Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,5,Mod(65,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("144.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.q (of order \(6\), degree \(2\), not 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: | \(14.8852746841\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.39400128.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} + 11x^{4} + 14x^{3} + 98x^{2} + 20x + 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 113.3 | ||
Root | \(-1.28901 + 2.23263i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.113 |
Dual form | 144.5.q.a.65.3 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 8.70335 | − | 2.29167i | 0.967039 | − | 0.254630i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.8760 | + | 8.01130i | 0.555039 | + | 0.320452i | 0.751152 | − | 0.660129i | \(-0.229499\pi\) |
−0.196113 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 36.2418 | + | 62.7727i | 0.739630 | + | 1.28108i | 0.952662 | + | 0.304031i | \(0.0983326\pi\) |
−0.213033 | + | 0.977045i | \(0.568334\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 70.4965 | − | 39.8904i | 0.870327 | − | 0.492474i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −83.2749 | + | 48.0788i | −0.688222 | + | 0.397345i | −0.802946 | − | 0.596052i | \(-0.796735\pi\) |
0.114723 | + | 0.993397i | \(0.463402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −76.9530 | + | 133.286i | −0.455343 | + | 0.788677i | −0.998708 | − | 0.0508193i | \(-0.983817\pi\) |
0.543365 | + | 0.839497i | \(0.317150\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 139.127 | + | 37.9260i | 0.618341 | + | 0.168560i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 72.7905i | 0.251870i | 0.992038 | + | 0.125935i | \(0.0401931\pi\) | ||||
−0.992038 | + | 0.125935i | \(0.959807\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 190.660 | 0.528145 | 0.264072 | − | 0.964503i | \(-0.414934\pi\) | ||||
0.264072 | + | 0.964503i | \(0.414934\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 459.280 | + | 463.279i | 1.04145 | + | 1.05052i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.5186 | + | 7.22762i | 0.0236647 | + | 0.0136628i | 0.511786 | − | 0.859113i | \(-0.328984\pi\) |
−0.488121 | + | 0.872776i | \(0.662318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −184.138 | − | 318.937i | −0.294621 | − | 0.510298i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 522.140 | − | 508.734i | 0.716242 | − | 0.697852i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 620.301 | − | 358.131i | 0.737575 | − | 0.425839i | −0.0836117 | − | 0.996498i | \(-0.526646\pi\) |
0.821187 | + | 0.570659i | \(0.193312\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −151.284 | + | 262.031i | −0.157423 | + | 0.272665i | −0.933939 | − | 0.357433i | \(-0.883652\pi\) |
0.776515 | + | 0.630098i | \(0.216985\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −614.590 | + | 609.285i | −0.564362 | + | 0.559490i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1161.38i | 0.948063i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 826.277 | 0.603562 | 0.301781 | − | 0.953377i | \(-0.402419\pi\) | ||||
0.301781 | + | 0.953377i | \(0.402419\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −364.300 | + | 1336.39i | −0.239514 | + | 0.878625i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 481.613 | + | 278.059i | 0.286504 | + | 0.165413i | 0.636364 | − | 0.771389i | \(-0.280438\pi\) |
−0.349860 | + | 0.936802i | \(0.613771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 446.340 | + | 773.084i | 0.241395 | + | 0.418109i | 0.961112 | − | 0.276159i | \(-0.0890616\pi\) |
−0.719717 | + | 0.694268i | \(0.755728\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1297.78 | + | 11.2508i | 0.640880 | + | 0.00555597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3425.50 | − | 1977.72i | 1.55070 | − | 0.895299i | 0.552619 | − | 0.833434i | \(-0.313628\pi\) |
0.998085 | − | 0.0618654i | \(-0.0197050\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1426.44 | + | 2470.67i | −0.594104 | + | 1.02902i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 166.812 | + | 633.521i | 0.0641337 | + | 0.243568i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1966.96i | − | 0.700234i | −0.936706 | − | 0.350117i | \(-0.886142\pi\) | ||
0.936706 | − | 0.350117i | \(-0.113858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1540.69 | −0.509320 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1659.38 | − | 436.930i | 0.510736 | − | 0.134481i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4689.48 | − | 2707.47i | −1.34716 | − | 0.777785i | −0.359316 | − | 0.933216i | \(-0.616990\pi\) |
−0.987847 | + | 0.155431i | \(0.950323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 856.210 | + | 1483.00i | 0.230102 | + | 0.398549i | 0.957838 | − | 0.287309i | \(-0.0927606\pi\) |
−0.727736 | + | 0.685858i | \(0.759427\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5058.95 | + | 2979.56i | 1.27462 | + | 0.750707i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2135.60 | + | 1232.99i | −0.505467 | + | 0.291831i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2317.24 | + | 4013.58i | −0.516205 | + | 0.894093i | 0.483618 | + | 0.875279i | \(0.339322\pi\) |
−0.999823 | + | 0.0188141i | \(0.994011\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 125.517 | + | 34.2160i | 0.0263636 | + | 0.00718672i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6697.12i | − | 1.32853i | −0.747497 | − | 0.664265i | \(-0.768744\pi\) | ||
0.747497 | − | 0.664265i | \(-0.231256\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4823.86 | −0.905208 | −0.452604 | − | 0.891712i | \(-0.649505\pi\) | ||||
−0.452604 | + | 0.891712i | \(0.649505\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2333.51 | − | 2353.83i | −0.414847 | − | 0.418459i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6036.07 | − | 3484.93i | −1.01806 | − | 0.587777i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2864.40 | − | 4961.28i | −0.458964 | − | 0.794950i | 0.539942 | − | 0.841702i | \(-0.318446\pi\) |
−0.998907 | + | 0.0467524i | \(0.985113\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3378.52 | − | 5624.26i | 0.514939 | − | 0.857227i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2452.78 | + | 1416.12i | −0.356044 | + | 0.205562i | −0.667344 | − | 0.744750i | \(-0.732569\pi\) |
0.311300 | + | 0.950312i | \(0.399235\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −583.147 | + | 1010.04i | −0.0807124 | + | 0.139798i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4577.98 | − | 4538.46i | 0.604832 | − | 0.599612i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14277.7i | − | 1.80251i | −0.433290 | − | 0.901255i | \(-0.642647\pi\) | ||
0.433290 | − | 0.901255i | \(-0.357353\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11155.7 | −1.34714 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −716.187 | + | 2627.24i | −0.0828058 | + | 0.303763i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2645.60 | + | 1527.44i | 0.293141 | + | 0.169245i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3582.65 | − | 6205.34i | −0.380769 | − | 0.659511i | 0.610403 | − | 0.792091i | \(-0.291007\pi\) |
−0.991172 | + | 0.132580i | \(0.957674\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3952.71 | + | 6711.25i | −0.403297 | + | 0.684752i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1696.72 | + | 979.600i | −0.166328 | + | 0.0960298i | −0.580853 | − | 0.814008i | \(-0.697281\pi\) |
0.414525 | + | 0.910038i | \(0.363948\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2577.74 | + | 4464.77i | −0.242976 | + | 0.420848i | −0.961561 | − | 0.274592i | \(-0.911457\pi\) |
0.718584 | + | 0.695440i | \(0.244790\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2661.49 | + | 10107.9i | 0.241405 | + | 0.916814i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9117.08i | − | 0.796321i | −0.917316 | − | 0.398161i | \(-0.869649\pi\) | ||
0.917316 | − | 0.398161i | \(-0.130351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16161.1 | −1.36024 | −0.680122 | − | 0.733099i | \(-0.738073\pi\) | ||||
