197 | ||||||||
\(452\) | − | 95423.5i | − | 0.467066i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 191086.i | 0.927078i | ||||||||
\(455\) | 95815.0 | + | 93997.2i | 0.462819 | + | 0.454038i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 55246.3 | − | 55246.3i | 0.264527 | − | 0.264527i | −0.562363 | − | 0.826890i | \(-0.690108\pi\) |
0.826890 | + | 0.562363i | \(0.190108\pi\) | |||||||
\(458\) | 487672. | 2.32486 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −177591. | + | 177591.i | −0.839277 | + | 0.839277i | ||||
\(461\) | 31473.0 | − | 31473.0i | 0.148093 | − | 0.148093i | −0.629172 | − | 0.777266i | \(-0.716606\pi\) |
0.777266 | + | 0.629172i | \(0.216606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 134703. | + | 134703.i | 0.628371 | + | 0.628371i | 0.947658 | − | 0.319287i | \(-0.103443\pi\) |
−0.319287 | + | 0.947658i | \(0.603443\pi\) | |||||||
\(464\) | −55333.9 | −0.257013 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −214231. | − | 214231.i | −0.986529 | − | 0.986529i | ||||
\(467\) | − | 106801.i | − | 0.489714i | −0.969559 | − | 0.244857i | \(-0.921259\pi\) | ||
0.969559 | − | 0.244857i | \(-0.0787410\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 56787.6 | 0.258171 | ||||||||
\(470\) | 8088.34 | − | 8088.34i | 0.0366154 | − | 0.0366154i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22765.0i | 0.102184i | ||||||||
\(473\) | −113507. | + | 113507.i | −0.507342 | + | 0.507342i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 93999.4 | + | 93999.4i | 0.416618 | + | 0.416618i | ||||
\(476\) | 216422. | + | 216422.i | 0.955186 | + | 0.955186i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 514301.i | 2.25093i | ||||||||
\(479\) | −69279.4 | − | 69279.4i | −0.301949 | − | 0.301949i | 0.539827 | − | 0.841776i | \(-0.318490\pi\) |
−0.841776 | + | 0.539827i | \(0.818490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2410.64 | + | 251709.i | 0.0104194 | + | 1.08795i | ||||
\(482\) | −219685. | −0.945597 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −214719. | −0.916599 | ||||||||
\(485\) | 146533.i | 0.622950i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 334191. | − | 334191.i | 1.40908 | − | 1.40908i | 0.644372 | − | 0.764713i | \(-0.277119\pi\) |
0.764713 | − | 0.644372i | \(-0.222881\pi\) | |||||||
\(488\) | 386195. | + | 386195.i | 1.62169 | + | 1.62169i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −70695.1 | −0.294440 | ||||||||
\(491\) | 204363.i | 0.847696i | 0.905733 | + | 0.423848i | \(0.139321\pi\) | ||||
−0.905733 | + | 0.423848i | \(0.860679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 198785.i | − | 0.817880i | ||||||
\(494\) | −372386. | + | 379588.i | −1.52595 | + | 1.55546i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 93554.7 | − | 93554.7i | 0.380279 | − | 0.380279i | ||||
\(497\) | −184287. | −0.746074 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 263314. | − | 263314.i | 1.05748 | − | 1.05748i | 0.0592381 | − | 0.998244i | \(-0.481133\pi\) |
0.998244 | − | 0.0592381i | \(-0.0188671\pi\) | |||||||
\(500\) | −330391. | + | 330391.i | −1.32157 | + | 1.32157i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −241773. | − | 241773.i | −0.959403 | − | 0.959403i | ||||
\(503\) | −120971. | −0.478131 | −0.239065 | − | 0.971003i | \(-0.576841\pi\) | ||||
−0.239065 | + | 0.971003i | \(0.576841\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 191758. | + | 191758.i | 0.751920 | + | 0.751920i | ||||
\(506\) | 267573.i | 1.04506i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −609990. | −2.36371 | ||||||||
\(509\) | 50199.3 | − | 50199.3i | 0.193759 | − | 0.193759i | −0.603559 | − | 0.797318i | \(-0.706251\pi\) |
0.797318 | + | 0.603559i | \(0.206251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50775.9i | 0.194454i | ||||||||
\(512\) | 102587. | − | 102587.i | 0.391337 | − | 0.391337i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −411688. | − | 411688.i | −1.55827 | − | 1.55827i | ||||
\(515\) | −171780. | − | 171780.i | −0.647677 | − | 0.647677i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7734.07i | − | 0.0289352i | ||||||
\(518\) | 297845. | + | 297845.i | 1.11002 | + | 1.11002i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −174967. | − | 171648.i | −0.647068 | − | 0.634792i | ||||
