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-6.33 ms +- 70.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-13.3 ms +- 43.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+4.76 ms +- 272 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+6.66 ms +- 167 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-5.18 ms +- 61 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-15.5 ms +- 19.9 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+3.91 ms +- 119 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+6.08 ms +- 141 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-27.2 ms +- 26.5 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-32.2 ms +- 39.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+13.3 ms +- 725 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+15.4 ms +- 355 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([0.78096509, 0.76423919, 0.57495978])\n+Out[7]: array([0.08975275, 0.94397116, 0.14762362])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.8527657 , 0.97919476, 0.71092075], dtype=float32)\n+Out[8]: array([0.5901301 , 0.52016 , 0.35208422], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([ 17, 167, 130], dtype=uint8)\n+Out[9]: array([ 99, 103, 220], 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([0.7819421, 0.9673652])\n+Out[12]: array([0.78201433, 0.34263272])\n \n In [13]: print(existing)\n-[0.7819421 0.9673652 0. 0. ]\n+[0.78201433 0.34263272 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([ 1.03075071, -0.08294672])\n+Out[4]: array([1.00699899, 0.44628089])\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([4.55543149, 4.63837821], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.97777634, 4.53149545], 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([-0.08294672, 1.03075071], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([0.44628089, 1.00699899], 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([ 1.03075071, -0.08294672])\n+Out[4]: array([1.00699899, 0.44628089])\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([4.55543149, 4.63837821], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.97777634, 4.53149545], 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([-0.08294672, 1.03075071], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([0.44628089, 1.00699899], 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": "@@ -32332,14 +32332,15 @@\n \"0024\": 477,\n \"003\": [2327, 2372, 2419],\n \"005\": 2188,\n \"0050000029\": [357, 359],\n \"0050045159\": [357, 359],\n \"00578369\": 1754,\n \"00625\": 1585,\n+ \"00699899\": 2488,\n \"007000999997857\": 1541,\n \"00867716\": [2319, 2363, 2410],\n \"00950034\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"009a87ff44bf\": 42,\n \"00j\": [514, 642, 2167],\n \"01\": [41, 42, 45, 54, 55, 62, 147, 162, 163, 164, 335, 361, 410, 514, 547, 557, 566, 669, 897, 1088, 1094, 1586, 1594, 1601, 1658, 1715, 1772, 1829, 1885, 2104, 2160, 2252, 2323, 2329, 2367, 2373, 2414, 2420, 2525, 2658],\n \"010\": [653, 1602, 