−0.680122 | + | 0.733099i | \(0.738073\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7191.38 | − | 1893.55i | 0.583668 | − | 0.153685i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18272.5 | + | 10549.6i | 1.43100 | + | 0.826189i | 0.997197 | − | 0.0748185i | \(-0.0238377\pi\) |
0.433804 | + | 0.901007i | \(0.357171\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.805 | + | 200.581i | 0.00875654 | + | 0.0151668i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −108.071 | + | 12465.9i | −0.00789470 | + | 0.910652i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4569.26 | + | 2638.06i | −0.322665 | + | 0.186291i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2697.36 | + | 4671.97i | −0.184233 | + | 0.319102i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4828.87 | + | 1316.35i | 0.319180 | + | 0.0870084i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 15914.9i | − | 1.01855i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20660.9 | 1.28098 | 0.640489 | − | 0.767968i | \(-0.278732\pi\) | ||||
0.640489 | + | 0.767968i | \(0.278732\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5656.31 | + | 5705.55i | 0.339902 | + | 0.342861i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2772.53 | − | 1600.72i | −0.161560 | − | 0.0932768i | 0.417040 | − | 0.908888i | \(-0.363067\pi\) |
−0.578600 | + | 0.815611i | \(0.696401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6909.88 | + | 11968.3i | 0.390631 | + | 0.676594i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11320.8 | − | 2876.17i | 0.621170 | − | 0.157814i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3353.18 | + | 1935.96i | −0.178655 | + | 0.103147i | −0.586661 | − | 0.809833i | \(-0.699558\pi\) |
0.408005 | + | 0.912980i | \(0.366224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5839.62 | + | 10114.5i | −0.302242 | + | 0.523499i | −0.976644 | − | 0.214866i | \(-0.931068\pi\) |
0.674401 | + | 0.738365i | \(0.264402\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25281.1 | − | 25062.9i | 1.27162 | − | 1.26064i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 14799.2i | − | 0.723714i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11476.4 | 0.545844 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6752.87 | + | 24772.1i | −0.312503 | + | 1.14638i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13069.8 | − | 7545.88i | −0.588705 | − | 0.339889i | 0.175880 | − | 0.984412i | \(-0.443723\pi\) |
−0.764585 | + | 0.644522i | \(0.777056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15127.7 | + | 26201.9i | 0.663465 | + | 1.14915i | 0.979699 | + | 0.200474i | \(0.0642481\pi\) |
−0.316234 | + | 0.948681i | \(0.602419\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2903.64 | + | 5131.48i | 0.124040 | + | 0.219210i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4198.42 | + | 2423.96i | −0.174752 | + | 0.100893i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10311.4 | + | 17859.8i | −0.418328 | + | 0.724565i | −0.995771 | − | 0.0918653i | \(-0.970717\pi\) |
0.577443 | + | 0.816431i | \(0.304050\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4507.61 | − | 17119.1i | −0.178300 | − | 0.677153i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1047.77i | 0.0404216i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −39790.7 | −1.49764 | −0.748818 | − | 0.662776i | \(-0.769378\pi\) | ||||
−0.748818 | + | 0.662776i | \(0.769378\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13409.2 | + | 3530.76i | −0.492533 | + | 0.129688i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23773.0 | + | 13725.3i | 0.852414 | + | 0.492141i | 0.861465 | − | 0.507818i | \(-0.169548\pi\) |
−0.00905084 | + | 0.999959i | \(0.502881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2436.98 | + | 4220.97i | 0.0853253 | + | 0.147788i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13440.9 | − | 7605.51i | 0.459659 | − | 0.260097i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8729.26 | − | 5039.84i | 0.291666 | − | 0.168393i | −0.347027 | − | 0.937855i | \(-0.612809\pi\) |
0.638693 | + | 0.769462i | \(0.279475\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13347.0 | − | 23117.7i | 0.435821 | − | 0.754864i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −47018.8 | − | 12817.3i | −1.50081 | − | 0.409120i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1215.45i | − | 0.0379343i | −0.999820 | − | 0.0189672i | \(-0.993962\pi\) | ||
0.999820 | − | 0.0189672i | \(-0.00603779\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 28359.9 | 0.865661 | 0.432831 | − | 0.901475i | \(-0.357515\pi\) | ||||
0.432831 | + | 0.901475i | \(0.357515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10850.4 | + | 10944.9i | 0.324000 | + | 0.326821i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11465.4 | + | 6619.55i | 0.335001 | + | 0.193413i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3499.68 | − | 6061.62i | −0.100079 | − | 0.173343i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 50858.0 | + | 14338.7i | 1.42376 | + | 0.401408i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8445.34 | − | 4875.92i | 0.231500 | − | 0.133656i | −0.379764 | − | 0.925083i | \(-0.623995\pi\) |
0.611264 | + | 0.791427i | \(0.290661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26701.4 | − | 46248.2i | 0.716836 | − | 1.24160i | −0.245411 | − | 0.969419i | \(-0.578923\pi\) |
0.962247 | − | 0.272177i | \(-0.0877436\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15761.2 | + | 15625.2i | −0.414497 | + | 0.410919i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 68537.7i | 1.76603i | 0.469349 | + | 0.883013i | \(0.344489\pi\) | ||||
−0.469349 | + | 0.883013i | \(0.655511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8237.42 | 0.208010 | 0.104005 | − | 0.994577i | \(-0.466834\pi\) | ||||
0.104005 | + | 0.994577i | \(0.466834\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10970.0 | + | 40242.0i | −0.271527 | + | 0.996064i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 44961.7 | + | 25958.7i | 1.09107 | + | 0.629927i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4455.24 | + | 7716.70i | 0.106014 | + | 0.183622i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1170.83 | + | 10.1503i | 0.0273246 | + | 0.000236884i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15877.2 | + | 9166.71i | −0.363481 | + | 0.209856i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20393.7 | − | 35322.9i | 0.458069 | − | 0.793399i | −0.540790 | − | 0.841158i | \(-0.681875\pi\) |
0.998859 | + | 0.0477587i | \(0.0152079\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15347.6 | − | 58287.4i | −0.338284 | − | 1.28474i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14303.1i | 0.309423i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21931.2 | −0.465740 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −41983.7 | + | 11054.7i | −0.875371 | + | 0.230493i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9701.99 | − | 5601.45i | −0.198644 | − | 0.114687i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29959.8 | − | 51891.9i | −0.602461 | − | 1.04349i | −0.992447 | − | 0.122672i | \(-0.960854\pi\) |
0.389986 | − | 0.920821i | \(-0.372480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25703.6 | − | 15138.6i | −0.507725 | − | 0.299034i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −85572.3 | + | 49405.2i | −1.66066 | + | 0.958785i | −0.688265 | + | 0.725459i | \(0.741627\pi\) |
−0.972399 | + | 0.233325i | \(0.925039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2658.97 | − | 4605.47i | 0.0507040 | − | 0.0878220i | −0.839559 | − | 0.543268i | \(-0.817187\pi\) |
0.890263 | + | 0.455446i | \(0.150520\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −60520.3 | − | 16497.9i | −1.13417 | − | 0.309175i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 18467.8i | − | 0.340176i | −0.985429 | − | 0.170088i | \(-0.945595\pi\) | ||