\(521\) | 307242. | 1.13189 | 0.565946 | − | 0.824443i | \(-0.308511\pi\) | ||||
0.565946 | + | 0.824443i | \(0.308511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 271249. | 0.991664 | 0.495832 | − | 0.868418i | \(-0.334863\pi\) | ||||
0.495832 | + | 0.868418i | \(0.334863\pi\) | |||||||
\(524\) | − | 46083.7i | − | 0.167836i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 531501. | − | 531501.i | 1.92102 | − | 1.92102i | ||||
\(527\) | 336092. | + | 336092.i | 1.21014 | + | 1.21014i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43420.3 | 0.155161 | ||||||||
\(530\) | − | 619895.i | − | 2.20682i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 564703.i | 1.99525i | ||||||||
\(533\) | 269173. | − | 2577.89i | 0.947494 | − | 0.00907424i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −187337. | + | 187337.i | −0.654508 | + | 0.654508i | ||||
\(536\) | −103699. | −0.360950 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26428.6 | − | 26428.6i | 0.0913081 | − | 0.0913081i | ||||
\(539\) | −33799.3 | + | 33799.3i | −0.116340 | + | 0.116340i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 184394. | + | 184394.i | 0.630017 | + | 0.630017i | 0.948072 | − | 0.318055i | \(-0.103030\pi\) |
−0.318055 | + | 0.948072i | \(0.603030\pi\) | |||||||
\(542\) | 34836.6 | 0.118587 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 141018. | + | 141018.i | 0.476515 | + | 0.476515i | ||||
\(545\) | − | 128439.i | − | 0.432419i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 373290. | 1.24759 | 0.623795 | − | 0.781588i | \(-0.285590\pi\) | ||||
0.623795 | + | 0.781588i | \(0.285590\pi\) | |||||||
\(548\) | 600433. | − | 600433.i | 1.99942 | − | 1.99942i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 153857.i | 0.508619i | ||||||||
\(551\) | 259341. | − | 259341.i | 0.854217 | − | 0.854217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −122216. | − | 122216.i | −0.399647 | − | 0.399647i | ||||
\(554\) | −148209. | − | 148209.i | −0.482898 | − | 0.482898i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 129461.i | 0.418784i | ||||||||
\(557\) | −200107. | − | 200107.i | −0.644987 | − | 0.644987i | 0.306790 | − | 0.951777i | \(-0.400745\pi\) |
−0.951777 | + | 0.306790i | \(0.900745\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 228460. | − | 232878.i | 0.731115 | − | 0.745254i | ||||
\(560\) | −56973.0 | −0.181674 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −101983. | −0.322891 | ||||||||
\(563\) | − | 488676.i | − | 1.54172i | −0.637007 | − | 0.770858i | \(-0.719828\pi\) | ||
0.637007 | − | 0.770858i | \(-0.280172\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45121.7 | + | 45121.7i | −0.141348 | + | 0.141348i | ||||
\(566\) | −145033. | − | 145033.i | −0.452725 | − | 0.452725i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 336525. | 1.04309 | ||||||||
\(569\) | 562947.i | 1.73877i | 0.494132 | + | 0.869387i | \(0.335486\pi\) | ||||
−0.494132 | + | 0.869387i | \(0.664514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 183359.i | − | 0.562380i | −0.959652 | − | 0.281190i | \(-0.909271\pi\) | ||
0.959652 | − | 0.281190i | \(-0.0907291\pi\) | |||||||
\(572\) | −390564. | + | 3740.47i | −1.19371 | + | 0.0114323i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 318509. | − | 318509.i | 0.966713 | − | 0.966713i | ||||
\(575\) | −135944. | −0.411173 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 196407. | − | 196407.i | 0.589938 | − | 0.589938i | −0.347677 | − | 0.937614i | \(-0.613029\pi\) |
0.937614 | + | 0.347677i | \(0.113029\pi\) | |||||||
\(578\) | −80064.2 | + | 80064.2i | −0.239653 | + | 0.239653i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 281736. | + | 281736.i | 0.837503 | + | 0.837503i | ||||
\(581\) | 124546. | 0.368958 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −296372. | − | 296372.i | −0.871966 | − | 0.871966i | ||||
\(584\) | − | 92721.6i | − | 0.271866i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.06254e6 | −3.09422 | ||||||||
\(587\) | 127057. | − | 127057.i | 0.368742 | − | 0.368742i | −0.498276 | − | 0.867018i | \(-0.666034\pi\) |
0.867018 | + | 0.498276i | \(0.166034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 876953.i | 2.52782i | ||||||||
\(590\) | 25370.2 | − | 25370.2i | 0.0728818 | − | 0.0728818i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −75551.7 | − | 75551.7i | −0.215576 | − | 0.215576i | ||||
