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-936 us +- 42 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-2.52 ms +- 33 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+928 us +- 46.6 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.53 ms +- 32 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-805 us +- 25.3 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-1.76 ms +- 6.78 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+804 us +- 28.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+1.76 ms +- 15.4 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-2.34 ms +- 19.4 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n-4.51 ms +- 57.2 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+2.35 ms +- 25.1 us per loop (mean +- std. dev. of 7 runs, 1 loop each)\n+4.48 ms +- 16.6 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@@ -571,21 +571,21 @@\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([0.99052012, 0.09317833, 0.33425345])\n+Out[7]: array([0.11183614, 0.99736855, 0.80213609])\n \n In [8]: rng.random(3, dtype=np.float32)\n-Out[8]: array([0.39850473, 0.32691497, 0.37080425], dtype=float32)\n+Out[8]: array([0.30092323, 0.8955594 , 0.8660922 ], dtype=float32)\n \n In [9]: rng.integers(0, 256, size=3, dtype=np.uint8)\n-Out[9]: array([155, 170, 45], dtype=uint8)\n+Out[9]: array([ 22, 27, 102], 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([0.49153086, 0.46068089])\n+Out[12]: array([0.52844528, 0.58459297])\n \n In [13]: print(existing)\n-[0.49153086 0.46068089 0. 0. ]\n+[0.52844528 0.58459297 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([0.8234164 , 0.81850388])\n+Out[4]: array([ 1.07847905, -0.50892079])\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([4.52387769, 3.70537381], domain=[0., 9.], window=[-1., 1.], symbol='x')\n+Out[6]: Polynomial([4.34423492, 4.85315571], 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([0.81850388, 0.8234164 ], domain=[-1., 1.], window=[-1., 1.], symbol='x')\n+Out[7]: Polynomial([-0.50892079, 1.07847905], 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([0.8234164 , 0.81850388])\n+Out[4]: array([ 1.07847905, -0.50892079])\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([4.52387769, 3.70537381], domain=[0., 9.], window=[-1.,\n+Out[6]: Polynomial([4.34423492, 4.85315571], 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([0.81850388, 0.8234164 ], domain=[-1., 1.], window=[-1.,\n+Out[7]: Polynomial([-0.50892079, 1.07847905], 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": "@@ -32393,14 +32393,15 @@\n \"06381726\": 349,\n \"0660\": [302, 2131],\n \"06959433e\": [420, 947],\n \"07\": [55, 164, 547, 896, 897, 1335, 2170, 2508],\n \"07106781e\": 514,\n \"07407407\": 1809,\n \"07779185\": 2458,\n+ \"07847905\": 2488,\n \"07937323\": 524,\n \"07944154\": [657, 2653],\n \"08\": [55, 91, 147, 410, 523, 548, 896, 1095, 2322, 2366, 2413, 2525, 2657],\n \"0800\": 2525,\n \"08187135\": 54,\n \"08333333\": [1645, 1871],\n \"08405657\": 1867,\n@@ -32409,15 +32410,14 @@\n \"085537\": 2640,\n \"0856306\": 1154,\n \"08618131\": 1526,\n \"08703704\": [1113, 1543],\n \"087300000000000003\": [2346, 2392, 2441],\n \"09\": [55, 2171, 2323, 2367, 2414],\n \"090097550553843\": 2640,\n- \"09317833\": 2461,\n \"09417735\": [349, 2457, 2637],\n \"0943951\": 1911,\n \"09640474436813\": 675,\n \"09861229\": [657, 2653],\n \"0999755859375\": 62,\n \"099975586\": 62,\n \"0a1\": 577,\n@@ -32491,15 +32491,15 @@\n \"100j\": 1909,\n \"100x5\": 652,\n \"101\": [86, 137, 138, 143, 145, 570, 1325, 2077, 2463, 2664],\n \"1010\": [145, 1519, 2077],\n \"10100\": [143, 570],\n \"1015\": 2592,\n \"10151\": 2560,\n- \"102\": [2463, 2635, 2664],\n+ \"102\": [2461, 2463, 2635, 2664],\n \"1023\": [141, 2583],\n \"1024\": [66, 72, 2656],\n \"10240\": 977,\n \"103\": 2463,\n \"10330\": 55,\n \"10339\": [2536, 2542],\n \"1035\": [1643, 1655],\n@@ -32591,14 +32591,15 @@\n \"11110010\": [142, 546],\n \"1111100\": [55, 162, 163, 164, 547],\n \"111111\": 1335,\n \"1111111111110010\": [142, 546],\n \"11170\": 2539,\n \"11174\": 2539,\n \"11181\": 2539,\n+ \"11183614\": 2461,\n \"11194\": 2539,\n \"11198\": 2539,\n \"11199\": 2539,\n \"112\": [333, 2158, 2463, 2664],\n \"11203\": 2539,\n \"11210\": 2542,\n \"11211\": 2539,\n@@ -33013,15 +33014,15 @@\n \"15302337\": 523,\n \"1534\": 485,\n \"15355\": 2566,\n \"15385\": 2566,\n \"154\": [2463, 2664],\n \"15427\": 2566,\n \"15463\": 2566,\n- \"155\": [2461, 2463, 2635],\n+ \"155\": [2463, 2635],\n \"15534\": 2566,\n \"15648\": 2566,\n \"15666\": 2572,\n \"15675\": 2562,\n \"15676\": 2562,\n \"15677\": 2562,\n \"15679\": 2562,\n@@ -33160,15 +33161,15 @@\n \"16986\": 2572,\n \"16987\": 2576,\n \"16998\": 2568,\n \"16bit\": 2517,\n \"16j\": [438, 514, 642, 2167],\n \"16x\": 2622,\n \"17\": [2, 12, 47, 54, 55, 56, 58, 61, 98, 140, 146, 147, 159, 164, 270, 351, 423, 438, 439, 453, 514, 547, 562, 642, 645, 669, 880, 1069, 1114, 1229, 1312, 1466, 1512, 1541, 1545, 1586, 1594, 1651, 1695, 1867, 1877, 1880, 1986, 2085, 2104, 2204, 2222, 2237, 2303, 2333, 2342, 2377, 2424, 2458, 2461, 2463, 2464, 2491, 2513, 2519, 2542, 2547, 2553, 2560, 2566, 2572, 2576, 2577, 2583, 2596, 2597, 2599, 2613, 2625, 2633, 2639, 2643, 2646, 2655, 2664],\n- \"170\": [544, 2461],\n+ \"170\": 544,\n \"17000\": 2568,\n \"17010\": 2572,\n \"17015\": 2568,\n \"17022005e\": 54,\n \"17029\": 2572,\n \"17067\": 2572,\n \"17068\": 2572,\n@@ -33738,15 +33739,15 @@\n \"219\": 2463,\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, 2633, 2635, 2639, 2655, 2664],\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, 