0.985429 | − | 0.170088i | \(-0.0544052\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 63376.3 | 1.14760 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −36299.5 | − | 36615.5i | −0.646254 | − | 0.651881i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22383.5 | − | 12923.1i | −0.391861 | − | 0.226241i | 0.291105 | − | 0.956691i | \(-0.405977\pi\) |
−0.682966 | + | 0.730450i | \(0.739310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −41536.2 | − | 71942.7i | −0.715142 | − | 1.23866i | −0.962905 | − | 0.269841i | \(-0.913029\pi\) |
0.247763 | − | 0.968821i | \(-0.420305\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16515.5 | − | 56692.4i | 0.279691 | − | 0.960090i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −39586.6 | + | 22855.3i | −0.659502 | + | 0.380764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14671.9 | + | 25412.4i | −0.240487 | + | 0.416536i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18102.2 | + | 17945.9i | −0.291966 | + | 0.289446i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 49051.6i | − | 0.778585i | −0.921114 | − | 0.389292i | \(-0.872720\pi\) | ||
0.921114 | − | 0.389292i | \(-0.127280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1389.98 | −0.0217154 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2760.65 | + | 10127.1i | −0.0424553 | + | 0.155742i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 84096.0 | + | 48552.9i | 1.27324 | + | 0.735104i | 0.975596 | − | 0.219574i | \(-0.0704668\pi\) |
0.297641 | + | 0.954678i | \(0.403800\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29945.8 | + | 51867.7i | 0.446413 | + | 0.773209i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 29443.1 | − | 49991.0i | 0.432217 | − | 0.733856i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −35921.0 | + | 20739.0i | −0.519323 | + | 0.299831i | −0.736658 | − | 0.676266i | \(-0.763597\pi\) |
0.217335 | + | 0.976097i | \(0.430264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15757.9 | − | 27293.5i | 0.224391 | − | 0.388657i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32719.7 | − | 124264.i | −0.458973 | − | 1.74310i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 115737.i | − | 1.59944i | −0.600370 | − | 0.799722i | \(-0.704980\pi\) | ||
0.600370 | − | 0.799722i | \(-0.295020\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5077.71 | 0.0691400 | 0.0345700 | − | 0.999402i | \(-0.488994\pi\) | ||||
0.0345700 | + | 0.999402i | \(0.488994\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −97091.7 | + | 25565.1i | −1.30274 | + | 0.343022i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30668.2 | + | 17706.3i | 0.405529 | + | 0.234133i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21192.9 | + | 36707.2i | 0.276205 | + | 0.478401i | 0.970438 | − | 0.241349i | \(-0.0775899\pi\) |
−0.694234 | + | 0.719750i | \(0.744257\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −212.459 | + | 24507.1i | −0.00272939 | + | 0.314835i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −35902.5 | + | 20728.3i | −0.454687 | + | 0.262513i | −0.709807 | − | 0.704396i | \(-0.751218\pi\) |
0.255121 | + | 0.966909i | \(0.417885\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19194.0 | − | 33245.0i | 0.239658 | − | 0.415100i | −0.720958 | − | 0.692979i | \(-0.756298\pi\) |
0.960616 | + | 0.277879i | \(0.0896313\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 26525.9 | + | 7230.98i | 0.326574 | + | 0.0890241i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40309.6i | 0.489378i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 78222.5 | 0.936561 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −45401.7 | − | 45797.0i | −0.536149 | − | 0.540818i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11239.5 | − | 6489.12i | −0.130922 | − | 0.0755876i | 0.433109 | − | 0.901342i | \(-0.357417\pi\) |
−0.564030 | + | 0.825754i | \(0.690750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −43380.7 | − | 75137.6i | −0.498486 | − | 0.863402i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19021.8 | + | 67468.7i | −0.215645 | + | 0.764873i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1926.69 | + | 1112.37i | −0.0215511 | + | 0.0124425i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32352.4 | + | 56036.0i | −0.357086 | + | 0.618492i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12522.2 | + | 12414.1i | −0.136394 | + | 0.135217i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27437.4i | 0.294947i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 126105. | 1.33799 | 0.668997 | − | 0.743265i | \(-0.266724\pi\) | ||||
0.668997 | + | 0.743265i | \(0.266724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12203.2 | + | 44765.8i | −0.127807 | + | 0.468845i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 86432.4 | + | 49901.7i | 0.893626 | + | 0.515935i | 0.875127 | − | 0.483894i | \(-0.160778\pi\) |
0.0184989 | + | 0.999829i | \(0.494111\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1112.68 | + | 1927.21i | 0.0113574 | + | 0.0196716i | 0.871648 | − | 0.490132i | \(-0.163051\pi\) |
−0.860291 | + | 0.509804i | \(0.829718\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 46327.8 | + | 81873.1i | 0.466896 | + | 0.825125i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −145552. | + | 84034.3i | −1.44843 | + | 0.836254i | −0.998388 | − | 0.0567515i | \(-0.981926\pi\) |
−0.450046 | + | 0.893005i | \(0.648592\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34437.0 | + | 59646.6i | −0.338410 | + | 0.586144i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20893.3 | − | 79349.1i | −0.202767 | − | 0.770073i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13878.3i | 0.133024i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 56679.9 | 0.536615 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −140655. | + | 37035.8i | −1.31541 | + | 0.346359i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 248293. | + | 143352.i | 2.29389 | + | 1.32438i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3379.43 | + | 5853.34i | 0.0308452 | + | 0.0534254i | 0.881036 | − | 0.473049i | \(-0.156847\pi\) |
−0.850191 | + | 0.526475i | \(0.823513\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 58249.6 | − | 32960.5i | 0.525297 | − | 0.297239i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −64308.1 | + | 37128.3i | −0.573028 | + | 0.330838i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 111046. | − | 192338.i | 0.977787 | − | 1.69358i | 0.307375 | − | 0.951589i | \(-0.400550\pi\) |
0.670413 | − | 0.741988i | \(-0.266117\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 183208. | + | 49942.5i | 1.59421 | + | 0.434581i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 29094.2i | − | 0.250206i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −32754.4 | −0.278408 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1467.56 | + | 1480.34i | 0.0123298 | + | 0.0124372i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 140770. | + | 81273.8i | 1.16910 | + | 0.674981i | 0.953468 | − | 0.301494i | \(-0.0974853\pi\) |
0.215633 | + | 0.976475i | \(0.430819\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36348.5 | + | 62957.4i | 0.298425 | + | 0.516887i | 0.975776 | − | 0.218773i | \(-0.0702054\pi\) |
−0.677351 | + | 0.735660i | \(0.736872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27627.2 | + | 108743.i | 0.224245 | + | 0.882646i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 111396. | − | 64314.6i | 0.893966 | − | 0.516131i | 0.0187281 | − | 0.999825i | \(-0.494038\pi\) |
0.875238 | + | 0.483693i | \(0.160705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 53652.7 | − | 92929.2i | 0.425730 | − | 0.737387i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33722.3 | + | 33431.2i | −0.264594 | + | 0.262310i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 95302.8i | − | 0.739463i | −0.929139 | − | 0.369732i | \(-0.879450\pi\) | ||