\(593\) | −168617. | − | 168617.i | −0.479503 | − | 0.479503i | 0.425470 | − | 0.904973i | \(-0.360109\pi\) |
−0.904973 | + | 0.425470i | \(0.860109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 204674.i | − | 0.578133i | ||||||
\(596\) | 10947.1 | + | 10947.1i | 0.0308181 | + | 0.0308181i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5207.65 | − | 543761.i | −0.0145626 | − | 1.52057i | ||||
\(599\) | 22624.2 | 0.0630550 | 0.0315275 | − | 0.999503i | \(-0.489963\pi\) | ||||
0.0315275 | + | 0.999503i | \(0.489963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 621958. | 1.72192 | 0.860958 | − | 0.508675i | \(-0.169865\pi\) | ||||
0.860958 | + | 0.508675i | \(0.169865\pi\) | |||||||
\(602\) | − | 545895.i | − | 1.50632i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −211802. | + | 211802.i | −0.580572 | + | 0.580572i | ||||
\(605\) | 101531. | + | 101531.i | 0.277389 | + | 0.277389i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −600769. | −1.63054 | −0.815268 | − | 0.579084i | \(-0.803410\pi\) | ||||
−0.815268 | + | 0.579084i | \(0.803410\pi\) | |||||||
\(608\) | 367953.i | 0.995371i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 860782.i | − | 2.31331i | ||||||
\(611\) | 150.525 | + | 15717.1i | 0.000403204 | + | 0.0421009i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −230276. | + | 230276.i | −0.612812 | + | 0.612812i | −0.943678 | − | 0.330866i | \(-0.892659\pi\) |
0.330866 | + | 0.943678i | \(0.392659\pi\) | |||||||
\(614\) | −703981. | −1.86734 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −196090. | + | 196090.i | −0.516767 | + | 0.516767i | ||||
\(617\) | −34766.2 | + | 34766.2i | −0.0913244 | + | 0.0913244i | −0.751293 | − | 0.659969i | \(-0.770570\pi\) |
0.659969 | + | 0.751293i | \(0.270570\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −420362. | − | 420362.i | −1.09709 | − | 1.09709i | −0.994750 | − | 0.102339i | \(-0.967367\pi\) |
−0.102339 | − | 0.994750i | \(-0.532633\pi\) | |||||||
\(620\) | −952680. | −2.47836 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 703892. | + | 703892.i | 1.81939 | + | 1.81939i | ||||
\(623\) | 364555.i | 0.939262i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 137714. | 0.352547 | ||||||||
\(626\) | −592423. | + | 592423.i | −1.51176 | + | 1.51176i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 711130.i | − | 1.80314i | ||||||
\(629\) | 271417. | − | 271417.i | 0.686018 | − | 0.686018i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 93922.3 | + | 93922.3i | 0.235890 | + | 0.235890i | 0.815146 | − | 0.579256i | \(-0.196657\pi\) |
−0.579256 | + | 0.815146i | \(0.696657\pi\) | |||||||
\(632\) | 223177. | + | 223177.i | 0.558748 | + | 0.558748i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 396347.i | 0.986045i | ||||||||
\(635\) | 288438. | + | 288438.i | 0.715327 | + | 0.715327i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 68029.0 | − | 69344.6i | 0.167654 | − | 0.170897i | ||||
\(638\) | 424487. | 1.04285 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −540888. | −1.32053 | ||||||||
\(641\) | 123299.i | 0.300084i | 0.988680 | + | 0.150042i | \(0.0479409\pi\) | ||||
−0.988680 | + | 0.150042i | \(0.952059\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −280732. | + | 280732.i | −0.678999 | + | 0.678999i | −0.959774 | − | 0.280774i | \(-0.909409\pi\) |
0.280774 | + | 0.959774i | \(0.409409\pi\) | |||||||
\(644\) | −408343. | − | 408343.i | −0.984586 | − | 0.984586i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 810850. | 1.94301 | ||||||||
\(647\) | 45435.6i | 0.108539i | 0.998526 | + | 0.0542697i | \(0.0172831\pi\) | ||||
−0.998526 | + | 0.0542697i | \(0.982717\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24258.9i | − | 0.0575946i | ||||||
\(650\) | −2994.45 | − | 312668.i | −0.00708746 | − | 0.740042i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −461375. | + | 461375.i | −1.08532 | + | 1.08532i | ||||
\(653\) | 378723. | 0.888168 | 0.444084 | − | 0.895985i | \(-0.353529\pi\) | ||||
0.444084 | + | 0.895985i | \(0.353529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21791.0 | + | 21791.0i | −0.0507920 | + | 0.0507920i | ||||
\(656\) | −80793.4 | + | 80793.4i | −0.187745 | + | 0.187745i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18597.9 | + | 18597.9i | 0.0429548 | + | 0.0429548i | ||||
