In [1]: import numpy.random\n \n In [2]: rng = np.random.default_rng()\n \n In [3]: %timeit -n 1 rng.standard_normal(100000)\n ...: %timeit -n 1 numpy.random.standard_normal(100000)\n ...: \n-1.36 ms +- 27.9 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-2.63 ms +- 68.7 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.37 ms +- 28.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.62 ms +- 22.8 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n In [4]: %timeit -n 1 rng.standard_exponential(100000)\n ...: %timeit -n 1 numpy.random.standard_exponential(100000)\n ...: \n-730 us +- 15.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-1.92 ms +- 8.22 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+742 us +- 35.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.92 ms +- 11 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n In [5]: %timeit -n 1 rng.standard_gamma(3.0, 100000)\n ...: %timeit -n 1 numpy.random.standard_gamma(3.0, 100000)\n ...: \n-2.69 ms +- 26.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-5.04 ms +- 22.4 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.69 ms +- 44.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+5.06 ms +- 14.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n integers is now the canonical way to generate integer\n random numbers from a discrete uniform distribution. This replaces both\n randint and the deprecated random_integers.
The rand and randn methods are only available through the legacy\n@@ -586,21 +586,21 @@\n
Standard Exponentials (standard_exponential)
In [6]: rng = np.random.default_rng()\n \n In [7]: rng.random(3, dtype=np.float64)\n-Out[7]: array([0.46632479, 0.91027615, 0.7069302 ])\n+Out[7]: array([0.59799319, 0.21212049, 0.99022154])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.80933726, 0.15478891, 0.15383297], dtype=float32)\n+Out[8]: array([0.5102923 , 0.09887606, 0.8792059 ], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([139, 91, 165], dtype=uint8)\n+Out[9]: array([45, 71, 91], dtype=uint8)\n Optional out argument that allows existing arrays to be filled for\n select distributions
Uniforms (random)
In [10]: rng = np.random.default_rng()\n \n In [11]: existing = np.zeros(4)\n \n In [12]: rng.random(out=existing[:2])\n-Out[12]: array([0.58007252, 0.39445772])\n+Out[12]: array([0.44852905, 0.9290714 ])\n \n In [13]: print(existing)\n-[0.58007252 0.39445772 0. 0. ]\n+[0.44852905 0.9290714 0. 0. ]\n Optional axis argument for methods like choice,\n permutation and shuffle that controls which\n axis an operation is performed over for multi-dimensional arrays.
Added a method to sample from the complex normal distribution\n (complex_normal)
With the legacy polynomial module, a linear fit (i.e. polynomial of degree 1)\n could be applied to these data with polyfit:
In [4]: np.polyfit(x, y, deg=1)\n-Out[4]: array([0.91892069, 0.25191506])\n+Out[4]: array([0.85848058, 0.25047881])\n With the new polynomial API, the fit\n class method is preferred:
In [5]: p_fitted = np.polynomial.Polynomial.fit(x, y, deg=1)\n \n In [6]: p_fitted\n-Out[6]: Polynomial([4.38705816, 4.13514311], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.1136414 , 3.86316259], domain=[0., 9.], window=[-1., 1.], symbol='x')\n Note that the coefficients are given in the scaled domain defined by the\n linear mapping between the window and domain.\n convert can be used to get the\n coefficients in the unscaled data domain.