0.929139 | − | 0.369732i | \(-0.120550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −93969.7 | −0.721063 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12769.5 | + | 46843.2i | −0.0969081 | + | 0.355495i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −66935.7 | − | 38645.4i | −0.502426 | − | 0.290076i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 52073.0 | + | 90193.1i | 0.386616 | + | 0.669639i | 0.991992 | − | 0.126301i | \(-0.0403104\pi\) |
−0.605376 | + | 0.795940i | \(0.706977\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 45043.9 | + | 390.499i | 0.330814 | + | 0.00286792i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 123471. | − | 71286.2i | 0.897053 | − | 0.517914i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −122915. | + | 212896.i | −0.883463 | + | 1.53020i | −0.0359975 | + | 0.999352i | \(0.511461\pi\) |
−0.847465 | + | 0.530851i | \(0.821872\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −36471.6 | − | 138513.i | −0.259354 | − | 0.984979i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 110237.i | 0.775612i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −200830. | −1.39814 | −0.699070 | − | 0.715053i | \(-0.746403\pi\) | ||||
−0.699070 | + | 0.715053i | \(0.746403\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 179819. | − | 47347.9i | 1.23875 | − | 0.326175i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −117206. | − | 67668.8i | −0.799008 | − | 0.461308i | 0.0441160 | − | 0.999026i | \(-0.485953\pi\) |
−0.843124 | + | 0.537719i | \(0.819286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −55837.6 | − | 96713.6i | −0.376708 | − | 0.652478i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 62304.0 | + | 36695.0i | 0.416001 | + | 0.245011i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −175090. | + | 101088.i | −1.15708 | + | 0.668039i | −0.950602 | − | 0.310413i | \(-0.899533\pi\) |
−0.206475 | + | 0.978452i | \(0.566199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −526.102 | + | 911.236i | −0.00344125 | + | 0.00596043i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27798.7 | − | 7577.92i | −0.179986 | − | 0.0490642i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 91790.2i | − | 0.588304i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 102384. | 0.649608 | 0.324804 | − | 0.945781i | \(-0.394702\pi\) | ||||
0.324804 | + | 0.945781i | \(0.394702\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 87566.4 | + | 88328.8i | 0.550037 | + | 0.554826i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −78026.4 | − | 45048.6i | −0.485236 | − | 0.280151i | 0.237360 | − | 0.971422i | \(-0.423718\pi\) |
−0.722596 | + | 0.691271i | \(0.757051\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23283.5 | − | 40328.2i | −0.143363 | − | 0.248313i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 91937.9 | − | 50975.9i | 0.560512 | − | 0.310781i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −68808.1 | + | 39726.4i | −0.415385 | + | 0.239823i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −74861.0 | + | 129663.i | −0.447517 | + | 0.775122i | −0.998224 | − | 0.0595770i | \(-0.981025\pi\) |
0.550707 | + | 0.834699i | \(0.314358\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24747.3 | + | 24533.7i | −0.146502 | + | 0.145238i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 392495.i | − | 2.30109i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45379.7 | −0.263491 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27645.1 | + | 101413.i | −0.158981 | + | 0.583203i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −109423. | − | 63175.3i | −0.623276 | − | 0.359848i | 0.154868 | − | 0.987935i | \(-0.450505\pi\) |
−0.778143 | + | 0.628087i | \(0.783838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 107645. | + | 186446.i | 0.607335 | + | 1.05194i | 0.991678 | + | 0.128745i | \(0.0410949\pi\) |
−0.384342 | + | 0.923191i | \(0.625572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 162594. | − | 276067.i | 0.908709 | − | 1.54288i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23215.6 | − | 13403.5i | 0.128529 | − | 0.0742063i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −62061.3 | + | 107493.i | −0.340381 | + | 0.589557i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −33914.9 | − | 128803.i | −0.184279 | − | 0.699859i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 121972.i | 0.656607i | 0.944572 | + | 0.328304i | \(0.106477\pi\) | ||||
−0.944572 | + | 0.328304i | \(0.893523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −152419. | −0.812951 | −0.406475 | − | 0.913662i | \(-0.633242\pi\) | ||||
−0.406475 | + | 0.913662i | \(0.633242\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 99882.9 | − | 26300.0i | 0.527853 | − | 0.138988i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2386.80 | + | 1378.02i | 0.0124984 | + | 0.00721593i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 115564. | + | 200162.i | 0.599643 | + | 1.03861i | 0.992874 | + | 0.119173i | \(0.0380242\pi\) |
−0.393230 | + | 0.919440i | \(0.628642\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2003.26 | + | 231075.i | −0.0103005 | + | 1.18816i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17481.4 | − | 10092.9i | 0.0890774 | − | 0.0514289i | −0.454800 | − | 0.890594i | \(-0.650289\pi\) |
0.543877 | + | 0.839165i | \(0.316956\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 114383. | − | 198117.i | 0.577618 | − | 1.00046i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −131044. | − | 35722.7i | −0.655847 | − | 0.178784i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 92962.8i | − | 0.461123i | −0.973058 | − | 0.230561i | \(-0.925944\pi\) | ||
0.973058 | − | 0.230561i | \(-0.0740562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53475.0 | −0.262905 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 191707. | + | 193376.i | 0.934205 | + | 0.942339i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −154796. | − | 89371.5i | −0.747716 | − | 0.431694i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −110443. | − | 191293.i | −0.528819 | − | 0.915941i | −0.999435 | − | 0.0336033i | \(-0.989302\pi\) |
0.470616 | − | 0.882338i | \(-0.344032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 37031.0 | + | 38006.9i | 0.175768 | + | 0.180400i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 91967.2 | − | 53097.3i | 0.432744 | − | 0.249845i | −0.267771 | − | 0.963483i | \(-0.586287\pi\) |
0.700515 | + | 0.713638i | \(0.252954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34090.0 | + | 59045.5i | −0.159025 | + | 0.275439i | −0.934517 | − | 0.355918i | \(-0.884168\pi\) |
0.775493 | + | 0.631357i | \(0.217502\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −30985.4 | + | 30718.0i | −0.143302 | + | 0.142065i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 224350.i | − | 1.02871i | −0.857578 | − | 0.514353i | \(-0.828032\pi\) | ||
0.857578 | − | 0.514353i | \(-0.171968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −335925. | −1.52720 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48814.7 | + | 179070.i | −0.220043 | + | 0.807202i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −74337.9 | − | 42919.0i | −0.332267 | − | 0.191835i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35107.8 | − | 60808.5i | −0.155603 | − | 0.269511i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −78462.7 | − | 138664.i | −0.344847 | − | 0.609433i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 94542.7 | − | 54584.3i | 0.412057 | − | 0.237901i | −0.279616 | − | 0.960112i | \(-0.590207\pi\) |
0.691673 | + | 0.722211i | \(0.256874\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −63584.5 | + | 110132.i | −0.274828 | + | 0.476016i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2401.14 | + | 9119.10i | 0.0102926 | + | 0.0390893i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 114807.i | − | 0.488073i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −106309. | −0.448240 | −0.224120 | − | 0.974562i | \(-0.571951\pi\) | ||||
−0.224120 | + | 0.974562i | \(0.571951\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −346312. | + | 91187.0i | −1.44827 | + | 0.381343i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 64472.7 | + | 37223.3i | 0.267432 | + | 0.154402i | 0.627720 | − | 0.778439i | \(-0.283988\pi\) |