\(659\) | −289116. | −0.665735 | −0.332867 | − | 0.942974i | \(-0.608016\pi\) | ||||
−0.332867 | + | 0.942974i | \(0.608016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −168774. | − | 168774.i | −0.386281 | − | 0.386281i | 0.487078 | − | 0.873359i | \(-0.338063\pi\) |
−0.873359 | + | 0.487078i | \(0.838063\pi\) | |||||||
\(662\) | 220807.i | 0.503845i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −227433. | −0.515842 | ||||||||
\(665\) | 267024. | − | 267024.i | 0.603819 | − | 0.603819i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 375065.i | 0.843054i | ||||||||
\(668\) | 1.05317e6 | − | 1.05317e6i | 2.36019 | − | 2.36019i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 115567. | + | 115567.i | 0.257444 | + | 0.257444i | ||||
\(671\) | −411539. | − | 411539.i | −0.914043 | − | 0.914043i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 163719.i | 0.361467i | 0.983532 | + | 0.180734i | \(0.0578472\pi\) | ||||
−0.983532 | + | 0.180734i | \(0.942153\pi\) | |||||||
\(674\) | 537482. | + | 537482.i | 1.18316 | + | 1.18316i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 793630. | − | 15202.7i | 1.73670 | − | 0.0332681i | ||||
\(677\) | −462025. | −1.00806 | −0.504032 | − | 0.863685i | \(-0.668151\pi\) | ||||
−0.504032 | + | 0.863685i | \(0.668151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −336931. | −0.730805 | ||||||||
\(680\) | 373753.i | 0.808290i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −717693. | + | 717693.i | −1.54301 | + | 1.54301i | ||||
\(683\) | 213724. | + | 213724.i | 0.458155 | + | 0.458155i | 0.898049 | − | 0.439895i | \(-0.144984\pi\) |
−0.439895 | + | 0.898049i | \(0.644984\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −567838. | −1.21016 | ||||||||
\(686\) | − | 841544.i | − | 1.78825i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 138473.i | 0.292541i | ||||||||
\(689\) | 608054. | + | 596517.i | 1.28087 | + | 1.25656i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −344817. | + | 344817.i | −0.722159 | + | 0.722159i | −0.969045 | − | 0.246886i | \(-0.920593\pi\) |
0.246886 | + | 0.969045i | \(0.420593\pi\) | |||||||
\(692\) | −47605.4 | −0.0994132 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 437094. | − | 437094.i | 0.907520 | − | 0.907520i | ||||
\(695\) | 61216.6 | − | 61216.6i | 0.126736 | − | 0.126736i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −290248. | − | 290248.i | −0.597452 | − | 0.597452i | ||||
\(698\) | 135507. | 0.278132 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −234801. | − | 234801.i | −0.479186 | − | 0.479186i | ||||
\(701\) | 83587.3i | 0.170100i | 0.996377 | + | 0.0850500i | \(0.0271050\pi\) | ||||
−0.996377 | + | 0.0850500i | \(0.972895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 708198. | 1.43299 | ||||||||
\(704\) | −368619. | + | 368619.i | −0.743760 | + | 0.743760i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.18928e6i | − | 2.38602i | ||||||
\(707\) | −440919. | + | 440919.i | −0.882104 | + | 0.882104i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 507737. | + | 507737.i | 1.01006 | + | 1.01006i | 0.999949 | + | 0.0101092i | \(0.00321793\pi\) |
0.0101092 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(710\) | −375037. | − | 375037.i | −0.743973 | − | 0.743973i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 665711.i | − | 1.31318i | ||||||
\(713\) | −634135. | − | 634135.i | −1.24739 | − | 1.24739i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 186450. | + | 182912.i | 0.364711 | + | 0.357792i | ||||
\(716\) | 75051.0 | 0.146396 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 379640. | 0.736415 | ||||||||
\(719\) | − | 50596.5i | − | 0.0978729i | −0.998802 | − | 0.0489364i | \(-0.984417\pi\) | ||
0.998802 | − | 0.0489364i | \(-0.0155832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 394982. | − | 394982.i | 0.759814 | − | 0.759814i | ||||
\(722\) | 448046. | + | 448046.i | 0.859505 | + | 0.859505i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 870610. | 1.66091 | ||||||||
\(725\) | 215666.i | 0.410304i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 891410.i | − | 1.68659i | −0.537453 | − | 0.843294i | \(-0.680613\pi\) | ||
0.537453 | − | 0.843294i | \(-0.319387\pi\) | |||||||