In [7]: p_fitted.convert()\n-Out[7]: Polynomial([0.25191506, 0.91892069], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([0.25047881, 0.85848058], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n polynomial package#In addition to standard power series polynomials, the polynomial package\n", "details": [{"source1": "html2text {}", "source2": "html2text {}", "unified_diff": "@@ -150,26 +150,26 @@\n \n In [2]: x = np.arange(10)\n \n In [3]: y = np.arange(10) + rng.standard_normal(10)\n With the legacy polynomial module, a linear fit (i.e. polynomial of degree 1)\n could be applied to these data with _\bp_\bo_\bl_\by_\bf_\bi_\bt:\n In [4]: np.polyfit(x, y, deg=1)\n-Out[4]: array([0.91892069, 0.25191506])\n+Out[4]: array([0.85848058, 0.25047881])\n With the new polynomial API, the _\bf_\bi_\bt class method is preferred:\n In [5]: p_fitted = np.polynomial.Polynomial.fit(x, y, deg=1)\n \n In [6]: p_fitted\n-Out[6]: Polynomial([4.38705816, 4.13514311], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.1136414 , 3.86316259], domain=[0., 9.], window=[-1.,\n 1.], symbol='x')\n Note that the coefficients are given i\bin\bn t\bth\bhe\be s\bsc\bca\bal\ble\bed\bd d\bdo\bom\bma\bai\bin\bn defined by the linear\n mapping between the window and domain. _\bc_\bo_\bn_\bv_\be_\br_\bt can be used to get the\n coefficients in the unscaled data domain.\n In [7]: p_fitted.convert()\n-Out[7]: Polynomial([0.25191506, 0.91892069], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([0.25047881, 0.85848058], domain=[-1., 1.], window=[-1.,\n 1.], symbol='x')\n *\b**\b**\b**\b**\b* D\bDo\boc\bcu\bum\bme\ben\bnt\bta\bat\bti\bio\bon\bn f\bfo\bor\br t\bth\bhe\be _\bp\bp_\bo\bo_\bl\bl_\by\by_\bn\bn_\bo\bo_\bm\bm_\bi\bi_\ba\ba_\bl\bl p\bpa\bac\bck\bka\bag\bge\be_\b#\b# *\b**\b**\b**\b**\b*\n In addition to standard power series polynomials, the polynomial package\n provides several additional kinds of polynomials including Chebyshev, Hermite\n (two subtypes), Laguerre, and Legendre polynomials. Each of these has an\n associated c\bco\bon\bnv\bve\ben\bni\bie\ben\bnc\bce\be c\bcl\bla\bas\bss\bs available from the _\bn_\bu_\bm_\bp_\by_\b._\bp_\bo_\bl_\by_\bn_\bo_\bm_\bi_\ba_\bl namespace that\n provides a consistent interface for working with polynomials regardless of\n"}]}, {"source1": "./usr/share/doc/python-numpy/html/searchindex.js", "source2": "./usr/share/doc/python-numpy/html/searchindex.js", "unified_diff": null, "details": [{"source1": "js-beautify {}", "source2": "js-beautify {}", "unified_diff": "@@ -32377,30 +32377,30 @@\n \"0326911\": [2335, 2378, 2425],\n \"0361\": 2607,\n \"03703704\": 1809,\n \"03943254e\": 2104,\n \"03968254\": [1113, 1543],\n \"0396842\": 680,\n \"03t13\": 55,\n- \"04\": [54, 55, 164, 410, 547, 1586, 2461, 2463, 2594, 2659],\n+ \"04\": [54, 55, 164, 410, 547, 1586, 2463, 2594, 2659],\n \"0400\": 360,\n \"04097352\": 2635,\n \"04166667\": [1544, 