1659, 1716, 1773, 1830, 1886],\n@@ -32369,15 +32370,14 @@\n \"02654825\": 1891,\n \"02658058e\": 2666,\n \"02755911\": 2666,\n \"027559113243068367\": 2666,\n \"02785049\": 1867,\n \"02i\": [513, 2644],\n \"03\": [55, 67, 163, 566, 669, 1335, 1586, 1816, 2658],\n- \"03075071\": 2488,\n \"03125\": [1585, 2491],\n \"0326911\": [2335, 2378, 2425],\n \"0361\": 2607,\n \"03703704\": 1809,\n \"03943254e\": 2104,\n \"03968254\": [1113, 1543],\n \"0396842\": 680,\n@@ -32406,27 +32406,27 @@\n \"06959433e\": [420, 947],\n \"07\": [55, 164, 547, 896, 897, 1335, 2170, 2508],\n \"07106781e\": 514,\n \"07407407\": 1809,\n \"07779185\": 2458,\n \"07937323\": 524,\n \"07944154\": [657, 2655],\n- \"08\": [55, 91, 147, 410, 523, 548, 896, 1095, 2322, 2366, 2413, 2525, 2659],\n+ \"08\": [55, 91, 147, 410, 523, 548, 896, 1095, 2322, 2366, 2413, 2461, 2525, 2659],\n \"0800\": 2525,\n \"08187135\": 54,\n- \"08294672\": 2488,\n \"08333333\": [1645, 1871],\n \"08405657\": 1867,\n \"0855\": 2642,\n \"08553692\": 38,\n \"085537\": 2642,\n \"0856306\": 1154,\n \"08618131\": 1526,\n \"08703704\": [1113, 1543],\n \"087300000000000003\": [2346, 2392, 2441],\n+ \"08975275\": 2461,\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 \"0999755859375\": 62,\n@@ -32506,15 +32506,15 @@\n \"10100\": [143, 570],\n \"1015\": 2592,\n \"10151\": 2560,\n \"102\": [2463, 2637, 2666],\n \"1023\": [141, 2583],\n \"1024\": [66, 72, 2658],\n \"10240\": 977,\n- \"103\": 2463,\n+ \"103\": [2461, 2463],\n \"10330\": 55,\n \"10339\": [2536, 2542],\n \"1035\": [1643, 1655],\n \"10352\": 2542,\n \"10368\": 2536,\n \"10375\": 2536,\n \"10395\": 2536,\n@@ -32659,15 +32659,15 @@\n \"11785\": 2543,\n \"11786\": 2543,\n \"1179\": 2463,\n \"118\": 2463,\n \"1180339887498949\": 2115,\n \"11803399\": 1228,\n \"11885628817151628\": 2458,\n- \"119\": 2616,\n+ \"119\": [2461, 2616],\n \"11902\": 2544,\n \"11981\": 2544,\n \"11982\": 2544,\n \"11985\": 2541,\n \"11986\": 2541,\n \"11987\": 2541,\n \"11992\": 2544,\n@@ -32742,15 +32742,15 @@\n \"12852\": [2533, 2534],\n \"12890\": 2548,\n \"129\": [863, 1048, 1116, 1904, 2463, 2639],\n \"12909\": 2549,\n \"12923\": 2549,\n \"12945251\": 2666,\n \"13\": [5, 26, 28, 30, 31, 36, 38, 47, 54, 55, 58, 61, 98, 107, 108, 114, 140, 141, 142, 144, 146, 163, 270, 336, 366, 367, 370, 374, 375, 409, 433, 530, 543, 546, 628, 647, 880, 949, 963, 1069, 1157, 1229, 1247, 1312, 1466, 1752, 1761, 1870, 1913, 1986, 2089, 2091, 2205, 2206, 2208, 2209, 2210, 2224, 2225, 2236, 2237, 2246, 2342, 2457, 2461, 2463, 2477, 2513, 2516, 2519, 2529, 2535, 2555, 2556, 2557, 2558, 2560, 2561, 2571, 2583, 2592, 2595, 2600, 2601, 2602, 2603, 2604, 2606, 2622, 2624, 2626, 2627, 2628, 2629, 2630, 2631, 2632, 2633, 2635, 2637, 2638, 2641, 2645, 2647, 2657, 2666],\n- \"130\": [409, 2461],\n+ \"130\": 409,\n \"1300000\": 2635,\n \"13020\": 2549,\n \"13026\": 2549,\n \"13028\": 2549,\n \"13038\": 2549,\n \"13041\": 2549,\n \"13090\": [186, 827, 999, 1172, 1259, 1414, 1933],\n@@ -32823,15 +32823,15 @@\n \"140497590272032\": 