\(728\) | 394678. | − | 402310.i | 0.744697 | − | 0.759099i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −103333. | + | 103333.i | −0.193906 | + | 0.193906i | ||||
\(731\) | −497458. | −0.930939 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −439182. | + | 439182.i | −0.817404 | + | 0.817404i | −0.985731 | − | 0.168327i | \(-0.946164\pi\) |
0.168327 | + | 0.985731i | \(0.446164\pi\) | |||||||
\(734\) | 190672. | − | 190672.i | 0.353912 | − | 0.353912i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −266071. | − | 266071.i | −0.491182 | − | 0.491182i | ||||
\(737\) | 110505. | 0.203445 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 83855.7 | + | 83855.7i | 0.153548 | + | 0.153548i | 0.779701 | − | 0.626153i | \(-0.215371\pi\) |
−0.626153 | + | 0.779701i | \(0.715371\pi\) | |||||||
\(740\) | 769353.i | 1.40495i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.42535e6 | 2.58890 | ||||||||
\(743\) | 153273. | − | 153273.i | 0.277643 | − | 0.277643i | −0.554524 | − | 0.832167i | \(-0.687100\pi\) |
0.832167 | + | 0.554524i | \(0.187100\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 10352.8i | − | 0.0186529i | ||||||
\(746\) | 207543. | − | 207543.i | 0.372933 | − | 0.372933i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 421143. | + | 421143.i | 0.752708 | + | 0.752708i | ||||
\(749\) | −430752. | − | 430752.i | −0.767827 | − | 0.767827i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 208551.i | − | 0.369771i | −0.982760 | − | 0.184886i | \(-0.940808\pi\) | ||
0.982760 | − | 0.184886i | \(-0.0591915\pi\) | |||||||
\(752\) | −4717.57 | − | 4717.57i | −0.00834225 | − | 0.00834225i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −862640. | + | 8261.59i | −1.51735 | + | 0.0145319i | ||||
\(755\) | 200304. | 0.351395 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −762290. | −1.33024 | −0.665118 | − | 0.746739i | \(-0.731619\pi\) | ||||
−0.665118 | + | 0.746739i | \(0.731619\pi\) | |||||||
\(758\) | − | 253308.i | − | 0.440870i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −487610. | + | 487610.i | −0.844201 | + | 0.844201i | ||||
\(761\) | −790313. | − | 790313.i | −1.36468 | − | 1.36468i | −0.867850 | − | 0.496826i | \(-0.834499\pi\) |
−0.496826 | − | 0.867850i | \(-0.665501\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 295326. | 0.507287 | ||||||||
\(764\) | 1.46682e6i | 2.51299i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.55746e6i | 2.65436i | ||||||||
\(767\) | 472.140 | + | 49298.9i | 0.000802565 | + | 0.0838005i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 170652. | − | 170652.i | 0.288574 | − | 0.288574i | −0.547942 | − | 0.836516i | \(-0.684589\pi\) |
0.836516 | + | 0.547942i | \(0.184589\pi\) | |||||||
\(770\) | 437061. | 0.737158 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 39070.1 | − | 39070.1i | 0.0655555 | − | 0.0655555i | ||||
\(773\) | −238774. | + | 238774.i | −0.399602 | + | 0.399602i | −0.878093 | − | 0.478490i | \(-0.841184\pi\) |
0.478490 | + | 0.878093i | \(0.341184\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −364634. | − | 364634.i | −0.607090 | − | 0.607090i | ||||
\(776\) | 615268. | 1.02174 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 77091.7 | + | 77091.7i | 0.127365 | + | 0.127365i | ||||
\(779\) | − | 757333.i | − | 1.24799i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −358610. | −0.587923 | ||||||||
\(782\) | −586335. | + | 586335.i | −0.958810 | + | 0.958810i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 41233.3i | 0.0670836i | ||||||||
\(785\) | −336263. | + | 336263.i | −0.545682 | + | 0.545682i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −460701. | − | 460701.i | −0.743823 | − | 0.743823i | 0.229488 | − | 0.973311i | \(-0.426295\pi\) |
−0.973311 | + | 0.229488i | \(0.926295\pi\) | |||||||
\(788\) | 282793. | + | 282793.i | 0.455424 | + | 0.455424i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 497435.i | − | 0.797044i | ||||||
\(791\) | −103750. | − | 103750.i | −0.165820 | − | 0.165820i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 844339. | + | 828320.i | 1.34267 | + | 1.31720i | ||||
\(794\) | 1.45872e6 | 2.31383 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −206762. | −0.326320 | ||||||||
\(797\) | 940096.i | 1.47998i | 0.672618 | + | 0.739989i | \(0.265170\pi\) | ||||