1585],\n \"04211c6\": 2521,\n \"04551152e\": 2104,\n \"04719755\": 1911,\n \"05\": [55, 91, 163, 410, 548, 669, 896, 1095, 1871, 2083, 2173, 2353, 2400, 2450, 2648],\n \"0500\": 360,\n \"05093587\": 2635,\n \"05208333\": 1585,\n \"05263157894736836\": 2257,\n \"0549999999999997\": 2083,\n \"055\": 2083,\n \"0596779\": 1153,\n- \"06\": [55, 566, 2083, 2508],\n+ \"06\": [55, 566, 2083, 2461, 2508],\n \"0614962j\": [439, 453],\n \"0625\": [418, 624, 1645],\n \"06369197489564249\": 2458,\n \"06381726\": 349,\n \"0660\": [302, 2131],\n \"06959433e\": [420, 947],\n \"07\": [55, 164, 547, 896, 897, 1335, 2170, 2508],\n@@ -32423,14 +32423,15 @@\n \"087300000000000003\": [2346, 2392, 2441],\n \"09\": [55, 2171, 2323, 2367, 2414],\n \"090097550553843\": 2642,\n \"09417735\": [349, 2457, 2639],\n \"0943951\": 1911,\n \"09640474436813\": 675,\n \"09861229\": [657, 2655],\n+ \"09887606\": 2461,\n \"0999755859375\": 62,\n \"099975586\": 62,\n \"0a1\": 577,\n \"0a2\": 577,\n \"0b00000011\": [1519, 2235],\n \"0b1\": [34, 50, 577, 2602],\n \"0b2\": 577,\n@@ -32614,14 +32615,15 @@\n \"11218\": 2542,\n \"11219\": 2539,\n \"11251\": 2539,\n \"11274\": 2540,\n \"11294\": 2540,\n \"113\": [674, 2463, 2666],\n \"11308\": 2542,\n+ \"1136414\": 2488,\n \"1138\": 2612,\n \"114\": 2463,\n \"11407192\": 1822,\n \"1142\": [2353, 2400, 2450],\n \"1149\": 2612,\n \"115\": [1654, 2463],\n \"1151\": 657,\n@@ -32763,15 +32765,14 @@\n \"13396\": 2551,\n \"134\": [542, 968, 969],\n \"13406828\": 2458,\n \"13421\": 2566,\n \"1344\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"13450292\": 54,\n \"135\": [105, 130],\n- \"13514311\": 2488,\n \"13516\": 2572,\n \"13523\": 2551,\n \"13533528\": 1774,\n \"13549\": 2551,\n \"13552\": 2551,\n \"13559\": 2551,\n \"13560\": 2551,\n@@ -32798,15 +32799,15 @@\n \"13823\": 2552,\n \"13829\": 2560,\n \"1383\": 2612,\n \"13845\": 2552,\n \"13867\": 2552,\n \"1387\": 2612,\n \"13899\": 2560,\n- \"139\": [655, 2461],\n+ \"139\": 655,\n \"13905\": 2552,\n \"13933\": 2552,\n \"13984\": 2552,\n \"13994\": 2552,\n \"13d7934\": 13,\n \"13j\": 1915,\n \"14\": [9, 47, 54, 55, 56, 57, 58, 59, 98, 107, 108, 114, 140, 141, 142, 270, 366, 367, 375, 460, 476, 486, 530, 542, 544, 546, 566, 645, 661, 880, 893, 905, 963, 968, 969, 1069, 1083, 1143, 1229, 1247, 1312, 1466, 1577, 1695, 1704, 1711, 1758, 1764, 1867, 1873, 1986, 2086, 2089, 2115, 2168, 2205, 2206, 2208, 2209, 2210, 2222, 2224, 2225, 2237, 2240, 2246, 2333, 2342, 2377, 2385, 2424, 2432, 2457, 2461, 2463, 2490, 2513, 2519, 2531, 2542, 2543, 2544, 2545, 2546, 2547, 2553, 2554, 2559, 2560, 2561, 2566, 2572, 2576, 2583, 2584, 2585, 2586, 2588, 2591, 2596, 2599, 2600, 2622, 2627, 2635, 2638, 2641, 2645, 2653, 2657, 2659, 2666],\n@@ -33019,20 +33020,18 @@\n \"15251\": 2566,\n \"15255\": 2566,\n \"15271\": 2576,\n \"153\": 2583,\n \"15302337\": 523,\n \"1534\": 485,\n \"15355\": 2566,\n- \"15383297\": 2461,\n \"15385\": 