2642,\n \"14051\": 2560,\n \"14052\": 2552,\n \"14056\": 2552,\n \"14057\": 2552,\n \"14058\": 2552,\n \"14084\": 2552,\n- \"141\": 669,\n+ \"141\": [669, 2461],\n \"14100\": 2560,\n \"141120\": 2642,\n \"14112001\": 2666,\n \"14142\": 2560,\n \"14156\": 2555,\n \"14157\": 2555,\n \"141571941375841\": 2202,\n@@ -32940,14 +32940,15 @@\n \"14692469\": 2635,\n \"146925\": 2635,\n \"14717\": 2560,\n \"14718\": 2560,\n \"14720\": 2560,\n \"14730\": 2560,\n \"14758\": 2558,\n+ \"14762362\": 2461,\n \"14771\": 2560,\n \"14777\": 2560,\n \"14781\": 2558,\n \"14787\": 2569,\n \"148\": [2344, 2386, 2433, 2463],\n \"14812\": 3,\n \"148293216\": 2666,\n@@ -33750,15 +33751,15 @@\n \"21925\": 2594,\n \"21949\": 2589,\n \"21951\": 2589,\n \"21952\": 2589,\n \"21976\": 2594,\n \"21995\": 2594,\n \"22\": [21, 22, 29, 30, 40, 47, 52, 54, 55, 58, 59, 98, 107, 108, 109, 163, 270, 336, 378, 425, 485, 628, 658, 669, 880, 905, 1045, 1069, 1113, 1211, 1229, 1294, 1312, 1336, 1337, 1340, 1341, 1343, 1344, 1345, 1346, 1347, 1348, 1349, 1358, 1448, 1466, 1514, 1521, 1522, 1543, 1591, 1905, 1908, 1913, 1968, 1986, 2091, 2208, 2236, 2237, 2342, 2513, 2517, 2519, 2534, 2588, 2635, 2637, 2641, 2657, 2666],\n- \"220\": [2238, 2576],\n+ \"220\": [2238, 2461, 2576],\n \"22004\": 2594,\n \"22014\": 2594,\n \"22030\": 2590,\n \"22031\": 2590,\n \"22032\": 2590,\n \"22033\": 2590,\n \"22034\": 2590,\n@@ -34330,15 +34331,15 @@\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@@ -34394,15 +34395,15 @@\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@@ -34424,14 +34425,15 @@\n \"27146\": 2624,\n \"27147\": [2625, 2629],\n \"27151\": 2624,\n \"27156\": 2629,\n \"27160\": 2629,\n \"27195\": 2624,\n \"27199\": 2625,\n+ \"272\": 2461,\n \"27213\": 2624,\n \"27236\": 2626,\n \"27252\": 2626,\n \"27256\": 2626,\n \"27257\": 2626,\n \"27259\": 2626,\n \"27266\": 2626,\n@@ -34701,27 +34703,27 @@\n \"3173\": 2617,\n \"3175\": 2617,\n \"317811\": 28,\n \"317j\": [411, 617],\n \"318\": 1526,\n \"3192\": 2615,\n \"31962608\": [196, 836, 1008, 1179, 1266, 1421, 1940],\n- \"32\": [1, 13, 21, 50, 54, 55, 56, 59, 61, 62, 63, 65, 69, 74, 137, 144, 215, 270, 336, 390, 434, 514, 584, 661, 880, 893, 1027, 1069, 1083, 1143, 1198, 1229, 1249, 1281, 1312, 1345, 1348, 1435, 1466, 1519, 1884, 1886, 1902, 1955, 1986, 2076, 2091, 2168, 2204, 2208, 2225, 2240, 2261, 2262, 2268, 2269, 2272, 2273, 2274, 2277, 2278, 2279, 2282, 2283, 2284, 2287, 2288, 2299, 2300, 2301, 2302, 2303, 2304, 2314, 2331, 2375, 2422, 2458, 2459, 2460, 2461, 2462, 2508, 2513, 2520, 2521, 2522, 2535, 2543, 2544, 2545, 2546, 2547, 2557, 2562, 2564, 2572, 2574, 2579, 2582, 2587, 2588, 2599, 2602, 2606, 2607, 2617, 2622, 2633, 2637, 2639, 2641, 2645, 2646, 2648, 2649, 2652, 2657, 2658, 2659, 2666],\n+ \"32\": [1, 13, 21, 50, 54, 55, 56, 59, 61, 62, 63, 65, 69, 74, 137, 144, 215, 270, 336, 390, 434, 514, 584, 661, 880, 893, 1027, 1069, 1083, 1143, 1198, 1229, 1249, 1281, 1312, 1345, 1348, 1435, 1466, 1519, 1884, 1886, 1902, 1955, 1986, 2076, 2091, 2168, 2204, 2208, 2225, 