−0.672618 | + | 0.739989i | \(0.734830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16947.7 | − | 16947.7i | 0.0265471 | − | 0.0265471i | ||||
\(800\) | −152993. | − | 152993.i | −0.239052 | − | 0.239052i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.33066e6 | −2.06880 | ||||||||
\(803\) | 98806.5i | 0.153234i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 386176.i | 0.595928i | ||||||||
\(806\) | 1.44453e6 | − | 1.47246e6i | 2.22359 | − | 2.26660i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 805159. | − | 805159.i | 1.23327 | − | 1.23327i | ||||
\(809\) | −612686. | −0.936140 | −0.468070 | − | 0.883691i | \(-0.655050\pi\) | ||||
−0.468070 | + | 0.883691i | \(0.655050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 431732. | − | 431732.i | 0.656406 | − | 0.656406i | −0.298121 | − | 0.954528i | \(-0.596360\pi\) |
0.954528 | + | 0.298121i | \(0.0963601\pi\) | |||||||
\(812\) | −647809. | + | 647809.i | −0.982505 | + | 0.982505i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 579585. | + | 579585.i | 0.874719 | + | 0.874719i | ||||
\(815\) | 436329. | 0.656900 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −648999. | − | 648999.i | −0.972300 | − | 0.972300i | ||||
\(818\) | 93111.7i | 0.139155i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 822730. | 1.22357 | ||||||||
\(821\) | 193284. | − | 193284.i | 0.286754 | − | 0.286754i | −0.549041 | − | 0.835795i | \(-0.685007\pi\) |
0.835795 | + | 0.549041i | \(0.185007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 547967.i | 0.809011i | 0.914536 | + | 0.404506i | \(0.132556\pi\) | ||||
−0.914536 | + | 0.404506i | \(0.867444\pi\) | |||||||
\(824\) | −721275. | + | 721275.i | −1.06230 | + | 1.06230i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 58334.8 | + | 58334.8i | 0.0855003 | + | 0.0855003i | ||||
\(827\) | 859953. | + | 859953.i | 1.25737 | + | 1.25737i | 0.952343 | + | 0.305029i | \(0.0986660\pi\) |
0.305029 | + | 0.952343i | \(0.401334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 726172.i | − | 1.05665i | −0.849043 | − | 0.528324i | \(-0.822821\pi\) | ||
0.849043 | − | 0.528324i | \(-0.177179\pi\) | |||||||
\(830\) | 253460. | + | 253460.i | 0.367919 | + | 0.367919i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 741933. | − | 756282.i | 1.07181 | − | 1.09254i | ||||
\(833\) | −148129. | −0.213477 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −995999. | −1.42852 | ||||||||
\(836\) | 1.09887e6i | 1.57230i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −83260.3 | + | 83260.3i | −0.118563 | + | 0.118563i | ||||
\(839\) | 507389. | + | 507389.i | 0.720804 | + | 0.720804i | 0.968769 | − | 0.247965i | \(-0.0797618\pi\) |
−0.247965 | + | 0.968769i | \(0.579762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −112265. | −0.158728 | ||||||||
\(842\) | − | 1.15338e6i | − | 1.62685i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.27501e6i | 1.78990i | ||||||||
\(845\) | −382462. | − | 368085.i | −0.535642 | − | 0.515507i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −233456. | + | 233456.i | −0.325415 | + | 0.325415i | ||||
\(848\) | −361557. | −0.502789 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −337148. | + | 337148.i | −0.466641 | + | 0.466641i | ||||
\(851\) | −512107. | + | 512107.i | −0.707133 | + | 0.707133i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 192677. | + | 192677.i | 0.264808 | + | 0.264808i | 0.827004 | − | 0.562196i | \(-0.190043\pi\) |
−0.562196 | + | 0.827004i | \(0.690043\pi\) | |||||||
\(854\) | 1.97924e6 | 2.71383 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 786593. | + | 786593.i | 1.07350 | + | 1.07350i | ||||
\(857\) | − | 96833.2i | − | 0.131845i | −0.997825 | − | 0.0659223i | \(-0.979001\pi\) | ||
0.997825 | − | 0.0659223i | \(-0.0209990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 248211. | 0.336383 | 0.168192 | − | 0.985754i | \(-0.446207\pi\) | ||||
0.168192 | + | 0.985754i | \(0.446207\pi\) | |||||||
\(860\) | 705042. | − | 705042.i | 0.953275 | − | 0.953275i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 763533.i | 1.02757i | ||||||||
\(863\) | −1.02273e6 | + | 1.02273e6i | −1.37321 | + | 1.37321i | −0.517571 | + | 0.855640i | \(0.673164\pi\) |
−0.855640 | + | 0.517571i | \(0.826836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22510.5 | + | 22510.5i | 0.0300853 | + | 0.0300853i | ||||