2566,\n \"154\": [2463, 2666],\n \"15427\": 2566,\n \"15463\": 2566,\n- \"15478891\": 2461,\n \"155\": [2463, 2637],\n \"15534\": 2566,\n \"15648\": 2566,\n \"15666\": 2572,\n \"15675\": 2562,\n \"15676\": 2562,\n \"15677\": 2562,\n@@ -33111,15 +33110,14 @@\n \"16354\": 2660,\n \"164\": 675,\n \"16434881e\": 2104,\n \"16439\": 2565,\n \"16441\": 2565,\n \"16476\": 2572,\n \"16484065\": 1154,\n- \"165\": 2461,\n \"16515\": 2572,\n \"16519\": 2572,\n \"1654503\": [2345, 2391, 2439],\n \"16551\": 2566,\n \"16554\": 2572,\n \"16558\": 2572,\n \"16570\": 2572,\n@@ -33694,14 +33692,15 @@\n \"21154\": 2588,\n \"21187\": 2588,\n \"21188\": 2588,\n \"21191\": 2587,\n \"21192\": 2587,\n \"21199\": 2622,\n \"212\": 2622,\n+ \"21212049\": 2461,\n \"21243\": 2587,\n \"21245\": 2587,\n \"21262\": 2588,\n \"21275\": 2587,\n \"21277\": 2587,\n \"213\": [12, 2491],\n \"21336384\": 2659,\n@@ -34182,14 +34181,15 @@\n \"24978\": 2622,\n \"25\": [10, 50, 54, 55, 56, 58, 69, 140, 361, 377, 409, 418, 440, 481, 489, 520, 526, 528, 544, 624, 645, 660, 667, 669, 680, 870, 881, 893, 917, 1056, 1070, 1083, 1135, 1142, 1143, 1240, 1349, 1526, 1527, 1542, 1581, 1606, 1651, 1694, 1702, 1834, 1907, 2089, 2090, 2091, 2204, 2239, 2240, 2251, 2265, 2266, 2323, 2325, 2337, 2348, 2349, 2367, 2380, 2390, 2396, 2414, 2427, 2438, 2446, 2463, 2473, 2476, 2491, 2513, 2515, 2519, 2567, 2602, 2604, 2622, 2623, 2635, 2641, 2645, 2654, 2657, 2659, 2666],\n \"250\": [361, 2463],\n \"2500\": 652,\n \"25000\": 652,\n \"25003\": 2604,\n \"25043\": 2604,\n+ \"25047881\": 2488,\n \"25049\": 2604,\n \"25054\": 2622,\n \"25071\": 2604,\n \"25079\": 2622,\n \"25080\": 2622,\n \"25083\": 2604,\n \"25086\": 2622,\n@@ -34224,15 +34224,14 @@\n \"25169\": 2622,\n \"25181\": 2622,\n \"25186\": 2622,\n \"25188\": 2605,\n \"25189\": 2605,\n \"25190\": 2605,\n \"25191\": 2605,\n- \"25191506\": 2488,\n \"25192\": 2605,\n \"25193\": 2622,\n \"25201\": 2605,\n \"25202\": 2605,\n \"25203\": 2605,\n \"25204\": 2605,\n \"25205\": 2605,\n@@ -34333,15 +34332,15 @@\n \"25914\": 2622,\n \"25943\": 2622,\n \"25954\": 2622,\n \"25d0\": 32,\n \"25j\": 2659,\n \"25t03\": 55,\n \"25x\": 138,\n- \"26\": [29, 30, 40, 50, 54, 55, 58, 63, 79, 146, 944, 2204, 2208, 2310, 2333, 2377, 2424, 2461, 2513, 2519, 2534, 2536, 2537, 2577, 2599, 2601, 2622, 2625, 2629, 2641, 2657, 2658, 2666],\n+ \"26\": [29, 30, 40, 50, 54, 55, 58, 63, 79, 146, 944, 2204, 2208, 2310, 2333, 2377, 2424, 2513, 2519, 2534, 2536, 2537, 2577, 2599, 2601, 2622, 2625, 2629, 2641, 2657, 2658, 2666],\n \"260\": [162, 1328, 2238, 2576, 2666],\n \"26064346e\": 147,\n \"26081\": 2625,\n \"26103\": 2625,\n \"26137788e\": 2104,\n \"26157\": 2625,\n \"262\": 2666,\n@@ -34397,15 +34396,15 @@\n \"26963\": 2623,\n \"26971\": 2623,\n \"26978671\": 2635,\n \"26981\": 2625,\n \"2699\": 1643,\n \"26995\": 2623,\n \"26aa21a\": 13,\n- \"27\": [54, 55, 58, 169, 470, 539, 554, 660, 680, 1142, 