2240, 2261, 2262, 2268, 2269, 2272, 2273, 2274, 2277, 2278, 2279, 2282, 2283, 2284, 2287, 2288, 2299, 2300, 2301, 2302, 2303, 2304, 2314, 2331, 2375, 2422, 2458, 2459, 2460, 2462, 2508, 2513, 2520, 2521, 2522, 2535, 2543, 2544, 2545, 2546, 2547, 2557, 2562, 2564, 2572, 2574, 2579, 2582, 2587, 2588, 2599, 2602, 2606, 2607, 2617, 2622, 2633, 2637, 2639, 2641, 2645, 2646, 2648, 2649, 2652, 2657, 2658, 2659, 2666],\n \"320\": 1149,\n \"32000\": 2094,\n \"32119158\": 1867,\n \"323\": [260, 421, 948, 1059, 1222, 1305, 1350, 1459, 1579, 1590, 1604, 1605, 1639, 1649, 1661, 1662, 1696, 1706, 1718, 1719, 1753, 1763, 1775, 1776, 1810, 1820, 1832, 1833, 1866, 1875, 1887, 1888, 1979, 2312],\n \"3263\": 2617,\n \"32767\": 535,\n \"32768\": 535,\n \"32_767\": 62,\n \"32_768\": 62,\n \"32bit\": [50, 61, 62, 2364, 2377, 2379, 2388, 2411, 2424, 2426, 2435, 2517, 2572, 2589],\n \"32x\": 2583,\n- \"33\": [54, 58, 144, 336, 838, 939, 941, 1010, 1907, 1922, 1999, 2173, 2175, 2176, 2208, 2303, 2461, 2513, 2621, 2637, 2641, 2657, 2666],\n+ \"33\": [54, 58, 144, 336, 838, 939, 941, 1010, 1907, 1922, 1999, 2173, 2175, 2176, 2208, 2303, 2513, 2621, 2637, 2641, 2657, 2666],\n \"330\": 363,\n \"3301\": 2615,\n \"330m\": 409,\n \"3312\": 2615,\n \"3324\": [13, 2615],\n \"333\": [652, 950, 2173],\n \"33333\": [2173, 2175],\n@@ -34739,14 +34741,15 @@\n \"3364\": 2615,\n \"3373\": 2615,\n \"33872321e\": 2104,\n \"34\": [12, 28, 144, 441, 1880, 1919, 2208, 2463, 2491, 2566, 2583, 2641, 2657, 2666],\n \"340\": [2238, 2576],\n \"34132519\": [680, 2659],\n \"3421\": 2615,\n+ \"34263272\": 2461,\n \"343\": 2666,\n \"34317802\": 1153,\n \"34376245\": 2635,\n \"3456\": 13,\n \"3458\": 2615,\n \"3471280\": 1923,\n \"3472\": 2615,\n@@ -34758,18 +34761,20 @@\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 \"350\": [544, 635],\n \"3504\": 2617,\n+ \"35208422\": 2461,\n \"3534857623790153\": 666,\n \"35355339\": 1636,\n \"3541\": 2615,\n \"35489284e\": 2104,\n+ \"355\": 2461,\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@@ -34806,15 +34811,15 @@\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, 2461, 2463, 2641, 2657],\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 \"3971\": 2615,\n@@ -34901,15 +34906,15 @@\n \"42667924\": 1154,\n \"4267\": 2617,\n \"4270\": 2617,\n \"4276\": 2617,\n \"429\": 136,\n \"4294967293\": 2639,\n \"4294967296\": [196, 836, 1008, 1179, 1266, 1421, 1940],\n- \"43\": [2208, 2461, 2583, 2635, 2641, 2657, 2666],\n+ \"43\": [2208, 2583, 2635, 2641, 2657, 2666],\n \"430148\": 2635,\n \"43014843\": 2635,\n \"43181166\": 2458,\n \"4354\": 2617,\n \"4359\": 2617,\n \"4368\": [287, 1241, 1324, 1478, 1998],\n \"4375\": 2491,\n@@ -34925,14 +34930,15 @@\n \"4408921e\": [1765, 2175],\n \"4409e\": 2091,\n \"442\": 2615,\n \"4428\": 2617,\n \"4434142\": 349,\n \"443469\": 680,\n \"444\": 485,\n+ \"44628089\": 2488,\n \"4465\": 2620,\n \"4466\": 2617,\n \"4472136\": 642,\n \"4472136j\": 642,\n \"4476\": 2621,\n \"4483\": 2617,\n \"4485\": 2617,\n@@ -35073,28 +35079,30 @@\n \"517\": 