−0.360288 | + | 0.932841i | \(0.617322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26068.5 | + | 45152.0i | 0.107256 | + | 0.185773i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −108614. | + | 61458.9i | −0.443275 | + | 0.250827i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 420397. | − | 242716.i | 1.70195 | − | 0.982621i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −55603.4 | + | 96308.0i | −0.223306 | + | 0.386777i | −0.955810 | − | 0.293985i | \(-0.905018\pi\) |
0.732504 | + | 0.680763i | \(0.238352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 238358. | + | 64976.6i | 0.949631 | + | 0.258870i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 115897.i | − | 0.458077i | −0.973417 | − | 0.229038i | \(-0.926442\pi\) | ||
0.973417 | − | 0.229038i | \(-0.0735581\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31391.5 | −0.123092 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30882.9 | + | 31151.8i | 0.120144 | + | 0.121190i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −170299. | − | 98322.1i | −0.657319 | − | 0.379503i | 0.133936 | − | 0.990990i | \(-0.457238\pi\) |
−0.791255 | + | 0.611487i | \(0.790572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −174825. | − | 302807.i | −0.669519 | − | 1.15964i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 99551.4 | − | 96995.4i | 0.378279 | − | 0.368567i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −71537.3 | + | 41302.1i | −0.269723 | + | 0.155725i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −190172. | + | 329388.i | −0.711486 | + | 1.23233i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 64424.2 | − | 63868.1i | 0.239174 | − | 0.237110i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 299306.i | 1.10266i | 0.834289 | + | 0.551328i | \(0.185879\pi\) | ||||
−0.834289 | + | 0.551328i | \(0.814121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 162892. | 0.595520 | 0.297760 | − | 0.954641i | \(-0.403760\pi\) | ||||
0.297760 | + | 0.954641i | \(0.403760\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 63185.6 | − | 231788.i | 0.229245 | − | 0.840955i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19073.4 | − | 11012.0i | −0.0686763 | − | 0.0396503i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −139816. | − | 242168.i | −0.499627 | − | 0.865379i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −438594. | − | 3802.29i | −1.55551 | − | 0.0134852i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −74123.1 | + | 42795.0i | −0.260915 | + | 0.150639i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 73039.7 | − | 126508.i | 0.255183 | − | 0.441989i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2785.41 | − | 10578.5i | −0.00965920 | − | 0.0366839i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 274327.i | − | 0.944257i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −62918.7 | −0.214974 | −0.107487 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107487 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 246826. | − | 64991.5i | 0.837128 | − | 0.220423i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −224251. | − | 129471.i | −0.754989 | − | 0.435893i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7403.57 | − | 12823.4i | −0.0247438 | − | 0.0428575i | 0.853388 | − | 0.521276i | \(-0.174544\pi\) |
−0.878132 | + | 0.478418i | \(0.841210\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 119517. | + | 70391.8i | 0.396539 | + | 0.233549i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 118267. | − | 68281.3i | 0.389547 | − | 0.224905i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 207622. | − | 359612.i | 0.678927 | − | 1.17594i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 114957. | + | 31337.4i | 0.373207 | + | 0.101736i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 254392.i | 0.819962i | 0.912094 | + | 0.409981i | \(0.134465\pi\) | ||||
−0.912094 | + | 0.409981i | \(0.865535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −137389. | −0.439671 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44350.2 | − | 44736.3i | −0.140919 | − | 0.142146i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −80806.7 | − | 46653.8i | −0.254936 | − | 0.147187i | 0.367087 | − | 0.930187i | \(-0.380355\pi\) |
−0.622022 | + | 0.783000i | \(0.713689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 169032. | + | 292772.i | 0.529508 | + | 0.917134i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 475494. | + | 8245.01i | 1.47904 | + | 0.0256463i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −136853. | + | 79012.1i | −0.422698 | + | 0.244045i | −0.696231 | − | 0.717818i | \(-0.745141\pi\) |
0.273533 | + | 0.961863i | \(0.411808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −219188. | + | 379644.i | −0.672270 | + | 1.16441i | 0.304988 | + | 0.952356i | \(0.401347\pi\) |
−0.977259 | + | 0.212050i | \(0.931986\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 62328.8 | − | 61790.8i | 0.189836 | − | 0.188198i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5323.52i | − | 0.0161014i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 214770. | 0.645094 | 0.322547 | − | 0.946554i | \(-0.395461\pi\) | ||||
0.322547 | + | 0.946554i | \(0.395461\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 126406. | − | 463705.i | 0.377061 | − | 1.38320i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −177787. | − | 102645.i | −0.526681 | − | 0.304079i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 94568.9 | + | 163798.i | 0.278235 | + | 0.481917i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −101368. | + | 172111.i | −0.296202 | + | 0.502918i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −568470. | + | 328206.i | −1.64980 | + | 0.952512i | −0.672649 | + | 0.739962i | \(0.734843\pi\) |
−0.977150 | + | 0.212550i | \(0.931823\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28843.8 | + | 49959.0i | −0.0831423 | + | 0.144007i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 157066. | + | 596507.i | 0.449683 | + | 1.70781i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 118369.i | − | 0.336612i | −0.985735 | − | 0.168306i | \(-0.946170\pi\) | ||
0.985735 | − | 0.168306i | \(-0.0538296\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −84537.3 | −0.238789 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 71693.1 | − | 18877.4i | 0.201154 | − | 0.0529656i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 306693. | + | 177069.i | 0.854772 | + | 0.493503i | 0.862258 | − | 0.506469i | \(-0.169050\pi\) |
−0.00748620 | + | 0.999972i | \(0.502383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 297820. | + | 515839.i | 0.824526 | + | 1.42812i | 0.902281 | + | 0.431148i | \(0.141891\pi\) |
−0.0777554 | + | 0.996972i | \(0.524775\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3254.27 | + | 375379.i | −0.00894992 | + | 1.03237i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −74857.1 | + | 43218.8i | −0.204514 | + | 0.118076i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4860.81 | − | 8419.17i | 0.0131926 | − | 0.0228503i | −0.859354 | − | 0.511382i | \(-0.829134\pi\) |
0.872546 | + | 0.488531i | \(0.162467\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 450806. | + | 122890.i | 1.21550 | + | 0.331346i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 608765.i | 1.63067i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 194450. | 0.517473 | 0.258736 | − | 0.965948i | \(-0.416694\pi\) | ||||
0.258736 | + | 0.965948i | \(0.416694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 56459.6 | + | 56951.2i | 0.149275 | + | 0.150575i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 422308. | + | 243819.i | 1.10932 | + | 0.640469i | 0.938654 | − | 0.344860i | \(-0.112073\pi\) |
0.170670 | + | 0.985328i | \(0.445407\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8628.23 | + | 14944.5i | 0.0225185 | + | 0.0390033i | 0.877065 | − | 0.480372i | \(-0.159498\pi\) |