1884, 1899, 1900, 2208, 2239, 2316, 2361, 2408, 2461, 2463, 2491, 2513, 2533, 2534, 2624, 2639, 2641, 2645, 2657, 2659, 2666],\n+ \"27\": [54, 55, 58, 169, 470, 539, 554, 660, 680, 1142, 1884, 1899, 1900, 2208, 2239, 2316, 2361, 2408, 2463, 2491, 2513, 2533, 2534, 2624, 2639, 2641, 2645, 2657, 2659, 2666],\n \"270\": 363,\n \"27000\": 2624,\n \"2700000\": 2635,\n \"27000000\": 2635,\n \"27001\": 2624,\n \"27008\": 2625,\n \"27021\": 2624,\n@@ -34512,15 +34511,15 @@\n \"27t00\": 360,\n \"27t01\": 360,\n \"27t02\": 360,\n \"27t04\": 360,\n \"27t05\": 360,\n \"27t06\": 360,\n \"27t07\": 360,\n- \"28\": [36, 54, 55, 146, 409, 661, 1695, 1704, 1707, 1862, 2168, 2208, 2225, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2641, 2649, 2657, 2659, 2666],\n+ \"28\": [36, 54, 55, 146, 409, 661, 1695, 1704, 1707, 1862, 2168, 2208, 2225, 2461, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2641, 2649, 2657, 2659, 2666],\n \"28000000e\": 1335,\n \"2800000e\": 1335,\n \"28006\": 2630,\n \"28007\": 2630,\n \"2801\": 2613,\n \"28021\": 2630,\n \"28044\": 2630,\n@@ -34758,35 +34757,35 @@\n \"34784527\": 2635,\n \"3480\": 2615,\n \"3484692283495345\": [648, 653],\n \"34889999999999999\": [2325, 2369, 2416],\n \"34890909\": 523,\n \"34960421\": 680,\n \"3497\": 2615,\n- \"35\": [409, 489, 669, 870, 1056, 2204, 2325, 2369, 2416, 2572, 2635, 2641, 2657, 2666],\n+ \"35\": [409, 489, 669, 870, 1056, 2204, 2325, 2369, 2416, 2461, 2572, 2635, 2641, 2657, 2666],\n \"350\": [544, 635],\n \"3504\": 2617,\n \"3534857623790153\": 666,\n \"35355339\": 1636,\n \"3541\": 2615,\n \"35489284e\": 2104,\n- \"36\": [58, 137, 355, 1752, 1761, 2204, 2225, 2323, 2367, 2414, 2461, 2463, 2491, 2536, 2649, 2657, 2659, 2666],\n+ \"36\": [58, 137, 355, 1752, 1761, 2204, 2225, 2323, 2367, 2414, 2463, 2491, 2536, 2649, 2657, 2659, 2666],\n \"360\": [544, 2103, 2238, 2576],\n \"36045180e\": 147,\n \"3608\": 2615,\n \"361\": [1344, 1346, 1522, 1908],\n \"362\": 12,\n \"3628523\": 2458,\n \"36363636\": 136,\n \"3644j\": [415, 621],\n \"365\": [544, 1344, 1346, 1522, 1908],\n \"366\": 55,\n \"36674\": 2098,\n \"36787944\": [1660, 1774],\n- \"37\": [59, 60, 136, 1913, 2083, 2204, 2236, 2463, 2641, 2657, 2666],\n+ \"37\": [59, 60, 136, 1913, 2083, 2204, 2236, 2461, 2463, 2641, 2657, 2666],\n \"370\": 652,\n \"3701\": 2615,\n \"37079802\": [349, 2639],\n \"3712\": 2615,\n \"3728\": 2615,\n \"3728973198\": 2594,\n \"3743\": 2615,\n@@ -34802,30 +34801,28 @@\n \"38268343j\": 642,\n \"3832\": 2615,\n \"38434191e\": 660,\n \"38446749\": 1867,\n \"385\": [2270, 2300],\n \"3854\": [287, 1241, 1324, 1478, 1998],\n \"38672696\": [2352, 2399, 2449],\n- \"38705816\": 2488,\n \"3871\": 2615,\n \"38777878e\": [147, 1651],\n \"38791518e\": [421, 948],\n \"38885\": [2361, 2408],\n \"389056\": 2642,\n \"3890561\": [38, 2666],\n \"3891\": 2642,\n \"39\": [30, 58, 2208, 2463, 2641, 2657],\n \"390\": [2270, 2300],\n \"3900\": 