10,\n \"5170\": 2620,\n \"5184\": 2620,\n \"51851852\": 1809,\n \"519928\": 2635,\n \"51992837\": 2635,\n \"52\": [10, 50, 62, 457, 1638, 1647, 1650, 2204, 2208, 2554, 2635, 2641, 2648, 2657, 2659, 2660, 2666],\n+ \"52016\": 2461,\n \"5203\": 2620,\n \"5225\": 2620,\n \"5231\": 2620,\n \"52338984\": [2345, 2391, 2439],\n \"52359878\": 1911,\n \"52380952e\": 1816,\n \"5240\": 2620,\n \"5251\": 2620,\n \"526\": 2463,\n \"5260\": [2353, 2400, 2450],\n \"5271\": 42,\n \"53\": [162, 457, 1638, 2208, 2551, 2554, 2657, 2666],\n \"5306\": [409, 661, 2168],\n \"5313\": 2621,\n+ \"53149545\": 2488,\n \"5316\": 2621,\n \"5324j\": [416, 417, 622, 623],\n \"5354\": 2621,\n \"5359\": 2621,\n \"5363922081269535\": 2458,\n \"53657292\": 2666,\n \"536870910\": 1902,\n@@ -35127,15 +35135,14 @@\n \"55000000074505806\": 1247,\n \"5510652\": 2635,\n \"55111512e\": 642,\n \"55131477\": 1153,\n \"5524\": 2621,\n \"55458479\": 349,\n \"55490914e\": 2666,\n- \"55543149\": 2488,\n \"5555555555555554\": 1349,\n \"55627469\": 349,\n \"55645993\": 2635,\n \"5580\": 2535,\n \"55914881e\": 2104,\n \"56\": [52, 55, 61, 544, 1764, 2204, 2463, 2657, 2659],\n \"5612\": 2621,\n@@ -35150,15 +35157,14 @@\n \"56917101\": 2635,\n \"57\": [58, 669, 2204, 2322, 2366, 2413, 2463, 2491, 2637, 2657],\n \"5707963267948966\": [102, 125],\n \"57079633\": [94, 105, 130, 1911, 2238, 2666],\n \"5708\": [412, 618],\n \"57115742\": 524,\n \"57136612e\": 2173,\n- \"57495978\": 2461,\n \"57510612\": 660,\n \"576\": 2615,\n \"57721\": [2326, 2371, 2418],\n \"5772156649015328606065120900824024310421\": 76,\n \"5773\": 2522,\n \"57860025\": 1154,\n \"579365079365115\": [1113, 1543],\n@@ -35167,14 +35173,15 @@\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+ \"5901301\": 2461,\n \"5910\": [287, 1241, 1324, 1478, 1998],\n \"595726\": 2635,\n \"59572603\": 2635,\n \"5969\": [99, 906],\n \"598150\": 2642,\n \"59815003\": 38,\n \"5982\": 2642,\n@@ -35196,15 +35203,15 @@\n \"60546483\": 523,\n \"60663578\": 2635,\n \"607\": [2339, 2382, 2429],\n \"60860684e\": 1594,\n \"609\": 2583,\n \"6094\": 2522,\n \"60x\": 2599,\n- \"61\": [13, 2461, 2657],\n+ \"61\": [13, 2657],\n \"610\": 28,\n \"61119\": 2098,\n \"614064523559687\": 2115,\n \"6143849206349179\": [1113, 1543],\n \"6176\": [99, 906],\n \"61799388\": 1911,\n \"618\": 669,\n@@ -35226,15 +35233,14 @@\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- \"63837821\": 2488,\n \"6390\": [2353, 2400, 2450],\n \"64\": [1, 5, 13, 21, 30, 50, 55, 56, 59, 61, 62, 63, 65, 66, 69, 74, 79, 315, 339, 409, 457, 470, 514, 584, 660, 669, 944, 1345, 1348, 1519, 1899, 1900, 2076, 2083, 2143, 2261, 2262, 2264, 2268, 2269, 2273, 2274, 2278, 2279, 2283, 2284, 2287, 2288, 2299, 2300, 2303, 2304, 2314, 2328, 2458, 2462, 2464, 2513, 2520, 2542, 2547, 2578, 2579, 2580, 2583, 2599, 2602, 2603, 2610, 2615, 2616, 2635, 2639, 2648, 2649, 2657, 2659, 2665, 2666],\n \"64023025\": 2098,\n \"6416010000000001\": 1114,\n \"64386512\": 349,\n \"64402274e\": 660,\n \"6446\": [2550, 2554],\n@@ -35297,15 +35303,15 @@\n \"6586976\": 1149,\n \"6590\": 2522,\n \"6596\": 2522,\n \"6596288841243357\": 2458,\n \"659885634118668e\": 645,\n \"65_535\": 62,\n \"65x\": 2594,\n- \"66\": [13, 58, 1922, 2547, 2657, 2666],\n+ \"66\": [13, 58, 1922, 2461, 2547, 2657, 2666],\n \"6600475\": 1149,\n \"6602\": 2522,\n \"6606\": 2522,\n \"6611\": 2522,\n \"6614\": 2522,\n \"6618\": 2522,\n \"6621\": 2522,\n@@ -35386,42 +35392,42 @@\n \"699\": 520,\n \"6ad92e5\": 13,\n \"6e17\": 55,\n \"6j\": [538, 851, 866, 1025, 1026, 1031, 1051, 1891, 1909, 1914, 2241],\n \"6th\": [513, 669],\n \"6x\": [1527, 2599],\n \"7\": [12, 31, 32, 38, 42, 47, 54, 55, 56, 58, 59, 60, 61, 63, 66, 68, 74, 75, 89, 91, 96, 97, 98, 99, 117, 118, 132, 135, 137, 139, 140, 141, 147, 149, 150, 160, 170, 171, 213, 227, 234, 261, 270, 337, 348, 353, 355, 357, 359, 364, 365, 366, 367, 369, 370, 372, 375, 408, 435, 467, 471, 472, 478, 514, 520, 527, 530, 542, 543, 544, 548, 565, 566, 567, 577, 608, 628, 640, 648, 651, 653, 659, 661, 664, 666, 669, 830, 853, 857, 860, 863, 864, 865, 880, 881, 883, 886, 887, 888, 893, 896, 897, 903, 904, 906, 912, 913, 914, 917, 919, 920, 921, 924, 926, 927, 928, 941, 943, 946, 950, 952, 953, 957, 963, 968, 969, 1002, 1033, 1040, 1044, 1048, 1049, 1050, 1060, 1069, 1070, 1072, 1076, 1077, 1078, 1083, 1101, 1106, 1107, 1116, 1119, 1127, 1135, 1143, 1148, 1149, 1157, 1159, 1160, 1161, 1164, 1166, 1167, 1191, 1193, 1194, 1195, 1200, 1203, 1204, 1205, 1206, 1212, 1213, 1223, 1228, 1229, 1230, 1236, 1240, 1242, 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2557, 2558, 2559, 2560, 2561, 2562, 2563, 2564, 2565, 2566, 2572, 2574, 2575, 2576, 2577, 2578, 2579, 2580, 2581, 2589, 2591, 2592, 2593, 2594, 2600, 2610, 2612, 2616, 2619, 2622, 2626, 2635, 2637, 2638, 2639, 2641, 2642, 2644, 2645, 2647, 2649, 2656, 2657, 2658, 2660, 2666],\n- \"70\": [59, 457, 567, 2241, 2248, 2461, 2657],\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 \"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 \"71080601\": 2659,\n- \"71092075\": 2461,\n \"71238898\": 1911,\n \"71387850e\": 1586,\n \"718281\": 431,\n \"71828182845904523536028747135266249775724709369995\": 76,\n \"71828183\": [38, 2666],\n \"718282\": 2642,\n \"7183\": 2642,\n \"7185\": [99, 906],\n \"71946897\": 1153,\n \"72\": [13, 355, 544, 669, 1764, 2463, 2572, 2657, 2659],\n \"720\": [55, 356, 358, 1897, 2225, 2238, 2576],\n \"72075441\": 680,\n \"721fc64\": 13,\n \"72375\": 1644,\n+ \"725\": 2461,\n \"72538256\": [103, 126],\n \"72686684e\": 566,\n \"72717132\": 2659,\n \"72727273\": 136,\n \"72847407\": 1154,\n \"729\": 2666,\n \"72904971\": 1153,\n@@ -35459,21 +35465,20 @@\n \"7568025\": 2666,\n \"75682846\": 2659,\n \"7578\": 2526,\n \"7590\": 2526,\n \"75958653\": 1911,\n \"7597\": 2526,\n \"75j\": 2659,\n- \"76\": [541, 1897, 2463, 2657, 2659],\n+ \"76\": [541, 1897, 2461, 2463, 2657, 2659],\n \"7608\": 2526,\n \"7611397\": [349, 2457, 2639],\n \"76190476e\": 1816,\n \"76322758\": 1154,\n \"7638\": 2526,\n- \"76423919\": 2461,\n \"76425276e\": 1149,\n \"76492172\": 