2461, 2513, 2517, 2519, 2534, 2588, 2633, 2635, 2639, 2655, 2664],\n \"220\": [2238, 2576],\n \"22004\": 2594,\n \"22014\": 2594,\n \"22030\": 2590,\n \"22031\": 2590,\n \"22032\": 2590,\n \"22033\": 2590,\n@@ -34383,15 +34384,15 @@\n \"26963\": 2623,\n \"26971\": 2623,\n \"26978671\": 2633,\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, 2463, 2491, 2513, 2533, 2534, 2624, 2637, 2639, 2643, 2655, 2657, 2664],\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, 2637, 2639, 2643, 2655, 2657, 2664],\n \"270\": 363,\n \"27000\": 2624,\n \"2700000\": 2633,\n \"27000000\": 2633,\n \"27001\": 2624,\n \"27008\": 2625,\n \"27021\": 2624,\n@@ -34498,15 +34499,15 @@\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, 2639, 2647, 2655, 2657, 2664],\n+ \"28\": [36, 54, 55, 146, 409, 661, 1695, 1704, 1707, 1862, 2168, 2208, 2225, 2461, 2463, 2513, 2538, 2539, 2540, 2543, 2629, 2639, 2647, 2655, 2657, 2664],\n \"28000000e\": 1335,\n \"2800000e\": 1335,\n \"28006\": 2630,\n \"28007\": 2630,\n \"2801\": 2613,\n \"28021\": 2630,\n \"28044\": 2630,\n@@ -34598,14 +34599,15 @@\n \"300\": [66, 363, 2238, 2576, 2643],\n \"3000\": 2594,\n \"30000\": 533,\n \"3000488281\": 476,\n \"3003003\": 1999,\n \"3006\": 2614,\n \"3007\": 2614,\n+ \"30092323\": 2461,\n \"301\": [438, 1923, 2477],\n \"30220482\": [2345, 2391, 2439],\n \"30278462\": 1154,\n \"3039\": 2614,\n \"304\": 22,\n \"30464\": 2094,\n \"30498948e\": 2664,\n@@ -34643,28 +34645,27 @@\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, 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, 2635, 2637, 2639, 2643, 2644, 2646, 2647, 2650, 2655, 2656, 2657, 2664],\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, 2635, 2637, 2639, 2643, 2644, 2646, 2647, 2650, 2655, 2656, 2657, 2664],\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- \"32691497\": 2461,\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, 2635, 2639, 2655, 2664],\n+ \"33\": [54, 58, 144, 336, 838, 939, 941, 1010, 1907, 1922, 1999, 2173, 2175, 2176, 2208, 2303, 2513, 2621, 2635, 2639, 2655, 2664],\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@@ -34672,42 +34673,42 @@\n \"333333333\": 2171,\n \"3333333333333\": 2171,\n \"33333334\": 2171,\n \"3333333e\": 1335,\n \"33339\": 2173,\n \"33340274885464394\": 2202,\n \"3340\": [287, 1241, 1324, 1478, 1998],\n- \"33425345\": 2461,\n \"3348\": 2617,\n \"33486982e\": 438,\n \"3361\": [99, 906],\n \"3364\": 2615,\n \"3373\": 2615,\n \"33872321e\": 2104,\n- \"34\": [12, 28, 144, 441, 1880, 1919, 2208, 2461, 2463, 2491, 2566, 2583, 2639, 2655, 2664],\n+ \"34\": [12, 28, 144, 441, 1880, 1919, 2208, 2463, 2491, 2566, 2583, 2639, 2655, 2664],\n \"340\": [2238, 2576],\n \"34132519\": [680, 2657],\n \"3421\": 2615,\n \"343\": 2664,\n \"34317802\": 1153,\n \"34376245\": 2633,\n+ \"34423492\": 2488,\n \"3456\": 13,\n \"3458\": 2615,\n \"3471280\": 1923,\n \"3472\": 2615,\n \"34732142857143039\": [1113, 1543],\n \"347845\": 2633,\n \"34784527\": 2633,\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, 2633, 2639, 2655, 2664],\n+ \"35\": [409, 489, 669, 870, 1056, 2204, 2325, 2369, 2416, 2461, 2572, 2633, 2639, 2655, 2664],\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, 2463, 2491, 2536, 2647, 2655, 2657, 2664],\n@@ -34723,15 +34724,14 @@\n \"366\": 55,\n \"36674\": 2098,\n \"36787944\": [1660, 1774],\n \"37\": [59, 60, 136, 1913, 2083, 2204, 2236, 2463, 2639, 2655, 2664],\n \"370\": 652,\n \"3701\": 2615,\n \"37079802\": [349, 2637],\n- \"37080425\": 2461,\n \"3712\": 2615,\n \"3728\": 2615,\n \"3728973198\": 2594,\n \"3743\": 2615,\n \"375\": [1634, 1663],\n \"37601032\": [2387, 2434],\n \"377\": 28,\n@@ -34760,15 +34760,14 @@\n \"3900\": 2615,\n \"3900x\": 2463,\n \"39015\": 2316,\n \"39211752\": 1153,\n \"39337286e\": 1149,\n \"3971\": 2615,\n \"39804426\": 1153,\n- \"39850473\": 2461,\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, 2633, 2635, 2655, 2664],\n \"3e\": [357, 359, 1596, 1653, 1710, 1767, 1824, 1879, 1893, 1915, 2086],\n \"3ej\": 2086,\n@@ -34823,15 +34822,15 @@\n \"4167\": 1643,\n \"4170\": 2617,\n \"4176\": 2617,\n \"4181\": [28, 2621],\n \"4187\": 2617,\n \"4191\": 2617,\n \"4197\": 2617,\n- \"42\": [31, 58, 63, 147, 349, 669, 896, 897, 974, 1029, 2090, 2208, 2256, 2332, 2376, 2423, 2457, 2461, 2566, 2605, 2622, 2633, 2637, 2655, 2662, 2663, 2664],\n+ \"42\": [31, 58, 63, 147, 349, 669, 896, 897, 974, 1029, 2090, 2208, 2256, 2332, 2376, 2423, 2457, 2566, 2605, 2622, 2633, 2637, 2655, 2662, 2663, 2664],\n \"420\": [2238, 2576],\n \"42016704\": 2664,\n \"4206\": 2617,\n \"4220\": 2617,\n \"4223\": 2617,\n \"4225\": 2617,\n \"423\": 55,\n@@ -34882,33 +34881,32 @@\n \"4476\": 2621,\n \"4483\": 2617,\n \"4485\": 2617,\n \"4486\": 2617,\n \"449294e\": 2170,\n \"44948974\": 2657,\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, 2461, 2635, 2642, 2655, 2664],\n+ \"45\": [12, 18, 38, 58, 94, 105, 130, 339, 666, 851, 866, 944, 1025, 1026, 1031, 1051, 1212, 1882, 1886, 2103, 2204, 2635, 2642, 2655, 2664],\n \"450\": 55,\n \"45000005\": 2115,\n \"45038594\": [349, 2637],\n \"45053314\": 2633,\n \"4511316\": 2664,\n \"4520525295346629\": 1228,\n \"4532\": [409, 661, 2168],\n \"4545724517479104\": 2460,\n \"45560727e\": 54,\n \"456\": 1921,\n \"4567\": 2642,\n \"45674898e\": 566,\n \"45a3d84\": 2521,\n- \"46\": [409, 523, 905, 1707, 2204, 2208, 2639, 2655],\n+ \"46\": [409, 523, 905, 1707, 2204, 2208, 2461, 2639, 2655],\n \"460\": [2238, 2576],\n \"46009194e\": 566,\n \"4602\": 2618,\n- \"46068089\": 2461,\n \"4610935\": 457,\n \"4613\": 2618,\n \"4628\": 2618,\n \"46351241j\": 2081,\n \"46368\": 28,\n \"464\": 680,\n \"4642\": 2618,\n@@ -34934,30 +34932,29 @@\n \"4733\": 2618,\n \"47458546\": 349,\n \"47536961\": 349,\n \"47613949\": [2335, 2378, 2425],\n \"4774\": 2618,\n \"479\": 2620,\n \"4796\": [409, 661, 2168],\n- \"48\": [58, 270, 355, 880, 1069, 1142, 1229, 1312, 1466, 1867, 1986, 2208, 2239, 2323, 2367, 2414, 2655, 2657],\n+ \"48\": [58, 270, 355, 880, 1069, 1142, 1229, 1312, 1466, 1867, 1986, 2208, 2239, 2323, 2367, 2414, 2461, 2655, 2657],\n \"480\": [238, 858, 1041, 1207, 1290, 1444, 1964],\n \"4800\": 57,\n \"48000000\": 2633,\n \"4809319\": 1153,\n \"4816\": [99, 906],\n \"48219694e\": [421, 948],\n \"4836\": 2618,\n \"484\": [2517, 2583, 2625],\n \"4853\": 2618,\n \"4861946401452\": 2334,\n \"4874\": [409, 661, 2168],\n \"4882\": [287, 1241, 1324, 1478, 1998],\n \"4896\": 2620,\n \"49\": [71, 2208, 2323, 2367, 2414, 2567, 2568, 2639, 2655, 2664],\n- \"49153086\": 2461,\n \"4928\": [409, 661, 2168],\n \"49293\": 1644,\n \"49313049\": [2387, 2434],\n \"49401501\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"496041986\": [420, 947],\n \"49778714\": 2238,\n \"49876311\": [2352, 2399, 2449],\n@@ -34995,16 +34992,17 @@\n \"50491112870\": 55,\n \"50491123200\": 55,\n \"50491123200000000\": 55,\n \"50629471\": 1154,\n \"5063\": 2620,\n \"5067\": 2620,\n \"5082\": 2620,\n+ \"50892079\": 2488,\n \"5095\": 2620,\n- \"51\": [58, 520, 1654, 1752, 1761, 1867, 1870, 2083, 2204, 2331, 2339, 2356, 2375, 2382, 2403, 2422, 2429, 2453, 2461, 2622, 2655, 2664],\n+ \"51\": [58, 520, 1654, 1752, 1761, 1867, 1870, 2083, 2204, 2331, 2339, 2356, 2375, 2382, 2403, 2422, 2429, 2453, 2622, 2655, 2664],\n \"510\": [143, 570],\n \"5100\": 2620,\n \"5104\": 2620,\n \"51182162\": 2664,\n \"512\": [69, 893, 1083, 1143, 1247, 2115, 2240, 2542, 2547, 2664],\n \"51327412\": 1891,\n \"5136\": 2620,\n@@ -35020,28 +35018,28 @@\n \"51658839e\": 1586,\n \"517\": 10,\n \"5170\": 2620,\n \"5184\": 2620,\n \"51851852\": 1809,\n \"519928\": 2633,\n \"51992837\": 2633,\n- \"52\": [10, 50, 62, 457, 1638, 1647, 1650, 2204, 2208, 2461, 2554, 2633, 2639, 2646, 2655, 2657, 2658, 2664],\n+ \"52\": [10, 50, 62, 457, 1638, 1647, 1650, 2204, 2208, 2554, 2633, 2639, 2646, 2655, 2657, 2658, 2664],\n \"5203\": 2620,\n \"5225\": 2620,\n \"5231\": 2620,\n \"52338984\": [2345, 2391, 2439],\n \"52359878\": 1911,\n \"52380952e\": 1816,\n- \"52387769\": 2488,\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, 2655, 2664],\n+ \"52844528\": 2461,\n+ \"53\": [162, 457, 1638, 2208, 2461, 2551, 2554, 2655, 2664],\n \"5306\": [409, 661, 2168],\n \"5313\": 2621,\n \"5316\": 2621,\n \"5324j\": [416, 417, 622, 623],\n \"5354\": 2621,\n \"5359\": 2621,\n \"5363922081269535\": 2458,\n@@ -35092,15 +35090,15 @@\n \"5620499351813308\": 86,\n \"5625\": 2491,\n \"56294995342131\": 2083,\n \"5640\": [2353, 