2615,\n \"3900x\": 2463,\n \"39015\": 2316,\n \"39211752\": 1153,\n \"39337286e\": 1149,\n- \"39445772\": 2461,\n \"3971\": 2615,\n \"39804426\": 1153,\n \"3992\": 2615,\n \"39924804\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"3_000\": 669,\n \"3abcd\": 513,\n \"3d\": [63, 2513, 2621, 2635, 2637, 2657, 2666],\n@@ -34917,15 +34914,15 @@\n \"4354\": 2617,\n \"4359\": 2617,\n \"4368\": [287, 1241, 1324, 1478, 1998],\n \"4375\": 2491,\n \"43857224\": 1153,\n \"43887844\": [349, 2457, 2639],\n \"43999999999998\": 1114,\n- \"44\": [16, 1525, 1758, 1905, 1907, 1922, 2208, 2463, 2624, 2657, 2658, 2659, 2666],\n+ \"44\": [16, 1525, 1758, 1905, 1907, 1922, 2208, 2461, 2463, 2624, 2657, 2658, 2659, 2666],\n \"440\": [10, 2520],\n \"4400\": [409, 661, 2168],\n \"44069024\": 349,\n \"4408\": 2617,\n \"44089210e\": 1527,\n \"4408921e\": [1765, 2175],\n \"4409e\": 2091,\n@@ -34937,19 +34934,20 @@\n \"4465\": 2620,\n \"4466\": 2617,\n \"4472136\": 642,\n \"4472136j\": 642,\n \"4476\": 2621,\n \"4483\": 2617,\n \"4485\": 2617,\n+ \"44852905\": 2461,\n \"4486\": 2617,\n \"449294e\": 2170,\n \"44948974\": 2659,\n \"44999999925494177\": 2115,\n- \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2637, 2644, 2657, 2666],\n+ \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2461, 2637, 2644, 2657, 2666],\n \"450\": 55,\n \"45000005\": 2115,\n \"45038594\": [349, 2639],\n \"45053314\": 2635,\n \"4511316\": 2666,\n \"4520525295346629\": 1228,\n \"4532\": [409, 661, 2168],\n@@ -34968,15 +34966,14 @@\n \"4628\": 2618,\n \"46351241j\": 2081,\n \"46368\": 28,\n \"464\": 680,\n \"4642\": 2618,\n \"465\": [58, 1157],\n \"4656\": 2618,\n- \"46632479\": 2461,\n \"4664\": [409, 661, 2168],\n \"46666491\": 349,\n \"46716228e\": 1586,\n \"46755891e\": 54,\n \"468\": [136, 147],\n \"4685006\": [2352, 2399, 2449],\n \"4686\": 12,\n@@ -35057,14 +35054,15 @@\n \"5063\": 2620,\n \"5067\": 2620,\n \"5082\": 2620,\n \"5095\": 2620,\n \"51\": [58, 520, 1654, 1752, 1761, 1867, 1870, 2083, 2204, 2331, 2339, 2356, 2375, 2382, 2403, 2422, 2429, 2453, 2622, 2657, 2666],\n \"510\": [143, 570],\n \"5100\": 2620,\n+ \"5102923\": 2461,\n \"5104\": 2620,\n \"51182162\": 2666,\n \"512\": [69, 893, 1083, 1143, 1247, 2115, 2240, 2542, 2547, 2666],\n \"51327412\": 1891,\n \"5136\": 2620,\n \"5138\": 2620,\n \"514229\": 28,\n@@ -35164,26 +35162,26 @@\n \"57721\": [2326, 2371, 2418],\n \"5772156649015328606065120900824024310421\": 76,\n \"5773\": 2522,\n \"57860025\": 1154,\n \"579365079365115\": [1113, 1543],\n \"57x\": 2594,\n \"58\": [669, 1748, 1777, 2204, 2208, 2332, 2376, 2423, 2464, 2572, 2635, 2657],\n- \"58007252\": 2461,\n \"582892\": 2635,\n \"58289208\": 2635,\n \"584388\": 55,\n \"585\": [378, 1358, 1514, 2583],\n \"58578644\": 1756,\n \"58826587\": 349,\n \"59\": [55, 2208, 2602, 2657],\n \"5910\": [287, 1241, 1324, 1478, 1998],\n \"595726\": 2635,\n \"59572603\": 2635,\n \"5969\": [99, 