349,\n \"7654\": 2526,\n \"7656\": 2526,\n \"7660\": 2526,\n \"7665\": 2526,\n \"7670\": 2526,\n@@ -35500,17 +35505,16 @@\n \"77714685\": 349,\n \"7774613834041182\": 2315,\n \"7776\": [99, 906],\n \"7778\": 2527,\n \"7793\": 2527,\n \"78\": [2091, 2644, 2657],\n \"78096262\": [2352, 2399, 2449],\n- \"78096509\": 2461,\n \"7816\": 2527,\n- \"7819421\": 2461,\n+ \"78201433\": 2461,\n \"7821\": 2527,\n \"7824\": 2527,\n \"7835\": 2527,\n \"784\": 2463,\n \"7847\": 2527,\n \"784728999999999\": 1114,\n \"7849\": 2527,\n@@ -35600,15 +35604,14 @@\n \"84147098j\": 2666,\n \"841471\": 2642,\n \"842523\": 2515,\n \"84680802e\": 2104,\n \"8480354764257312\": 653,\n \"85\": [409, 2657],\n \"85099543\": 1822,\n- \"8527657\": 2461,\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@@ -35662,15 +35665,15 @@\n \"9\": [10, 12, 26, 30, 31, 32, 38, 42, 47, 54, 55, 57, 58, 59, 60, 79, 89, 91, 96, 97, 98, 114, 117, 118, 119, 132, 141, 147, 149, 150, 158, 171, 175, 202, 227, 261, 270, 287, 299, 305, 312, 320, 321, 322, 337, 348, 355, 357, 359, 364, 365, 366, 367, 369, 372, 375, 409, 420, 435, 441, 442, 447, 460, 478, 483, 514, 520, 529, 530, 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\"9223372036854775807\": 2648,\n \"9223372036854775808\": 2648,\n \"92346708\": 349,\n@@ -35706,14 +35709,15 @@\n \"9378\": 2532,\n \"9379\": 2532,\n \"9390\": [2533, 2534],\n \"94\": [409, 669, 2635, 2657],\n \"940\": 2587,\n \"941257\": 2635,\n \"94125714\": 2635,\n+ \"94397116\": 2461,\n \"94708397920832\": 2642,\n \"9475673279178444\": 2348,\n \"94864945\": 2666,\n \"94909878\": [2387, 2434],\n \"95\": [37, 39, 646, 2353, 2400, 2450, 2635, 2654, 2657],\n \"9504637\": 2666,\n \"950684\": 2635,\n@@ -35726,15 +35730,14 @@\n \"9580\": [2533, 2534],\n \"95892427\": 2666,\n \"96\": [62, 69, 1577, 1867, 2303, 2463, 2566, 2648, 2657, 2659, 2668],\n \"96139749\": 2666,\n \"96202397\": [2335, 2378, 2425],\n \"96360618\": [2387, 2434],\n \"9665554\": 349,\n- \"9673652\": 2461,\n \"96767474e\": 54,\n \"96875\": 2491,\n \"96979195\": 2635,\n \"969792\": 2635,\n \"96e7\": 42,\n \"97\": [2463, 2635, 2657, 2666],\n \"9700\": 2666,\n@@ -35755,15 +35758,15 @@\n \"9764\": [2533, 2534],\n \"9765\": [2533, 2534],\n \"9766\": [2533, 2534],\n \"9767\": [2533, 2534],\n \"9771\": [2533, 2534],\n \"97719\": 1644,\n \"9772\": 2534,\n- \"97919476\": 2461,\n+ \"97777634\": 2488,\n \"9794\": 2534,\n \"9797\": 2666,\n \"97974649\": 524,\n \"9798\": 2666,\n \"9799\": 2666,\n \"98\": [481, 647, 1157, 2635, 2657, 2666],\n \"9800\": 2666,\n@@ -35775,15 +35778,15 @@\n \"98136677\": 523,\n \"987\": 28,\n \"987654321\": 2393,\n \"98935825\": 2666,\n \"9897\": 2666,\n \"9898\": 2666,\n \"9899\": [105, 130, 2666],\n- \"99\": [12, 302, 408, 544, 672, 1096, 1906, 2131, 2460, 2635, 2657, 2658, 2666],\n+ \"99\": [12, 302, 408, 544, 672, 1096, 1906, 2131, 2460, 2461, 2635, 2657, 2658, 2666],\n \"9900\": 2666,\n \"99004057\": 349,\n \"9901\": 2666,\n \"9902\": 2666,\n \"990278\": 2635,\n \"99027828\": 2635,\n \"99060736\": 2666,\n"}]}]}]}]}]}