\(866\) | 284499. | + | 284499.i | 0.379355 | + | 0.379355i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 2.19054e6i | − | 2.90745i | ||||||
\(869\) | −237824. | − | 237824.i | −0.314931 | − | 0.314931i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −224567. | + | 2150.70i | −0.296013 | + | 0.00283494i | ||||
\(872\) | −539294. | −0.709239 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.52990e6 | −2.00282 | ||||||||
\(875\) | 718444.i | 0.938376i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 263404. | − | 263404.i | 0.342470 | − | 0.342470i | −0.514825 | − | 0.857295i | \(-0.672143\pi\) |
0.857295 | + | 0.514825i | \(0.172143\pi\) | |||||||
\(878\) | −1.28702e6 | − | 1.28702e6i | −1.66954 | − | 1.66954i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −110866. | −0.143163 | ||||||||
\(881\) | − | 580702.i | − | 0.748171i | −0.927394 | − | 0.374086i | \(-0.877957\pi\) | ||
0.927394 | − | 0.374086i | \(-0.122043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.28367e6i | 1.64638i | 0.567763 | + | 0.823192i | \(0.307809\pi\) | ||||
−0.567763 | + | 0.823192i | \(0.692191\pi\) | |||||||
\(884\) | −864042. | − | 847649.i | −1.10568 | − | 1.08470i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40787.4 | + | 40787.4i | −0.0519587 | + | 0.0519587i | ||||
\(887\) | −166700. | −0.211879 | −0.105940 | − | 0.994373i | \(-0.533785\pi\) | ||||
−0.105940 | + | 0.994373i | \(0.533785\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −663219. | + | 663219.i | −0.839176 | + | 0.839176i | ||||
\(890\) | −741894. | + | 741894.i | −0.936617 | + | 0.936617i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −727805. | − | 727805.i | −0.914714 | − | 0.914714i | ||||
\(893\) | 44221.1 | 0.0554532 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35488.4 | − | 35488.4i | −0.0443037 | − | 0.0443037i | ||||
\(896\) | − | 1.24369e6i | − | 1.54916i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.30820e6 | 2.86234 | ||||||||
\(899\) | −1.00601e6 | + | 1.00601e6i | −1.24475 | + | 1.24475i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.29888e6i | − | 1.60000i | ||||||
\(902\) | 619796. | − | 619796.i | 0.761791 | − | 0.761791i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 189458. | + | 189458.i | 0.231833 | + | 0.231833i | ||||
\(905\) | −411674. | − | 411674.i | −0.502639 | − | 0.502639i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.06525e6i | 1.29490i | 0.762108 | + | 0.647450i | \(0.224164\pi\) | ||||
−0.762108 | + | 0.647450i | \(0.775836\pi\) | |||||||
\(908\) | −567464. | − | 567464.i | −0.688282 | − | 0.688282i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −888194. | + | 8506.32i | −1.07257 | + | 0.0102721i | ||||
\(911\) | 794671. | 0.957526 | 0.478763 | − | 0.877944i | \(-0.341085\pi\) | ||||
0.478763 | + | 0.877944i | \(0.341085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 242358. | 0.290747 | ||||||||
\(914\) | 517031.i | 0.618905i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.44823e6 | + | 1.44823e6i | −1.72603 | + | 1.72603i | ||||
\(917\) | −50105.1 | − | 50105.1i | −0.0595859 | − | 0.0595859i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 514196. | 0.608833 | 0.304416 | − | 0.952539i | \(-0.401539\pi\) | ||||
0.304416 | + | 0.952539i | \(0.401539\pi\) | |||||||
\(920\) | − | 705193.i | − | 0.833168i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 294545.i | 0.346489i | ||||||||
\(923\) | 728766. | − | 6979.46i | 0.855431 | − | 0.00819254i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −294466. | + | 294466.i | −0.344153 | + | 0.344153i | ||||
\(926\) | −1.26064e6 | −1.47018 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −422104. | + | 422104.i | −0.490143 | + | 0.490143i | ||||
\(929\) | 746377. | − | 746377.i | 0.864823 | − | 0.864823i | −0.127071 | − | 0.991894i | \(-0.540558\pi\) |
0.991894 | + | 0.127071i | \(0.0405576\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −193254. | − | 193254.i | −0.222961 | − | 0.222961i | ||||
\(932\) | 1.27240e6 | 1.46484 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 499758. | + | 499758.i | 0.572884 | + | 0.572884i | ||||
\(935\) | − | 398281.i | − | 0.455582i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 379998. | 0.432815 | 0.216408 | − | 0.976303i | \(-0.430566\pi\) | ||||