906],\n+ \"59799319\": 2461,\n \"598150\": 2642,\n \"59815003\": 38,\n \"5982\": 2642,\n \"59903635e\": 147,\n \"5d0\": 32,\n \"5e\": [114, 117, 119, 260, 669, 674, 675, 1059, 1222, 1305, 1350, 1459, 1579, 1590, 1596, 1604, 1605, 1639, 1649, 1653, 1661, 1662, 1696, 1706, 1710, 1718, 1719, 1753, 1763, 1767, 1775, 1776, 1810, 1820, 1824, 1832, 1833, 1866, 1875, 1879, 1887, 1888, 1893, 1979],\n \"5e16\": 55,\n@@ -35212,26 +35210,26 @@\n \"6143849206349179\": [1113, 1543],\n \"6176\": [99, 906],\n \"61799388\": 1911,\n \"618\": 669,\n \"6180\": [2353, 2400, 2450],\n \"61988120985\": [2323, 2367, 2414],\n \"61c54bbd\": 42,\n- \"62\": [542, 968, 969, 2323, 2333, 2367, 2377, 2414, 2424, 2657],\n+ \"62\": [542, 968, 969, 2323, 2333, 2367, 2377, 2414, 2424, 2461, 2657],\n \"6208\": 2522,\n \"6227766\": 514,\n \"623\": [2394, 2444],\n \"62318272\": [2319, 2363, 2410],\n \"62341325\": 514,\n \"62374854\": 2666,\n \"624\": [2300, 2370, 2394, 2417, 2444, 2462],\n \"625\": [99, 478, 645, 906, 2390, 2438],\n \"6273591314603949\": [2335, 2378, 2425],\n \"62949953e\": 645,\n- \"63\": [58, 514, 669, 1748, 1777, 2336, 2461, 2463, 2520, 2566, 2594, 2642, 2657],\n+ \"63\": [58, 514, 669, 1748, 1777, 2336, 2463, 2520, 2566, 2594, 2642, 2657],\n \"631198583\": 55,\n \"631198588\": 55,\n \"63317787e\": [2166, 2167],\n \"63526532\": 2458,\n \"636363636364\": [2353, 2400, 2450],\n \"63696169\": 2635,\n \"6376\": 2522,\n@@ -35350,15 +35348,15 @@\n \"6765\": 28,\n \"6771\": 2522,\n \"6775\": 2522,\n \"6780\": 2522,\n \"6781\": 2522,\n \"6783\": 2522,\n \"6785\": 2522,\n- \"68\": [2461, 2657, 2659, 2666],\n+ \"68\": [2657, 2659, 2666],\n \"6805\": [2353, 2400, 2450],\n \"6807\": 2522,\n \"68080986\": 349,\n \"6813\": 2522,\n \"6817\": 2522,\n \"6819\": 2522,\n \"68206631e\": 2104,\n@@ -35397,20 +35395,19 @@\n \"70\": [59, 457, 567, 2241, 2248, 2657],\n \"700\": 567,\n \"70000000\": 2635,\n \"701\": 2463,\n \"703\": 2625,\n \"7054\": 2535,\n \"706\": 520,\n- \"7069302\": 2461,\n \"70710678\": [216, 247, 641, 1199, 1216, 1282, 1299, 1436, 1453, 1636, 1642, 1956, 1973, 2103],\n \"70710678118654746\": 637,\n \"70710678j\": 641,\n \"7083\": 2529,\n- \"71\": [354, 650, 2460, 2657],\n+ \"71\": [354, 650, 2460, 2461, 2657],\n \"71080601\": 2659,\n \"71238898\": 1911,\n \"71387850e\": 1586,\n \"718281\": 431,\n \"71828182845904523536028747135266249775724709369995\": 76,\n \"71828183\": [38, 2666],\n \"718282\": 2642,\n@@ -35427,24 +35424,24 @@\n \"72717132\": 2659,\n \"72727273\": 136,\n \"72847407\": 1154,\n \"729\": 2666,\n \"72904971\": 1153,\n \"72949656\": 2635,\n \"73\": [2463, 2657],\n- \"730\": 2461,\n \"7320508075688772j\": 59,\n \"73472348e\": 1816,\n \"73496154e\": 1867,\n \"73603959e\": 2666,\n \"73799541\": 1153,\n \"74\": [2463, 2513, 2514, 2657],\n \"74000000\": 2635,\n \"7416573867739413\": 653,\n \"74165739\": 653,\n+ \"742\": 2461,\n \"74499359e\": [420, 947],\n \"745966692414834\": [648, 