−0.854547 | + | 0.519375i | \(0.826165\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10213.4 | − | 2594.81i | 0.0264842 | − | 0.00672857i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 896249. | − | 517449.i | 2.30915 | − | 1.33319i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12412.5 | − | 21499.1i | 0.0317760 | − | 0.0550376i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −117178. | + | 116166.i | −0.298065 | + | 0.295492i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 60145.1i | 0.152019i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 429836. | 1.07955 | 0.539777 | − | 0.841808i | \(-0.318509\pi\) | ||||
0.539777 | + | 0.841808i | \(0.318509\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 96545.0 | − | 354163.i | 0.240948 | − | 0.883886i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 286690. | + | 165521.i | 0.710993 | + | 0.410492i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −219538. | − | 380251.i | −0.541042 | − | 0.937113i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −267151. | − | 472124.i | −0.654266 | − | 1.15626i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27979.5 | + | 16154.0i | −0.0680964 | + | 0.0393155i | −0.533662 | − | 0.845698i | \(-0.679184\pi\) |
0.465565 | + | 0.885014i | \(0.345851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 138524. | − | 239931.i | 0.335045 | − | 0.580315i | −0.648448 | − | 0.761259i | \(-0.724582\pi\) |
0.983494 | + | 0.180943i | \(0.0579150\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32777.9 | + | 124485.i | 0.0787882 | + | 0.299224i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 125452.i | 0.299689i | 0.988710 | + | 0.149844i | \(0.0478773\pi\) | ||||
−0.988710 | + | 0.149844i | \(0.952123\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 520687. | 1.23620 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −190875. | + | 50259.1i | −0.450388 | + | 0.118591i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 245936. | + | 141991.i | 0.576760 | + | 0.332992i | 0.759845 | − | 0.650105i | \(-0.225275\pi\) |
−0.183085 | + | 0.983097i | \(0.558608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25647.8 | − | 44423.2i | −0.0597815 | − | 0.103545i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −340065. | + | 192425.i | −0.787828 | + | 0.445791i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −311139. | + | 179636.i | −0.716446 | + | 0.413640i | −0.813443 | − | 0.581644i | \(-0.802410\pi\) |
0.0969973 | + | 0.995285i | \(0.469076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −98902.1 | + | 171303.i | −0.226362 | + | 0.392070i | −0.956727 | − | 0.290987i | \(-0.906016\pi\) |
0.730366 | + | 0.683057i | \(0.239350\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −97276.5 | − | 26517.6i | −0.221300 | − | 0.0603264i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 221429.i | 0.500715i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10353.7 | 0.0232726 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −379669. | − | 382975.i | −0.848307 | − | 0.855693i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −142602. | − | 82331.1i | −0.316723 | − | 0.182860i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −119036. | − | 206176.i | −0.262814 | − | 0.455207i | 0.704175 | − | 0.710027i | \(-0.251317\pi\) |
−0.966989 | + | 0.254820i | \(0.917984\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −258400. | − | 72852.2i | −0.567133 | − | 0.159895i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 216636. | − | 125075.i | 0.472666 | − | 0.272894i | −0.244689 | − | 0.969602i | \(-0.578686\pi\) |
0.717355 | + | 0.696708i | \(0.245353\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 259684. | − | 449786.i | 0.563256 | − | 0.975588i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −631545. | + | 626094.i | −1.36179 | + | 1.35004i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 267358.i | − | 0.573129i | −0.958061 | − | 0.286564i | \(-0.907487\pi\) | ||
0.958061 | − | 0.286564i | \(-0.0925132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −62038.2 | −0.132214 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12587.7 | − | 46176.5i | 0.0266707 | − | 0.0978380i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 262169. | + | 151363.i | 0.552259 | + | 0.318847i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 168343. | + | 291579.i | 0.352565 | + | 0.610660i | 0.986698 | − | 0.162564i | \(-0.0519763\pi\) |
−0.634133 | + | 0.773224i | \(0.718643\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −564537. | − | 4894.13i | −1.17551 | − | 0.0101908i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −162061. | + | 93565.9i | −0.335513 | + | 0.193708i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20240.1 | + | 35056.9i | −0.0416627 | + | 0.0721618i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −42322.1 | − | 160732.i | −0.0866189 | − | 0.328963i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 635795.i | 1.29384i | 0.762557 | + | 0.646921i | \(0.223944\pi\) | ||||
−0.762557 | + | 0.646921i | \(0.776056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 157538. | 0.318768 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 551586. | − | 145237.i | 1.10978 | − | 0.292214i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −122984. | − | 71005.0i | −0.246043 | − | 0.142053i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −215513. | − | 373280.i | −0.428728 | − | 0.742578i | 0.568033 | − | 0.823006i | \(-0.307705\pi\) |
−0.996760 | + | 0.0804279i | \(0.974371\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −399837. | − | 235491.i | −0.790941 | − | 0.465839i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3787.73 | + | 2186.84i | −0.00745074 | + | 0.00430169i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 118561. | − | 205354.i | 0.231916 | − | 0.401690i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −224427. | − | 61178.9i | −0.436553 | − | 0.119004i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 798370.i | 1.54435i | 0.635409 | + | 0.772176i | \(0.280832\pi\) | ||||
−0.635409 | + | 0.772176i | \(0.719168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −373688. | −0.718850 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −526372. | − | 530956.i | −1.00697 | − | 1.01574i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −228442. | − | 131891.i | −0.434610 | − | 0.250922i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 158557. | + | 274628.i | 0.299996 | + | 0.519609i | 0.976135 | − | 0.217166i | \(-0.0696812\pi\) |
−0.676139 | + | 0.736775i | \(0.736348\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13819.7 | − | 531261.i | 0.0260043 | − | 0.999662i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −56273.2 | + | 32489.3i | −0.105309 | + | 0.0608004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 488922. | − | 846837.i | 0.909979 | − | 1.57613i | 0.0958883 | − | 0.995392i | \(-0.469431\pi\) |
0.814091 | − | 0.580738i | \(-0.197236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −292159. | + | 289637.i | −0.540810 | + | 0.536142i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 445641.i | − | 0.820446i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 392565. | 0.718825 | 0.359412 | − | 0.933179i | \(-0.382977\pi\) | ||||
0.359412 | + | 0.933179i | \(0.382977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −69457.6 | + | 254796.i | −0.126498 | + | 0.464041i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −899450. | − | 519298.i | −1.62929 | − | 0.940673i | −0.984304 | − | 0.176482i | \(-0.943528\pi\) |
−0.644990 | − | 0.764191i | \(-0.723139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −120905. | − | 209413.i | −0.217836 | − | 0.377304i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −116423. | + | 197674.i | −0.208641 | + | 0.354248i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 572304. | − | 330420.i | 1.02015 | − | 0.588983i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 159783. | − | 276752.i | 0.283302 | − | 0.490694i | −0.688894 | − | 0.724862i | \(-0.741903\pi\) |