0.216408 | + | 0.976303i | \(0.430566\pi\) | |||||||
\(938\) | −265728. | + | 265728.i | −0.302017 | + | 0.302017i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 48039.7i | 0.0543681i | ||||||||
\(941\) | 906449. | − | 906449.i | 1.02368 | − | 1.02368i | 0.0239676 | − | 0.999713i | \(-0.492370\pi\) |
0.999713 | − | 0.0239676i | \(-0.00762984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 547636. | + | 547636.i | 0.615841 | + | 0.615841i | ||||
\(944\) | −14797.3 | − | 14797.3i | −0.0166050 | − | 0.0166050i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 1.06227e6i | − | 1.18701i | ||||||
\(947\) | −290385. | − | 290385.i | −0.323798 | − | 0.323798i | 0.526424 | − | 0.850222i | \(-0.323532\pi\) |
−0.850222 | + | 0.526424i | \(0.823532\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1923.03 | − | 200794.i | −0.00213527 | − | 0.222956i | ||||
\(950\) | −879709. | −0.974747 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −859388. | −0.948234 | ||||||||
\(953\) | 1.13841e6i | 1.25347i | 0.779234 | + | 0.626733i | \(0.215608\pi\) | ||||
−0.779234 | + | 0.626733i | \(0.784392\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 693596. | − | 693596.i | 0.760501 | − | 0.760501i | ||||
\(956\) | −1.52731e6 | − | 1.52731e6i | −1.67114 | − | 1.67114i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 648362. | 0.706459 | ||||||||
\(959\) | − | 1.30566e6i | − | 1.41968i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 2.47827e6i | − | 2.68350i | ||||||
\(962\) | −1.18911e6 | − | 1.16655e6i | −1.28491 | − | 1.26053i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 652395. | − | 652395.i | 0.702032 | − | 0.702032i | ||||
\(965\) | −36949.1 | −0.0396780 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19218.1 | − | 19218.1i | 0.0205521 | − | 0.0205521i | −0.696756 | − | 0.717308i | \(-0.745374\pi\) |
0.717308 | + | 0.696756i | \(0.245374\pi\) | |||||||
\(968\) | 426312. | − | 426312.i | 0.454964 | − | 0.454964i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −685678. | − | 685678.i | −0.728747 | − | 0.728747i | ||||
\(971\) | −416812. | −0.442080 | −0.221040 | − | 0.975265i | \(-0.570945\pi\) | ||||
−0.221040 | + | 0.975265i | \(0.570945\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 140758. | + | 140758.i | 0.148678 | + | 0.148678i | ||||
\(974\) | 3.12758e6i | 3.29679i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −502056. | −0.527051 | ||||||||
\(977\) | −394416. | + | 394416.i | −0.413205 | + | 0.413205i | −0.882853 | − | 0.469649i | \(-0.844381\pi\) |
0.469649 | + | 0.882853i | \(0.344381\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 709399.i | 0.740159i | ||||||||
\(980\) | 209942. | − | 209942.i | 0.218599 | − | 0.218599i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −956284. | − | 956284.i | −0.991663 | − | 0.991663i | ||||
\(983\) | 159479. | + | 159479.i | 0.165043 | + | 0.165043i | 0.784796 | − | 0.619754i | \(-0.212767\pi\) |
−0.619754 | + | 0.784796i | \(0.712767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 267441.i | − | 0.275649i | ||||||
\(986\) | 930181. | + | 930181.i | 0.956783 | + | 0.956783i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21386.9 | − | 2.23313e6i | −0.0219095 | − | 2.28770i | ||||
\(989\) | 938598. | 0.959593 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 869851. | 0.885722 | 0.442861 | − | 0.896590i | \(-0.353964\pi\) | ||||
0.442861 | + | 0.896590i | \(0.353964\pi\) | |||||||
\(992\) | − | 1.42733e6i | − | 1.45044i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 862340. | − | 862340.i | 0.872782 | − | 0.872782i | ||||
\(995\) | 97768.8 | + | 97768.8i | 0.0987539 | + | 0.0987539i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 798123. | 0.802934 | 0.401467 | − | 0.915874i | \(-0.368501\pi\) | ||||
0.401467 | + | 0.915874i | \(0.368501\pi\) | |||||||
\(998\) | 2.46427e6i | 2.47415i | ||||||||
\(999\) | 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.109.2 | 20 | ||
3.2 | odd | 2 | 39.5.g.a.31.9 | ✓ | 20 | ||
13.8 | odd | 4 | inner | 117.5.j.b.73.2 | 20 | ||
39.8 | even | 4 | 39.5.g.a.34.9 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.9 | ✓ | 20 | 3.2 | odd | 2 | ||
39.5.g.a.34.9 | yes | 20 | 39.8 | even | 4 | ||
117.5.j.b.73.2 | 20 | 13.8 | odd | 4 | inner | ||
117.5.j.b.109.2 | 20 | 1.1 | even | 1 | trivial |