653],\n \"75\": [58, 135, 440, 478, 516, 520, 528, 544, 645, 667, 870, 1056, 1542, 1606, 1634, 1663, 1834, 2091, 2257, 2491, 2657, 2659, 2666],\n \"7500\": 652,\n \"75000\": 652,\n \"75008178\": 349,\n \"75025\": 28,\n@@ -35558,15 +35555,14 @@\n \"8010\": 2527,\n \"8020\": 2527,\n \"8024\": 2527,\n \"8031\": 2527,\n \"804\": 2508,\n \"8044\": 2527,\n \"8058837395885292\": 666,\n- \"80933726\": 2461,\n \"80b3a34\": 2614,\n \"81\": [1650, 1884, 2635, 2641, 2645, 2657, 2666],\n \"81299683\": 2635,\n \"812997\": 2635,\n \"813\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"81327024\": 2635,\n \"81349206\": [1113, 1543],\n@@ -35610,31 +35606,34 @@\n \"85355339\": 1756,\n \"85569\": 2098,\n \"85602287\": [2335, 2378, 2425],\n \"857\": 410,\n \"8570331885190563e\": [648, 653],\n \"85715698e\": 2171,\n \"8577\": 2539,\n+ \"85848058\": 2488,\n \"85859792\": [349, 2457, 2639],\n \"8595784\": 2635,\n \"86\": [59, 88, 101, 103, 106, 126, 131, 542, 968, 969, 2323, 2367, 2414, 2491, 2657],\n \"8601\": [55, 62, 67, 2613],\n \"86260211e\": 54,\n \"8630830\": 13,\n+ \"86316259\": 2488,\n \"86399\": 55,\n \"86400\": 55,\n \"86401\": 55,\n \"8660254\": 2103,\n \"86820401\": [2345, 2391, 2439],\n \"86864911e\": 1586,\n \"87\": [2616, 2657],\n \"875\": [478, 2491],\n \"8755\": [186, 827, 999, 1172, 1259, 1414, 1933],\n \"87649168120691\": 674,\n \"8770\": [2353, 2400, 2450],\n+ \"8792059\": 2461,\n \"88\": [408, 2462, 2463, 2657, 2659, 2668],\n \"8801\": [99, 906],\n \"88031624\": 2666,\n \"88079259\": 533,\n \"881943016134134\": 666,\n \"88622693\": 1642,\n \"888\": [2514, 2658],\n@@ -35665,18 +35664,16 @@\n \"90\": [25, 29, 33, 37, 39, 55, 68, 78, 363, 1910, 2082, 2103, 2248, 2463, 2610, 2654, 2657],\n \"90384387e\": 2104,\n \"90476190e\": 1816,\n \"90909091\": 136,\n \"909297\": 2642,\n \"90929743\": 2666,\n \"91\": [2461, 2657],\n- \"91027615\": 2461,\n \"91275558\": 2635,\n \"916666666666666\": 1240,\n- \"91892069\": 2488,\n \"92\": [98, 2461, 2657, 2659],\n \"921fb54442d18p\": 2520,\n \"9223372036854775807\": 2648,\n \"9223372036854775808\": 2648,\n \"92346708\": 349,\n \"92362781e\": 2104,\n \"92387953\": 642,\n@@ -35686,14 +35683,15 @@\n \"9261\": 2532,\n \"9262\": 2532,\n \"9263\": 2532,\n \"9267\": 2532,\n \"92676499\": [349, 2639],\n \"927\": [539, 554],\n \"92771843\": 1154,\n+ \"9290714\": 2461,\n \"9299\": 2532,\n \"93\": 2657,\n \"9304e\": 2091,\n \"931\": 2587,\n \"9317\": 2532,\n \"9319\": 2532,\n \"9339\": 2532,\n@@ -35782,14 +35780,15 @@\n \"9898\": 2666,\n \"9899\": [105, 130, 2666],\n \"99\": [12, 302, 408, 544, 672, 1096, 1906, 2131, 2460, 2635, 2657, 2658, 2666],\n \"9900\": 2666,\n \"99004057\": 349,\n \"9901\": 2666,\n \"9902\": 2666,\n+ \"99022154\": 2461,\n \"990278\": 2635,\n \"99027828\": 2635,\n \"99060736\": 2666,\n \"99091858\": [2345, 2391, 2439],\n \"99149989\": [2345, 2391, 2439],\n \"9917\": 2343,\n \"99256089\": 349,\n"}]}]}]}]}]}