0.972196 | + | 0.234168i | \(0.0752367\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −112410. | − | 426913.i | −0.198251 | − | 0.752921i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 484769.i | 0.850435i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 500321. | 0.873085 | 0.436543 | − | 0.899684i | \(-0.356203\pi\) | ||||
0.436543 | + | 0.899684i | \(0.356203\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12097.5 | + | 3185.37i | −0.0209996 | + | 0.00552939i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −783645. | − | 452437.i | −1.35316 | − | 0.781249i | −0.364471 | − | 0.931215i | \(-0.618750\pi\) |
−0.988691 | + | 0.149966i | \(0.952083\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −585707. | − | 1.01447e6i | −1.00608 | − | 1.74258i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −818.955 | + | 94466.2i | −0.00139938 | + | 0.161419i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 721738. | − | 416696.i | 1.22684 | − | 0.708318i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −71688.6 | + | 124168.i | −0.121227 | + | 0.209970i | −0.920252 | − | 0.391327i | \(-0.872016\pi\) |
0.799025 | + | 0.601298i | \(0.205349\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 843184. | + | 229852.i | 1.41845 | + | 0.386670i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 710063.i | 1.18833i | 0.804342 | + | 0.594166i | \(0.202518\pi\) | ||||
−0.804342 | + | 0.594166i | \(0.797482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 111428. | 0.185521 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 379492. | + | 382796.i | 0.628580 | + | 0.634053i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 91824.5 | + | 53014.9i | 0.151316 | + | 0.0873621i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 321990. | + | 557702.i | 0.527885 | + | 0.914324i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 141691. | − | 502563.i | 0.231109 | − | 0.819723i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −286161. | + | 165215.i | −0.464377 | + | 0.268108i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −300855. | + | 521097.i | −0.485745 | + | 0.841335i | −0.999866 | − | 0.0163827i | \(-0.994785\pi\) |
0.514121 | + | 0.857718i | \(0.328118\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −265106. | + | 262818.i | −0.425859 | + | 0.422183i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.52935e6i | 2.44429i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −263552. | −0.419102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 74598.8 | − | 273656.i | 0.118031 | − | 0.432983i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −372227. | − | 214905.i | −0.585991 | − | 0.338322i | 0.177519 | − | 0.984117i | \(-0.443193\pi\) |
−0.763511 | + | 0.645795i | \(0.776526\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 143959. | + | 249344.i | 0.225499 | + | 0.390576i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −569542. | − | 1.00653e6i | −0.887688 | − | 1.56877i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 401706. | − | 231925.i | 0.622984 | − | 0.359680i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8393.99 | + | 14538.8i | −0.0129532 | + | 0.0224356i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −265232. | − | 1.00730e6i | −0.407266 | − | 1.54672i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 629639.i | 0.962042i | 0.876709 | + | 0.481021i | \(0.159734\pi\) | ||||
−0.876709 | + | 0.481021i | \(0.840266\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −577760. | −0.878428 | −0.439214 | − | 0.898383i | \(-0.644743\pi\) | ||||
−0.439214 | + | 0.898383i | \(0.644743\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44193.1 | − | 11636.4i | 0.0668610 | − | 0.0176051i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −552135. | − | 318775.i | −0.831246 | − | 0.479920i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 85099.3 | + | 147396.i | 0.127492 | + | 0.220822i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −786436. | + | 445004.i | −1.17245 | + | 0.663431i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38728.3 | − | 22359.8i | 0.0574569 | − | 0.0331727i | −0.470996 | − | 0.882135i | \(-0.656106\pi\) |
0.528453 | + | 0.848962i | \(0.322772\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −146289. | + | 253380.i | −0.215979 | + | 0.374087i | −0.953575 | − | 0.301155i | \(-0.902628\pi\) |
0.737596 | + | 0.675242i | \(0.235961\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 307493. | + | 83822.6i | 0.451780 | + | 0.123155i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 806491.i | − | 1.17920i | −0.807694 | − | 0.589601i | \(-0.799285\pi\) | ||
0.807694 | − | 0.589601i | \(-0.200715\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 204904. | 0.298154 | 0.149077 | − | 0.988826i | \(-0.452370\pi\) | ||||
0.149077 | + | 0.988826i | \(0.452370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 268570. | + | 270908.i | 0.388916 | + | 0.392302i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −179842. | − | 103832.i | −0.259179 | − | 0.149637i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 219915. | + | 380905.i | 0.315415 | + | 0.546315i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 54313.0 | + | 213780.i | 0.0775269 | + | 0.305152i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −667796. | + | 385552.i | −0.948681 | + | 0.547721i | −0.892671 | − | 0.450709i | \(-0.851171\pi\) |
−0.0560100 | + | 0.998430i | \(0.517838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −97125.1 | + | 168226.i | −0.137322 | + | 0.237848i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −264970. | + | 262682.i | −0.372856 | + | 0.369637i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 78093.4i | 0.109371i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −391030. | −0.545058 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 90865.5 | − | 333329.i | 0.126062 | − | 0.462442i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10343.8 | + | 5972.02i | 0.0142831 | + | 0.00824635i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −541184. | − | 937358.i | −0.743784 | − | 1.28827i | −0.950761 | − | 0.309925i | \(-0.899696\pi\) |
0.206977 | − | 0.978346i | \(-0.433637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 247435. | + | 2145.09i | 0.338477 | + | 0.00293436i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −461890. | + | 266672.i | −0.628893 | + | 0.363092i | −0.780323 | − | 0.625376i | \(-0.784945\pi\) |
0.151430 | + | 0.988468i | \(0.451612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 565525. | − | 979517.i | 0.766417 | − | 1.32747i | −0.173077 | − | 0.984908i | \(-0.555371\pi\) |
0.939494 | − | 0.342565i | \(-0.111296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 92376.1 | + | 350828.i | 0.124610 | + | 0.473247i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 110025.i | 0.147730i | 0.997268 | + | 0.0738649i | \(0.0235334\pi\) | ||||
−0.997268 | + | 0.0738649i | \(0.976467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 161503. | 0.215848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 680798. | − | 179260.i | 0.905691 | − | 0.238476i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 477065. | + | 275433.i | 0.631739 | + | 0.364735i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −356638. | − | 617715.i | −0.470101 | − | 0.814238i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −500098. | − | 294541.i | −0.656185 | − | 0.386472i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 999020. | − | 576784.i | 1.30484 | − | 0.753351i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 204377. | − | 353991.i | 0.265725 | − | 0.460249i | −0.702028 | − | 0.712149i | \(-0.747722\pi\) |
0.967753 | + | 0.251900i | \(0.0810554\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −112692. | − | 30719.9i | −0.145853 | − | 0.0397596i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 235809.i | 0.303815i | 0.988395 | + | 0.151907i | \(0.0485416\pi\) | ||||
−0.988395 | + | 0.151907i | \(0.951458\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 273719. | 0.351061 | 0.175531 | − | 0.984474i | \(-0.443836\pi\) | ||||