2400, 2450],\n \"567\": 2642,\n \"56826729e\": 2104,\n \"56917101\": 2633,\n- \"57\": [58, 669, 2204, 2322, 2366, 2413, 2461, 2463, 2491, 2635, 2655],\n+ \"57\": [58, 669, 2204, 2322, 2366, 2413, 2463, 2491, 2635, 2655],\n \"5707963267948966\": [102, 125],\n \"57079633\": [94, 105, 130, 1911, 2238, 2664],\n \"5708\": [412, 618],\n \"57115742\": 524,\n \"57136612e\": 2173,\n \"57510612\": 660,\n \"576\": 2615,\n@@ -35110,14 +35108,15 @@\n \"57860025\": 1154,\n \"579365079365115\": [1113, 1543],\n \"57x\": 2594,\n \"58\": [669, 1748, 1777, 2204, 2208, 2332, 2376, 2423, 2464, 2572, 2633, 2655],\n \"582892\": 2633,\n \"58289208\": 2633,\n \"584388\": 55,\n+ \"58459297\": 2461,\n \"585\": [378, 1358, 1514, 2583],\n \"58578644\": 1756,\n \"58826587\": 349,\n \"59\": [55, 2208, 2602, 2655],\n \"5910\": [287, 1241, 1324, 1478, 1998],\n \"595726\": 2633,\n \"59572603\": 2633,\n@@ -35337,15 +35336,14 @@\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, 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2248, 2257, 2315, 2320, 2323, 2328, 2333, 2339, 2341, 2342, 2347, 2352, 2367, 2377, 2382, 2384, 2388, 2389, 2395, 2399, 2414, 2424, 2429, 2431, 2435, 2436, 2445, 2449, 2457, 2458, 2460, 2461, 2463, 2488, 2491, 2513, 2518, 2519, 2520, 2521, 2522, 2525, 2526, 2527, 2528, 2529, 2530, 2531, 2532, 2533, 2534, 2535, 2536, 2537, 2538, 2539, 2540, 2541, 2542, 2543, 2544, 2545, 2546, 2547, 2548, 2549, 2550, 2551, 2552, 2553, 2554, 2555, 2556, 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, 2633, 2635, 2636, 2637, 2639, 2640, 2642, 2643, 2645, 2647, 2654, 2655, 2656, 2658, 2664],\n \"70\": [59, 457, 567, 2241, 2248, 2655],\n \"700\": 567,\n \"70000000\": 2633,\n \"701\": 2463,\n \"703\": 2625,\n- \"70537381\": 2488,\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, 2655],\n@@ -35443,15 +35441,15 @@\n \"77555756e\": 1877,\n \"77598074\": 349,\n \"77714685\": 349,\n \"7774613834041182\": 2315,\n \"7776\": [99, 906],\n \"7778\": 2527,\n \"7793\": 2527,\n- \"78\": [2091, 2461, 2642, 2655],\n+ \"78\": [2091, 2642, 2655],\n \"78096262\": [2352, 2399, 2449],\n \"7816\": 2527,\n \"7821\": 2527,\n \"7824\": 2527,\n \"7835\": 2527,\n \"784\": 2463,\n \"7847\": 2527,\n@@ -35494,35 +35492,33 @@\n \"800\": [2335, 2378, 2425],\n \"8000\": [2350, 2352, 2397, 2399, 2447, 2449],\n \"80000000000000204\": [1113, 1543],\n \"8005\": 2527,\n \"801\": [941, 1114, 1123, 1124, 1131],\n \"8010\": 2527,\n \"8020\": 2527,\n+ \"80213609\": 2461,\n \"8024\": 2527,\n \"8031\": 2527,\n- \"804\": 2508,\n+ \"804\": [2461, 2508],\n \"8044\": 2527,\n- \"805\": 2461,\n \"8058837395885292\": 666,\n \"80b3a34\": 2614,\n \"81\": [1650, 1884, 2633, 2639, 2643, 2655, 2664],\n \"81299683\": 2633,\n \"812997\": 2633,\n \"813\": [270, 880, 1069, 1229, 1312, 1466, 1986],\n \"81327024\": 2633,\n \"81349206\": [1113, 1543],\n \"81814867\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n- \"81850388\": 2488,\n \"8192\": [72, 517, 2092, 2619],\n \"82\": [1650, 2323, 2367, 2414, 2463, 2655, 2664],\n \"8207540608310198\": [2353, 2400, 2450],\n \"82276161\": 349,\n \"8230\": [2353, 2400, 2450],\n- \"8234164\": 2488,\n \"82485143\": 2633,\n \"82502011\": 349,\n \"8255\": 2566,\n \"826716f\": 2521,\n \"82743037\": 524,\n \"82770259\": 2664,\n \"8277025938204418\": 2664,\n@@ -35546,14 +35542,15 @@\n \"84147098j\": 2664,\n \"841471\": 2640,\n \"842523\": 2515,\n \"84680802e\": 2104,\n \"8480354764257312\": 653,\n \"85\": [409, 2655],\n \"85099543\": 1822,\n+ \"85315571\": 2488,\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@@ -35563,14 +35560,15 @@\n \"8601\": [55, 62, 67, 2613],\n \"86260211e\": 54,\n \"8630830\": 13,\n \"86399\": 55,\n \"86400\": 55,\n \"86401\": 55,\n \"8660254\": 2103,\n+ \"8660922\": 2461,\n \"86820401\": [2345, 2391, 2439],\n \"86864911e\": 1586,\n \"87\": [2616, 2655],\n \"875\": [478, 2491],\n \"8755\": [186, 827, 999, 1172, 1259, 1414, 1933],\n \"87649168120691\": 674,\n \"8770\": [2353, 2400, 2450],\n@@ -35589,14 +35587,15 @@\n \"890\": 2642,\n \"8900451\": 1154,\n \"89086505\": [2352, 2399, 2449],\n \"89206682e\": 2104,\n \"8922078\": 2458,\n \"89442719\": 642,\n \"89442719j\": 642,\n+ \"8955594\": 2461,\n \"89721355\": 349,\n \"89804309e\": 2104,\n \"89920014\": [2319, 2363, 2410],\n \"8999999999999999\": 2107,\n \"8b2\": 2554,\n \"8b3\": 2555,\n \"8b4\": 2556,\n@@ -35627,24 +35626,24 @@\n \"9261\": 2532,\n \"9262\": 2532,\n \"9263\": 2532,\n \"9267\": 2532,\n \"92676499\": [349, 2637],\n \"927\": [539, 554],\n \"92771843\": 1154,\n+ \"928\": 2461,\n \"9299\": 2532,\n \"93\": 2655,\n \"9304e\": 2091,\n \"931\": 2587,\n \"9317\": 2532,\n \"9319\": 2532,\n \"9339\": 2532,\n \"9340\": 2532,\n \"934284\": 349,\n- \"936\": 2461,\n \"93657855\": 349,\n \"9371\": 2532,\n \"9372\": 2532,\n \"9373\": 2532,\n \"9374\": 2532,\n \"9376\": 2532,\n \"9377\": 2532,\n@@ -35726,25 +35725,25 @@\n \"99\": [12, 302, 408, 544, 672, 1096, 1906, 2131, 2460, 2633, 2655, 2656, 2664],\n \"9900\": 2664,\n \"99004057\": 349,\n \"9901\": 2664,\n \"9902\": 2664,\n \"990278\": 2633,\n \"99027828\": 2633,\n- \"99052012\": 2461,\n \"99060736\": 2664,\n \"99091858\": [2345, 2391, 2439],\n \"99149989\": [2345, 2391, 2439],\n \"9917\": 2343,\n \"99256089\": 349,\n \"99322285\": [88, 101],\n \"99394529\": [2339, 2352, 2382, 2389, 2399, 2429, 2436, 2449],\n \"99417356\": 1754,\n \"99507202\": 349,\n \"99734545\": 1154,\n+ \"99736855\": 2461,\n \"998\": 2535,\n \"99822295\": [103, 126],\n \"99827656\": 1754,\n \"99885316e\": 566,\n \"999\": [543, 844, 864, 887, 1020, 1049, 1077, 1125, 2535, 2642],\n \"9990000e\": 1335,\n \"99923895\": 349,\n"}]}]}]}]}]}