0.175531 | + | 0.984474i | \(0.443836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −549748. | − | 554534.i | −0.701903 | − | 0.708014i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −322071. | − | 185948.i | −0.409359 | − | 0.236344i | 0.281155 | − | 0.959662i | \(-0.409282\pi\) |
−0.690514 | + | 0.723319i | \(0.742616\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 748789. | + | 1.29694e6i | 0.947449 | + | 1.64103i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10937.9 | + | 630795.i | −0.0137778 | + | 0.794571i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 653108. | − | 377072.i | 0.818996 | − | 0.472848i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9737.36 | − | 16865.6i | 0.0121561 | − | 0.0210550i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14219.4 | + | 14096.7i | −0.0176725 | + | 0.0175199i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 216718.i | 0.268148i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 143176. | 0.176368 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −153158. | + | 561842.i | −0.187830 | + | 0.689030i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 393522. | + | 227200.i | 0.480476 | + | 0.277403i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −71965.4 | − | 124648.i | −0.0874801 | − | 0.151520i | 0.818965 | − | 0.573843i | \(-0.194548\pi\) |
−0.906445 | + | 0.422323i | \(0.861215\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −80536.0 | + | 136741.i | −0.0974680 | + | 0.165490i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 772201. | − | 445830.i | 0.930451 | − | 0.537196i | 0.0434969 | − | 0.999054i | \(-0.486150\pi\) |
0.886954 | + | 0.461857i | \(0.152817\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 136170. | − | 235854.i | 0.163358 | − | 0.282944i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 62877.5 | + | 238798.i | 0.0751023 | + | 0.285225i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 232053.i | − | 0.275961i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 582156. | 0.689300 | 0.344650 | − | 0.938731i | \(-0.387998\pi\) | ||||
0.344650 | + | 0.938731i | \(0.387998\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.09753e6 | − | 288990.i | 1.29389 | − | 0.340693i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 892636. | + | 515364.i | 1.04778 | + | 0.604937i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −152149. | − | 263530.i | −0.177822 | − | 0.307997i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3620.10 | + | 417578.i | −0.00421271 | + | 0.485935i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −668027. | + | 385685.i | −0.774038 | + | 0.446891i | −0.834313 | − | 0.551291i | \(-0.814136\pi\) |
0.0602751 | + | 0.998182i | \(0.480802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −271966. | + | 471059.i | −0.313773 | + | 0.543470i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 866609. | + | 236238.i | 0.995543 | + | 0.271385i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 112148.i | − | 0.128283i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.46097e6 | −1.66403 | −0.832015 | − | 0.554753i | \(-0.812813\pi\) | ||||
−0.832015 | + | 0.554753i | \(0.812813\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14100.5 | + | 14223.3i | 0.0159921 | + | 0.0161313i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 146658. | + | 84673.2i | 0.165626 | + | 0.0956240i | 0.580522 | − | 0.814245i | \(-0.302849\pi\) |
−0.414896 | + | 0.909869i | \(0.636182\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4019.42 | + | 6961.83i | 0.00452001 | + | 0.00782889i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 590833. | + | 606402.i | 0.661608 | + | 0.679042i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −514322. | + | 296944.i | −0.573503 | + | 0.331112i | −0.758547 | − | 0.651618i | \(-0.774090\pi\) |
0.185044 | + | 0.982730i | \(0.440757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 371210. | − | 642955.i | 0.412180 | − | 0.713917i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.07421e6 | + | 1.06494e6i | −1.18776 | + | 1.17750i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.25477e6i | − | 1.38159i | −0.723050 | − | 0.690796i | \(-0.757260\pi\) | ||
0.723050 | − | 0.690796i | \(-0.242740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 156250. | 0.171322 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −163027. | + | 598043.i | −0.178006 | + | 0.652993i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −243051. | − | 140326.i | −0.264278 | − | 0.152581i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 415987. | + | 720510.i | 0.450436 | + | 0.780178i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −363684. | − | 642722.i | −0.392167 | − | 0.693060i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 741017. | − | 427826.i | 0.795744 | − | 0.459423i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −528928. | + | 916130.i | −0.565645 | + | 0.979725i | 0.431345 | + | 0.902187i | \(0.358039\pi\) |
−0.996989 | + | 0.0775381i | \(0.975294\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31804.4 | + | 120787.i | 0.0338719 | + | 0.128639i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 775745.i | − | 0.822774i | −0.911461 | − | 0.411387i | \(-0.865044\pi\) | ||
0.911461 | − | 0.411387i | \(-0.134956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −846555. | −0.894189 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 493305. | − | 129892.i | 0.518927 | − | 0.136638i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −429995. | − | 248258.i | −0.450479 | − | 0.260084i | 0.257554 | − | 0.966264i | \(-0.417084\pi\) |
−0.708032 | + | 0.706180i | \(0.750417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 686453. | + | 1.18897e6i | 0.716218 | + | 1.24053i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.13930e6 | + | 644671.i | −1.18386 | + | 0.669885i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −260643. | + | 150482.i | −0.269736 | + | 0.155732i | −0.628768 | − | 0.777593i | \(-0.716440\pi\) |
0.359032 | + | 0.933325i | \(0.383107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −549076. | + | 951028.i | −0.565927 | + | 0.980214i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.48950e6 | + | 678638.i | 2.55551 | + | 0.696633i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12903.9i | 0.0131925i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.70094e6 | −1.73197 | −0.865987 | − | 0.500067i | \(-0.833309\pi\) | ||||
−0.865987 | + | 0.500067i | \(0.833309\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 42826.3 | + | 43199.1i | 0.0434322 | + | 0.0438103i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 114302. | + | 65992.4i | 0.115454 | + | 0.0666573i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 312919. | + | 541991.i | 0.314805 | + | 0.545258i | 0.979396 | − | 0.201949i | \(-0.0647276\pi\) |
−0.664591 | + | 0.747207i | \(0.731394\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 431432. | − | 420355.i | 0.432297 | − | 0.421197i |
(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 | 144.5.q.a.113.3 | 6 | ||
3.2 | odd | 2 | 432.5.q.a.17.1 | 6 | |||
4.3 | odd | 2 | 9.5.d.a.5.3 | yes | 6 | ||
9.2 | odd | 6 | inner | 144.5.q.a.65.3 | 6 | ||
9.4 | even | 3 | 1296.5.e.c.161.2 | 6 | |||
9.5 | odd | 6 | 1296.5.e.c.161.5 | 6 | |||
9.7 | even | 3 | 432.5.q.a.305.1 | 6 | |||
12.11 | even | 2 | 27.5.d.a.17.1 | 6 | |||
36.7 | odd | 6 | 27.5.d.a.8.1 | 6 | |||
36.11 | even | 6 | 9.5.d.a.2.3 | ✓ | 6 | ||
36.23 | even | 6 | 81.5.b.a.80.2 | 6 | |||
36.31 | odd | 6 | 81.5.b.a.80.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.5.d.a.2.3 | ✓ | 6 | 36.11 | even | 6 | ||
9.5.d.a.5.3 | yes | 6 | 4.3 | odd | 2 | ||
27.5.d.a.8.1 | 6 | 36.7 | odd | 6 | |||
27.5.d.a.17.1 | 6 | 12.11 | even | 2 | |||
81.5.b.a.80.2 | 6 | 36.23 | even | 6 | |||
81.5.b.a.80.5 | 6 | 36.31 | odd | 6 | |||
144.5.q.a.65.3 | 6 | 9.2 | odd | 6 | inner | ||
144.5.q.a.113.3 | 6 | 1.1 | even | 1 | trivial | ||
432.5.q.a.17.1 | 6 | 3.2 | odd | 2 | |||
432.5.q.a.305.1 | 6 | 9.7 | even | 3 | |||
1296.5.e.c.161.2 | 6 | 9.4 | even | 3 | |||
1296.5.e.c.161.5 | 6 | 9.5 | odd | 6 |